Mass Fundamental Plane Research Articles

The impact of black hole scaling relation assumptions on the mass density of black holes

ABSTRACT We examine the effect of supermassive black hole (SMBH) mass scaling relation choice on the inferred SMBH mass population since redshift z ∼ 3. To make robust predictions for the gravitational wave background (GWB), we must have a solid understanding of the underlying SMBH demographics. Using the SDSS and 3D-HST + CANDELS surveys for 0 < z < 3, we evaluate the inferred SMBH masses from two SMBH–galaxy scaling relations: MBH–Mbulge and MBH–σ. Our SMBH mass functions come directly from stellar mass measurements for MBH–Mbulge, and indirectly from stellar mass and galaxy radius measurements along with the galaxy mass fundamental plane for MBH–σ. We find that there is a substantial difference in predictions especially for z > 1, and this difference increases out to z = 3. In particular, we find that using velocity dispersion predicts a greater number of SMBHs with masses greater than 109 M⊙. The GWB that pulsar timing arrays find evidence for is higher in amplitude than expected from GWB predictions which rely on high-redshift extrapolations of local SMBH mass–galaxy scaling relations. The difference in SMBH demographics resulting from different scaling relations may be the origin for the mismatch between the signal amplitude and predictions. Generally, our results suggest that a deeper understanding of the potential redshift evolution of these relations is needed if we are to draw significant insight from their predictions at z > 1.

A common origin for the fundamental plane of quiescent and star-forming galaxies in the EAGLE simulations

ABSTRACT We use the EAGLE cosmological simulations to perform a comprehensive and systematic analysis of the z = 0.1 fundamental plane (FP), the tight relation between galaxy size, mass, and velocity dispersion. We first measure the total mass and velocity dispersion (including both random and rotational motions) within the effective radius to show that simulated galaxies obey a total mass FP that is very close to the virial relation ($\lt 10{{\ \rm per\ cent}}$ deviation), indicating that the effects of non-homology are weak. When we instead use the stellar mass, we find a strong deviation from the virial plane, which is driven by variations in the dark matter content. The dark matter fraction is a smooth function of the size and stellar mass, and thereby sets the coefficients of the stellar mass FP without substantially increasing the scatter. Hence, both star-forming and quiescent galaxies obey the same FP, with equally low scatter ($0.02\,$dex). We employ simulations with a variable stellar initial mass function (IMF) to show that IMF variations have a modest additional effect on this FP. Moreover, when we use luminosity-weighted mock observations of the size and spatially integrated velocity dispersion, the inferred FP changes only slightly. However, the scatter increases significantly, due to the luminosity-weighting and line-of-sight projection of the velocity dispersions, and measurement uncertainties on the half-light radii. Importantly, we find significant differences between the simulated FP and observations, which likely reflects a systematic difference in the stellar mass distributions. Therefore, we suggest the stellar mass FP offers a simple test for cosmological simulations, requiring minimal post-processing of simulation data.

The SAMI–Fornax Dwarfs Survey – II. The Stellar Mass Fundamental Plane and the dark matter fraction of dwarf galaxies

ABSTRACT We explore the kinematic scaling relations of 38 dwarf galaxies in the Fornax Cluster using observations from the SAMI integral field spectrograph. We focus on the Fundamental Plane (FP), defined by the physical properties of the objects (scale length, surface brightness, and velocity dispersion) and the Stellar Mass (Fundamental) Plane, where surface brightness is replaced by stellar mass, and investigate their dynamical-to-stellar-mass ratio. We confirm earlier results that the Fornax dEs are significantly offset above the FP defined by massive, hot stellar systems. For the Stellar Mass (Fundamental) Plane, which shows much lower scatter, we find that young and old dwarf galaxies lie at about the same distance from the plane, all with comparable scatter. We introduce the perpendicular deviation of dwarf galaxies from the Stellar Mass Plane defined by giant early-types as a robust estimate of their DM fraction, and find that the faintest dwarfs are systematically offset above the plane, implying that they have a higher dark matter fraction. This result is confirmed when estimating the dynamical mass of our dEs using a virial mass estimator, tracing the onset of dark matter domination in low mass stellar systems. We find that the position of our galaxies on the Stellar Mass FP agrees with the galaxies in the Local Group. This seems to imply that the processes determining the position of dwarf galaxies on the FP depend on the environment in the same way, whether the galaxy is situated in the Local Group or in the Fornax Cluster.

