Morphology/Classification

This page provides detailed descriptions of various morphological outputs of the photometry pipelines. We also provide discussion of some methodology; for details of the Photo pipeline processing please read the corresponding EDR paper section. Other photometric outputs, specifically the various magnitudes, are described on the photometry page.

• Star/Galaxy Classification
• Model Fit Likelihoods and Parameters
• Radial Profiles
• Surface Brightness & Concentration Index
• Ellipticities
• Isophotal Quantities
• Adaptive Moments

The frames pipeline also provides several characterizations of the shape and morphology of an object.

Star/Galaxy Classification
The frames pipeline provides a simple star/galaxy separator in its type parameters (provided separately for each band) and its objc_type parameters (one value per object); these are set to:

Class	Name	Code
Unknown	UNK	0
Cosmic Ray	CR	1
Defect	DEFECT	2
Galaxy	GALAXY	3
Ghost	GHOST	4
Known object	KNOWNOBJ	5
Star	STAR	6
Star trail	TRAIL	7
Sky	SKY	8

The photometric pipeline version used for DR2 and later data (5_4) classifies objects as extended ("galaxy") or point-like ("star") based on the difference between the cmodel and PSF magnitude. An object is classified as extended if

If satisfied, type is set to GALAXY for that band; otherwise, type is set to STAR . The global type objc_type is set according to the same criterion, applied to the summed fluxes from all bands in which the object is detected.

Experimentation has shown that simple variants on this scheme, such as defining galaxies as those objects classified as such in any two of the three high signal-to-noise ratio bands (namely, g, r, and i), work better in some circumstances. This scheme occasionally fails to distinguish pairs of stars with separation small enough (<2'') that the deblender does not split them; it also occasionally classifies Seyfert galaxies with particularly bright nuclei as stars.

Further information to refine the star-galaxy separation further may be used, depending on scientific application. For example, Scranton et al. (2001) advocate applying a Bayesian prior to the above difference between the PSF and exponential magnitudes, depending on seeing and using prior knowledge about the counts of galaxies and stars with magnitude.

Radial Profiles
The frames pipeline extracts an azimuthally-averaged radial surface brightness profile. In the catalogs, it is given as the average surface brightness in a series of annuli. This quantity is in units of ``maggies'' per square arcsec, where a maggie is a linear measure of flux; one maggie has an AB magnitude of 0 (thus a surface brightness of 20 mag/square arcsec corresponds to 10<sup>-8</sup> maggies per square arcsec). The number of annuli for which there is a measurable signal is listed as nprof, the mean surface brightness is listed as profMean, and the error is listed as profErr. This error includes both photon noise, and the small-scale ``bumpiness'' in the counts as a function of azimuthal angle.

When converting the profMean values to a local surface brightness, it is not the best approach to assign the mean surface brightness to some radius within the annulus and then linearly interpolate between radial bins. Do not use smoothing splines, as they will not go through the points in the cumulative profile and thus (obviously) will not conserve flux. What frames does, e.g., in determining the Petrosian ratio, is to fit a taut spline to the cumulative profile and then differentiate that spline fit, after transforming both the radii and cumulative profiles with asinh functions. We recommend doing the same here.
The annuli used are:

Aperture	Radius (pixels)	Radius (arcsec)	Area (pixels)
1	0.56	0.23	1
2	1.69	0.68	9
3	2.58	1.03	21
4	4.41	1.76	61
5	7.51	3.00	177
6	11.58	4.63	421
7	18.58	7.43	1085
8	28.55	11.42	2561
9	45.50	18.20	6505
10	70.15	28.20	15619
11	110.50	44.21	38381
12	172.50	69.00	93475
13	269.50	107.81	228207
14	420.50	168.20	555525
15	657.50	263.00	1358149

Surface Brightness & Concentration Index
The frames pipeline also reports the radii containing 50% and 90% of the Petrosian flux for each band, petroR50 and petroR90 respectively. The usual characterization of surface-brightness in the target selection pipeline of the SDSS is the mean surface brightness within petroR50.

It turns out that the ratio of petroR50 to petroR90, the so-called ``inverse concentration index'', is correlated with morphology (Shimasaku et al. 2001, Strateva et al. 2001). Galaxies with a de Vaucouleurs profile have an inverse concentration index of around 0.3; exponential galaxies have an inverse concentration index of around 0.43. Thus, this parameter can be used as a simple morphological classifier.

An important caveat when using these quantities is that they are not corrected for seeing. This causes the surface brightness to be underestimated, and the inverse concentration index to be overestimated, for objects of size comparable to the PSF. The amplitudes of these effects, however, are not yet well characterized.

Model Fit Likelihoods and Parameters
In addition to the model and PSF magnitudes described on the photometry page, the likelihoods deV_L, exp_L, and star_L are also calculated by frames. These are the probabilities of achieving the measured chi-squared for the deVaucouleurs, exponential, and PSF fits, respectively. For instance, star_L is the probability that an object would have at least the measured value of chi-squared if it is really well represented by a PSF. If one wishes to make use of a trinary scheme to classify objects, calculation of the fractional likelihoods is recommended:

f(deV_L)=deV_L/[deV_L+exp_L+star_L]

and similarly for f(exp_L) and f(star_L). A fractional likelihood greater than 0.5 for any of these three profiles is generally a good threshold for object classification. This works well in the range 18<r<21.5; at the bright end, the likelihoods have a tendency to underflow to zero, which makes them less useful. In particular, star_L is often zero for bright stars. For future data releases we will incorporate improvements to the model fits to give more meaningful results at the bright end.

Ellipticities
The model fits yield an estimate of the axis ratio and position angle of each object, but it is useful to have model-independent measures of ellipticity. In the data released here, frames provides two further measures of ellipticity, one based on second moments, the other based on the ellipticity of a particular isophote. The model fits do correctly account for the effect of the seeing, while the methods presented here do not.

The first method measures flux-weighted second moments, defined as:
M_xx = <x²/r²>
M_yy = <y²/r²>
M_xy = <xy/r²>

In the case that the object's isophotes are self-similar ellipses, one can show:
Q = M_xx - M_yy = [(a-b)/(a+b)]cos2φ
U = M_xy = [(a-b)/(a+b)]sin2φ

where a and b are the semi-major and semi-minor axes, and φ is the position angle. Q and U are Q and U in PhotoObj and are referred to as ``Stokes parameters.'' They can be used to reconstruct the axis ratio and position angle, measured relative to row and column of the CCDs. This is equivalent to the normal definition of position angle (East of North), for the scans on the Equator. The performance of the Stokes parameters are not ideal at low S/N. As of DR1, frames provides measurements of adaptive moments which are better shape estimators than the Stokes parameters. Read the detailed description of adaptive moments.

Isophotal Quantities
A second measure of ellipticity is given by measuring the ellipticity of the 25 magnitudes per square arcsecond isophote (in all bands). In detail, frames measures the radius of a particular isophote as a function of angle and Fourier expands this function. It then extracts from the coefficients the centroid (isoRowC,isoColC), major and minor axis (isoA,isoB), position angle (isoPhi), and average radius of the isophote in question (Profile). Placeholders exist in the database for the errors on each of these quantities, but they are not currently calculated. It also reports the derivative of each of these quantities with respect to isophote level, necessary to recompute these quantities if the photometric calibration changes.

Adaptive Moments
The adaptive moments are new quantities which were not present in the Early Data release. Read the detailed description of adaptive moments.