Frederic A. Rasio

Northwestern University, Evanston, Illinois, United States

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Publications (241)991.15 Total impact

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    ABSTRACT: Many exoplanets have now been detected in orbits with ultra-short periods, very close to the Roche limit. Building upon our previous work, we study the possibility that mass loss through Roche lobe overflow (RLO) may affect the evolution of these planets, and could possibly transform a hot Jupiter into a lower-mass planet (hot Neptune or super-Earth). We focus here on systems in which the mass loss occurs slowly ("stable mass transfer" in the language of binary star evolution) and we compute their evolution in detail with the binary evolution code MESA. We include the effects of tides, RLO, irradiation and photo-evaporation of the planet, as well as the stellar wind and magnetic braking. Our calculations all start with a hot Jupiter close to its Roche limit, in orbit around a sun-like star. The initial orbital decay and onset of RLO are driven by tidal dissipation in the star. We confirm that such a system can indeed evolve to produce lower-mass planets in orbits of a few days. The RLO phase eventually ends and, depending on the details of the mass transfer and on the planetary core mass, the orbital period can remain around a few days for several Gyr. The remnant planets have a rocky core and some amount of envelope material, which is slowly removed via photo-evaporation at nearly constant orbital period; these have properties resembling many of the observed super-Earths and sub-Neptunes. For these remnant planets we also predict an anti-correlation between mass and orbital period; very low-mass planets ($M_{\rm pl}\,\lesssim\,5\,M_{\oplus}$) in ultra-short periods ($P_{\rm orb}$<1d) cannot be produced through this type of evolution.
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    ABSTRACT: Massive stars are usually found in binaries, and binaries with periods less than 10 days may have a preference for near equal component masses. In this paper we investigate the evolution of these binaries all the way to contact and the possibility that these systems can be progenitors of double neutron star binaries. The small orbital separations of observed double neutron star binaries suggest that the progenitor systems underwent a common envelope phase at least once during their evolution. Bethe & Brown (1998) proposed that massive binary twins will undergo a common envelope evolution while both components are ascending the red giant branch or asymptotic giant branch simultaneously, also known as double-core evolution. Using models generated from the stellar evolution code Evolve Zero Age Main Sequence, we determine the range of mass ratios resulting in both components simultaneously ascending the RGB or AGB as a function of the difference in birth times, t. We find that, even for a generous t=5 Myr, the minimum mass ratio qmin=0.933 for an 8 Solar Mass primary and increases for larger primaries. We use a hydrodynamics code, StarSmasher, to study specifically the evolution of q=1 common envelope systems as a function of initial component mass, age, and orbital separation. We find the dynamical stability limit, the largest orbital separation where the binary becomes dynamically unstable, as a function of the component mass and age. Finally, we calculate the efficiency of ejecting matter during the inspiral phase to extrapolate the properties of the remnant binary from our numerical results, assuming the common envelope is completely ejected. We find that for the nominal core masses, there is a minimum orbital separation for a given component mass such that the helium cores survive common envelope evolution in a tightly bound binary and are viable progenitors for double neutron stars.
    The Astrophysical Journal 05/2015; 806(1). DOI:10.1088/0004-637X/806/1/135 · 6.28 Impact Factor
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    ABSTRACT: The predicted rate of binary black hole mergers from galactic fields can vary over several orders of magnitude and is extremely sensitive to the assumptions of stellar evolution. But in dense stellar environments such as globular clusters, binary black holes form by well-understood gravitational interactions. In this letter, we study the formation of black hole binaries in an extensive collection of realistic globular cluster models. By comparing these models to observed Milky Way and extragalactic globular clusters, we find that the mergers of dynamically-formed binaries could be detected at a rate of ~100 per year, potentially dominating the binary black hole merger rate. We also find that a majority of cluster-formed binaries are more massive than their field-formed counterparts, suggesting that Advanced LIGO could identify certain binaries as originating from dense stellar environments.