Inferences on Relations between Distant Supermassive Black Holes and Their Hosts Complemented by the Galaxy Fundamental Plane

The realization of fundamental relations between supermassive black holes and their host galaxies would have profound implications in astrophysics. To add further context to studies of their coevolution, an investigation is carried out to gain insight as to whether quasars and their hosts at earlier epochs follow the local relation between black hole mass (M BH) and stellar velocity dispersion (σ *). We use 584 Sloan Digital Sky Survey quasars at 0.2 < z < 0.8 with black hole measurements and properties of their hosts from the Hyper Suprime-Cam Subaru Strategic Program. An inference of σ * is achieved for each based on the total stellar mass (M *) and size of the host galaxy by using the galaxy mass fundamental plane for inactive galaxies at similar redshifts. In agreement with past studies, quasars occupy elevated positions from the local M BH−σ * relation which can be considered as a flattening of the relation. Based on a simulated sample, we demonstrate that an evolving intrinsic M BH−σ * relation can match the observations. However, we hypothesize that these changes are simply a consequence of a nonevolving intrinsic relationship between M BH and M *. Reassuringly, there is evidence of migration onto the local M BH−σ * for galaxies that are either massive, quiescent or compact. Thus, the bulges of quasar hosts at high redshift are growing and likely to align onto the mass scaling relation with their black holes at later times.

The Fundamental Plane in the LEGA-C Survey: Unraveling the M/L Ratio Variations of Massive Star-forming and Quiescent Galaxies at z ∼ 0.8

Abstract We explore the connection between the kinematics, structures and stellar populations of massive galaxies at 0.6 &lt; z &lt; 1.0 using the fundamental plane (FP). Combining stellar kinematic data from the Large Early Galaxy Astrophysics Census (LEGA-C) survey with structural parameters measured from deep Hubble Space Telescope imaging, we obtain a sample of 1419 massive ( log ( M * / M ⊙ ) &gt; 10.5 ) galaxies that span a wide range in morphology, star formation activity, and environment, and therefore is representative of the massive galaxy population at z ∼ 0.8. We find that quiescent and star-forming galaxies occupy the parameter space of the g-band FP differently and thus have different distributions in the dynamical mass-to-light ratio (M dyn/L g ), largely owing to differences in the stellar age and recent star formation history, and to a lesser extent, the effects of dust attenuation. In contrast, we show that both star-forming and quiescent galaxies lie on the same mass FP at z ∼ 0.8, with a comparable level of intrinsic scatter about the plane. We examine the variation in M dyn/M * through the thickness of the mass FP, finding no significant residual correlations with stellar population properties, Sérsic index, or galaxy overdensity. Our results suggest that, at fixed size and velocity dispersion, the variations in M dyn/L g of massive galaxies reflect an approximately equal contribution of variations in M */L g , and variations in the dark matter fraction or initial mass function.

Tightly Coupled Morpho-kinematic Evolution for Massive Star-forming and Quiescent Galaxies across 7 Gyr of Cosmic Time

Abstract We use the Fundamental Plane (FP) to measure the redshift evolution of the dynamical mass-to-light ratio (M dyn/L) and the dynamical-to-stellar mass ratio (M dyn/M *). Although conventionally used to study the properties of early-type galaxies, we here obtain stellar kinematic measurements from the Large Early Galaxy Astrophysics Census (LEGA-C) Survey for a sample of ∼1400 massive ( ) galaxies at 0.6 &lt; z &lt; 1.0 that span a wide range in star formation activity. In line with previous studies, we find a strong evolution in M dyn/L g with redshift. In contrast, we find only a weak dependence of the mean value of M dyn/M * on the specific star formation rate, and a redshift evolution that likely is explained by systematics. Therefore, we demonstrate that star-forming and quiescent galaxies lie on the same, stable mass FP across 0 &lt; z &lt; 1, and that the decrease in M dyn/L g toward high redshift can be attributed entirely to evolution of the stellar populations. Moreover, we show that the growth of galaxies in size and mass is constrained to occur within the mass FP. Our results imply either minimal structural evolution in massive galaxies since z ∼ 1, or a tight coupling in the evolution of their morphological and dynamical properties, and establish the mass FP as a tool for studying galaxy evolution with low impact from progenitor bias.

