The changing interstellar medium of massive elliptical galaxies and cosmic evolution of radio galaxies and quasars

The recently discovered apparent dramatic expansion in the effective radii of massive elliptical galaxies from   z ≃ 2  to ≃0.1 has been interpreted in terms of either galaxy mergers or the rapid loss of cold gas due to active galactic nuclei (AGN) feedback. In examining the latter case, we have quantified the extent of the expansion, which is uncertain observationally, in terms of the star formation parameters and time of the expulsion of the cold gas. In either case, the large global decrease in stellar density should translate into a major drop in the interstellar medium density and pressure with cosmic epoch. These cosmological changes are expected to have a major influence on the gas accretion mode, which will shift from 'cold' thin disc accretion at high redshifts towards 'hot' Bondi fed Advection Dominated Accretion Flow (ADAF) accretion at low redshifts. The decline of angular momentum inflow would then lead to a spin down of the black hole, for which we have calculated more precise time-scales; a value of about 0.2 Gyr is typical for a  10⁹ M_⊙  central black hole. These results have implications for the different cosmological evolutionary patterns found for the luminosity functions of powerful and weak radio galaxies.     

Contribution of galaxies to the background hydrogen-ionizing flux

We estimate the evolution of the contribution of galaxies to the cosmic background flux at 912 Å by means of a semi-analytic model of galaxy formation and evolution. Such modelling has been quite successful in reproducing the optical properties of galaxies. We assume that high-redshift damped Lyman α systems are the progenitors of present-day galaxies, and we design a series of models that are consistent with the evolution of cosmic comoving emissivities in the available near-infrared, optical, ultraviolet and far-infrared bands along with the evolution of the neutral hydrogen content and average metallicity of damped Lyman α systems. We use these models to compute the galactic contribution to the Lyman-limit emissivity and background flux for 0 ≃  z  ≤ 4. We take into account the absorption of Lyman-limit photons by H  I and dust in the interstellar medium of the galaxies. We find that the background Lyman-limit flux due to galaxies might dominate (or be comparable to) the contribution from quasars at almost all redshifts if the absorption by H  I in the interstellar medium is neglected. Such H  I absorption would result in a severe diminishing of this flux — by almost three orders of magnitude at high redshifts and by one to two orders at z  ≃ 0. Though the resulting galaxy flux is completely negligible at high redshifts, it is comparable to the quasar flux at z  ≃ 0.     

High-redshift voids in the excursion set formalism

Voids are a dominant feature of the low-redshift galaxy distribution. Several recent surveys have found evidence for the existence of large-scale structure at high redshifts as well. We present analytic estimates of galaxy void sizes at redshifts   z ∼ 5–10  using the excursion set formalism. We find that recent narrow-band surveys at   z ∼ 5–6.5  should find voids with characteristic scales of roughly 20 comoving Mpc and maximum diameters approaching 40 Mpc. This is consistent with existing surveys, but a precise comparison is difficult because of the relatively small volumes probed so far. At   z ∼ 7–10  , we expect characteristic void scales of ∼14–20 comoving Mpc assuming that all galaxies within dark matter haloes more massive than  10¹⁰ M_⊙  are observable. We find that these characteristic scales are similar to the sizes of empty regions resulting from purely random fluctuations in the galaxy counts. As a result, true large-scale structure will be difficult to observe at   z ∼ 7–10  , unless galaxies in haloes with masses  ≲10⁹ M_⊙  are visible. Galaxy surveys must be deep and only the largest voids will provide meaningful information. Our model provides a convenient picture for estimating the 'worst-case' effects of cosmic variance on high-redshift galaxy surveys with limited volumes.     

On the galaxy stellar mass function, the mass–metallicity relation and the implied baryonic mass function

A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ω_b= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α₂≃−1.6  . At masses below  ∼10^8.5 M_⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α₂≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼10¹¹ M_⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.     

