Frederic A. Rasio

Northwestern University, Evanston, Illinois, United States

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Publications (243)985.26 Total impact

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    ABSTRACT: We present the first detailed comparison between million-body globular cluster simulations computed with a H\'enon-type Monte Carlo code, CMC, and a direct $N$-body code, NBODY6++GPU. Both simulations start from an identical cluster model with $10^6$ particles, and include all of the relevant physics needed to treat the system in a highly realistic way. With the two codes "frozen" (no fine-tuning of any free parameters or internal algorithms of the codes) we find excellent agreement in the overall evolution of the two models. Furthermore, we find that in both models, large numbers of stellar-mass black holes (> 1000) are retained for 12 Gyr. Thus, the very accurate direct $N$-body approach confirms recent predictions that black holes can be retained in present-day, old globular clusters. We find only minor disagreements between the two models and attribute these to the small-$N$ dynamics driving the evolution of the cluster core for which the Monte Carlo assumptions are less ideal. Based on the overwhelming general agreement between the two models computed using these vastly different techniques, we conclude that our Monte Carlo approach, which is more approximate, but dramatically faster compared to the direct $N$-body, is capable of producing a very accurate description of the long-term evolution of massive globular clusters even when the clusters contain large populations of stellar-mass black holes.
    No preview · Article · Jan 2016
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    ABSTRACT: DOI:http://dx.doi.org/10.1103/PhysRevLett.116.029901
    No preview · Article · Jan 2016 · Physical Review Letters
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    ABSTRACT: The "gravitational million-body problem," to model the dynamical evolution of a self-gravitating, collisional N-body system with N ~10^6 over many relaxation times, remains a major challenge in computational astrophysics. Unfortunately, current techniques to model such a system suffer from severe limitations. A direct N-body simulation with more than 10^5 particles can require months or even years to complete, while an orbit-sampling Monte Carlo approach cannot adequately treat the details of the core dynamics, particularly in the presence of many black holes. We have developed a new technique combining the precision of direct N-body codes with the speed of a Monte Carlo approach. Our Rapid And Precisely Integrated Dynamics code, the RAPID code, statistically models interactions between neighboring stars and stellar binaries while integrating directly the orbits of stars in the cluster core. This allows us to accurately simulate the dynamics of the black holes in a realistic globular cluster environment without the burdensome N^2 scaling of a full N-body integration. We compare models of idealized globular clusters created by the RAPID approach to direct N-body and Monte Carlo models. Our tests show that RAPID can reproduce the half-mass and core radii of the direct N-body models far more accurately than the Monte Carlo approach and in ~1/200th of the computing time. With this technique, it will be possible to create realistic models of Milky Way globular clusters with sufficient rapidity to explore the full parameter space of dense stellar clusters.
    No preview · Article · Nov 2015
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    ABSTRACT: The formation of Black Hole (BH) Low-Mass X-ray Binaries (LMXB) poses a theoretical challenge, as low-mass companions are not expected to survive the common-envelope scenario with the BH progenitor. Here we propose a formation mechanism that skips the common-envelope scenario and relies on triple-body dynamics. We study the evolution of hierarchical triples, following the secular dynamical evolution up to the octupole-level of approximation, including general relativity, tidal effects and post-main-sequence evolution, such as mass loss, changes to stellar radii and supernovae. During the dynamical evolution of the triple system, the "eccentric Kozai-Lidov" mechanism can cause large eccentricity excitations in the LMXB progenitor, resulting in three main BH-LMXB formation channels. Here we define BH-LMXB candidates as systems where the inner BH companion star crosses its Roche limit. In the "eccentric" channel (~ 81% of the LMXBs in our simulations), the donor star crosses its Roche limit during an extreme eccentricity excitation, while still on a wide orbit. Second, we find a "giant" LMXB channel (~ 11%), where a system undergoes only moderate eccentricity excitations, but the donor star fills its Roche lobe after evolving toward the giant branch. Third, we identify a "classical" channel (~8%), where tidal forces and magnetic braking shrink and circularize the orbit to short periods, triggering mass transfer. Finally, for the giant channel, we predict an eccentric ($\sim 0.3-0.6$), preferably inclined (~40, ~140 degreed) tertiary, typically on a wide enough orbit (~10^4AU), to potentially become unbound later in the triple evolution.
    No preview · Article · Oct 2015
