Recovering the real-space correlation function from photometric redshift surveys

Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real-space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated with the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large-scale distribution of galaxies.     

CDFS天区中喑蓝星系的测光红移研究

从COMBO-17数字巡天数据里,选择了CDFS(Chandra Deep Field South)天区中1231个测光红移在0.1～0.3之间的暗蓝星系作为样本,研究了这些星系分别在只有光学波段和光学加近红外波段数据情况下做测光红移得到的红移分布,以及这些星系在静止参考系下的能谱分布(Spectral Energy Distributions,SEDs)特征.结果表明有183个星系在利用光学加近红外波段数据做测光红移时得到的红移大于1.2,它们的误差为0.046,提高测光的信噪比也有利于区分这类被光学波段误认为低红移的星系.这些暗蓝星系中高红移星系的观测近红外流量相对于光学流量有上升的趋势,而低红移星系的观测近红外流量相对于光学流量有下降的趋势.     

Photometric redshifts of galaxies from SDSS and 2MASS

In order to find the physical parameters which determine the accuracy of pho- tometric redshifts, we compare the spectroscopic and photometric redshifts (photo-z's) for a large sample of ～ 80 000 SDSS-2MASS galaxies. Photo-z's in this paper are es- timated by using the artificial neural network photometric redshift method (ANNz). For a subset of～40000 randomly selected galaxies, we find that the photometric redshift recovers the spectroscopic redshifi distribution very well with rms of 0.016. Our main results are as follows: (1) Using magnitudes directly as input parameters produces more accurate photo-z's than using colors; (2) The inclusion of 2MASS (3, H, Ks) bands does not improve photo-z's significantly, which indicates that near infrared data might not be important for the low-redshift sample; (3) Adding the concentration index (essentially the steepness of the galaxy brightness profile) as an extra input can improve the photo-z's estimation up to～10 percent; (4) Dividing the sample into early- and late-type galaxies by using the concentration index, normal and abnormal galaxies by using the emission line flux ratios, and red and blue galaxies by using color index (g - r), we can improve the accuracy of photo-z's significantly; (5) Our analysis shows that the outliers (where there is a big difference between the spectroscopic and photometric redshifts) are mainly correlated with galaxy types, e.g., most outliers are late-type (blue) galaxies.     

Photometric redshifts with surface brightness priors

We use galaxy surface brightness as prior information to improve photometric redshift (photo- z ) estimation. We apply our template-based photo- z method to imaging data from the ground-based VVDS survey and the space-based GOODS field from HST , and use spectroscopic redshifts to test our photometric redshifts for different galaxy types and redshifts. We find that the surface brightness prior eliminates a large fraction of outliers by lifting the degeneracy between the Lyman and 4000-Å breaks. Bias and scatter are improved by about a factor of 2 with the prior in each redshift bin in the range  0.4 < z < 1.3  , for both the ground and space data. Ongoing and planned surveys from the ground and space will benefit, provided that care is taken in measurements of galaxy sizes and in the application of the prior. We discuss the image quality and signal-to-noise ratio requirements that enable the surface brightness prior to be successfully applied.     

Spectroscopic needs for imaging dark energy experiments

Ongoing and near-future imaging-based dark energy experiments are critically dependent upon photometric redshifts (a.k.a. photo-z’s): i.e., estimates of the redshifts of objects based only on flux information obtained through broad filters. Higher-quality, lower-scatter photo-z’s will result in smaller random errors on cosmological parameters; while systematic errors in photometric redshift estimates, if not constrained, may dominate all other uncertainties from these experiments. The desired optimization and calibration is dependent upon spectroscopic measurements for secure redshift information; this is the key application of galaxy spectroscopy for imaging-based dark energy experiments.Hence, to achieve their full potential, imaging-based experiments will require large sets of objects with spectroscopically-determined redshifts, for two purposes:

• •Training: Objects with known redshift are needed to map out the relationship between object color and z (or, equivalently, to determine empirically-calibrated templates describing the rest-frame spectra of the full range of galaxies, which may be used to predict the color-z relation). The ultimate goal of training is to minimize each moment of the distribution of differences between photometric redshift estimates and the true redshifts of objects, making the relationship between them as tight as possible. The larger and more complete our “training set” of spectroscopic redshifts is, the smaller the RMS photo-z errors should be, increasing the constraining power of imaging experiments.

