The individual measurements which are combined to obtain our detections of the EBL are summarized in Table 1. We summarize our confidence intervals on the detected EBL23 in Table 2 and Figure 1. For comparison with the EBL23 fluxes, we have included in Table 2 the integrated flux from individually photometered sources in the HDF, as measured using the photometry package FOCAS (Jarvis & Tyson 1981, Valdes 1982) and published in Williams et al. (1996). As the values in this table show, the mean EBL23 detections in each bandpass are more than 5 × higher than the integrated flux in HDF galaxies as measured by standard photometry.
|
Figure 1. Summary of EBL23 measurements,
repeated from
Paper I. Filled circles show the EBL23 obtained from surface
photometry of the total background measured from HST/WFPC2, the
zodiacal light as measured from Las Campanas Observatory, and models
of the diffuse galactic light as summarized in
Section 3.
The solid, dotted, and long-dashed error bars show the combined,
systematic, and random
1 |
To help understand this large difference between the detected EBL and the flux in HDF number counts, we have measured the total flux from resolved galaxies in our WFPC2 images (23 < V555 < 27.5) using a method which we call "ensemble aperture photometry." This method is uniquely suited to both our goal of a very accurate measurement of the ensemble flux of all galaxies in our images and to our data set, which has zero-point calibration accurate to ±0.1% over each image and negligible scattered light. This method is described in detail in Paper I and summarized below.
Briefly, we identify the total flux from detectable galaxies fainter than Vcut = 23 A B mag by simply masking out galaxies with V < Vcut A B mag (and all stars) and averaging the flux of every pixel in the frame. From this, we obtain the mean surface brightness of foregrounds plus all extragalactic sources, or the average surface brightness per pixel from "objects + sky." We then mask out all detected objects using standard detection apertures (twice the isophotal area) and calculate the average flux in the remaining pixels. From this, we obtain the mean surface brightness outside of the galaxy masks, or the average surface brightness per pixel from "sky." The difference between these two measurements is then the ensemble surface brightness of all sources within the area of the masks. This assumes that the sky level is uniform, which is the case to better than 1% accuracy in our images. By varying the bright magnitude cut-off (Vcut) we choose for measuring "objects + sky," we can isolate the flux coming from sources fainter than Vcut.
As discussed in Paper I, we find that the recovered flux increases
steadily with increasing mask size. For example, roughly 20% of the
light from galaxies 4 magnitudes above the detection limit lies at
radii 
2riso
< r < 4riso (see
Figure 2), beyond the standard-size galaxy apertures
(2riso)
used in faint galaxy photometry packages, such as SExtractor
(Bertin & Arnouts 1996)
or FOCAS. Because
estimates of the sky level in standard photometry packages come from
just beyond the detection apertures, these sky estimates will include
some fraction of the galaxies' light and will doubly compound this
error. In addition, because galaxy apertures start to significantly
overlap in our images and the HDF images when they extend to
r ~ 4riso, we find that some flux from the
wings of detected
galaxies will inevitably contribute a pedestal level to the mean sky
level in any image. We have estimated this pedestal level by Monte
Carlo simulations as described in Appendix B of Paper I. The pedestal
is independent of field, but does dependent on the detection limits
and surface brightness characteristics of the data. For
V606 HDF
images, this pedestal level is roughly 10% of the total flux from
V > 23 AB mag galaxies and, again, this error is compounded by the
fact that any flux at radii beyond galaxy apertures can be include in
the "sky" estimate. The true flux from V > 23 AB mag galaxies in
the HDF is therefore almost twice what is recovered by standard
methods (see Section 4.1).
|
Figure 2. Aperture corrections as a
function of
|
Using different values of
Vcut, we can quantify systematic
errors in faint galaxy photometry as a function of the isophotal
surface brightness limit of the data,
µiso, and the central
surface brightness of the source, µ0. The smaller
the value of
µ =
µiso - µ0 is for a
particular galaxy, the
larger the photometric error in standard aperture photometry. This
problem has been discussed in the literature at length with respect to
low surface brightness galaxies at low redshifts based on
extrapolations of simple exponential light profiles
(Disney 1976,
Disney & Phillips 1983,
Davies 1990);
the same principle begins to
apply to normal surface brightness galaxies which have low
apparent surface brightness at higher redshifts due to (1 +
z)4 surface brightness dimming
(Dalcanton 1998).
Finally, we note that the direct measurements of the EBL23 in our data
- based on surface photometry of the total integrated background,
zodiacal light, and diffuse galactic light - are
2
-
3 detections.
However, the mean flux from detected sources is obviously an absolute
minimum value for the EBL.
Therefore, the strongest lower limit we can place on the flux from sources
fainter than V = 23 AB mag (EBL23) is the mean flux in
detected galaxies as measured by ensemble aperture photometry in
our WFPC2 data and the HDF.
The strongest upper limits we can place on EBL23 are the
2
upper limits of our direct measurements of the EBL23.
In Table 2 we list
(1) our direct measurements of the EBL23, and (2) the minimum
values for the EBL23 (minEBL23) as identified by ensemble aperture
photometry of detected sources in our WFPC2 data and the HDF. For
comparison, the flux in published HDF galaxy counts and ground based
counts are also listed there.
28 A B mag in the EBL
fields.