SearcharxivSearch

arXiv subjects

Masao Mori

Publications and source records attributed to Masao Mori.

At least 19 recordsLinked to original sources

Formation of Parallel Stellar Streams through Encounters with Dark Matter Subhalos and Intermediate-Mass Black Holes

Dark matter subhalos and intermediate-mass black holes wandering in the Milky Way and the Andromeda galaxy are difficult to directly detect through electromagnetic observations, yet knowing their abundance is essential for understanding galaxy formation and evolution. We propose parallel stellar streams as dynamical imprints left on stellar streams by dark perturbers, including starless dark matter subhalos and wandering intermediate-mass black holes. We report that a single stream can split into two parallel structures after an encounter with a dark perturber. This scenario is supported by analytical modelling and N-body simulations. We also discuss how we can distinguish parallel stellar streams from other formation processes based on observables. We extend the theoretical picture of stream-subhalo interactions by showing that encounters with dark perturbers can generate density depletions perpendicular to the stream elongation, leading to parallel stellar stream morphologies beyond conventional gap-like signatures.

astro-ph.GA

The Characteristic Mass and Energy Conversion Efficiency in the Cusp-Core Transition of Dark Matter Haloes: Implications for Scaling Relations and Supernova feedbacks

Galaxies in the nearby Universe, particularly dwarf systems, exhibit inner mass profiles of dark matter haloes that systematically depart from canonical cold dark matter expectations, signalling an interplay between baryonic feedback and the collisionless halo. We update an analytical cusp-core transition model by incorporating the effect of supernova-driven mass loss. Adapting this model to SPARC galaxies, we measure the energy conversion efficiency epsilon, defined as the fraction of supernova feedback energy that is used to change the central dark-matter potential. We find epsilon ~ 0.01 for nearby SPARC galaxies. Building on these measurements, we compare the dynamical energy required for a cusp-core transformation with the feedback energy available over burst cycles and identify a cusp-core transition forbidden region on the halo-stellar mass plane where transformation cannot occur. Galaxies with halo masses from 10^8 to 10^11 M_sun lie outside the forbidden region, whereas ultra-faint dwarf galaxies < 10^8 M_sun, galaxy groups and clusters > 10^11 M_sun fall within it, consistent with their high central densities and the inefficiency of core formation at very low and very high masses. This approach also explains the observed diversity of inner density profiles in low-mass systems, showing that both the star formation rate and the energy conversion efficiency govern them, with the latter emerging as a key parameter setting the strength of the cusp-core transition. Beyond the cusp-core problem, our observationally inferred energy conversion efficiency provides a model independent benchmark that strongly constrains galaxy formation models.

astro-ph.GA

Cusp-to-Core Transition of Dark Matter Halos across Galaxy Mass Scales

We investigate the diversity of dark matter (DM) density profiles in a large sample of late-type galaxies from the SPARC database, with the goal of testing whether a cusp-to-core transition occurs across galaxy mass scales. We perform Bayesian fits to high-quality rotation curves using flexible halo models that allow for variations in the inner slopes of DM density profiles. We quantify the central dark matter structure using the surface density within the inner region of the halo, defined as $Σ_{\rm DM}(<0.01r_{V_{\rm max}})$, and compare the SPARC galaxies with Milky Way dwarf satellites as well as galaxy groups and clusters. Our results reveal significant diversity in the inner density slopes of SPARC galaxies, ranging from steep cusps to shallow cores, and show that many of them lie below the cuspy profiles predicted by the cold dark matter model, consistent with core-like structures. In contrast, both lower-mass dwarf galaxies and higher-mass galaxy clusters tend to follow the cuspy DM halos. These findings suggest that baryonic feedback may induce a cusp-to-core transition in Milky Way-mass galaxies, as predicted by hydrodynamical simulations. However, observational limitations and modeling uncertainties still prevent a definitive conclusion. This study provides new empirical insights into the halo mass-dependent nature of DM inner structures and the role of baryonic processes in shaping them.