    Physical Review Letters 05/2015; 115(5). DOI:10.1103/PhysRevLett.115.051101 · 7.51 Impact Factor
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    ABSTRACT: Our current understanding of the stellar initial mass function and of massive star evolution suggests that young globular clusters (GC) may have formed hundreds to thousands of stellar-mass black holes (BH), the remnants of massive stars with initial masses in the range 20 to 100 MSun. Birth kicks from supernova explosions may eject some of these BHs from their birth clusters, but many if not most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of GCs containing large numbers of BHs. Our parallel Monte Carlo code allows us to construct many models of clusters containing up to 1.6x10^6 stars initially. Here we describe numerical results for 42 models, covering a broad range of realistic initial conditions. In almost all cases we find that significant numbers of BHs (up to 10^3) are retained in the cluster all the way to the present. This is in contrast to previous theoretical expectations that most BHs in clusters should be ejected dynamically on a timescale of a few Gyr. The main reason for this difference is that core collapse driven by BHs (through the Spitzer "mass segregation instability") is easily reverted through three-body processes that form binaries, and involves only a small number of the most massive BHs, while lower-mass BHs remain well mixed with ordinary stars far away from the central cusp. Thus the rapid mass segregation of BHs in a cluster can drive gravothermal oscillations involving the most massive BHs, but it does not lead to a long-term physical separation of most BHs into a dynamically decoupled inner core. Combined with the recent detections of several BH X-ray binary candidates in Galactic GCs, our results suggest that BHs could still be present in large numbers in many GCs today, and that they may play a significant role in shaping the long-term evolution and the present-day dynamical structure of GCs.
    The Astrophysical Journal 09/2014; 800(1). DOI:10.1088/0004-637X/800/1/9 · 6.28 Impact Factor
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    Francesca Valsecchi · Frederic A. Rasio · Jason H. Steffen
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    ABSTRACT: Through tidal dissipation in a slowly spinning host star the orbits of many hot Jupiters may decay down to the Roche limit. We expect that in most cases the ensuing mass transfer will be stable. Using detailed numerical calculations we find that this evolution is quite rapid, potentially leading to complete removal of the gaseous envelope in a few Gyr, and leaving behind an exposed rocky core ("hot super-Earth"). Final orbital periods are quite sensitive to the details of the planet's mass-radius relation, and to the effects of irradiation and photo-evaporation, but could be as short as a few hours, or as long as several days. Our scenario predicts the existence of planets with intermediate masses ("hot Neptunes") that should be found precisely at their Roche limit and in the process of losing mass through Roche lobe overflow. The observed excess of small single-planet candidate systems observed by Kepler may also be the result of this process. If so, the properties of their host stars should track those of the hot Jupiters. Moreover, the number of systems that produced hot Jupiters could be 2-3 times larger than one would infer from contemporary observations.
    The Astrophysical Journal Letters 08/2014; 793(1). DOI:10.1088/2041-8205/793/1/L3 · 5.60 Impact Factor
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    ABSTRACT: Kepler-56 is a multi-planet system containing two coplanar inner planets that are in orbits misaligned with respect to the spin axis of the host star, and an outer planet. Various mechanisms have been proposed to explain the broad distribution of spin-orbit angles among exoplanets, and these theories fall under two broad categories. The first is based on dynamical interactions in a multi-body system, while the other assumes that disk migration is the driving mechanism in planetary configuration and that the star (or disk) is titled with respect to the planetary plane. Here we show that the large observed obliquity of Kepler-56 system is consistent with a dynamical origin. In addition, we use observations by Huber et al. (2013) to derive the obliquity's probability distribution function, thus improving the constrained lower limit. The outer planet may be the cause of the inner planets' large obliquities, and we give the probability distribution function of its inclination, which depends on the initial orbital configuration of the planetary system. We show that even in the presence of precise measurement of the true obliquity, one cannot distinguish the initial configurations. Finally we consider the fate of the system as the star continues to evolve beyond the main sequence, and we find that the obliquity of the system will not undergo major variations as the star climbs the red giant branch. We follow the evolution of the system and find that the innermost planet will be engulfed in ~129 Myr. Furthermore we put an upper limit of ~155 Myr for the engulfment of the second planet. This corresponds to ~ 3% of the current age of the star.
