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Gravitational Waves from Stars Orbiting the Sagittarius A* Black Hole
Abstract
One of the main astrophysical processes leading to strong emission of gravitational waves to be detected by the future space-borne interferometer LISA is the capture of a compact star by a black hole with a mass of a few million solar masses in the center of a galaxy. In previous studies, main sequence stars were thought not to contribute because they suffer from early tidal disruption. Here we show that, according to our simulations of the stellar dynamics of the Sgr A* cluster, there must be one to a few low-mass main sequence stars sufficiently bound to the central Galactic black hole to be conspicuous sources in LISA observations. The probability that a white dwarf may be detectable is lower than 0.5 and, in spite of mass segregation, detection of a captured neutron star or stellar black hole in the center of the Milky Way is highly unlikely. Comment: 5 pages, 3 figures, accepted for publication in ApJL, new version shortened to fit in 4 journal pages. Slightly longer version available at http://obswww.unige.ch/~freitag/papers/article_SgrA_long.ps.gz
... The parameters at capture for the radii at periapsis were found to be r p = 8M-100M, with an orbital eccentricity of 0.999 < e < 0.999 999. These were determined by Freitag (2003) who performed a Monte Carlo simulation studying the stellar mass objects in the cusp of the Milky Way galaxy scattered due to gravitational interactions [33]. The radius at periapsis values were then converted into semi-latus rectum using r p = p 1+e with the eccentricity range from the same source. ...
... The parameters at capture for the radii at periapsis were found to be r p = 8M-100M, with an orbital eccentricity of 0.999 < e < 0.999 999. These were determined by Freitag (2003) who performed a Monte Carlo simulation studying the stellar mass objects in the cusp of the Milky Way galaxy scattered due to gravitational interactions [33]. The radius at periapsis values were then converted into semi-latus rectum using r p = p 1+e with the eccentricity range from the same source. ...
... This will allow us to look at prograde and retrograde orbits. To our knowledge, no studies were found to improve upon the initial work for the semi-latus rectum at capture determined by Freitag (2003). However, after re-examining the data from Freitag's Monte Carlo simulation, we chose to focus only on the higher concentrated regions of the simulated 'stars' at capture, thereby constraining the radius at periapsis to r p = 30M. ...
Scattering events around the center of massive galaxies will occasionally toss a stellar-mass compact object into an orbit around the massive black hole (MBH) at the center, beginning an extreme mass ratio inspiral (EMRI). The early stages of such a highly eccentric orbit are not likely to produce detectable gravitational waves (GWs), as the source will only be in a suitable frequency band briefly when it is close to periapsis during each long-period orbit. This repeated burst of emission, firmly in the millihertz band, is the GW peep. While a single peep is not likely to be detectable, if we consider an ensemble of such subthreshold sources, spread across the Universe, together they may produce an unresolvable background noise that could obscure sources otherwise detectable by the Laser Interferometer Space Antenna. Previous studies of the extreme mass ratio signal confusion background focused either on parabolic orbits near the MBH or events closer to merger. We seek to improve this characterization by implementing numerical kludge waveforms that can calculate highly eccentric orbits with relativistic effects. Our focus is on orbits at the point of capture that are farther away from the MBH. Here we present the waveforms and spectra of peeps generated from recent calculations of EMRIs/extreme mass ratio bursts capture parameters and discuss how these can be used to estimate the signal confusion noise generated by such events. We demonstrate the effects of changing the orbital parameters on the resulting spectra as well as showing direct comparisons to parabolic orbits and why the GW ‘peep’ needs to be studied further. The results of this study will be expanded upon in a further paper that aims to provide an update on the EMRI signal confusion noise problem.
... The parameters at capture for the radius at periapsis were found to be r p = 8M −100M , with an orbital eccentricity of 0.999 < e < 0.999999. These were determined from Freitag (2003) who performed a Monte Carlo simulation studying the stellar mass objects in the cusp of the Milky Way galaxy scattered due to gravitational interactions [31]. The radius at periapsis values were then converted into semi-latus rectum using r p = p 1+e with the eccentricity range from the same source. ...
... The parameters at capture for the radius at periapsis were found to be r p = 8M −100M , with an orbital eccentricity of 0.999 < e < 0.999999. These were determined from Freitag (2003) who performed a Monte Carlo simulation studying the stellar mass objects in the cusp of the Milky Way galaxy scattered due to gravitational interactions [31]. The radius at periapsis values were then converted into semi-latus rectum using r p = p 1+e with the eccentricity range from the same source. ...
... While we have ambitions to do inclination, at this early stage it is not critical, and so the figures seen in this paper will be equatorial orbits. To our knowledge, no studies were found to improve upon the initial work for the semi-latus rectum at capture determined by Freitag (2003). However, after reexamining the data from Freitag's Monte Carlo simulation, we chose to focus only on the higher concentrated regions of the simulated "stars" at capture, thereby constraining the radius at periapsis to r p = 30M . ...
Scattering events around a supermassive black hole will occasionally toss a stellar-mass compact object into an orbit around the supermassive black hole, beginning an extreme mass ratio inspiral. The early stages of such a highly eccentric orbit will not produce detectable gravitational waves as the source will only be in a suitable frequency band briefly when it is close to periapsis during each long-period orbit. This burst of emission, firmly in the millihertz band is the gravitational wave peep. While a single peep is not likely to be detectable, if we consider an ensemble of such subthreshold sources, spread across the universe, together they produce an unresolvable background noise that may obscure sources otherwise detectable by the Laser Interferometer Space Antenna, the proposed space-based gravitational wave detector. Previous studies of the extreme mass ratio burst signal confusion background focused more on parabolic orbits going very near the supermassive black hole and on events near the galactic center. We seek to improve this characterization by implementing numerical kludge waveforms that can calculate highly eccentric orbits with relativistic effects focusing on orbits which are farther away from the supermassive black hole and thus less likely to be detectable on their own, but will otherwise contribute to the background signal confusion noise. Here we present the waveforms and spectra of the gravitational wave peeps generated from recent calculations of extreme mass ratio inspirals/bursts capture parameters and discuss how these can be used to estimate the signal confusion noise generated by such events.
... Considering cosmological constraints, the strongest candidate sources for monochromatic gravitational wave illumination in our spatial neighbourhood are the binary systems consisting of a compact object captured in close orbit by the supermassive black hole (from now on SMBH) Sgr A * at our galaxy centre (Sigurdsson & Rees 1997;Freitag 2003;Barack & Cutler 2004). Extensive numerical simulations of the capture and orbital evolution of such systems (ibid.) ...
... Emission occurs in progressively more circular orbits, and mostly consists of monochromatic GW in the 10 −5 −10 −2 Hz frequency band, with a longer life for the light compact body binaries. In particular, a SMSS-SMBH binary would emit most GW energy in the sub-millihertz and millihertz band by orbiting with eccentricities around 0.5 for 10 4 yr (Freitag 2003). Such inspiral orbits terminate by a slow tidal disruption of the SMSS lasting several decades (Lin et al. 2017) without any high-frequency chirp (Abbott et al. 2016), that would only occur for the 10 2 . ...
... = 10 3 times more rare binaries in which the compact body is either a neutron star or a black hole (Freitag 2003). ...
Independent multi-year analyses of Earth tremor have suggested a continuous excitation of Earth normalmodes by ocean storms, but also a number of unexplained spectral peaks extraneous to them, mostly in the 0.2-2 mHz frequency band.We reassess the worldwide existence of such peaks by stacking themultitaper high-resolution spectra of all stations of the International Geodynamics and Earth Tide Service superconducting gravimeter network with at least 30 months of uninterrupted record, analysing a global epoch of 656 months. The analysis, beyond showing the predominance of 0Sn, n = 0, .., 12 Earth spheroidal modes, confirms the existence of unexplained spectral peaks which (1) cannot be ascribed to instrumental noise, (2) occur at frequencies extraneous to Earth normal modes, (3) have a statistical significance comparable to them and (4) appear incompatible with any natural or anthropic terrestrial source. While at odds with the hypothetical Earth 'tune in' on a continuum detectable gravitational wavefield, the peaks appear to be compatible in terms of amplitude, frequency and-according to cosmological constraints-expected number, with the independently calculated gravitational wave monochromatic emission of a few binary systems consisting of a star with mass ~1/10 of the sun captured in close orbit by the supermassive black hole at the centre of our galaxy.
... The question about the distribution and capture of stellar-mass black holes at the Galactic Centre has been addressed a number of times by different authors, from both a semior analytical and numerical standpoint, see e.g., Sigurdsson and Rees (1997), Miralda-Escudé and Gould (2000), Freitag (2001Freitag ( , 2003b, Freitag et al. (2006a, b), Hopman and Alexander (2006b), Amaro-Seoane et al. (2007), Preto and Amaro-Seoane (2010), Amaro-Seoane and Preto (2011). Addressing this problem has implications for a variety of astrophysical questions, including of course inspirals of compact objects onto the central MBH, but also on the distribution of X-ray binaries at the Galactic Centre, tidal disruptions of main sequence stars, and the behaviours of the so-called "source" stars, which were introduced in Sect. ...
... We note, incidentally, that even in the LISA band (in the final year of inspiral), the eccentricity of the typical EMRI in the standard picture is high enough that a large number of harmonics are likely to contribute to the gravitational waves (Freitag 2003b; Barack and Cutler 2004;Hopman and Alexander 2005). In addition, the orbital plane of the EMRIs is unlikely to be significantly correlated with the spin plane of the MBH. ...
... In this section, I review the idea described in Freitag (2003b) that MS stars can be potential sources of GWs in our Galactic Centre. I include this in this section because in the whole review our standard CO is considered to be a SBH and so, it falls into the category of "not in the standard model". ...
It is now well-established that a dark, compact object, very likely a massive black hole (MBH) of around four million solar masses is lurking at the centre of the Milky Way. While a consensus is emerging about the origin and growth of supermassive black holes (with masses larger than a billion solar masses), MBHs with smaller masses, such as the one in our galactic centre, remain understudied and enigmatic. The key to understanding these holes—how some of them grow by orders of magnitude in mass—lies in understanding the dynamics of the stars in the galactic neighbourhood. Stars interact with the central MBH primarily through their gradual inspiral due to the emission of gravitational radiation. Also stars produce gases which will subsequently be accreted by the MBH through collisions and disruptions brought about by the strong central tidal field. Such processes can contribute significantly to the mass of the MBH and progress in understanding them requires theoretical work in preparation for future gravitational radiation millihertz missions and X-ray observatories. In particular, a unique probe of these regions is the gravitational radiation that is emitted by some compact stars very close to the black holes and which could be surveyed by a millihertz gravitational-wave interferometer scrutinizing the range of masses fundamental to understanding the origin and growth of supermassive black holes. By extracting the information carried by the gravitational radiation, we can determine the mass and spin of the central MBH with unprecedented precision and we can determine how the holes “eat” stars that happen to be near them.
