Bivariate Luminosity Function Research Articles

The NIBLES bivariate luminosity–H I mass distribution function revised using Arecibo follow-up observations

We present a modified optical luminosity–H I mass bivariate luminosity function based on H I line observations from the Nançay Interstellar Baryons Legacy Extragalactic Survey (NIBLES), including data from our new, four times more sensitive follow-up H I line observations obtained with the Arecibo radio telescope. The follow-up observations were designed to probe the underlying H I mass distribution of the NIBLES galaxies that were undetected or marginally detected in H I at the Nançay Radio Telescope. Our total follow-up sample consists of 234 galaxies, and it spans the entire luminosity and color range of the parent NIBLES sample of 2600 nearby (900 < cz < 12 000 km s−1) SDSS galaxies. We incorporated the follow-up data into the bivariate analysis by scaling the NIBLES undetected fraction by an Arecibo-only distribution. We find the resulting increase in low H I mass-to-light ratio densities to be about 10% for the bins −1.0 ≤ log(MHI/M⊙/Lr/L⊙) ≤ −0.5, which produces an increased H I mass function (HIMF) low mass slope of α = −1.14 ± 0.07, being slightly shallower than the values of −1.35 ± 0.05 obtained by recent blind H I surveys. Applying the same correction to the optically corrected bivariate luminosity function from our previous paper produces a larger density increase of about 0.5 to 1 dex in the lowest H I mass-to-light ratio bins for a given luminosity while having a minimal effect on the resulting HIMF low mass slope, which still agrees with blind survey HIMFs. This indicates that while low H I-mass-to-light ratio galaxies do not contribute much to the one-dimensional HIMF, their inclusion has a significant impact on the densities in the two-dimensional distribution.

Constructing a multivariate distribution function with a vine copula: towards multivariate luminosity and mass functions

ABSTRACTThe need for a method to construct multidimensional distribution function is increasing recently, in the era of huge multiwavelength surveys. We have proposed a systematic method to build a bivariate luminosity or mass function of galaxies by using a copula. It allows us to construct a distribution function when only its marginal distributions are known, and we have to estimate the dependence structure from data. A typical example is the situation that we have univariate luminosity functions at some wavelengths for a survey, but the joint distribution is unknown. Main limitation of the copula method is that it is not easy to extend a joint function to higher dimensions (d > 2), except some special cases like multidimensional Gaussian. Even if we find such a multivariate analytic function in some fortunate case, it would often be inflexible and impractical. In this work, we show a systematic method to extend the copula method to unlimitedly higher dimensions by a vine copula. This is based on the pair-copula decomposition of a general multivariate distribution. We show how the vine copula construction is flexible and extendable. We also present an example of the construction of a stellar mass–atomic gas–molecular gas three-dimensional mass function. We demonstrate the maximum likelihood estimation of the best functional form for this function, as well as a proper model selection via vine copula.

Bivariate Luminosity Function of Galaxy Pairs

Abstract We measure the bivariate luminosity function (BLF) of galaxy pairs and use it to probe and characterize the galaxy–galaxy interaction between pair members. The galaxy pair sample is selected from the main galaxy sample of Sloan Digital Sky Survey and supplied with a significant number of redshifts from the LAMOST spectral and GAMA surveys. We find the BLFs depend on the projected distance d p between pair members. At large separation d p > 150 h −1 kpc, the BLF degenerates into a luminosity function of single galaxies, indicating few interactions between pair members. At 100 h −1 kpc ≤ d p ≤ 150 h −1 kpc, the BLF starts to show a correlation between pair members, in the sense that the shape of the conditional luminosity function (CLF) of one member galaxy starts to depend on the luminosity of the other member galaxy. Specifically, the CLF with a brighter companion has a steeper faint-end slope, which becomes even more significant at 50 h −1 kpc ≤ d p ≤ 100 h −1 kpc. This behavior is consistent with the scenario—and also is the observational evidence—that dynamic friction drives massive major merger pairs to merge more quickly. At close distance d p ≤ 50 h −1 kpc, aside from the merging timescale effect, the BLF also shows an overall brightening of ΔM r ≥ 0.04 mag, which reveals the enhanced star formation of the close-pair phase. By combining this with the statistical conclusion that the star formation rate of late-type galaxies in close pairs is enhanced at a level of about 40%, we further conclude that the average starburst timescale of close pairs is as long as 0.4 Gyr.