A robust two-parameter description of the stellar profile of elliptical galaxies

Context. The stellar density profile of a galaxy is typically summarised with two numbers: the total stellar mass and half-light radius. The total mass of a galaxy, however, is not a well-defined quantity, due to the finite depth of photometric observations and the arbitrariness of the distinction between galaxy and diffuse intra-group light. This limits our ability to make accurate comparisons between models and observations. Aims. I wish to provide a more robust two-parameter description of the stellar density distribution of elliptical galaxies, in terms of quantities that can be measured unambiguously. Methods. I propose using the stellar mass enclosed within 10 kpc in projection, M*,10, and the mass-weighted stellar density slope within the same aperture, Γ*,10, for this purpose. I measured the distribution in M*,10 and Γ*,10 of a sample of elliptical galaxies from the Sloan Digital Sky Survey and the Galaxy And Mass Assembly survey, using photometry from the Hyper Suprime-Cam survey. I measured, at fixed (M*,10, Γ*,10), what the spread is in the galaxy surface brightness profile and central stellar velocity dispersion within the sample. As a first application, I then compared the observed M*,10 − Γ*,10 relation of elliptical galaxies with that of similarly selected galaxies in the EAGLE REFERENCE simulation. Results. The pair of values of (M*,10, Γ*,10) can be used to predict the stellar density profile in the inner 10 kpc of a galaxy with better than 20% accuracy. Similarly, M*,10 and Γ*,10 can be combined to obtain a proxy for stellar velocity dispersion that is at least as good as the stellar mass fundamental plane. The average stellar density slope of EAGLE elliptical galaxies matches that of observed ones at M*,10 = 1011 M⊙ well, but the EAGLE M*,10 − Γ*,10 relation is shallower and has a larger intrinsic scatter compared to observations. Conclusions. This new parameterisation of the stellar density profile of massive elliptical galaxies provides a more robust way of comparing results from different photometric surveys and from hydrodynamical simulations, with respect to a description based on total stellar mass and half-light radius.

The stellar mass Fundamental Plane: the virial relation and a very thin plane for slow rotators

ABSTRACT Early-type galaxies – slow and fast rotating ellipticals (E-SRs and E-FRs) and S0s/lenticulars – define a Fundamental Plane (FP) in the space of half-light radius Re, enclosed surface brightness Ie, and velocity dispersion σe. Since Ie and σe are distance-independent measurements, the thickness of the FP is often expressed in terms of the accuracy with which Ie and σe can be used to estimate sizes Re. We show that: (1) The thickness of the FP depends strongly on morphology. If the sample only includes E-SRs, then the observed scatter in Re is $\sim 16{{\ \rm per\ cent}}$, of which only $\sim 9{{\ \rm per\ cent}}$ is intrinsic. Removing galaxies with M* &amp;lt; 1011 M⊙ further reduces the observed scatter to $\sim 13{{\ \rm per\ cent}}$ ($\sim 4{{\ \rm per\ cent}}$ intrinsic). The observed scatter increases to $\sim 25{{\ \rm per\ cent}}$ usually quoted in the literature if E-FRs and S0s are added. If the FP is defined using the eigenvectors of the covariance matrix of the observables, then the E-SRs again define an exceptionally thin FP, with intrinsic scatter of only 5 per cent orthogonal to the plane. (2) The structure within the FP is most easily understood as arising from the fact that Ie and σe are nearly independent, whereas the Re−Ie and Re−σe correlations are nearly equal and opposite. (3) If the coefficients of the FP differ from those associated with the virial theorem the plane is said to be ‘tilted’. If we multiply Ie by the global stellar mass-to-light ratio M*/L and we account for non-homology across the population by using Sérsic photometry, then the resulting stellar mass FP is less tilted. Accounting self-consistently for M*/L gradients will change the tilt. The tilt we currently see suggests that the efficiency of turning baryons into stars increases and/or the dark matter fraction decreases as stellar surface brightness increases.