... The question about the distribution and capture of stellar black holes at the Galactic Centre has been addressed a number of times by different authors, from both a semi-or analytical and numerical standpoint (Sigurdsson and Rees, 1997;Miralda-Escudé and Gould, 2000;Freitag, 2001aFreitag, , 2003bFreitag et al., 2006b,a;Hopman and Alexander, 2006a;Amaro-Seoane et al., 2007;Preto and Amaro-Seoane, 2010;Amaro-Seoane and Preto, 2011). Addressing of this problem has direct bearing on a variety of astrophysical questions, including of course in-spirals of compact objects onto the central MBH, but also on the distribution of X-ray binaries at the Galactic Centre, tidal disruptions of main sequence stars, and the behaviors of "source" stars. ...
... Only self-consistent stellar dynamical modeling of galactic nuclei will allow us a beer understanding of these questions. Some steps in that direction have been made by (Freitag, 2001b(Freitag, , 2003b with Monte Carlo simulations 1 . Later, Freitag et al. (2006b,a) improved upon these results. ...
... We note, incidentally, that even in the LISA band (in the final year of inspiral), the eccentricity of the typical EMRI in the standard picture is high enough that a large number of harmonics are likely to contribute to the gravitational waves Freitag (2003b); Barack and Cutler (2004); Hopman and Alexander (2005a). In addition, the orbital plane of the EMRIs is unlikely to be significantly correlated with the spin plane of the MBH. ...
Nowadays it is well-established that in the centre of the Milky Way a massive
black hole (MBH) with a mass of about four million solar masses is lurking.
While there is an emerging consensus about the origin and growth of
supermassive black holes (with masses larger than a billion solar masses), MBHs
with smaller masses such as the one in our galactic centre remain an
understudied enigma. The key to understanding these holes, how some of them
grow by orders of magnitude in mass is to understand the dynamics of the stars
in the galactic neighborhood. Stars and the central MBH chiefly interact
through the gradual inspiral of the stars into the MBH due to the emission of
gravitational radiation. Also stars produce gases which will be subsequently
accreted by the MBH by collisions and disruptions brought about by the strong
central tidal field. Such processes can contribute significantly to the mass of
the MBH and progress in understanding them requires theoretical work in
preparation for future gravitational radiation millihertz missions and X-ray
observatories. In particular, a unique probe of these regions is the
gravitational radiation that is emitted by some compact stars very close to the
black holes and which will could be surveyed by a millihertz gravitational wave
interferometer scrutinizing the range of masses fundamental to the
understanding of the origin and growth of supermassive black holes. By
extracting the information carried by the gravitational radiation, we can
determine the mass and spin of the central MBH with unprecedented precision and
we can determine how the holes "eat" stars that happen to be near them.
... An EMRI is the GW-emitting inspiral of a stellar-mass compact object, either a black hole, neutron star or white dwarf, into a MBH in the center of a galaxy. A main-sequence star with mean densityρ = 10 g cm −3 will be tidally disrupted by a black hole of mass 10 6 M at a distance of ∼ 25 Schwarzschild radii [187]. At such separations an extra-galactic EMRI system will not be generating detectable amounts of gravitational radiation in the low-frequency band. ...
... The tidaldisruption radius increases with decreasing stellar density and decreasing central-black-hole mass, and the reference values used above are at the upper end of suitable values for main-sequence stars and mHz GW sources. Therefore, it is not expected that the inspiral of a main-sequence star will be a candidate for an EMRI, with the possible exception of such sources in the galactic center, which is sufficiently nearby that radiation from an object orbiting at several tens of Schwarzschild radii might be detectable [187]. ...
We review the tests of general relativity that will become possible with
space-based gravitational-wave detectors operating in the ~0.01mHz - 1Hz
low-frequency band. The fundamental aspects of gravitation that can be tested
include the presence of additional gravitational fields other than the metric;
the number and tensorial nature of gravitational-wave polarization states; the
velocity of propagation of gravitational waves; the binding energy and
gravitational-wave radiation of binaries, and therefore the time evolution of
binary inspirals; the strength and shape of the waves emitted from binary
mergers and ringdowns; the true nature of astrophysical black holes; and much
more. The strength of this science alone calls for the swift implementation of
a space-based detector; the remarkable richness of astrophysics, astronomy, and
cosmology in the low-frequency gravitational-wave band make the case even
stronger.
... Others are important sources of gravitational-wave events, such as extreme-mass-ratio inspirals (EMRIs; e.g., Sigurdsson & Rees 1997;Freitag 2003;Hopman & Alexander 2005;Amaro-Seoane et al. 2013;Brem et al. 2014;Amaro-Seoane 2018, 2019Amaro Seoane 2022), and the dynamical mergers of stellar binary black holes (e.g., Quinlan & Shapiro 1987;Wen 2003;O'Leary et al. 2009;Antonini & Perets 2012;Hong & Lee 2015;Chen & Han 2018;Hoang et al. 2018;Fragione et al. 2019;Zhang et al. 2019Zhang et al. , 2021Xuan et al. 2023). ...
In this study we present a novel Monte Carlo code, referred to as GNC , which enables the investigation of dynamical relaxation in clusters comprising multiple mass components in the vicinity of supermassive black holes at the centers of galaxies. Our method is based on two-dimensional Fokker–Planck equations in the energy and angular momentum space, and allows the evolution of multiple mass components, including stars and compact objects. The code demonstrates remarkable flexibility in incorporating additional complex dynamics. By employing a weighting method, we effectively enhance the statistical accuracy of rare particle results. In this initial publication, we present the fundamental version of our method, focusing on two-body relaxations and loss cone effects. Through comparisons with previous studies, we establish consistent outcomes in terms of relaxation processes, energy and angular momentum distributions, density profiles, and loss cone consumption rates. We consistently observe the development of tangential anisotropy within the cluster, while the outer regions tend to retain near-isotropic characteristics. GNC holds great promise for exploring a wide range of intriguing phenomena within galactic nuclei, including relativistic stellar dynamics, providing detailed and insightful outcomes.
... Once such an inspiraling system forms, it emits GWs that can potentially be detected by space-based detectors such as LISA and TianQin. Considering Sgr A * as the bigger component of such a source was first proposed in Freitag (2003) where main-sequence (MS) stars orbiting Sgr A * were studied. In Barack & Cutler (2004), MS stars around Sgr A * are also studied but going to masses as low as 0.06 M e . ...
Estimating the spin of Sagittarius A* (Sgr A*) is one of the current challenges we face in understanding the center of our Galaxy. In the present work, we show that detecting the gravitational waves (GWs) emitted by a brown dwarf inspiraling around Sgr A* will allow us to measure the mass and the spin of Sgr A* with unprecedented accuracy. Such systems are known as extremely large mass-ratio inspirals (XMRIs) and are expected to be abundant and loud sources in our Galactic center. We consider XMRIs with a fixed orbital inclination and different spins of Sgr A* ( s ) between 0.1 and 0.9. For both cases, we obtain the number of circular and eccentric XMRIs expected to be detected by space-borne GW detectors like LISA and TianQin. We find that if the orbit is eccentric, then we expect to always have several XMRIs in band while for almost circular XMRIs, we only expect to have one source in band if Sgr A* is highly spinning. We later perform a Fisher matrix analysis to show that by detecting a single XMRI the mass of Sgr A* can be determined with an accuracy of the order 10 ⁻² M ⊙ , while the spin can be measured with an accuracy between 10 ⁻⁷ and 10 ⁻⁴ depending on the orbital parameters of the XMRI.
... Brown dwarfs are substellar objects with insufficient mass to sustain nuclear fusion and become main-sequence stars [17]. Brown dwarfs are denser than main-sequence stars, and their Roche limit is closer to the horizon of MBH [15,18]. Therefore, brown dwarfs could survive very close to the MBH. ...
In the galaxy, extremely large mass-ratio inspirals (X-MRIs) composed of brown dwarfs and the massive black hole at the galactic center are expected to be promising gravitational wave sources for space-borne detectors. In this work, we simulate the gravitational wave signals from twenty X-MRI systems by an axisymmetric Konoplya–Rezzolla–Zhidenko metric with varied parameters. We find that the mass, spin, and deviation parameters of the Kerr black hole can be determined accurately (∼10−5−10−6) with only one X-MRI event with a high signal-to-noise ratio. The measurement of the above parameters could be improved with more X-MRI observations.
... (ii) In our calculation, the event rate of WD-MBH mergers is about 2.7Gpc −3 yr −1 /(6 × 10 6 galaxies Gpc −3 ) ; 4 × 10 −7 yr −1 per galaxy. Such a rate is roughly consistent with the model in which WDs are delivered to MBHs by two-body relaxation (Sigurdsson & Rees 1997;Freitag 2003). However, it is almost two orders of magnitude lower than the predicted rate if WDs are captured by MBHs due to the partial tidal disruption of redgiant stars (Bogdanović et al. 2014). ...
Extreme-mass-ratio inspirals (EMRIs) are important targets for future space-borne gravitational-wave (GW) detectors, such as the Laser Interferometer Space Antenna (LISA). Recent works suggest that EMRIs may reside in a population of newly discovered X-ray transients called “quasiperiodic eruptions” (QPEs). Here, we follow this scenario and investigate whether LISA could in the future detect the QPEs. We consider two specific models, in which the QPEs are made of either stellar-mass objects moving on circular orbits around massive black holes (MBHs) or white dwarfs (WDs) on eccentric orbits around MBHs. We find that in either case the five QPEs detected so far are too weak to be resolvable by LISA. However, if QPEs are made of eccentric WD–MBH binaries, they radiate GWs over a wide range of frequencies. The broad spectra overlap to form a background that peaks in the milli-Hertz band and has a signal-to-noise ratio of 9–17 even in the most pessimistic scenario. The presence of this GW background in the LISA band could impact future searches for seed black holes at high redshift as well as stellar-mass binary black holes in the local universe.
... Up to 20k such DWDs will be individually resolvable (Nissanke et al., 2012), along with several tens of NSBs (Lau et al., 2020) and few BHBs (Seto, 2016;Sesana et al., 2020). Moreover, LISA has the unique potential to detect the presence of planets around nearby DWDs (Tamanini and Danielski, 2019) and perhaps dozens of brown dwarfs and sub-stellar objects orbiting SgrA * (Freitag, 2003), known as X-MRI (Amaro-Seoane, 2019). ...
I review the scientific potential of the Laser Interferometer Space Antenna (LISA), a space-borne gravitational wave (GW) observatory to be launched in the early 30s'. Thanks to its sensitivity in the milli-Hz frequency range, LISA will reveal a variety of GW sources across the Universe, from our Solar neighbourhood potentially all the way back to the Big Bang, promising to be a game changer in our understanding of astrophysics, cosmology and fundamental physics. This review dives in the LISA Universe, with a specific focus on black hole science, including the formation and evolution of massive black holes in galaxy centres, the dynamics of dense nuclei and formation of extreme mass ratio inspirals, and the astrophysics of stellar-origin black hole binaries.
