The Sloan Digital Sky Survey

1 Introduction

including properties and distribution of high-redshift quasars, properties of galaxies and galaxy clusters, detailed investigation of the stellar populations in galaxies, the stellar structure of our own Galaxy, stars, and asteroids in the Solar System.

1.4.1.1 Photometry

The imaging survey covers π steradians of the northern sky and provides im-ages in five pass-band filters (u, g, r, i, z) that span the entire optical spec-tral range, from the atmospheric ultra-violet cut-off to the near-infrared.

The imaging data are acquired at the dedicated 2.5m f/5 modified Ritchey-Chretien altitude-azimuth telescope located at Apache Point Observatory (APO) in south-east New Mexico. The 3 degree field of view is covered with 30 2048×2048 CCDs arranged in six columns of five CCDs each. The camera operates in a drift-scan mode and produces five images of a given object with an effective exposure time of 54 seconds.

Automated pipelines have been developed to reduce the imaging data, per-forming the standard reduction and calibration procedures. These include sky subtraction, deblending of overlapping sources, extraction of the catalogue of objects and measurement of their photometric properties (Lupton et al. 2001).

It is worth mentioning some of the photometric quantities provided for each object by the SDSS, in particular the magnitude of galaxies. Contrary to stars, galaxies do not have sharp edges and have different surface brightness profiles. Different types of magnitudes can thus be measured. The SDSS pipeline calculates model magnitudes and Petrosian magnitudes.

Themodelmagnitudes are calculated by fitting to the two-dimensional im-age in the r-band a de Vaucouleurs and an exponential surface brightness profile¹⁰. Total magnitudes are then calculated from the better fit of the two models. The same model is fitted to the images in the other bands and the corresponding flux is obtained from the normalization constant relative to the r-band. In this way, the flux is measured at the same effective aperture in all bands. These models are also corrected for the point spread function¹¹. Another version of the model magnitude is the cmodel magnitude. This is obtained from the best-fit de Vaucouleurs and exponential model and com-bining them into the best-fit linear combination. The flux of the composite model is obtained by summing the fluxes of the two models, weighted by the

10The surface brightness I(r) is proportional toexp(−r^1/4) for a de Vaucouleurs profile and toexp(−r) for an exponential profile.

11The point spread function (PSF) measures the typical size of a point source, due to finite resolution and atmospheric distortions.

1.4 Extragalactic surveys

corresponding coefficient in the linear combination. The coefficients are also stored and they can be useful quantities to separate different galaxy types (e.g. elliptical galaxies can be selected according to the criterion that they prefer a de Vaucouleurs rather than an exponential profile).

ThePetrosianmagnitudes have the advantage of measuring a constant frac-tion of the total galaxy light, independent of the distance of the object. The idea is to measure fluxes in an aperture of radius defined by the shape of the azimuthally averaged light profile. First, the Petrosian radiusr_P is defined as the radius at which the local surface brightness in an annulus atr_P is 20 per-cent of the mean surface brightness withinrP. The Petrosian flux is obtained integrating the surface brightness profile out to 2r_P. The aperture in all bands is set by the profile in the r band. This ensures that the colours, measured by comparing the Petrosian fluxes in different bands, are measured through a consistent aperture. For a de Vaucouleurs profile, the Petrosian flux is about 98 percent of the total flux, and about 80 percent for an exponential profile.

Finally, fibre magnitudes are also estimated. These are obtained from the flux contained within an aperture of 3 arcsec diameter, which corresponds to the aperture of the spectroscopic fibre (see below). These magnitudes can be useful when combining spectroscopic and photometric measurements.

Galaxy sizes are often given in terms of Petrosian radii, defined as the radius that contains a given fraction of the Petrosian flux. Particularly used are the Petrosian R50 and R90 radii (containing respectively 50 and 90 percent of the total flux). Their ratio defines the concentration parameter of a galaxy, which is the fundamental tool for the morphological classification in the SDSS.

