arXiv subjects

Zhaozhou Li

Publications and source records attributed to Zhaozhou Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Scaling Relations in the Phase-Space Structure of Dark Matter Haloes

We present new scaling relations for the isotropic phase-space distribution functions (DFs) and energy distributions of simulated dark matter haloes. These relations are inspired by those for the singular isothermal sphere with density profile $ρ(r)\propto r^{-2}$, for which the DF satisfies $f(E) \propto r_{\max}^{-2}(E)$ and the energy distribution satisfies $dM/dE \propto r_{\max}(E)$, with $r_{\max}(E)$ being the radius where the gravitational potential equals energy $E$. For the simulated haloes, we find $f(E)\propto r_{\max}^{-2.08}(E)$ and $dM/dE \propto r_{\max}(E)$ across broad energy ranges. In addition, the proportionality coefficients depend on the gravitational constant and the parameters of the best-fit Navarro-Frenk-White density profile. These scaling relations are satisfied by haloes over a wide mass range and provide an efficient method to approximate their DFs and energy distributions. Understanding the origin of these relations may shed more light on halo formation.

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arXiv2025

emPDF: Inferring the Milky Way mass with data-driven distribution function in phase space

We introduce the emPDF (Empirical Distribution Function), a novel dynamical modeling method that infers the gravitational potential from kinematic tracers with optimal statistical efficiency under the minimal assumption of steady state. emPDF determines the best-fit potential by maximizing the similarity between instantaneous kinematics and the time-averaged phase-space distribution function (DF), which is empirically constructed from observation upon the theoretical foundation of oPDF (Han et al. 2016). This approach eliminates the need for presumed functional forms of DFs or orbit libraries required by conventional DF- or orbit-based methods. emPDF stands out for its flexibility, efficiency, and capability in handling observational effects, making it preferable to the popular Jeans equation or other minimal assumption methods, especially for the Milky Way (MW) outer halo where tracers often have limited sample size and poor data quality. We apply emPDF to infer the MW mass profile using Gaia DR3 data of satellite galaxies and globular clusters, obtaining enclosed masses of $M(<r)=26\pm8, 46\pm8, 90\pm13$, and $149\pm40 \times 10^{10}M_\odot$ at r=30, 50, 100, and 200 kpc, respectively. These are consistent with the updated constraints from simulation-informed DF fitting (Li et al. 2020). While the simulation-informed DF offers superior precision owing to the additional information extracted from simulations, emPDF is independent of such supplementary knowledge and applicable to general tracer populations. emPDF is currently implemented for tracers with complete 6D kinematics within spherical potentials, but it can potentially be extended to address more general problems.

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arXiv2024

Growth of Massive Black-Holes in FFB Galaxies at Cosmic Dawn

The scenario of feedback-free starbursts (FFB), which predicts excessively bright galaxies at cosmic dawn as observed using JWST, may provide a natural setting for black hole (BH) growth. This involves the formation of intermediate-mass seed BHs and their runaway mergers into super-massive BHs with high BH-to-stellar mass ratios and low AGN luminosities. We present a scenario of merger-driven BH growth in FFB galaxies and study its feasibility. BH seeds form within the building blocks of the FFB galaxies, namely, thousands of compact star clusters, each starbursting in a free-fall time of a few Myr before the onset of stellar and supernova feedback. The BH seeds form by rapid core collapse in the FFB clusters, in a few free-fall times, sped up by the migration of massive stars due to the young, broad stellar mass function and stimulated by a `gravo-gyro' instability due to internal cluster rotation and flattening. BHs of $10^4 M_\odot$ are expected in $10^6 M_\odot$ FFB clusters within sub-kpc galactic disks at $z \sim 10$. The BHs then migrate to the galaxy center by dynamical friction, hastened by the compact FFB stellar galactic disk configuration. Efficient mergers of the BH seeds will produce $10^{6-8} M_\odot$ BHs with a BH-to-stellar mass ratio $\sim 0.01$ by $z \sim 4-7$, as observed. The growth of the central BH by mergers can overcome the bottleneck introduced by gravitational wave recoils if the BHs inspiral within a relatively cold disk or if the escape velocity from the galaxy is boosted by a wet compaction event. Such events, common in massive galaxies at high redshifts, can also help by speeding up the inward BH migration and by providing central gas to assist with the final parsec problem. The cold disk version of the FFB scenario provides a feasible route for the formation of supermassive BHs.