... Up to 20 k such DWDs will be individually resolvable (Nissanke et al., 2012), along with several tens of NSBs (Lau et al., 2020) and few BHBs (Seto, 2016;Sesana et al., 2020). Moreover, LISA has the unique potential to detect the presence of planets around nearby DWDs (Tamanini and Danielski, 2019) and perhaps dozens of brown dwarfs and substellar objects orbiting SgrA* (Freitag, 2003), known as X-MRI (Amaro-Seoane, 2019). LISA will detect many more BHBs outside the MW, being sensitive to the early inspiral of these systems centuries to weeks before they enter the ground-based detector sensitivity band, out to z ≈ 0.5 Sesana (2016). ...
The author reviews the scientific potential of the Laser Interferometer Space Antenna (LISA), a space-borne gravitational wave (GW) observatory to be launched in the early 30s. Thanks to its sensitivity in the milli-Hz frequency range, LISA will reveal a variety of GW sources across the Universe, from our Solar neighborhood potentially all the way back to the Big Bang, promising to be a game changer in our understanding of astrophysics, cosmology, and fundamental physics. This review dives in the LISA Universe, with a specific focus on black hole science, including the formation and evolution of massive black holes in galaxy centers, the dynamics of dense nuclei and formation of extreme mass ratio inspirals, and the astrophysics of stellar-origin black hole binaries.
... The Laser Interferometer Space Antenna (LISA) [56], is a space-based gravitational-wave detector which will operate in the 10 −4 -10 −1 Hz band. The detectability of individual macros/objects orbiting Sgr A * with LISA has been discussed in Ref. [57]. Sesana [58] and Clesse et al. [59] have suggested that if the dark matter is composed of multisolar-mass black holes that LISA could detect their merger. ...
A significant fraction of cosmological dark matter can be formed by very dense macroscopic objects, for example primordial black holes. Gravitational waves offer a promising way to probe these kinds of dark-matter candidates, in a parameter space region that is relatively untested by electromagnetic observations. In this work we consider an ensemble of macroscopic dark matter with masses in the range – orbiting a super-massive black hole. While the strain produced by an individual dark-matter particle will be very small, gravitational waves emitted by a large number of such objects will add incoherently and produce a stochastic gravitational-wave background. We show that LISA can be a formidable machine for detecting the stochastic background of such objects orbiting the black hole in the centre of the Milky Way, Sgr , if a dark-matter spike of the type originally predicted by Gondolo and Silk forms near the central black hole.
... Recent work suggests that many of the latter, in the form of brown dwarfs, could be on highly relativistic orbits [12]. Fortuitously, the mass of SgrA * is just right so that if any of these bodies orbit sufficiently close to it they will emit GWs in the µ-to-milli-Hz band [107,121]. This will allow us to measure the orbital properties of any faint or dark objects that orbit very close to the MBHs that are invisible or near invisible to other techniques. ...
We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to -Hz frequency range. By the 2040s', the -Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a -Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe.
... However, if the star is orbiting the black hole in a nearly circular orbit just on the tidal radius, it will transfer mass slowly, without being violently disrupted. A few studies have suggested that these systems may indeed form through gravitational encounters between stars in a cluster around the black hole (Freitag 2003). Later works proposed that EMRIs with very low eccentricities can form via tidal separation of binaries by the SMBH (Miller et al. 2005). ...
We consider stable mass transfer from the secondary to the primary of an extreme mass ratio binary system. We show that when the mass transfer is sufficiently fast, mass leakage occurs through the outer Lagrange point L2, in addition to the usual transfer through L1. We provide an analytical estimate for the mass leakage rate through L2 and find the conditions in which it is comparable to the mass transfer rate through L1. Focusing on a binary system of a main-sequence star and a super-massive black hole, driven by the emission of gravitational radiation, we show that it may sustain stable mass transfer, along with mass loss through L2. If such a mass-transferring system occurs at our Galactic Centre, it produces a gravitational wave signal detectable by future detectors, such as eLISA. The signal evolves according to the star's adiabatic index and cooling time. For low mass stars, the evolution is faster than the Kelvin-Helmholtz cooling rate driving the star out of the main-sequence. In some cases, the frequency and amplitude of the signal may both decrease with time, contrary to the standard chirp of a coalescing binary. Mass loss through L2, when occurs, decreases the evolution timescale of the emitted gravitational wave signal by up to a few tens of per cent. We conclude that L2 mass ejection is a crucial factor in analyzing gravitational waves signals produced by such systems.
... The interaction of stars and stellar remnants amongst each other as well as with the large mass at the center of the Milky Way may provide tools to explore the nature of SgrA* using gravitational waves (e.g. Amaro-Seoane et al, 2012;Freitag, 2003;Pierro et al, 2001). ...
The compact and, with about 4.3+-0.3 million solar masses, very massive object located at the center of the Milky Way is currently the very best candidate for a supermassive black hole (SMBH) in our immediate vicinity. If SgrA* is indeed a SMBH it will, in projection onto the sky, have the largest event horizon and will certainly be the first and most important target for Very Long Baseline Interferometry (VLBI) observations currently being prepared by the Event Horizon Telescope (EHT). These observations in combination with the infrared interferometry experiment GRAVITY at the Very Large Telescope Interferometer (VLTI) and other experiments across the electromagnetic spectrum might yield proof for the presence of a black hole at the center of the Milky Way. This manuscript reviews the observational facts, theoretical grounds and conceptual aspects for the case of SgrA* being a black hole. We treat theory and observations in the framework of the philosophical discussions about "(Anti)Realism and Underdetermination", as this line of arguments allows us to describe the situation in observational astrophysics with respect to supermassive black holes. Questions concerning the existence of supermassive black holes and in particular SgrA* are discussed using causation as an indispensable element. We show that the results of our investigation are convincingly mapped out by this combination of concepts.
... They have recently been worked out in Ref. [69] for general orbital configurations, i.e., without making a priori assumptions on their inclinations and eccentricities of the perturbed test particle, and arbitrary directions of incidence for the wave. Conversely, L. IORIO PHYSICAL REVIEW D 84, 124001 (2011) 124001-6 gravitational waves can be generated within the stellar system of Sgr A Ã , as discussed in Ref. [70]. ...
Empirically determining the averaged variations of the orbital parameters of
the stars orbiting the Supermassive Black Hole (SBH) hosted by the Galactic
Centre (GC) in Sgr A* is, in principle, a valuable tool to put on the test the
General Theory of Relativity (GTR), in regimes far stronger than those tested
so far, and certain key predictions of it like the no-hair theorems. We
analytically work out the long-term variations of all the six osculating
Keplerian orbital elements of a test particle orbiting a non-spherical,
rotating body with quadrupole moment Q_2 and angular momentum S for a generic
spatial orientation of its spin axis k. This choice is motivated by the fact
that, basically, we do not know the position in the sky of the spin axis of the
SBH in Sgr A* with sufficient accuracy. We apply our results to S2, which is
the closest star discovered so far having an orbital period P_b = 15.98 yr, and
to a hypothetical closer star X with P_b = 0.5 yr. Our calculations are quite
general, not being related to any specific parameterization of k, and can be
applied also to astrophysical binary systems, stellar planetary systems, and
planetary satellite geodesy in which different reference frames, generally not
aligned with the primary's rotational axis, are routinely used.
... In a subsequent chapter, we shall increase complexity and realism one step further and consider systems with a mass spectrum. Using both this gaseous code and the Monte Carlo algorithm ( Benz, 2001, 2002), we will investigate the role of mass segregation around a massive black hole (Amaro-Seoane, Freitag & Spurzem, in preparation), a mechanism which may have important observational consequences as it probably affects the structure of the central cluster of the Milky Way (Morris, 1993; Miralda-Escudé and Gould, 2000; Freitag, 2003b,a; Pfahl and Loeb, 2003) and impacts rates of tidal disruptions and capture of compact stars by emission of gravitational waves in dense galactic nuclei (Magorrian and Tremaine, 1999; Syer and Ulmer, 1999; Sigurdsson, 2003, and references therein). Unfortunately, the literature has relatively little to offer to check our models. ...
This thesis embraces several aspects of theoretical stellar dynamics in clusters, both analytically and numerically. We try to elucidate the phenomena currently observed in all types of galaxies, including AGNs and quasars, some of the most powerful objects in the universe. The interactions between the stellar system and the central black hole give rise to a lot of interesting phenomena. The scheme we employ enables a study of clean-cut aspects without any noise that particle methods suffer from. We study the most important physical processes that are readily available in the evolution of a spherical cluster, like self-gravity, two-body relaxation etc, the interaction with a central black hole and the role of a mass spectrum. Not only embark we upon this subject, but we set about an analysis on super-massive stars. How these stars could power the quasar activity by star accretion and energy flows is one of the questions that arises. We undertake other questions, such as the uncertain evolution of such an object and its interaction with the surrounding stellar system. This is of crucial importance in astrophysics, for these objects could be regarded as super-massive black holes progenitors.
In this study we present a novel Monte-Carlo code, referred to as GNC, which enables the investigation of dynamical relaxation in clusters comprising multiple mass components in the vicinity of supermassive black holes at the centers of galaxies. Our method is based on two-dimensional Fokker-Planck equations in the energy and angular momentum space, and allows the evolution of multiple mass components, including stars and compact objects. The code demonstrates remarkable flexibility to incorporate additional complex dynamics, such as resonant relaxations and gravitational wave orbital decay. By employing a weighting method, we effectively enhance the statistical accuracy of rare particle results. In this initial publication, we present the fundamental version of our method, focusing on two-body relaxations and loss cone effects. Through comparisons with previous studies, we establish consistent outcomes in terms of relaxation processes, energy and angular momentum distributions, density profiles, and loss cone consumption rates. We consistently observe the development of tangential anisotropy within the cluster, while the outer regions tend to retain near-isotropic characteristics. Moving forward, GNC holds great promise for exploring a wide range of intriguing phenomena within galactic nuclei, in particular relativistic stellar dynamics, providing detailed and insightful outcomes.
We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to μ-Hz frequency range. By the 2040s, the μ-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a μ-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe.
Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo’s telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein’s gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our Universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature.
Stars can be consumed (either tidally disrupted or swallowed whole) by massive black holes (MBHs) at galactic centers when they move into the vicinity of the MBHs. In this study, we investigate the rates of stellar consumption by central MBHs and their cosmic distributions, including the effects of triaxial galaxy shapes in enhancing the reservoir of low-angular-momentum stars and incorporating realistic galaxy distributions. We find that the enhancement in the stellar consumption rates due to triaxial galaxy shapes can be significant, by a factor of ∼3 for MBH mass – and up to more than one order of magnitude for . Only for are the stellar consumption rates significantly higher in galaxies with steeper inner surface brightness profiles. The average (per galaxy) stellar consumption rates correlate with central MBH masses positively for and negatively for . The volumetric stellar tidal disruption rates are for MBHs in the mass range 10 ⁵ – at z = 0; and the volumetric stellar consumption rates by MBHs with higher masses are , which can be the stellar tidal disruption rate if the high-mass BHs are extremely spinning Kerr BHs or the rate of being swallowed if those BHs are Schwarzschild ones. The volumetric stellar consumption rates decrease with increasing redshift, and the decrease is relatively mild for – and stronger for higher . Most of the stellar tidal disruption events (TDEs) at z = 0 occur in galaxies with mass , and about 1%–2% of the TDEs can occur in high-mass galaxies with .
