arXiv subjects

Ping He

Publications and source records attributed to Ping He.

108 records · Page 6Linked to original sources

arXiv2011

Saddle-point entropy states of equilibrated self-gravitating systems

In this Letter, we investigate the stability of the statistical equilibrium of spherically symmetric collisionless self-gravitating systems. By calculating the second variation of the entropy, we find that perturbations of the relevant physical quantities should be classified as long- and short-range perturbations, which correspond to the long- and short-range relaxation mechanisms, respectively. We show that the statistical equilibrium states of self-gravitating systems are neither maximum nor minimum, but complex saddle-point entropy states, and hence differ greatly from the case of ideal gas. Violent relaxation should be divided into two phases. The first phase is the entropy-production phase, while the second phase is the entropy-decreasing phase. We speculate that the second-phase violent relaxation may just be the long-wave Landau damping, which would work together with short-range relaxations to keep the system equilibrated around the saddle-point entropy states.

astro-ph.CO↗

arXiv2011

A statistical-mechanical explanation of dark matter halo properties

Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics for self-gravitating systems have encountered many formal difficulties, and little progress has been made for about fifty years. The aim of this work is to strengthen the validity of the statistical-mechanical approach we have proposed previously to explain the dark matter halo properties. By introducing an effective pressure instead of the radial pressure to construct the specific entropy, we use the entropy principle and proceed in a similar way as previously to obtain an entropy stationary equation. An equation of state for equilibrated dark halos is derived from this entropy stationary equation, by which the dark halo density profiles with finite mass can be obtained. We also derive the anisotropy parameter and pseudo-phase-space density profile. All these predictions agree well with numerical simulations in the outer regions of dark halos. Our work provides further support to the idea that statistical mechanics for self-gravitating systems is a viable tool for investigation.

astro-ph.CO↗

arXiv2010

Entropy principle and complementary second law of thermodynamics for self-gravitating systems

(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the first-order variation of the entropy, subject to the mass- and energy-conservation constraints, we obtain an entropy stationary equation. Incorporated with the Jeans equation, and by specifying some functional form for the anisotropy parameter beta, we numerically solve the two equations, and demonstrate that the velocity anisotropy parameter plays an important role to attain a density profile that is finite in mass, energy, and spatial extent. If incorporated again with some empirical density profile from simulations, our theoretical predictions of the anisotropy parameter, and the radial pseudo-phase-space density in the outer non-gravitationally degenerate region of the dark matter halo, agree rather well with the simulation data, and the predictions are also acceptable in the middle weak-degenerate region of the dark halo. The second-order variational calculus reveals the seemingly paradoxical but actually complementary consequence that the equilibrium state of self-gravitating systems is the global minimum entropy state for the whole system under long-range violent relaxation, but simultaneously the local maximum entropy state for every and any small part of the system under short-range two-body relaxation and Landau damping. This minimum-maximum entropy duality means that the standard second law of thermodynamics needs to be re-expressed or generalized for self-gravitating systems. We believe that our findings, especially the complementary second law of thermodynamics, may provide crucial clues to the development of the statistical physics of self-gravitating systems as well as other long-range interaction systems.

astro-ph.CO↗

arXiv2009

Irreducibility and uniqueness of stationary distribution

In this paper, we shall prove that the irreducibility in the sense of fine topology implies the uniqueness of invariant probability measures. It is also proven that this irreducibility is strictly weaker than the strong Feller property plus irreducibility in the sense of original topology, which is the usual uniqueness condition.

math.PR↗

arXiv2008

Distribution Function of Dark Matter with Constant Anisotropy

N-body simulations of dark matter halos show that the density is cusped near the center of the halo. The density profile behaves as $r^{-γ}$ in the inner parts, where $γ\simeq 1$ for the NFW model and $γ\simeq 1.5$ for the Moore's model, but in the outer parts, both models agree with each other in the asymptotic behavior of the density profile. The simulations also show the information about anisotropy parameter $β(r)$ of velocity distribution. $β\approx 0$ in the inner part and $β\approx 0.5$ (radially anisotropic) in the outer part of the halo. We provide some distribution functions $F(E,L)$ with the constant anisotropy parameter $β$ for the two spherical models of dark matter halos: a new generalized NFW model and a generalized Moore model. There are two parameters $α$ and $ε$ for those two generalized models to determine the asymptotic behavior of the density profile. In this paper, we concentrate on the situation of $β(r)=1/2$ from the viewpoint of the simulation.