Ages of elliptical galaxies: single- versus multi-population interpretation

New calibrations of spectrophotometric indices of elliptical galaxies as functions of spectrophotometric indices are presented, permitting estimates of mean stellar population ages and metallicities. These calibrations are based on evolutionary models including a two-phase interstellar medium, infall and a galactic wind. Free parameters were fixed by requiring that models reproduce the mean trend of data in the colour–magnitude diagram as well as in the plane of indices  Hβ–Mg₂  and  Mg₂–〈Fe〉  . To improve the location of faint ellipticals  ( M _B > −20)  in the  Hβ–Mg₂  diagram, downsizing was introduced. An application of our calibrations to a sample of ellipticals and a comparison with results derived from single stellar population models are given. Our models indicate that mean population ages span an interval of 7–12 Gyr and are correlated with metallicities, which range from approximately half up to three times solar.     

The SCUBA Half Degree Extragalactic Survey (SHADES) – IX. The environment, mass and redshift dependence of star formation

We present a comparison between the SCUBA (Submillimetre Common User Bolometer Array) Half Degree Extragalactic Survey (SHADES) at 450 and  850 μm  in the Lockman Hole East with a deep Spitzer Space Telescope survey at  3.6–24 μm  conducted in guaranteed time. Using stacking analyses we demonstrate a striking correspondence between the galaxies contributing the submm extragalactic background light, with those likely to dominate the backgrounds at Spitzer wavelengths. Using a combination BRIzK plus Spitzer photometric redshifts, we show that at least a third of the Spitzer -identified submm galaxies at  1 < z < 1.5  appear to reside in overdensities when the density field is smoothed at 0.5–2 Mpc comoving diameters, supporting the high-redshift reversal of the local star formation–galaxy density relation. We derive the dust-shrouded cosmic star formation history of galaxies as a function of assembled stellar masses. For model stellar masses  <10¹¹ M_⊙  , this peaks at lower redshifts than the ostensible   z ∼ 2.2  maximum for submm point sources, adding to the growing consensus for 'downsizing' in star formation. Our surveys are also consistent with 'downsizing' in mass assembly. Both the mean star formation rates  〈d M _*/d t 〉  and specific star formation rates  〈(1/ M _*) d M _*/d t 〉  are in striking disagreement with some semi-analytic predictions from the Millenium Simulation. The discrepancy could either be resolved with a top-heavy initial mass function, or a significant component of the submm flux heated by the interstellar radiation field.     

Lyman break galaxies at z= 4–6 in cosmological smoothed particle hydrodynamics simulations

We perform a spectrophotometric analysis of galaxies at redshifts z = 4–6 in cosmological smoothed particle hydrodynamics simulations of a Λ cold dark matter universe. Our models include radiative cooling and heating by a uniform ultraviolet (UV) background, star formation, supernova feedback, and a phenomenological model for galactic winds. Analysing a series of simulations of varying box size and particle number allows us to isolate the impact of numerical resolution on our results. Specifically, we determine the luminosity functions in B , V , R , i ' and z ' filters, and compare the results with observational surveys of Lyman break galaxies (LBGs) performed with the Subaru telescope and the Hubble Space Telescope . We find that the simulated galaxies have UV colours consistent with observations and fall in the expected region of the colour–colour diagrams used by the Subaru group. The stellar masses of the most massive galaxies in our largest simulation increase their stellar mass from   M _★∼ 10¹¹ M_⊙  at z = 6 to   M _★∼ 10^11.7 M_⊙  at z = 3. Assuming a uniform extinction of E ( B − V ) = 0.15, we also find reasonable agreement between simulations and observations in the space density of UV bright galaxies at z = 3–6, down to the magnitude limit of each survey. For the same moderate extinction level of E ( B − V ) ∼ 0.15, the simulated luminosity functions match observational data, but have a steep faint-end slope with α∼−2.0. We discuss the implications of the steep faint-end slope found in the simulations. Our results confirm the generic conclusion from earlier numerical studies that UV bright LBGs at z ≥ 3 are the most massive galaxies with E ( B − V ) ∼ 0.15 at each epoch.     

