arXiv subjects

Takayuki R. Saitoh

Publications and source records attributed to Takayuki R. Saitoh.

66 records · Page 4Linked to original sources

arXiv2011

A Natural Symmetrization for the Plummer Potential

We propose a symmetrized form of the softened gravitational potential which is a natural extension of the Plummer potential. The gravitational potential at the position of particle i (x_i,y_i,z_i), induced by particle j at (x_j,y_j,z_j), is given by: phi_ij = -G m_j/|r_ij^2+e_i^2+e_j^2|^1/2, where G is the gravitational constant, m_j is the mass of particle j, r_ij = |(x_i-x_j)^2+(y_i-y_j)^2+(z_i-z_j)^2|^1/2 and e_i and e_j are the gravitational softening lengths of particles i and j, respectively. This form is formally an extension of the Newtonian potential to five dimensions. The derivative of this equation in the x,y, and z directions correspond to the gravitational accelerations in these directions and these are always symmetric between two particles. When one applies this potential to a group of particles with different softening lengths, as is the case with a tree code, an averaged gravitational softening length for the group can be used. We find that the most suitable averaged softening length for a group of particles is = sum_j^N m_j e_j^2 / M, where M = sum_j^N m_j and N are the mass and number of all particles in the group, respectively. The leading error related to the softening length is O(sum_j r_j d(e_j^2)/r_ij^3), where r_j is the distance between particle j and the center of mass of the group and d(e_j^2) = e_j^2 - . Using this averaged gravitational softening length with the tree method, one can use a single tree to evaluate the gravitational forces for a system of particles with a wide variety of gravitational softening lengths. Consequently, this will reduce the calculation cost of the gravitational force for such a system with different softenings without the need for complicated forms of softening. We present the result of simple numerical tests. We found that our modification of the Plummer potential works well.

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arXiv2010

On the Interpretation of the l-v Features in the Milky Way Galaxy

We model the gas dynamics of barred galaxies using a three-dimensional, high-resolution, $N$-body+hydrodynamical simulation and apply it to the Milky Way in an attempt to reproduce both the large-scale structure and the clumpy morphology observed in Galactic H\emissiontype{I} and CO $l-v$ diagrams. Owing to including the multi-phase interstellar medium, self-gravity, star-formation and supernovae feedback, the clumpy morphology, as well as the large-scale features, in observed $l-v$ diagrams are naturally reproduced. We identify in our $l-v$ diagrams with a number of not only large-scale peculiar features such as the '3-kpc arm', '135-km s$^{-1}$ arm' and 'Connecting arm' but also clumpy features such as `Bania clumps', and then link these features in a face-on view of our model. We give suggestions on the real structure of the Milky Way and on the fate of gas clumps in the central region.

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arXiv2010

FAST: A Fully Asynchronous Split Time-Integrator for Self-Gravitating Fluid

We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system to the gravitational potential and others (kinetic and internal energies) and use different time-steps for their integrations. The time integration is done in the way similar to that used in the mixed variable or multiple stepsize symplectic schemes. We performed three test calculations. One was the spherical collapse and the other was an explosion. We also performed a realistic test, in which the initial model was taken from a simulation of merging galaxies. In all test calculations, we found that the number of time-steps for gravitational interaction were reduced by nearly an order of magnitude when we adopted our integration method. In the case of the realistic test, in which the dark matter potential dominates the total system, the total calculation time was significantly reduced. Simulation results were almost the same with those of simulations with the ordinary individual time-step method. Our new method achieves good performance without sacrificing the accuracy of the time integration.

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arXiv2009

The origin of large peculiar motions of star-forming regions and spiral structures of our Galaxy

Recent VLBI (Very Long Baseline Interferometer) observations determined the distances and proper motions of star-forming regions in spiral arms directly. They showed that star-forming regions and young stars have large peculiar motions, as large as 30 km/s with complex structures. Such a large peculiar motion is incompatible with the prediction of the standard theory of quasi-stationary spiral arms. We use a high-resolution, self-consistent N-body+hydrodynamical simulation to explore how the spiral arms are formed and maintained, and how star-forming regions move. We found that arms are not quasi-stationary but transient and recurrent, as suggested in alternative theories of spiral structures. Because of this transient nature of the spiral arms, star-forming regions exhibit a trend of large and complex non-circular motions, which is qualitatively consistent with the VLBI observations. Owing to this large non-circular motion, a kinematically estimated gas map of our Galaxy has a large systematic errors of ~2-3 kpc in the distance from the Sun.