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arXiv2024

The mass and redshift dependence of halo star clustering

We adopt the two point correlation function (2PCF) as a statistical tool to quantify the spatial clustering of halo stars, for galaxy systems spanning a wide range in host halo virial mass ($11.25<\log_{10}M_{200c}/\mathrm{M}_\odot<15$) and redshifts ($0<z<1.5$) from the IllustrisTNG simulations. Consistent with a previous study \cite[][Paper I]{2024ApJ...961..223Z}, we identify clear correlations between the strength of the 2PCF signals and galaxy formation redshifts, but over a much wider mass range. We find that such correlations are slightly stronger at higher redshifts, and get weakened with the increase of host halo mass. We demonstrate that the spatial clustering of halo stars is affected by two factors: 1) the clustering gets gradually weakened as time passes (phase mixing); 2) newly accreted stars at more recent times would increase the clustering. For more massive galaxy systems, they assemble late and the newly accreted stars would increase the clustering. The late assembly of massive systems may also help to explain the weaker correlations between the 2PCF signals and the galaxy formation redshifts in massive halos, as their 2PCFs are affected more by recently accreted stars, while formation redshift characterizes mass accretion on a much longer timescale. We find that the orbits of satellite galaxies in more massive halos maintain larger radial anisotropy, reflecting the more active accretion state of their hosts while also contributing to their stronger mass loss rates.

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arXiv2024

Why artificial disruption is not a concern for current cosmological simulations

Recent studies suggest that cold dark matter subhalos are hard to disrupt and almost all cases of subhalo disruption observed in numerical simulations are due to numerical effects. However, these findings primarily relied on idealized numerical experiments, which do not fully capture the realistic conditions of subhalo evolution within a hierarchical cosmological context. Based on the Aquarius simulations, we identify clear segregation in the population of surviving and disrupted subhalos, which corresponds to two distinct acquisition channels of subhalos. We find that all of the first-order subhalos accreted after redshift 2 survive to the present time without suffering from artificial disruption. On the other hand, most of the disrupted subhalos are sub-subhalos accreted at high redshift. Unlike the first-order subhalos, sub-subhalos experience pre-processing and many of them are accreted through major mergers at high redshift, resulting in very high mass loss rates. We confirm these high mass loss rates are physical through both numerical experiments and semi-analytical modeling, thus supporting a physical origin for their rapid disappearance in the simulation. Even though we cannot verify whether these subhalos have fully disrupted or not, their extreme mass loss rates dictate that they can at most contribute a negligible fraction to the very low mass end of the subhalo mass function. We thus conclude that current state-of-the-art cosmological simulations have reliably resolved the subhalo population.

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arXiv2024

How does the velocity anisotropy of halo stars, dark matter and satellite galaxies depend on host halo properties?

We investigate the mass ($M_{200}$) and concentration ($c_{200}$) dependencies of the velocity anisotropy ($β$) profiles for different components in the dark matter halo, including halo stars, dark matter and subhalos, using systems from the IllustrisTNG simulations. Beyond a critical radius, $β$ becomes more radial with the increase of $M_{200}$, reflecting more prominent radial accretion around massive halos. The critical radius is $r\sim r_s$, $0.3~r_s$ and $r_s$ for halo stars, dark matter and subhalos, with $r_s$ the scale radius of host halos. This dependence on $M_{200}$ is the strongest for subhalos, and the weakest for halo stars. In central regions, $β$ of halo stars and dark matter particles gets more isotropic with the increase of $M_{200}$ in TNG300 due to baryons. By contrast, $β$ of dark matter from the dark matter only TNG300-Dark run shows much weaker dependence on $M_{200}$ within $r_s$. Dark matter in TNG300 is slightly more isotropic than in TNG300-Dark at $0.2~r_s r_s$ as $β_\mathrm{star}-β_\mathrm{DM}=(-0.028 \pm 0.008)\log_{10}M_{200}/M_\odot + (0.690\pm0.010)$.