Bivariate luminosity-HI mass distribution function of galaxies based on the NIBLES survey

We present a new optical luminosity-HImass bivariate luminosity function (BLF) based on HIline observations from the Nançay Interstellar Baryons Legacy Extragalactic Survey (NIBLES). NIBLES sources lie within the local universe (900 ≤ cz ≤ 12 000 km s−1) and were chosen from SDSS DR5 such that the optical luminosity function was sampled as uniformly as possible. The HImass function (HIMF) derived from our raw-data BLF, which is based on HIdetections only, is consistent with the HIMFs derived from other optically selected surveys in that the low-mass slope is flatter than those derived from blind HIsurveys. However, spanning the entire luminosity range of NIBLES, we identify a highly consistent distribution of the HIgas mass to luminosity ratio (gas-to-light ratio) with a predictable progression in the meanMHI/Lrratio as a function ofLr. This consistency allows us to construct plausible gas-to-light ratio distributions for very low-luminosity bins which lie outside the NIBLES sample. We also identify a ∼10% decrease in detection fraction for galaxies fainter than log(Lr) = 9.25, consistent with the expected decrease due to distance and sensitivity effects. Accounting for these trends, we reconstruct plausible gas-to-light distributions spanning luminosity bins down to log(Lr) = 5.25, thus producing a corrected BLF. This corrected BLF is in good qualitative agreement with optical luminosity-HImass distributions from the ALFALFA survey and is able to accurately reproduce blind survey HIMFs, lending credibility that this two dimensional optical luminosity-HImass distribution is an accurate representation of the volume density distribution of galaxies in the local universe. We also note that our agreement with HIMFs from other surveys is dependent on accounting for all systematic differences such as selection method, Hubble constant and HIflux scale.

The bivariate luminosity and mass functions of the local HRS galaxy sample

Aims.We discuss the results of the relationships between theK-band and stellar mass, FIR luminosities, star formation rate, and the masses of the dust and gas of nearby galaxies computing the bivariateK-band-luminosity function (BLF) and bivariateK-band-mass function (BMF) of theHerschelReference Survey (HRS), a volume-limited sample with full wavelength coverage.Methods.We derive the BLFs and BMFs from theK-band and stellar mass, FIR luminosities, star formation rate, dust and gas masses cumulative distributions using a copula method, which is outlined in detail. The use of the computed bivariate taking into account the upper limits allows us to derive a more solid statistical ground for the relationship between the observed physical quantities.Results.The analysis shows that the behaviour of the morphological (optically selected) subsamples is quite different. A statistically meaningful result can be obtained over the whole HRS sample only from the relationship between theK-band and the stellar mass, while for the remaining physical quantities (dust and gas masses, far-infrared luminosity, and star formation rate), the analysis is distinct for late-type (LT) and early-type galaxies (ETG). However, the number of ETGs is small to perform a robust statistical analysis, and in most of the case results are discussed only for the LTG subsample. The luminosity and mass functions (LFs, MFs) of LTGs are generally dependent on theK-band and the various dependencies are discussed in detail. We are able to derive the corresponding LFs and MFs and compare them with those computed with other samples. Our statistical analysis allows us to characterise the HRS which, although non-homogeneously selected and partially biased towards low IR luminosities, may be considered as representative of the local LT galaxy population.