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arXiv2009

A Necessary Condition for Individual Time-Steps in SPH Simulations

We show that the smoothed particle hydrodynamics (SPH) method, used with individual time-steps in the way described in the literature, cannot handle strong explosion problems correctly. In the individual time-step scheme, particles determine their time-steps essentially from a local Courant condition. Thus they cannot respond to a strong shock, if the pre-shock timescale is too long compared to the shock timescale. This problem is not severe in SPH simulations of galaxy formation with a temperature cutoff in the cooling function at $10^4 {\rm K}$, while it is very dangerous for simulations in which the multiphase nature of the interstellar medium under $10^4 {\rm K}$ is taken into account. A solution for this problem is to introduce a time-step limiter which reduces the time-step of a particle if it is too long compared to the time-steps of its neighbor particles. Thus this kind of time-step constraint is essential for the correct treatment of explosions in high-resolution SPH simulations with individual time-steps.

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arXiv2009

Toward First-Principle Simulations of Galaxy Formation: II. Shock-Induced Starburst at a Collision Interface During the First Encounter of Interacting Galaxies

We investigated the evolution of interacting disk galaxies using high-resolution $N$-body/SPH simulations, taking into account the multiphase nature of the interstellar medium (ISM). In our high-resolution simulations, a large-scale starburst occurred naturally at the collision interface between two gas disks at the first encounter, resulting in the formation of star clusters. This is consistent with observations of interacting galaxies. The probability distribution function (PDF) of gas density showed clear change during the galaxy-galaxy encounter. The compression of gas at the collision interface between the gas disks first appears as an excess at $n_{\rm H} \sim 10{\rm cm^{-3}}$ in the PDF, and then the excess moves to higher densities ($n_{\rm H} \gtrsim 100{\rm cm^{-3}}$) in a few times $10^7$ years where starburst takes place. After the starburst, the PDF goes back to the quasi-steady state. These results give a simple picture of starburst phenomena in galaxy-galaxy encounters.

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arXiv2008

Mass Supply to Galactic Center due to Nested Bars in the Galaxy

We investigate rapid mass supply process by nested bars in the Galaxy by numerical simulation. We simulate gas flow in the whole galaxy disk with nested bars, which are the outer bar and the inner bar, especially with highly spatial resolution in the galactic central region. We assume two cases of inner bar size which are a smaller one and a larger one than the radius of the 200 pc gas ring which is corresponds to the Central Molecular Zone. From our numerical results, in the large size bar cases, the inner bars with large elongation induce sufficient mass inflow and destroy the 200 pc gas ring. On the other hand, in the small size bar cases, the inner bars with large elongation induce large mass inflow and do not destroy the 200 pc gas ring. This mass inflow is caused by straight shocks excited by the inner bar. In this case, nuclear gas disks of ~ 15 pc radius are formed. The nuclear gas disks are self-gravitationally unstable and we expect formation of compact star clusters under strong tidal force in the nuclear gas disks. We discuss evolution of the nuclear gas disk.

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arXiv2008

Toward first-principle simulations of galaxy formation: I. How should we choose star formation criteria in high-resolution simulations of disk galaxies?

We performed 3-dimensional N-body/SPH simulations to study how mass resolution and other model parameters such as the star formation efficiency parameter, C* and the threshold density, nth affect structures of the galactic gaseous/stellar disk in a static galactic potential. We employ 10^6 - 10^7 particles to resolve a cold and dense (T < 100 K & n_H > 100 cm^{-3}) phase. We found that structures of the ISM and the distribution of young stars are sensitive to the assumed nth. High-nth models with nth = 100 cm^{-3} yield clumpy multi-phase features in the ISM. Young stars are distributed in a thin disk of which half-mass scale height is 10 - 30 pc. In low-nth models with nth = 0.1 cm^{-3}, the stellar disk is found to be several times thicker, and the gas disk appears smoother than the high-nth models. A high-resolution simulation with high-nth is necessary to reproduce the complex structure of the gas disk. The global properties of the model galaxies in low-nth models, such as star formation histories, are similar to those in the high-nth models when we tune the value of C* so that they reproduce the observed relation between surface gas density and surface star formation rate density. We however emphasize that high-nth models automatically reproduce the relation, regardless of the values of C*. The ISM structure, phase distribution, and distributions of young star forming region are quite similar between two runs with values of C* which differ by a factor of 15. We also found that the timescale of the flow from n_H ~1 cm^{-3} to n_H > 100 cm^{-3} is about 5 times as long as the local dynamical time and is independent of the value of C*. The use of a high-nth criterion for star formation in high-resolution simulations makes numerical models fairy insensitive to the modelling of star formation. (Abridged)

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arXiv2006

Effects of a Supermassive Black Hole Binary on a Nuclear Gas Disk

We study influence of a galactic central supermassive black hole (SMBH) binary on gas dynamics and star formation activity in a nuclear gas disk by making three-dimensional Tree+SPH simulations. Due to orbital motions of SMBHs, there are various resonances between gas motion and the SMBH binary motion. We have shown that these resonances create some characteristic structures of gas in the nuclear gas disk, for examples, gas elongated or filament structures, formation of gaseous spiral arms, and small gas disks around SMBHs. In these gaseous dense regions, active star formations are induced. As the result, many star burst regions are formed in the nuclear region.