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arXiv2024

Inferring the mass content of galaxy clusters with satellite kinematics and Jeans Anisotropic modeling

Satellite galaxies can be used to indicate the dynamical mass of galaxy groups and clusters. In this study, we apply the axis-symmetric Jeans Anisotropic Multi-Gaussian Expansion JAM modeling to satellite galaxies in 28 galaxy clusters selected from the TNG300-1 simulation with halo mass of $\log_{10}M_{200}/M_\odot>14.3$. If using true bound satellites as tracers, the best constrained total mass within the half-mass radius of satellites, $M(<r_\mathrm{half})$, and the virial mass, $M_{200}$, have average biases of -0.01 and $0.03$~dex, with average scatters of 0.11~dex and 0.15~dex. If selecting companions in redshift space with line-of-sight depth of 2,000~km/s, the biases are -0.06 and $0.01$~dex, while the scatters are 0.12 and 0.18~dex for $M(<r_\mathrm{half})$ and $M_{200}$. By comparing the best-fitting and actual density profiles, we find $\sim$29% of best-fitting density profiles show very good agreement with the truth, $\sim$32% display over or under estimates at most of the radial range with biased $M(<r_\mathrm{half})$, and 39% show under/over estimates in central regions and over/under estimates in the outskirts, with good constraints on $M(<r_\mathrm{half})$, yet most of the best constraints are still consistent with the true profiles within 1-$σ$ statistical uncertainties for the three circumstances. Using a mock DESI Bright Galaxy Survey catalog with the effect of fiber incompleteness, we find DESI fiber assignments and the choice of flux limits barely modify the velocity dispersion profiles and are thus unlikely to affect the dynamical modeling outcomes. Our results show that with current and future deep spectroscopic surveys, JAM can be a powerful tool to constrain the underlying density profiles of individual massive galaxy clusters.

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arXiv2024

Effects of feedback-free starburst galaxies on the 21-cm signal and reionization history

Different star-formation models at Cosmic Dawn produce detectable signatures in the observables of upcoming 21-cm experiments. In this work, we consider the physical scenario of feedback-free starbursts (FFB), according to which the star-formation efficiency (SFE) is enhanced in sufficiently massive halos at early enough times, thus explaining the indication from the James Webb Space Telescope for an excess of bright galaxies at $z \geq 10$. We model the contribution of FFBs to popII SFE and compute the impact these have on the 21-cm global signal and power spectrum. We show that FFBs affect the evolution of the brightness temperature and the 21-cm power spectrum, but they only have a limited effect on the neutral hydrogen fraction. We investigate how the observables are affected by changes in the underlying star formation model and by contribution from popIII stars. Finally, we forecast the capability of next-generation Hydrogen Epoch of Reionization Array (HERA) to detect the existence of FFB galaxies via power spectrum measurements. Our results show the possibility of a significant detection, provided that popII stars are the main drivers of lowering the spin temperature. Efficient popIII star formation will make the detection more challenging.

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arXiv2024

Feedback-Free Starbursts at Cosmic Dawn: Observable Predictions for JWST

We extend the analysis of a physical model within the standard cosmology that robustly predicts a high star-formation efficiency (SFE) in massive galaxies at cosmic dawn due to feedback-free starbursts (FFBs). It implies an excess of bright galaxies at z>~10 compared to the standard models based on the low SFE at later epochs, an excess indicated by JWST observations. Here we provide observable predictions based on the analytic FFB scenario. These can be compared with simulations and JWST observations. We approximate the SFE as a function of redshift and mass, assuming a maximum SFE of 0.2~1 in the FFB regime. From this, we derive the evolution of the galaxy mass and luminosity functions as well as the evolution of stellar and star-formation densities. We then predict the star-formation history (SFH), galaxy sizes, outflows, gas fractions, metallicities, and dust attenuation, all as functions of mass and redshift in the FFB regime. The major distinguishing feature is the occurrence of FFBs above a mass threshold that declines with redshift. The luminosities and star formation rates in bright galaxies are predicted to be in excess of extrapolations of standard empirical models and cosmological simulations, an excess that grows from z~9 to higher redshifts. The FFB phase of ~100 Myr is predicted to show a characteristic SFH that fluctuates on a timescale of ~10 Myr. The stellar systems are compact (Re~0.3 kpc at z~10 and declining with z). The galactic gas consists of a steady wind driven by supernovae from earlier generations, with high outflow velocities (FWHM~1400-6700km/s), low gas fractions (<0.1), low metallicities (<~0.1 solar), and low dust attenuation ($A_{UV}$~0.5 at z~10 and declining with z). We make tentative comparisons with current JWST observations for initial insights, anticipating more complete and reliable datasets for detailed quantitative comparisons in the future.

