Stars superimposed on galaxies are a major problem for 2MASS and
DENIS. If no effort is made to subtract stars, galaxy fluxes are
biased high by >10% for 5-10% of galaxies at the pole, 10-20% of
galaxies at b=20 deg, and 50-80% at b=5 deg,
where the lower number refers to a very local
isophotal magnitude and the higher number refers to the total observed
magnitude. The bias and number of galaxies affected is nearly
independent of galaxy magnitude. We have therefore investigated a
number of different star subtraction techniques to derive the least
biased measure. We used the observed galaxies from two prototype
camera scans through the Coma Cluster as a baseline. We then add
artificial stars to these scans and determine the change in the galaxy
photometry relative to the actual scans.
For 2MASS, the measure with the smallest bias and scatter is one that
computes a global background and subtracts nearly every detected
neighboring source. The bias is less than 4% (3sigma upper limit)
even at densities corresponding to b=5 deg, and the scatter due solely
to stellar contamination is ~8%. Doing the same full subtraction
at high Galactic latitudes causes only 2% of the galaxies to have a
flux change of over 5%, and most of these changes are due to distinct
stars on top of the galaxies or flux from a neighboring galaxy.
Introduction
One of the major scientific goals for 2MASS is to produce a galaxy
catalog that is as uniform as possible over nearly the entire sky.
Galaxy catalogs derived from the optical necessarily suffer from
the extinction due to dust in our Galaxy, which removes over half the flux
from external galaxies below b=25 deg. In contrast,
at K the corresponding latitude is about 2 deg.
Unfortunately, there are evils at low Galactic latitude other
than dust, namely stars. Bright stars within the boundaries of galaxies can
cause galaxies to be lost from the galaxy catalog, and faint stars can boost
faint galaxies above the catalog threshold. These effects on completeness
and reliability will not be discussed here.
This paper examines the effect of stars on galaxy photometry. Stars
2.5 mag. fainter than a given galaxy boost the reported flux
of that galaxy by over 10% unless they are removed or compensated
for. In the best case, using an isophotal magnitude of 20 Kmag. per
square arcsecond, 5% of all galaxies at b=90 deg and 50% of
all galaxies at b=5 deg will be so affected. In the worst case, using a
``total'' magnitude measure, 10% of all galaxies will be so affected at
the Galactic pole and nearly all, 80%, at b=5 deg. This effect is nearly
independent of the magnitude of the galaxy.
There are two ways to mitigate this problem. First, a local
background derived from an annulus surrounding the source can be
subtracted from the galaxy measurement. This annulus should
on average have the same number of stars in it, which removes the
bias. However, this has several potential problems. The noise
of the resulting magnitude measure has been increased by sqrt[2].
The number of galaxies affected by a star has been doubled at
higher Galactic latitudes. Finally, due to the galaxy correlation
function, the local background has more galaxies in it than the true
background farther away from the galaxy, but fewer galaxies in it than
in the galaxy aperture.
Second, one can subtract stars directly. If done correctly, the upward
bias should be significantly lessened. This method suffers from none
of the problems of subtracting a local background. However, there are
several different potential problems. Stars that fall directly on top of
the nucleus of a galaxy can never be subtracted. Stars superimposed on
the rest of the galaxy may look fuzzy and not be subtracted. The
galaxy may enhance the derived stellar flux, and cause an incorrect
flux to be subtracted. Parts of the galaxy that look star-like may
inadvertently be subtracted.
We have analyzed both methods by taking actual prototype camera data
from high Galactic latitudes and placing simulated stars representative
of lower Galactic latitudes in those data. We then ran the 2MASS
prototype galaxy processor over these simulated scans and determined
the change in the galaxy photometry relative to the actual scans.
This paper is organized as follows. Section 2 reports how the
simulation was done. Section 3 gives the expected photometric
contamination rate as a function of Galactic latitude and magnitude.
Section 4 gives the results of the simulation, and Section 5
gives our summary.
We used the observed galaxies from two prototype camera scans through
the Coma Cluster at the North Galactic Pole as a baseline. These scans
are each 6 deg long by 0.14 deg wide, and were taken in April and May
1995. The prototype galaxy processor found 45 galaxies above an
isophotal K magnitude of 13.0 mag, using the 20 mag per square
arcsec isophote.
We work with the image product produced by the prototype processing
pipeline in place at IPAC. The image product combines the 6
camera frames taken with a pixel size of 2 arcsec and creates an image
with 1 arcsec pixels. We characterize the point sources in these
two scans by fitting the functional form
We pick a stellar source density and a log N / mag power law slope
representative of a given Galactic latitude, and then draw random
sources from that distribution down to K = 16 mag. and place them
randomly on those images until we have achieved the desired source
density. Because the noise in the images is heavily dominated by the
background noise, we added no additional Poisson noise in the stellar
flux. The additional noise in these simulated images is thus solely due to
the stellar contribution.
We then run the prototype galaxy processor ab initio on these simulated
scans, redoing the detect step, etc. without any knowledge of where
the galaxies are. We match the detected sources with the original
galaxies and determine the change in the galaxy
photometry relative to the actual scans.
For definiteness, define a galaxy flux to be
contaminated by a star
if the star contributes more than 10% of the galaxy flux. The
number of such contaminating stars depends on the magnitude of the
galaxy m, and stars brighter than m+2.5 mag. will then contaminate.
The number of contaminating stars also
depends on the size of the galaxy. Because of a coincidence in the
way these numbers scale with magnitude, the probability of stellar
contamination is essentially independent of magnitude.