Stellar Velocity Dispersion of a Massive Quenching Galaxy at z = 4.01

Abstract We present the first stellar velocity dispersion measurement of a massive quenching galaxy at z = 4. The galaxy is first identified as a massive z ≥ 4 galaxy with suppressed star formation from photometric redshifts based on deep multiband data. A follow-up spectroscopic observation with MOSFIRE on Keck revealed strong multiple absorption features, which are identified as Balmer lines, giving a secure redshift of z = 4.01. This is the most distant quiescent galaxy known to date. Thanks to the high S/N of the spectrum, we are able to estimate the stellar velocity dispersion, , making a significant leap from the previous highest redshift measurement at z = 2.8. Interestingly, we find that the velocity dispersion is consistent with that of massive galaxies today, implying no significant evolution in velocity dispersion over the last 12 Gyr. Based on a stringent upper limit on its physical size from deep optical images (r eff &lt; 1.3 kpc), we find that its dynamical mass is consistent with the stellar mass inferred from photometry. Furthermore, the galaxy is located on the mass fundamental plane extrapolated from lower redshift galaxies. The observed no strong evolution in σ suggests that the mass in the core of massive galaxies does not evolve significantly, while most of the mass growth occurs in the outskirts of the galaxies, which also increases the size. This picture is consistent with a two-phase formation scenario in which mass and size growth is due to accretion in the outskirts of galaxies via mergers. Our results imply that the first phase may be completed as early as z ∼ 4.

Modeling Nearly Spherical Pure-bulge Galaxies with a Stellar Mass-to-light Ratio Gradient under the ΛCDM and MOND Paradigms. I. Methodology, Dynamical Stellar Mass, and Fundamental Mass Plane

Abstract We carry out spherical Jeans modeling of nearly round pure-bulge galaxies selected from the ATLAS3D sample. Our modeling allows for gradients in the stellar mass-to-light ratio (M ⋆/L) through analytic prescriptions parameterized with a “gradient strength” K introduced to accommodate any viable gradient. We use a generalized Osipkov–Merritt model for the velocity dispersion (VD) anisotropy. We produce Monte Carlo sets of models based on the stellar VD profiles under both the ΛCDM and MOND paradigms. Here, we describe the galaxy data, the empirical inputs, and the modeling procedures of obtaining the Monte Carlo sets. We then present the projected dynamical stellar mass, , within the effective radius R e, and the fundamental mass plane (FMP) as a function of K. We find the scaling of the K-dependent mass with respect to the ATLAS3D reported mass as: with a′ = −0.019 ± 0.012 and b′ = −0.18 ± 0.02 (ΛCDM), or a′ = −0.023 ± 0.014 and b′ = −0.23 ± 0.03 (MOND), for 0 ≤ K &lt; 1.5. The FMP has coefficients consistent with the virial expectation and only the zero-point scales with K. The median value of K for the ATLAS3D galaxies is . We perform a similar analysis of the much larger SDSS DR7 spectroscopic sample. In this case, only the VD within a single aperture is available, so we impose the additional requirement that the VD slope be similar to that in the ATLAS3D galaxies. Our analysis of the SDSS galaxies suggests a positive correlation of K with stellar mass.

Forming first-ranked early-type galaxies through hierarchical dissipationless merging

We have developed a computationally competitive N-body model of a previrialized aggregation of galaxies in a flat Lambda cold dark matter Universe to assess the role of the multiple mergers that take place during the formation stage of such systems in the configuration of the remnants assembled at their centres. An analysis of a suite of 48 simulations of low-mass forming groups (M-tot,M- (gr) similar to 10(13) h(-1)M(circle dot)) demonstrates that the gravitational dynamics involved in their hierarchical collapse is capable of creating realistic first-ranked galaxies without the aid of dissipative processes. Our simulations indicate that the brightest group galaxies (BGGs) constitute a distinct population from other group members, sketching a scenario in which the assembly path of these objects is dictated largely by the formation of their host system. We detect significant differences in the distribution of S ` ersic indices and total magnitudes, as well as a luminosity gap between BGGs and the next brightest galaxy that is positively correlated with the total luminosity of the parent group. Such gaps arise from both the grow of BGGs at the expense of lesser companions and the decrease in the relevance of secondranked objects in equal measure. This results in a dearth of intermediate-mass galaxies which explains the characteristic central dip detected in their luminosity functions in dynamically young galaxy aggregations. The fact that the basic global properties of our BGGs define a thin mass Fundamental Plane strikingly similar to that followed by giant early-type galaxies in the local Universe reinforces confidence in the results obtained.

