Structural Scaling Relations Research Articles

The scaling relations of galaxies back in time: The road toward virialization

Context. The structural scaling relations (SSRs) of galaxies, that is, the observed correlations between effective radius, effective surface intensity, and velocity dispersion, are important tools for understanding how evolution proceeds. Aims. In this paper, we aim to demonstrate that the evolution of the SSRs back in time is governed by a combination of virial theorem (VT) and the relation L = L0′(t)σβ(t), where the parameters β and L0′ vary with time and from galaxy to galaxy. Methods. Using the WINGS database for the galaxies at redshift z = 0 and the Illustris-1 and IllustrisTNG databases of artificial galaxies, for the galaxies up to redshift z = 4, we analyse the SSRs back in time and, by means of simple algebraic expressions for L0′ and β (functions of time and other physical quantities), we derive the expected paths followed by galaxies in the various SSRs toward the distributions observed at z = 0. Results. The distribution of galaxies in the SSRs is ultimately related to the evolution in luminosity and velocity dispersion, which are empirically mirrored by the L = L0′(t)σβ(t) law. Furthermore, the β parameter works as a thermometer of the virialization of a galaxy. This parameter can assume either positive or negative values, and its absolute value attains high values when the galaxy is close to the virial condition, while it tends to zero when the galaxy is far from this condition. Conclusions. As the SSRs change with time, the method proposed in this paper allows us to decipher the temporal evolution of galaxies.

MaNGA galaxy properties – I. An extensive optical, mid-infrared photometric, and environmental catalogue

ABSTRACT We present an extensive catalogue of non-parametric structural properties derived from optical and mid-infrared imaging for 4585 galaxies from the MaNGA survey. DESI and Wide-field Infrared Survey Explorer (WISE) imaging are used to extract surface brightness profiles in the g, r, z, W1, W2 photometric bands. Our optical photometry takes advantage of the automated algorithm autoprof and probes surface brightnesses that typically reach below 29 mag arcsec−2 in the r-band, while our WISE photometry achieves 28 mag arcsec−2 in the W1-band. Neighbour density measures and central/satellite classifications are also provided for a large subsample of the MaNGA galaxies. Highlights of our analysis of galaxy light profiles include (i) an extensive comparison of galaxian structural properties that illustrates the robustness of non-parametric extraction of light profiles over parametric methods; (ii) the ubiquity of bimodal structural properties, suggesting the existence of galaxy families in multiple dimensions; and (iii) an appreciation that structural properties measured relative to total light, regardless of the fractional levels, are uncertain. We study galaxy scaling relations based on photometric parameters, and present detailed comparisons with literature and theory. Salient features of this analysis include the near-constancy of the slope and scatter of the size–luminosity and size–stellar mass relations for late-type galaxies with wavelength, and the saturation of central surface density, measured within 1 kpc, for elliptical galaxies with $M_* \gt 10.7\, {\rm M}_{\odot }$ (corresponding to $\Sigma _1 \simeq 10^{10}\, {\rm M}_{\odot }\, {\rm kpc}^{-2}$). The multiband photometry, environmental parameters, and structural scaling relations presented are useful constraints for stellar population and galaxy formation models.

The Intrinsic Scatter of Galaxy Scaling Relations

Abstract We present a compendium of disk galaxy scaling relations and a detailed characterization of their intrinsic scatter. Observed scaling relations are typically characterized by their slope, intercept, and scatter; however, these parameters are a mixture of observational errors and astrophysical processes. We introduce a novel Bayesian framework for computing the intrinsic scatter of scaling relations that accounts for nonlinear error propagation and covariant uncertainties. Bayesian intrinsic scatters are ∼25% more accurate than those obtained with a first-order classical method, which systematically underestimates the true intrinsic scatter. Structural galaxy scaling relations based on velocity (V 23.5), size (R 23.5), luminosity (L 23.5), color (g − z), central stellar surface density (Σ1), stellar mass (M *), dynamical mass (M dyn), stellar angular momentum (j *), and dynamical angular momentum (j dyn) are examined to demonstrate the power and importance of the Bayesian formalism. Our analysis is based on a diverse selection of over 1000 late-type galaxies from the Photometry and Rotation Curve Observations from Extragalactic Surveys compilation with deep optical photometry and extended rotation curves. We determine the tightest relation for each parameter by intrinsic orthogonal scatter, finding M * − V 23.5, R 23.5 − j *, and L 23.5 − j dyn to be especially tight. The scatter of the R 23.5 − L 23.5, V 23.5 − (g − z), and R 23.5 − j dyn relations is mostly intrinsic, making them ideal for galaxy formation and evolutionary studies. Our code to compute the Bayesian intrinsic scatter of any scaling relation is also presented. We quantify the correlated nature of many uncertainties in galaxy scaling relations and scrutinize the uncertain nature of disk inclination corrections and their effect on scatter estimates.

