Introduction: Motivation
A proper study of galaxy evolution requires either a complete or representative sample of
galaxies in some fair (co-moving) volume of the Universe. Yet there are significant
selection effects associated with detecting extended diffuse objects whose flux per
detector pixel competes with flux noise from the sky. Thus, for any combination of
detector and redshift (through the presence of (1+z)4 surface brightness dimming) there is
a range of intrinsic galaxy properties (e.g. diameter and/or average surface brightness)
that will preclude their detection and subsequent inclusion in any sample. A natural
question to then ask is the following: if one took all galaxies in our local co-moving
volume of radius 10 Mpc and observed that volume at various redshift intervals (e.g.
z=0.4,0.5,0.6, etc), at what redshift would selection effects begin to significantly prevent
galaxy detection and present the observer with a non-representative sample of galaxies?
The Madau plot is essentially a parameterization of the evolution of the star formation
rate per unit volume per unit redshift. In our local volume with radius = 10 Mpc, the
integrated star formation rate is dominated by 2-3 galaxies (e.g. NGC 253, M82 and, to a
lesser extent M83). At redshift z = 0.7, these 3 galaxies might be the only surviving
nearby objects that could be detected (due to their intrinsically high surface brightness
and relatively large physical diameter) and thus that z=0.7 sample would be missing
roughly 99% of the remaining galaxies in our local volume. That would greatly skew
the inferred star formation rate per galaxy. Is this hypothetical situation a real problem
for extant studies of intermediate redshift (z = 0.2 – 1.0) galaxies as detected in HST ACS
Fields? We propose to statistically address this issue. To justify this request, we present
some early results that indeed suggest the presence of significant selection effects against
galaxy detection that are operating in this intermediate redshift range.
Evidence for Selection Effects:
The basic galaxy detection problem was first characterized as the galaxy visibility
function by Disney (1976) who mathematically showed the expected surface brightness
(SB) distribution of detected objects is a positively skewed normal distribution with a
peak approximately 1 magnitude lower than the average background level. This
prediction was indeed strongly verified by the photographic observations of Freeman
(1970) and a host of other investigators. In the B-band, the result was B(0) = 21.65 +/0.4 mag/[]”. Over time, using detection strategies to specifically search for low contrast
galaxies, a large population of low surface brightness (LSB) galaxies has been discovered
and characterized, thus supporting Disney’s original claim. Cosmological SB dimming
clearly exacerbates this situation at higher redshift. For instance, at z = 1, the canonical
value of 21.65 mag/[]” would dim by 3 magnitudes , making this population rather
difficult to detect as the HST background sky from 5000-8000 angstroms is not 3
magnitudes fainter as well. Therefore, the most easily detected z=1 galaxies, at these
wavelengths, are those that have high intrinsic UV/Blue SB. In turn, this raises the
question of whether or not such “normal” galaxies are even detected at z = 1. If not, we
have a (weakly/strongly) biased sample (see Wolf etal 2005). One manifestation of this
bias would be the apparent overabundance of bright, high SB, massive galaxies at
redshift 1-2 as detected, for instance, by Glazebrook etal 2004. Without a valid statistical
correction for potential redshift dependent SB biasing, studies of galaxy evolution (e.g.
de Mello etal 2006; Papovich etal 2005), number counts (e.g. Ranalli etal 2005),
merging rates (Bundy etal 2004,2005), will remain compromised and uncertain. In fact,
O’Neil etal 2000 showed that the SB distribution of background galaxies serendipitously
detected in the F814W filter with WFPC had a SB distribution like that of the Freeman
distribution which peaks 1 magnitude below the F814W sky brightness. Pixel based
galaxy detection from space, is therefore not immune to these kinds of selection effects.
Proposed Archival Research Program:
Our basic hypothesis/premise is that if one were to take a sample of the nearby disk
galaxies with known scale length, disk color and central SB and then observe that sample
in various intermediate redshift ranges, then increasingly large percentages of those
galaxies would become undetected due to the combined effects of angular diameter
reduction, cosmological SB dimming, and band pass reddening (e.g. K-correction). We
therefore wish to statistically measure, using the procedures outlined below, the drop out
rate as a function of redshift. As a baseline, consider the case of the Milky Way, perhaps
a good model for galaxy evolution (see Naab and Ostriker 2006), which we can
characterize as an L* Freeman disk with a scale length of approximately 3kpc. The table
below shows the angular size of a redshifted Milky Way at an isophotal diameter of 25.0
mag/[]” (in rest frame B-band) using a cosmology of H = 70; = 0.8; m = 0.2; as well
as the 606W-814W K-correction:
z = 0.2 d = 4.3” K = 0.07
z = 0.6 d = 1.1” K= 0.51
z = 0.4 d = 2.0” K = 0.22 z=0.5 d=1.4” K=0.34
z= 0.7 d = 0.8” K= 0.67 z=1.0 d=0.2” K=0.87
Out to redshift of z = 0.4, the MW could still be detected as a small (d= 2”) galaxy of
intermediate color but by redshift 0.8, detection of the MW as a resolved red galaxy is
problematical at best. Hence, the apparent absence of any MW-like galaxies at z=0.8
could be a direct signature of galaxy evolution, galaxy merging, or, selection bias. This
problem is compounded with ACS data because the small pixel size makes the detection
of extended low SB light very difficult due to very low signal to noise per pixel.