astro-ph.GA

Collision frequency between dark matter subhaloes within Milky Way-like galaxies

In the standard cold dark matter (CDM) model, sub-galactic structures hierarchically collide and merge to build up larger structures. Mergers and collisions between dwarf galaxies and dark matter subhaloes (DMSHs) play an important role in the evolution and formation of structures within a massive galaxy. We investigate the collision frequency between DMSHs associated with a massive host galaxy such as the Milky Way. We analytically estimate the density distribution of DMSH pairs for the relative distance and relative velocity ($r_\mathrm{rel}$-$v_\mathrm{rel}$) and the distance from the centre of the host halo and relative velocity ($r$-$v_\mathrm{rel}$) planes, based on the distribution function of the host halo in the phase space. Then, we evaluate the collision frequencies of DMSHs by integrating the orbital evolution of DMSHs in Milky-Way-like host haloes selected from cosmological $N$-body simulations. The frequency of violent encounters, in which the relative distance of DMSHs is shorter than the sum of scale radii, is averaged as $2.1\times 10^2\,\mathrm{Gyr}^{-1}$. Since the time scale of violent encounters, $4.7\,\mathrm{Myr}$, is shorter than the dynamical time of the host halo, collisions between DMSHs occur frequently within the host halo. Although interactions between DMSHs produce pairs with higher relative velocities, the density distributions of all and colliding pairs between DMSHs provided by numerical results are approximately similar to those of the analytical model neglecting the interactions of DMSHs on $r_\mathrm{rel}$-$v_\mathrm{rel}$ plane for all pairs and $r$-$v_\mathrm{rel}$ plane for colliding pairs. We compare our results with observed colliding dwarf galaxies and provide insight into the abundance of DMSHs.

astro-ph.GA

Simultaneous Formation of the Andromeda Giant Southern Stream and the Substructures in the Andromeda Halo

We investigate a minor merger event in M31 that simultaneously forms the Andromeda Giant Southern Stream (AGSS), Eastern Extent (EE), North-Eastern Shelf (NES), and Western Shel (WS), offering a unified model for these substructures. By varying the scale radius and mass of the progenitor's dark matter halo (DMH), around the range predicted by the $Λ$CDM model, we successfully reproduce the spatial features of these substructures. Across the limited range of parameters considered in this study, our analysis shows that the spatial evolution of NES and WS is independent of the gravitational potential of the DMH associated with the progenitor, while a shallower potential shifts EE further north. The simulations clearly demonstrate that the progenitor with a DMH mass of $9\times10^9M_\odot$ colliding with M31 850 Myr ago could simultaneously form al thes esubstructures. The simulation results indicate that EE lies several 10kpc closer to us than the aligned Stream Cp, which is actually a metal-poor component of Stream C, whose farther distance suggests overlapping debris from distinct collision events, while both remain closely aligned in celestial coordinates. Furthermore, we predict the existence of a positive stream along the AGSS, characterized by positive line-of-sight velocities relative to M31, which complements an already observed negative stream exhibiting negative line-of-sight velocities. Finally, we propose that three objects, namely Stream B, a metal-rich component of Stream C known as Stream Cr, and EE, are components of the Andromeda Giant Southern Arc (AGSA) connected to the AGSS. Although the existence of the positive stream and a complete picture of AGSA have yet to be confirmed observationally, we anticipate that future spectroscopic observations and further advances in theoretical studies will verify their existence.

astro-ph.GA

The structure of the stellar halo of the Andromeda galaxy explored with the NB515 for Subaru/HSC. I.: New Insights on the stellar halo up to 120 kpc

We analyse the M31 halo and its substructure within a projected radius of 120 kpc using a combination of Subaru/HSC $\textit{NB515}$ and CFHT/MegaCam $\textit{g}$- \& $\textit{i}$-bands. We succeed in separating M31's halo stars from foreground contamination with $\sim$ 90 \% accuracy by using the surface gravity sensitive $\textit{NB515}$ filter. Based on the selected M31 halo stars, we discover three new substructures, which associate with the Giant Southern Stream (GSS) based on their photometric metallicity estimates. We also produce the distance and photometric metallicity estimates for the known substructures. While these quantities for the GSS are reproduced in our study, we find that the North-Western stream shows a steeper distance gradient than found in an earlier study, suggesting that it is likely to have formed in an orbit closer to the Milky Way. For two streams in the eastern halo (Stream C and D), we identify distance gradients that had not been resolved. Finally, we investigate the global halo photometric metallicity distribution and surface brightness profile using the $\textit{NB515}$-selected halo stars. We find that the surface brightness of the metal-poor and metal-rich halo populations, and the all population can be fitted to a power-law profile with an index of $α=-1.65\pm0.02$, $-2.82\pm0.01$, and $-2.44\pm0.01$, respectively. In contrast to the relative smoothness of the halo profile, its photometric metallicity distribution appears to be spatially non-uniform with nonmonotonic trends with radius, suggesting that the halo population had insufficient time to dynamically homogenize the accreted populations.