Conditions for galaxy quenching at 0.5 < z < 2.5 from CANDELS: compact cores and environment

We investigate two classes of conditions for galaxy quenching at 0.5 < z < 2.5 based on the structural scaling relations of galaxies in the five Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) fields: the formation of a compact core and the environment. We confirm that in the entire redshift range, massive quiescent galaxies (M* > 1010 M⊙) have much higher stellar mass surface densities within the central 1 kpc (Σ1) and smaller sizes than star-forming galaxies in the same stellar mass range. In addition, the quiescent fractions significantly increase with the increase of Σ1 regardless of whether galaxies are centrals or satellites. In contrast, we find that the overall lower-mass quiescent galaxies (M* <∼ 1010 M⊙) have slightly higher Σ1 and comparable sizes compared to star-forming galaxies of the same mass and at the same redshift. At z < 1.5, satellites have higher halo masses and larger quiescent fractions than those of centrals at a given Σ1 (stellar mass). Our findings indicate that the significant growth of the galaxy cores is closely related to the quenching of massive galaxies since z ∼ 2.5, while the environmental effect plays an important role in the quenching of low-mass galaxies at z ≲ 1.5.

EDGE: the mass–metallicity relation as a critical test of galaxy formation physics

ABSTRACT We introduce the ‘Engineering Dwarfs at Galaxy Formation’s Edge’ (EDGE) project to study the cosmological formation and evolution of the smallest galaxies in the Universe. In this first paper, we explore the effects of resolution and sub-grid physics on a single low-mass halo ($M_{\rm halo}=10^{9}{\, \rm M}_\odot$), simulated to redshift z = 0 at a mass and spatial resolution of $\sim 20{\, \rm M}_\odot$ and ∼3 pc. We consider different star formation prescriptions, supernova feedback strengths, and on-the-fly radiative transfer (RT). We show that RT changes the mode of galactic self-regulation at this halo mass, suppressing star formation by causing the interstellar and circumgalactic gas to remain predominantly warm (∼104 K) even before cosmic reionization. By contrast, without RT, star formation regulation occurs only through starbursts and their associated vigorous galactic outflows. In spite of this difference, the entire simulation suite (with the exception of models without any feedback) matches observed dwarf galaxy sizes, velocity dispersions, V-band magnitudes, and dynamical mass-to-light-ratios. This is because such structural scaling relations are predominantly set by the host dark matter halo, with the remaining model-to-model variation being smaller than the observational scatter. We find that only the stellar mass–metallicity relation differentiates the galaxy formation models. Explosive feedback ejects more metals from the dwarf, leading to a lower metallicity at a fixed stellar mass. We conclude that the stellar mass–metallicity relation of the very smallest galaxies provides a unique constraint on galaxy formation physics.

Numerical convergence of simulations of galaxy formation: the abundance and internal structure of cold dark matter haloes

