arXiv subjects

Yuexing Li

Publications and source records attributed to Yuexing Li.

At least 19 recordsLinked to original sources

arXiv2023

Star Clusters in Tidal Debris

We present results of a Hubble Space Telescope (HST) UBVI-band study of star clusters in tidal tails, using new WFC3 and ACS imaging to complement existing WFPC2 data. We survey 12 tidal tails across seven merging systems, deriving ages and masses for 425 star cluster candidates (SCCs). The stacked mass distribution across all systems follows a power law of the form $dN/dM \propto M^β$, with $β= -2.02 \pm 0.15$, consistent with what is seen in other star forming environments. GALEX and Swift UV imaging provide star formation rates (SFRs) for our tidal tails, which when compared with ages and masses of our SCCs, allows for a determination of the cluster formation efficiency (CFE). We find the CFE increases with increasing SFR surface density, matching the theoretical model. We confirm this fit down at SFR densities lower than previously measured (log $Σ_\text{SFR} \: (\text{M}_\odot \: \text{yr}^{-1} \: \text{kpc}^{-2}) \approx -4.2$), as related to the CFE. We determine the half-light radii for a refined sample of 57 SCCs with our HST WFC3 and ACS imaging, and calculate their dynamical age, finding the majority of them to be gravitationally bound. We also provide evidence of only low-mass ($< 10^4 \: \text{M}_\odot$) cluster formation in our nearest galaxy, NGC 1487, consistent with the theory that this system is a dwarf merger.

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arXiv2022

FOREVER22: galaxy formation in protocluster regions

We present results from a new cosmological hydrodynamics simulation campaign of protocluster (PC) regions, FOREVER22: FORmation and EVolution of galaxies in Extremely-overdense Regions motivated by SSA22. The simulations cover a wide range of cosmological scales using three different zoom set-ups in a parent volume of $(714.2~\rm cMpc)^{3}$: PCR (Proto-Cluster Region; $V= (28.6~{\rm cMpc})^{3} $, SPH particle mass, $m_{\rm{SPH}} = 4.1 \times 10^{6}~\rm M_{\odot}$ and final redshift, $z_{\rm end}=2.0$), BCG (Brightest proto-Cluster Galaxy; $V \sim (10~{\rm cMpc})^{3} $, $m_{\rm SPH} = 5.0\times10^{5}~\rm M_{\odot}$ and $z_{\rm end}=4.0$ ), and First ( $V \sim (3~{\rm cMpc})^{3} $, $m_{\rm SPH} = 7.9 \times 10^{3}~\rm M_{\odot}$ and $z_{\rm end}=9.5$) runs, that allow to focus on different aspects of galaxy formation. In the PCR runs, we follow 10 PCs, each harbouring 1 - 4 SMBHs with $M_{\rm BH} \ge 10^{9}~\rm M_{\odot}$. One of the PC cores shows a spatially close arrangement of seven starburst galaxies with ${\rm SFR} \gtrsim 100~\rm M_{\odot}~yr^{-1}$ each, that are dust-obscured and would appear as submillimeter galaxies with flux $\gtrsim 1~$ mJy at $1.1~ \rm mm$ in observations. The BCG runs show that the total SFRs of haloes hosting BCGs are affected by AGN feedback, but exceed $1000~\rm M_{\odot}~yr^{-1}$ at $z \lesssim 6$. The First runs resolve mini-haloes hosting population (Pop) III stars and we show that, in PC regions, the dominant stellar population changes from Pop III to Pop II at $z \gtrsim 20$, and the first galaxies with ${\rm SFR} \gtrsim 18~\rm M_{\odot}~yr^{-1}$ form at $z \sim 10$. These can be prime targets for future observations with the James Webb Space Telescope. Our simulations successfully reproduce the global star formation activities in observed PCs and suggest that PCs can kickstart cosmic reionization.