Galaxy And Mass Assembly (GAMA): bivariate functions of Hα star-forming galaxies

We present bivariate luminosity and stellar mass functions of H$\alpha$ star forming galaxies drawn from the Galaxy And Mass Assembly (GAMA) survey. While optically deep spectroscopic observations of GAMA over a wide sky area enable the detection of a large number of $0.001<{SFR}_{H\alpha}$ (M$_{\odot}$ yr$^{-1}$)$<100$ galaxies, the requirement for an H$\alpha$ detection in targets selected from an $r$-band magnitude limited survey leads to an incompleteness due to missing optically faint star forming galaxies. Using $z<0.1$ bivariate distributions as a reference we model the higher-$z$ distributions, thereby approximating a correction for the missing optically faint star forming galaxies to the local SFR and stellar mass densities. Furthermore, we obtain the $r$-band LFs and stellar mass functions of H$\alpha$ star forming galaxies from the bivariate LFs. As our sample is selected on the basis of detected H$\alpha$ emission, a direct tracer of on-going star formation, this sample represents a true star forming galaxy sample, and is drawn from both photometrically classified blue and red sub-populations, though mostly from the blue population. On average 20-30% of red galaxies at all stellar masses are star forming, implying that these galaxies may be dusty star forming systems.

Far-ultraviolet and far-infrared bivariate luminosity function of galaxies: Complex relation between stellar and dust emission

Far-ultraviolet (FUV) and far-infrared (FIR) luminosity functions (LFs) of galaxies show a strong evolution from $z = 0$ to $z = 1$, but the FIR LF evolves much stronger than the FUV one. The FUV is dominantly radiated from newly formed short-lived OB stars, while the FIR is emitted by dust grains heated by the FUV radiation field. It is known that dust is always associated with star formation activity. Thus, both FUV and FIR are tightly related to the star formation in galaxies, but in a very complicated manner. In order to disentangle the relation between FUV and FIR emissions, we estimate the UV-IR bivariate LF (BLF) of galaxies with {\sl GALEX} and {\sl AKARI} All-Sky Survey datasets. Recently we invented a new mathematical method to construct the BLF with given marginals and prescribed correlation coefficient. This method makes use of a tool from mathematical statistics, so called "copula". The copula enables us to construct a bivariate distribution function from given marginal distributions with prescribed correlation and/or dependence structure. With this new formulation and FUV and FIR univariate LFs, we analyze various FUV and FIR data with {\sl GALEX}, {\sl Spitzer}, and {\sl AKARI} to estimate the UV-IR BLF. The obtained BLFs naturally explain the nonlinear complicated relation between FUV and FIR emission from star-forming galaxies. Though the faint-end of the BLF was not well constrained for high-$z$ samples, the estimated linear correlation coefficient $\rho$ was found to be very high, and is remarkably stable with redshifts (from 0.95 at $z = 0$ to 0.85 at $z = 1.0$). This implies the evolution of the UV-IR BLF is mainly due to the different evolution of the univariate LFs, and may not be controlled by the dependence structure.

Radio Sources in Galaxy Clusters: Radial Distribution, and 1.4 GHz andK‐band Bivariate Luminosity Function

We present a statistical study of several fundamental properties of radio sources in nearby clusters, including the radial distribution within clusters, the radio luminosity function (RLF), and the fraction of galaxies that is radio-active (radio active fraction, RAF). The analysis is carried out for a sample of 573 clusters detected in the X-ray and also observed at 1.4 GHz in the NVSS. K-band data from the 2MASS are used to identify the brightest cluster galaxies (BCGs), and to construct the K-band LF. Our main results include: (1) The surface density profile of radio-loud AGNs is much more concentrated than that of all galaxies, and can be described by the NFW profile with concentration ~ 25. (2) A comparison of the RLFs in the clusters and in the field shows that the cluster AGN number density is about 5,700 times higher, corresponding to a factor of 6.8 higher probability of a galaxy being radio active in the cluster than in the field. We suggest that about 40-50% of radio-loud AGNs in clusters may reside in low mass galaxies (M_K>-23). (3) The RAFs of cluster galaxies of different stellar mass are estimated. About 5% of galaxies more luminous than the characteristic luminosity (M_K 30%, and depends on the cluster mass. Compare to the field population, cluster galaxies have 5-10 times higher RAF. Combining the AGN RLF and spatial distribution within clusters, we estimate that they may inject an energy of ~0.13 keV per particle to the intracluster medium near the cluster center. We also investigate the degree of contamination by cluster radio sources on the yields of SZE cluster surveys, and estimate that as many as 10% of clusters detected at 150 GHz may host AGNs whose flux is comparable to the cluster SZE signal. (abridged)