ABSTRACT We study the impact of numerical parameters on the properties of cold dark matter haloes formed in collisionless cosmological simulations. We quantify convergence in the median spherically averaged circular velocity profiles for haloes of widely varying particle number, as well as in the statistics of their structural scaling relations and mass functions. In agreement with prior work focused on single haloes, our results suggest that cosmological simulations yield robust halo properties for a wide range of gravitational softening parameters, ϵ, provided: (1) ϵ is not larger than a ‘convergence radius’, rconv, which is dictated by two-body relaxation and determined by particle number, and (2) a sufficient number of time-steps are taken to accurately resolve particle orbits with short dynamical times. Provided these conditions are met, median circular velocity profiles converge to within ≈10 per cent for radii beyond which the local two-body relaxation time-scale exceeds the Hubble time by a factor $\kappa \equiv t_{\rm relax}/t_{\rm H}\rm{\,\, \buildrel\gt \over \sim \,\,}0.177$, with better convergence attained for higher κ. We provide analytic estimates of rconv that build on previous attempts in two ways: first, by highlighting its explicit (but weak) softening-dependence and, second, by providing a simpler criterion in which rconv is determined entirely by the mean inter-particle spacing, l, for example better than 10 per cent convergence in circular velocity for $r\rm{\,\, \buildrel\gt \over \sim \,\,}0.05\, l$. We show how these analytic criteria can be used to assess convergence in structural scaling relations for dark matter haloes as a function of their mass or maximum circular speed.

A dynamical view on stellar metallicity gradient diversity across the Hubble sequence with CALIFA

We analyze radial stellar metallicity and kinematic profiles out to 1Re in 244 CALIFA galaxies ranging from morphological type E to Sd, to study the evolutionary mechanisms of stellar population gradients. We find that linear metallicity gradients exhibit a clear correlation with galaxy morphological type - with early type galaxies showing the steepest gradients. We show that the metallicity gradients simply reflect the local mass-metallicity relation within a galaxy. This suggests that the radial stellar population distribution within a galaxys effective radius is primarily a result of the \emph{in-situ} local star formation history. In this simple picture, the dynamically derived stellar surface mass density gradient directly predicts the metallicity gradient of a galaxy. We show that this correlation and its scatter can be reproduced entirely by using independent empirical galaxy structural and chemical scaling relations. Using Schwarzschild dynamical models, we also explore the link between a galaxys local stellar populations and their orbital structures. We find that galaxies angular momentum and metallicity gradients show no obvious causal link. This suggests that metallicity gradients in the inner disk are not strongly shaped by radial migration, which is confirmed by the lack of correlation between the metallicity gradients and observable probes of radial migration in the galaxies, such as bars and spiral arms. Finally, we find that galaxies with positive metallicity gradients become increasingly common towards low mass and late morphological types - consistent with stellar feedback more efficiently modifying the baryon cycle in the central regions of these galaxies.

Evolution of the anti-truncated stellar profiles of S0 galaxies since z = 0.6 in the SHARDS survey

Context. Anti-truncated lenticular galaxies (Type-III S0s) present tight scaling relations between their surface brightness photometric and structural parameters. Although several evolutionary models have been proposed for the formation of these structures, the observations of Type-III S0 galaxies are usually limited to the local Universe. Aims. We aim to compare the properties of Type-III discs in a sample of S0 galaxies at 0.2 &lt; z &lt; 0.6 with those of the local Universe. In this paper, we study the evolution of the photometric and structural scaling relations measured in the rest-frame R-band with z and the possible differences between the rest-frame (B − R) colours of the inner and outer disc profiles. Methods. We make use of a sample of 14 Type-III E/S0–S0 galaxies at 0.2 &lt; z &lt; 0.6 from the GOODS-N field identified and characterised in a previous paper. We study whether or not the correlations found in local Type-III S0 galaxies were present ~6 Gyr ago. We analyse the distribution of the surface brightness characteristic parameters (Rbreak, μbreak, hi, ho, μ0,i and μ0,o) as a function of the stellar mass and look to see if there is a significant change with z. We also derive their rest-frame (B − R) colour profiles. Finally, we compare these results with the predictions from a grid of SSP models. Results. We find that the inner and outer scale-lengths of Type-III S0 galaxies at 0.4 &lt; z &lt; 0.6 follow compatible trends and scaling relations with those observed in local S0 galaxies as a function of the break radius, Rbreak. We do not detect any significant differences between the location of Rbreak between z ~ 0.6 and z ~ 0 for a fixed stellar mass of the object, whereas the surface brightness at the break radius μbreak is ~1.5 mag arcsec-2 dimmer in the local Universe than at z ~ 0.6 for a fixed stellar mass. We find no significant differences in the (B − R) colour between the inner and outer profiles of the Type-III S0 galaxies at 0.2 &lt; z &lt; 0.6. Conclusions. In contrast to Type-II (down-bending) profiles, the anti-truncated surface brightness profiles of S0 galaxies present compatible Rbreak values and scaling relations during the last 6 Gyr. This result and the similarity of the colours of the inner and outer discs point to a highly scalable and stable formation process, probably more related to gravitational and dynamical processes than to the evolution of stellar populations.

