I R A F
Image Reduction and Analysis Facility
PACKAGE = astutil
TASK = ccdtime
(time = INDEF) Time (seconds)
(magnitu= 20.) Magnitude
(snr = 20.) Signal-to-noise ratio
(databas= ccdtime$ouo.dat) Database file
(telesco= GOT) Telescope name (? for list)
(detecto= ST8-15) Detector name (? for list)
(sum = 1) CCD summing factor
(seeing = 3.) Seeing (arcsec)
(airmass= 1.4) Airmass
(phase = 7.) Moon phase (0-28)
(f1 = V) Filter 1
(f2 = R) Filter 2
(f3 = I) Filter 3
(f4 = ) Filter 4
(f5 = ) Filter 5
(mode = ql)
For calculating exposures for the GOT, make sure that the database and
telescope are set to the values shown above. The detector name can be
set to any of ST8+10, ST8+5, ST8+0, ST8-5, ST8-10, ST8-15, ST8-20, or ST8-25,
where the trailing digits refer to the CCD operating temperature in
degrees C. This makes a difference because the detector dark rate is a
steep function of temperature.
The CCD summing factor refers to on-chip binning, and will be set to 1 unless you have a clever and cunning reason not to. The moon phase refers to days after or before new moon. Note that despite what it says, phases >14 will not produce correct results!
The filters can be set to any of the broadband filters we have, namely V, R, and I, in any order. (See section 2 below for using CCDTIME with the narrow-band filters.) They can also be blanked out, but you do need to have at least one filter listed to get any results.
If one runs CCDTIME with the parameters set as above, one gets the following output:
Database: ccdtime$ouo.dat Telescope: GOT Detector: ST8-15
Sum: 1 Arcsec/pixel: 0.72 Pixels/star: 25.0
Seeing: 3.0 Airmass: 1.40 Phase: 7.0
Filter Time Mag SNR Star Sky/pix Noise contributions
Star Sky CCD
V 8810.42 20.0 20.0 5196.7 1648.7 72.09 203.02 145.26
R 8615.68 20.0 20.0 6080.7 2625.8 77.98 256.21 143.92
I 18812.5 20.0 20.0 10307.1 8567.2 101.52 462.80 202.75
This is a table showing the required exposure time in seconds to reach a
signal-to-noise ratio (SNR, or S/N) of 20 for a star of 20th magnitude
(in the respective bandpasses), in 3 arcsecond seeing, through 1.4 airmasses,
in a single exposure. S/N=20 means an accuracy in the brightness measurement
of 5%, or about 0.05 magnitudes. You'll notice that the exposure times are
rather long, ranging from about 2 to 5 hours. This shows that it is very
difficult to work to 20th magnitude with a 10-inch telescope.
If you like, you can give the task a definite exposure time, say, 600 seconds, and leave the magnitude as INDEF. Then you will get a list of the faintest magnitude star you can observe with S/N=20 in a 10 minute exposure. Or, you can make the SNR INDEF and see what ratio you can achieve for a given star in a given time.
Some of the other input parameters deserve special attention. We can expect seeing to range from (optimistically) 1.5 arcsec to (realistically) 5 arcsec or more. In very short exposures (10 seconds or less) we have seen the GOT perform well and deliver 2" images, about the best we should expect in Ohio weather. For longer exposures the image size seems to be limited not by optics but by mechanical vibration of the fork mount. We may find a way to reduce the vibration, but until then it is recommended that for purposes of writing proposals one plan pessimistically. The airmass is the column density of air along the line of sight, normalized to 1 at the zenith. Thus the airmass is sec z, where z is the zenith angle, and it changes continuously during your observation.
The 5th through 9th columns of the table list:
5. the total number of electrons (i.e., the number of detected photons) in
the stellar image, spread out over the seeing disk;
6. the number of electron per pixel expected from the sky;
and the contribution to the total noise budget from
7. the star (counting statistics);
8. the sky (also counting statistics);
9. the detector (counting statistics on dark current plus readnoise).
Noise sources add in quadrature (the total is the square root of the sum
of the squares), so the S/N ratio is column 5 divided by the quadrature
sum of columns 7 to 9. Also, keep in mind that CCDTIME is counting
electrons, whereas what will be recorded in your image is ADUs
(the output of the analog-to-digital converter). This will
not change the statistics, but don't panic when you find that the pixel values
in your images are about a factor of 3 smaller than what you
calculated. This is simply a reflection of the gain factor of the CCD,
which is about 2.9 electrons/ADU.
According to the output, the sky is the primary source of noise in this observation, and you may be thinking, "Hey, a 2 hour exposure isn't that long!" But a few things are being overlooked here. In practice, taking a single 2 hour exposure is crazy. For one thing, suppose somebody accidentally bumped the telescope 1 hour and 55 minutes into your exposure? A felony would probably result. But more important, exposures longer than 30 minutes accumulate so many cosmic ray hits that cleaning them out starts to get difficult. It is highly recommended that exposures be kept to under 15 minutes on the GOT.
Combining multiple exposures is NOT the same thing as having one long exposure of the same total duration, because the detector noise gets added in on each exposure. Generally if you add N equal exposures, you can expect the S/N ratio to go up as the square root of N. Let's try the 20th magnitude object again, limiting exposures to 900 seconds and setting the SNR to INDEF:
Filter Time Mag SNR Star Sky/pix Noise contributions
Star Sky CCD
V 900.00 20.0 5.3 530.9 168.4 23.04 64.89 72.67
R 900.00 20.0 5.6 635.2 274.3 25.20 82.81 72.67
I 900.00 20.0 3.9 493.1 409.9 22.21 101.22 72.67
In the best case (R band), one 15-minute exposure gets you to S/N=5.9,
two will get you to S/N=8.3, three to S/N=10.2, and so on. To get to the
desired S/N=20 will require 12 exposures, or 3 hours total. When you add
in the overhead for reading out the detector, refocusing the telescope,
and of course doing standard stars (if you can't calibrate your measurement,
what's the point?), this is likely to take up the entire time that your
target is above 2 airmasses. Working on 20th magnitude objects with a 10-inch
telescope requires real dedication!