astro-ph↗

arXiv2008

Distribution Function in Center of Dark Matter Halo

N-body simulations of dark matter halos show that the density profiles of halos behave as $ρ(r)\propto r^{-α(r)}$, where the density logarithmic slope $α\simeq 1\sim1.5$ in the center and $α\simeq 3\sim 4$ in the outer parts of halos. However, some observations are not in agreement with simulations in the very central region of halos. The simulations also show that velocity dispersion anisotropy parameter $β\approx 0$ in the inner part of the halo and the so called "pseudo phase-space density" $ρ/σ^3$ behaves as a power-law in radius $r$. With these results in mind, we study the distribution function and the pseudo phase-space density $ρ/σ^3$ of the center of dark matter halos and find that they are closely-related.

astro-ph↗

arXiv2006

X-ray Emission of Baryonic Gas in the Universe: Luminosity-Temperature Relationship and Soft-Band Background

We study the X-ray emission of baryon fluid in the universe using the WIGEON cosmological hydrodynamic simulations. It has been revealed that cosmic baryon fluid in the nonlinear regime behaves like Burgers turbulence, i.e. the fluid field consists of shocks. Like turbulence in incompressible fluid, the Burgers turbulence plays an important role in converting the kinetic energy of the fluid to thermal energy and heats the gas. We show that the simulation sample of the $Λ$CDM model without adding extra heating sources can fit well the observed distributions of X-ray luminosity versus temperature ($L_{\rm x}$ vs. $T$) of galaxy groups and is also consistent with the distributions of X-ray luminosity versus velocity dispersion ($L_{\rm x}$ vs. $σ$). Because the baryonic gas is multiphase, the $L_{\rm x}-T$ and $L_{\rm x}-σ$ distributions are significantly scattered. If we describe the relationships by power laws $L_{\rm x}\propto T^{α_{LT}}$ and $L_{\rm x}\propto σ^{α_{LV}}$, we find $α_{LT}>2.5$ and $α_{LV}>2.1$. The X-ray background in the soft $0.5-2$ keV band emitted by the baryonic gas in the temperature range $10^5 50\barρ_{\rm dm}$ is generally clustered and discretely distributed. Therefore, almost all of the soft X-ray background comes from clustered sources, and the contribution from truly diffuse gas is probably negligible. This point agrees with current X-ray observations.

astro-ph↗

arXiv2006

Low-Redshift Cosmic Baryon Fluid on Large Scales and She-Leveque Universal Scaling

We investigate the statistical properties of cosmic baryon fluid in the nonlinear regime, which is crucial for understanding the large-scale structure formation of the universe. With the hydrodynamic simulation sample of the Universe in the cold dark matter model with a cosmological constant, we show that the intermittency of the velocity field of cosmic baryon fluid at redshift z=0 in the scale range from the Jeans length to about 16 Mpc/h can be extremely well described by She-Leveque's universal scaling formula. The baryon fluid also possesses the following features: (1) for volume weight statistics, the dissipative structures are dominated by sheets, and (2) the relation between the intensities of fluctuations is hierarchical. These results imply that the evolution of highly evolved cosmic baryon fluid is similar to a fully developed turbulence.

astro-ph↗

arXiv2005

The velocity field of baryonic gas in the universe

The dynamic evolution of the baryonic intergalactic medium (IGM) caused by the underlying dark matter gravity is governed by the Navier-Stokes equations in which many cooling and heating processes are involved. However, it has long been recognized that the growth mode dynamics of cosmic matter clustering can be sketched by a random force driven Burgers' equation if cooling and heating are ignored. Just how well the dynamics of the IGM can be described as a Burgers fluid has not been fully investigated probably because cooling and heating are essential for a detailed understanding of the IGM. Using IGM samples produced by a cosmological hydrodynamic simulation in which heating and cooling processes are properly accounted for, we show that the IGM velocity field in the nonlinear regime shows the features of a Burgers fluid, that is, when the Reynolds number is high, the velocity field consists of an ensemble of shocks. Consequently, (1) the IGM velocity $v$ is generally smaller than that of dark matter; (2) for the smoothed field, the IGM velocity shows tight correlation with dark matter given by $v \simeq s v_{dm}$, with $s<1$, such that the lower the redshift, the smaller $s$; (3) the velocity PDFs are asymmetric between acceleration and deceleration events; (4) the PDF of velocity difference $Δv=v(x+r)-v(x)$ satisfies the scaling relation for a Burgers fluid, i.e., $P(Δv)=(1 r^y)F(Δv/r^y)$. We find the scaling function and parameters for the IGM which are applicable to the entire scale range of the samples (0.26 - 8 h$^{-1}$ Mpc). These properties show that the similarity mapping between the IGM and dark matter is violated on scales much larger than the Jeans length of the IGM.

