4 Extracting vertical profiles

 

 

Table 4: Typical errors for ESO 342-G017 vertical profiles.

Uncertainty	R-band		V-band
[electrons]	Galaxy Center (%)	$\pm$4kpc (%)	Galaxy Center (%)	$\pm$4kpc (%)
Averaged flux per pixel	30640	16703	5498	2958
Sky flux per pixel	16651.5	16651.5	2950.2	2950.2
Net flux per pixel	13988.5	51.5	2547.8	7.8
Read Noise ( $\sigma_{\rm RN}$)	0.04 (0.0003)	0.04 (0.08)	0.05 (0.002)	0.05 (0.6)
Flat-Fielding ( $\sigma_{\rm FF}$)	7.4 (0.05)	4.0 (7.8)	1.8 (0.07)	1.0 (12.5)
Photon Noise ( $\sigma_{\rm PN}$)	1.0 (0.007)	0.8 (1.5)	0.5 (0.02)	0.4 (5.4)
Mosaicing Error ( $\sigma_{\rm M}$)	1.7 (0.01)	0.9 (1.8)	2.6 (0.1)	1.4 (17.9)
Surface Brightness Fluctuations ( $\sigma_{\rm L}$)	0.2 (0.001)	0.01 (0.02)	0.06 (0.002)	0.003 (0.04)
Total Statistical Error ( $\sigma_{\rm STAT}$)	7.6 (0.05)	4.2 (8.1)	3.2 (0.1)	1.7 (22.3)
Sky Subtraction ( $\sigma_{\rm SS}$)$^{\ast}$	0.4 (0.003)	0.4 (0.8)	0.2 (0.008)	0.2 (2.6)
Total ${ m \pm \Delta m}$ [ mag/sqarcsec]	21.17 $\pm$ 0.04	27.3 +0.13-0.12	21.76 $\pm$ 0.03	28.0 +0.30-0.25

The numbers in parentheses are the errors as a percentage of the sky-subtracted flux.
$^{\ast}$ Note: the sky subtraction error is a systematic error and, therefore, does not enter into $\sigma_{\rm STAT}$.

Achieving acceptable signal-to-noise at surface brightness levels 6 to 8  mag/sqarcsec below sky requires averaging over a large number of pixels. We begin by extracting a number of vertical rectangular regions, each of dimension $21 \times 530$ pixels ( $0.9\times 24$kpc), perpendicular to the disk of ESO 342-G017. These extracted areas are centered on the major axis of the galaxy, avoid the most prominent HII regions, and extend well beyond the visible disk. The positions of the extractions were identical for both the R and V-band images; 71 regions were extracted from the R-band image and 52 from the smaller V-band image. Figure 5 shows these areas atop on our masked mosaic R-band image.

From these initial extractions four levels of averaging were performed in order to increase the signal-to-noise:

1.

The sum of the flux across the 21 pixel wide x-direction was determined for each extraction, and normalized by the number of non-masked pixels contained in each row.

2.

Due to the extremely symmetrical cross-section of ESO 342-G017 (see Fig. 6) we were able to average the profiles above and below the disk.

3.

In the vertical direction (z-axis), each profile was averaged over the size of the seeing FWHM ($\sim$10 pixels) for all points above the plane of the galaxy.

4.

Finally, a number of profiles were averaged together. An average of the three innermost profiles (extractions 36 to 38) was made to create one central profile, groups of four profiles (28-31 and 32-35 to the east and 39-42 and 43-46 to the west) were averaged on each side of the center, groups of six (16-21 and 22-27 to the east and 47-52 and 53-58 to the west) were averaged on the outermost ends of the galaxy. The extractions averaged together are shown at the top of Fig. 5. In the case of the V-band image, the averaging process ends with extraction number 52.

The resulting masks made from the R and V images separately, were then multiplied together to create a master mask frame that was applied to each mosaic. This procedure masked 10.3% and 11.0% of the total image areas in the final R and V mosaics respectively. The masked images are shown in Fig. 3.