astro-ph.GA

Cosmological evolution of dark matter subhaloes under tidal stripping by growing Milky Way-like galaxies

We present the findings of a comprehensive and detailed analysis of merger tree data from ultra-high-resolution cosmological $N$-body simulations. The analysis, conducted with a particle mass resolution of $5 \times 10^3 h^{-1} M_{\odot}$ and a halo mass resolution of $10^7 h^{-1} M_{\odot}$, provides sufficient accuracy to suppress numerical artefacts. This study elucidates the dynamical evolution of subhaloes associated with the Milky Way-like host haloes. Unlike more massive dark matter haloes, which have been extensively studied, these subhaloes follow a distinct mass evolution pattern: an initial accretion phase, followed by a tidal stripping phase where mass is lost due to the tidal forces of the host halo. The transition from accretion to stripping, where subhaloes reach their maximum mass, occurs around a redshift of $z\simeq1$. Smaller subhaloes reach this point earlier, while larger ones do so later. Our analysis reveals that over 80 per cent of subhaloes have experienced mass loss, underscoring the universality of tidal stripping in subhalo evolution. Additionally, we derived the eccentricities and pericentre distances of subhalo orbits from the simulations and compare them with those of nearby satellite galaxies observed by the Gaia satellite. The results demonstrate a significant alignment between the orbital elements predicted by the cold dark matter model and the observed data, providing robust support for the model as a credible candidate for dark matter.

astro-ph.GA

A universal scaling relation incorporating the cusp-to-core transition of dark matter haloes

The dark matter haloes associated with galaxies have hitherto established strong correlations within a range of observed parameters, known as scaling relations of dark matter haloes. The origin of these scaling relations still contains significant ambiguities and requires comprehensive exploration for complete understanding. Utilising the correlation between the concentration and mass of dark matter haloes inferred from cosmological $N$-body simulations based on the cold dark matter paradigm ($c$-$M$ relation), we derive theoretical scaling relations among other physical quantities such as the surface mass density, the maximum circular velocity, and the scale radius of the dark matter halo. By comparing theoretical and observed scaling relations at various mass scales, it is found that the scaling relations observed in dwarf galaxies and galaxies originate in the $c$-$M$ relation of the dark matter halo. We predict that this theoretical scaling relation is also established in galaxy clusters. Moreover, we propose a novel theoretical scaling relation that incorporates the effects of the cusp-to-core transition, which is supposed to occur in cold dark matter haloes. Our discussion concludes with the exploration of potential observational verification of the cusp-to-core transition process in dark matter haloes.

astro-ph.GA

Novel Hydrodynamic Schemes Capturing Shocks and Contact Discontinuities and Comparison Study with Existing Methods

We present a new hydrodynamic scheme named Godunov Density-Independent Smoothed Particle Hydrodynamics (GDISPH), that can accurately handle shock waves and contact discontinuities without any manually tuned parameters. This is in contrast to the standard formulation of smoothed particle hydrodynamics (SSPH), which requires the parameters for an artificial viscosity term to handle the shocks and struggles to accurately handle the contact discontinuities due to unphysical repulsive forces, resulting in surface tension that disrupts pressure equilibrium and suppresses fluid instabilities. While Godunov SPH (GSPH) can handle the shocks without the parameters by using solutions from a Riemann solver, it still cannot fully handle the contact discontinuities. Density-Independent Smoothed Particle Hydrodynamics (DISPH), one of several schemes proposed to handle contact discontinuities more effectively than SSPH, demonstrates superior performance in our tests involving strong shocks and contact discontinuities. However, DISPH still requires the artificial viscosity term. We integrate the Riemann solver into DISPH in several ways, yielding some patterns of GDISPH. The results of standard tests such as the one-dimensional Riemann problem, pressure equilibrium, Sedov-Taylor, and Kelvin-Helmholtz tests are favourable to GDISPH Case 1 and GDISPH Case 2, as well as DISPH. We conclude that GDISPH Case 1 has an advantage over GDISPH Case 2, effectively handling shocks and contact discontinuities without the need for specific parameters or introducing any additional numerical diffusion.