We simulate the star cluster, made of stars in the main sequence and different black hole (BH) remnants, around SgrA* at the center of the Milky Way galaxy. Tracking stellar evolution, we find the BH remnant masses and construct the BH mass function. We sample 4 BH species and consider the impact of the mass-function in the dynamical evolution of system. Starting from an initial 6 dimensional family of parameters and using an MCMC approach, we find the best fits to various parameters of model by directly comparing the results of the simulations after t = 10.5 Gyrs with current observations of the stellar surface density, stellar mass profile and the mass of SgrA*. Using these parameters, we study the dynamical evolution of system in detail. We also explore the mass-growth of SgrA* due to tidally disrupted stars and swallowed BHs. We show that the consumed mass is dominated for the BH component with larger initial normalization as given by the BH mass-function. Assuming that about 10% of the tidally disrupted stars contribute in the growth of SgrA* mass, stars make up the second dominant effect in enhancing the mass of SgrA*. We consider the detectability of the GW signal from inspiralling stellar mass BHs around SgrA* with LISA . Computing the fraction of the lifetime of every BH species in the LISA band, with signal to noise ratio ≳ 8, to their entire lifetime, and rescaling this number with the total number of BHs in the system, we find that the total expected rate of inspirals per Milky-Way sized galaxy per year is 10⁻⁵. Quite interestingly, the rate is dominated for the BH component with larger initial normalization as dictated by the BH mass-function. We interpret it as the second signature of the BH mass-function.
The detection of the gravitational waves emitted in the capture process of a compact object by a massive black hole (MBH) is known as an extreme-mass ratio inspiral (EMRI), it represents a unique probe of gravity in the strong regime, and it is one of the main targets of the Laser Interferometer Space Antenna (LISA). The possibility of observing a compact-object EMRI at the Galactic Center (GC) when LISA is taking data is very low. However, the capture of a brown dwarf, an X-MRI, is more frequent because these objects are much more abundant and can plunge without being tidally disrupted. An X-MRI covers some ∼108 cycles before merger, and hence stays on band for millions of years. About 2×106 yrs before merger they have a signal-to-noise ratio (SNR) at the GC of 10. Later, 104 yrs before merger, the SNR is of several thousands, and 103 yrs before the merger a few 104. Based on these values, this kind of EMRIs is also detectable at neighbor MBHs, albeit with fainter SNRs. We calculate the event rate of X-MRIs at the GC taking into account the asymmetry of pro- and retrograde orbits on the location of the last stable orbit (LSO). We estimate that at any given moment, and using a conservative approach, there are of the order of ≳20 sources in band. From these, ≳5 are circular and are located at higher frequencies, and about ≳15 are highly eccentric and are at lower frequencies. Because of their proximity, X-MRIs represent a unique probe of gravity in the strong regime. The mass ratio for a X-MRI at the GC is q∼108, i.e., 3 orders of magnitude larger than stellar-mass black hole EMRIs. Since backreaction depends on q, the orbit more closely follows a standard geodesic, which means that approximations work better in the calculation of the orbit. X-MRIs can be sufficiently loud so as to track the systematic growth of their SNR, which can be high enough to bury that of MBH binaries.
Aims. We present the first fully relativistic study of gravitational radiation from bodies in circular equatorial orbits around the massive black hole at the Galactic center, Sgr A* and we assess the detectability of various kinds of objects by the gravitational wave detector LISA.
Methods. Our computations are based on the theory of perturbations of the Kerr spacetime and take into account the Roche limit induced by tidal forces in the Kerr metric. The signal-to-noise ratio in the LISA detector, as well as the time spent in LISA band, are evaluated. We have implemented all the computational tools in an open-source SageMath package, within the Black Hole Perturbation Toolkit framework.
Results. We find that white dwarfs, neutrons stars, stellar black holes, primordial black holes of mass larger than 10 ⁻⁴ M⊙ , main-sequence stars of mass lower than ∼2.5 M⊙ , and brown dwarfs orbiting Sgr A* are all detectable in one year of LISA data with a signal-to-noise ratio above 10 for at least 10 ⁵ years in the slow inspiral towards either the innermost stable circular orbit (compact objects) or the Roche limit (main-sequence stars and brown dwarfs). The longest times in-band, of the order of 10 ⁶ years, are achieved for primordial black holes of mass ∼10 ⁻³ M⊙ down to 10 ⁻⁵ M⊙ , depending on the spin of Sgr A*, as well as for brown dwarfs, just followed by white dwarfs and low mass main-sequence stars. The long time in-band of these objects makes Sgr A* a valuable target for LISA. We also consider bodies on close circular orbits around the massive black hole in the nucleus of the nearby galaxy M 32 and find that, among them, compact objects and brown dwarfs stay for 10 ³ –10 ⁴ years in LISA band with a one-year signal-to-noise ratio above ten.
A preliminary estimation of gravitational waves (GWs) from the extreme-mass-ratio-inspirals (EMRIs) system in the Galactic Centre (GC) is given for the 37 observed S-stars revolving around the supermassive black hole (SMBH) at Sagittarius (Sgr) A∗. Within this century, the total strain of the gravitational waveform calculated from the post-Newtonian (PN) method with eccentricity is well below the current planned sensitivity of pulsar-timing-array (PTA). New technology might be required in order to extract GW signal from this EMRIs system for future PTA detections.
In a recent paper (Leibowitz 2017) I have shown that the 39 large X-ray flares of Sgr A* that were recorded by Chandra observatory in the year 2012, are concentrated preferably around tick marks of an equi-distance grid on the time axis. The period of this grid as found in L1 is 0.1033 days. In this work I show that the effect can be found among all the large X-ray flares recoded by Chandra and XMM-Newton along 15 years. The midpoints of all the 71 large flares recorded between the years 2000 and 2014 are also tightly grouped around tick marks of a grid with this period, or more likely, 0.1032 day. This result is obtained with a confidence level of at least 3.27{\sigma} and very likely of 4.62{\sigma}. I find also a possible hint that a similar grid is underlying IR flares of the object. I suggest that the pacemaker in the occurrences of the large X-ray flares of Sgr A* is a mass of the order of a low mass star or a small planet, in a slightly eccentric Keplerian orbit around the SMBH at the centre of the Galaxy. The radius of this orbit is about 6.6 Schwarzschild radii of the BH.
IntroductionTidal Spin-up by star-star encountersTidal scattering by the central black holeSqueezars: Tidally powered starsPrompt disruption .vs. slow inspiralSummary
A massive black hole (MBH) consumes stars whose orbits evolve into the small phase-space volume of unstable orbits, the "loss-cone", which take them directly into the MBH, or close enough to interact strongly with it. The resulting phenomena: tidal heating and tidal disruption, binary capture and hyper-velocity star ejection, gravitational wave (GW) emission by inspiraling compact remnants, or hydrodynamical interactions with an accretion disk, are of interest as they can produce observable signatures and thereby reveal the existence of the MBH, affect its mass and spin evolution, probe strong gravity, and provide information on stars and gas near the MBH. The continuous loss of stars and the processes that resupply them shape the central stellar distribution. We investigate relativistic stellar dynamics near the loss-cone of a non-spinning MBH in steady-state analytically and by Monte Carlo simulations of the diffusion of the orbital parameters. These take into account Newtonian mass precession due to enclosed stellar mass, in-plane precession due to general relativity, dissipation by GW, uncorrelated two-body relaxation, correlated resonant relaxation (RR) and adiabatic invariance due to secular precession, using a rigorously derived description of correlated post-Newtonian dynamics in the diffusion limit. We argue that general maximal entropy considerations strongly constrain orbital diffusion in steady-state, irrespective of the relaxation mechanism. We identify the exact phase-space separatrix between plunges and inspirals, predict their steady-state rates, and verify they are robust under a wide range of assumptions. We derive the dependence of the rates on the mass of the MBH, show that the contribution of RR is small, and discuss special cases where unquenched RR in restricted volumes of phase-space may affect the steady-state substantially.
White dwarfs (WDs) can be tidally disrupted only by massive black holes
(MBHs) with masses less than approximately . These tidal
interactions feed material to the MBH well above its Eddington limit, with the
potential to launch a relativistic jet. The corresponding beamed emission is a
promising signpost to an otherwise quiescent MBH of relatively low mass. We
show that the mass transfer history, and thus the lightcurve, are quite
different when the disruptive orbit is parabolic, eccentric, or circular. The
mass lost each orbit exponentiates in the eccentric-orbit case leading to the
destruction of the WD after several tens of orbits and making it difficult to
produce a Swift J1644+57-like lightcurve via this channel. We then examine the
stellar dynamics of clusters surrounding these MBHs to show that single-passage
WD disruptions are substantially more common than repeating encounters in
eccentric orbits. The erg s peak luminosity of these events
makes them visible to cosmological distances and means that they may be
detectible at rates of as many as tens per year by instruments like Swift. In
fact, WD-disruption transients significantly outshine their main-sequence star
counterparts, and are the most likely tidal interaction to be detected arising
from MBHs with masses less than . The detection or non-detection
of such WD-disruption transients by Swift is, therefore, a powerful tool to
constrain lower end of the MBH mass function. The emerging class of ultra-long
gamma ray bursts, such as GRB 101225A, GRB 111209A, and GRB 121027A, all have
peak luminosities and durations reminiscent of those arising of WD disruptions,
offering a hint that WD-disruption transients may already be present in
existing datasets.
Large ground-based laser beam interferometers are presently in operation both in the USA (LIGO) and in Europe (VIRGO) and potential sources that might be detected by these instruments are revisited. The present generation of detectors does not have a sensitivity high enough to probe a significant volume of the universe and, consequently, predicted event rates are very low. The planned advanced generation of interferometers will probably be able to detect, for the first time, a gravitational signal. Advanced LIGO and EGO instruments are expected to detect few (some): binary coalescences consisting of either two neutron stars, two black holes or a neutron star and a black hole. In space, the sensitivity of the planned LISA spacecraft constellation will allow the detection of the gravitational signals, even within a "pessimistic" range of possible signals, produced during the capture of compact objects by supermassive black holes, at a rate of a few tens per year.
Gravitational waves and X-ray flares are expected from tidal disruption of stars by a massive black hole. Using a relativistic smoothed particle hydrodynamics code, we investigate the fate of main-sequence and helium stars in plunge orbits passing near Schwarzschild or Kerr black holes of mass ~105-106M☉. We show that quadrupole gravitational waves emitted during the tidal disruption process are described reasonably well by a point-particle approximation even in the strong-encounter case. An additional hydrodynamic calculation based on the Godunov method indicates that shocks develop for sufficiently high tidal compressions. The shock heating results in an X-ray flare, which for solar-type stars disrupted by ~106M☉ black holes is in the keV range associated with the gravitational wave signal. The hardness and duration of the X-ray flare may serve as a diagnostic of the mass of the central black hole.
