2.2.4 What is the required exposure time?

Having a qualitative characterization of the background, based on the target ecliptic/Galactic latitude, and an estimate of the instrument sensitivity, all we need now is the target flux in order to calculate the time required to reach a desired S/N. If you have this in-hand for one of the Spitzer passbands, you are (almost) in business. If not, you will need to use some other mechanism, and we provide some suggestions for that in a moment.

First, though, what is the flux in the Spitzer passbands? For photometry, Spitzer is following the same calibration methodology as used with IRAS (Beichman 1988), COBE/DIRBE (Hauser 1988) and ISO (Siebenmorgen 1999). See the instrument Data Handbooks for more discussion, because IRAC and MIPS calculate color corrections differently!

With IRAC, we quote flux densities at some nominal wavelengths that are accurate for sources with a flat spectrum

$$\nu \; F_\nu = {\rm constant}.$$ (2.1)

For other sources, we need to calculate the color correction.

For IRAC, we can proceed as follows. Define $K$ as

$$K = \frac { \int \left( F_\nu/F_{\nu_0} \right) R_\nu d\nu } { \int \left( v/v_0 \right)^{-1} R_\nu d\nu }$$ (2.2)

where $\nu_0$ is the nominal frequency where we will quote flux densities (see the IRAC Data Handbook), and $R_\nu$ is the system response function. The form of $R_\nu$ is tabulated on the SSC webpages. For IRAC, see:

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

Finally, then, the quoted flux density (in Spitzer units), $F^{\rm quot}_\nu$ for a source with intrinsic flux density $F_\nu$ will be

$$F^{\rm quot}_\nu = K \; F_\nu.$$ (2.3)

More details may be found in the IRAC and MIPS Data Handbooks.

What does this all mean? Well, suppose you wish to do photometry on an object and you know its flux density, $F_\nu$. To estimate exposure times, etc., you should convert this to the Spitzer system by calculating the color correction, $K$, for the passband in question.

Now what if you don't have an estimate for the object's flux density, but instead have a magnitude? If you are like the authors of this Cookbook (coming from an optical astronomy background), flux densities (for which the units are Jy for point sources, and Jy/arcsec$^2$ for extended sources) are rather nebulous quantities. With this in mind, we have explicitly provided the formalism for converting between the various unit systems in an Appendix of this Cookbook (see Appendix A). As well, the SSC has created an online tool for converting between magnitudes (in various systems) and flux densities; see:

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

Now what if you don't have a good estimate of your target flux? For example, suppose you wish to detect high-z star-forming galaxies, but are unsure what is the expected flux at $70 \; \mu {\rm m}$? The SSC has developed some tools to help with this. Part of the PET is for extragalactic point source objects. Based on the observed SEDs of some ``famous'' objects in the Universe, as well as composite SEDs of various classes of objects (e.g., ellipticals, LINERs, starbursts, etc.), this tool can serve as a guide for predicting the expected flux in the Spitzer bands. See the SSC tools webpage:

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