Crater 2: An Extremely Cold Dark Matter Halo

Abstract We present results from MMT/Hectochelle spectroscopy of 390 red giant candidate stars along the line of sight to the recently discovered Galactic satellite Crater 2. Modeling the joint distribution of stellar positions, velocities, and metallicities as a mixture of Crater 2 and Galactic foreground populations, we identify ∼62 members of Crater 2, for which we resolve a line-of-sight velocity dispersion of = km s−1 and a mean velocity of = km s−1 (solar rest frame). We also resolve a metallicity dispersion of = dex and a mean of = dex that is 0.28 ± 0.14 dex poorer than estimated from photometry. Despite Crater 2's relatively large size (projected halflight radius R h ∼ 1 kpc) and intermediate luminosity (M V ∼ −8), its velocity dispersion is the coldest that has been resolved for any dwarf galaxy. These properties make Crater 2 the most extreme low-density outlier in dynamical as well as structural scaling relations among the Milky Way’s dwarf spheroidals. Even so, under assumptions of dynamical equilibrium and negligible contamination by unresolved binary stars, the observed velocity distribution implies a gravitationally dominant dark matter halo, with a dynamical mass of M ⊙ and a mass-to-light ratio of enclosed within a radius of ∼1 kpc, where the equivalent circular velocity is km s−1.

The mass discrepancy acceleration relation in a ΛCDM context

Abstract The mass discrepancy acceleration relation (MDAR) describes the coupling between baryons and dark matter (DM) in galaxies: the ratio of total-to-baryonic mass at a given radius anticorrelates with the acceleration due to baryons. The MDAR has been seen as a challenge to the Λ cold dark matter (ΛCDM) galaxy formation model, while it can be explained by Modified Newtonian Dynamics. In this Letter, we show that the MDAR arises in a ΛCDM cosmology once observed galaxy scaling relations are taken into account. We build semi-empirical models based on ΛCDM haloes, with and without the inclusion of baryonic effects, coupled to empirically motivated structural relations. Our models can reproduce the MDAR: specifically, a mass-dependent density profile for DM haloes can fully account for the observed MDAR shape, while a universal profile shows a discrepancy with the MDAR of dwarf galaxies with M⋆ &amp;lt; 109.5 M⊙, a further indication suggesting the existence of DM cores. Additionally, we reproduce slope and normalization of the baryonic Tully–Fisher relation (BTFR) with 0.17 dex scatter. These results imply that in ΛCDM (i) the MDAR is driven by structural scaling relations of galaxies and DM density profile shapes, and (ii) the baryonic fractions determined by the BTFR are consistent with those inferred from abundance-matching studies.

Understanding the structural scaling relations of early-type galaxies

We use a large suite of hydrodynamical simulations of binary galaxy mergers to construct and calibrate a physical prescription for computing the effective radii and velocity dispersions of spheroids. We implement this prescription within a semi-analytic model embedded in merger trees extracted from the Bolshoi Lambda-CDM N-body simulation, accounting for spheroid growth via major and minor mergers as well as disk instabilities. We find that without disk instabilities, our model does not predict sufficient numbers of intermediate mass early-type galaxies in the local universe. Spheroids also form earlier in models with spheroid growth via disk instabilities. Our model correctly predicts the normalization, slope, and scatter of the low-redshift size-mass and Fundamental Plane relations for early type galaxies. It predicts a degree of curvature in the Faber-Jackson relation that is not seen in local observations, but this could be alleviated if higher mass spheroids have more bottom-heavy initial mass functions. The model also correctly predicts the observed strong evolution of the size-mass relation for spheroids out to higher redshifts, as well as the slower evolution in the normalization of the Faber-Jackson relation. We emphasize that these are genuine predictions of the model since it was tuned to match hydrodynamical simulations and not these observations.

Is the universe simpler than ΛCDM?