The brightnesses of emission line sources are usually not quoted in terms of magnitudes, but rather as fluxes in ordinary physical units. CCDTIME, of course, works in magnitudes. For the H-alpha filter only, the CCDTIME magnitude is -2.5 times the base 10 logarithm of the integrated line flux in cgs units (erg/cm^2/s). The other parameters work as described above. The filter bandpass is included in the calculations, and the assumption is that the line is at the center of the bandpass. If your object has a radial velocity greater than 100 km/s (approaching or receding), you will need to take into account the lower transmissivity of the filter at the Doppler-shifted wavelength.
If your source is a pure emission-line object, then, depending on your science goals, it may be sufficient to image it only in H-alpha. However, if there is an underlying continuum, e.g. from starlight, then you must also image in the continuum filter in order to remove this contribution and get the emission line alone. For exposure time estimates in the H-continuum filter, use the R band magnitude of the continuum source.
Np = 1.4 X [(seeing FWHM in arcsec)/(arcsec per pixel)]^2If your goal is simply to measure the total flux of an extended object that covers A square arcseconds, then replace the seeing FWHM with the square root of (FWHM^2 + A) and proceed as before.
On the other hand, suppose we have an extended source with a surface brightness I, measured in mag/arcsec^2. This is equivalent to the light of an Ith-magnitude star spread out over an area of 1 arcsec^2. This area corresponds to Nx pixels, where
Nx = 1 / (arcsec per pixel)^2Thus, IN PRINCIPLE, if we set the stellar magnitude in CCDTIME to I and the seeing FWHM to 0.845 arcsec, CCDTIME would spread the light of an Ith-magnitude star over a number of pixels corresponding to 1 arcsec^2, as desired. HOWEVER, CCDTIME does not permit fewer than 9 pixels in the image. At the scale of the GOT/ST8, 1 arcsec^2 is about 2 pixels, so we can't do this. Instead, let's make the fake "star" 10 times brighter and spread it out over 10 times the area; this gives us the same surface brightness. A factor of 10 in brightness is 2.5 magnitudes, so that suggests the following way to "fake out" CCDTIME: Set the "stellar magnitude" to the surface brightness minus 2.5 magnitudes, and the seeing FWHM to 2.67. This will give you the signal to noise ratio for counts summed up over a 10 arcsec^2 area.
Optimistically, we can expect seeing and guiding to give us stellar images 2.5 to 3 arcsec wide, so with this recipe CCDTIME will give basically a S/N per resolution element. This number should correspond to the level of noise fluctuations that we see in the image at that surface brightness level. E.g. S/N = 20 means brightness fluctuations due to noise of +/- 5% RMS.
However, for extended sources S/N per resolution element may not be what we need to know. More likely we are planning on averaging many pixels over the image to get a more accurate measurement of, for instance, the mean surface brightness in a circular annulus. In this case we need to know the area of the region we are averaging over. Suppose this area is k square arcsec. This corresponds to k/10 ten-arcsec^2 resolution elements; thus averaging will increase the S/N by a factor of sqrt(k/10).
For very long exposures (>10 min) it is advisable to split them into several shorter exposures, and add them up later. This is equivalent to averaging over more area, so in this case the exposure time would be that for each of the short exposures, and the area k in the last paragraph would be multiplied by the number of exposures.
From published data, M87 falls to 22.1 R mag/arcsec^2 (1/5 of the sky at new moon) at r = 150". The area of a 3" wide ring at this radius is about 660 arcsec^2. Imagine we take a single 300s exposure at 1.2 airmasses with no on-chip binning. We set the CCDTIME parameters as follows:
I R A F
Image Reduction and Analysis Facility
PACKAGE = astutil
TASK = ccdtime
(time = 300.) Time (seconds)
(magnitu= 19.6) Magnitude
(snr = INDEF) Signal-to-noise ratio
(databas= ccdtime$ouo.dat) Database file
(telesco= GOT) Telescope name (? for list)
(detecto= ST8-15) Detector name (? for list)
(sum = 1) CCD summing factor
(seeing = 2.67) Seeing (arcsec)
(airmass= 1.2) Airmass
(phase = 0.) Moon phase (0-28)
(f1 = R) Filter 1
(f2 = ) Filter 2
(f3 = ) Filter 3
(f4 = ) Filter 4
(f5 = ) Filter 5
(mode = ql)
The output is:
Database: ccdtime$ouo.dat Telescope: GOT Detector: ST8-15
Sum: 1 Arcsec/pixel: 0.72 Pixels/star: 20.0
Seeing: 2.7 Airmass: 1.20 Phase: 0.0
Filter Time Mag SNR Star Sky/pix Noise contributions
Star Sky CCD
R 300.00 19.6 4.4 317.5 78.8 17.82 39.70 57.14
The reduced, sky-subtracted image will appear very noisy (25% RMS) at this
surface brightness level. Trying to detect small structures at this level
will be very hard. The good news, however, is that the galaxy is big,
so when we average over 660 arcsec^2 (that is, 66 ten-arcsec^2 resolution
elements) we get S/N = 36, or slightly better than
3% accuracy in the mean surface brightness
around the ring.
Moral of the story: the exposure time you need for an extended object depends both on the surface brightness where you want to work and the size scale over which you need to resolve detail.