4.5 Sensitivity and Exposure Time

Armed with the characterization of the background level (see § 4.4), we can proceed to estimate the required exposure time. The first stop is the IRAC webpage for the instrument sensitivity. See:

http://ssc.spitzer.caltech.edu/irac/

For IRAC, the current estimate of the confusion limit is $\simeq 0.6 \; \mu {\rm Jy}$ (this does not represent a hard sensitivity limit, but rather indicates where source confusion affects the reliability of source extractions; see the IRAC chapter of the SOM for more information). At 3.6 microns, we reach the limit quickly: with a single cycle of the 100 sec frame time for low background. The longest IRAC waveband, 8 microns, reaches the confusion limit last, requiring $> 260 \times 100 \; {\rm sec}$ total integration (for low background) to be confusion limited. See the SOM for more information.

We determine the exposure time required for this proposal to reach $\simeq 1.7 \; \mu {\rm Jy}\; (1 \sigma)$ at 8 microns. For medium background, with a 100 sec frame time^4.3, the $1\sigma$ IRAC point-source sensitivity is $0.73, 1.4, 9.3, {\rm and} \; 12.0 \; \mu {\rm Jy}$ for the 3.6, 4.5, 5.8 and 8.0 micron bands respectively. For long frame times, the noise essentially scales with $t^{-1/2}$. Hence, to reach $\simeq 1.7 \; \mu {\rm Jy}\; (1 \sigma)$ in the 8.0 micron band, we require $49 \times 100 \; {\rm sec.}$

One word of caution however: while our science goal is to probe deeply at 8 microns, the 3.6 and 4.5 micron arrays will be well below the confusion limit with $t_{\rm tot} \simeq 49 \times 100 \; {\rm sec.}$ Since the 3.6 and 5.8 arrays are paired (data are obtained in both arrays simultaneously), and similarly for the 4.5 and 8 micron arrays. So, if we also want (for whatever scientific reasons) the deep 5.8 micron data from 49 repeats of the 100 sec frame time, we must be aware that we will not be increasing the S/N as $\propto \sqrt{t}$ in the 3.6 micron data once the confusion limit is reached in that waveband. A similar argument applies for 4.5 micron data, while we collect the deep 8 micron data.