arXiv subjects

Taeho Ryu

Publications and source records attributed to Taeho Ryu.

At least 55 records · Page 3Linked to original sources

arXiv2023

Close Encounters of Star - Black Hole Binaries with Single Stars

Multi-body dynamical interactions of binaries with other objects are one of the main driving mechanisms for the evolution of star clusters. It is thus important to bring our understanding of three-body interactions beyond the commonly employed point-particle approximation. To this end we here investigate the hydrodynamics of three-body encounters between star-black hole (BH) binaries and single stars, focusing on the identification of final outcomes and their long-term evolution and observational properties, using the moving-mesh hydrodynamics code AREPO. This type of encounters produces five types of outcomes: stellar disruption, stellar collision, weak perturbation of the original binary, binary member exchange, and triple formation. The two decisive parameters are the binary phase angle, which determines which two objects meet at the first closest approach, and the impact parameter, which sets the boundary between violent and non-violent interactions. When the impact parameter is smaller than the semimajor axis of the binary, tidal disruptions and star-BH collisions frequently occur when the BH and the incoming star first meet, while the two stars mostly merge when the two stars meet first instead. In both cases, the BHs accrete from an accretion disk at super-Eddington rates, possibly generating flares luminous enough to be observed. The stellar collision products either form a binary with the BH or remain unbound to the BH. Upon collision, the merged stars are hotter and larger than main sequence stars of the same mass at similar age. Even after recovering their thermal equilibrium state, stellar collision products, if isolated, would remain hotter and brighter than main sequence stars until becoming giants.

astro-ph.HE↗

arXiv2023

Close encounters of black hole - star binaries with stellar-mass black holes

Dynamical interactions involving binaries play a crucial role in the evolution of star clusters and galaxies. We continue our investigation of the hydrodynamics of three-body encounters, focusing on binary black hole (BBH) formation, stellar disruption, and electromagnetic (EM) emission in dynamical interactions between a BH-star binary and a stellar-mass BH, using the moving-mesh hydrodynamics code {\small AREPO}. This type of encounters can be divided into two classes depending on whether the final outcome includes BBHs. This outcome is primarily determined by which two objects meet at the first closest approach. BBHs are more likely to form when the star and the incoming BH encounter first with an impact parameter smaller than the binary's semimajor axis. In this case, the star is frequently disrupted. On the other hand, when the two BHs encounter first, frequent consequences are an orbit perturbation of the original binary or a binary member exchange. For the parameters chosen in this study, BBH formation, accompanied by stellar disruption, happens in roughly 1 out of 4 encounters. The close correlation between BBH formation and stellar disruption has possible implications for EM counterparts at the binary's merger. The BH that disrupts the star is promptly surrounded by an optically and geometrically thick disk with accretion rates exceeding the Eddington limit. If the debris disk cools fast enough to become long-lived, EM counterparts can be produced at the time of the BBH merger.

astro-ph.HE↗

arXiv2023

Partial stellar tidal disruption events and their rates

Tidal disruption events (TDEs) of stars operated by massive black holes (MBHs) will be detected in thousands by upcoming facilities such as the Vera Rubin Observatory. In this work, we assess the rates of standard total TDEs, destroying the entire star, and partial TDEs, in which a stellar remnant survives the interaction, by solving 1-D Fokker-Planck equations. Our rate estimates are based on a novel definition of the loss cone whose size is commensurate to the largest radius at which partial disruptions can occur, as motivated by relativistic hydrodynamical simulations. Our novel approach unveils two important results. First, partial TDEs can be more abundant than total disruptions by a factor of a few to a few tens. Second, the rates of complete stellar disruptions can be overestimated by a factor of a few to a few tens if one neglects partial TDEs, as we find that many of the events classified at total disruptions in the standard framework are in fact partial TDEs. Accounting for partial TDEs is particularly relevant for galaxies harbouring a nuclear stellar cluster featuring many events coming from the empty loss cone. Based on these findings, we stress that partial disruptions should be considered when constraining the luminosity function of TDE flares; accounting for this may reconcile the theoretically estimated TDE rates with the observed ones.

astro-ph.HE↗

arXiv2023

Quasi-periodic eruptions from impacts between the secondary and a rigidly precessing accretion disc in an extreme mass-ratio inspiral system

