arXiv subjects

Hyung Mok Lee

Publications and source records attributed to Hyung Mok Lee.

119 records · Page 7Linked to original sources

arXiv1999

Effects of Tidal Shocks on the Evolution of Globular Clusters

We present new Fokker-Planck models of the evolution of globular clusters, including gravitational tidal shocks. We extend our calculations beyond the core collapse by adopting three-body binary heating. Effects of the shocks are included by adding the tidal shock diffusion coefficients to the ordinary Fokker-Planck equation: the first order heating term, , and the second order energy dispersion term, . As an example, we investigate the evolution of models for the globular cluster NGC 6254. Using the Hipparcos proper motions, we are now able to construct orbits of this cluster in the Galaxy. Tidal shocks accelerate significantly both core collapse and the evaporation of the cluster and shorten the destruction time from 24 Gyr to 18 Gyr. We examine various types of adiabatic corrections and find that they are critical for accurate calculation of the evolution. Without adiabatic corrections, the destruction time of the cluster is twice as short. We examine cluster evolution for a wide range of the concentration and tidal shock parameters, and determine the region of the parameter space where tidal shocks dominate the evolution. We present fitting formulae for the core collapse time and the destruction time, covering all reasonable initial conditions. In the limit of strong shocks, the typical value of the core collapse time decreases from 10 t_{rh} to 3 t_{rh} or less, while the destruction time is just twice that number. The effects of tidal shocks are rapidly self-limiting: as clusters lose mass and become more compact, the importance of the shocks diminishes. This implies that tidal shocks were more important in the past.

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arXiv1999

Fitting Formulae for Cross Sections of Tidal Capture Binary Formation

Tidal captures can produce objects that are observationally and dynamically important in dense stellar systems. Recent discoveries of compact young clusters in and out of the Galaxy have prompted the studies of dynamics of star clusters with a large range in stellar masses. The tidal interactions between high and low mass stars are found to be rather frequent in such clusters. In this Research Note, we present fitting formulae for the cross sections of tidal capture binary formation between two stars with a large mass ratio. We present the cases between two main-sequence stars, and between a degenerate star and a main-sequence star.

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arXiv1999

The Stream-Stream Collision after the Tidal Disruption of a Star Around a Massive Black Hole

A star can be tidally disrupted around a massive black hole. It has been known that the debris forms a precessing stream, which may collide with itself. The stream collision is a key process determining the subsequent evolution of the stellar debris: if the orbital energy is efficiently dissipated, the debris will eventually form a circular disk (or torus). In this paper, we have numerically studied such stream collision resulting from the encounter between a 10^6 Msun black hole and a 1 Msun normal star with a pericenter radius of 100 Rsun. A simple treatment for radiative cooling has been adopted for both optically thick and thin regions. We have found that approximately 10 to 15% of the initial kinetic energy of the streams is converted into thermal energy during the collision. The angular momentum of the incoming stream is increased by a factor of 2 to 3, and such increase, together with the decrease in kinetic energy, significantly helps the circularization process. Initial luminosity burst due to the collision may reach as high as 10^41 erg/sec in 10^4 sec, after which the luminosity increases again (but slowly this time) to a steady value of a few 10^40 erg/sec in a few times of 10^5 sec. The radiation from the system is expected to be close to Planckian with effective temperature of \~10^5K.

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arXiv1997

Core-Collapse Times of Two-Component Clusters

We examine the corecollapse times of isolated, two-mass-component star clusters using Fokker-Planck models. With initial condition of Plummer models, we find that the corecollapse times of clusters with M_1/M_2 >> 1 are well correlated with (N_1/N_2)^{1/2}(m_1/m_2)^{2} t_{rh}, where M_1/M_2 and m_1/m_2 are the light to heavy component total and individual mass ratios, respectively, N_1/N_2 is the number ratio, and t_{rh} is the initial half-mass relaxation time scale. We also find two-component cluster parameters that best match multi-component (thus more realistic) clusters with power-law mass functions.

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arXiv1997

Two-Component Fokker-Planck Models for the Evolution of Isolated Globular Clusters

Two-component (normal and degenerate stars) models are the simplest realization of clusters with a mass spectrum because high mass stars evolve quickly into degenerates, while low mass stars remain on the main-sequence for the age of the universe. Here we examine the evolution of isolated globular clusters using two-component Fokker-Planck (FP) models that include heating by binaries formed in tidal capture and in three-body encounters. Three-body binary heating dominates and the postcollapse expansion is self-similar, at least in models with total mass M <= 3 x 10^5 M_\odot, initial half-mass radius r_{h,i} >= 5 pc, component mass ratio m_2/m_1 <= 2, and number ratio N_1/N_2 <= 300 when m_2=1.4 M_\odot. We derive scaling laws for ρ_c, v_c, r_c, and r_h as functions of m_1/m_2, N, M, and time t from simple energy-balance arguments, and these agree well with the FP simulations. We have studied the conditions under which gravothermal oscillations (GTOs) occur. If E_{tot} and E_c are the energies of the cluster and of the core, respectively, and t_{rh} and t_c are their relaxation times, then ε\equiv (E_{tot}/t_{rh})/(E_c/t_{rc}) is a good predictor of GTOs: all models with ε>0.01 are stable, and all but one with ε< 0.01 oscillate. We derive a scaling law for εagainst N and m_1/m_2 and compared with our numerical results. Clusters with larger m_2/m_1 or smaller N are stabler.

