Observing Background Limited Targets with the STIS FUV MAMA
For the STIS FUV MAMA the current version of the Exposure Time Calculator (ETC) adopts a uniform detector background rate of 1.5e-4 counts/pixel/second (c/p/s). This value is a conservative estimate of the typical mean background rate. However, the actual background for this detector varies by large factors both over time and as a function of position on the detector. For observations of faint sources where the source rate is comparable to or less than the background, it is sometimes possible to take advantage of these variations and reduce the actual background and the exposure time required to reach a given signal-to-noise (S/N) by a large factor relative to the ETC estimate.
For the STIS MAMAs, the high voltage (HV) is only ramped up during those orbits where HST does not intersect the South Atlantic Anomaly (SAA). This limits STIS MAMA usage to a single roughly 8 hour long block each day. When the FUV MAMA HV is first ramped up for the day, the initial detector background is only about 1e-5 c/p/s, a factor of ~15 lower than the canonical number. However, the background increases with time, reaching rates as high as 6e-4 c/p/s after several hours (see Figure 7.22 in the Cycle 23 STIS IHB). The rate at which this increase occurs can be highly variable, so the exact results shown in this and other figures should be considered as illustrative examples and won't necessarily include the full range of possible background rates. This extra detector glow is not uniformly distributed, with the peak rate being in the upper left quadrant (assuming the usual display and orientation conventions used in the STIS IHB and DHB). While the glow does cover a very broad area it is much fainter near the bottom of the detector and especially in the lower right corner. An illustration of the pattern of this extra glow is shown in Figure 7.21 of the IHB.
One way to reduce the dark rate would be to confine any dark sensitive FUV MAMA observations to the 1st orbit in each day's SAA-free block. This will usually ensure a dark rate near 1e-5 c/p/s. However as there is no way to request this kind of scheduling in APT, observers who wish to use this option need to discuss the detailed scheduling requirements with their program coordinator (PC). Because there is only one such orbit available each day and because the scheduling needs of different programs may conflict, it may not always be practical to honor such requests, especially for programs requiring a large number of total orbits to complete.
For a point or compact source less than about 1" in diameter, using the D1 aperture position which puts the source near the bottom edge of the detector, offers a more straightforward way to minimize the FUV MAMA detector background (see Section 4.2.3 of the STIS IHB). Remember that for our usual coordinate conventions the spectrum is dispersed along the X or horizontal direction, while relocating the source to different positions in one of the long slits will move it in the Y or vertical direction. An example of this is illustrated in Figure 4.9 of the IHB. For the D1 position a conservative upper limit to the average background in the vicinity of the D1 aperture position over a span of several orbits can be taken to be about 2e-5 c/p/s. Manually redoing the S/N calculation for this lower dark rate can often provide a substantial reduction to the estimated exposure time.
Since the STIS ETC does not currently support multiple dark rates for the STIS FUV MAMA, we provide here an example of how to estimate the exposure time for a faint source using an alternate dark background rate.
For the MAMA detectors, which have no read-noise, the exposure time calculation reduces to
Texp = (StoN)2 (C + Npix(Bdet+Bsky))/C2
where the “C” is the expected source rate summed over the 2D resolution element (resel) adopted for the calculation, Npix is the number of pixels in that resolution element, Bdet is the detector background rate per pixel, and Bsky is the sky background rate per pixel. Here, by pixels we mean the MAMA “LO-RES” 1024 X 1024 format pixels.
Suppose we want to achieve a S/N of 2 per resolution element with the STIS G140L grating with the 52x0.5 aperture for a source with a flux of 1e-17 ergs/cm2/s/Å at a wavelength of 1325 Å. Putting these requirements into the current ETC gives the results seen in ETC calculation STIS.sp.664744 and predicts a required exposure time of 19138 s. Looking at this calculation, we see that the ETC has adopted a resolution element of 2 pixels in the dispersion direction and 7 pixels in the spatial direction, so Npix=14. The source count rate, C, in this resolution element is the source counts reported in the total counts column of the ETC output page divided by the exposure time or C = 14.84/19138 = 7.75e-4 c/resel/s. The ETC calculation assumed a detector background rate per pixel of Bdet=1.5e-4 counts/pixel/s, which we can confirm by dividing the reported background counts by Npix and the exposure time; 40.19/19138/14 = 1.5e-4 c/p/s. For this example, the background contribution from the sky is negligible, but if necessary, the value of Bsky could be calculated in the same way. Putting these numbers into the above equation then gives the same time estimate as the ETC calculation.
If we instead adopt the lower detector background rate of 2e-5 c/p/s expected at the D1 position, the revised calculation now predicts an exposure time estimate of only 7023 s instead of the ETC estimate of 19138 s!
Observing Background Limited Targets with the COS FUV XDL
How do these results compare to requirements for a comparable observation with the COS FUV/G140L grating? The ETC adopts a smaller spectral resolution element for the COS FUV/G140L grating than it does for the STIS G140L grating, (about 0.48 vs. 1.17 Angstroms per resel respectively). Assuming the observations are to be binned to some common and perhaps coarser wavelength scale, a COS FUV/G140L observation with a S/N = 1.28 per resolution element is equivalent to a STIS G140L observation with S/N = 2.0. Putting these numbers into the ETC and adopting the COS FUV/G140L CENWAVE=1280 setting and the same source as our STIS example gives the results shown in COS.sp.664803 and yields a estimated exposure time of 20,636 s.
However, this COS calculation adopts a very large resolution element with 57 pixels in the cross-dispersion direction to ensure that all of the detected flux at all wavelengths of the G140L fits into the resolution element. At most wavelengths, the COS G140L cross-dispersion profile is considerably narrower than this. The height of the 80% enclosed energy curve as a function of wavelength for each of the two G140L CENWAVE settings can be approximated by interpolating in the following table
Approximate 80% Enclosed Energy Heights for COS G140L settings at LP3
For the original COS ETC calculation, C = 3.71e-4 c/resel/s, while Bdet = 4e-6 c/p/s, and Npix = 57 X 6 = 342. For the revised calculation, C is reduced by 20% to 2.97e-4 c/resel/s, while Npix becomes 11 X 6 = 66. So the exposure time estimate is reduced to about 10430 s or about 50% of the ETC estimate.
All of the exposure time calculations above, for STIS and COS, assume that the target can be reasonably well approximated as a point source. To the extent that the target is spatially extended, a larger extraction box might be required to include most of the flux, with a corresponding increase in Npix and the resulting total detector background. At some wavelengths, geo-coronal emission may dominate the detector background, and this will reduce the advantages of relocating the spectrum to the alternate detector location. Remember that using wider slits will increase the geometric footprint of geo-coronal emission lines, so when working close to the geo-coronal wavelengths, it may be necessary to use a narrow slit to minimize this additional background contribution.