X-ray quasi-periodic eruptions (QPEs) represent a recently discovered example of extreme X-ray variability associated with supermassive black holes. These are high-amplitude bursts recurring every few hours that are detected in the soft X-ray band from the nuclei of nearby galaxies whose optical spectra lack the broad emission lines typically observed in unobscured active galaxies. The physical origin of this new X-ray variability phenomenon is still unknown and several theoretical models have been presented. However, no attempt has been made so far to account for the varying QPE recurrence time and luminosity in individual sources, nor for the diversity of the QPE phenomenology in the different known erupters. We present a semi-analytical model based on an extreme mass-ratio inspiral (EMRI) system where the secondary intersects, along its orbit, a rigidly precessing accretion disc surrounding the primary. We assume that QPEs result from emission from an adiabatically expanding, initially optically thick gas cloud expelled from the disc plane at each impact. We produced synthetic X-ray light curves, which we then compared with X-ray data from four QPE sources: GSN 069, eRO-QPE1, eRO-QPE2, and RX J1301.9+2747. Our model aptly reproduces the diversity of QPE properties between the considered objects and it is also able to naturally account for the varying QPE amplitudes and recurrence times in individual sources. Future implementations will enable us to refine the match with the data and to estimate the system parameters precisely, making additional use of multi-epoch QPE data. We briefly discuss the nature of the secondary object, as well as the possible implications of our findings for the EMRI population at large.

astro-ph.HE↗

arXiv2023

Tidal Peeling Events: low-eccentricity tidal disruption of a star by a stellar-mass black hole

Close encounters between stellar-mass black holes (BHs) and stars occur frequently in dense star clusters and in the disks of active galactic nuclei (AGNs). Recent studies have shown that in highly eccentric close encounters, the star can be tidally disrupted by the BH (micro-tidal disruption event, or micro-TDE), resulting in rapid mass accretion and possibly bright electromagnetic signatures. Here we consider a scenario in which the star might approach the stellar-mass BH in a gradual, nearly circular inspiral, under the influence of dynamical friction on a circum-binary gas disk or three-body interactions in a star cluster. We perform hydro-dynamical simulations of this scenario using the smoothed particle hydrodynamics code PHANTOM. We find that the mass of the star is slowly stripped away by the BH. We call this gradual tidal disruption a "tidal-peeling event", or a TPE. Depending on the initial distance and eccentricity of the encounter, TPEs might exhibit significant accretion rates and orbital evolution distinct from those of a typical (eccentric) micro-TDE.

astro-ph.HE↗

arXiv2023

Extremely Relativistic Tidal Disruption Events

Extreme tidal disruption events (eTDEs), which occur when a star passes very close to a supermassive black hole, may provide a way to observe a long-sought general relativistic effect: orbits that wind several times around a black hole and then leave. Through general relativistic hydrodynamics simulations, we show that such eTDEs are easily distinguished from most tidal disruptions, in which stars come close, but not so close, to the black hole. Following the stellar orbit, the debris in eTDEs is initially distributed in a crescent that quickly turns into tight spirals, from which some mass later falls back toward the black hole, while the remainder is ejected. Internal shocks within the infalling debris power the observed emission. The resulting light-curve rises rapidly to roughly the Eddington luminosity, maintains this level for between a few weeks and a year (depending on both the stellar mass and the black hole mass), and then drops. Most of its power is in thermal X-rays at a temperature $\sim (1-2)\times 10^{6}$ K ($\sim 100-200$ eV). The debris evolution and observational features of eTDEs are qualitatively different from ordinary TDEs, making eTDEs a new type of TDE. Although eTDEs are relatively rare for lower-mass black holes, most tidal disruptions around higher-mass black holes are extreme. Their detection offers a view of an exotic relativistic phenomenon previously inaccessible.

astro-ph.HE↗

arXiv2023

Close Encounters of Tight Binary Stars with Stellar-mass Black Holes

Strong dynamical interactions among stars and compact objects are expected in a variety of astrophysical settings, such as star clusters and the disks of active galactic nuclei. Via a suite of 3D hydrodynamics simulations using the moving-mesh code AREPO, we investigate the formation of transient phenomena and their properties in close encounters between an $2M_{\odot}$ or $20M_{\odot}$ equal-mass circular binary star and single $20M_{\odot}$ black hole (BH). Stars can be disrupted by the BH during dynamical interactions, naturally producing electromagnetic transient phenomena. Encounters with impact parameters smaller than the semimajor axis of the initial binary frequently lead to a variety of transients whose electromagnetic signatures are qualitatively different from those of ordinary disruption events involving just two bodies. These include the simultaneous or successive disruptions of both stars and one full disruption of one star accompanied by successive partial disruptions of the other star. On the other hand, when the impact parameter is larger than the semimajor axis of the initial binary, the binary is either simply tidally perturbed or dissociated into bound and unbound single stars ("micro-Hills" mechanism). The dissociation of $20M_{\odot}$ binaries can produce a runaway star and an active BH moving away from one another. Also, the binary dissociation can either produce an interacting binary with the BH, or a non-interacting, hard binary; both could be candidates of BH high- and low-mass X-ray binaries. Hence our simulations especially confirm that strong encounters can lead to the formation of the (generally difficult to form) BH low-mass X-ray binaries.