    The Astrophysical Journal 07/2014; 794(2). DOI:10.1088/0004-637X/794/2/131 · 6.28 Impact Factor
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    Francesca Valsecchi · Frederic A. Rasio
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    ABSTRACT: Hot Jupiters formed through circularization of high-eccentricity orbits should be found at orbital separations $a$ exceeding $twice$ that of their Roche limit $a_{\rm R}$. Nevertheless, about a dozen giant planets have now been found well within this limit ($a_{\rm R}< a< 2 a_{\rm R}$), with one coming as close as 1.2$a_{\rm R}$. In this Letter, we show that orbital decay (starting beyond 2$a_{\rm R}$) driven by tidal dissipation in the star can naturally explain these objects. For a few systems (WASP-4 and 19), this explanation requires the linear reduction in convective tidal dissipation proposed originally by Zahn (1966) and verified by recent numerical simulations (Penev et al. 2007), but rules out the quadratic prescription proposed by Goldreich and Nicholson (1977). Additionally, we find that WASP-19-type systems could potentially provide empirical support to the Zahn's (1966) prescription through high precision transit timing measurements of their orbital decay rate.
    The Astrophysical Journal Letters 03/2014; 787(1). DOI:10.1088/2041-8205/787/1/L9 · 5.60 Impact Factor
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    Francesca Valsecchi · Frederic A. Rasio
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    ABSTRACT: Two formation scenarios have been proposed to explain the tight orbits of hot Jupiters. These giant planets could be formed in low-obliquity orbits via disk migration or in high-obliquity orbits via high-eccentricity migration, where gravitational interactions with a companion are at play, together with tidal dissipation. Here we target the observed misaligned hot Jupiter systems to investigate whether their current properties are consistent with high-eccentricity migration. Specifically, we study whether tidal dissipation in the star can be responsible for the observed distribution of misalignments and orbital separations. Improving on previous studies, we use detailed models for the stellar component, thus accounting for how convection (and thus tidal dissipation) depends on the host star properties. We find that the currently observed degree of misalignment increases as the amount of surface convection in the host star decreases. This trend supports the hypothesis that tides are the mechanism shaping the observed distribution of misalignments. Furthermore, we study the past orbital evolution of four representative systems. We consider various initial orbital configurations and integrate the equations describing the coupled evolution of the orbital separation, stellar spin, and misalignment. We account for tidal dissipation in the star, stellar wind mass loss, changes in the star's internal structure as a result of stellar evolution, and magnetic braking. We show that the current properties of these four representative systems can be explained naturally, given our current understanding of tidal dissipation and with physically motivated assumptions for the effects driving the orbital evolution.
    The Astrophysical Journal 02/2014; 786(2). DOI:10.1088/0004-637X/786/2/102 · 6.28 Impact Factor
  • Frederic A. Rasio · M. Morscher
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    ABSTRACT: We study the formation and evolution of black holes in globular clusters using a Monte Carlo code for stellar dynamics. Our models include stellar evolution for both single and binary stars, as well as all relevant dynamical processes. We find that old globular clusters can retain large numbers (up to hundreds) of stellar black holes all the way to the present, in agreement with other recent theoretical analyses and observations. We explore the implications of these results for the formation of black hole X-ray binaries and merging double black hole binaries in clusters.
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    Jean Teyssandier · Smadar Naoz · Ian M. Lizarraga · Frederic A. Rasio
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    ABSTRACT: Observations of exoplanets over the last two decades have revealed a new class of Jupiter-size planets with orbital periods of a few days, the so-called "hot Jupiters". Recent measurements using the Rossiter-McLaughlin effect have shown that many (~ 50%) of these planets are misaligned; furthermore, some (~ 15%) are even retrograde with respect to the stellar spin axis. Motivated by these observations, we explore the possibility of forming retrograde orbits in hierarchical triple configurations consisting of a star-planet inner pair with another giant planet, or brown dwarf, in a much wider orbit. Recently Naoz et al. (2011) showed that in such a system, the inner planet's orbit can flip back and forth from prograde to retrograde, and can also reach extremely high eccentricities. Here we map a significant part of the parameter space of dynamical outcomes for these systems. We derive strong constraints on the orbital configurations for the outer perturber that could lead to the formation of hot Jupiters with misaligned or retrograde orbits. We focus only on the secular evolution, neglecting other dynamical effects such as mean-motion resonances, as well as all dissipative forces. For example, with an inner Jupiter-like planet initially on a nearly circular orbit at 5 AU, we show that a misaligned hot Jupiter is likely to be formed in the presence of a more massive planetary companion (> 2 MJ) within 140 AU of the inner system, with mutual inclination 50 degrees and eccentricity above 0.25. This is in striking contrast to the test-particle approximation, where an almost perpendicular configuration can still cause large eccentricity excitations, but flips of an inner Jupiter-like planet are much less likely to occur. The constraints we derive can be used to guide future observations, and, in particular, searches for more distant companions in systems containing a hot Jupiter.
