Deep Galaxy Counts and the Optical Extragalactic Background

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Deep Galaxy Counts and the Optical Extragalactic
Background
T. Dolch (JHU), H.C. Ferguson (STScI)
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Abstract

• The number densities of galaxies
  (galaxies/deg2/magnitude) as a function of
  magnitude can be an excellent test of
  evolutionary and large-scale structure models.
  Measurements of counts across a wide spectral
  range can help constrain the evolution of dust
  and star formation. Comparisons of the integrated
  light from resolved galaxies to measurements of
  the diffuse background are also important for
  understanding galaxy evolution and assessing the
  importance of low-surface brightness structures
  to the overall stellar mass density of the
  universe. Here we compare number counts from
  recent galaxy surveys, correcting for their
  differing passbands by adopting first-order
  changes in the typical galaxy template with
  respect to magnitude. Surveys used include the
  Sloan Digital Sky Survey (SDSS), the Great
  Observatories Origins Deep Survey (GOODS), the
  Hubble Ultra-Deep Field (UDF), and a number of
  other projects. The observed spectral bands range
  from the SDSS-g to the SDSS-z bands. With some
  assumptions about galaxy sizes and
  surface-brightness profiles, we attempt to
  account for the light missed in standard
  photometric estimates, and integrate the
  resulting corrected counts to estimate the total
  extra-galactic background due to resolved
  galaxies.

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Introduction and Motivation

• One of the most straightforward glimpses of
  structure over cosmic time is the variation of
  galaxy number density with magnitude. Given an
  understanding of the luminosity function at
  different redshifts, a comparison with galaxy
  counts can show the importance of factors not
  intrinsic to large-scale structure models, such
  as star formation rates and absorption due to
  dust. Most uniquely, galaxy counts (as opposed to
  simply being one of many structure evolution
  constraints) can be compared to the extragalactic
  background light (EBL) at a given wavelength if
  one integrates the number densities over
  magnitude. The EBL itself is the most readily
  visible signature of energy inputs after
  recombination. It also arises from the integrated
  flux of galaxies too faint to be detected as
  discrete objects. Thus, the integrated density
  leads to an estimate of the "optical background"
  of the universe. Here, we contribute to these
  efforts by deriving counts from the UDF and
  GOODS-HDF fields and using them to obtain an
  empirical model for missing light.

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Procedure
Description Of Data

• counts in non-SDSS bands were shifted into the
  nearest SDSS passbands using the appropriate
  color corrections
• other effects (template used, variation of
  template with magnitude) second order, ignored
  here
• counts extracted from UDF and GOODS-HDF data-from
  SExtractor-derived catalog
• used root-n errors when errors in number density
  not published

• UDF (Beckwith et al.), GOODS-HDF B, V, I, Z
• Capak et al B, R, I, z
• counts compiled in McLeod et al Bj, Gunn-r, I, z
• Postman et al Cousins-i
• SDSS (Yasuda et al.) g, r, i, z
• counts from other surveys shifted into the four
  SDSS bands (Fukugita et al.), respectively

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Galaxy Number Counts Compared With A Euclidian
Distriubtion

• deviation from Euclidian universe (Mattig et
  al.) shown here, where
• log(galaxies/deg2/magnitude) 0.6m
• McLeod/SDSS-g bright magnitude differences due
  to inhomogeneities because
• different patches of sky covered in each
• distributions match at faint end
• northern celestial hemisphere (where SDSS
  primarily covered) known to have brighter
  luminosity function than the southern (where
  McLeod-compiled surveys covered)
• magnitude dependent color shift changed
  discrepancy little in bright mags

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Correcting For Missing Light

• We adopt a simple, purely empirical, bivariate
  size-magnitude relation

Number-magnitude relation
Size-magnitude relation
Both mean size and width vary with magnitude
We construct a two-dimensional probability
distribution from this model, convolve it with
the observational transfer function, and
determine the best fit via maximum likelihood. We
fit GOODS and the UDF separately. The transfer
function is a smooth approximation to the scatter
and incompleteness of the surveys determined from
simulations where artificial galaxies were
inserted into the images and measured using
Sextractor (Ferguson et al. 2004).
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Data and Model Probability Distributions
Illustration using the GOODS z band. The white
square shows the region used for the fits.
Roughly 28000 galaxies are used in the fit.
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Number-magnitude and magnitude-size relations
Galaxy Counts Blue points are the GOODS z-band
data. The green line is the best-fit model after
application of the transfer function. The red
line is the input model with no observational
selection or measurement biases. Dotted lines
show the boundaries of the region used for the
fitting.
Galaxy Sizes in different intervals of apparent
magnitude (Sextractor MAG_AUTO).
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Observational Transfer Function
Two factors influence galaxy counts
detectability and bias. Detectability Galaxy
detectability depends on total flux and size
galaxies can be missed if the are too small (i.e.
mistaken for point sources) or are so large that
they fall below the surface-brightness detection
threshold. Bias The apertures used to measure
galaxy magnitudes typically miss some fraction of
the light. Therefore, the recorded magnitudes are
too faint. This bias is a function of magnitude
and size (and profile shape). The observational
transfer function is a model of both bias and
incompleteness that can be applied to a
theoretical model for the number counts and
size-distribution to predict the observed
quantities.
Transfer kernels Artificial galaxies were drawn
from a uniform distribution in half-light radii
re (up to 2) and magnitude (20ltMABlt30) and
inserted into the GOODS and UDF images. The
distribution includes a 50/50 mixture of oblate
spheroids with an r1/4 light profile and disks
with an exponential profile. Galaxies were
recovered using SExtractor. The results of these
simulations were adaptively smoothed using an
Epanechnikov kernel density estimator to produce
a set of transfer kernels, which map each input
m,re to an observed m,re. An example of such a
grid is shown at right. For fitting the data we
used a grid with a spacing of 0.4 in mag and 0.14
in log re.
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Transfer Kernels
Larger galaxies
Each panel shows the distribution of magnitude
and half-light radius that would be observed for
an input m,re at the center of the panel. The
completeness of each interval is shown in the
upper left.
Fainter galaxies
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Implications For EBL How Much Light In The Sky
Is From Galaxies?

• take integral of counts adjusted for missing
  light over all magnitudes should equal the
  contribution to the EBL from galaxies
• for a given magnitude range, only one survey is
  used in integral
• after extrapolating the missing light models low
  magnitudes (30th mag) and integrating, we found
  that contribution below the UDF completeness
  limit (28th mag) is minimal (blue to black
  below)
• also shown EBL measurements from Bernstein et
  al. (listed in Totani et al.) and Dwek et al. as
  well as corrected counts from models from Totani
  et al.

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References
Conclusions

• EBL still not fully accounted for
• missing light corrections are surprisingly
  large, and may be an essential contributing
  factor to the EBL-galaxy light discrepancy

• Beckwith, S., et al., 2004, AAS 202.1705B
• Bernstein, R. A. 1998, Ph.D. thesis,
• California Institute of Technology
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• Dwek Krennrich, 2005, ApJ, 618, 657
• Ferguson, H. C., et al., 2004, ApJ, 600, L107
• Fukugita et al., 1996, AJ, 111, 1748
• Mcleod Rieke 1995, ApJ, 454, 611
• Mattig 1958, ZA, 44, 280M
• Postman et al. 1998 ApJ, 506, 33
• Totani, T., et al., 2001, ApJ, 550, L137
• Yasuda et al. AJ, 2001, 122, 1104