THE STELLAR MASS FUNDAMENTAL PLANE AND COMPACT QUIESCENT GALAXIES AT z &lt; 0.6

ABSTRACT We examine the evolution of the relation between stellar mass surface density, velocity dispersion, and half-light radius—the stellar mass fundamental plane (MFP)—for quiescent galaxies at z &lt; 0.6. We measure the local relation from galaxies in the Sloan Digital Sky Survey and the intermediate redshift relation from ∼500 quiescent galaxies with stellar masses 10 ≲ log(M */M ⊙) ≲ 11.5. Nearly half of the quiescent galaxies in our intermediate redshift sample are compact. After accounting for important selection and systematic effects, the velocity dispersion distribution of galaxies at intermediate redshifts is similar to that of galaxies in the local universe. Galaxies at z &lt; 0.6 appear to be smaller (≲0.1 dex) than galaxies in the local sample. The orientation of the stellar MFP is independent of redshift for massive quiescent galaxies at z &lt; 0.6 and the zero-point evolves by ∼0.04 dex. Compact quiescent galaxies fall on the same relation as the extended objects. We confirm that compact quiescent galaxies are the tail of the size and mass distribution of the normal quiescent galaxy population.

The environmental dependence of the stellar mass fundamental plane of early-type galaxies

Aims. We investigate the environmental dependence of the stellar mass fundamental plane (FP$_*$) using the early-type galaxy sample from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). Methods. The FP$_*$ is calculated by replacing the luminosity in the fundamental plane (FP) with stellar mass. Based on the SDSS group catalog, we characterize the galaxy environment according to the mass of the host dark matter halo and the position in the halo. In halos with the same mass bin, the color distributions of central and satellite galaxies are different. Therefore, we calculate FP$_*$ coefficients of galaxies in different environments and compare them with those of the FP to study the contribution of the stellar population. Results. We find that coefficient $a$ of the FP$_*$ is systematically larger than that of the FP, but coefficient $b$ of the FP$_*$ is similar to the FP. Moreover, the environmental dependence of the FP$_*$ is similar to that of the FP. For central galaxies, FP$_*$ coefficients are significantly dependent on the halo mass. For satellite galaxies, the correlation between FP$_*$ coefficients and the halo mass is weak. Conclusions. We conclude that the tilt of the FP is not primarily driven by the stellar population.

A STELLAR VELOCITY DISPERSION FOR A STRONGLY LENSED, INTERMEDIATE-MASS QUIESCENT GALAXY AT z = 2.8

ABSTRACT Measuring stellar velocity dispersions of quiescent galaxies beyond z &sim; 2 ?> is observationally challenging. Such measurements require near-infrared spectra with a continuum detection of at least moderate signal to noise, often necessitating long integrations. In this paper, we present deep X-Shooter spectroscopy of one of only two known gravitationally lensed massive quiescent galaxies at z &gt; 2 ?> . This galaxy is quadruply imaged, with the brightest images magnified by a factor of ∼5. The total exposure time of our data is 9.8 hr on-source; however, the magnification, and the slit placement encompassing two images, provides a total equivalent exposure time of 215 hr. From this deep spectrum we measure a redshift of ( z spec = 2.756 &PlusMinus; 0.001 ?> ), making this one of the highest redshift quiescent galaxies that is spectroscopically confirmed. We simultaneously fit both the spectroscopic and photometric data to determine stellar population parameters and conclude that this galaxy is relatively young ( 560 &minus; 80 &plus; 100 Myr ?> ), of intermediate mass ( log M &ast; / M &CircleDot; = 10.59 &minus; 0.05 &plus; 0.04 ?> ), consistent with low dust content ( A V = 0.20 &minus; 0.20 &plus; 0.26 ?> ), and has quenched only relatively recently. This recent quenching is confirmed by strong Balmer absorption, particularly H &delta; ?> ( H &delta; A = 6.66 &minus; 0.92 &plus; 0.96 ?> ). Remarkably, this proves that at least some intermediate-mass galaxies have already quenched as early as z &sim; 2.8 ?> . Additionally, we have measured a velocity dispersion of ( &sgr; = 187 &PlusMinus; 43 km s &minus; 1 ?> ), making this the highest-redshift quiescent galaxy with a dispersion measurement. We confirm that this galaxy falls on the same mass fundamental plane (MFP) as galaxies at z = 2.2, consistent with little to no evolution in the MFP up to z = 2.8. Overall this galaxy is proof of the existence of intermediate-mass quenched galaxies in the distant universe, and that lensing is a powerful tool for determining their properties with improved accuracy.