An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted
when a compact object passes through periapsis on a highly eccentric orbit
about a much more massive object, in our case a stellar mass object about a
10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the
spacetime of massive black holes (MBHs). We conduct an investigation of the
properties of EMRBs and how they could allow us to constrain the parameters,
such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the
Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu =
10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The
signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) +
4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good
constraints on both the MBH's mass and spin. Closer orbits provide better
constraints, with the best giving accuracies of better than one part in 10^4
for both the mass and spin parameter.
Black hole binaries with extreme (104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany.
A massive black hole (MBH) in a galactic center drives a flow of stars into nearly radial orbits to replace those it destroyed. Stars whose orbits cross the event horizon rS or the tidal disruption radius rt are promptly destroyed in an orbital period P. Stars with orbital periapse rp slightly larger than the sink radius q ≡ max(rS, rt) may slowly spiral in as a result of dissipative interactions with the MBH, e.g., gravitational wave emission, tidal heating, or accretion disk drag, with observable consequences and implications for the MBH growth rate. Unlike prompt destruction, the in-spiral time is typically P. This time is limited by the same scattering process that initially deflected the star into its eccentric orbit, since it can deflect it again to a wider orbit where dissipation is inefficient. The ratio between slow and prompt event rates is therefore much smaller than that implied by the ratio of cross sections, ~rp/q, and so only prompt disruption contributes significantly to the mass of the MBH. Conversely, most stars that scatter off the MBH survive the extreme tidal interaction ("tidal scattering"). We derive general expressions for the in-spiral event rate and the mean number of in-spiraling stars, and we show that the survival probability of tidally scattered stars is ~1 and that the number of tidally heated stars ("squeezars") and gravity-wave-emitting stars in the galactic center is ~0.1-1.
Stellar mass compact objects in short-period (P 103 s) orbits about a 104.5-107.5 M☉ massive black hole (MBH) are thought to be a significant continuous-wave source of gravitational radiation for the ESA/NASA Laser Interferometer Space Antenna (LISA) gravitational wave detector. These extreme mass ratio inspiral sources began in long-period, nearly parabolic orbits that have multiple close encounters with the MBH. The gravitational radiation emitted during the close encounters may be detectable by LISA as a gravitational wave burst if the characteristic passage timescale is less than 105 s. Scaling a static, spherical model to the size and mass of the Milky Way bulge, we estimate an event rate of ~15 yr-1 for such burst signals, detectable by LISA with signal-to-noise ratio greater than 5, originating in our Galaxy. When extended to include Virgo Cluster galaxies, our estimate increases to a gravitational wave burst rate of ~18 yr-1. We conclude that these extreme mass ratio burst sources may be a steady and significant source of gravitational radiation in the LISA data streams.
To be presented is a study of the secular evolution of a spherical stellar system with a central star-accreting black hole (BH) using the anisotropic gaseous model. This method solves numerically moment equations of the full Fokker-Planck equation, with Boltzmann-Vlasov terms on the left-and collisional terms on the right-hand sides. We study the growth of the central BH due to star accretion at its tidal radius and the feedback of this process on to the core collapse as well as the post-collapse evolution of the surrounding stellar cluster in a self-consistent manner. Diffusion in velocity space into the loss-cone is approximated by a simple model. The results show that the self-regulated growth of the BH reaches a certain fraction of the total mass cluster and agree with other methods. Our approach is much faster than competing ones (Monte Carlo, N –body) and provides detailed informations about the time and space dependent evolution of all relevant properties of the system. In this work we present the method and study simple models (equal stellar masses, no stellar evolution or collisions). Nonetheless, a generalisation to include such effects is conceptually simple and under way.
The accessibility of the ∼ 3×106M⊙massive black hole (MBH) in the Galactic Center (GC) offers a unique opportunity to probe a variety of strong tidal interactions of stars with a MBH or with other stars in the high density cusp around aMBH. We show that such interactions can affect a significant fraction of the stellar population within the MBH radius of influence. We consider three processes that could possibly modify stellar structure and evolution there. (1) Tidal spin-up by hyperbolic star-star encounters. (2) Tidal scattering of stars on the MBH. (3) Tidal heating of tidally captured inspiraling stars — “squeezars”. We discuss the implications for stellar populations near MBHs and for the growth of MBHs by tidal disruption, and the possible signatures of such processes in the GC. We compare the event rates of prompt tidal encounters (tidal disruption and tidal scattering) with slow inspiral events (squeezars / tidal capture), and find that, contrary to what was assumed in past studies, tidal capture in the presence of scattering is an order of magnitude less efficient than prompt disruption and so does not contribute significantly to the growth of the MBH.
In this chapter I describe a fast, approximate, particle-based algorithm to compute the long-term evolution of stellar clusters
and galactic nuclei. It
relies on the assumptions of spherical symmetry of the stellar system, dynamical equilibrium and local, diffusive two-body
relaxation. It allows for velocity anisotropy, an arbitrary stellar mass spectrum, stellar evolution, a central massive object,
collision between stars, binary processes and two-body encounters leading to large deflection angles. Using
There is increasing evidence that many galaxies host both a nuclear star
cluster (NC) and a super-massive black hole (SMBH). Their coexistence is
particularly prevalent in spheroids with stellar mass 10^8-10^10 solar masses.
We study the possibility that a stellar-mass black hole (BH) hosted by a NC
inspirals and merges with the central SMBH. Due to the high stellar density in
NCs, extreme mass-ratio inspirals (EMRIs) of BHs onto SMBHs in NCs may be
important sources of gravitational waves (GWs). We consider sensitivity curves
for three different space-based GW laser interferometric mission concepts: the
Laser Interferometer Space Antenna (LISA), the New Gravitational wave
Observatory (NGO) and the DECi-hertz Interferometer Gravitational wave
Observatory (DECIGO). We predict that, under the most optimistic assumptions,
LISA and DECIGO will detect up to thousands of EMRIs in NCs per year, while NGO
will observe up to tens of EMRIs per year. We explore how a number of factors
may affect the predicted rates. In particular, if we assume that the mass of
the SMBH scales with the square of the host spheroid mass in galaxies with NCs,
rather than a linear scaling, then the event rates are more than a factor of 10
lower for both LISA and NGO, while they are almost unaffected in the case of
DECIGO.
One component of a massive black hole binary (MBHB) might capture a small
third body, and then a hierarchical, inclined triple system would be formed.
With the post-Newtonian approximation including radiation reaction, we analyzed
the evolution of the triple initially with small eccentricities. We found that
an essentially new resonant relation could arise in the triple system. Here
relativistic effects are crucial. Relativistic resonances, including the new
one, stably work even for an outer MBHB of comparable masses, and significantly
change the orbit of the inner small body.
Several galaxies have exhibited X-ray flares that are consistent with the tidal disruption of a star by a central supermassive
black hole. In theoretical treatments of this process it is usually assumed that the star was initially on a nearly parabolic
orbit relative to the black hole. Such an assumption leads in the simplest approximation to a t−5/3 decay of the bolometric luminosity and this is indeed consistent with the relatively poorly sampled light curves of such
flares. We point out that there is another regime in which the decay would be different: if a binary is tidally separated
and the star that remains close to the hole is eventually tidally disrupted from a moderate eccentricity orbit, the decay
is slower, typically ∼t−1.2. As a result, careful sampling of the light curves of such flares could distinguish between these processes and yield insight
into the dynamics of binaries as well as single stars in galactic centres. We explore this process using three-body simulations
and analytic treatments and discuss the consequences for present-day X-ray detections and future gravitational wave observations.
A gravitational wave stochastic background of astrophysical origin may have
resulted from the superposition of a large number of unresolved sources since
the beginning of stellar activity. Its detection would put very strong
constrains on the physical properties of compact objects, the initial mass
function or the star formation history. On the other hand, it could be a
'noise' that would mask the stochastic background of cosmological origin. We
review the main astrophysical processes able to produce a stochastic background
and discuss how it may differ from the primordial contribution by its
statistical properties. Current detection methods are also presented.
One of the most interesting sources of gravitational waves (GWs) for LISA is
the inspiral of compact objects on to a massive black hole (MBH), commonly
referred to as an "extreme-mass ratio inspiral" (EMRI). The small object,
typically a stellar black hole (bh), emits significant amounts of GW along each
orbit in the detector bandwidth. The slowly, adiabatic inspiral of these
sources will allow us to map space-time around MBHs in detail, as well as to
test our current conception of gravitation in the strong regime. The event rate
of this kind of source has been addressed many times in the literature and the
numbers reported fluctuate by orders of magnitude. On the other hand, recent
observations of the Galactic center revealed a dearth of giant stars inside the
inner parsec relative to the numbers theoretically expected for a fully relaxed
stellar cusp. The possibility of unrelaxed nuclei (or, equivalently, with no or
only a very shallow cusp) adds substantial uncertainty to the estimates. Having
this timely question in mind, we run a significant number of direct-summation
body simulations with up to half a million particles to calibrate a much
faster orbit-averaged Fokker-Planck code. We then investigate the regime of
strong mass segregation (SMS) for models with two different stellar mass
components. We show that, under quite generic initial conditions, the time
required for the growth of a relaxed, mass segregated stellar cusp is shorter
than a Hubble time for MBHs with
(i.e. nuclei in the range of LISA). SMS has a significant impact boosting the
EMRI rates by a factor of for our fiducial models of Milky Way type
galactic nuclei.
I discuss four key questions about Galactic Center dynamics, their implications for understanding both the environment of the Galactic MBH and galactic nuclei in general, and the progress made in addressing them. The questions are (1) Is the stellar system around the MBH relaxed? (2) Is there a "dark cusp" around the MBH? (3) What is the origin of the stellar disk(s)?, and (4) What is the origin of the S-stars? Comment: Invited overview lecture in "The Galactic Center, a window to the nuclear environment of disk galaxies" (Shanghai 19-23/10/2009). To appear in ASP Conf. Proc. Ser. "Galactic center workshop 2009" ed. Mark Morris (12 pp 5 fig)
White dwarfs inspiraling into black holes of mass \MBH\simgt 10^5M_\odot
are detectable sources of gravitational waves in the LISA band. In many of
these events, the white dwarf begins to lose mass during the main observational
phase of the inspiral. The mass loss starts gently and can last for thousands
of orbits. The white dwarf matter overflows the Roche lobe through the
point at each pericenter passage and the mass loss repeats periodically. The
process occurs very close to the black hole and the released gas can accrete,
creating a bright source of radiation with luminosity close to the Eddington
limit, ~erg~s. This class of inspirals offers a promising
scenario for dual detections of gravitational waves and electromagnetic
radiation.
Free fall has signed the greatest markings in the history of physics through
the leaning Pisa tower, the Cambridge apple tree and the Einstein lift. The
perspectives offered by the capture of stars by supermassive black holes are to
be cherished, because the study of the motion of falling stars will constitute
a giant step forward in the understanding of gravitation in the regime of
strong field. After an account on the perception of free fall in ancient times
and on the behaviour of a gravitating mass in Newtonian physics, this chapter
deals with last century debate on the repulsion for a Schwarzschild black hole
and mentions the issue of an infalling particle velocity at the horizon.