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arXiv2020

The Formation of the First Quasars. I. The Black Hole Seeds, Accretion and Feedback Models

Supermassive black holes (SMBHs) of $\sim 10^9\, M_\odot$ are generally believed to be the central engines of the luminous quasars observed at $z\gtrsim6$, but their astrophysical origin remains elusive. The $z\gtrsim$ quasars reside in rare density peaks, which poses several challenges to uniform hydrodynamic simulations. To investigate the formation of these distant quasars, we perform a suite of zoom-in simulations on a favorable halo, with a mass of $\sim 10^{13}\, M_\odot$ at $z = 6$ and a history of multiple major mergers, ideal for BH growth. We test BH seeds of $10 - 10^6\, M_\odot$, and various accretion and feedback models, including thin-disk and slim-disk accretion. We find, contrary to previous studies, that light seeds of $\lesssim 10^3\, M_\odot$ fail to grow to $10^8\, M_\odot$ by $z\sim 6$ even with super-critical accretion; that the hyper-Eddington mode leads to lower accretion rates than the Eddington-limited case due to stronger feedback, resulting in significantly smaller BHs by two orders of magnitude; and that while the super-critical model boosts the growth of low-spin BHs, for high-spin BHs the mass may be reduced due to increased radiative feedback. Our simulations show that the first $10^8 - 10^9\, M_\odot$ SMBHs may grow from heavy seeds of $\gtrsim 10^4\, M_\odot$ via Eddington-limited or mild super-critical accretion facilitated by gas-rich mergers and self-regulated by feedback, and they co-evolve with their host galaxies, producing bright quasars such as those at $z\sim$6 and ULAS J1342+0928, currently the most distant quasar at z = 7.54.

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arXiv2020

ART$^2$: A 3D Parallel Multi-wavelength Radiative Transfer Code for Continuum and Atomic and Molecular Lines

ART$^2$ is a 3D multi-wavelength Monte Carlo radiative transfer (RT) code that couples continuum and emission lines to track the propagation of photons and their interactions with the interstellar medium (ISM). The previous version of ART$^2$, which included continuum and Ly$α$ line, has been extensively applied to hydrodynamics simulations to study multi-band properties of galaxies and ISM. Here, we describe new implementations of non-local thermodynamic equilibrium RT of molecular and atomic fine structure emission lines, and the parallelization of the code using a number of novel methods. The new ART$^2$ can efficiently and self-consistently produce a full spectrum that includes both continuum and lines such as [CII], [NII], [OIII], Ly$α$, and CO. These essential features, together with the multi-phase ISM model and the adaptive grid, make ART$^2$ a multi-purpose code to study multi-wavelength properties of a wide range of astrophysical systems from planetary disks to large-scale structures. To demonstrate the capability of the new ART$^2$, we applied it to two hydrodynamics simulations: the zoom-in Milky Way Simulation to obtain panchromatic properties of individual galaxies, and the large-scale IllustrisTNG100 Simulation to obtain global properties such as the line intensity mappings. These products are essential for a broad array of studies such as the correlations between physical and panchromatic properties and their evolution. By enabling direct comparison between numerical simulations and multi-band observations, ART$^2$ provides a crucial theoretical framework for the interpretations of existing observations, the plan for future surveys, and the synergy between multi-band galaxy surveys and line intensity mappings. Therefore, ART$^2$ is a powerful and versatile tool to bridge the gap between theories and observations of cosmic structures.

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arXiv2019

Galaxy evolution and radiative properties in the early Universe: multi-wavelength analysis in cosmological simulations

Recent observations have successfully detected UV or infrared flux from galaxies at the epoch of reionization. However, the origin of their radiative properties has not been fully understood yet. Combining cosmological hydrodynamic simulations and radiative transfer calculations, we present theoretical predictions of multi-wavelength radiative properties of the first galaxies at z=6-15. We find that most of the gas and dust are ejected from star-forming regions due to supernova (SN) feedback, which allows UV photons to escape. We show that the peak of SED rapidly shifts between UV and infrared wavelengths on a timescale of 100 Myr due to intermittent star formation and feedback. When dusty gas covers the star-forming regions, the galaxies become bright in the observed-frame sub-millimeter wavelengths. In addition, we find that the escape fraction of ionizing photons also changes between 1-40% at z>10. The mass fraction of HII region changes with the star formation history, resulting in the fluctuations of metal lines and Lyman-alpha line luminosities. In the starbursting phase of galaxies with the halo mass $\sim 10^{11}\,{\rm M_{\odot}}$ ($10^{12}\,{\rm M_{\odot}}$), the simulated galaxy has $L_{\rm [O\,III]} \sim 10^{42}\, (10^{43})\, {\rm erg\,s^{-1}}$, which is consistent with the observed star-forming galaxies at z>7. Our simulations suggest that deep [C II] observation with ALMA can trace the distribution of neutral gas extending over $\sim 20$ physical kpc. We also find that the luminosity ratio $L_{\rm [O\,III]}/L_{\rm [C\,II]}$ decreases with bolometric luminosity due to metal enrichment. Our simulations show that the combination of multi-wavelength observations by ALMA and JWST will be able to reveal the multi-phase ISM structure and the transition from starbursting to outflowing phases of high-z galaxies.

