5.7 Expected Accuracy in Surface Photometry

Whenever a significant signal is detected in a sky region in the ASM1, this should be observed in the BBPs with a suitable sample size and the corresponding data should be sent to the ground for data analysis. A possible way to combine the observations obtained during different scans of the same sky region into a two-dimensional image will be described in Chapter 6. Here, proceeding much like it was done in the previous Section for detection, only an estimation of the accuracy achievable in surface photometry at different surface brightness levels will be derived as function of the adopted sample size.

The baseline sample size for the observation of stars in the Astro 1 and Astro 2 BBPs is of $1\times8$ and $6\times8$ pixels, respectively. These must be considered as starting points for the choice of the sample size for galaxy observation, since it would be desirable to use the same size to observe both stars and galaxies. These two sample sizes, however, are very elongated across-scan, and this could result in problems when trying to reconstruct the two-dimensional morphology of galaxies. Besides, the sample size can be reduced in the across-scan, but not in the along-scan, direction without upsetting the TDI process. Accordingly, four sample sizes of $6\times8$, $6\times4$, $6\times2$, and $1\times8$ pixels were considered. Note that the same sample sizes will be used in Chapters 6 and 7 to numerically simulate galaxy observations as they could be obtained by GAIA.

Table 5.6: All-Mission Accuracy in Galaxy Surface Photometry. Expected all-mission standard error in magnitudes $\sigma_{mag,g}$ in galaxy surface photometry in the $g$ band for different values of sample size and $I$-band average surface brightness within the sample $<\!\mu\!>_{sam}$, according to Equation 5.6 and assuming a total number of 75 scans. $\sigma_{mag,g}$ expressed in magnitudes, sample size in pixels, $<\!\mu\!>_{sam}$ in mag/arcsec$^2$.

$\sigma_{mag,g}$		Sample Size										.
		$6\times8$		$6\times4$		.	$6\times2$		.	$1\times8$		.
$<\!\mu\!>_{sam}$	18.00	0	.	024769	0	.	046959	0	.	10659	0	.	18314
	19.00	0	.	050259	0	.	105942	0	.	25750	0	.	45118
	20.00	0	.	112068	0	.	253102	0	.	63627	1	.	12433
	21.00	0	.	266003	0	.	622273	1	.	58759	2	.	81517
	22.00	0	.	652025	1	.	54938	3	.	97714	7	.	06232
	23.00	1	.	62138	3	.	87809	9	.	97940	17	.	7307

The expected all-mission accuracy in surface photometry in the $g$ band $\sigma_{mag,g}$ for these sample sizes and for different levels of surface brightness is given in Table 5.6, where a total number of 75 scans was assumed. Note that the $g$ band is very similar to the $V$ band (see Table 2.1) and that an average number of 75 scans is expected for each Astro from a 5-year mission (see Figure 2.4). From the tabulated values it appears that the surface brightness limit for surface photometry accurate at a given level increases with the sample size by about one magnitude per different sample size. For instance, the limit for surface photometry accurate to within 0.2 mag/arcsec$^2$ is about 21.0 mag/arcsec$^2$ for $6\times8$ pixels/sample, 20.0 mag/arcsec$^2$ for $6\times4$ pixels/sample and so on.

The surface brightness at the effective radius of a galaxy of $I_{det}=17$ is typically about $\mu_I=22.0$ mag/arcsec$^2$ for E galaxies and $\mu_I=21.5$ mag/arcsec$^2$ for D galaxies, according to Table 4.5. Comparing these values with those in Table 5.6, it appears that a sample size of $6\times8$ or $6\times4$ pixels/sample is preferable in order to obtain multi-color surface photometry in the innermost regions, i.e. down to the effective radius, of most galaxies brighter than $I_{det}=17$. This in turn suggests to carry out galaxy observations in the Astro 2, where both a sample size of $6\times8$ and $6\times4$ pixels could be adopted without upsetting the TDI process for star observations. Note, however, that while an increase in the sample size obviously increases the photometric accuracy, on the other hand this leads to a decrease in the achievable angular resolution. The previous considerations will therefore be combined with those developed in Chapters 6 and 7 to establish the best trade-off between photometric accuracy and angular resolution.