1.4.1.2 Spectroscopy

The spectroscopic survey provides complete samples of three categories of objects:

• Bright galaxies, which constitute the ‘main’ sample, selected to have Petrosian r-band magnitude brighter than 17.77;

• Luminous Red Galaxies, selected on the basis of their colour and mag-nitude to yield a sample of luminous intrinsically red galaxies extending to higher redshift than the main sample (z∼0.45);

• Quasars, selected by their distinct colours in the SDSS photometric sys-tem, and by radio detection in the FIRST survey catalog.

The spectra are taken with two fibre-fed spectrographs, mounted on the im-age rotator of the APO telescope. In the spectroscopic mode the camera is

1 Introduction

substituted with a fibre plug plate, which is drilled according to the astromet-ric coordinates obtained from the imaging data to accommodate 640 fibres.

The fibres have a fixed aperture diameter of 3 arcsec. The light collected by the fibre is thus only a limited fraction of the total light emitted by a galaxy, depending on the apparent size of the galaxy on the sky, hence on the dis-tance of the galaxy and the concentration of its light profile. On average this fraction is 30 percent and this means that the spectra represent more properly the light coming from the inner region or bulge of the galaxies.

The spectra cover the wavelength range from 3800 to 9200˚A and have an average spectral resolution of λ/∆λ = 2000. The spectra are reduced with automated devoted pipelines, which perform the flux and wavelength calibra-tion of the spectra and the sky subtraccalibra-tion. The redshift of each spectrum is obtained using emission and absorption lines independently. Emission lines are identified by positive peaks in the spectrum and are compared to known emission lines of galaxies and quasars. For the absorption, the observed spec-trum is cross-correlated to a high signal-to-noise template specspec-trum. The most reliable redshift estimate is given as fiducial redshift of the object. Finally, sources are classified into different classes (star, galaxy, QSO, high-redshift QSO) by comparison with template spectra of different astronomical sources.

Several other quantities are measured from the spectra of galaxies, in par-ticular velocity dispersion, emission lines and absorption features. Velocity dispersions are measured by comparing the observed galaxy spectrum whose velocity dispersion is to be determined with a fiducial template spectrum, which can be the spectrum of a star or of a high signal-to-noise galaxy with known velocity dispersion. The template spectra are convolved to a maxi-mum velocity dispersion of 420 km s⁻¹, so velocity dispersions higher than this are not reliable. Likewise, velocity dispersions below 70 km s⁻¹, which is the instrumental resolution of the SDSS, are not accurate.

The emission lines and absorption features are estimated from the spec-tra using the procedure developed and outlined by Tremonti et al. (2004), which is optimised for use on SDSS galaxy spectra. This consists in per-forming first a non-negative least-squares fit of the emission-line-free regions of the observed spectrum, using a set of model template spectra broadened to the observed velocity dispersion (the template spectra correspond to 30 instantaneoburst models of different ages and metallicities computed us-ing the Bruzual&Charlot 2003 code). Once the fitted spectrum is subtracted from the observed spectrum, the residuals can be fitted to Gaussian-broadened emission-line templates. The method assumes a single broadening width for all the Balmer lines, and another (independent) width for all the forbidden lines. The strength of each line is fitted independently.

The accurate measurement of the emission lines, obtained with this procedure

1.4 Extragalactic surveys

and thanks to the high resolution of the model template spectra, is useful not just in itself but is fundamental in order to obtain an accurate measure of ab-sorption lines from the spectra of star-forming galaxies. In order to measure spectral absorption features, the fitted emission lines are subtracted from the original observed spectrum to produce a ‘pure’ absorption-line spectrum suited to our analysis. The measured absorption features relevant for this work are the indices define in the Lick system. A calibration onto the Lick system is not possible, because spectra of Lick stars are not available in the SDSS. Moreover it would require to broaden the observed spectra to the lower resolution of the Lick system. Instead, the absorption features are measured directly from the spectrum adopting the band-pass definition of Worthey (1994) and Worthey

& Ottaviani (1997).