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
visit the Photo pipeline
page. Other photometric outputs, specifically the various
magnitudes, are described on the photometry
page.
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 
In particular, Lupton et al. (2001a) show that the following simple cut
works at the 95% confidence level for our data to r=21
and even somewhat fainter:
psfMag  (dev_L>exp_L)?deVMag:expMag)>0.145
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 signaltonoise 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 stargalaxy 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 azimuthallyaveraged 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^{8} 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
smallscale "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 surfacebrightness 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
socalled "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,
the likelihoods deV_L, exp_L, and star_L are also
calculated by frames. These are the probabilities of achieving the
measured chisquared 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 chisquared 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 modelindependent 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 fluxweighted second moments,
defined as:
M_{xx} = <x^{2}/r^{2}>
M_{yy} = <y^{2}/r^{2}>
M_{xy} = <xy/r^{2}>
In the case that the object's isophotes are selfsimilar ellipses, one
can show:
Q = M_{xx}  M_{yy} = [(ab)/(a+b)]cos2φ
U = M_{xy} = [(ab)/(a+b)]sin2φ
where a and b are the semimajor and semiminor 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.
For future data releases, frames will also output variants
of the adaptive shape measures used in the weak lensing analysis of
Fischer et al. (2000), which are closer to optimal measures of shape for
small objects.
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.