• Requirements: Spectroscopic redshift measurements for ∼30,000 objects over >∼15 widely-separated regions, each at least ∼20 arcmin in diameter, and reaching the faintest objects used in a given experiment, will likely be necessary if photometric redshifts are to be trained and calibrated with conventional techniques. Larger, more complete samples (i.e., with longer exposure times) can improve photo-z algorithms and reduce scatter further, enhancing the science return from planned experiments greatly (increasing the Dark Energy Task Force figure of merit by up to ∼50%).
• Options: This spectroscopy will most efficiently be done by covering as much of the optical and near-infrared spectrum as possible at modestly high spectral resolution (λ/Δλ > ∼3000), while maximizing the telescope collecting area, field of view on the sky, and multiplexing of simultaneous spectra. The most efficient instrument for this would likely be either the proposed GMACS/MANIFEST spectrograph for the Giant Magellan Telescope or the OPTIMOS spectrograph for the European Extremely Large Telescope, depending on actual properties when built. The PFS spectrograph at Subaru would be next best and available considerably earlier, c. 2018; the proposed ngCFHT and SSST telescopes would have similar capabilities but start later. Other key options, in order of increasing total time required, are the WFOS spectrograph at TMT, MOONS at the VLT, and DESI at the Mayall 4 m telescope (or the similar 4MOST and WEAVE projects); of these, only DESI, MOONS, and PFS are expected to be available before 2020. Table 2-3 of this white paper summarizes the observation time required at each facility for strawman training samples. To attain secure redshift measurements for a high fraction of targeted objects and cover the full redshift span of future experiments, additional near-infrared spectroscopy will also be required; this is best done from space, particularly with WFIRST-2.4 and JWST.
• Calibration: The first several moments of redshift distributions (the mean, RMS redshift dispersion, etc.), must be known to high accuracy for cosmological constraints not to be systematics-dominated (equivalently, the moments of the distribution of differences between photometric and true redshifts could be determined instead). The ultimate goal of calibration is to characterize these moments for every subsample used in analyses - i.e., to minimize the uncertainty in their mean redshift, RMS dispersion, etc. – rather than to make the moments themselves small. Calibration may be done with the same spectroscopic dataset used for training if that dataset is extremely high in redshift completeness (i.e., no populations of galaxies to be used in analyses are systematically missed). Accurate photo-z calibration is necessary for all imaging experiments.
• Requirements: If extremely low levels of systematic incompleteness (<∼0.1%) are attained in training samples, the same datasets described above should be sufficient for calibration. However, existing deep spectroscopic surveys have failed to yield secure redshifts for 30–60% of targets, so that would require very large improvements over past experience. This incompleteness would be a limiting factor for training, but catastrophic for calibration. If <∼0.1% incompleteness is not attainable, the best known option for calibration of photometric redshifts is to utilize cross-correlation statistics in some form. The most direct method for this uses cross-correlations between positions on the sky of bright objects of known spectroscopic redshift with the sample of objects that we wish to calibrate the redshift distribution for, measured as a function of spectroscopic z. For such a calibration, redshifts of ∼100,000 objects over at least several hundred square degrees, spanning the full redshift range of the samples used for dark energy, would be necessary.
• Options: The proposed BAO experiment eBOSS would provide sufficient spectroscopy for basic calibrations, particularly for ongoing and near-future imaging experiments. The planned DESI experiment would provide excellent calibration with redundant cross-checks, but will start after the conclusion of some imaging projects. An extension of DESI to the Southern hemisphere would provide the best possible calibration from cross-correlation methods for DES and LSST.

We thus anticipate that our two primary needs for spectroscopy – training and calibration of photometric redshifts – will require two separate solutions. For ongoing and future projects to reach their full potential, new spectroscopic samples of faint objects will be needed for training; those new samples may be suitable for calibration, but the latter possibility is uncertain. In contrast, wide-area samples of bright objects are poorly suited for training, but can provide high-precision calibrations via cross-correlation techniques. Additional training/calibration redshifts and/or host galaxy spectroscopy would enhance the use of supernovae and galaxy clusters for cosmology. We also summarize additional work on photometric redshift techniques that will be needed to prepare for data from ongoing and future dark energy experiments.     