Further, black hole perturbations and numerical methods are presented, paving
the way to the introduction of the self-force and other back-action related
methods. The impact of the perturbations on the motion of the falling particle
is computed via the tail, the back-scattered part of the perturbations, or via
a radiative Green function. In the former approach, the self-force acts upon
the background geodesic; in the latter, the geodesic is conceived in the total
(background plus perturbations) field. Regularisation techniques (mode-sum and
Riemann-Hurwitz z function) intervene to cancel divergencies coming from the
infinitesimal size of the particle. An account is given on the state of the
art, including the last results obtained in this most classical problem,
together with a perspective encompassing future space gravitational wave
interferometry and head-on particle physics experiments. As free fall is
patently non-adiabatic, it requires the most sophisticated techniques for
studying the evolution of the motion. In this scenario, the potential of the
self-consistent approach, by means of which the background geodesic is
continuously corrected by the self-force contribution, is examined.
This review paper is devoted to the theory of orbits. We start with the
discussion of the Newtonian problem of motion then we consider the relativistic
problem of motion, in particular the PN approximation and the further
gravitomagnetic corrections. Finally by a classification of orbits in
accordance with the conditions of motion, we calculate the gravitational waves
luminosity for different types of stellar encounters and orbits.
Gravitational waveforms and production could be considerably affected by gravitomagnetic corrections considered in relativistic theory of orbits. Beside the standard periastron effect of General Relativity, new nutation effects come out when c^{-3} corrections are taken into account. Such corrections emerge as soon as matter-current densities and vector gravitational potentials cannot be discarded into dynamics. We study the gravitational waves emitted through the capture, in the gravitational field of massive binary systems (e.g. a very massive black hole on which a stellar object is inspiralling) via the quadrupole approximation, considering precession and nutation effects. We present a numerical study to obtain the gravitational wave luminosity, the total energy output and the gravitational radiation amplitude. From a crude estimate of the expected number of events towards peculiar targets (e.g. globular clusters) and in particular, the rate of events per year for dense stellar clusters at the Galactic Center (SgrA*), we conclude that this type of capture could give signatures to be revealed by interferometric GW antennas, in particular by the forthcoming laser interferometer space antenna LISA. Comment: 14 pages, 7 figures
We analyze the dynamical evolution of binary stars that interact with a static background of single stars in the environment of a massive black hole (MBH). All stars are considered to be single mass, Newtonian point particles. We follow the evolution of the energy E and angular momentum J of the center of mass of the binaries with respect to the MBH, as well as their internal semi-major axis a, using a Monte Carlo method. For a system like the Galactic center, the main conclusions are the following: (1) The binary fraction can be of the order of a few percent outside 0.1 pc, but decreases quickly closer to the MBH. (2) Within ~0.1 pc, binaries can only exist on eccentric orbits with apocenters much further away from the MBH. (3) Far away from the MBH, loss-cone effects are the dominant mechanism that disrupts binaries with internal velocities close to the velocity dispersion. Closer to the MBH, three-body encounters are more effective in disrupting binaries. (4) The rate at which hard binaries become tighter is usually less than the rate at which a binary diffuses to orbits that are more bound to the MBH. (5) Binaries are typically disrupted before they experience an exchange interaction; as a result, the number of exchanges is less than one would estimate from a simple "nv\sigma estimate''. We give applications of our results to the formation of X-ray binaries near MBHs and to the production rates of hyper-velocity stars by intermediate mass MBHs. Comment: Accepted to ApJ
WFPC-2 images are used to study the central structure of M31, M32, and M33. The dimmer peak, P2, of the M31 double nucleus is centered on the bulge to 0.1", implying that it is the dynamical center of M31. P2 contains a compact source discovered by King et al. (1995) at 1700 A. This source is resolved, with r_{1/2} approx0.2 pc. It dominates the nucleus at 3000 A, and is consistent with late B-early A stars. This probable cluster may consist of young stars and be an older version of the cluster of hot stars at the center of the Milky Way, or it may consist of heavier stars built up from collisions in a possible cold disk of stars orbiting P2. In M32, the central cusp rises into the HST limit with gamma approx0.5, and the central density rho_0>10^7M_sol pc^-3. The V-I and U-V color profiles are flat, and there is no sign of an inner disk, dust, or any other structure. This total lack of features seems at variance with a nominal stellar collision time of 2 X 10^10 yr, which implies that a significant fraction of the light in the central pixel should come from blue stragglers. InM33, the nucleus has an extremely steep gamma=1.49 power-law profile for 0.05"<r<0.2" that becomes shallower as the HST resolution limit is approached. The profile for r<0.04" has either a gamma approx 0.8 cusp or a small core with r_c ~<0.13 pc. The central density is rho_0 > 2 10^6M_sol pc^-3, and the implied relaxation time is only ~3 X 10^6 yr, indicating that the nucleus is highly relaxed. The accompanying short collision time of 7 X 10^9 yr predicts a central blue straggler component quantitatively consistent with the strong V-I and B-R color gradients seen with HST and from the ground.
Cross sections for the tidal capture binary formation process are
calculated for a variety of stellar models. The formalism used in the
determination of the energy dissipated by a close encounter between two
unbound stars and the associated capture cross sections are reviewed.
The case of an n = 3/2 polytropic structure is calculated with the
formalism, and the behavior of realistic stellar models is considered,
including Population II main-sequence stars with masses of 0.4, 0.8, and
1.5 solar. The calculation is repeated for a 'slightly evolved' 0.8
solar mass star just as it begins to leave the main sequence, and the
behavior of more evolved stars is discussed. A quasi-adiabatic analysis
is used to estimate the time scale on which the pulsation energy is
actually dissipated internally or radiated away. This analysis also
indicates where in the star most of the dissipation takes place,
allowing the stellar response to be estimated by including the heating
in the equations of stellar structure.
We review the motivation and search for supermassive black holes (BHs) in galaxies. Energetic nuclear activity provides indirect but compelling evidence for BH engines. Ground-based dynamical searches for central dark objects are reviewed in Kormendy & Richstone (1995, ARA&A, 33, 581). Here we provide an update of results from the
Hubble Space Telescope
(HST). This has greatly accelerated the detection rate. As of 2001 March, dynamical BH detections are available for at least 37 galaxies. The demographics of these objects lead to the following conclusions: (1) BH mass correlates with the luminosity of the bulge component of the host galaxy, albeit with considerable scatter. The median BH mass fraction is 0.13% of the mass of the bulge. (2) BH mass correlates with the mean velocity dispersion of the bulge inside its effective radius, i.e., with how strongly the bulge stars are gravitationally bound to each other. For the best mass determinations, the scatter is consistent with the measurement errors. (3) BH mass correlates with the luminosity of the high-density central component in disk galaxies independent of whether this is a real bulge (a mini-elliptical, believed to form via a merger-induced dissipative collapse and starburst) or a “pseudobulge” (believed to form by inward transport of disk material). (4) BH mass does not correlate with the luminosity of galaxy disks. If pure disks contain BHs (and active nuclei imply that some do), then their masses are much smaller than 0.13% of the mass of the disk. We conclude that present observations show no dependence of BH mass on the details of whether BH feeding happens rapidly during a collapse or slowly via secular evolution of the disk. The above results increasingly support the hypothesis that the major events that form a bulge or elliptical galaxy and the main growth phases of its BH-when it shone like a quasar-were the same events.
Recent measurements of the velocities of stars near the centre of the Milky Way have provided the strongest evidence for the presence of a supermassive black hole in a galaxy, but the observational uncertainties poorly constrain many of the black hole's properties. Determining the accelerations of stars in their orbits around the centre provides much more precise information about the position and mass of the black hole. Here we report measurements of the accelerations of three stars located approximately 0.005 pc (projected on the sky) from the central radio source Sagittarius A* (Sgr A*); these accelerations are comparable to those experienced by the Earth as it orbits the Sun. These data increase the inferred minimum mass density in the central region of the Galaxy by an order of magnitude relative to previous results, and localize the dark mass to within 0.05 +/- 0.04 arcsec of the nominal position of Sgr A*. In addition, the orbital period of one of the observed stars could be as short as 15 years, allowing us the opportunity in the near future to observe an entire period.
Many galaxies are thought to have supermassive black holes at their centres-more than a million times the mass of the Sun. Measurements of stellar velocities and the discovery of variable X-ray emission have provided strong evidence in favour of such a black hole at the centre of the Milky Way, but have hitherto been unable to rule out conclusively the presence of alternative concentrations of mass. Here we report ten years of high-resolution astrometric imaging that allows us to trace two-thirds of the orbit of the star currently closest to the compact radio source (and massive black-hole candidate) Sagittarius A*. The observations, which include both pericentre and apocentre passages, show that the star is on a bound, highly elliptical keplerian orbit around Sgr A*, with an orbital period of 15.2 years and a pericentre distance of only 17 light hours. The orbit with the best fit to the observations requires a central point mass of (3.7 +/- 1.5) x 10(6) solar masses (M(*)). The data no longer allow for a central mass composed of a dense cluster of dark stellar objects or a ball of massive, degenerate fermions.