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arXiv2019

Titans of the Early Universe: The Prato Statement on the Origin of the First Supermassive Black Holes

In recent years, the discovery of massive quasars at z~7 has provided a striking challenge to our understanding of the origin and growth of supermassive black holes in the early Universe. Mounting observational and theoretical evidence indicates the viability of massive seeds, formed by the collapse of supermassive stars, as a progenitor model for such early, massive accreting black holes. Although considerable progress has been made in our theoretical understanding, many questions remain regarding how (and how often) such objects may form, how they live and die, and how next generation observatories may yield new insight into the origin of these primordial titans. This review focusses on our present understanding of this remarkable formation scenario, based on discussions held at the Monash Prato Centre from November 20--24, 2017, during the workshop "Titans of the Early Universe: The Origin of the First Supermassive Black Holes."

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arXiv2018

Radiative properties of the first galaxies: rapid transition between blue and red

Recent observations have successfully detected UV-bright and infrared-bright galaxies in the epoch of reionization. However, the origin of their radiative properties has not been understood yet. Combining cosmological hydrodynamic simulations and radiative transfer calculations, we present predictions of multi-wavelength radiative properties of the first galaxies at $z\sim 6-15$. Using zoom-in initial conditions, we investigate three massive galaxies and their satellites in different environment and halo masses: $M_{\rm h} = 2.4\times 10^{10}{\rm M_{\odot}}$ (Halo-10), $1.6\times 10^{11}{\rm M_{\odot}}$ (Halo-11) and $0.7\times 10^{12}{\rm M_{\odot}}$ (Halo-12) at $z=6$. We find that most of gas and dust are ejected from star-forming regions by supernova feedback, which allows UV photons to escape. We show that the peak of the spectral energy distribution (SED) rapidly changes between UV and infrared wavelengths on a time-scale of $\sim$\,100\,Myrs due to intermittent star formation and feedback, and the escape fraction of UV photons fluctuates in the range of $0.2-0.8$ at $z<10$ with a time-averaged value of 0.3. When dusty gas covers the star-forming regions, the galaxies become bright in the observed-frame sub-millimeter wavelengths. We predict the detectability of high-$z$ galaxies with the Atacama Large Millimeter Array (ALMA). For a sensitivity limit of $0.1\,{\rm mJy}$ at $850\,{\rm μm}$, the detection probability of galaxies in halos $M_{\rm h} \gtrsim 10^{11}\,{\rm M_{\odot}}$ at $z\lesssim 7$ exceeds fifty per cent. We argue that supernova feedback can produce the observed diversity of SEDs for high-$z$ galaxies.

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arXiv2018

Formation of a Malin 1 analogue in IllustrisTNG by stimulated accretion

The galaxy Malin 1 contains the largest stellar disk known but the formation mechanism of this structure has been elusive. In this paper, we report a Malin 1 analogue in the 100 Mpc IllustrisTNG simulation and describe its formation history. At redshift zero, this massive galaxy, having a maximum circular velocity $V_{\rm max}$ of 430 ${\rm km\ s^{-1}}$, contains a 100 kpc gas/stellar disk with morphology similar to Malin 1. The simulated galaxy reproduces well many observed features of Malin 1's vast disk, including its stellar ages, metallicities, and gas rotation curve. We trace the extended disk back in time and find that a large fraction of the cold gas at redshift zero originated from the cooling of hot halo gas, triggered by the merger of a pair of intruding galaxies. Our finding provides a novel way to form large galaxy disks as extreme as Malin 1 within the current galaxy formation framework.