Gigahertz-peaked spectrum (GPS) galaxies and quasars

The results of a comprehensive analysis of continuous radio spectra of a sample of Gigahertz-Peaked Spectrum (GPS) sources are reported. The sources are selected from a flux-density-complete sample (S _ν ≥ 200 mJy at 4.8 or 5 GHz) using multifrequency measurements of the RATAN-600 radio telescope and data from the CATS astrophysical catalogs support system. The analysis revealed a very small number (1–2%) of “classical” GPS objects, which is significantly less than the expected fraction of 10%. GPS galaxies are found to have narrower and steeper radio spectra than quasars. The low-frequency part of the spectrum is seen to become steeper with increasing redshift. Galaxies and quasars at the same z have comparable angular sizes, whereas their luminosities may differ by one order of magnitude. At large redshifts there is a deficit of objects with low (several GHZ) peak frequencies. The number of GPS galaxies decreases sharply with redshift, and most of them are found at z between 0.01 and 1.81. GPS quasars are found at large redshifts, from 0.11 to 3.99. A quarter of the sample consists of blazars whose spectra may temporarily have a convex shape when the object is in active state.     

Measuring the Evolution of the M/L Ratio from the Fundamental Plane

The Fundamental plane provides a sensitive tool to measure the change in the M/L ratio of early type galaxies with redshift. The evolution of the M/L ratio is a function of the star formation history. It depends on the IMF, the formation redshift, and cosmology. Some model examples are shown, and a first result on the cluster Abell 665 at z=0.18 is given. The measurements confirm the cosmological surface brightness dimming, and imply an evolution of the (red) L/M ratio ∝ (1 + z)^1.8±0.7. More data are needed to extend this result to higher redshifts, and to test the underlying assumptions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Faint field galaxies: an explanation of the faint blue excessusing number evolution models

Pure luminosity evolution models for galaxies provide an unacceptable fit to the redshifts and colors of faint galaxies. In this paper we demonstrate, using HST morphological number counts derived both from the I ₈₁₄-band of WFPC2 in the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF) and from the H _1.6-band of NICMOS, and ground-based spectroscopic data of the Hawaii Deep Field and the Canada-France Redshift Survey, that number evolution is necessary for galaxies, regardless of whether the cosmic geometry is flat, open, or Λ-dominated. Furthermore, we show that the number evolution is small at redshifts of z<1, but large at z>1, and that this conclusion is valid for all the three cosmological models under consideration. If the universe is open or Λ-dominated, the models, which are subject to the constraint of the conservation of the comoving mass density of galaxies, naturally predict a population of star-forming galaxies with the redshift distribution peaking at z=2∼ 3, which seems to be consistent with the recent findings from Lyman-break photometric selection techniques. If the cosmological model is flat, however, the conservation of the comoving mass density is invalid. Hence, in order to account for the steep slope of B-band number counts at faint magnitudes in the flat universe, such a star-forming galaxy population has to be introduced ad hoc into the modelling alongside the merger assumption. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimating the redshift distribution of photometric galaxy samples – II. Applications and tests of a new method

In Lima et al. we presented a new method for estimating the redshift distribution,   N ( z )  , of a photometric galaxy sample, using photometric observables and weighted sampling from a spectroscopic subsample of the data. In this paper, we extend this method and explore various applications of it, using both simulations and real data from the Sloan Digital Sky Survey (SDSS). In addition to estimating the redshift distribution for an entire sample, the weighting method enables accurate estimates of the redshift probability distribution,   p ( z )  , for each galaxy in a photometric sample. Use of   p ( z )  in cosmological analyses can substantially reduce biases associated with traditional photometric redshifts, in which a single redshift estimate is associated with each galaxy. The weighting procedure also naturally indicates which galaxies in the photometric sample are expected to have accurate redshift estimates, namely those that lie in regions of photometric-observable space that are well sampled by the spectroscopic subsample. In addition to providing a method that has some advantages over standard photo- z estimates, the weights method can also be used in conjunction with photo- z estimates e.g. by providing improved estimation of   N ( z )  via deconvolution of   N ( z _phot)  and improved estimates of photo- z scatter and bias. We present a publicly available   p ( z )  catalogue for ∼78 million SDSS DR7 galaxies.     

