Kernel regression for determining photometric redshifts from Sloan broad-band photometry

We present a new approach, namely kernel regression, to determine photometric redshifts for 399 929 galaxies in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS). Kernel regression is a weighted average of spectral redshifts of the neighbours for a query point, and higher weights are associated with points that are closer to the query point. One important design decision when using kernel regression is the choice of bandwidth. We apply 10-fold cross-validation to choose the optimal bandwidth, which is obtained as the cross-validation error approaches its minimum. The results show that the optimal bandwidth is different for different input patterns: the lowest rms error of photometric redshift estimation arrives at 0.019 using colour+eClass as the inputs, the lowest rms errors comes to 0.020 using ugriz +eClass as the inputs. Where eClass is a galaxy spectral type, and 0.021 using colour+ r as the inputs. Thus, in addition to parameters such as magnitude and colour, eClass is a valid parameter with which to predict photometric redshifts. Moreover, the results suggest that the accuracy of estimating photometric redshifts is improved when the sample is divided into early-type and late-type galaxies; in particular, for early-type galaxies, the rms scatter is 0.016 with colour+eClass as the inputs. In addition, kernel regression achieves high accuracy when predicting the photometric eClass  (σ_rms= 0.034)  using colour+ r as the input pattern. For kernel regression, the accuracy of the photometric redshifts does not always increase with the number of parameters considered, but is satisfactory only when appropriate parameters are chosen. Kernel regression is a comprehensible and accurate regression method. Experiments reveal the superiority of kernel regression over other empirical training approaches.     

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.     

Photometric redshifts for an optical/near-infrared catalogue in the Chandra Deep Field South

Photometric redshifts have proven a powerful tool in identifying galaxies over a large range of lookback times. We have been generalising this technique to incorporate the selection of candidate high redshift QSOs. We have applied this to a large optical/near-infrared imaging survey in 6 wavebands aiming to push farther in redshift (and fainter in luminosity) than previous studies. We believe that study of these very faint and distant objects provides valuable insights into galaxy formation and evolution. Here we present work in progress and preliminary results for a catalogue of objects detected as part of the Las Campanas Infrared Survey. This is a stepping stone to the type of survey data that will become available in the next few years from projects such as UKIDSS and VISTA. This revised version was published online in August 2006 with corrections to the Cover Date.     

The final two redshifts for radio sources from the equatorial BRL sample

Best, Röttgering & Lehnert (BRL) defined a new sample of powerful radio sources from the Molonglo Reference Catalogue, for which redshifts were compiled or measured for 177 of the 178 objects. For the final object, MRC1059−010 (3C 249), the host galaxy is identified here using near-infrared imaging, and the redshift is determined from Very Large Telescope (VLT) spectroscopy. For one other object in the sample, MRC0320+053 (4C05.14), the literature redshift has been questioned: new spectroscopic observations of this object are presented, deriving a corrected redshift. With these two results, the spectroscopic completeness of this sample is now 100 per cent.
New redshifts are also presented for PKS0742+10 from the Wall & Peacock 2.7-GHz catalogue, and for PKS1336+003 from the Parkes Selected Regions. PKS0742+10 shows a strong neutral hydrogen absorption feature in its Lyman α emission profile.     

Reconstructing galaxy fundamental distributions and scaling relations from photometric redshift surveys. Applications to the SDSS early-type sample

Noisy distance estimates associated with photometric rather than spectroscopic redshifts lead to a biased estimate of the luminosity distribution, and produce a correlated misestimate of the sizes. We consider a sample of early-type galaxies from the Sloan Digital Sky Survey Data Release 6 for which both spectroscopic and photometric information is available, and apply the generalization of the V _max method to correct for these biases. We show that our technique recovers the true redshift, magnitude and size distributions, as well as the true size–luminosity relation. We find that using only 10 per cent of the spectroscopic information randomly spaced in our catalogue is sufficient for the reconstructions to be accurate within  ∼3 per cent  , when the photometric redshift error is  δ z ≃ 0.038  . We then address the problem of extending our method to deep redshift catalogues, where only photometric information is available. In addition to the specific applications outlined here, our technique impacts a broader range of studies, when at least one distance-dependent quantity is involved. It is particularly relevant for the next generation of surveys, some of which will only have photometric information.     

Clustering of luminous red galaxies – II. Small-scale redshift-space distortions

This is the second paper of a series where we study the clustering of luminous red galaxies (LRG) in the recent spectroscopic Sloan Digital Sky Survey (SDSS) data release, DR6, which has 75 000 LRG covering over  1 Gpc³  h ⁻³  for  0.15 < z < 0.47  . Here, we focus on modelling redshift-space distortions in  ξ(σ, π)  , the two-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic two-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG on all scales. We show that to describe with accuracy the so-called 'fingers-of-God' (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias b and the pairwise rms peculiar velocity σ₁₂ with the distance. We show how both quantities can be inferred from the  ξ(σ, π)  data. From   r ≃ 10 Mpc  h ⁻¹  to   r ≃ 1 Mpc  h ⁻¹  , both the bias and σ₁₂ are shown to increase by a factor of 2: from   b = 2  to 4 and from  σ₁₂= 400  to  800 km s⁻¹  . The latter is in good agreement, within a 5 per cent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with  Ω_m= 0.25  and  σ₈= 0.85  .     