This can be illustrated as follows. Consider a circularly-symmetric
galaxy (in the plane of the sky) of radius R. The number of
contaminating stars that fall within the area of the galaxy (neglecting
edge effects of stars falling on the edge of the galaxy at radius R)
is:
The flux of a galaxy with an exp{-{(r/R)}**{1/beta}} profile is proportional
to R**2, and hence R**2 can be written as alpha{10}**{-0.4m}. The density
of stars is ~N0{10}**{+0.4m}. Hence the number of contaminating
stars is:
The stellar density exponent is actually slightly less than 0.4,
leaving a weak dependence on m. However, the simulation shows
that the contamination rate is independent of magnitude within the
simulation statistics.
Fig. 1 shows the empirical radius --- magnitude relation for Coma cluster
galaxies in the two scans. Using a rough fit to the isophotal radius
at K=20 mag. per square arcsecond and to the radius of the ellipse that
corresponds to the total flux, and using stellar densities at various
Galactic latitudes corresponding to Galactic longitudes near 50 deg,
the probability that a given galaxy is contaminated by a star is shown
in Fig. 2. We have assumed galaxies circularly symmetric in the plane
of the sky.
In the best case, using an isophotal magnitude of 20 mag. per
square arcsecond, 5% of all galaxies at the Galactic pole, 10% of
all galaxies at b=20 deg, and 50% of all galaxies at b=5 deg will be
so affected. In the worst case, using a ``total'' magnitude measure,
10% of all galaxies will be so affected at the Galactic pole, 20% at
b=20 deg and nearly all, 80%, at b=5 deg.
Simulation results
Figs. 3 and 4 show the change in magnitude for the Coma galaxies
resulting from stellar contamination of 4,000 sources / square degree for
K < 14 mag., which corresponds to l=50 deg and b=10 deg,
distributed in flux using a power law exponent of 0.32 down to K
= 16 mag., for various stellar subtraction schemes. These results
are for the least contaminated measure, the isophotal magnitude
corresponding to K = 20 mag. per square arcsecond, at b=10 deg .
The ordinate in
each of these plots is the magnitude difference of the galaxy as
computed in the simulation and as computed in the actual Coma scan.
Negative values correspond to the simulated galaxy being brighter,
usually due to unsubtracted stars on top of the galaxy. The abscissa
is the isophotal magnitude found in the simulation scans. Only
points brighter than 13 mag. will be discussed below.
Fig. 3a shows the results for no star subtraction using an annular background.
The scatter is quite high --- 11-16%, depending on whether the one
point with -0.8 delta mag is included, but there is no bias within
the precision allowed by the high scatter (< 7%, 3 sigma).
For Fig. 3b, everything is the same except that now we subtract stars
whose peak pixel flux is brighter than that of the peak pixel flux of
the given galaxy. The big outlier is now tamed, but the scatter is
still 11%, with the same limits to any bias.
For Fig. 4a, we now subtract nearly all stars. In this simulation, we
subtracted everything 4 sigma above the global
background and 3.5 sigma above a local background. The
improvement is significant --- the scatter is now 8%, and there is still
no bias above 5% (3 sigma).
For Fig. 4b, we subtract nearly all stars in the same way, but dispense
with using the local background. As expected, the scatter decreases
markedly since we have dropped the scatter due entirely to noise by
the sqrt{2}. The scatter is now 6%, and there is still no bias above
3% (3 sigma).
We have also simulated b=5 deg, and the same trend holds: the biases
are all small, and the algorithm with the least scatter is the one
that subtracts nearly all stars and uses only the global background
subtraction, with a bias less than 4% and a scatter of about 8%.
Subtracting a local background produces a bias less than 7% and a
scatter of about 12%.
Conclusions
Subtracting nearly all stars that are brighter than 4 sigma above the
global background and 3.5 sigma above an extremely local background
works amazingly well. This algorithm results in no bias
within the limits of our simulations. It produces magnitudes that have
only slightly worse scatter at the faint end than comes solely from the
Poisson noise. Magnitudes for brighter galaxies will be dominated by this
scatter at low Galactic latitudes, but with a scatter of only 6% even
at b=10 deg, these magnitudes are still quite precise. Additionally
subtracting a local background offers no advantages, but exacts a clear
noise penalty.
Biases will always remain. Stars falling very close to the
nucleus of galaxies cannot reliably be subtracted, leaving a positive
bias. Sometimes parts of a given galaxy may unintentionally be
subtracted, resulting in a negative bias. However, the results of this
analysis shows that these biases are probably less than that caused by
interstellar absorption at low Galactic latitudes.
Abstract
The Simulation
f0exp{-{(r/alpha)}**{1/beta}}
to every source. All the point sources are well described in these
images by alpha = 2.0 arcsec and beta = 0.54, which corresponds to a
seeing FWHM of 2 arcsec prior to convolution with the large 2MASS
camera pixels.
Expected stellar contamination rate versus latitude
pi * R**2 * rho
where
rho is the density of stars brighter than m+2.5 mag.
pi * alpha {10}**{-0.4m} * N0{10}**{+0.4(m+2.5)} = {10} pi alpha N0
independent of m.
Two key comparisons set the scale for the biases and scatter. First,
at b=10 deg, Galactic absorption removes ~8% of the flux of a
galaxy, with comparable scatter. At 5 deg, ~12% of the flux of a
galaxy is lost, with comparable scatter. Second, the scatter caused by
Poisson noise within the aperture of a galaxy varies from ~5% for
K < 12 mag., using the 20 mag. per square arcsecond isophote, to
10 at K = 13.2 mag. Again, this noise is constant in the
following comparisons to isolate the effect of stellar contamination.