astro-ph.HE↗

arXiv2022

Tidal Disruption Events by Compact Supermassive Black Hole Binaries

Stars can be tidally destroyed or swallowed by supermassive black hole binaries. Using a large number of accurate few-body simulations, we investigate the enhancement and suppression of full and partial disruption and direct capture events by hard supermassive black hole binaries with a wide ranges of key parameters, i.e., the primary black hole mass ($10^{5}-10^{8}M_{\odot}$), the binary mass ratio ($10^{-3}-1$), the ratio of the binary semimajor axis to the hardening radius ($10^{-4}-1$), the binary eccentricity ($0.0-0.9$) and the stellar mass ($0.3-3M_{\odot}$). This is a significant extension of the parameter space compared to previous work. We show that the encounter probabilities of all three events are well-described by the encounter cross section, which is proportional to the pericenter distance. The probability of full disruptions by supermassive black hole binaries can be enhanced by up to a factor of $40-50$ or suppressed by up to a factor of $10$, relative to that by single black holes, depending on the binary parameters. Relativistic effects are not important for the primary black hole mass $\leq 10^{7}M_{\odot}$, but can provide an additional enhancement of the full disruption probability by less than a factor of $2-3$ for higher primary black hole masses. We provide a fitting formula for the full disruption probability by the hard supermassive black hole binaries that works for a wide range of parameters. We also find that partial disruption events can occur multiple times before full disruptions or direct captures, and their probabilities can be greater than that of full disruption events by a factor of three. Because partial disruption events can induce stellar spins and mass loss and change the orbits, it can significantly affect the overall full disruption event rate and the shape of the light curves.

astro-ph.HE↗

arXiv2022

Close Encounters of Stars with Stellar-mass Black Hole Binaries

Many astrophysical environments, from star clusters and globular clusters to the disks of Active Galactic Nuclei, are characterized by frequent interactions between stars and the compact objects that they leave behind. Here, using a suite of $3-D$ hydrodynamics simulations, we explore the outcome of close interactions between $1M_{\odot}$ stars and binary black holes (BBHs) in the gravitational wave regime, resulting in a tidal disruption event (TDE) or a pure scattering, focusing on the accretion rates, the back reaction on the BH binary orbital parameters and the increase in the binary BH effective spin. We find that TDEs can make a significant impact on the binary orbit, which is often different from that of pure scattering. Binaries experiencing a prograde (retrograde) TDE tend to be widened (hardened) by up to $\simeq 20\%$. Initially circular binaries become more eccentric by $\lesssim 10\%$ by a prograde or retrograde TDE, whereas the eccentricity of initially eccentric binaries increases (decreases) by a retrograde (prograde) TDE by $\lesssim 5\%$. Overall a single TDE can generally result in changes of the gravitational wave-driven merger time scale by order unity. The accretion rates of both black holes are very highly super-Eddington, showing modulations (preferentially for retrograde TDEs) on a time scale of the orbital period, which can be a characteristic feature of BBH-driven TDEs. Prograde TDEs result in the effective spin parameter $χ$ to vary by $\lesssim 0.02$ while $χ\gtrsim -0.005$ for retrograde TDEs.

astro-ph.HE↗

arXiv2021

The Impact of Shocks on the Vertical Structure of Eccentric Disks

Accretion disks whose matter follows eccentric orbits can arise in multiple astrophysical situations. Unlike circular orbit disks, the vertical gravity in eccentric disks varies around the orbit. In this paper, we investigate some of the dynamical effects of this varying gravity on the vertical structure using $1D$ hydrodynamics simulations of individual gas columns assumed to be mutually non-interacting. We find that time-dependent gravitational pumping generically creates shocks near pericenter; the energy dissipated in the shocks is taken from the orbital energy. Because the kinetic energy per unit mass in vertical motion near pericenter can be large compared to the net orbital energy, the shocked gas can be heated to nearly the virial temperature, and some of it becomes unbound. These shocks affect larger fractions of the disk mass for larger eccentricity and/or disk aspect ratio. If the orbit can be maintained despite orbital energy loss, diverse initial structures evolve in only a few orbits so that they follow a limit-cycle characterized by a low-entropy midplane and a much higher entropy outer layer. In favorable cases (such as the tidal disruption of stars by supermassive black holes), these effects could be a potentially important energy dissipation and mass loss mechanism.