If the stellar population of the bulge contains black holes formed in the final core collapse of ordinary stars with M \ga 30 M_{\odot}, then about 25,000 stellar mass black holes should have migrated by dynamical friction into the central parsec of the Milky Way, forming a black hole cluster around the central supermassive black hole. These black holes can be captured by the central black hole when they randomly reach a highly eccentric orbit due to relaxation, either by direct capture (when their Newtonian peribothron is less than 4 Schwarzschild radii), or after losing orbital energy through gravitational waves. The overall depletion timescale is ~ 30 Gyr, so most of the 25,000 black holes remain in the central cluster today. The presence of this black hole cluster would have several observable consequences. First, the low-mass, old stellar population should have been expelled from the region occupied by the black hole cluster due to relaxation, implying a core in the profile of solar-mass red giants with a radius of ~ 2 pc (i.e., 1'). The observed central density cusp (which has a core radius of only a few arc seconds) should be composed primarily of young (\la 1 Gyr) stars. Second, flares from stars being captured by supermassive black holes in other galaxies should be rarer than usually expected because the older stars will have been expelled from the central regions by the black hole clusters of those galaxies. Third, the young (\la 2 Gyr) stars found at distances ~ 3 - 10 pc from the Galactic center should be preferentially on highly eccentric orbits. Fourth, if future high-resolution K-band images reveal sources microlensed by the Milky Way's central black hole, then the cluster black holes could give rise to secondary (``planet-like'') perturbations on the main event. Comment: submitted to ApJ
We describe a one-parameter family of models of stable spherical stellar systems in which the phase-space distribution function depends only on energy. The models have similar density profiles in their outer parts () and central power-law density cusps, , . The family contains the Jaffe (1983) and Hernquist (1990) models as special cases. We evaluate the surface brightness profile, the line-of-sight velocity dispersion profile, and the distribution function, and discuss analogs of King's core-fitting formula for determining mass-to-light ratio. We also generalize the models to a two-parameter family, in which the galaxy contains a central black hole; the second parameter is the mass of the black hole. Our models can be used to estimate the detectability of central black holes and the velocity-dispersion profiles of galaxies that contain central cusps, with or without a central black hole. Comment: 24 pages, uuencoded compressed Postscript file 0.3 Mbyte
We analyze HST/STIS spectra (see Paper I) of the central region of the dense globular cluster M15. We infer the velocities of 64 individual stars, two-thirds of which have their velocity measured for the first time. This triples the number of stars with measured velocities in the central 1 arcsec of M15 and doubles the number in the central 2 arcsec. Combined with existing ground-based data we obtain the radial profiles of the projected kinematical quantities. The RMS velocity sigma_RMS rises to 14 km/s in the central few arcsec, somewhat higher than the values of 10-12 km/s inferred previously from ground-based data. To interpret the results we construct dynamical models based on the Jeans equation, which imply that M15 must have a central concentration of non-luminous material. If this is due to a single black hole, then its mass is M_BH = (3.9 +/- 2.2) x 10^3 solar masses. This is consistent with the relation between M_BH and sigma_RMS that has been established for galaxies. Also, the existence of intermediate-mass black holes in globular clusters is consistent with several scenarios for globular cluster evolution proposed in the literature. Therefore, these results may have important implications for our understanding of the evolution of globular clusters, the growth of black holes, the connection between globular cluster and galaxy formation, and the nature of the recently discovered `ultra-luminous' X-ray sources in nearby galaxies. Instead of a single black hole, M15 could have a central concentration of dark remnants (e.g., neutron stars) due to mass segregation. However, the best-fitting Fokker-Planck models that have previously been constructed for M15 do not predict a central mass concentration that is sufficient to explain the observed kinematics.[ABRIDGED] Comment: 43 pages, LaTeX, with 14 PostScript figures. Astronomical Journal, in press (Dec 2002). Please note that the results reported here are modified by the Addendum available at astro-ph/0210158 (Astronomical Journal, in press, Jan 2003). This second version submitted to astro-ph is identical to first, with the exception of the preceeding remark
The expansion of the field equations of general relativity in powers of the gravitational coupling constant yield conservation laws of energy, momentum, and angular momentum. From these laws, the loss of energy, momentum and angular momentum of a system due to the radiation of gravitational waves is found. Two techniques, radiation reaction and flux across a large sphere, are used in this calculation and are shown to be in agreement over a time average. These results are then applied to the system of two point masses moving in elliptical orbits around each other. The secular decays of the semi-major axis and eccentricity are found as functions of time and are integrated to specify the decay by gravitational radiation of such systems as functions of their initial conditions. For completeness, the secular change in the perihelion of the orbit for two arbitrary masses is found by a method which is in the spirit of the above calculations. The case of gravitational radiation when the bodies are relativistic is then considered, and an equation for the radiation similar to that of electromagnetic radiation is found. Also a proof is given that, regardless of coordinate systems or conditions, the energy of a system must decrease as a result of the radiation of gravitational waves, providing the potentials are inversely proportional to the distance from the source for large distances.
We present the detection of a 2.0+1.4-0.8×104 Msolar black hole (BH) in the stellar cluster G1 (Mayall II), based on data taken with the Space Telescope Imaging Spectrograph on board the Hubble Space Telescope. G1 is one of the most massive stellar clusters in M31. The central velocity dispersion (25 km s-1) and the measured BH mass of G1 place it on a linear extrapolation of the correlation between BH mass and bulge velocity dispersion established for nearby galaxies. The detection of a BH in this low-mass stellar system suggests that (1) the most likely candidates for seed massive BHs come from stellar clusters, (2) there is a direct link between massive stellar clusters and normal galaxies, and (3) the formation process of both bulges and massive clusters is similar because of their concordance in the M•-sigma relation. Globular clusters in our Galaxy should be searched for central BHs. Based on observations made with the Hubble Space Telescope, which is operated by AURA, Inc., under NASA contract NAS5-26555.
Basic notions Collisional dynamics : theory Qualitative description of the effect of encounters Approximate computation of the relaxation time Detailed computation of the effect of encounters Single encounter Population of field stars: particular case General population of field stars The isotropic case Physical interpretation Dependence on time Dependence on mass Dependence on velocity Evolution equation Local equation Global equation Collisional dynamics: Monte Carlo models Introduction Philosophy of the Monte Carlo approach Detailed description Superstars Initial conditions Potential Time step Encounters New positions Selection of next pair Comparisons of results Comparison between two Monte Carlo approaches Comparison with the fluid-dynamical approach Comparison with exact N-body integrations
The gravitational radiation from two point masses going around each other under their mutual gravitational influence is calculated. Two different methods are outlined; one involves a multipole expansion of the radiation field, while the other uses the inertia tensor of the source. The calculations apply for arbitrary eccentricity of the relative orbit, but assume orbital velocities are small. The total rate, angular distribution, and polarization of the radiated energy are discussed.
We consider roughly 106 to 107 solar mass black
holes (MBHs) in galactic nuclei. As such objects grow by accretion, some
fraction of the accreted mass is in the form of compact stars. If the
approach to coalescence proceeds gradually, many orbital revolutions
will occur, and substantial amounts of gravitational radiation will be
emitted. We estimate the cosmological rate of such events, assuming MBHs
are quite common in galaxies. Despite large uncertainties about the
conditions in galactic nuclei, particularly during the early growth
phase, the event rates are encouraging. The chances of such signals
being observable with a laser gravitational radiation antenna in space
appear to be good.
Stars in galactic nuclei can be captured or tidally disrupted by a
central black hole. Some debris would be ejected at high speed; the
remainder would be swallowed by the hole, causing a bright flare lasting
at most a few years. Such phenomena are compatible with the presence of
10 to the 6th-10 to the 8th solar mass holes in the nuclei of many
nearby galaxies. Stellar disruption may have interesting consequences in
our own Galactic Center if an approximately 10 to the 6th solar mass
hole lurks there.
The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized.
Computationally effective (fast and accurate) tools for constructing gravitational wave templates from binary stars with any
orbital eccentricity are introduced including tight estimation criteria of the pertinent truncation and approximation errors.
A universal initial mass function (IMF) is not intuitive, but so far no convincing evidence for a variable IMF exists. The detection of systematic variations of the IMF with star-forming conditions would be the Rosetta Stone for star formation.
In this contribution an average or Galactic-field IMF is defined, stressing that there is evidence for a change in the power-law index at only two masses: near 0.5 M⊙ and near 0.08 M⊙. Using this supposed universal IMF, the uncertainty inherent in any observational estimate of the IMF is investigated by studying the scatter introduced by Poisson noise and the dynamical evolution of star clusters. It is found that this apparent scatter reproduces quite well the observed scatter in power-law index determinations, thus defining the fundamental limit within which any true variation becomes undetectable. The absence of evidence for a variable IMF means that any true variation of the IMF in well-studied populations must be smaller than this scatter.
Determinations of the power-law indices α are subject to systematic errors arising mostly from unresolved binaries. The systematic bias is quantified here, with the result that the single-star IMFs for young star clusters are systematically steeper by Δα≈0.5 between 0.1 and 1 M⊙ than the Galactic-field IMF, which is populated by, on average, about 5-Gyr-old stars. The MFs in globular clusters appear to be, on average, systematically flatter than the Galactic-field IMF (Piotto & Zoccali; Paresce & De Marchi), and the recent detection of ancient white-dwarf candidates in the Galactic halo and the absence of associated low-mass stars (Ibata et al.; Méndez & Minniti) suggest a radically different IMF for this ancient population. Star formation in higher metallicity environments thus appears to produce relatively more low-mass stars. While still tentative, this is an interesting trend, being consistent with a systematic variation of the IMF as expected from theoretical arguments.
We have developed a new simulation code aimed at studying the stellar dynamics of a galactic central star cluster surrounding a massive black hole. In order to include all the relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption,...), we chose to revive a numerical scheme pioneered by Hénon in the 70's Hénon 1971b, a; Hénon 1973. It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collissions into account in a very realistic way. This first paper covers the basic version of our code which treats the relaxation-driven evolution of a stellar cluster without a central BH. A technical description of the code is presented, as well as the results of test computations. Thanks to the use of a binary tree to store potential and rank information and of variable time steps, cluster models with up to 2 × 106 particles can be simulated on a standard personal computer and the CPU time required scales as Np In(Np) with the particle number Np. Furthermore, the number of simulated stars needs not be equal to Np can be arbitrarily larger. A companion paper will treat further physical elements, mostly relevant to galactic nuclei.
Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/62978/1/254295a0.pdf
More than 80 years ago, Einstein has predicted that accelerated masses will emit gravitational waves, propagating distortions of the spacetime fabric. The gravitational wave spectrum of known and expected sources covers many decades in frequency. While sources in the audio-frequency regime above 1 Hz are accessible to ground-based detectors, sources in the low-frequency regime can only be observed from space because of the unshieldable background of Newtonian gravitational noise. LISA is a laser-interferometric gravitational wave detector in space designed to observe gravitational wave signals from galactic as well as cosmological sources in the frequency range from 0.1 mHz to 1 Hz. LISA comprises a cluster of three spacecraft at the corners of an equilateral triangle of 5 Mio km size. The cluster is in an earth-like heliocentric orbit trailing the earth by 20 degrees. Each spacecraft carries lasers and free-flying proof masses and is kept on a purely inertial orbit by drag-free technology using field emission electric propulsion
We have revised our earlier rough estimate of the combined galactic and extragalactic binary confusion noise level curve for gravitational waves. This was done to correct some numerical errors and to allow for roughly three frequency bins worth of information about weaker sources being lost for each galactic binary signal that is removed from the data. The results are still based on the spectral amplitude estimates for different types of galactic binaries reported by Hils et al in 1990, and assume that the gravitational wave power spectral densities for other galaxies are proportional to the optical luminosities. The estimated confusion noise level drops to the LISA instrumental noise level at between roughly 3 and 8 MHz.
A significant fraction of the stellar population in the cusps around central black holes of galaxies consists of compact remnants
of evolved stars, such as white dwarfs, neutron stars and stellar mass black holes. We estimate the rate of capture of compact
objects by massive central black holes, assuming that most spiral galaxies have a central black hole of modest mass ( ∼ 106 M⊙), and a cuspy spheroid. It is likely that the total capture rate is dominated by nucleated spirals. We estimate the flux
of gravitational wave radiation from such coalescences, and the estimated detectable source count for proposed space-based
gravitational wave observatories such as LISA. About one event per year should be detectable within 1 Gpc, given very conservative estimates of the black hole masses and
central galactic densities. We expect 102−103 detectable sources at lower frequencies (10−4 Hz) ‘en route’ to capture. If stellar mass black holes are ubiquitous, the signal may be dominated by stellar mass black
holes coalescing with massive black holes. The rate of white dwarf-white dwarf mergers in the cores of nucleated spirals is
estimated at ∼ 10−6 per year per galaxy.
