arXiv subjects

Naoteru Gouda

Publications and source records attributed to Naoteru Gouda.

33 records · Page 2Linked to original sources

arXiv2000

The Detection Rate of Molecular Gas in Elliptical Galaxies: Constraints on Galaxy Formation Theories

In order to constrain parameters in galaxy formation theories, especially those for a star formation process, we investigate cold gas in elliptical galaxies. We calculate the detection rate of cold gas in them using a semi-analytic model of galaxy formation and compare it with observations. We show that the model with a long star formation time-scale (~20 Gyr) is inconsistent with observations. Thus, some mechanisms of reducing the mass of interstellar medium, such as the consumption of molecular gas by star formation and/or reheating from supernovae, are certainly effective in galaxies. Our model predicts that star formation induced when galaxies in a halo collide each other reduces the cold gas left until the present. However, we find that the reduction through random collisions of satellite (non-central) galaxies in mean free time-scale in a halo is not required to explain the observations. This may imply that the collisions and mergers between satellite galaxies do not occur so often in clusters or that they do not stimulate the star formation activity as much as the simple collision model we adopted. For cD galaxies, the predicted detection rate of cold gas is consistent with observations as long as the transformation of hot gas into cold gas is prevented in halos whose circular velocities are larger than 500 km s^-1. Moreover, we find that the cold gas brought into cDs through captures of gas-rich galaxies is little. We also show that the fraction of galaxies with observable cold gas should be small for cluster ellipticals in comparison with that for field ellipticals.

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arXiv1999

A Universal Profile of the Dark Matter Halo and the Two-point Correlation Function

We have investigated the relation between the two-point spatial correlation function and the density profile of the dark matter halo in the strongly non-linear regime. It is well known that when the density fluctuation grows into dark matter halo whose density profile is $ρ\propto r^{-ε}$(${3/2}<ε<3$) on almost all mass scales, the two-point spatial correlation function obeys a power law with the power index $γ= 2ε-3$ in the strongly non-linear regime. We find the form of the two-point spatial correlation function, which does not obey the power law when the power index $ε$ is smaller than 3/2, such as the density profile $ρ\propto r^{-1}$ around the center of the halo which is proposed by Navarro, Frenk & White (1996,1997). By using the BBGKY equation in the strongly non-linear regime, it is also found that velocity parameter $h \equiv - < v > / \dot{a}x$ is not a constant even in the strongly non-linear regime ($\tilde{x} \equiv x/x_{nl} \to 0$) although it is a constant when $ε> 3/2$ and then the two-point spatial correlation function can be regarded as the power law. The velocity parameter $h$ becomes 0 at the non-linear limit of $\tilde{x} \to 0$, that is, the stable clustering hypothesis cannot be satisfied when $ε< 3/2$.

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arXiv1999

What determines the slope of the colour-magnitude relation of elliptical galaxies in the hierarchical clustering scenario?

We examined the physical origin of the colour-magnitude relation of elliptical galaxies in clusters of galaxies in the hierarchical clustering scenario by using a semi-analytic model of galaxy formation. We particularly investigate the effects of the star formation process, the supernova feedback and the UV background on the formation and evolution of elliptical galaxies. It is suggested by observation that the colour-magnitude relation reflects the metallicity-luminosity relation of galaxies, and that for reproducing the colour-magnitude relation it is important to suppress the chemical enrichment of stars in faint galaxies. For suppressing the chemical enrichment, we propose some solutions. One is assuming a strong supernova feedback. Another is introducing the effect of the UV background radiation. These solutions degenerate, but they may be distinguished by studying other properties of galaxies, like the luminosity function, colour distribution, etc. Moreover, we find that the supernova feedback model in the starburst which make the bulge component is important when the star formation time-scale in disc is longer than the age of the Universe. On the other hand, when the star formation time-scale is short, the resulting colour-magnitude relation does not depend on such a starburst model because most of stars are formed not by the burst but by the ordinary star formation process in disc.

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arXiv1999

Effects of the UV background radiation on galaxy formation

We investigate the effects of the UV background radiation on galaxy formation by using the semi-analytic model including the photoionization process. The semi-analytic model is based on Cole et al. (1994) and we use almost the same parameters of their `fiducial' model. We find that the UV background mainly affects the formation of dwarf galaxies. Because of the suppression of star formation, the number density of small objects corresponding to dwarf galaxies decreases compared to the case of no UV radiation when the UV background exists until the present epoch. When the UV background vanishes at a low redshift, the number density of small objects is hardly changed but the colour becomes bluer, compared to the case of no UV radiation, because stars are newly formed after the UV background vanishes. On the other hand, the UV radiation hardly affects massive galaxies. This is because the massive galaxies are formed by mergers of small galaxies.

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arXiv1998

Time scales of relaxation and Lyapunov instabilities in a one-dimensional gravitating sheet system

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to $N^{-1/5}$. The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigations. The relaxation time to quasiequilibria (microscopic relaxation) is found to coincide with the inverse of the minimum positive Lyapunov exponent. The relaxation time to the final thermal equilibrium differs to the inverse of the Lyapunov exponents and the Kolmogorov-Sinai time.