In the standard cosmological model, the Universe consists mainly of two invisible substances: vacuum energy with constant mass-density (where is a ‘cosmological constant’ originally proposed by Einstein and is Newton’s gravitational constant) and cold dark matter (CDM) with mass density that is currently . This ‘CDM’ model has the virtue of simplicity, enabling straightforward calculation of the formation and evolution of cosmic structure against the backdrop of cosmic expansion. Here, we review apparent discrepancies with observations on small galactic scales, which CDM must attribute to complexity in the baryon physics of galaxy formation. Yet, galaxies exhibit structural scaling relations that evoke simplicity, presenting a clear challenge for formation models. In particular, tracers of gravitational potentials dominated by dark matter show a correlation between orbital size, , and velocity, , that can be expressed most simply as a characteristic acceleration, kmspc cm s, perhaps motivating efforts to find a link between localised and global manifestations of the Universe’s dark components.

THE ACS FORNAX CLUSTER SURVEY. VI. THE NUCLEI OF EARLY-TYPE GALAXIES IN THE FORNAX CLUSTER

The Advanced Camera for Surveys (ACS) Fornax Cluster Survey is a Hubble Space Telescope program to image 43 early-type galaxies in the Fornax cluster, using the F475W and F850LP bandpasses of the ACS. We employ both 1D and 2D techniques to characterize the properties of the stellar nuclei in these galaxies, defined as the central "luminosity excesses" relative to a Sersic model fitted to the underlying host. We find 72+/-13% of our sample (31 galaxies) to be nucleated, with only three of the nuclei offset by more than 0.5" from their galaxy photocenter, and with the majority of nuclei having colors bluer than their hosts. The nuclei are observed to be larger, and brighter, than typical Fornax globular clusters, and to follow different structural scaling relations. A comparison of our results to those from the ACS Virgo Cluster Survey reveals striking similarities in the properties of the nuclei belonging to these different environments. We briefly review a variety of proposed formation models and conclude that, for the low-mass galaxies in our sample, the most important mechanism for nucleus growth is probably infall of star clusters through dynamical friction, while for higher mass galaxies, gas accretion triggered by mergers, accretions and tidal torques is likely to dominate, with the relative importance of these two processes varying smoothly as a function of galaxy mass. Some intermediate-mass galaxies in our sample show a complexity in their inner structure that may be the signature of "hybrid nuclei" that arose through parallel formation channels.

The GALEX view of theHerschelReference Survey

We present GALEX far-ultraviolet (FUV) and near-ultraviolet (NUV) as well as SDSS g, r, i photometry and structural parameters for the Herschel Reference Survey, a magnitude-, volume-limited sample of nearby galaxies in different environments. We use this unique dataset to investigate the ultraviolet (UV) structural scaling relations of nearby galaxies and to determine how the properties of the UV disk vary with atomic hydrogen content and environment. We find a clear change of slope in the stellar mass vs. effective surface brightness relation when moving from the optical to the UV, with more massive galaxies having brighter optical but fainter UV surface brightnesses than smaller systems. A similar change of slope is also seen in the radius vs. surface brightness relation. By comparing our observations with the predictions of a simple multi-zone chemical model of galaxy evolution, we show that these findings are a natural consequence of a much more efficient inside-out growth of the stellar disk in massive galaxies.

DEEP ABSORPTION LINE STUDIES OF QUIESCENT GALAXIES ATz∼ 2: THE DYNAMICAL-MASS–SIZE RELATION AND FIRST CONSTRAINTS ON THE FUNDAMENTAL PLANE