New axes for the stellar mass fundamental plane

AbstractWe argue that the stellar velocity dispersion observed in an elliptical galaxy is a good proxy for the halo velocity dispersion. As dark matter halos are almost completely characterized by a single scale parameter, the stellar velocity dispersion tells us the virial radius of the halo and the mass contained within. This permits non-dimensionalizing of the stellar mass and effective radius axes of the stellar mass fundamental plane by the virial radius and halo mass, respectively.

ONE PLANE FOR ALL: MASSIVE STAR-FORMING AND QUIESCENT GALAXIES LIE ON THE SAME MASS FUNDAMENTAL PLANE ATz∼ 0 ANDz∼ 0.7

Scaling relations between galaxy structures and dynamics have been studied extensively for early and late-type galaxies, both in the local universe and at high redshifts. The abundant differences between the properties of disky and elliptical, or star-forming and quiescent, galaxies seem to be characteristic of the local Universe; such clear distinctions begin to disintegrate as observations of massive galaxies probe higher redshifts. In this Paper, we investigate the existence the mass fundamental plane of all massive galaxies ($\sigma\gtrsim$ 100 km/s). This work includes local galaxies (0.05<z<0.07) from the SDSS, in addition to 31 star-forming and 72 quiescent massive galaxies at intermediate redshift (z~0.7) with absorption line kinematics from deep Keck-DEIMOS spectra and structural parameters from HST imaging. In two parameter scaling relations, star-forming and quiescent galaxies differ structurally and dynamically. However, we show that massive star-forming and quiescent galaxies lie on nearly the same mass fundamental plane, or the relationship between stellar mass surface density, stellar velocity dispersion, and effective radius. The scatter in this relation (measured about $\log\sigma$) is low: 0.072 dex (0.055 dex intrinsic) at z~0 and 0.10 dex (0.08 dex intrinsic) at z~0.7. This three dimensional surface is not unique: virial relations, with or without a dependence on luminosity profile shapes, can connect galaxy structures and stellar dynamics with similar scatter. This result builds on the recent finding that mass fundamental plane has been stable for early-type galaxies since z~2 (Bezanson et al. 2013). As we now find this also holds for star-forming galaxies to z~0.7, this implies that these scaling relations of galaxies will be minimally susceptible to progenitor biases due to the evolving stellar populations, structures, and dynamics of galaxies through cosmic time.

A CALIBRATION OF THE STELLAR MASS FUNDAMENTAL PLANE ATz∼ 0.5 USING THE MICRO-LENSING-INDUCED FLUX RATIO ANOMALIES OF MACRO-LENSED QUASARS,,

We measure the stellar mass surface densities of early type galaxies by observing the micro-lensing of macro-lensed quasars caused by individual stars, including stellar remnants, brown dwarfs and red dwarfs too faint to produce photometric or spectroscopic signatures. Instead of observing multiple micro-lensing events in a single system, we combine single epoch X-ray snapshots of ten quadruple systems, and compare the measured relative magnifications for the images with those computed from macro-models. We use these to normalize a stellar mass fundamental plane constructed using a Salpeter IMF with a low mass cutoff of 0.1 solar mass and treat the zeropoint of the surface mass density as a free parameter. Our method measures the graininess of the gravitational potential produced by individual stars, in contrast to methods that decompose a smooth total gravitational potential into two smooth components, one stellar and one dark. We find the median likelihood value for the normalization factor F by which the Salpeter stellar masses must be multiplied is 1.23, with a one sigma confidence range, dominated by small number statistics, of 0.77 < F < 2.10