The observed structure of extremely distant galaxies

We have identified 22 galaxies with photometric redshifts z_ph=5–7 in the northern and southern Hubble Space Telescope deep fields. An analysis of the images of these objects shows that they are asymmetric and very compact (～1 kpc) structures with high surface brightness and absolute magnitudes of M_B≈?20^m. The average spectral energy distribution for these galaxies agrees with the distributions for galaxies with active star formation. The star formation rate in galaxies with z_ph=5–7 was estimated from their luminosity at λ=1500 Å to be ~30 M_⊙yr^?1. The spatial density of these objects is close to the current spatial density of bright galaxies. All the above properties of the distant galaxies considered are very similar to those of the so-called Lyman break galaxies (LBGs) with z ～ 3–4. The similarity between the objects considered and LBGs suggests that at z ～6, we observe the progenitors of present-day galaxies that form duringmergers of protogalactic objects and that undergo intense starbursts.     

Galaxy Evolution from Deep Multicolor Surveys

A composite sample of NIR-selected galaxies having extended multicolor coverage has been used to probe the cosmological evolution of the blue luminosity function and of the stellar mass function. The bright fraction of the sample has spectroscopic redshifts, and the remaining fraction well-calibrated photometric redshifts. The resulting blue luminosity function shows an increasing brightening with redshift respect to the local luminosity function. Hierarchical CDM models predictions are in agreement only at low and intermediate redshifts but fail to reproduce the observed brightening at high redshifts (z ∼ 2–3). This brightening marks the epoch where starburst activity triggered by galaxy interactions could be an important physical mechanism for the galaxy evolution. At the same time the NIR galaxy sample has been used to trace the evolution of the cosmological stellar mass density up to ∼3. A clear decrease of the average mass density is apparent with a fraction ∼15% of the local value at z ∼ 3. UV bright star-forming galaxies are substancial contributors to the evolution of the stellar mass density. Although these results are globally consistent with Λ–CDM scenarios, they tend to underestimate the mass density produced by more massive galaxies present at z > 2.     

The Hubble relation: Differences between galaxy types Sb and Sc

The most accurate data on galaxy types, corrected apparent magnitudes and redshifts as given in the Sandage-TammanRevised Shapley-Ames catalog are analyzed. It is shown that Sb galaxies of the same luminosity class as M31 and M81 define a narrow Hubble relation withH ₀=65 _–6 ⁺¹⁵ km s^–1 Mpc^–1.In contrast, Sc galaxies deviate strongly towars higher redshift from a linear, log redshift—apparent magnitude relation. Not all this deviation can be selection effect due to increasing volume sampled at increasing redshift (Malmquist bias). Physical associations of groups of galaxies in theRSA Catalog are used to establish the existence of various amounts of excess (non-velocity) redshifts among Sc and allied types of galaxies.Independent distances fromHi line width — luminosity criterion (Tully-Fisher) are analyzed. It is shown that this criterion gives much smaller distances than redshifts do for galaxies which deviate above the Hubble line. Unless the Tully-Fisher relation gives too small distances for more luminous galaxies, this confirms the excess redshift to be intrinsic to the Galaxy. But it is next demonstrated, that for low redshift galaxies, there is no discrepancy between redshift and Tully-Fisher distance even though there is a wide range of absolute magnitudes.If Tully-Fisher distances are accepted, the onlly alternative to having a Hubble constant which increases strongly with distance is to have a component of the higher redshift Sc's contributed by a non-recessional redshift. Streaming motions would have to be large, increase with distance and be always in the receding sence. It is shown here that the Sc's which deviate most from the Hubble relation and have the largest discrepancies with Tully-Filsher distances lie predominantly in the sky toward very nearby groups of galaxies. If they were at these closer distances the discordant galaxies, mostly ScI's, would have dwarfish physical properties but not so unprecedented as the large sizes which result from redshift distances.Finally the interaction of specific high redshift ScI's with nearby galaxies is presented as an independent proof that ScI's are generally small, low luminosity galaxies. This result furnishes insight into the long standing puzzle of how apparently distant ScI's can interact with nearby galaxies such as in Stephan's Quintet, Seyfert's Sextet and NGC 4151/4156.     

Testing Cosmological Models using the Kinematics of High Redshift Galaxies

The scaling of the apparent angular diameter of galaxies with redshift θ(z) is a powerful discriminator of cosmological models. In this paper we argue that the rotational velocity of distant galaxies, when interpreted as size indicator, may be used as an interesting tool to select high redshift standard rods. Upcoming deep redshift surveys will allow an implementation of this classical geometrical test to measure directly the amplitude of the cosmological constant Λ, or to constrain the cosmic equation of state parameter for a smooth dark energy component (w = p/ρ, —1 ≤ w < 0).     