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arXiv2024

Phase Space Distribution Functions and Energy Distributions of Dark Matter Particles in Haloes

For a spherical dark matter halo with isotropic velocity distribution, the phase space distribution function (DF), the energy distribution, and the density profile form a set of self-consistent description of its equilibrium state, and knowing one is sufficient to determine the other two. The Navarro-Frenk-White density profile (NFW profile) is known to be a good approximation to the spherically-averaged density distribution in simulated haloes. The DARKexp energy distribution is also known to compare well with the simulated energy distribution. We present a quantitative assessment of the NFW and DARKexp fits to the simulated DF and energy distribution for a wide range of haloes in a dark-matter-only simulation from the IllustrisTNG Project. As expected, we find that the NFW fits work well except at low energy when the density at small radii deviates from the NFW profile. Further, the NFW and DARKexp fits have comparable accuracy in the region where both fit well, but the DARKexp fits are better at low energy because they require matching of the central gravitational potential. We also find an approximate relation between the energy scale parameterizing the DARKexp energy distribution and that defined by the characteristic density and radius of the NFW profile. This relation may be linked to the relaxation process during halo formation.

astro-ph.CO↗

arXiv2024

Are Odd Radio Circles virial shocks around massive galaxies? Implications for cosmic-ray diffusion in the circumgalactic medium

Recently, a new population of circular radio ($\sim$GHz) objects have been discovered at high Galactic latitudes, called the Odd Radio Circles (ORCs). A fraction of the ORCs encircles massive galaxies in the sky with stellar mass $\sim 10^{11}\, M_\odot$ situated at $z=0.2$-$0.6$, suggesting a possible physical connection. In this work, we explore the possibility that these radio circles originate from the accretion shocks/virial shocks around massive ($\gtrsim10^{13}\, M_\odot$) dark matter halo at $z\sim0.5$. We found that the radio flux density of the emitting shell is marginally consistent with the ORCs. We also find that pure advection of electrons from the shock results in a radio-emitting shell that is considerably narrower than the observed one due to strong inverse-Compton cooling of electrons. Instead, we show that the diffusion of cosmic-ray (CR) electrons plays a significant role in increasing the width of the shell. We infer a diffusion coefficient, $D_{\rm cr} \sim 10^{30}\ {\rm cm^2\,s^{-1}}$, consistent with the values expected for low-density circumgalactic medium (CGM). If ORCs indeed trace virial shocks, then our derived CR diffusion coefficient represents one of the few estimations available for the low-density CGM. Finally, we show that the apparent discrepancy between ORC and halo number density can be mitigated by considering an incomplete halo virialization and the limited radiation efficiency of shocks. This study, therefore, opens up new avenues to probe such shocks and non-thermal particle acceleration within them. Furthermore, our results suggest that low-mass galaxies ($\lesssim 10^{13}\, M_\odot$) may not show ORCs due to their significantly lower radio surface brightness.

astro-ph.HE↗

arXiv2023

Evidence for a Shallow Evolution in the Volume Densities of Massive Galaxies at $z=4$ to $8$ from CEERS

We analyze the evolution of massive (log$_{10}$ [$M_\star/M_\odot$] $>10$) galaxies at $z \sim$ 4--8 selected from the JWST Cosmic Evolution Early Release Science (CEERS) survey. We infer the physical properties of all galaxies in the CEERS NIRCam imaging through spectral energy distribution (SED) fitting with dense basis to select a sample of high redshift massive galaxies. Where available we include constraints from additional CEERS observing modes, including 18 sources with MIRI photometric coverage, and 28 sources with spectroscopic confirmations from NIRSpec or NIRCam wide-field slitless spectroscopy. We sample the recovered posteriors in stellar mass from SED fitting to infer the volume densities of massive galaxies across cosmic time, taking into consideration the potential for sample contamination by active galactic nuclei (AGN). We find that the evolving abundance of massive galaxies tracks expectations based on a constant baryon conversion efficiency in dark matter halos for $z \sim$ 1--4. At higher redshifts, we observe an excess abundance of massive galaxies relative to this simple model. These higher abundances can be explained by modest changes to star formation physics and/or the efficiencies with which star formation occurs in massive dark matter halos, and are not in tension with modern cosmology.