Bivariate galaxy luminosity functions in the Sloan Digital Sky Survey

Bivariate luminosity functions (LFs) are computed for galaxies in the New York Value-Added Galaxy Catalogue, based on the Sloan Digital Sky Survey Data Release 4. The galaxy properties investigated are the morphological type, inverse concentration index, Sersic index, absolute effective surface brightness, reference frame colours, absolute radius, eClass spectral type, stellar mass and galaxy environment. The morphological sample is flux-limited to galaxies with r < 15.9 and consists of 37,047 classifications to an RMS accuracy of +/- half a class in the sequence E, S0, Sa, Sb, Sc, Sd, Im. These were assigned by an artificial neural network, based on a training set of 645 eyeball classifications. The other samples use r < 17.77 with a median redshift of z ~ 0.08, and a limiting redshift of z < 0.15 to minimize the effects of evolution. Other cuts, for example in axis ratio, are made to minimize biases. A wealth of detail is seen, with clear variations between the LFs according to absolute magnitude and the second parameter. They are consistent with an early type, bright, concentrated, red population and a late type, faint, less concentrated, blue, star forming population. This bimodality suggests two major underlying physical processes, which in agreement with previous authors we hypothesize to be merger and accretion, associated with the properties of bulges and discs respectively. The bivariate luminosity-surface brightness distribution is fit with the Choloniewski function (a Schechter function in absolute magnitude and Gaussian in surface brightness). The fit is found to be poor, as might be expected if there are two underlying processes.

The Star Formation Rate Function of the Local Universe

We have derived the bivariate luminosity function for the far-ultraviolet (1530 A) and far-infrared (60 μm). We use matched GALEX and IRAS data, and redshifts from NED and the PSCz survey. We have derived a total formation luminosity function (Ltot), with Ltot = LFUV + LFIR. Using these, we determined the cosmic star formation rate (SFR) function and density for the local universe. The total SFR function (Ltot) is fitted very well by a lognormal distribution over 5 decades of luminosity. We find that the bivariate luminosity function (LFUV, LFIR) shows a bimodal behavior, with LFIR tracking LFUV for Ltot < 1010 L☉ and LFUV saturating at ~1010 L☉, while Ltot ~ LFIR for higher luminosities. We also calculate the SFR density and compare it with other measurements.

The Bivariate Luminosity‐Color Distribution ofIRASGalaxies and Implications for the High‐Redshift Universe

We present a characterization of the local luminosity-color bivariate distribution of IRAS galaxies from the 1.2 Jy sample, selected at 60 μm. The R(60, 100) infrared (IR) color is used as the best single-parameter description of the IR spectral energy distribution of galaxies. We derive an analytical form of the distribution and use it to constrain the effect of the IR color distribution on evolution models for high-redshift, far-infrared (FIR)-luminous galaxies. Our adopted evolution retains the locally observed correlation between luminosity and color, such that the larger characteristic luminosities at higher redshift have a warmer characteristic color. The width of the color distribution at a given luminosity remains constant for all redshifts. We demonstrate that there is the potential for both hotter and colder sources to be missed in cosmological surveys. An evolving bivariate luminosity function coupled with the cold-source bias of submillimeter-selected surveys suggests the existence of a large population of cold sources appearing in such surveys. Likewise, a hot-source bias for most SIRTF wave bands together with a bivariate model suggests an excess of hot sources being selected. We test the evolutionary form against available data for higher redshift, FIR galaxies. The data do not reveal evidence for any strong evolution in the characteristic luminosity-color distribution as a function of redshift over 0 < z < 1. However, there is marginal evidence for a broadening of the color distribution at higher redshifts, consistent with our locally characterized trend of a broadening in the IR color distribution at the highest luminosities.