astro-ph.IM

Transonic galactic wind model including stellar feedbacks and application to outflows in high/low-$z$ galaxies

Galactic winds play a crucial role in the ejection of the interstellar medium (ISM) into intergalactic space. This study presents a model that classifies possible transonic solutions of galactic winds in the gravitational potential of the dark matter halo and stellar component under spherically symmetric and steady assumptions. Our model includes injections of mass and energy resulting from supernovae feedback along a flow line. The mass flux in galactic winds is a critical factor in determining the acceleration process of the flow and revealing the impact of galactic winds on galaxy evolution. We apply the transonic galactic wind model to the observed outflow velocities of star-forming galaxies to estimate the mass flux. Dividing the mass flux by the star formation rate (SFR) yields the mass loading rate (and mass loading factor), which indicates the entrainment effect of the ISM by the hot gas flow. Our results demonstrate that the mass loading rate is inversely correlated with galaxy mass and SFR. In less massive galaxies (stellar mass $\sim 10^{7-8} M_\odot$), the mass loading rate exceeds unity, indicating effective ejection of the ISM into intergalactic space. However, in massive galaxies (stellar mass $\sim 10^{10-11} M_\odot$), the mass loading rate falls below unity, meaning that the mass flux cannot exceed the injected mass by supernovae, thus resulting in the ineffective ejection of the ISM.

astro-ph.GA

Frequency of the dark matter subhalo collisions and bifurcation sequence arising formation of dwarf galaxies

The cold dark matter (CDM) model predicts galaxies have 100 times more dark matter mass than stars. Nevertheless, recent observations report the existence of dark-matter-deficient galaxies with less dark matter than expected. To solve this problem, we investigate the physical processes of galaxy formation in head-on collisions between gas-containing dark matter subhaloes (DMSHs). Analytical estimation of the collision frequency between DMSHs associated with a massive host halo indicates that collisions frequently occur within 1/10th of the virial radius of the host halo, with a collision timescale of about 10 Myr, and the most frequent relative velocity increases with increasing radius. Using analytical models and numerical simulations, we show the bifurcation channel of the formation of dark-matter-dominated and dark-matter-deficient galaxies. In the case of low-velocity collisions, a dark-matter-dominated galaxy is formed by the merging of two DMSHs. In the case of moderate-velocity collisions, the two DMSHs penetrate each other. However the gas medium collides, and star formation begins as the gas density increases, forming a dwarf galaxy without dark matter at the collision surface. In the case of high-velocity collisions, shock-breakout occurs due to the shock waves generated at the collision surface reaching the gas surface, and no galaxy forms. For example, the simulation demonstrates that a pair of DMSHs with a mass of 10^9 Msun containing gas of 0.1 solar metallicity forms a dark-matter-deficient galaxy with a stellar mass of 10^7 Msun for a relative velocity of 200 km/s.

astro-ph.GA

Destruction of the central black hole gas reservoir through head-on galaxy collisions

A massive black hole exists in almost every galaxy. They occasionally radiate a vast amount of light by releasing gravitational energy of accreting gas, with a cumulative active period of only a few $10^8$ years, so-called the duty cycle of the Active Galactic Nuclei. Namely, many galaxies today host a starving massive black hole. Although galaxy collisions have been thought to enhance nucleus activity, the origin of the duty cycle, especially the shutdown process, is a still critical issue. Here we show that galaxy collisions are also capable of suppressing black hole fueling by using an analytic model and three-dimensional hydrodynamic simulations, applying the well-determined parameter sets for the galactic collision in the Andromeda galaxy. Our models demonstrate that a central collision of galaxies can strip the torus-shaped gas surrounding the massive black hole, the putative fueling source. The derived condition for switching-off the black hole fueling indicates that a significant fraction of currently bright nuclei can become inactive, reminiscent of fading/dying active nucleus phenomena associated with galaxy merging events. Galaxy collisions may therefore be responsible both for switching-off and turning-on the nucleus activity, depending on the collision orbit (head-on or far-off-centre).

astro-ph.GA

Discrimination of heavy elements originating from Pop III stars in z = 3 intergalactic medium

