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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

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 1sigma errors, respectively. The hatch-marked region shows the 1sigma uncertainty in the detected EBL due to uncertainty in ZL color. The lower limit arrows connected by a dashed line indicate the total flux from individually photometered galaxies with magnitudes 23 < V555 < 30 A B mag in the HDF catalog. The u-shaped lower limit arrows show minEBL23, which is the flux as determined by ensemble photometry from galaxies with 23 < V555 leq 28 A B mag in the EBL fields.

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.

Table 2

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 sqrt2riso < r < 4riso (see Figure 2), beyond the standard-size galaxy apertures (sqrt2riso) 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

Figure 2. Aperture corrections as a function of Deltaµ = µiso - µ0 (isophotal minus central surface brightness) derived by "ensemble aperture photometry" of the EBL field for V (thick line) and I (thin line). The mean apparent magnitude in V606 and I814 corresponding to a particular value of Deltaµ in the HDF images is indicated by the x-axes at the top of the plot. Error bars show the 1sigma statistical error in the mean corrections derived from 18 WFPC2 images of the EBL field (six exposures, three WF chips).

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 Deltaµ = 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 2sigma - 3sigma 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 2sigma 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.

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