    The Astrophysical Journal 10/2013; 779(2). DOI:10.1088/0004-637X/779/2/166 · 6.28 Impact Factor
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    Sanghamitra Goswami · Paul Kiel · Frederic A. Rasio
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    ABSTRACT: We present theoretical models for stellar black hole (BH) properties in young, massive star clusters. Using a Monte Carlo code for stellar dynamics, we model realistic star clusters with $N\simeq 5\times10^5$ stars and significant binary fractions (up to 50%) with self-consistent treatments of stellar dynamics and stellar evolution. We compute the formation rates and characteristic properties of single and binary BHs for various representative ages, cluster parameters, and metallicities. Because of dynamical interactions and supernova (SN) kicks, more single BHs end up retained in clusters compared to BHs in binaries. We also find that the ejection of BHs from a cluster is a strong function of initial density. In low-density clusters (where dynamical effects are negligible), it is mainly SN kicks that eject BHs from the cluster, whereas in high-density clusters (initial central density $\rho_c(0) \sim 10^5 \, M_\odot\, {\rm pc}^{-3} $ in our models) the BH ejection rate is enhanced significantly by dynamics. Dynamical interactions of binary systems in dense clusters also modify the orbital period and eccentricity distributions while also increasing the probability of a BH having a more massive companion.
    The Astrophysical Journal 09/2013; 781(2). DOI:10.1088/0004-637X/781/2/81 · 6.28 Impact Factor
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    Alison Sills · Evert Glebbeek · Sourav Chatterjee · Frederic A. Rasio
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    ABSTRACT: We created artificial color-magnitude diagrams of Monte Carlo dynamical models of globular clusters, and then used observational methods to determine the number of blue stragglers in those clusters. We compared these blue stragglers to various cluster properties, mimicking work that has been done for blue stragglers in Milky Way globular clusters to determine the dominant formation mechanism(s) of this unusual stellar population. We find that a mass-based prescription for selecting blue stragglers will choose approximately twice as many blue stragglers than a selection criterion that was developed for observations of real clusters. However, the two numbers of blue stragglers are well-correlated, so either selection criterion can be used to characterize the blue straggler population of a cluster. We confirm previous results that the simplified prescription for the evolution of a collision or merger product in the BSE code overestimates their lifetimes. We show that our model blue stragglers follow similar trends with cluster properties (core mass, binary fraction, total mass, collision rate) as the true Milky Way blue stragglers, as long as we restrict ourselves to model clusters with an initial binary fraction higher than 5%. We also show that, in contrast to earlier work, the number of blue stragglers in the cluster core does have a weak dependence on the collisional parameter Gamma in both our models and in Milky Way globular clusters.
    The Astrophysical Journal 03/2013; 777(2). DOI:10.1088/0004-637X/777/2/105 · 6.28 Impact Factor
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    Sourav Chatterjee · Frederic A. Rasio · Alison Sills · Evert Glebbeek
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    ABSTRACT: Blue straggler stars (BSS) are abundantly observed in all Galactic globular clusters (GGC) where data exist. However, observations alone cannot reveal the relative importance of various formation channels or the typical formation times for this well studied population of anomalous stars. Using a state-of-the-art H\'enon-type Monte Carlo code that includes all relevant physical processes, we create 128 models with properties typical of the observed GGCs. These models include realistic numbers of single and binary stars, use observationally motivated initial conditions, and span large ranges in central density, concentration, binary fraction, and mass. Their properties can be directly compared with those of observed GGCs. We can easily identify the BSSs in our models and determine their formation channels and birth times. We find that for central densities above ~10^3 Msun/pc^3 the dominant formation channel is stellar collisions while for lower density clusters, mass transfer in binaries provides a significant contribution (up to ~ 60% in our models). The majority of these collisions are binary-mediated, occurring during 3-body and 4-body interactions. As a result a strong correlation between the specific frequency of BSSs and the binary fraction in a cluster can be seen in our models. We find that the number of BSSs in the core shows only a weak correlation with the collision rate estimator \Gamma traditionally used by observers, in agreement with the latest Hubble Space Telescope (ACS) data. Using an idealized "full mixing" prescription for collision products, our models indicate that the BSSs observed today may have formed several Gyrs ago. However, denser clusters tend to have younger (~1 Gyr) BSSs.