The Luminosity Functions and Stellar Masses of Galactic Disks and Spheroids

We present a method to obtain quantitative measures of galaxy morphology and apply it to a spectroscopic sample of field galaxies in order to determine the luminosity and stellar mass functions of galactic disks and spheroids. For our sample of approximately 600 galaxies, we estimate, for each galaxy, the bulge-to-disk luminosity ratio in the I band using a two-dimensional image fitting procedure. Monte Carlo simulations indicate that reliable determinations are only possible for galaxies approximately 2 mag brighter than the photometric completeness limit, leaving a sample of 90 galaxies with well-determined bulge-to-total light ratios. Using our measurements of individual disk and bulge luminosities for these 90 galaxies, we construct the luminosity functions of disks and spheroids and, using a stellar population synthesis model, we estimate the stellar mass functions of each of these components. The disk and spheroid luminosity functions are remarkably similar, although our rather small sample size precludes a detailed analysis. We do, however, find evidence in the bivariate luminosity function that spheroid-dominated galaxies occur only among the brightest spheroids, while disk-dominated galaxies span a much wider range of disk luminosities. Remarkably, the total stellar mass residing in disks and spheroids is approximately the same. For our sample (which includes galaxies brighter than M* + 2, where M* is the magnitude corresponding to the characteristic luminosity), we find the ratio of stellar masses in disks and spheroids to be 1.3 ± 0.2. This agrees with the earlier estimates of Schechter & Dressler but differs significantly from that of Fukugita, Hogan, & Peebles. Ongoing large photometric and redshift surveys will lead to a large increase in the number of galaxies to which our techniques can be applied and thus to an improvement in the current estimates.

20 CM VLA Survey of Abell Clusters of Galaxies. VI. Radio/Optical Luminosity Functions

From a statistically complete sample of 188 radio galaxies in Abell clusters, we examine the radio/optical correlations, the FR I/II division, and the univariate and bivariate luminosity functions. As suggested by Owen (1993), the FR I/II division is shown to be a strong function of the optical luminosity of the host galaxy (proportional to L_opt^2). This dependence is also seen in the bivariate luminosity function, which suggests that the evolutionary tracks of radio sources and/or the initial conditions in the source are governed by the host galaxy properties. The probability for detecting radio emission increases with optical luminosity. The optical dependence is clearly separated in the integral luminosity functions which can be used as a constraint to models of FR I radio power evolution. Additionally, the source counts from the integrated univariate radio luminosity function (RLF) are consistent with our suggestion in paper V that radio sources may be a transient phenomenon which occurs in all elliptical galaxies at some time (or several times) over their lifetime. We find no statistically significant differences in the luminosity functions between rich cluster samples and radio sources not selected to reside in clusters. These results suggest that all radio galaxies live in similar environments in that the optical luminosity and the properties of the host galaxy are the most important parameters which affect radio source formation and evolution.

A proposed method for the determination of the bivariate luminosity function utilizing an incomplete sample with an application to Seyfert galaxies

A proposed method for the determination of the bivariate luminosity function utilizing an incomplete sample with an application to Seyfert galaxies

The cosmological evolution of flat-spectrum quasars

The spatial distribution and luminosity functions of a complete sample of quasars from the ±4° declination strip of the Parkes 2.7-GHz survey have been investigated. The luminosity–volume (V/Vm) test strongly suggests that the flat-spectrum quasars which dominate the sample have an evolutionary history different from that of the steep-spectrum quasars which dominate the 3CR and 4C samples investigated previously. The bivariate luminosity function for the flat-spectrum quasars shows the same strong correlation between radio and optical luminosities exhibited by steep-spectrum quasars. The results of the luminosity–volume test considered in conjunction with radio structures, spectra, and source counts, lead to the tentative suggestion that the cosmological evolution of radio-active quasars is confined to those with extended radio structures.