Spectroscopic confirmation of redshifts predicted by gravitational lensing

We present deep spectroscopic measurements of 18 distant field galaxies identified as gravitationally lensed arcs in a Hubble Space Telescope image of the cluster Abell 2218. Redshifts of these objects were predicted by Kneib et al. using a lensing analysis constrained by the properties of two bright arcs of known redshift and other multiply imaged sources. The new spectroscopic identifications were obtained using long exposures with the LDSS-2 spectrograph on the William Herschel Telescope, and demonstrate the capability of that instrument to reach new limits, R ≃24; the lensing magnification implies true source magnitudes as faint as R ≃25. Statistically, our measured redshifts are in excellent agreement with those predicted from Kneib et al.'s lensing analysis, and this gives considerable support to the redshift distribution derived by the lensing inversion method for the more numerous and fainter arclets extending to R ≃25.5. We explore the remaining uncertainties arising from both the mass distribution in the central regions of Abell 2218 and the inversion method itself, and conclude that the mean redshift of the faint field population at R ≃25.5 ( B ∼26–27) is low, 〈 z 〉=0.8–1. We discuss this result in the context of redshift distributions estimated from multicolour photometry. Although such comparisons are not straightforward, we suggest that photometric techniques may achieve a reasonable level of agreement, particularly when they include near-infrared photometry with discriminatory capabilities in the 1< z <2 range.     

More redshifts of powerful equatorial radio sources from the Best, Röttgering & Lehnert sample

A new sample of very powerful radio sources, defined from the Molonglo Reference Catalogue, was recently compiled by Best, Röttgering & Lehnert. These authors provided redshifts for 174 of the 178 objects in the sample, making the sample 98 per cent spectroscopically complete. Here, redshifts for three of the remaining galaxies are presented, confirming the optical identifications and raising the spectroscopic completeness of the sample to 99.5 per cent; only 1059−010 (3C 249) is currently without redshift.     

MegaZ-LRG: a photometric redshift catalogue of one million SDSS luminous red galaxies

We describe the construction of MegaZ-LRG, a photometric redshift catalogue of over one million luminous red galaxies (LRGs) in the redshift range  0.4 < z < 0.7  with limiting magnitude   i < 20  . The catalogue is selected from the imaging data of the Sloan Digital Sky Survey (SDSS) Data Release 4. The 2dF-SDSS LRG and Quasar (2SLAQ) spectroscopic redshift catalogue of 13 000 intermediate-redshift LRGs provides a photometric redshift training set, allowing use of ann z, a neural network-based photometric-redshift estimator. The rms photometric redshift accuracy obtained for an evaluation set selected from the 2SLAQ sample is  σ _z = 0.049  averaged over all galaxies, and  σ _z = 0.040  for a brighter subsample  ( i < 19.0)  . The catalogue is expected to contain ∼5 per cent stellar contamination. The ann z code is used to compute a refined star/galaxy probability based on a range of photometric parameters; this allows the contamination fraction to be reduced to 2 per cent with negligible loss of genuine galaxies. The MegaZ-LRG catalogue is publicly available on the World Wide Web from http://www.2slaq.info .     

Intrinsic correlation of galaxy shapes: implications for weak lensing measurements

Weak gravitational lensing is now established as a powerful method to measure mass fluctuations in the universe. It relies on the measurement of small coherent distortions of the images of background galaxies. Even low-level correlations in the intrinsic shapes of galaxies could however produce a significant spurious lensing signal. These correlations are also interesting in their own right, since their detection would constrain models of galaxy formation. Using     haloes found in N -body simulations, we compute the correlation functions of the intrinsic ellipticity of spiral galaxies assuming that the disc is perpendicular to the angular momentum of the dark matter halo. We also consider a simple model for elliptical galaxies, in which the shape of the dark matter halo is assumed to be the same as that of the light. For deep lensing surveys with median redshifts ∼1, we find that intrinsic correlations of ∼10⁻⁴ on angular scales     are generally below the expected lensing signal, and contribute only a small fraction of the excess signals reported on these scales. On larger scales we find limits to the intrinsic correlation function at a level ∼10⁻⁵, which gives a (model-dependent) range of separations for which the intrinsic signal is about an order of magnitude below the ellipticity correlation function expected from weak lensing. Intrinsic correlations are thus negligible on these scales for dedicated weak lensing surveys. For wider but shallower surveys such as SuperCOSMOS, APM and SDSS, we cannot exclude the possibility that intrinsic correlations could dominate the lensing signal. We discuss how such surveys could be used to calibrate the importance of this effect, as well as study spin–spin correlations of spiral galaxies.