Edge-on Galaxies in the Hubble Ultra Deep Field

We have produced a sample of 58 edge-on spiral galaxies at redshifts z ~ 1 selected in the Hubble Ultra Deep Field. For all galaxies we have analyzed the 2D brightness distributions in the V₆₀₆ and i₇₇₅ filters and measured the radial (h_r) and vertical (h_z) exponential scale lengths of the brightness distribution. We have obtained evidence that the relative thickness of the disks of distant galaxies, i.e., the ratio of the vertical and radial scale lengths, on average, exceeds the relative thickness of the disks of nearby spiral galaxies. The vertical scale length h_z of the stellar disks of galaxies shows no big changes at z = 1. The possibility of the evolution of the radial scale length h_z for the brightness distribution with redshift is discussed.

     

Surface brightness bias in galaxy catalogues; distance effects

We have investigated the apparent variation of the surface brightness distribution of disc galaxies with distance within three different samples 1) a diameter limited sample of ESO catalogue galaxies in the direction of the cluster A3574 in Centaurus, 2) all ESO catalogue disc galaxies with redshifts, and 3) a sample of fainter galaxies from our surveys of the Fornax Cluster area. In each case we find, as predicted for a sample dominated by surface brightness selection effects, that the distribution narrows with distance. Both high and low surface brightness galaxies are underrepresented in galaxy catalogues. Not because they are rare, but because the volume over which they are sampled is considerably smaller than that of their normal surface brightness counterparts. The question of how many galaxies there are in the Universe remains un-answered. In addition, since selection is byapparent surface brightness, the most distant sample (where cosmological dimming becomes important) contains galaxies of higher intrinsic surface brightness than do the nearby samples, again confirming a previous theoretical prediction. The galaxies we observe in the distant Universe are very different to those we observe close by because of observational selection.     

Magnitude-Redshift Relation in Clusters,Groups and Pairs of Galaxies

Magnitude-redshift (m, z) relation within systems of galaxies is studied in detail in several kinds of systems. The main data contains 17 clusters, 64 groups, 121 pairs and 14 systems with two measured members, altogether 1043 galaxies in 162 separate systems. In addition, another sample of nearby groups and pairs, recently published data on six clusters with 121 measured members, as well as 65 compact galaxies in four groups and 23 pairs are studied. In Section 2 the data and the method are described. The numerical results for the main data are given in Table 1. There exists a significant positive (m, z)-relation in groups and pairs, but for clusters the same is valid only with a rather loose selection of members. The (m, z)-relations are calculated separately for each morphological type, but systematic differences between the types are not found. In Section 3 some properties of the velocity (redshift) dispersion σ_V are discussed. The joint dispersion decreases significantly from the early to the late types. This may point to an early dynamical state of the systems but it is also quite possible that this result is due to a selection effect. The presence of a selection effect in some commonly used samples of systems is indicated by the increase of velocity dispersion σ_V with increasing distance (Section 4). This effect which was first found for clusters and groups by SCOTT is present also in the larger sample of these systems and in the sample of pairs. Implications of this feature are discussed. As one of them, it is concluded in Section 5 that there exists no separate Canes Venatici cluster of galaxies but the galaxies supposed to form it belong to the Ursa Major cloud of galaxies. Several independent arguments supporting this conclusion are pointed out. In the Ursa Major-Canes Venatici complex of galaxies a distinct positive (m, z)-relation is found. In Section 4 the distance-dependence of the (m, z)-relations is studied and it is found that positive relations are most common for nearby systems. This is natural if the effect is an intergalactic one, the redshift being dependent on the distance of the galaxy. The (m, z)-relations is are studied as function of size of the systems in Section 6. It is found that σ_V, (m, z) regression coefficient b_m, and parameter h which measures strength of redshift within the system, are largest in the systems with smallest radii. The result is opposite to that obtained using the virial theorem. In the Dopplerian context it would mean that the systems disperse the more rapidly the more dense these are. Dependence of the results on the number of data is studied in Section 7. As expected for a real effect, the frequency of positive relations increases with increasing number. The dispersion σ_V is usually larger in the central areas of the clusters than in the outskirts (Section 8). In these areas, σ_V is systematically larger for faint galaxies than for bright ones. The reason for large σ_V for faint galaxies projected on the centre is considered, studying in particular in the Coma cluster the velocity (redshift) distribution, colour-redshirt relation and morphological features which might be used in localization of the galaxies along the line of sight. The results of these three kinds of tests point to the possibility that redshift increases along the line of sight, but the results refer to sparse data and are very uncertain. A similar effect is suggested independently by observations of the galaxies in the background of the clusters. If true, the effect must be non-Dopplerian. In combination with brightness seggregation and preponderance of measured galaxies in the near side over those in the rear, this may cause the observed negative (m, z)-relations for some clusters. In SANDAGE 's and TAMMANN 's sample of nearby groups and pairs redshift appears dependent on luminosity class. This points to intrinsic redshifts in faint galaxies (Section 9). A similar implication is valid for the positive (m, z)-relations in the case of pairs and groups of compact galaxies (Section 10). Since there are indications of physical association in the latter case, the result cannot be explained by optical members. The present results are compared with previous ones in Section 11. This includes a study of redshifts with regard to brightness and surface brightness simultaneously, leading to a new statistical definition of relative compacity of galaxies belonging to the systems. Recent observations not included in the main data are viewed in Section 12. These show a positive (m, z)-relation. Interpretation of the results is discussed in Sections 13 and 14. From the numerous ones, three main possibilities remain, i. e. projected galaxies, intrinsic redshifts in faint galaxies and non-Dopplerian integalactic redshifts. There are several arguments suggesting that chance projections are not the principal explanation of the positive (m, z)-relations. If so, intrinsic redshifts in faint galaxies give probably the main explanation for pairs and small groups and integralactic redshifts for larger systems. This is in accordance with the general view of the redshift phenomenon in other scales. However, definitive proof of this conclusion could not be obtained from the present data which, though considerably large in number, is too small regarding the complexity of the problem.     