astro-ph.HE↗

arXiv2020

Tidal disruptions of main sequence stars -- IV. Relativistic effects and dependence on black hole mass

Using a suite of fully relativistic hydrodynamic simulations applied to main-sequence stars with realistic internal density profiles, we examine full and partial tidal disruptions across a wide range of black hole mass ($10^{5}\leq M_{\rm BH}/\mathrm{M}_{\odot}\leq 5\times 10^{7}$) and stellar mass ($0.3 \leq M_{\star} /\mathrm{M}_{\odot}\leq 3$) as larger $M_{\rm BH}$ leads to stronger relativistic effects. For fixed $M_{\star}$, as $M_{\rm BH}$ increases, the ratio of the maximum pericenter distance yielding full disruptions ($\mathcal{R}_{\rm t}$) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for $M_{\rm BH} = 5\times10^{7}~{\rm M}_\odot$, while the ratio of the energy width of the stellar debris for full disruptions to the Newtonian prediction decreases steeply, resulting in a factor of two correction at $M_{\rm BH} = 5 \times 10^7~{\rm M}_\odot$. We find that for partial disruptions, the fractional remnant mass for a given ratio of the pericenter to $\mathcal{R}_{\rm t}$ is higher for larger $M_{\rm BH}$. These results have several implications. As $M_{\rm BH}$ increases above $\sim 10^7~{\rm M}_\odot$, the cross section for complete disruptions is suppressed by competition with direct capture. However, the cross section ratio for partial to complete disruptions depends only weakly on $M_{\rm BH}$. The relativistic correction to the debris energy width delays the time of peak mass-return rate and diminishes the magnitude of the peak return rate. For $M_{\rm BH} \gtrsim 10^7~{\rm M}_\odot$, the $M_{\rm BH}$-dependence of the full disruption cross section and the peak mass-return rate and time is influenced more by relativistic effects than by Newtonian dynamics.

astro-ph.HE↗

arXiv2020

Tidal disruptions of main sequence stars -- II. Simulation methodology and stellar mass dependence of the character of full tidal disruptions

This is the second in a series of papers presenting the results of fully general relativistic simulations of stellar tidal disruptions in which the stars' initial states are realistic main-sequence models. In the first paper (Paper I), we gave an overview of this program and discussed the principal observational implications of our work. Here we describe our calculational method and provide details about the outcomes of full disruptions, focusing on the stellar mass dependence of the outcomes for a black hole of mass $10^{6}\rm{M}_{\odot}$. We consider eight different stellar masses, from $0.15~{\rm M}_\odot$ to $10~{\rm M}_\odot$. We find that, relative to the traditional order-of-magnitude estimate $r_{\rm t}$, the physical tidal radius of low-mass stars ($M_{\star} \lesssim 0.7~ {\rm M}_\odot$) is larger by tens of percent, while for high-mass stars ($M_{\star} \gtrsim1~ {\rm M}_\odot$) it is smaller by a factor 2--2.5. The traditional estimate of the range of energies found in the debris is $\approx 1.4\times$ too large for low-mass stars, but is a factor $\sim 2$ too small for high-mass stars; in addition, the energy distribution for high-mass stars has significant wings. For all stars undergoing tidal encounters, we find that mass-loss continues for many stellar vibration times because the black hole's tidal gravity competes with the instantaneous stellar gravity at the star's surface until the star has reached a distance from the black hole $\sim O(10)r_{\rm t}$.

astro-ph.HE↗

arXiv2020

Measuring stellar and black hole masses of tidal disruption events

The flare produced when a star is tidally disrupted by a supermassive black hole holds potential as a diagnostic of both the black hole mass and the star mass. We propose a new method to realize this potential based upon a physical model of optical/UV light production in which shocks near the apocenters of debris orbits dissipate orbital energy, which is then radiated from that region. Measurement of the optical/UV luminosity and color temperature at the peak of the flare leads directly to the two masses. The black hole mass depends mostly on the temperature observed at peak luminosity, while the mass of the disrupted star depends mostly on the peak luminosity. We introduce {\sc TDEmass}, a method to infer the black hole and stellar masses given these two input quantities. Using {\sc TDEmass}, we find, for 21 well-measured events, black hole masses between $5\times 10^5$ and $10^7 M_\odot$ and disrupted stars with initial masses between 0.6 and $13M_\odot$. An open-source {\sc python}-based tool for {\sc TDEmass} is available at https://github.com/taehoryu/TDEmass.git.