    The Astrophysical Journal 02/2013; 777(2). DOI:10.1088/0004-637X/777/2/106 · 6.28 Impact Factor
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    ABSTRACT: Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which doesn't suffer of the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extension of the Riccati method to investigate dynamic tides in close binaries. We demonstrate CAFein's capabilities as a stellar pulsation code both in the adiabatic and non-adiabatic regime, by reproducing previously published eigenfrequencies of a polytrope, and by successfully identifying the unstable modes of a stellar model in the $\beta$ Cephei/SPB region of the Hertzsprung-Russell diagram. Finally, we verify CAFein's behavior in the dynamic tides regime by investigating the effects of dynamic tides on the eigenfunctions and orbital and spin evolution of massive Main Sequence stars in eccentric binaries, and of hot Jupiter host stars. The plethora of asteroseismic data provided by the NASA's Kepler satellite, some of which include the direct detection of tidally excited stellar oscillations, make CAFein quite timely. Furthermore, the increasing number of observed short-period detached double white dwarfs (WD) and the observed orbital decay in the tightest of such binaries open up a new possibility of investigating WD interiors through the effects of tides on their orbital evolution
    The Astrophysical Journal 01/2013; 773(1). DOI:10.1088/0004-637X/773/1/39 · 6.28 Impact Factor
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    ABSTRACT: Measuring the frequency and orbital properties of planets around stars in open clusters would provide insight into planet formation and the evolution of planetary systems. While several transiting-planet searches found no planets in open clusters, recently the radial velocity technique has identified planets in two small open clusters, Hyades and Praesepe. We consider how these and future transiting-planet searches with the Kepler mission can address whether planet formation in clusters differs from planet formation around field stars. We model NGC 6791, an open cluster in the Kepler field of view, including a population of planet-harboring stars, using a fast and accurate Hénon-type Monte Carlo code. We evaluate the prospects for Kepler to detect transiting planets around normal main-sequence stars in NGC 6791. We make predictions for the number of detectable planets, and the properties of such planets and their host stars, assuming that planets form in this cluster at the same rate as is observed in the field. We show that the most promising hunting grounds for transiting planets in this cluster are around main sequence stars at a distance of about 5' from the cluster center.
  • J. F. Sepinsky · B. Willems · V. Kalogera · F. A. Rasio
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    ABSTRACT: We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, assuming conservation of total system mass and orbital angular momentum. Assuming a delta function mass transfer rate centered at periastron, we find rates of secular change of the orbital semi-major axis and eccentricity which are linearly proportional to the magnitude of the mass transfer rate at periastron. The rates can be positive as well as negative, so that the semi-major axis and eccentricity can increase as well as decrease in time. Adopting a delta-function mass-transfer rate of 10 −9 M ⊙ yr −1 at periastron yields orbital evolution timescales ranging from a few Myr to a Hubble time or more, depending on the binary mass ratio and orbital eccentricity. Comparison with orbital evolution timescales due to dissipative tides furthermore shows that tides cannot, in all cases, circularize the orbit rapidly enough to justify the often adopted assumption of instantaneous circularization at the onset of mass transfer. The formalism presented can be incorporated in binary evolution and population synthesis codes to create a self-consistent treatment of mass transfer in eccentric binaries.
  • Edward W. Thommes · Geoffrey Bryden · Yanqin Wu · Frederic A. Rasio
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    ABSTRACT: We show that interaction with a gas disk may produce young planetary systems with closely-spaced orbits, stabilized by mean-motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant planetesimal disk tends to pull these configurations apart, eventually inducing dynamical instability. We show that this can lead to a variety of outcomes; some cases resemble the Solar System, while others end up with high-eccentricity orbits reminiscent of the observed exoplanets. A similar mechanism has been previously suggested as the cause of the lunar Late Heavy Bombardment. Thus, it may be that a large-scale dynamical instability, with more or less cataclysmic results, is an evolutionary step common to many planetary systems, including our own. Subject headings: planetary systems:formation, solar system:formation 1.