astro-ph↗

arXiv2005

A Parameter-free Statistical Measurement of Halos with Power Spectra

We show that, in the halo model of large-scale structure formation, the difference between the Fourier and the DWT (discrete wavelet transform) power spectra provides a statistical measurement of the halos. This statistical quantity is free from parameters related to the shape of the mass profile and the identification scheme of halos. That is, the statistical measurement is invariant in the sense that models with reasonably defined and selected parameters of the halo models should yield the same difference of the Fourier and DWT spectra. This feature is useful to extract ensemble averaged properties of halos, which cannot be obtained with the identification of individual halo. To demonstrate this point, we show with WIGEON hydrodynamical simulation samples that the spectrum difference provides a quantitative measurement of the discrepancy of the distribution of baryonic gas from that of the underlying dark matter field within halos. We also show that the mass density profile of halos in physical space can be reconstructed with this statistical measurement. This profile essentially is the average over an ensemble of halos, including well virialized halos as well as halos with significant internal substructures. Moreover, this reconstruction is sensitive to the tail of the mass density profile. We showed that the profile with $1/r^3$ tail gives very different result from that of $1/r^2$. Other possible applications of this method are discussed as well.

astro-ph↗

arXiv2005

Time changes of symmetric diffusions and Feller measures

We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using the approach of time change of Markov processes.

math.PR↗

arXiv2005

Distributions of the Baryon Fraction on Large Scales in the Universe

(Abridged) The nonlinear evolution of a system consisting of baryons and dark matter is generally characterized by strong shocks and discontinuities. The baryons slow down significantly at postshock areas of gravitational strong shocks, which can occur in high overdense as well as low overdense regions. Consequently, the baryon fraction would be nonuniform on large scales. We studied these phenomena with simulation samples produced by the WENO hybrid cosmological hydrodynamic/N-body code. We find that the baryon fraction in high mass density regions is lower on average than the cosmic baryon fraction, and many baryons accumulate in the regions with moderate mass density to form a high baryon fraction phase (HBFP). In dense regions with rho>100, which are the possible hosts for galaxy clusters, the baryon fraction can be lower than the cosmic baryon fraction by about 10%--20% at z ~ 0. Our simulation samples show that about 3% of the cosmic baryon budget was hidden in the HBFP at redshift z=3, while this percentage increases to about 14% at the present day. The gas in the HBFP cannot be detected either by Ly-alpha forests of QSO absorption spectra or by soft X-ray background. That is, the HBFP would be missed in the baryon budget given by current observations.

astro-ph↗

arXiv2004

Statistical features of 21-cm emission from the epoch between reionization and Gunn-Peterson transparency

We investigate the 21 cm emission from the epoch between reionization z_r and Gunn-Peterson transparency z_{gp}. According to the lognormal model of the thermal history around reionization, hydrogen clouds in z_r > z > z_{gp} are hot and a predominant part of baryonic gas is ionized, but still opaque to Ly-alpha photons. Therefore, 21 cm emission is a distinctive characteristic of this epoch. We show that the 21 cm emission comes from both uncollapsed and collapsing hydrogen clouds. The spatial distribution of the brightness temperature excess $δT_b$ is highly non-Gaussian. It consists of spikes with high $δT_b$ and a low $δT_b$ area between the spikes. The field has the following statistical features: (1) the one-point distributions of $δT_b$ are described approximately by power-law tailed probability distribution functions; (2) the nth-order moment of $δT_b$ is increasing much faster with n than that of a Gaussian field, but slower than that of a lognormal field; (3) the scale-scale correlation of the $δT_b$ field is significant for all scales larger than the Jeans length of the gas. These features would be useful for distinguishing the 21 cm emission of the early clustering from the noise of foreground contamination.

astro-ph↗

arXiv2004

Temperature and Entropy Fields of Baryonic Gas in the Universe

(Abridged)The temperature (T) and entropy (S) fields of baryonic gas/IGM are analyzed using simulation samples by a cosmological hydro/N-body code. We show that in the nonlinear regime the dynamical similarity between the IGM and dark matter will be broken by strong shocks. The heating and entropy production by the shocks breaks the IGM into multiple phases. The mean entropy, or the cosmological entropy floor, is found to be more than 100 h^(-1/3) keV cm^2 in all regions when z < 1. At redshift z ~ 2 - 3, high-entropy gas (S > 50 h^(-1/3) keV cm^2) mostly resides in areas on scales larger than 1 h^(-1) Mpc and with density $ρ_{dm}>10^2$. Therefore, gravitational shocks are an effective preheating mechanism of the IGM, and probably enough to provide the entropy excess of clusters and groups if the epoch of the gas falling in cluster cores is not earlier than z ~ 2 - 3. On the other hand, at redshifts z < 4, there is always a more than 90% volume of the low dark matter mass density regions filled by the IGM with T < 10^4.5 K. Therefore, the multiphased character and non-Gaussianity of the IGM field would explain the high-temperature and high-entropy gas observed in groups and clusters.