astro-ph.HE↗

arXiv2020

Tidal Disruptions of Main Sequence Stars -- V. The Varieties of Disruptions

Tidal disruption events (TDEs), events in which a star passes very close to a supermassive black hole, are generally imagined as leading either to the star's complete disruption or to its passage directly into the black hole. In the former case it is widely believed that in all cases the bound portion of the debris quickly "circularizes" due to relativistic apsidal precession, i.e., forms a compact accretion disk, and emits a flare of standardized lightcurve and spectrum. We show here that TDEs are more diverse and can be grouped into several distinct categories on the basis of stellar pericenter distance $r_p$; we calculate the relative frequency of these categories. In particular, because rapid circularization requires $r_p \lesssim 10r_g$ ($r_g \equiv GM_{\rm BH}/c^2$), it can happen in only a minority of total disruptions, $\lesssim 1/4$ when the black hole has mass $M_{\rm BH} = 10^6 M_\odot$. For larger pericenter distances, $10 < r_p/r_g < 27$ (for $M_{\rm BH}=10^6M_\odot$), main sequence stars are completely disrupted, but the bound debris orbits are highly eccentric and possess semimajor axes $\sim 100\times$ the scale of the expected compact disk. Partial disruptions with fractional mass-loss $\gtrsim 10\%$ should occur with a rate similar to that of total disruptions; for fractional mass-loss $\gtrsim 50\%$, the rate is $\approx 1/3$ as large. Partial disruptions -- which must precede total disruptions when the stars' angular momenta evolve in the "empty loss-cone" regime -- change the orbital energy by factors $\gtrsim O(1)$. Remnants of partial disruptions are in general far from thermal equilibrium. Depending on the orbital energy of the remnant and conditions within the stellar cluster surrounding the SMBH, it may return after hundreds or thousands of years and be fully disrupted, or it may rejoin the stellar cluster.

astro-ph.HE↗

arXiv2020

Tidal disruptions of main sequence stars -- III. Stellar mass dependence of the character of partial disruptions

In this paper, the third in this series, we continue our study of tidal disruption events of main-sequence stars by a non-spinning $10^{6}~\rm{M}_\odot$ supermassive black hole. Here we focus on the stellar mass dependence of the outcomes of partial disruptions. As the encounter becomes weaker, the debris mass is increasingly concentrated near the outer edges of the energy distribution. As a result, the mass fallback rate can deviate substantially from a $t^{-5/3}$ power-law, becoming more like a single peak with a tail declining as $t^{-p}$ with $p\simeq2-5$. Surviving remnants are spun-up in the prograde direction and are hotter than main sequence stars of the same mass. Their specific orbital energy is $\simeq10^{-3}\times$ that of the debris, but of either sign with respect to the black hole potential, while their specific angular momentum is close to that of the original star. Even for strong encounters, remnants have speeds at infinity relative to the black hole potential $\lesssim 300$ km s$^{-1}$, so they are unable to travel far out into the galactic bulge. The remnants most deeply bound to the black hole go through a second tidal disruption event upon their first return to pericenter; if they have not thermally relaxed, they will be completely disrupted.

astro-ph.HE↗

arXiv2020

Tidal Disruptions of Main Sequence Stars -- I. Observable Quantities and their Dependence on Stellar and Black Hole Mass