Further constraints on the evolution of Ks-selected galaxies in the GOODS/CDFS field

We have selected and analysed the properties of a sample of  2905 K_s < 21.5  galaxies in  ∼131 arcmin²  of the Great Observatories Origins Deep Survey (GOODS) Chandra Deep Field South (CDFS), to obtain further constraints on the evolution of K_s -selected galaxies with respect to the results already obtained in previous studies. We made use of the public deep multiwavelength imaging from the optical B through the infrared (IR) 4.5-μm bands, in conjunction with available spectroscopic and COMBO17 data in the CDFS, to construct an optimized redshift catalogue for our galaxy sample. We computed the K_s -band luminosity function and determined that its characteristic magnitude has a substantial brightening and a decreasing total density from   z = 0  to  〈 z 〉= 2.5  . We also analysed the colours and number density evolution of galaxies with different stellar masses. Within our sample, and in contrast to what is observed for less massive systems, the vast majority (∼85–90 per cent) of the most massive  ( M > 2.5 × 10¹¹ M_⊙)  local galaxies appear to be in place before redshift   z ∼ 1  . Around 65–70 per cent of the total assemble between redshifts   z = 1  and 3 and most of them display extremely red colours, suggesting that plausible star formation in these very massive systems should mainly proceed in obscured, short-time-scale bursts. The remaining fraction (up to ∼20 per cent) could be in place at even higher redshifts   z = 3–4  , pushing the first epoch of formation of massive galaxies beyond the limits of current near-IR surveys.     

The galaxy environment of a quasar at z= 1.226: a possible cluster merger

We have conducted ultra-deep optical and deep near-infrared observations of a field around the z =1.226 radio-quiet quasar 104420.8+055739 from the Clowes–Campusano LQG of 18 quasars at z ∼1.3, in search of associated galaxy clustering. Galaxies at these redshifts are distinguished by their extremely red colours, with I − K >3.75, and we find a factor ∼11 overdensity of such galaxies in a 2.25×2.25 arcmin² field centred on the quasar. In particular, we find 15–18 galaxies that have colours consistent with being a population of passively evolving massive ellipticals at the quasar redshift. They form 'fingers' in the V − K K , I − K K colour–magnitude plots at V − K ≃6.9, I − K ≃4.3 comparable to the red sequences observed in other z ≃1.2 clusters. We find suggestive evidence for substructure among the red sequence galaxies in the K image, in the form of two compact groups, 40 arcsec to the north, and 60 arcsec to the south-east of the quasar. An examination of the wider optical images indicates that this substructure is significant, and that the clustering extends to form a large-scale structure 2–3  h ⁻¹ Mpc across. We find evidence for a high (≳50 per cent) fraction of blue galaxies in this system, in the form of 15–20 'red outlier' galaxies with I − K >3.75 and V − I <2.00, which we suggest are dusty, star-forming galaxies at the quasar redshift. Within 30 arcsec of the quasar we find a concentration of blue ( V − I <1) galaxies in a band that bisects the two groups of red sequence galaxies. This band of blue galaxies is presumed to correspond to a region of enhanced star formation. We explain this distribution of galaxies as the early stages of a cluster merger which has triggered both the star formation and the quasar.     

Towards a precision cosmology from starburst galaxies at z > 2

This work investigates the use of a well-known empirical correlation between the velocity dispersion, metallicity and luminosity in Hβ of nearby H  ii galaxies to measure the distances to H  ii -like starburst galaxies at high redshifts. This correlation is applied to a sample of 15 starburst galaxies with redshifts between   z = 2.17  and   z = 3.39  to constrain  Ω_m  , using data available from the literature. A best-fitting value of  Ω_m= 0.21^+0.30_−0.12  in a Λ-dominated universe and of  Ω_m= 0.11^+0.37_−0.19  in an open universe is obtained. A detailed analysis of systematic errors, their causes and their effects on the values derived for the distance moduli and  Ω_m  is carried out. A discussion of how future work will improve constraints on  Ω_m  by reducing the errors is also presented.     

The imprint of cosmic reionization on galaxy clustering

We consider the effect of reionization on the clustering properties of galaxy samples at intermediate redshifts ( z ∼ 0.3–5.5). Current models for the reionization of intergalactic hydrogen predict that overdense regions will be reionized early, thus delaying the build-up of stellar mass in the progenitors of massive lower redshift galaxies. As a result, the stellar populations observed in intermediate-redshift galaxies are somewhat younger and hence brighter in overdense regions of the Universe. Galaxy surveys would therefore be sensitive to galaxies with a somewhat lower dark matter mass in overdense regions. The corresponding increase in the observed number density of galaxies can be parametrized as a galaxy bias due to reionization. We model this process using merger trees combined with a stellar synthesis code. Our model demonstrates that reionization has a significant effect on the clustering properties of galaxy samples that are selected based on their star formation properties. The bias correction in Lyman-break galaxies (including those in proposed baryonic oscillation surveys at z < 1) is at the level of 10–20 per cent for a halo mass of  10¹² M_⊙  , leading to corrections factors of 1.5–2 in the halo mass inferred from measurements of clustering length. The reionization of helium could also lead to a sharp increase in the amplitude of the galaxy correlation function at z ∼ 3. We find that the reionization bias is approximately independent of scale and halo mass. However, since the traditional galaxy bias is mass dependent, the reionization bias becomes relatively more important for lower mass systems. The correction to the bias due to reionization is very small in surveys of luminous red galaxies at z < 1.     