astro-ph↗

arXiv2002

Constraints on primordial black holes and primeval density perturbations from the epoch of reionization

We investigate the constraint on the abundance of primordial black holes (PBHs) and the spectral index $n$ of primeval density perturbations given by the ionizing photon background at the epoch of reionization. Within the standard inflationary cosmogony, we show that the spectral index $n$ of the power-law power spectrum of primeval density perturbations should be $n<$1.27. Since the universe is still optical thick at the reionization redshift $z\sim 6$ - 8, this constraint is independent of the unknown parameter of reheating temperature of the inflation. The ionizing photon background from the PBHs can be well approximated by a power law spectrum $J(ν)\proptoν^3$, which is greatly different from those given by models of massive stars and quasars.

astro-ph↗

arXiv2001

Faint field galaxies: an explanation of the faint blue excess using number evolution models

Pure luminosity evolution models for galaxies provide an unacceptable fit to the redshifts and colors of faint galaxies. In this paper we demonstrate, using HST morphological number counts derived both from the $I_{814}$-band of WFPC2 in the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF) and from the $H_{1.6}$-band of NICMOS, and ground-based spectroscopic data of the Hawaii Deep Field and the Canada-France Redshift Survey, that number evolution is necessary for galaxies, regardless of whether the cosmic geometry is flat, open, or $Λ$-dominated. Furthermore, we show that the number evolution is small at redshifts of z<1, but large at z>1, and that this conclusion is valid for all the three cosmological models under consideration. If the universe is open or $Λ$-dominated, the models, which are subject to the constraint of the conservation of the comoving mass density of galaxies, naturally predict a population of star-forming galaxies with the redshift distribution peaking at $z=2\sim3$, which seems to be consistent with the recent findings from Lyman-break photometric selection techniques. If the cosmological model is flat, however, the conservation of the comoving mass density is invalid. Hence, in order to account for the steep slope of B-band number counts at faint magnitudes in the flat universe, such a star-forming galaxy population has to be introduced ad hoc into the modelling alongside the merger assumption.

astro-ph↗

arXiv1998

Questions on pure luminosity evolution for ellipticals

The explanation for the existence of an excess population of faint blue galaxies (FBGs) has been a mystery for nearly two decades, and remains one of the grand astronomical issues to date. Existing models cannot explain all of the observational data such as galaxy number counts in the optical and infrared passbands and the redshift distributions of galaxies. Here, by modelling the morphological number counts derived from the Hubble Space Telescope, as well as the number counts in optical and infrared passbands, and the redshift and color distributions of galaxies obtained from ground-based observations, we show that the `FBG problem' cannot be resolved if elliptical galaxies are assumed to have formed in an instantaneous burst of star formation at high redshift with no subsequent star formation events, which is just the conventional scenario for formation and evolution of ellipticals. There exist great discrepancies between the observed $B-K$ color distribution and the predicted distribution for ellipticals by such a pure luminosity evolution (PLE) model in the context of the conventional scenario. Neither can the mild evolution (i.e., the star formation events have lasted for a longer time than those of the instantaneous burst and passive evolution since the formation of galaxies) for ellipticals be accepted in the context of PLE assumption. The introduction of dust extinction also cannot save the PLE models. This conclusion holds for each of the three cosmological models under consideration: flat, open and $Λ$-dominated. Hence, our investigation suggests that PLE assumption for elliptical galaxies is questionable, and number evolution may be essential for ellipticals.

astro-ph↗

arXiv1998

Modelling the number counts of early-type galaxies by pure luminosity evolution

In this paper, we explore the plausible luminosity evolution of early-type galaxies in different cosmological models by constructing a set of pure luminosity evolution (PLE) models via the choices of the star formation rate (SFR) parameters and formation redshift $z_f$ of galaxies, with the observational constraints derived from the Hubble Space Telescope (HST) morphological number counts for elliptical and S0 galaxies of the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of early-type galaxies can be explained by the pure luminosity evolution models, without invoking exotic scenarios such as merging or introducing an additional population. But the evolution should be nearly passive, with a high $z_f$ assumed. The conclusion is valid in all of the three cosmological models we adopted in this paper. We also present the redshift distributions for three bins of observed magnitudes in F814w pass-band, to show at which redshift are the objects that dominate the counts at a given magnitude. The predictions of the redshift distribution of $22.5<b_j<24.0$ are also presented for comparison with future data.

astro-ph↗