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    ABSTRACT: Hierarchical triple-star systems are expected to form frequently via close binary-binary encounters in the dense cores of globular clusters. In a sufficiently inclined triple, gravitational interactions between the inner and outer binary can cause large-amplitude oscillations in the eccentricity of the inner orbit ("Lidov-Kozai cycles"), which can lead to a collision and merger of the two inner components. In this paper we use Monte Carlo models of dense star clusters to identify all triple systems formed dynamically and we compute their evolution using a highly accurate three-body integrator which incorporates relativistic and tidal effects. We find that a large fraction of these triples evolve through a non-secular dynamical phase which can drive the inner binary to higher eccentricities than predicted by the standard secular perturbation theory (even including octupole-order terms). We place constraints on the importance of Lidov-Kozai-induced mergers for producing: (i) gravitational wave sources detectable by Advanced LIGO (aLIGO), for triples with an inner pair of stellar black holes; and (ii) blue straggler stars, for triples with main-sequence-star components. We find a realistic aLIGO detection rate of black hole mergers due to the Lidov-Kozai mechanism of 2yr^-1, with about 20% of these having a finite eccentricity when they first chirp into the aLIGO frequency band. While rare, these events are likely to dominate among eccentric compact object inspirals that are potentially detectable by aLIGO. For blue stragglers, we find that the Lidov-Kozai mechanism can contribute up to ~10% of their total numbers in globular clusters. In clusters with low central densities, ~10^{3}-10^{4} M_Sun pc^-3, up to ~40% of binary blue stragglers could have formed in dynamically assembled triples.
    Full-text · Article · Sep 2015 · The Astrophysical Journal
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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.
    Preview · Article · Jun 2015 · The Astrophysical Journal
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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.
    Full-text · Article · May 2015 · The Astrophysical Journal
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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.
    Full-text · Article · May 2015 · Physical Review Letters
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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.
    Full-text · Article · Sep 2014 · The Astrophysical Journal
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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.
    Full-text · Article · Aug 2014 · The Astrophysical Journal Letters
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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.
    Full-text · Article · Jul 2014 · The Astrophysical Journal
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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 R. Nevertheless, about a dozen giant planets have now been found well within this limit (a R < a < 2 a R), with one coming as close as 1.2 a R. In this Letter, we show that orbital decay (starting beyond 2 a 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 and verified by recent numerical simulations, but rules out the quadratic prescription proposed by Goldreich & Nicholson. Additionally, we find that WASP-19-like systems could potentially provide direct empirical constraints on tidal dissipation, as we could soon be able to measure their orbital decay through high precision transit timing measurements.
    Full-text · Article · Mar 2014 · The Astrophysical Journal Letters
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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.
    Full-text · Article · Feb 2014 · The Astrophysical Journal
  • 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.
    No preview · Article · Jan 2014
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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.
    Full-text · Article · Oct 2013 · The Astrophysical Journal
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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 5 × 105 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 ρc (0) ~ 105M ☉ 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 increasing the probability of a BH having a more massive companion.
    Preview · Article · Sep 2013 · The Astrophysical Journal
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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.
    Full-text · Article · Mar 2013 · The Astrophysical Journal
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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.
    Full-text · Article · Feb 2013 · The Astrophysical Journal
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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
    Full-text · Article · Jan 2013 · The Astrophysical Journal
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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.
    No preview · Article · Jan 2013

Publication Stats

8k Citations
985.26 Total Impact Points

Institutions

  • 2001-2015
    • Northwestern University
      • • Department of Physics and Astronomy
      • • Center for Interdisciplinary Exploration and Research in Astrophysics
      Evanston, Illinois, United States
  • 1995-2008
    • Massachusetts Institute of Technology
      • Department of Physics
      Cambridge, MA, United States
  • 2007
    • University of Toronto
      • Canadian Institute for Theoretical Astrophysics
      Toronto, Ontario, Canada
  • 2004
    • University of Warsaw
      • Astronomical Observatory
      Warszawa, Masovian Voivodeship, Poland
  • 1994
    • Institute for Advanced Study
      Princeton Junction, New Jersey, United States
    • Yale University
      • Department of Astronomy
      New Haven, Connecticut, United States
  • 1988-1994
    • Cornell University
      • Center for Radiophysics and Space Research (CRSR)
      Итак, New York, United States