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arXiv1998

Effects of Merging Histories on Angular Momentum Distribution of Dark Matter Haloes

The effects of merging histories of proto-objects on the angular momentum distributions of the present-time dark matter haloes are analysed. An analytical approach to the analysis of the angular momentum distributions assumes that the haloes are initially homogeneous ellipsoids and that the growth of the angular momentum of the haloes halts at their maximum expansion time. However, the maximum expansion time cannot be determined uniquely, because in the hierarchical clustering scenario each progenitor, or subunit, of the halo has its own maximum expansion time. Therefore the merging history of the halo may be important in estimating its angular momentum. Using the merger tree model by Rodrigues & Thomas, which takes into account the spatial correlations of the density fluctuations, we have investigated the effects of the merging histories on the angular momentum distributions of dark matter haloes. It was found that the merger effects, that is, the effects of the inhomogeneity of the maximum expansion times of the progenitors which finally merge together into a halo, do not strongly affect the final angular momentum distributions, so that the homogeneous ellipsoid approximation happens to be good for the estimation of the angular momentum distribution of dark matter haloes. This is because the effect of the different directions of the angular momenta of the progenitors cancels out the effect of the inhomogeneity of the maximum expansion times of the progenitors.

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arXiv1998

Evolution of the Power Spectrum and the Self-Similarity in the Expanding One-Dimensional Universe

We have investigated time evolutions of power spectra of density fluctuations for long time after the first appearance of caustics in the expanding one-dimensional universe. It is found that when an initial power spectrum is sale-free with a power index $n$, a self-similarity of the time evolution of the power spectrum is achieved. We find that the power spectrum can be separated roughly into three regimes according to the shape of the power spectrum: the linear regime ($k < k_{nl}$ : the regime {\cal 1}),the single-caustic regime($k_{nl} < k < k_{snl}$ : the regime 2), and the multi-caustics regime($k > k_{snl}$ : the regime 3). The power index of the power spectrum in each regime has the values of $n,-1$, and $μ$ which depends on $n$, respectively. Even in the case of an initial power-law spectrum with a cutoff scale, there might be the possibility of the self-similar evolution of the power spectrum after the appearance of the caustics. It is found, however, the self-similarity is not achieved in this case. The shape of the power spectrum on scales smaller than the cutoff scale can be separated roughly in two regimes: the virialized regime ($k_{cut}< k < k_{cs}$ : the regime 4), and the smallest-single-caustic regime ($ k > k_{cs}$ : the regime 5). The power index of the power spectrum is $ν$ which may be determined by the distribution of singular points in the regime 4. In the regime 5, the value of the power index is -1. Moreover we show the general property about the shape of a power spectrum with a general initial condition.

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arXiv1997

Stability of Scale-Invariant Cosmological Correlation Functions in the Strongly Non-Linear Clustering Regime

We investigate stability of the scale-invariant solutions of the BBGKY equations for two-point spatial correlation functions of the density fluctuations in the strongly non-linear regime. In the case that the background skewness of the velocity field is equal to 0, we found that there is no local instability in the strongly non-linear regime. The perturbation does not grow nor does it decay. It has an only marginal stable mode. This result means that no special value of the power index of the two-point spatial correlation function are favored in terms of the stability of the solutions. In other words, the argument about the stability does not determine the power index of the two-point spatial correlation functions in the strongly non-linear regime.

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arXiv1996

Chaotic itinerancy and thermalization in one-dimensional self-gravitating systems

This is the third paper of the series of our studies of the one-dimensional self-gravitating many-body systems. In this paper, we thus study the transition phenomena after the first transition from a quasiequilibrium. We found that irrespective of the initial conditions, the system wanders between many states which yield the same properties of the quasiequilibrium as the water-bag. This itinerancy is most prominent in the time scale $t\sim 10^5 \sim 10^6 t_c$. In the midway between two succeeding quasiequilibria, the system experiences a transient state, where one particle keeps exclusive high energy and its motion decouples with the others. Though the transient state is not the thermally relaxed equilibrium, its distribution quite resembles the isothermal distribution. Thus the macroscopic relaxation we discussed in the previous papers corresponds to the transition from one of quasiequilibria to a transient state. Averaging the behavior over a time scale much longer than the macroscopic relaxation time gives the isothermal distribution. Distribution of lifetime $τ$ of the transient states yields a power-law distribution of $τ^{-2}$. The transient state gives a clear example of chaotic itinerancy in conserved dynamical systems. The mechanism of the onset of itinerancy is examined.