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arXiv2023

DESI Legacy Imaging Surveys Data Release 9: Cosmological Constraints from Galaxy Clustering and Weak Lensing using the Minimal Bias Model

We present a tentative constraint on cosmological parameters $Ω_m$ and $σ_8$ from a joint analysis of galaxy clustering and galaxy-galaxy lensing from DESI Legacy Imaging Surveys Data Release 9 (DR9), covering approximately 10000 square degrees and spanning the redshift range of 0.1 to 0.9. To study the dependence of cosmological parameters on lens redshift, we divide lens galaxies into seven approximately volume-limited samples, each with an equal width in photometric redshift. To retrieve the intrinsic projected correlation function $w_{\rm p}(r_{\rm p})$ from the lens samples, we employ a novel method to account for redshift uncertainties. Additionally, we measured the galaxy-galaxy lensing signal $ΔΣ(r_{\rm p})$ for each lens sample, using source galaxies selected from the shear catalog by applying our \texttt{Fourier\_Quad} pipeline to DR9 images. We model these observables within the flat $Λ$CDM framework, employing the minimal bias model. To ensure the reliability of the minimal bias model, we apply conservative scale cuts: $r_{\rm p} > 8$ and $12 ~h^{-1}{\rm Mpc}$, for $w_{\rm p}(r_{\rm p})$ and $ΔΣ(r_{\rm p})$, respectively. Our findings suggest a mild tendency that $S_8 \equiv σ_8 \sqrt{Ω_m/0.3} $ increases with lens redshift, although this trend is only marginally significant. When we combine low redshift samples, the value of $S_8$ is determined to be $0.84 \pm 0.02$, consistent with the Planck results but significantly higher than the 3$\times$ 2pt analysis by 2-5$σ$. Despite the fact that further refinements in measurements and modeling could improve the accuracy of our results, the consistency with standard values demonstrates the potential of our method for more precise and accurate cosmology in the future.

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arXiv2023

Unraveling the Complexity of Dwarf Galaxy Dynamics: A study of Binary Orbital Motions

We investigate the impact of binary orbital motions on the dynamical modeling of dwarf galaxies with intrinsic line-of-sight velocity dispersions ($σ_{v_r}$) of 1 to 9 km/s. Using dwarf galaxies from the Auriga level-2 and level-3 simulations, we apply the Jeans Anisotropic Multi-Gaussian Expansion modelling to tracer stars before and after including binaries to recover the dynamical masses. The recovered total masses within the half-mass radius of tracers, $M(<r_\mathrm{half})$, are always inflated due to binary motions, with greater inflations occurring for smaller $σ_{v_r}$. However, many dwarf galaxies experience central density deflated due to binary motions, with little dependences on $σ_{v_r}$. This is due to the negative radial gradients in the velocity dispersion profiles, with the fractional inflation in $σ_{v_r}$ due to binaries more significant in outskirts. An extreme binary fraction of 70% can lead to central density deflation of up to 10-20% at 3 km/s$<σ_{v_r}<$8 km/s, with $M(<r_\mathrm{half})$ inflated by 4% at 9 km/s and up to 15% at 3 km/s. A lower binary fraction of 36% leads to similar deflations, with the inflations decreasing to approximately 10% at 3 km/s and becoming statistically insignificant. The choice of binary orbit distribution models does not result in significant differences, and observational errors tend to slightly weaken the deflations in the recovered central density. Two observations separated by one year to exclude binaries lead to almost zero inflations/deflations for a binary fraction of 36% over 3 km/s$<σ_{v_r}<$9 km/s. For $σ_{v_r}\sim$1 km/s to 3 km/s, a binary fraction of 70% (36%) still results in 60% (30%) to 10% (1%) of inflations in $M(<r_\mathrm{half})$, even with two-epoch observation.

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arXiv2023

Physical evolution of dark matter halo around the depletion boundary

We investigate the build-up of the halo profile out to large scale in a cosmological simulation, focusing on the roles played by the recently proposed depletion radii. We explicitly show that halo growth is accompanied by the depletion of the environment, with the inner depletion radius demarcating the two. This evolution process is also observed via the formation of a trough in the bias profile, with the two depletion radii identifying key scales in the evolution. The ratio between the inner depletion radius and the virial radius is approximately a constant factor of 2 across redshifts and halo masses. The ratio between their enclosed densities is also close to a constant of 0.18. These simple scaling relations reflect the largely universal scaled mass profile on these scales, which only evolves weakly with redshift. The overall picture of the boundary evolution can be broadly divided into three stages according to the maturity of the depletion process, with cluster halos lagging behind low mass ones in the evolution. We also show that the traditional slow and fast accretion dichotomy of halo growth can be identified as accelerated and decelerated depletion phases respectively.

astro-ph.CO↗

arXiv2023

Efficient Formation of Massive Galaxies at Cosmic Dawn by Feedback-Free Starbursts