We present dynamical and structural scaling relations of quiescent galaxies at z = 2, including the dynamical-mass–size relation and the first constraints on the fundamental plane (FP). The backbone of the analysis is a new, very deep Very Large Telescope/X-shooter spectrum of a massive, compact, quiescent galaxy at z = 2.0389. We detect the continuum between 3700 and 22,000 Å and several strong absorption features (Balmer series, Ca H+K, G band) from which we derive a stellar velocity dispersion of 318 ± 53 km s−1. We perform detailed modeling of the continuum emission and line indices and derive strong simultaneous constraints on the age, metallicity, and stellar mass. The galaxy is a dusty (AV = 0.77+0.36−0.32) solar metallicity (log(Z/Z☉) = 0.02+0.20−0.41) post-starburst galaxy, with a mean-luminosity-weighted log(age/yr) of 8.9 ± 0.1. The galaxy formed the majority of its stars at z > 3 and currently has little or no ongoing star formation. We compile a sample of three other z ∼ 2 quiescent galaxies with measured velocity dispersions, two of which are also post-starburst like. Their dynamical-mass–size relation is offset significantly less than the stellar-mass–size relation from the local early-type relations, which we attribute to a lower central dark matter fraction. Recent cosmological merger simulations agree qualitatively with the data, but cannot fully account for the evolution in the dark matter fraction. The z ∼ 2 FP requires additional evolution beyond passive stellar aging to be in agreement with the local FP. The structural evolution predicted by the cosmological simulations is insufficient, suggesting that additional, possibly non-homologous, structural evolution is needed.

A deep view on the Virgo cluster core

In this study we investigate the optical photometric properties of early-type galaxies in the Virgo cluster core region, by analysing their location on the colour magnitude relation (CMR) and the structural scaling relations down to faint magnitudes, and by constructing the luminosity function to compare it with theoretical expectations. We visually select potential cluster members based on morphology and angular size, excluding spiral galaxies. A photometric analysis has been carried out for 295 galaxies, using surface brightness profile shape and colour as further criteria to identify probable background contaminants. 216 galaxies are considered to be certain or probable Virgo cluster members. Our study reveals 77 galaxies not catalogued in the VCC (with 13 of them already found in previous studies) that are very likely Virgo cluster members because they follow the Virgo CMR and exhibit low Sersic indices. Those galaxies reach -8.7 mag in V band. The CMR shows a clear change in slope from dEs to dSphs, while the scatter of the CMR in the dSph regime does not increase significantly. Our sample might, however, be somewhat biased towards redder colours. The scaling relations given by the dEs appear to be continued by the dSphs indicating a similar origin. The observed change in the CMR slope may mark the point at which gas loss prevented significant metal enrichment. The almost constant scatter around the CMR possibly indicates a short formation period, resulting in similar stellar populations. The luminosity function shows a Schechter function's faint end slope of -1.50\pm0.17, implying a lack of galaxies related to the expected number of low-mass dark matter haloes from theoretical models. Our findings could be explained by suppressed star formation in low-mass dark matter halos or by tidal disruption of dwarfs in the dense core region of the cluster.

The angular momentum of disc galaxies: implications for gas accretion, outflows, and dynamical friction

We combine constraints on the galaxy-dark matter connection with structural and dynamical scaling relations to investigate the angular momentum content of disc galaxies. For haloes with masses in the interval 10^{11.3} < M_vir/M_sun < 10^{12.7} we find that the galaxy spin parameters are independent of halo mass with <\lambda'_gal> = (J_gal/M_gal) / (\sqrt{2} R_vir V_vir) = 0.019^{+0.004}_{-0.003} (1sigma). This is significantly lower than for relaxed LCDM haloes, which have an average spin parameter <\lambda'_halo> = 0.031. The average ratio between the specific angular momentum of disk galaxies and their host dark matter haloes is therefore R_j = \lambda'_gal/\lambda'_halo = 0.61^{+0.13}_{-0.10}. This calls into question a standard assumption made in the majority of all (semi-analytical) models for (disc) galaxy formation, namely that R_j=1. Using simple disc formation models we show that it is particularly challenging to understand why R_j is independent of halo mass, while the galaxy formation efficiency (\epsilon_GF, proportional to the ratio of galaxy mass to halo mass) reveals a strong halo mass dependence. We argue that the empirical scaling relations between \epsilon_GF, R_j and halo mass require both feedback (i.e., galactic outflows) and angular momentum transfer from the baryons to the dark matter (i.e., dynamical friction). The efficiency of angular momentum loss need to decrease with increasing halo mass. Such a mass dependence may reflect a bias against forming stable discs in high mass, low spin haloes or a transition from cold-mode accretion in low mass haloes to hot-mode accretion at the massive end. However, current hydrodynamical simulations of galaxy formation, which should include these processes, seem unable to reproduce the empirical relation between \epsilon_GF and R_j. We conclude that the angular momentum build-up of galactic discs remains poorly understood.