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    ABSTRACT: Interacting galaxies often have complexes of hundreds of young stellar clusters of individual masses ~ 10^{4-6} Msun in regions that are a few hundred parsecs across. These cluster complexes interact dynamically, and their coalescence is a candidate for the origin of some ultracompact dwarf galaxies (UCDs). Individual clusters with short relaxation times are candidates for the production of intermediate-mass black holes of a few hundred solar masses, via runaway stellar collisions prior to the first supernovae in a cluster. It is therefore possible that a cluster complex hosts multiple intermediate-mass black holes that may be ejected from their individual clusters due to mergers or binary processes, but bound to the complex as a whole. Here we explore the dynamical interaction between initially free-flying massive black holes and clusters in an evolving cluster complex. We find that, after hitting some clusters, it is plausible that the massive black hole will be captured in an ultracompact dwarf forming near the center of the complex. In the process, the hole typically triggers electromagnetic flares via stellar disruptions, and is also likely to be a prominent source of gravitational radiation for the advanced ground-based detectors LIGO and VIRGO. We also discuss other implications of this scenario, notably that the central black hole could be considerably larger than expected in other formation scenarios for ultracompact dwarfs.
    The Astrophysical Journal 11/2012; 782(2). DOI:10.1088/0004-637X/782/2/97 · 6.28 Impact Factor
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    ABSTRACT: Recent observations of the white dwarf (WD) populations in globular clusters suggest that WDs receive a kick of a few kms −1 shortly before they are born. Using our Monte Carlo cluster evolution code, which includes accurate treatments of all relevant physical processes operating in globular clusters, we study the effects of the kicks on the cluster and on the WD population itself. We find that in clusters whose velocity dispersion is comparable to the kick speed, WD kicks are a significant energy source for the cluster, prolonging the initial cluster core contraction phase significantly so that at late times the cluster core to half-mass radius ratio is a factor of up to ∼ 10 larger than in the no-kick case. WD kicks thus represent a possible resolution of the large discrepancy between observed and theoretically predicted values of this key structural parameter. Our modeling also reproduces the observed trend for younger WDs to be more extended in their radial distribution in the cluster than older WDs.
  • J. F. Sepinsky · B. Willems · V. Kalogera · F. A. Rasio
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    ABSTRACT: We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, allowing for both mass and angular momentum loss from the system. Adopting a delta function mass transfer rate at the periastron of the binary orbit, we find that, depending on the initial binary properties at the onset of mass transfer, the orbital semi-major axis and eccentricity can either increase or decrease at a rate linearly proportional to the magnitude of the mass transfer rate at periastron. The range of initial binary mass ratios and eccentricities that leads to increasing orbital semi-major axes and eccentricities broadens with increasing degrees of mass loss from the system and narrows with increasing orbital angular momentum loss from the binary. Comparison with tidal evolution timescales shows that the usual assumption of rapid circularization at the onset of mass transfer in eccentric binaries is not justified, irrespective of the degree of systemic mass and angular momentum loss. This work extends our previous results for conservative mass transfer in eccentric binaries and can be incorporated into binary evolution and population synthesis codes to model non-conservative mass transfer in eccentric binaries.

Publication Stats

7k Citations
991.15 Total Impact Points

Institutions

  • 2002–2014
    • Northwestern University
      • • Department of Physics and Astronomy
      • • Center for Interdisciplinary Exploration and Research in Astrophysics
      Evanston, Illinois, United States
  • 2009
    • University of British Columbia - Vancouver
      • Department of Physics and Astronomy
      Vancouver, British Columbia, Canada
  • 1996–2008
    • Massachusetts Institute of Technology
      • Department of Physics
      Cambridge, MA, United States
  • 2007
    • University of Toronto
      • Canadian Institute for Theoretical Astrophysics
      Toronto, Ontario, Canada
  • 2005
    • University of California, Berkeley
      • Department of Astronomy
      Berkeley, MO, United States
  • 2004
    • University of Warsaw
      • Astronomical Observatory
      Warszawa, Masovian Voivodeship, Poland
  • 1988–1999
    • Cornell University
      • • Center for Radiophysics and Space Research (CRSR)
      • • Department of Physics
      Итак, New York, United States
  • 1994
    • Institute for Advanced Study
      Princeton Junction, New Jersey, United States