The formation rate of a close binary consisting of a super-massive black hole and a compact object (presumably a white dwarf)
in galactic cusps is calculated with the help of the so-called loss cone approximation. For a power-law cusp of radius ra, the black hole mass M∼ 106 M⊙, and the fraction of the compact objects δ∼ 0.1, this rate . The function K(p) depends on parameter p determining the cusp profile, and for the standard cusp profiles with p= 1/4, K(p) ∼ 2. We estimate the probability Pr of finding of a compact object orbiting around a black hole with the period P in one particular galaxy to be Pr∼ 10−7[(P/103 s)/(M/106 M⊙)]8/3[(M/106 M⊙)/(ra/1 pc)]3/2. The object with the period P∼ 103 s emits gravitational waves with amplitude sufficient to be detected by the LISA-type gravitational wave antenna from the
distance ∼103 Mpc. Based on estimates of masses of super-massive black holes in nearby galaxies, we speculate that LISA would detect several
such events during its mission.
The capture and gradual inspiral of stellar mass objects by a massive black hole at the centre of a galaxy has been proposed as one of the most promising source of gravitational radiation to be detected by LISA. Unfortunately rate estimates for this process suffer from many uncertainties. Here we report on the use of our newly developed Monte Carlo stellar dynamics code to tackle this problem. We present results from simple galactic nuclei models that demonstrate the high potential of our approach and point out the aspects of the problem where an improved treatment seems desirable. Comment: 6 pages, 2 figures, Invited talk at the 3rd LISA Symposium, accepted for publication as a symposium paper in Classical and Quantum Gravity. Slightly longer version available at http://obswww.unige.ch/~freitag/papers/proc_LISA2000_l.ps.gz
Since the discovery of the first bona-fide brown dwarfs and extra-solar planets in 1995, the field of low mass stars and substellar objects has considerably progressed, both from theoretical and observational viewpoints.Recent developments in the physics entering the modeling of these objects have led to significant improvements in the theory and to a better understanding of their mechanical and thermal properties. This theory can now be confronted with observations directly in various observational diagrams (color-color, color-magnitude, mass-magnitude, mass-spectral type), a stringent and unavoidable constraint which became possible only recently, with the generation of synthetic spectra. In this paper, we present the current state-of-the-art general theory of low-mass stars and sub-stellar objects, from one solar mass to one Jupiter mass, regarding primarily their interior structure and evolution. This review is a natural complement to the previous review on the atmosphere of low-mass stars and brown dwarfs (Allard et al 1997). Special attention is devoted to the comparison of the theory with various available observations. The contribution of low-mass stellar and sub-stellar objects to the Galactic mass budget is also analysed. Comment: 81 pages, Latex file, uses aasms4.sty, review for Annual Review of Astronomy and Astrophysics, vol. 38 (2000)
We report a new analysis of the stellar dynamics in the Galactic Centre, based on improved sky and line-of-sight velocities for more than 100 stars in the central few arcseconds from the black hole candidate SgrA*. The main results are as follows.
• (1)Overall, the stellar motions do not deviate strongly from isotropy. For those 32 stars with a determination of all three velocity components, the absolute, line-of-sight and sky velocities are in good agreement, consistent with a spherical star cluster. Likewise the sky-projected radial and tangential velocities of all 104 proper motion stars in our sample are also consistent with overall isotropy.
• (2)However, the sky-projected velocity components of the young, early-type stars in our sample indicate significant deviations from isotropy, with a strong radial dependence. Most of the bright He i emission-line stars at separations from 1 to 10 arcsec from SgrA* are on tangential orbits. This tangential anisotropy of the He i stars and most of the brighter members of the IRS 16 complex is largely caused by a clockwise (on the sky) and counter-rotating (line of sight, compared to the Galaxy), coherent rotation pattern. The overall rotation of the young star cluster may be a remnant of the original angular momentum pattern in the interstellar cloud from which these stars were formed.
• (3)The fainter, fast-moving stars within ≈1 arcsec of SgrA* may be largely moving on radial or very elliptical orbits. We have so far not detected deviations from linear motion (i.e., acceleration) for any of them. Most of the SgrA* cluster members are also on clockwise orbits. Spectroscopy indicates that they are early-type stars. We propose that the SgrA* cluster stars are those members of the early-type cluster that happen to have small angular momentum, and thus can plunge to the immediate vicinity of SgrA*.
• (4)We derive an anisotropy-independent estimate of the Sun—Galactic Centre distance between 7.8 and 8.2 kpc, with a formal statistical uncertainty of ±0.9 kpc.
• (5)We explicitly include velocity anisotropy in estimating the central mass distribution. We show how Leonard—Merritt and Bahcall—Tremaine mass estimates give systematic offsets in the inferred mass of the central object when applied to finite concentric rings for power-law clusters. Corrected Leonard—Merritt projected mass estimators and Jeans equation modelling confirm previous conclusions (from isotropic models) that a compact central mass concentration (central density ≥1012.6 M⊙ pc⁻³) is present and dominates the potential between 0.01 and 1 pc. Depending on the modelling method used, the derived central mass ranges between 2.6×10⁶ and 3.3×10⁶ M⊙ for R⊙=8.0 kpc.
To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted (after averaging over source position and polarization) by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first (mostly) analytic calculation of the gravitational wave transfer function is presented. Example sensitivity curve calculations are presented for the proposed LISA interferometer. We find that previous treatments of LISA have underestimated its sensitivity by a factor of . Comment: 27 pages + 5 figures, REVTeX, accepted for publication in Phys Rev D; Update reflects referees comments, figure 3 clarified, figure 5 corrected for LISA baseline
In the coming decade, gravitational waves will convert the study of general relativistic aspects of black holes and stars from a largely theoretical enterprise to a highly interactive, observational/theoretical one. For example, gravitational-wave observations should enable us to observationally map the spacetime geometries around quiescient black holes, study quantitatively the highly nonlinear vibrations of curved spacetime in black-hole collisions, probe the structures of neutron stars and their equation of state, search for exotic types of general relativistic objects such as boson stars, soliton stars, and naked singularities, and probe aspects of general relativity that have never yet been seen such as the gravitational fields of gravitons and the influence of gravitational-wave tails on radiation reaction.
We present a new approximate method for constructing gravitational radiation driven inspirals of test-bodies orbiting Kerr black holes. Such orbits can be fully described by a semi-latus rectum p, an eccentricity e, and an inclination angle ; or, by an energy E, an angular momentum component , and a third constant Q. Our scheme uses expressions that are exact (within an adiabatic approximation) for the rates of change (, , ) as linear combinations of the fluxes (, , ), but uses quadrupole-order formulae for these fluxes. This scheme thus encodes the exact orbital dynamics, augmenting it with approximate radiation reaction. Comparing inspiral trajectories, we find that this approximation agrees well with numerical results for the special cases of eccentric equatorial and circular inclined orbits, far more accurate than corresponding weak-field formulae for (, , ). We use this technique to study the inspiral of a test-body in inclined, eccentric Kerr orbits. Our results should be useful tools for constructing approximate waveforms that can be used to study data analysis problems for the future LISA gravitational-wave observatory, in lieu of waveforms from more rigorous techniques that are currently under development. Comment: 15 pages, 5 figures, submitted to PRD
We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a geodesic (justifiable as long as the orbital evolution is adiabatic) we calculate numerically the fluxes of energy and angular momentum radiated to infinity and to the black hole horizon, via the Teukolsky-Sasaki-Nakamura formalism. We can then infer the rate of change of orbital energy and angular momentum and thus the evolution of the orbit. The orbits are fully described by a semi-latus rectum p and an eccentricity e. We find that while, during the inspiral, e decreases until shortly before the orbit reaches the separatrix of stable bound orbits (which is defined by ), in many astrophysically relevant cases the eccentricity will still be significant in the last stages of the inspiral. In addition, when a critical value is reached, the eccentricity begins to increase as a result of continued radiation induced inspiral. The two values , (for given e) move closer to each other, in coordinate terms, as the black hole spin is increased, as they do also for fixed spin and increasing eccentricity. Of particular interest are moderate and high eccentricity orbits around rapidly spinning black holes, with . We call these ``zoom-whirl'' orbits, because of their characteristic behaviour involving several revolutions around the central body near periastron. Gravitational waveforms produced by such orbits are calculated and shown to have a very particular signature. Such signals may well prove of considerable astrophysical importance for the future LISA detector. Comment: RevteX, 47 pages, 16 figures, submitted to Phys. Rev. D
We calculate the damping of quadrupole f and low order g modes (primary modes) by nonlinear coupling to other modes of the star. This damping is orders of magnitude more rapid than direct radiative damping when the primary amplitude is large, as in tidal capture. Primary modes destabilize high degree g-modes of half their frequency (daughter modes) by 3-mode coupling in radiative zones. In sunlike stars, the growth time days, where is the initial energy of the primary mode in units of erg, and of order daughters are unstable. The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, . Although the daughter modes are limited by their own nonlinearities, collectively they absorb most of the primary mode's energy after a time provided E_{0}> 10^{40}~\mbox{erg}. In fact nonlinear mode interaction may be the dominant damping process if E_0\gtrsim 10^{37}~\mbox{erg}. Our results have application to tidally captured main sequence globular cluster stars of mass \ge 0.5 M_{\sun}; the tidal energy is dissipated in the radiative core of the star in about a month, which is less than the initial orbital period. Comment: AASTeX, 25 pages, plus 4 figures in compressed postscript. Revised only to wrap lines longer than 80 characters
We have recently written a new code to simulate the long term evolution of spherical clusters of stars. It is based on the pioneering Monte Carlo scheme proposed by Henon in the 70's. Our code has been devised in the specific goal to treat dense galactic nuclei. After having described how we treat relaxation in a first paper, we go on and include further physical ingredients that are mostly pertinent to galactic nuclei, namely the presence of a central (growing) black hole (BH) and collisions between MS stars. Stars that venture too close to the BH are destroyed by the tidal field. This process is a channel to feed the BH and a way to produce accretion flares. Collisions between stars have often been proposed as another mechanism to drive stellar matter into the central BH. To get the best handle on the role of this process in galactic nuclei, we include it with unpreceded realism through the use of a set of more than 10000 collision simulations carried out with a SPH (Smoothed Particle Hydrodynamics) code. Stellar evolution has also been introduced in a simple way, similar to what has been done in previous dynamical simulations of galactic nuclei. To ensure that this physics is correctly simulated, we realized a variety of tests whose results are reported here. This unique code, featuring most important physical processes, allows million particle simulations, spanning a Hubble time, in a few CPU days on standard personal computers and provides a wealth of data only rivalized by N-body simulations. Comment: 32 pages, 19 figures. Slightly shortened and clarified following referee's suggestions. Accepted for publication in A&A. Version with high quality figures available at http://obswww.unige.ch/~freitag/papers/article_MC2.ps.gz
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