Star counts, and counts from stars
The table below shows, for stars of each apparent magnitude, two sets of
useful numbers: (1) the density of such stars on the sky; and (2) the counts of
photons per sec expected when observing such stars with WEAVE.
(1) The first four columns of the table below show, for each apparent
magnitude m, the approximate numbers of star brighter than m, per sq deg,
at each of 3 galactic latitudes.
(2) The remaining columns show, for each apparent magnitude, the expected
counts of detected photons when observing with
WEAVE, using the focal-plane imager
(FPI), or one of the MOS modes
(LR blue, LR red, HR1 blue, HR2 blue (also known as 'green'), HR red).
| Star counts | Counts from stars
|
|---|
|
| FPI
| LR B
| LR R
| HR1 B
| HR2 B
| HR R
|
|---|
| App. mag
| b = 0o | b = 30o | b = 90o
| 0.1 "/pix
| 0.26 A/pix
| 0.42 A/pix
| 0.062 A/pix
| 0.074 A/pix
| 0.093 A/pix
|
|---|
| m
| Stars (mag < m) / deg2
| Total ph/sec
| photons/sec/pixel-step-in-wavelength
|
| 4 | 0.018 | 0.007 | 0.004 | 0.35E+10 | 0.15E+06 | 0.14E+06 | 0.17E+05 | 0.37E+05 | 0.30E+01
|
| 5 | 0.052 | 0.021 | 0.013 | 0.14E+10 | 0.58E+05 | 0.56E+05 | 0.68E+04 | 0.15E+05 | 0.12E+01
|
| 6 | 0.151 | 0.060 | 0.038 | 0.56E+09 | 0.23E+05 | 0.22E+05 | 0.27E+04 | 0.59E+04 | 0.47E+00
|
| 7 | 0.407 | 0.170 | 0.107 | 0.22E+09 | 0.92E+04 | 0.90E+04 | 0.11E+04 | 0.23E+04 | 0.19E+00
|
| 8 | 1.1 | 0.479 | 0.288 | 0.88E+08 | 0.37E+04 | 0.36E+04 | 0.43E+03 | 0.93E+03 | 0.75E-01
|
| 9 | 3.3 | 1.3 | 0.759 | 0.35E+08 | 0.15E+04 | 0.14E+04 | 0.17E+03 | 0.37E+03 | 0.30E-01
|
| 10 | 9.3 | 3.5 | 1.9 | 0.14E+08 | 0.58E+03 | 0.56E+03 | 0.68E+02 | 0.15E+03 | 0.12E-01
|
| 11 | 26 | 9.1 | 4.6 | 0.56E+07 | 0.23E+03 | 0.22E+03 | 0.27E+02 | 0.59E+02 | 0.47E-02
|
| 12 | 75 | 23 | 10 | 0.22E+07 | 0.92E+02 | 0.90E+02 | 0.11E+02 | 0.23E+02 | 0.19E-02
|
| 13 | 199 | 57 | 24 | 0.88E+06 | 0.37E+02 | 0.36E+02 | 0.43E+01 | 0.93E+01 | 0.75E-03
|
| 14 | 524 | 131 | 51 | 0.35E+06 | 0.15E+02 | 0.14E+02 | 0.17E+01 | 0.37E+01 | 0.30E-03
|
| 15 | 1318 | 288 | 93 | 0.14E+06 | 0.58E+01 | 0.57E+01 | 0.68E+00 | 0.15E+01 | 0.12E-03
|
| 16 | 2511 | 588 | 173 | 0.56E+05 | 0.23E+01 | 0.22E+01 | 0.27E+00 | 0.59E+00 | 0.47E-04
|
| 17 | 6760 | 1174 | 301 | 0.22E+05 | 0.92E+00 | 0.90E+00 | 0.11E+00 | 0.23E+00 | 0.19E-04
|
| 18 | 15848 | 2238 | 524 | 0.88E+04 | 0.37E+00 | 0.36E+00 | 0.43E-01 | 0.93E-01 | 0.75E-05
|
| 19 | 31622 | 3981 | 794 | 0.35E+04 | 0.15E+00 | 0.14E+00 | 0.17E-01 | 0.37E-01 | 0.30E-05
|
| 20 | 50118 | 6309 | 1258 | 0.14E+04 | 0.58E-01 | 0.56E-01 | 0.68E-02 | 0.15E-01 | 0.12E-05
|
| 21 | 100000 | 10000 | 1995 | 0.56E+03 | 0.23E-01 | 0.22E-01 | 0.27E-02 | 0.59E-02 | 0.47E-06
|
(1) Star counts
The star counts (per sq deg) are taken from Allen's 'Astrophysical quantities'. More recent information about
the differential star counts with mag, and the contributions from different galactic components, can be found in
Robin et al
(2003, A&A 409, 523).
(2) Counts of photons from stars
The predicted counts of photons per sec for the FPI are based on the known QE of the detector
and are integrated over the PSF (which in typical seeing will cover 100s of pixels). There is no filter in
front of the detector, so the counts are higher than we are used to seeing with the WHT PF imager or with ACAM.
The predicted counts for the MOS modes were obtained from the signalWEAVE exposure-time calculator
(link on Confluence),
assuming 0.95-arcsec seeing (with Moffat profile, beta = 2.5) and airmass 1.2.
These counts are per pixel step in wavelength, integrated over the PSF of the fibre in the direction
orthogonal to dispersion.
The scales, dispersions and throughputs assumed for the various modes are approximate (estimates on other
web pages may differ slightly) and will be known more accurately after commissioning.
The individual mIFU fibres have the same diameter on-sky as the MOS fibres (1.3 arcsec), and the counts
from MOS or mIFU fibres centred on a star will be the same (discounting fibre-to-fibre variations in
throughput).
The above counts can also be used as an approximate guide to the expected counts for LIFU
(large integral field unit) mode. The individual fibres are twice as big (2.6 arcsec), but in good seeing, that
won't make much difference. Note that the scales in A/pixel are the same for MOS, mIFU and LIFU modes.
Example: how long can you expose on an 11th-mag star in LIFU LR red mode before you get close to saturation?
From the above table, one expects 220 counts per sec per pixel-step-in-wavelength.
Assuming these counts have a gaussian distribution, FWHM ~ 3 pixels, in the direction perpendicular to dispersion, then
the peak counts will be ~ 70 counts per pixel, and the exposure time needs to be < 600 sec to avoid counts > 40000 per
pixel.
The counts at the guide-star detectors (AG3 for MOS/mIFU, AG2
for LFU) will probably be similar to those at the FPI.
Areas subtended on sky:
| Focal-plane component | Sq deg
|
|---|
| WHT field of view | 3.14 (pi)
|
| FPI | 1.3e-3
|
|
|
|
|
| LIFU autoguider | 4.0e-3
|
| LIFU (including fibre-cladding) | 5.4e-4
|
|
|
|
|
| MOS fibre | 1.0e-7
|
| Single mIFU (including fibre-cladding) | 8.0e-6
|
| MOS/mIFU guide-fibre bundle | 7.4e-7
|