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arXiv2005

Tidal disruption of dark matter halos around proto-globular clusters

Tidal disruption of dark matter halos around proto-globular clusters in a halo of a small galaxy is studied in the context of the hierarchical clustering scenario by using semi-cosmological N-body/SPH simulations assuming the standard cold dark matter model ($Ω_0 = 1$). Our analysis on formation and evolution of the galaxy and its substructures archives until $z = 2.0$. In such a high-redshift universe, the Einstein-de Sitter universe is still a good approximation for a recently favored $Λ$-dominated universe, and then our results does not depend on the choice of cosmology. In order to resolve small gravitationally-bound clumps around galaxies and consider radiative cooling below $T = 10^4 K$, we adopt a fine mass resolution ($m_{\rm SPH} = 1.12 \times 10^3 \Msun$). Because of the cooling, each clump immediately forms a `core-halo' structure which consists of a baryonic core and a dark matter halo. The tidal force from the host galaxy mainly strips the dark matter halo from clumps and, as a result, theses clumps get dominated by baryons. Once a clump is captured by the host halo, its mass drastically decreases each pericenter passage. At $z = 2$, more than half of the clumps become baryon dominated systems (baryon mass/total mass $> 0.5$). Our results support the tidal evolution scenario of the formation of globular clusters and baryon dominated dwarf galaxies in the context of the cold dark matter universe.

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arXiv2005

Growth of Intermediate Massive Black Holes in the Hierarchical Formation of Small Spiral Galaxies in the High-z Universe

Combining a theoretical model of mass accretion onto a galactic center with a high-resolution $N$-body/SPH simulation, we investigate the formation of an intermediate massive black hole (IMBH) during the hierarchical formation of a small spiral galaxy (with a total mass of $10^{10}M_{\odot}$) in the high-$z$ universe. We found that the rate of average mass accretion to the nucleus due to the radiation drag exerted by newly formed stars in the forming galaxy is $\approx 10^{-5}M_{\odot}$yr$^{-1}$. As a result of this accretion, an IMBH with $\approx 10^{4}M_{\odot}$ can be formed in the center of the spiral galaxy at $z\sim 4$. We found that a central BH coevolves with the dark matter halo from $z\sim 15$ to $z\sim 2$. The mass ratio of the BH to the dark matter halo is nearly constant $\approx (1-3) \times 10^{-6}$ from $z\sim 10$ to $z\sim 2$. This is because that change in the dark matter potential enhances star formation in the central part of the galaxy, and as a result the BH evolves due to mass accretion via the radiation drag. Therefore, our model naturally predicts a correlation between massive BHs and dark matter halos. Moreover, it is found that the final BH-to-bulge mass ratio ($\approx 5\times 10^{-5}$) in a small spiral galaxy at high-$z$ is much smaller than that in the large galaxies ($\approx 10^{-3}$). Our results also suggest that the scatter in the observed scaling relations between the bulge mass and black hole mass are caused by a time lag between BH growth and growth of bulge. We also predict that the X-ray luminosity of AGN is positively correlated with the CO luminosity in the central region. By comparing our results with the properties of Lyman break galaxies (LBGs), it is predicted that some LBGs have massive BHs of $\approx 10^{6}-10^{7}M_{\odot}$.

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arXiv2004

Coevolution of the galactic cores and spiral galaxies

Using high-resolution N-body/SPH simulations with $2\times 10^6$ particles, we investigate the evolution of stellar and gaseous galactic cores during the hierarchical formation of a spiral galaxy. We find that the galactic core ($r < 300 $ pc) coevolves with the host galaxy. The average mass ratio between the baryonic core and the halo is nearly constant, $\sim $ 0.04 from $z \sim 10$ to $z \sim 2$. However, there are several `rapid-growing phases' during the evolution, in which the rate of mass accretion to the central sub-kpc region is ten times higher ($\sim 1 M_\odot$ yr pc$^{-1}$) than the average accretion rate. The rapid growth of the inner core is associated with the major merger events with a time-delay. We also find that the spin-axis of the gas core frequently changes. As a result, the angular momentum vector of the central part of the galaxy is independent of the rotation of the outer part. Our results suggest that if a constant fraction of the baryonic mass in the central several 100 pc of a galaxy is converted into a massive black hole, the black hole mass should correlate with the total mass of the galaxies.

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