This paper introduces a series of papers presenting a quantitative theory for the tidal disruption of main sequence stars by supermassive black holes. Using fully general relativistic hydrodynamics simulations and MESA-model initial conditions, we explore the pericenter-dependence of tidal disruption properties for eight stellar masses ($0.15 \leq M_*/M_\odot \leq 10$) and six black hole masses ($10^5 \leq M_{BH}/M_\odot \leq 5 \times 10^7$). We present here the results most relevant to observations. The effects of internal stellar structure and relativity decouple for both the disruption cross section and the characteristic energy width of the debris. Moreover, the full disruption cross section is almost independent of $M_*$ for $M_*/M_\odot \lesssim 3$. Independent of $M_*$, relativistic effects increase the critical pericenter distance for full disruptions by up to a factor $\sim 3$ relative to the Newtonian prediction. The probability of a direct capture is also independent of $M_*$; at $M_{BH}/M_\odot \simeq 5 \times 10^6$ this probability is equal to that of a complete disruption. The width of the debris energy distribution $ΔE$ can differ from the standard estimate by factors from 0.35 to 2, depending on $M_*$ and $M_{BH}$, implying a corresponding change in the characteristic mass-return timescale. The "frozen-in approximation" is inconsistent with $ΔE$, and mass-loss continues over a long span of time. We provide analytic forms, suitable for use in both event rate estimates and parameter inference, to describe all these trends. For partial disruptions, we find a nearly-universal relation between the star's angular momentum and the fraction of $M_*$ remaining. Within the "empty loss-cone" regime, partial disruptions must precede full disruptions. These partial disruptions can drastically affect the rate and appearance of subsequent total disruptions.

astro-ph.HE↗

arXiv2020

Tidal radii of main sequence stars -- I. Physical tidal radius, semi-analytic model and their implications

A star is tidally disrupted by a supermassive black hole when their separation is shorter than the "tidal radius". This quantity is often estimated on an order-of-magnitude basis without reference to the star's internal structure. Using MESA models for main sequence stars and fully general relativistic dynamics, we find the physical tidal radius for complete disruption $\cal{R}_t$ for a $10^6M_\odot$ black hole (BH). We find that across a factor $\sim20$ in stellar mass $M_*$, i.e., $0.15M_{\odot}\leq M_*\leq3M_\odot$, $\cal{R}_t\sim27\times$(BH's gravitational radius). When comparing $\cal{R}_t$ with the commonly used order-of-magnitude estimate $r_t$, we find that $\cal{R}_t\sim1.05-1.45r_t$ for $0.15M_\odot\leq M_*\leq0.5M_\odot$, but between $0.5 M_\odot$ and $1 M_\odot$, $\cal{R}_t$ drops to $\sim 0.45r_t$, and it remains at this value up to $10 M_\odot$. The near-constancy of $\cal{R}_t$ implies a weaker dependence of the full disruption rate on $M_*$ than when predicted with $r_t$. The characteristic energy width of the debris $ΔE$ ranges from $\sim1.2Δ\cal{E}$ for low-mass stars to $\sim 0.35Δ\cal{E}$ for higher-mass stars, where $Δ\cal{E}=GM_{\rm BH}R_*/\cal{R}_t^{2}$. We present analytic fits for the $M_*$ dependence of $\cal{R}_t$ and $ΔE$; these fits lead to analytic expressions for the time of peak mass fallback rate and the maximal mass fallback rate. Our results also bear on the fraction of events leading to fast or slow circularization, as well as on the character of the tidal event occurring when the remnant of a partial disruption returns to the black hole. Using a semi-analytic model, we show that $\cal{R}_t$ is primarily determined by the star's central density rather than its mean density. For high-mass stars, the full disruption rate is roughly 1/4 the partial disruption rate, while this ratio is close to unity for low-mass stars.

astro-ph.GA↗

arXiv2020

Tidal radii of main sequence stars -- II. Simulation methodology and the character of full tidal disruptions

This is the second in a series of papers presenting the results of fully general relativistic simulations of stellar tidal disruptions in which the stars' initial states are realistic main-sequence models. We consider eight different stellar masses, from $0.15~{\rm M}_\odot$ to $10~{\rm M}_\odot$. In the first paper (Ryu et al. 2019a), we gave an overview of this program and discussed the principal observational implications of our work. Here we describe our calculational method and provide details about the outcomes of full disruptions. We find that, relative to the traditional order-of-magnitude estimate $r_{\rm t}$, the physical tidal radius of low-mass stars is larger by tens of percent, while for high-mass stars ($M_{\star} \gtrsim1~ {\rm M}_\odot$) it is smaller by a factor $2-2.5$. The traditional estimate of the range of energies found in the debris is approximately accurate for low-mass stars, but is a factor $\sim 2$ too small for high-mass stars; in addition, the energy distribution for high-mass stars has significant wings. For all stars undergoing tidal encounters, we find that mass-loss continues for a long time because the ${\it instantaneous}$ tidal radius, the distance out to which the black hole's tidal gravity competes with the instantaneous stellar gravity at the star's surface, stays comparable to the distance to the black hole until the star has reached $O(10)~r_{\rm t}$. These findings indicate significant failings in the popular "frozen-in" approximation.

astro-ph.GA↗