JWST observations indicate a surprising excess of luminous galaxies at $z\sim 10$ and above, consistent with efficient conversion of the accreted gas into stars, unlike the suppression of star formation by feedback at later times. We show that the high densities and low metallicities at this epoch {\it guarantee} a high star-formation efficiency (SFE) in the most massive dark-matter haloes. Feedback-free starbursts (FFBs) occur when the free-fall time is shorter than $\sim 1$ Myr, below the time for low-metallicity massive stars to develop winds and supernovae. This corresponds to a characteristic density of $\sim 3\times 10^3$cm$^{-3}$. A comparable threshold density permits a starburst by allowing cooling to star-forming temperatures in a free-fall time. The galaxies within $\sim 10^{11} M_\odot$ haloes at $z \sim 10$ are expected to have FFB densities. The halo masses allow efficient gas supply by cold streams in a halo crossing time $\sim 80$ Myr. The FFBs gradually turn all the accreted gas into stars in clusters of $\sim 10^{4-7} M_\odot$ within galaxies that are rotating discs or shells. The starbursting clouds are insensitive to radiative feedback and are shielded against feedback from earlier stars. We predict high SFE above thresholds in redshift and halo mass, where the density is $10^{3-4}$cm$^{-3}$. The $z\sim 10$ haloes of $\sim 10^{10.8} M_\odot$ are predicted to host galaxies of $\sim 10^{10} M_\odot$ with SFR $\sim 65 M_\odot$ yr$^{-1}$ and sub-kpc sizes. The metallicity is $\leq 0.1 Z_\odot$ with little gas, dust, outflows and hot circumgalactic gas, allowing a top-heavy IMF but not requiring it. The compact galaxies with thousands of young FFB clusters may have implications on reionization, black-hole growth and globular clusters.

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arXiv2023

The Response of Dark Matter Haloes to Gas Ejection: CuspCore II

We propose an analytic model, CuspCore II, for the response of dark matter (DM) haloes to central gas ejection, as a mechanism for generating DM-deficient cores in dwarfs and high-z massive galaxies. We test this model and three other methods using idealized N-body simulations. The current model is physically justified and provides more accurate predictions than the earlier version, CuspCore I (Freundlich et al. 2020). The CuspCore model assumes an instantaneous change of potential, followed by a relaxation to a new Jeans equilibrium. The relaxation turns out to be violent relaxation during the first orbital period, followed by phase mixing. By tracing the energy diffusion dE=dU(r) iteratively, the model reproduces the simulated DM profiles with ~10% accuracy or better. A method based on adiabatic invariants shows similar precision for moderate mass change but underestimates the DM expansion for strong gas ejection. A method based on a simple empirical relation between DM and total mass ratios makes slightly inferior predictions. The crude assumption used in CuspCore I, of energy conservation for shells that encompass a fixed DM mass, turns out to underestimate the DM response, which can be partially remedied by introducing an alternative "energy" definition. Our model is being generalized to address the differential response of a multi-component system of stars and DM in the formation of DM-deficient galaxies.

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arXiv2022

Is the core-cusp problem a matter of perspective: Jeans Anisotropic Modeling against numerical simulations

Mock member stars for 28 dwarf galaxies are constructed from the cosmological Auriga simulation, which reflect the dynamical status of realistic stellar tracers. The axis-symmetric Jeans Anisotropic Multi-Gaussian Expansion (JAM) modeling is applied to 6,000 star particles for each system, to recover the underlying matter distribution. The stellar or dark matter component individually is poorly recovered, but the total profile is constrained more reasonably. The mass within the half-mass radius of tracers is recovered the tightest, and the mass between 200 and 300 pc, $M(200-300\mathrm{pc})$, is constrained ensemble unbiasedly, with a scatter of 0.167 dex. If using 2,000 particles and only line-of-sight velocities with typical errors, the scatter in $M(200-300\mathrm{pc})$ is increased by $\sim$50%. Quiescent Sagittarius dSph-like systems and star-forming systems with strong outflows show distinct features, with $M(200-300\mathrm{pc})$ mostly under-estimated for the former, and likely over-estimated for the latter. The biases correlate with the dynamical status, which is a result of contraction motions due to tidal effects in quiescent systems or galactic winds in star-forming systems, driving them out of equilibrium. After including Gaia DR3 proper motion errors, we find proper motions can be as useful as line-of-sight velocities for nearby systems at $<\sim$60 kpc. By extrapolating the actual density profiles and the dynamical constraints down to scales below the resolution, we find the mass within 150 pc can be constrained ensemble unbiasedly, with a scatter of $\sim$0.255 dex. In the end, we show that the contraction of member stars in nearby systems is detectable based on Gaia DR3 proper motion errors.

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