In the following sections you will find a set of examples for the two different channels and for different types of sources. The examples were chosen in order to present typical objects for the two channels and also to present interesting cases as they may arise with the use of WFC3.
What is the exposure time needed to obtain a signal-to-noise of 10 for a point source of spectral type F0 V, normalized to
V = 27.5, when using the UVIS F555W filter? Assume a photometry box size of 5×5 pixels, and average sky values.
The WFC3 Exposure Time Calculator (ETC) gives a total exposure time of 4419 s to obtain this S/N in a single exposure. Since such an exposure would be riddled with cosmic rays and essentially useless, it is necessary to specify how many exposures to split the observation into. WFC3/UVIS observations generally should be split if the exposure time is longer than about 5 minutes, but for multi-orbit observations, splitting into two exposures per orbit is generally sufficient.
For a typical object visibility of 53 minutes, after applying the requisite overheads, there is time for two exposures of approximately 1200 s per orbit. The required exposure time can thus be reached in 4 exposures, but re-running the ETC using
CR-SPLIT=4 raises the required exposure time to 4936 s (because of the extra noise introduced by the three extra readouts). To achieve the required exposure time would require
CR-SPLIT=5, or three orbits; iterating the ETC one more time shows a total exposure time of 5089 s with this number of reads.
Using the pencil-and-paper method, Table 9.1 gives the integral
∫QTdλ/λ as 0.0835. An F0 V star has an effective temperature of 7,240 K; looking in
Table A.1 the AB
ν correction term for an effective temperature of 7,500 K is 0.03. According to
Table 9.1, a 5×5 pixel square aperture encloses about 78% of the light from a star. The count rate can then be calculated from the equation
or 2.5×1011*0.0835*0.79*10
-0.4(27.5+0.03) = 0.1584 e
− s
−1, which agrees with the ETC-returned value of 0.160. The exposure time can then be found by using the equation
to give t = 5359 s, which is close to the ETC-derived value of 5089 s. We have inserted the background rates of
Bsky = 0.0377 (
Table 9.1),
Bdet = 0.0008 (
Chapter 5), a read noise of 3.1 e
− per read (
Chapter 5), and 5 reads.
What is the exposure time needed to obtain a signal-to-noise of 10 for an E0 elliptical galaxy that subtends an area of 1 arcsec
2 with an integrated
V-magnitude of 26.7, when using the IR F140W filter? Assume a photometry box size of 9
×9 pixels, and average sky values. The galaxy has a diameter of 1.13 arcsec, a surface brightness of 26.7 mag/arcsec
2, and fits within the 9
×9 pixel box. For simplicity we will assume a redshift of 0.
The WFC3 Exposure Time Calculator (ETC) gives a total exposure time of 1206 s to obtain this S/N in a single exposure. Although the non-destructive MULTIACCUM sequences on the IR channel can mitigate cosmic rays in a single read sequence, users are encouraged to dither their observations so that there are least 2 read sequences per field, to mitigate hot pixels and resample the point spread function. Re-running the calculation with 2 exposures gives an exposure time of 1320 s. If we assume (as in Example 1) that we can fit two 1200-second exposures in an orbit, this program fits within a single orbit. Two SPARS50 sequences, with 15 samples (703 s) per sequence should work well for this program.
Using the pencil-and-paper method, Table 9.2 gives the integral
∫QTdλ/λ as 0.1550. We will assume that the elliptical galaxy resembles an old (10 Gyr) burst of star formation; looking in
Table A.2, the
ABν correction term is
−1.41. We will assume that the 9
×9 pixel box encloses all of the light for this object. The count rate can then be calculated from the equation
or 2.5×1011*0.1550*1.0*10
-0.4(26.7-1.41) = 2.97 e
− s
−1, which is close to the ETC-returned value of 3.24. The exposure time can then be found by using the equation
to give t = 1364 s, which is close to the ETC-derived value of 1320 s. We have inserted the background rates of B
sky = 1.1694 (
Table 9.2), B
det = 0.05 (
Chapter 5), an effective read noise of 12.5 e
− per read (
Chapter 5, assuming we are fitting the MULTIACCUM sequence), and 2 reads.
What is the exposure time needed to obtain a signal-to-noise of 10 for an HII region in M83 in H
α which has a diameter of 2" and a flux
Fλ in H
α of 5×10
–16 ergs/cm
2/s? M83 has a redshift of 0.0017 so H
α appears at 6574 Å approximately. From an inspection of the throughput curves in
Appendix A, we find the H
α (F656N) filter cuts off at too short a wavelength, so we elect to use the Wide H
α + [N II] (F657N) filter, which has a system throughput (
QT)
λ of 25% at 6574 Å.
We use the equation in Section 9.4.3 to estimate the total count rate
C for the emission line to be 2.28×10
12 * 0.25 * 5×10
–16 * 6574 = 1.87 e
–/s. The source subtends approximately 2012 pixels, and the sky for this filter contributes 0.0029 e
–/s/pixel (
Table 9.1) while the dark rate is 0.0008 e
−/s/pixel (
Chapter 5). Thus the total background rate is 6.67 e
–/s. Assuming 2 reads, no binning and a read noise of 3.1 e
– per read (
Chapter 5), we find using the same formula as in the previous section that the time to reach a S/N of 10 is 1195 s.
For comparison, using the ETC, specifying the size as 2" in diameter, entering the flux in ergs/cm
2/s/arcsec
2 as 1.59×10
–16 at 6574 Å, and using a circular 1 arcsec radius extraction region we find similar results: an almost identical count rate and a slightly shorter exposure of 1145 s to reach the same S/N. We conclude, on the basis of these simple estimates that such bright HII regions are easily observed with
HST and WFC3.