On the evolution of the black hole: spheroid mass ratio

We present the results of a study which uses the 3C RR sample of radio-loud active galactic nuclei to investigate the evolution of the black hole:spheroid mass ratio in the most massive early-type galaxies from  0 < z < 2  . Radio-loud unification is exploited to obtain virial (linewidth) black hole mass estimates from the 3C RR quasars, and stellar mass estimates from the 3C RR radio galaxies, thereby providing black hole and stellar mass estimates for a single population of early-type galaxies. At low redshift  ( z ≲ 1)  , the 3C RR sample is consistent with a black hole:spheroid mass ratio of   M _bh/ M _sph≃ 0.002  , in good agreement with that observed locally for quiescent galaxies of similar stellar mass  ( M _sph≃ 5 × 10¹¹ M_⊙)  . However, over the redshift interval  0 < z < 2  the 3C RR black hole:spheroid mass ratio is found to evolve as   M _bh/ M _sph∝ (1 + z )^2.07±0.76  , reaching   M _bh/ M _sph≃ 0.008  by redshift   z ≃ 2  . This evolution is found to be inconsistent with the local black hole:spheroid mass ratio remaining constant at a moderately significant level (98 per cent). If confirmed, the detection of evolution in the 3C RR black hole:spheroid mass ratio further strengthens the evidence that, at least for massive early-type galaxies, the growth of the central supermassive black hole may be completed before that of the host spheroid.     

Impact of cosmic rays on Population III star formation

We explore the implications of a possible cosmic-ray (CR) background generated during the first supernova explosions that end the brief lives of massive Population III stars. We show that such a CR background could have significantly influenced the cooling and collapse of primordial gas clouds in minihaloes around redshifts of   z ∼ 15–20  , provided the CR flux was sufficient to yield an ionization rate greater than about 10⁻¹⁹ s⁻¹ near the centre of the minihalo. The presence of CRs with energies  ≲10⁷  eV would indirectly enhance the molecular cooling in these regions, and we estimate that the resulting lower temperatures in these minihaloes would yield a characteristic stellar mass as low as  ∼10 M_⊙  . CRs have a less-pronounced effect on the cooling and collapse of primordial gas clouds inside more massive dark matter haloes with virial masses  ≳10⁸ M_⊙  at the later stages of cosmological structure formation around   z ∼ 10–15  . In these clouds, even without CR flux the molecular abundance is already sufficient to allow cooling to the floor set by the temperature of the cosmic microwave background.     

The ages of quasar host galaxies

We present the results of fitting deep off-nuclear optical spectra of radio-quiet quasars, radio-loud quasars and radio galaxies at z ≃0.2 with evolutionary synthesis models of galaxy evolution. Our aim was to determine the age of the dynamically dominant stellar populations in the host galaxies of these three classes of powerful active galactic nuclei (AGN). Some of our spectra display residual nuclear contamination at the shortest wavelengths, but the detailed quality of the fits longward of the 4000-Å break provides unequivocal proof, if further proof were needed, that quasars lie in massive galaxies with (at least at z ≃0.2) evolved stellar populations. By fitting a two-component model we have separated the very blue (starburst and/or AGN contamination) from the redder underlying spectral energy distribution, and find that the hosts of all three classes of AGN are dominated by old stars of age 8–14 Gyr. If the blue component is attributed to young stars, we find that, at most, 1 per cent of the visible baryonic mass of these galaxies is involved in star formation activity at the epoch of observation, at least over the region sampled by our spectroscopic observations. These results strongly support the conclusion reached by McLure et al. that the host galaxies of luminous quasars are massive ellipticals which have formed by the epoch of peak quasar activity at z ≃2.5.     