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arXiv2017

Primordial Black Holes as Dark Matter: Constraints From Compact Ultra-Faint Dwarfs

The ground-breaking detections of gravitational waves from black hole mergers by LIGO have rekindled interest in primordial black holes (PBHs) and the possibility of dark matter being composed of PBHs. It has been suggested that PBHs of tens of solar masses could serve as dark matter candidates. Recent analytical studies demonstrated that compact ultra-faint dwarf galaxies can serve as a sensitive test for the PBH dark matter hypothesis, since stars in such a halo-dominated system would be heated by the more massive PBHs, their present-day distribution can provide strong constraints on PBH mass. In this study, we further explore this scenario with more detailed calculations, using a combination of dynamical simulations and Bayesian inference methods. The joint evolution of stars and PBH dark matter is followed with a Fokker-Planck code PhaseFlow. We run a large suite of such simulations for different dark matter parameters, then use a Markov Chain Monte Carlo approach to constrain the PBH properties with observations of ultra-faint galaxies. We find that two-body relaxation between the stars and PBH drives up the stellar core size, and increases the central stellar velocity dispersion. Using the observed half-light radius and velocity dispersion of stars in the compact ultra-faint dwarf galaxies as joint constraints, we infer that these dwarfs may have a cored dark matter halo with the central density in the range of 1-2 $\rm{M_{\odot}/pc^3}$, and that the PBHs may have a mass range of 2-14 $\rm{M_{\odot}}$ if they constitute all or a substantial fraction of the dark matter.

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arXiv2017

Is there a disk of satellites around the Milky Way?

The "Disk of satellites" (DoS) around Milky Way is a highly debated topic with conflicting interpretations of observations and their theoretical models. We perform a comprehensive analysis of all dwarfs detected in the Milky Way and find that the DoS structure depends strongly on the plane identification method and the sample size. In particular, we demonstrate that a smaller sample size produces a higher anisotropy of the spatial distribution and a stronger clustering of the angular momentum of the satellites. Moreover, we calculate the evolution of the 11 classical satellites with proper motion measurements and find that the thin DoS they currently reside in is transient. Furthermore, we analyze two cosmological simulations using the same initial conditions of a Milky Way-sized galaxy, an N-body run with dark matter only and a hydrodynamic one with both baryonic and dark matter, and find that the hydrodynamic simulation produces more anisotropic distribution of satellites than the N-body one. Our results suggest that an anisotropic distribution of satellites in galaxies can originate from baryonic processes in the hierarchical structure formation model, but the claimed highly-flattened, coherently-rotating DoS of the Milky Way may be a small-number selection effect. These findings may help resolve the contradictory claims of DoS in other galaxies and the discrepancy among numerical simulations.

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arXiv2017

The formation and evolution of star clusters in interacting galaxies

Observations of globular clusters show that they have universal lognormal mass functions with a characteristic peak at $\sim 2\times 10^{5}\, {\rm{M_{\odot}}}$, but the origin of this peaked distribution is highly debated. Here we investigate the formation and evolution of star clusters in interacting galaxies using high-resolution hydrodynamical simulations performed with two different codes in order to mitigate numerical artifacts. We find that massive star clusters in the range of $\sim 10^{5.5} - 10^{7.5}\, {\rm{M_{\odot}}}$ form preferentially in the highly-shocked regions produced by galaxy interactions. The nascent cluster-forming clouds have high gas pressures in the range of $P/k \sim 10^8 - 10^{12}\, \rm{K}\,\rm{cm^{-3}}$, which is $\sim 10^4 - 10^8$ times higher than the typical pressure of the interstellar medium but consistent with recent observations of a pre-super star cluster cloud in the Antennae Galaxies. Furthermore, these massive star clusters have quasi-lognormal initial mass functions with a peak around $\sim 10^{6}\, {\rm{M_{\odot}}}$. The number of clusters declines with time due to destructive processes, but the shape and the peak of the mass functions do not change significantly during the course of galaxy collisions. Our results suggest that gas-rich galaxy mergers may provide a favorable environment for the formation of massive star clusters such as globular clusters, and that the lognormal mass functions and the unique peak may originate from the extreme high-pressure conditions of the birth clouds and may survive the dynamical evolution.

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arXiv2017

The nature of disk of satellites around Milky Way-like galaxies

It has been suggested that the satellite galaxies of the Milky Way reside in a highly-flattened, kinematically-coherent plane called Disk of Satellites (DoS). The origin of the DoS, however, has been hotly debated, and a number of conflicting claims have been reported in the literature on whether or not the DoS is consistent with predictions from the standard Lambda Cold Dark Matter ($Λ$CDM) cosmological model. Here we investigate this issue by comparing a high-resolution, hydrodynamic $Λ$CDM simulation of a Milky Way sized galaxy with its dark matter only counterpart. We find the following results: (1) The abundance and distribution of satellite galaxies around a host galaxy is significantly different in the hydro simulation compared to its N-body counterpart; (2) No clear coherent rotation is found in the satellite system, as the fractions of corotating and counter-corotating satellites remain comparable across cosmic time; (3) The satellite distribution evolves significantly with time, from nearly isotropic at high redshift to anisotropic at the present day; (4) The DoS properties strongly depend on sample selection and plane identification methods. Our results imply that the spatially-thin and coherently-rotating DoS reported in Milky Way and other galaxies may be a selection effect of small sample size.