TIGHT CORRELATIONS BETWEEN MASSIVE GALAXY STRUCTURAL PROPERTIES AND DYNAMICS: THE MASS FUNDAMENTAL PLANE WAS IN PLACE BY z ∼ 2

The Fundamental Plane (FP) is an empirical relation between the size, surface brightness, and velocity dispersion of early-type galaxies. This relation has been studied extensively for early-type galaxies in the local universe to constrain galaxy formation mechanisms. The evolution of the zeropoint of this plane has been extended to high redshifts to study the luminosity evolution of massive galaxies, under the assumption of structural homology. In this work, we assess this assumption by replacing surface brightness with stellar mass density and present the evolution of the "mass FP" for massive, quiescent galaxies since z~2. By accounting for stellar populations, we thereby isolate and trace structural and dynamical evolution. Despite the observed dramatic evolution in the sizes and morphologies of massive galaxies since z~3, we find that quiescent galaxies lie on the mass FP out to z~2. In contrast with ~1.4 dex evolution in the luminosity FP, average residuals from the z~0 mass FP are less than ~0.15 dex since z~2. Assuming the Hyde & Bernardi (2009) mass FP slope, we find that this minimal offset scales as (1+z)^{-0.095+/-0.043}. This result lends credence to previous studies that derived luminosity evolution from the FP. Therefore, despite their compact sizes and suggestions that massive galaxies are more disk-like at z~2, the relationship between their dynamics and structural properties are consistent with local early-type galaxies. Finally, we find no strong evidence for a tilt of the mass FP relative to the Virial plane, but emphasize the need for full models including selection biases to fully investigate this issue.

The luminosity and stellar mass Fundamental Plane of early-type galaxies

From a sample of ~50000 early-type galaxies from the SDSS, we measured the traditional Fundamental Plane in four bands. We then replaced luminosity with stellar mass, and measured the "stellar mass" FP. The FP steepens slightly as one moves from shorter to longer wavelengths: the orthogonal fit has slope 1.40 in g and 1.47 in z. The FP is thinner at longer wavelengths: scatter is 0.062 dex in g, 0.054 dex in z. The scatter is larger at small galaxy sizes/masses; at large masses measurement errors account for essentially all of the observed scatter. The FP steepens further when luminosity is replaced with stellar mass, to slope ~ 1.6. The intrinsic scatter also reduces further, to 0.048 dex. Since color and stellar mass-to-light ratio are closely related, this explains why color can be thought of as the fourth FP parameter. However, the slope of the stellar mass FP remains shallower than the value of 2 associated with the virial theorem. This is because the ratio of dynamical to stellar mass increases at large masses as M_d^0.17. The face-on view of the stellar mass kappa-space suggests that there is an upper limit to the stellar density for a given dynamical mass, and this decreases at large masses: M_*/R_e^3 ~ M_d^-4/3. We also study how the estimated coefficients a and b of the FP are affected by other selection effects (e.g. excluding small sigma biases a high; excluding fainter L biases a low). These biases are seen in FPs which have no intrinsic curvature, so the observation that a and b scale with L and sigma is not, by itself, evidence that the Plane is warped. We show that the FP appears to curve sharply downwards at the small mass end, and more gradually downwards towards larger masses. Whereas the drop at small sizes is real, most of the latter effect is due to correlated errors.

A Supermassive Black Hole Fundamental Plane for Ellipticals

We obtain the coefficients of a new fundamental plane for supermassive black holes at the centers of elliptical galaxies, involving measured central black hole mass and photometric parameters that define the light distribution. The galaxies are tightly distributed around this mass fundamental plane, with improvement in the rms residual over those obtained from the MBH-σ and MBH-L relations. This implies a strong multidimensional link between central massive black hole formation and global photometric properties of elliptical galaxies, and provides an improved estimate of black hole mass from galaxy data.