Our procedure will be to construct SB, color and angular diameter distributions on all
detected galaxies (using SEXtractor methods) with diameters larger than 0.5 arc seconds
from 4 HST high galactic latitude fields for which minimum exposure times of 1000
seconds in the F606W and F814W have been obtained. These fields are summarized in
the table below. We have already analyzed our own blank field (GO Program #09830) as
well as the Groth strip (see below). Our analysis has produced results very similar to
those of Benitez etal 2004, which contained the first statistical analysis of faint galaxies
detected in the ACS. The analysis of our high galactic latitude produced approximately
1000 SExtractor galaxies in the two filters. Thus an analysis of 4 additional fields would
produce a total sample of 5000 galaxies. We emphasize that we have already mastered
the relatively large SExtractor learning and optimization curve and are now in a position
to efficiently process more fields.
Preliminary Results:
Figures 1-3 show our distributions of angular diameters, central surface brightnesses and
606-814 colors for our sample. Central surface brightnesses were calculated by doing
aperture photometry within circular apertures of 4 and 9 square pixels. To measure
colors, SExtractor was run using the IR frame as a detection image and "associating" with
the list of objects obtained through earlier visual inspection. Isophotal magnitudes were
obtained using the pixels associated with the identified object that are above the detection
threshold minus the background in the detection image. Diameters reported are derived
from the Kron radii measured by SExtractor on the IR field.
The Diameter Distribution (Figure 1): This obviously skewed distribution suffers from
incompletion at the low diameter end which we estimate occurs at approximately 0.8
arcseconds. Clearly the majority of the detected objects have diameters in the range of
0.8 to 1.5 arcseconds which suggests a median redshift of 0.5-0.6 if the sample is
dominated by conventional disk galaxies like the MW. Disk galaxies with a factor of 2
less scale length than the MW (and those galaxies are very common in the nearby
Universe) would not likely appear in this sample if their redshifts were greater than ~0.3.
The Central Surface Brightness Distribution (Figure 3): The measured SB
distribution is strongly peaked (direct evidence for SB selection effects) and clearly has a
strong fall off beyond a value of 25.5/[]”. The bulk of the sample falls in a +/- 1
magnitude range centered on 24.5/[]” in the F814W filter. Obviously, without redshift
information, we can not transform this to a rest band SB. However, statistically the data
is again consistent with a median redshift of 0.5-0.6 which represents 1.75 to 2
magnitudes of cosmological SB dimming. The data is not consistent with the detection
of MW like galaxies at redshift of 1 else we would observe more galaxies in the range
25.5-26.5/[]”. Moreover, our data does not show any correlation between central surface
brightness and angular diameter, which would occur if the sample were dominated by
galaxies of similar scale length and central SB but with a large range in redshift.
The Color Distribution (Figure 2): This distribution is also strongly peaked and the
mean value is close to zero, in excellent agreement with Benitez etal 2004. This
agreement also gives us a good independent reality check on SExtractor image recovery
and color measurement. The formal mean value for this distribution is 0.34 but that
value is clearly dominated by the presence of 10% of the sample with colors larger than
1.5. The vast majority of this sample has colors in the range -.3 to +.3. These colors are
far too blue to be consistent with MW like galaxies at median redshift 0.5-0.6.
While this is certainly not a new result we are using it to point out that the color
distribution becomes an extremely strong constraint on our objective. MW like galaxies
at redshift 0.5-0.6 would have K-shifted colors that place them in the range 1.5-2.0 and
there are rather few such galaxies in either this field or the sample of Benitez etal.
In sum, we propose to perform SExtractor image identification and measurement on a
sample of 4000 additional galaxies in order to construct statistical distributions of angular
diameter, color and central surface brightness. From those distributions we will be able
to determine the probability that nearby galaxies of a given scale length, color and central
surface brightness are not being detected in the ACS fields. In turn, that will provide a
statistical measure of population incompleteness as a function of redshift (out to z~1).
With this information, the measured properties of the detected sample can be corrected
for these kinds of drop out biases resulting in a more robust measure of galaxy evolution
and a better sense of the overall selection biases associated with the detection of passively
evolving disk galaxies.
References:
Benitez etal 2004 ApJ Supp 150,1
Bundy etal 2004 ApJ 691, L123
Bundy etal 2005 ApJ 625, 621
Disney 1976 Nature 256, 473
De Mello etal 2006 AJ 131, 216
Freeman 1970 ApJ 160, 811
Glazebrook etal 2004 Nature 430,182
Naab and Ostriker 2006 MNRAS in press
O’Neil etal 2000 ApJ Supp 128,990
O’Neil and Bothun 2000 ApJ 529,811
Papovich etal 2005, ApJ 631,101
Ranalli etal 2005 A&A 440, 23
Wolf etal 2005 ApJ 630, 771
The Figures below show the diameter, color distributions and central SB distributions for
the approximately 1000 galaxies in our SExtractor sample.
The Potential Archived Fields to Analyze in Priority Order of Usefulness:
The first 5 fields are acceptable/ideal; the latter 2 may be problematical. We already have
reduced most of the Groth Strip but have not yet completely the statistical analysis of the
SExtractor identified images.
Proposal 10134 has 2260s exposures for f606w and 2100s for f814w. The Extended
Groth Strip
Proposal 9361 has 2520s exposures for f606w and 10080s for f814w. Target is resolved
dwarf galaxy SBS 1515+437 so plenty of blank sky available
Proposal 9498 has 1020s exposures for f606w and 4080s for f814w. Close Binary
Quasar 0103-2753; Plenty of blank sky available
Proposal 9764 has 2420s exposures for f606w and 2500s for f814w. Distant field to
search for Giant Ellipticals at z ~ 1.5
Proposal 10413 has 1280s for both; Original Target is NGC 3379 but there is plenty of
blank sky to work with
Proposal 10200 has 2336s exposures for f606w and 4944s for f814w. Original Target is
galaxy cluster at z=0.3
Proposal 10420 has 2000s exposures for f606w and 4000s for f814w. Original Target is
massive distant galaxy cluster so this field might not be ideal.