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arXiv2017

Baryonic impact on the dark matter orbital properties of Milky Way-sized haloes

We study the orbital properties of dark matter haloes by combining a spectral method and cosmological simulations of Milky Way-sized galaxies. We compare the dynamics and orbits of individual dark matter particles from both hydrodynamic and $N$-body simulations, and find that the fraction of box, tube and resonant orbits of the dark matter halo decreases significantly due to the effects of baryons. In particular, the central region of the dark matter halo in the hydrodynamic simulation is dominated by regular, short-axis tube orbits, in contrast to the chaotic, box and thin orbits dominant in the $N$-body run. This leads to a more spherical dark matter halo in the hydrodynamic run compared to a prolate one as commonly seen in the $N$-body simulations. Furthermore, by using a kernel based density estimator, we compare the coarse-grained phase-space densities of dark matter haloes in both simulations and find that it is lower by $\sim0.5$ dex in the hydrodynamic run due to changes in the angular momentum distribution, which indicates that the baryonic process that affects the dark matter is irreversible. Our results imply that baryons play an important role in determining the shape, kinematics and phase-space density of dark matter haloes in galaxies.

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arXiv2017

Baryonic impact on the dark matter distribution in Milky Way-size galaxies and their satellites

We study the impact of baryons on the distribution of dark matter in a Milky Way-size halo by comparing a high-resolution, moving-mesh cosmological simulation with its dark matter-only counterpart. We identify three main processes related to baryons -- adiabatic contraction, tidal disruption and reionization -- which jointly shape the dark matter distribution in both the main halo and its subhalos. The relative effect of each baryonic process depends strongly on the subhalo mass. For massive subhalos with maximum circular velocity $v_{\rm max} > 35 km/s$, adiabatic contraction increases the dark matter concentration, making these halos less susceptible to tidal disruption. For low-mass subhalos with $v_{\rm max} < 20 km/s$, reionization effectively reduces their mass on average by $\approx$ 30% and $v_{\rm max}$ by $\approx$ 20%. For intermediate subhalos with $20 km/s < v_{\rm max} < 35 km/s$, which share a similar mass range as the classical dwarf spheroidals, strong tidal truncation induced by the main galaxy reduces their $v_{\rm max}$. Moreover, the stellar disk of the main galaxy effectively depletes subhalos near the central region. As a combined result of reionization and increased tidal disruption, the total number of low-mass subhalos in the hydrodynamic simulation is nearly halved compared to that of the $\textit{N-}$body simulation. We do not find dark matter cores in dwarf galaxies, unlike previous studies that employed bursty feedback-driven outflows. The substantial impact of baryons on the abundance and internal structure of subhalos suggests that galaxy formation and evolution models based on $\textit{N}$-body simulations should include these physical processes as major components.

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arXiv2017

The Formation of a Milky Way-sized Disk Galaxy 1. A Comparison of Numerical Methods

The long-standing challenge of creating a Milky Way-like disk galaxy from cosmological simulations has motivated significant developments in both numerical methods and physical models in recent years. We investigate these two fundamental aspects in a new comparison project using a set of cosmological hydrodynamic simulations of the formation and evolution of a Milky Way-size galaxy. In this study, we focus on the comparison of two particle-based hydrodynamics methods: the improved smoothed particle hydrodynamics (SPH) code Gadget, and the Lagrangian Meshless Finite-Mass (MFM) code GIZMO. All the simulations in this paper use the same initial conditions and physical models, which include physics of both dark matter and baryons, star formation, "energy-driven" outflow, metal-dependent cooling, stellar evolution and metal enrichment from supernovae. We find that both numerical schemes produce a late-type galaxy with extended gaseous and stellar disks. However, notable differences are present in a wide range of galaxy properties and their evolution, including star formation history, gas content, disk structure and kinematics. In particular, there is significant difference in gas properties and their evolution between the two simulations. Compared to GIZMO, Gadget simulation produces a larger fraction of cold, dense gas at high redshift which fuels rapid star formation and results in a higher stellar mass by $20\%$ and a lower gas fraction by $10\%$ at $z = 0$, and the resulting gas disk is smoother and more coherent in rotation due to damping of turbulent motion by the numerical viscosity in SPH, in contrast to the GIZMO simulation which shows more prominent spiral structure. Given its better convergence properties and lower computational cost, we argue that MFM method is a promising alternative to the widely used SPH in cosmological hydrodynamic simulations.