Constraining the role of star cluster mergers in nuclear cluster formation: simulations confront integral-field data

We present observations and dynamical models of the stellar nuclear clusters (NCs) at the centres of NGC 4244 and M33. We then compare these to an extensive set of simulations testing the importance of purely stellar dynamical mergers on the formation and growth of NCs. Mergers of star clusters are able to produce a wide variety of observed properties, including densities, structural scaling relations, shapes (including the presence of young discs) and even rapid rotation. Nonetheless, difficulties remain, most notably that the second order kinematic moment V_rms = (V^2 + sigma^2)^(1/2) of the models is too centrally peaked to match observations. This can be remedied by the merger of star clusters onto a pre-existing nuclear disc, but the line-of-sight velocity V is still more slowly rising than in NGC 4244. Our results therefore suggest that purely stellar dynamical mergers cannot form NCs, and that gas dissipation is a necessary ingredient for at least ~50% of a NC's mass. The negative vertical anisotropy found in NGC 4244 however requires at least 10% of the mass to be accreted as stars, since gas dissipation and in situ star formation leads to positive vertical anisotropy.

The origin of the $\langle\mu_{\mathsf e}\rangle$-MB and Kormendy relations in dwarf elliptical galaxies

Aims. The present work is aimed at studying the distribution of galaxies of different types and luminosities along different structural scaling relations to see whether massive and dwarf ellipticals have been shaped by the same formation process. Methods. This exercise is done by comparing the distribution of Virgo cluster massive and dwarf ellipticals and star forming galaxies along the B band effective surface brightness and effective radius vs. absolute magnitude relations and the Kormendy relation to the predictions of models tracing the effects of ram-pressure stripping on disc galaxies entering the cluster environment and galaxy harassment. Results. Dwarf ellipticals might have been formed from low luminosity, late-type spirals that recently entered into the cluster and lost their gas because of a ram-pressure stripping event, stopping their star formation. The perturbations induced by the abrupt decrease of the star formation activity are sufficient to modify the structural properties of disc galaxies into those of dwarf ellipticals. Galaxy harassment induces a truncation of the disc and generally an increase of the effective surface brightness of the perturbed galaxies. The lack of dynamical simulations of perturbed galaxies spanning a wide range in luminosity prevents us from deriving any firm conclusion on a possible harassment-induced origin of the low surface brightness dwarf elliptical galaxy population inhabiting the Virgo cluster. Conclusions. Although the observed scaling relations are consistent with the idea that the distribution of elliptical galaxies along the mentioned scaling relation is due to a gradual variation with luminosity of the Sersic index n, the comparison with models indicates that dwarf ellipticals might have been formed by a totally different process to giant ellipticals.

Scaling relations and the fundamental line of the local group dwarf galaxies

We study the scaling relations between global properties of dwarf galaxies in the local group. In addition to quantifying the correlations between pairs of variables, we explore the 'shape' of the distribution of galaxies in log parameter space using standardized principal component analysis, the analysis is performed first in the 3D structural parameter space of stellar mass M * , internal velocity V and characteristic radius R* (or surface brightness μ*). It is then extended to a 4D space that includes a stellar population parameter such as metallicity Z or star formation rate M * . We find that the local group dwarfs basically define a one-parameter 'fundamental line' (FL), primarily driven by stellar mass, M * . A more detailed inspection reveals differences between the star formation properties of dwarf irregulars (dl's) and dwarf ellipticals (dE's), beyond the tendency of the latter to be more massive. In particular, the metallicities of dl's are typically lower by a factor of 3 at a given M * and they grow faster with increasing M * , showing a tighter FL in the 4D space for the dE's. The structural scaling relations of dl's resemble those of the more massive spirals, but the dl's have lower star formation rates for a given M. which also grow faster with increasing M * . On the other hand, the FL of the dE's departs from the fundamental plane of bigger ellipticals. While the one-parameter nature of the FL and the associated slopes of the scaling relations are consistent with the general predictions of supernova feedback from Dekel & Woo, the differences between the FL's of the dE's and the dl's remain a challenge and should serve as a guide for the secondary physical processes responsible for these two types.