Confirmation of the effectiveness of submm source redshift estimation based on rest-frame radio–FIR photometry

We present a comparison between the published optical, infrared (IR) and CO spectroscopic redshifts of 15 (sub)mm galaxies and their photometric redshifts as derived from long-wavelength (radio–mm–far-IR) photometric data. The redshift accuracy measured for 12 submillimetre (submm) galaxies with at least one robustly determined colour in the radio–mm–far-IR regime is  δ z ≈ 0.30 (rms)  . Despite the wide range of spectral energy distributions in the local galaxies that are used in an unbiased manner as templates, this analysis demonstrates that photometric redshifts can be efficiently derived for submm galaxies with a precision of  δ z < 0.5  using only the rest-frame far-IR to radio wavelength data.     

Global structure of the local universe according to 2MRS survey

We report the results of a statistical analysis of the space distribution of galaxies of the 2MRS catalog, which contains redshifts of 43533 galaxies of the 2MASS all-sky IR survey. Because of the unique features of the 2MRS survey, such as its 90% sky coverage, galaxy selection in the IR, the complete incorporation of the old stellar population of galaxies, weakness of the dust extinction effects, and the smallness of the k- and e-corrections allowed us to determine the statistical properties of the global distribution of galaxies in the Local Universe. We took into account the main methodological factors that distort the theoretically expected relations compared to those actually observed. We construct the radial galaxy number counts N(R), SL(R, r) statistics, and the complete correlation function (conditional density) Γ(r) for volume-limited (VL) galaxy samples. The observed conditional density Γ(r) in the redshift space is independent of the luminosity of galaxies and has the form of a power-law function with exponent γ ≈ 1.0 over a large range scale-length spanning from 0.1 to 100 Mpc. We compare the statistical properties of the space distribution of galaxies of the 2MRS catalog with the corresponding properties of simulated catalogs: stochastic fractal distributions and galaxies of the Millennium catalog.     

A photometric study of faint galaxies in the field of GRB 000926

We present our B, V, R_c, and I_c observations of a \(3'.6 \times 3'\) field centered on the host galaxy of GRB 000926 (α_2000.0=17^h04^m11^s, \(\delta _{2000.0} = + 51^ \circ 47'9\mathop .\limits^{''} 8\)). The observations were carried out on the 6-m Special Astrophysical Observatory telescope using the SCORPIO instrument. The catalog of galaxies detected in this field includes 264 objects for which the signal-to-noise ratio is larger than 5 in each photometric band. The following limiting magnitudes in the catalog correspond to this limitation: 26.6 (B), 25.7 (V), 25.8 (R), and 24.5 (I). The differential galaxy counts are in good agreement with previously published CCD observations of deep fields. We estimated the photometric redshifts for all of the cataloged objects and studied the color variations of the galaxies with z. For luminous spiral galaxies with M(B)z～1.