For each of the vertical extractions covering the visible disk of ESO 342-G017 (profiles 16 to 58 in R and 16 to 52 in V), a least-squares fit to the thin disk component was made. A simultaneous two-component (thin and thick disk) fit was made to each extraction, using an exponential parametrization given by

$$f(z) = f_\circ^{\rm thin} {\rm exp}(-\vert z\vert/h_z^{\rm th... ... f_\circ^{\rm thick} {\rm exp}(-\vert z\vert/h_z^{\rm thick})$$ (1)

for both components, where $f_\circ$ is the surface flux at the position the extraction crosses the major axis of the galaxy, z is the projected distance from the major axis, and h_z is the exponential scale height. The fitted parameters are $f_\circ^{\rm thin}$, $h_z^{\rm thin}$, $f_\circ^{\rm thick}$, and $h_z^{\rm thick}$. Regions strongly affected by dust or clumpy HII regions were excluded from the fit. For comparison, a single-component (thin disk) fit was also performed for those data that lie between 1 and 3 mag/sqarcsec below the central galaxy surface brightness. Results are presented in Sect. 5.

Figure 6: The symmetry of the vertical surface brightness profiles of ESO 342-G017. The north (dashed lines) and south (dotted lines) profiles extracted at various positions along the disk. The object-masked images have been used.

   
4.1 Error analysis

Figure 7: The R-band averaged profiles through the disk of ESO 342-G017, perpendicular to the major axis. The average position from the galaxy center is given at the top of each panel (east of center is indicated by R>0; west of center by R<0). The insets show, on a linear scale, the background-subtracted flux levels of each profile at distances more than 6kpc from the galaxy disk. The simultaneous thin and thick disk fit and the range of data used for the fit is shown by a solid line; the dotted line is the extrapolation of the fit. The dashed line is intended as a guide, and indicates a single-component fit to data dominated by the thin disk. This fit was restricted to data between 1 and 3 mag/sqr arcsec fainter than the peak flux.

Figure 8: As in Fig. 7, but for the V-band averaged profiles through the disk of ESO 342-G017.

We present here a brief summary of the sources of photometric uncertainty and their magnitudes; the reader is referred to the Appendix for a more detailed discussion.

For illustration, Table 4 shows the average flux levels and uncertainties at two positions along the central vertical profile (the average of extractions 36 to 38) of ESO 342-G017, one at the galaxy center and another at the much fainter light levels 4kpc above the galaxy disk. For each of the two flux extremes in each of R and V-bands, we give the uncertainties associated with the average flux per pixel (averaged over the unmasked area of $3\times21\times10$ pixels) in units of electrons and as a percentage of the sky-subtracted flux (given in parentheses).

The systematic uncertainties in the sky level of $\delta {\sc S}_{R} = 0.4~{\rm e}^{-}~{\rm pix}^{-1}$and $\delta {\sc S}_{V} = 0.2~{\rm e}^{-}~{\rm pix}^{-1}$ correspond to errors of only 0.0024% and 0.0068% per pixel in the R and V bands, respectively. These systematic uncertainties are present in the sky-subtracted profiles we present in the next section, but because they correspond to light levels $\Delta R = 11.5$ and $\Delta V = 10.4$ mag below the sky ( $m_{\rm sky}({R}) = 20.98$ mag/sqarcsec and $m_{\rm sky}(V) = 21.60$ mag/sqarcsec), they are of no importance (<10%) over the range of surface brightness we consider. The systematic uncertainty in overall calibration to a standard system of about 5% is relevant, but simply corresponds to a possible overall shift in the surface brightness scale by that amount. Note that at bright flux levels, the error in the magnitudes is dominated by the error in the photometric conversion term, not by $\sigma_{\rm STAT}$. At faint flux levels, the situation is reversed.