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arXiv1997

Stellar Evolution and Dynamics in Star Clusters

Dynamical models of star clusters are maturing in the sense that effects other than simple point particle dynamics are taken into account. We summarize the relevance of and prospects for this new generation of N-body models.

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arXiv1996

Evolution of Debris of a Tidally Disrupted Star by a Massive Black Hole: Development of a Hybrid Scheme of the SPH and TVD Methods

The evolution of the stellar debris after tidal disruption due to the super massive black hole's tidal force is difficult to solve numerically because of the large dynamical range of the problem. We developed an SPH (Smoothed Particle Hydrodynamics) - TVD (Total Variation Diminishing) hybrid code in which the SPH is used to cover a widely spread debris and the TVD is used to compute the stream collision more accurately. While the code in the present form is not sufficient to obtain desired resoultion, it could provide a useful tool in studying the aftermath of the stellar disruption by a massive black hole.

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arXiv1996

Close Encounters between a Neutron Star and a Main-Sequence Star

We have examined consequences of strong tidal encounters between a neutron star and a normal star using SPH as a possible formation mechanism of isolated recycled pulsars in globular clusters. We have made a number of SPH simulations for close encounters between a main-sequence star of mass ranging from 0.2 to 0.7 Solar masses represented by an n=3/2 polytrope and a neutron star represented by a point mass. The outcomes of the first encounters are found to be dependent only on the dimensionless parameter eta' = (m/(m+M))^(1/2) (r_min/R_MS)^(3/2) (m/M)^(1/6), where m and M are the masses of the main-sequence star and the neutron star, respectively, r_min the minimum separation between two stars, and R_MS the size of the main-sequence star. The material from the (at least partially) disrupted star forms a disk around the neutron star. If all material in the disk is to be acctreted onto the neutron star's surface, the mass of the disk is enough to spin up the neutron star to spin period of 1 ms.

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arXiv1995

Supersonic Collisions between Two Gas Streams

A star around a massive black hole can be disrupted tidally by the gravity of the black hole. Then, its debris may form a precessing stream which may even collide with itself. In order to understand the dynamical effects of the stream-stream collision on the eventual accretion of the stellar debris onto the black hole, we have studied how gas flow behaves when the outgoing stream collides supersonically with the incoming stream. We have investigated the problem analytically with one-dimensional plane-parallel streams and numerically with more realistic three-dimensional streams. A shock formed around the contact surface converts the bulk of the orbital streaming kinetic energy into thermal energy. In three-dimensional simulations, the accumulated hot post-shock gas then expands adiabatically and drives another shock into the low density ambient region. Through this expansion, thermal energy is converted back to the kinetic energy associated with the expanding motion. Thus, in the end, only a small fraction of the orbital kinetic energy is actually converted to the thermal energy, while most of it is transferred to the kinetic energy of the expanding gas. Nevertheless the collision is effective in circularizing the debris orbit, because the shock efficiently transforms the ordered motion of the streams into the expanding motion in directions perpendicular to the streams. The circularization efficiency decreases, if two colliding streams have a large ratio of cross sections and a large density contrast. But even in such cases, the main shock extends beyond the overlapping contact surface and the high pressure region behind the shock keeps the stream of the larger cross section from passing freely. Thus the stream-stream collisions are still expected to circularize the stellar debris rather efficiently, unless the ratio

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arXiv1994

Influence of the Stellar Mass Function on the Evaporation Rate of Tidally Limited Postcollapse Globular Clusters

We study the rate of escape of stars (``evaporation'') from tidally-limited postcollapse globular clusters having a power-law distribution of stellar masses. We use a multi-mass Fokker-Planck code and assume a steady tidal field. Stellar-dynamical processes cause the inner parts of the cluster to expand, which in turn causes stars to overflow the tidal boundary. Mass loss by stellar evolution is assumed to be unimportant in these later evolutionary stages. The fraction of the cluster mass lost per half-mass relaxation time ($\trh$) is roughly constant, in agreement with simple homologous models with equal-mass stars. If $\trh$ is computed in the conventional way from the mean stellar mass, however, a broad stellar mass function can double the loss of mass per $\trh$. We discuss implications of our results for the evolution of globular-cluster systems in our own and other galaxies. In particular, the number of Galactic clusters destroyed by evaporation alone may be as large or larger than the present cluster population.

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arXiv1994

Evolution of Galactic Nuclei with 10 $M_\odot$ Black Holes

A star with main sequence mass greater than $25\sim 30\msun$ may collapse to a black hole of about 10 $\msun$ at the final stage of the evolution. About an order of 1\% of stellar mass is likely to be in form of such black holes in galaxies. We have examined the dynamics of two-component stellar systems composed of 0.7 $\msun$ main-sequence stars, representing the old population of stars whose main-sequence lifetimes are longer than the Hubble time, and a small fraction of 10 $\msun$ black holes. The dynamical friction leads to the segregation of black holes to the core and the core collapse takes place among the black holes in a time scale much shorter than that required for a single component cluster. The ultimate evolution of the two-component stellar system depends on the role of three-body binaries formed among the black holes. For a system with $v\gta 100\kms$ binaries merge by gravitational radiation at some hardness instead of being ejected. The critical hardness, at which the collision time and the merger time become comparable, determines the efficiency of the binary as a heat source. The efficiency is found to be inversely proportional to the velocity dispersion. For the clusters without serious reduction in heating efficiency (i.e., velocity dispersion well below 500 $\kms$), heating by three-body binaries have the effect of stopping the core-collapse. The cluster

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