We investigate the distribution of metals in the cosmological volume at $z\sim3$, in particular, provided by massive population III (Pop III) stars using a cosmological $N$-body simulation in which a model of Pop III star formation is implemented. Owing to the simulation, we can choose minihaloes where Pop III star formation occurs at $z>10$ and obtain the spatial distribution of the metals at lower-redshifts. To evaluate the amount of heavy elements provided by Pop III stars, we consider metal yield of pair-instability or core-collapse supernovae (SNe) explosions of massive stars. By comparing our results to the Illustris-1 simulation, we find that heavy elements provided by Pop III stars often dominate those from galaxies in low density regions. The median value of the volume averaged metallicity is $Z\sim 10^{-4.5 - -2} Z_{\odot}$ at the regions. Spectroscopic observations with the next generation telescopes are expected to detect the metals imprinted on quasar spectra.

astro-ph.GA

Stellar Stream and Halo Structure in the Andromeda Galaxy From a Subaru/Hyper Suprime-Cam Survey

We present wide and deep photometry of the northwest part of the halo of the Andromeda galaxy (M31) using Hyper Suprime-Cam on the Subaru Telescope. The survey covers 9.2 deg$^{2}$ field in the $g$, $i$, and $NB515$ bands and shows a clear red giant branch (RGB) of M31's halo stars and a pronounced red clump (RC) feature. The spatial distribution of RC stars shows a prominent stream feature, the North Western (NW) Stream, and a diffuse substructure in the south part of our survey field. We estimate the distances based on the RC method and obtain $(m-M)$ = 24.63$\pm 0.191$(random)$\pm0.057$(systematic) and 24.29$\pm 0.211$(random)$\pm0.057$(systematic) mag for the NW stream and diffuse substructure, respectively, implying that the NW Stream is located behind M31, whereas the diffuse substructure is located in front. We also estimate line-of-sight distances along the NW Stream and find that the south part of the stream is $\sim$20 kpc closer to us relative to the north part. The distance to the NW Stream inferred from the isochrone fitting to the color-magnitude diagram favors the RC-based distance, but the TRGB-based distance estimated for $NB515$-selected RGB stars does not agree with it. The surface number density distribution of RC stars across the NW Stream is found to be approximately Gaussian with a FWHM of $\sim$25 arcmin (5.7 kpc), with a slight skew to the south-west side. That along the NW Stream shows a complicated structure including variations in number density and a significant gap in the stream.

astro-ph.GA

Systematic Identification of LAEs for Visible Exploration and Reionization Research Using Subaru HSC (SILVERRUSH). I. Program Strategy and Clustering Properties of ~2,000 Lya Emitters at z=6-7 over the 0.3-0.5 Gpc$^2$ Survey Area

We present the SILVERRUSH program strategy and clustering properties investigated with $\sim 2,000$ Ly$α$ emitters at $z=5.7$ and $6.6$ found in the early data of the Hyper Suprime-Cam (HSC) Subaru Strategic Program survey exploiting the carefully designed narrowband filters. We derive angular correlation functions with the unprecedentedly large samples of LAEs at $z=6-7$ over the large total area of $14-21$ deg$^2$ corresponding to $0.3-0.5$ comoving Gpc$^2$. We obtain the average large-scale bias values of $b_{\rm avg}=4.1\pm 0.2$ ($4.5\pm 0.6$) at $z=5.7$ ($z=6.6$) for $\gtrsim L^*$ LAEs, indicating the weak evolution of LAE clustering from $z=5.7$ to $6.6$. We compare the LAE clustering results with two independent theoretical models that suggest an increase of an LAE clustering signal by the patchy ionized bubbles at the epoch of reionization (EoR), and estimate the neutral hydrogen fraction to be $x_{\rm HI}=0.15^{+0.15}_{-0.15}$ at $z=6.6$. Based on the halo occupation distribution models, we find that the $\gtrsim L^*$ LAEs are hosted by the dark-matter halos with the average mass of $\log (\left < M_{\rm h} \right >/M_\odot) =11.1^{+0.2}_{-0.4}$ ($10.8^{+0.3}_{-0.5}$) at $z=5.7$ ($6.6$) with a Ly$α$ duty cycle of 1 % or less, where the results of $z=6.6$ LAEs may be slightly biased, due to the increase of the clustering signal at the EoR. Our clustering analysis reveals the low-mass nature of $\gtrsim L^*$ LAEs at $z=6-7$, and that these LAEs probably evolve into massive super-$L^*$ galaxies in the present-day universe.

