The ETC gives a total exposure time of 4410 seconds 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. ACS WFC observations generally should be split if the exposure time is larger than about 11 minutes, but for multi-orbit observations, splitting into 2 exposures per orbit is generally sufficient.
For a typical object visibility of 53 minutes, after applying the requisite overheads (see Chapter 8), there is time for two 1200 seconds exposures 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 5303 seconds (because of the extra noise introduced by the four extra readouts). To achieve the required exposure time would require
CR-SPLIT=5, or three orbits.
Using the pencil and paper method, Table 9.1 gives the integral QTd
λ/
λ as 0.0775, and the AB
ν correction term can be retrieved from
Table 10.3.2 as 0.040. According to
Figure 5.13, a circular aperture of radius 0.3 arcseconds (which has an area of 116 pixels, close to the 121 pixel box specified) encloses about 90% of the
light from a star.
The count rate is given by 2.5x1011*0.0775*0.9*10
-0.4(26.5+0.040) = 0.423 counts/second, which agrees with the
ETC-returned value of 0.42.
to give t = 4172 seconds, which is close to the
ETC-derived value of 4410 seconds. We have inserted the background rate from
Table 9.1 (B
sky = 0.055) and
Table 9.4 (B
det = 0.0032), and assumed that the noise on the background is much greater than the readout noise.
Note that this can be greatly shortened by specifying a smaller analysis box (for example, 5 x 5) and using LOW-SKY. Dropping the aperture size to 5 x 5 at average sky which still encloses 81% of the
light requires 1532 seconds. Including both the smaller 5 x 5 box and
LOW-SKY (
Zodiacal =
LOW, Earthshine =
AVERAGE), using the
ETC gives the required exposure time as only 1306 seconds (using
CR-SPLIT=1), or 1540 seconds with
CR-SPLIT=2. The LOW-SKY visibility per orbit is 47 minutes, which allows a total on-target exposure time of 2000 seconds in one orbit with
CR-SPLIT=2.
What is the peak count rate using the PR110L prism in the SBC for the HST standard star HS2027+0651 (V = 16.9) that was used for the STIS prism calibration (this spectrum is not in the
ETC list, therefore we quote below the flux which could be found by dearchiving the STIS spectrum)?
The sensitivity peaks in the 1500 е to 1600 е region. To find the count rate at 1537 е, inspection of Figure 6.22 gives the sensitivity of 9.9x10
14 counts/second per erg/cm
2/s/е. Multiplying by the stellar flux of 5.3587x10
-14 gives 53.0 counts/second, summed in the cross dispersion direction. For the fraction of
light in the central pixel
ε = 0.31, the brightest pixel at 1437.6 е is 17.6 counts/second/pixel, well below the bright object limit.
The SBC has no readout noise, and the dark current rate is negligible, while the main sky contribution for PR110L is from Lyman-α. For daytime Ly-
α intensity of 20kR = 6.1x10
-13 ergs/cm
2/second/arcseconds
2, S
′ = 1.7x10
14, and
d, the dispersion in е/pixel, is 2.58. Therefore, the background count rate is:
6.1x10
-13*1.7x10
14*0.032
2/2.58 = 0.041counts/second/pixel.
This value varies somewhat over the field, as the plate scale varies from the nominal 0.032 arcseconds/pixel. For faint source spectroscopy, it is better to use PR130L, which is on a CaF
2 substrate to block Ly-
α.
If the M87 jet region has μV = 17 magnitudes/arcseconds
2, using the
ETC with a flat continuum spectral distribution and an exposure time of 2400 seconds (
CR-SPLIT=2), gives S/N = 131.6 for an observation with each VIS polarizer filter (which is an average of the polarizer at the 3 available position angles 0
°, 60°, and 120
°). If the polarization P is 20%, then P*S/N = 26.3, so using
from Chapter 6,
σP/P = 0.031, or
σP = 6.2x10
-3, which is the error on the fractional polarization. The error on the position angle should be ~1.0
°using the formula, again from
Chapter 6, of
The equation from Section 9.2.1 can be used to calculate the expected count rate. The aurora is variable, up to ~100kR. The value of (QT) for the SBC+F122M filter at 1216 е is 0.0009, from inspection of
Figure 10.106. For a surface brightness of 40kR = 1.22x10
-12 erg/cm
2/second/arcseconds
2 (see
Section 9.4.2 for conversion), the total counts per pixel are given by the following calculation:
The background contributions are the detector dark of 1.2x10-5 counts/pixel/second (which can be ignored in this case) and a sky background which is dominated by geocoronal Lyman-
α. During the daytime, the geocoronal background is 20kR, or 30.5 counts, while at night the background drops to one tenth of this, or 3.05 counts.
Finally, we calculate the signal-to-noise ratio Σ for a 2 x 2 pixel resolution element: in the daytime:
= 12.7; and at night:
= 15.2
In this example, using the now inoperative HRC, we shall consider the case where we are trying to determine the S/N achieved on the Beta Pictoris disk, assuming a disk surface brightness of R magnitude of 16 arcseconds2 at a distance of 6 arcseconds from the central star with a V magnitude of 3.9, for an exposure time of 1000 seconds with an F435W filter. Assume that the star and disk have an A5 V-type spectrum. Using the
ETC and considering the case for the 3.0
arcseconds occulting mask:
and also to contact help@stsci.edu for expert advice on the suitability of WFC post-flash for their observations.
.