A sample of 6C radio sources designed to find objects at redshift z>4– III. Imaging and the radio galaxy K–z relation

In this paper, the third and final of a series, we present complete K -band imaging and some complementary I -band imaging of the filtered 6C* sample. We find no systematic differences between the K – z relation of 6C* radio galaxies and those from complete samples, so the near-infrared properties of luminous radio galaxies are not obviously biased by the additional 6C* radio selection criteria (steep spectral index and small angular size). The 6C* K – z data significantly improve delineation of the K – z relation for radio galaxies at high redshift ( z >2) . Accounting for non-stellar contamination, and for correlations between radio luminosity and stellar mass, we find little support for previous claims that the underlying scatter in the stellar luminosity of radio galaxies increases significantly at z >2 . In a particular spatially flat universe with a cosmological constant (Ω_M=0.3 and Ω_Λ=0.7) , the most luminous radio sources appear to be associated with galaxies with a luminosity distribution with a high mean (≈5  L *), and a low dispersion ( σ ∼0.5 mag) which formed their stars at epochs corresponding to z ≳2.5 . This result is in line with recent submillimetre studies of high-redshift radio galaxies and the inferred ages of extremely red objects from faint radio samples.     

Evolution of the u-band luminosity function from redshift 1.2 to 0

We produce and analyse u -band (  λ≈ 355  nm) luminosity functions (LFs) for the red and blue populations of galaxies using data from the Sloan Digital Sky Survey (SDSS) u -band Galaxy Survey ( u GS) and Deep Evolutionary Exploratory Probe 2 (DEEP2) survey. From a spectroscopic sample of 41 575 SDSS u GS galaxies and 24 561 DEEP2 galaxies, we produce colour magnitude diagrams and make use of the colour bimodality of galaxies to separate red and blue populations. LFs for eight redshift slices in the range  0.01 < z < 1.2  are determined using the  1/ V _max  method and fitted with Schechter functions showing that there is significant evolution in   M *  , with a brightening of 1.4 mag for the combined population. The integration of the Schechter functions yields the evolution in the u -band luminosity density (LD) out to   z ∼ 1  . By parametrizing the evolution as  ρ∝ (1 + z )^β  , we find that  β= 1.36 ± 0.2  for the combined populations and  β= 2.09 ± 0.2  for the blue population. By removing the contribution of the old stellar population to the u -band LD and correcting for dust attenuation, we estimate the evolution in the star formation rate (SFR) of the Universe to be  β_SFR= 2.5 ± 0.3  . Discrepancies between our result and higher evolution rates measured using the infrared and far-UV can be reconciled by considering possibilities such as an underestimated dust correction at high redshifts or evolution in the stellar initial mass function.     

Dry mergers: a crucial test for galaxy formation

We investigate the role that dry mergers play in the build-up of massive galaxies within the cold dark matter paradigm. Implementing an empirical shut-off mass scale for star formation, we find a nearly constant dry merger rate of  ∼6 × 10⁻⁵ Mpc⁻³ Gyr⁻¹  at   z ≤ 1  and a steep decline at larger z . Less than half of these mergers are between two galaxies that are morphologically classified as early-types, and the other half is mostly between an early- and late-type galaxy. Latter are prime candidates for the origin of tidal features around red elliptical galaxies. The introduction of a transition mass scale for star formation has a strong impact on the evolution of galaxies, allowing them to grow above a characteristic mass scale of   M _{*, c} ∼ 6.3 × 10¹⁰ M_⊙  by mergers only. As a consequence of this transition, we find that around   M _{*, c}   , the fraction of 1:1 mergers is enhanced with respect to unequal mass major mergers. This suggests that it is possible to detect the existence of a transition mass scale by measuring the relative contribution of equal mass mergers to unequal mass mergers as a function of galaxy mass. The evolution of the high-mass end of the luminosity function is mainly driven by dry mergers at low z . We however find that only 10–20 per cent of galaxies more massive than   M _{*, c}   experience dry major mergers within their last Gyr at any given redshift   z ≤ 1  .     