astro-ph.GA

Polytropic transonic galactic outflows in a dark matter halo with a central black hole

Polytropic transonic solutions of spherically symmetric and steady galactic winds in the gravitational potential of a dark matter halo (DMH) with a supermassive black hole (SMBH) are studied. The solutions are classified in terms of their topological features, and the gravitational potential of the SMBH adds a new branch to the transonic solutions generated by the gravity of the DMH. The topological types of the transonic solutions depend on the mass distribution, the amount of supplied energy, the polytropic index $γ$, and the slope $α$ of the DMH mass distribution. When $α$ becomes larger than a critical value $α_\mathrm{c}$, the transonic solution types change dramatically. Further, our model predicts that it is possible for a slowly accelerating outflow to exist, even in quiescent galaxies with small $γ$. This slowly accelerating outflow differs from those considered in many of the previous studies focusing on supersonic outflows in active star-forming galaxies. In addition, our model indicates that outflows in active star-forming galaxies have only one transonic point in the inner region ($\sim$ 0.01 kpc). The locus of this transonic point does not strongly depend on $γ$. We apply the polytropic model incorporating mass flux supplied by stellar components to the Sombrero Galaxy, and conclude that it can reproduce the observed gas density and the temperature distribution well. This result differs significantly from the isothermal model, which requires an unrealistically large mass flux (Igarashi et al. 2014). Thus, we conclude that the polytropic model is more realistic than the isothermal model, and that the Sombrero Galaxy can have a slowly accelerating outflow.

astro-ph.GA

The nature of the progenitor of the M31 North-western stream: globular clusters as milestones of its orbit

We examine the nature, possible orbits and physical properties of the progenitor of the North-western stellar stream (NWS) in the halo of the Andromeda galaxy (M31). The progenitor is assumed to be an accreting dwarf galaxy with globular clusters (GCs). It is, in general, difficult to determine the progenitor's orbit precisely because of many necessary parameters. Recently, Veljanoski et al. 2014 reported five GCs whose positions and radial velocities suggest an association with the stream. We use this data to constrain the orbital motions of the progenitor using test-particle simulations. Our simulations split the orbit solutions into two branches according to whether the stream ends up in the foreground or in the background of M31. Upcoming observations that will determine the distance to the NWS will be able to reject one of the two branches. In either case, the solutions require that the pericentric radius of any possible orbit be over 2 kpc. We estimate the efficiency of the tidal disruption and confirm the consistency with the assumption for the progenitor being a dwarf galaxy. The progenitor requires the mass $\ga 2\times10^6 M_{\sun}$ and half-light radius $\ga 30$ pc. In addition, $N$-body simulations successfully reproduce the basic observed features of the NWS and the GCs' line-of-sight velocities.

astro-ph.GA

Universal dark halo scaling relation for the dwarf spheroidal satellites

Motivated by a recently found interesting property of the dark halo surface density within a radius, $r_{\rm max}$, giving the maximum circular velocity, $V_{\rm max}$, we investigate it for dark halos of the Milky Way's and Andromeda's dwarf satellites based on cosmological simulations. We select and analyze the simulated subhalos associated with Milky Way-sized dark halos and find that the values of their surface densities, $Σ_{V_{\rm max}}$, are in good agreement with those for the observed dwarf spheroidal satellites even without employing any fitting procedures. This implies that this surface density would not be largely affected by any baryonic feedbacks and thus universal. Moreover, all subhalos on the small scales of dwarf satellites are expected to obey the relation $Σ_{V_{\rm max}}\propto V_{\rm max}$, irrespective of differences in their orbital evolutions, host halo properties, and observed redshifts. Therefore, we find that the universal scaling relation for dark halos on dwarf galaxy mass scales surely exists and provides us important clues to understanding fundamental properties of dark halos. We also investigate orbital and dynamical evolutions of subhalos to understand the origin of this universal dark halo relation and find that most of subhalos evolve generally along the $r_{\rm max}\propto V_{\rm max}$ sequence, even though these subhalos have undergone different histories of mass assembly and tidal stripping. This sequence, therefore, should be the key feature to understand the nature of the universality of $Σ_{V_{\rm max}}$.

astro-ph.GA