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arXiv1996

The Effect of Spatial Correlations on Merger Trees of Dark Matter Haloes

The effects of spatial correlations of density fluctuations on merger histories of dark matter haloes (so-called `{\it merger trees}') are analysed. We compare the mass functions of dark haloes derived by a new method for calculating merger trees, that proposed by Rodrigues \& Thomas (RT), with those given by other methods such as the Block model, the Press-Schechter formula and our own formula in which the mass functions are analytically expressed in a way that takes into consideration the spatial correlations. It is found that the mass functions given by the new method are well fit by those given by our formula. We believe that new method (RT) {\it naturally} and correctly takes into account the spatial correlations of the density fluctuations due to a calculated, grid-based realisation of the density fluctuations and so is very useful for estimating the merger tree accurately in a way that takes into consideration spatial correlations. Moreover, by applying our formula, we present an analytic expression which reproduces the mass function derived by the Block model. We therefore show clearly why and how the mass functions given by the new method and the Block model are different from each other. Furthermore, we note that the construction of merger trees is sensitive to the criterion of collapse and merging of overlapped haloes in cases in which two or more haloes happen to overlap. In fact, it is shown that the mass function is very much affected when the criterion of overlapping is changed.

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arXiv1996

Scale-Invariant Correlation Functions of Cosmological Density Fluctuations in the Strong Clustering Regime

We have investigated the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the solutions for the mean relative physical velocity depend on the three-point spatial correlation function and the skewness of the velocity fields. We find that the stable condition in which the mean relative physical velocity vanishes on the virialized regions is satisfied only under the assumptions which Davis \& Peebles took in his paper. It is found, however, that their assumptions may not be general in real. The power index of the two-point correlation function in the strongly nonlinear regime depends on the mean relative peculiar velocity, the three-point correlation function and the skewness. If the self-similar solutions exist, the power index in the strongly nonlinear regime is related to the power index of the initial power spectrum and its relation depends on the three-point correlation function and the skewness through the mean relative peculiar velocity. Furthermore it is found that the mean relative physical velocity should have the values between 0 and the Hubble expanding velocity. When the mean relative physical velocity equals to the Hubble expanding velocity, there might exist self-similar solutions in which the power index of the two-point correlation function in the strongly nonlinear regime is independent of the initial power index $n$.

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arXiv1995

Analysis of Non-Linear Mode Coupling of Cosmological Density Fluctuations by the Pseudo-Spectral Method

The pseudo-spectral method is proposed for following the evolution of density and velocity fluctuations at the weakly non-linear stage in the expanding universe with a good accuracy. In this method, the evolution of density and velocity fluctuations is integrated in the Fourier Space with using FFT. This method is very useful to investigate accurately the non-linear dynamics in the weakly non-linear regime. Because the pseudo-spectral method works directly in the Fourier space, it should be especially useful for examining behavior in the Fourier domain, for an example, the effects of the non-linear coupling of different wave modes on the evolution of the power spectrum. I show the results of this analysis both in one and three dimensional systems.

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arXiv1995

Relaxation processes in one-dimensional self-gravitating many-body systems

Though one dimensional self-gravitating $N$-body systems have been studied for three decade, the nature of relaxation was still unclear. There were inconsistent results about relaxation time; some initial state relaxed in the time scale $T\sim N\,t_c$, but another state did not relax even after $T\sim N^2\,t_c$, where $t_c$ is the crossing time. The water-bag distribution was believed not to relax after $T\sim N^2\,t_c$. In our previous paper, however, we found there are two different relaxation times in the water-bag distribution;in the faster relaxation ( microscopic relaxation ) the equipartition of energy distribution is attains but the macroscopic distribution turns into the isothermal distribution in the later relaxation (macroscopic relaxation). In this paper, we investigated the properties of the two relaxation. We found that the microscopic relaxation time is $T\sim N\,t_c$, and the macroscopic relaxation time is proportional to $N\,t_c$, thus the water-bag does relax. We can see the inconsistency about the relaxation times is resolved as that we see the two different aspect of relaxations. Further, the physical mechanisms of the relaxations are presented.

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arXiv1995

Hubble Parameter in Void Universe

We investigate the distance-redshift relation in the simple void model. As discussed by Moffat and Tatarski, if the observer stays at the center of the void, the observed Hubble parameter is not so different from the background Hubble parameter. However, if the position of observer is off center of the void, we must consider the peculiar velocity correction which is measured by the observed dipole anisotropy of cosmic microwave background. This peculiar velocity correction for the redshift is crucial to determine the Hubble parameter and we shall discuss this effect. Further the results of Turner et al by the N-body simulation will be also considered.

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arXiv1994

Quasi-equilibria in one-dimensional self-gravitating many body systems

The microscopic dynamics of one-dimensional self-gravitating many-body systems is studied. We examine two courses of the evolution which has the isothermal and stationary water-bag distribution as initial conditions. We investigate the evolution of the systems toward thermal equilibrium. It is found that when the number of degrees of freedom of the system is increased, the water-bag distribution becomes a quasi-equilibrium, and also the stochasticity of the system reduces. This results suggest that the phase space of the system is effectively not ergodic and the system with large degreees of freedom approaches to the near-integrable one.

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