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arXiv2015

Cold accretion in early galaxy formation and its Lyman-alpha signatures

The Lyman-alpha (Lya) emission has played an important role in detecting high-redshift galaxies, including recently distant ones at redshift z > 7. It may also contain important information on the origin of these galaxies. Here, we investigate the formation of a typical L* galaxy and its observational signatures at the earliest stage, by combining a cosmological hydrodynamic simulation with three-dimensional radiative transfer calculations using the newly improved ART^2 code. Our cosmological simulation uses the Aquila initial condition which zooms in onto a Milky Way-like halo with high resolutions, and our radiative transfer couples multi-wavelength continuum, Lya line, and ionization of hydrogen. We find that the modeled galaxy starts to form at redshift z ~ 24 through efficient accretion of cold gas, which produces a strong Lya line with a luminosity of L(Lya) ~ 10^42 erg/s as early as z ~ 14. The Lya emission appears to trace the cold, dense gas. The lines exhibit asymmetric, single-peak profiles, and are shifted to the blue wing, a characteristic feature of gas inflow. Moreover, the contribution to the total Lya luminosity by excitation cooling increases with redshift, and it becomes dominant at z >~ 6. We predict that L* galaxies such as the modeled one may be detected at z <~ 8 by JWST and ALMA with a reasonable integration time. Beyond redshift 12, however, only Lya line may be observable by spectroscopic surveys. Our results suggest that Lya line is one of the most powerful tools to detect the first generation of galaxies, and to decipher their formation mechanism.

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arXiv2014

Numerical Convergence in Smoothed Particle Hydrodynamics

We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit $N \rightarrow \infty$, $h \rightarrow 0$, and $N_{nb} \rightarrow \infty$, where $N$ is the total number of particles, $h$ is the smoothing length, and $N_{nb}$ is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions $N \rightarrow \infty$ and $h \rightarrow 0$ are sufficient to achieve convergence, while holding $N_{nb}$ fixed. We demonstrate that if $N_{nb}$ is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as $N \rightarrow \infty$ and $h \rightarrow 0$. Formal numerical convergence in SPH is possible only if $N_{nb}$ is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for $N_{nb}$ by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find $N_{nb} \propto N^{1/2}$. This means that if SPH is to be used as a numerically convergent method, the required computational cost does not scale with particle number as $O(N)$, but rather as $O(N^{1+δ})$, where $δ\approx 1/2$, with a weak dependence on the form of the smoothing kernel.

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arXiv2014

Origin of the Correlations Between Supermassive Black Holes and Their Host Galaxies

Observations have shown that supermassive black holes in nearby elliptical galaxies correlate tightly with the stellar velocity dispersion (the $\MBH - σ$ relation) and the stellar mass (the $\MBH - \Mhost$ relation) of their host spheroids. However, the origin of these correlations remains ambiguous. In a previous paper by Zhu et al., we proposed a model which links the M-$σ$ relation to the the dynamical state of the system and the $\MBH - \Mhost$ relation to the self-regulation of galaxy growth. To test this model, we compile a sample of observed galaxies with different properties and examine the dependence of the above correlations on these parameters. We find that galaxies that satisfy the the $\MBH - σ$ correlation appear to have reached virial equilibrium, as indicated by the ratio between kinetic energy and gravitational potential, 2K/U $\sim$ 1. Furthermore, the ratio of black hole accretion rate to star formation rate remains nearly constant, BHAR /SFR $\sim$ $10^{-3}$, in active galaxies over a wide range of mass in the redshift range z=0 - 3. These results confirm our theoretical model that the observed correlations have different origins: the $\MBH - σ$ relation may result from galaxy relaxation, while the $\MBH$ - $\Mhost$ relation may be due to self-regulated black hole accretion and star formation in galaxies.

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