On the formation of massive galaxies: a simultaneous study of number density, size and intrinsic colour evolution in GOODS

The evolution of number density, size and intrinsic colour is determined for a volume-limited sample of visually classified early-type galaxies selected from the Hubble Space Telescope /Advanced Camera for Surveys images of the Great Observatories Origins Deep Survey (GOODS) North and South fields (version 2). The sample comprises 457 galaxies over 320 arcmin² with stellar masses above  3 × 10¹⁰ M_⊙  in the redshift range  0.4 < z < 1.2  . Our data allow a simultaneous study of number density, intrinsic colour distribution and size. We find that the most massive systems  (≳3 × 10¹¹ M_⊙)  do not show any appreciable change in comoving number density or size in our data. Furthermore, when including the results from 2dF galaxy redshift survey, we find that the number density of massive early-type galaxies is consistent with no evolution between   z = 1.2  and 0, i.e. over an epoch spanning more than half of the current age of the Universe. We find large discrepancies between the predictions of semi-analytic models. Massive galaxies show very homogeneous intrinsic colour distributions, with nearly flat radial colour gradients, but with a significant negative correlation between stellar mass and colour gradient, such that red cores appear predominantly in massive galaxies. The distribution of half-light radii – when compared to   z ∼ 0  and   z > 1  samples – is compatible with the predictions of semi-analytic models relating size evolution to the amount of dissipation during major mergers.     

The cataclysmic variable period gap: still there

We have measured central line strengths for a complete sample of early-type galaxies in the Fornax cluster, comprising 11 elliptical and 11 lenticular galaxies, more luminous than M _B  = −17. In contrast to the elliptical galaxies in the sample studied by González (and recently revisited by Trager) we find that the Fornax ellipticals follow the locus of galaxies of fixed age in Worthey's models and have metallicities varying from roughly solar to three times solar. The lenticular galaxies, however, exhibit a substantial spread to younger luminosity-weighted ages, indicating a more extended star formation history. We present measurements of the more sensitive indices: C4668 and Hγ_A; these confirm and reinforce the conclusions that the elliptical galaxies are coeval and that only the lenticular galaxies show symptoms of late star formation. The inferred difference in the age distribution between lenticular and elliptical galaxies is a robust conclusion as the models generate consistent relative ages using different age and metallicity indicators even though the absolute ages remain uncertain. The young luminosity-weighted ages of the S0s in the Fornax cluster are consistent with the recent discovery that the fraction of S0 galaxies in intermediate-redshift clusters is a factor of 2–3 lower than found locally, and suggest that a fraction of the cluster spiral galaxy population has evolved to quiescence in the 5-Gyr interval from z  = 0.5 to the present. Two of the faintest lenticular galaxies in our sample have blue continua and strong Balmer-line absorption, suggesting starbursts ≲2 Gyr ago. These may be the low-redshift analogues of the starburst or post-starburst galaxies seen in clusters at z  = 0.3, similar to the Hδ-strong galaxies in the Coma cluster.     

The host galaxy of a narrow-line Seyfert 1 galaxy, RE J1034+396, with X-ray quasi-periodic oscillations

Using simple stellar population synthesis, we model the bulge stellar contribution in the optical spectrum of a narrow-line Seyfert 1 galaxy, RE J1034+396. We find that its bulge stellar velocity dispersion is  67.7 ± 8 km s⁻¹  . The supermassive black hole (SMBH) mass is about  (1–4) × 10⁶ M_⊙  if it follows the well-known   M _BH–σ_*  relation found in quiescent galaxies. We also derive the SMBH mass from the Hβ second moment, which is consistent with that from its bulge stellar velocity dispersion. The SMBH mass of (1–4)  × 10⁶ M_⊙  implies that the X-ray quasi-periodic oscillation (QPO) of RE J1034+396 can be scaled to a high-frequency QPO at 27–108 Hz found in Galactic black hole binaries with a  10-M_⊙  black hole. With the mass distribution in different age stellar populations, we find that the mean specific star formation rate (SSFR) over the past 0.1 Gyr is  0.0163 ± 0.0011  Gyr⁻¹, the stellar mass in the logarithm is  10.155 ± 0.06  in units of solar mass and the current star formation rate is  0.23 ± 0.016 M_⊙ yr⁻¹  . For RE J1034+396, there is no relation between the Eddington ratio and the SSFR as suggested by Chen et al., despite a larger scatter in their relation. We also suggest that about 7.0 per cent of the total Hα luminosity and 50 per cent of the total [O  ii ] luminosity come from the star formation process.