Revised values for signals from stars and sky

Michael Richmond
Apr 23, 2004
Apr 24, 2004

After receiving comments and suggestions from several people, I have revised my calculations of the signal we can expect from stars and the sky background. The changes include

I have not included the efficiency of the detectors, or the size of each pixel, in the calculations below. Those more detailed results will have to wait for another day. But I hope that the more general values below will make it easy for others to compare their calculations against mine.

The SNAP filters

Here are the transmission curves I adopted for each of the 9 SNAP filters.

For quick reference, their properties:

 Filter     Center wavelength      effective wavelength
 index        (Angstroms)               (Angstroms)
   0              4415                    951
   1              5121                   1104
   2              5941                   1280
   3              6891                   1485
   4              7994                   1723
   5              9273                   1998
   6             10757                   2317
   7             12478                   2689
   8             14474                   3119

Flux from a star

Convolving the spectrum of Vega with the transmission curves yields the following fluxes. Again, I have not included any terms for efficiency of the detectors, imperfect optics, etc.

  Filter        flux             SNAP count rate
  index     erg/cm^2-sec           photons/sec
    0        5.997E-6               4.142E10
    1        4.926E-6               3.924E10
    2        3.734E-6               3.443E10
    3        2.731E-6               2.922E10
    4        2.027E-6               2.517E10
    5        1.562E-6               2.256E10
    6        1.189E-6               1.983E10
    7        8.312E-5               1.606E10
    8        5.712E-5               1.280E10

Sky background

I took sky background values from the sources quoted above. Note that the Bernstein et al. papers describe the sky at a location of ecliptic latitude -36 degrees, considerably smaller than the SNAP northern field's ecliptic latitude +74 degrees. I therefore estimated the zodiacal contribution to the values of Bernstein et al. and multiplied them by 0.65 to reflect the lower zodiacal light we ought to see.

The sky values from the NICMOS handbook include instrumental effects. I therefore found a multiplicative factor which caused the NICMOS values to match the Bernstein values at wavelengths in common (around 8000 Angstroms), and applied this same factor to all the NICMOS values. Since zodiacal light dominates the sky background seen by NICMOS over nearly the entire SNAP range (up to 1.6 microns), this should be reasonable. In order to calculate the flux through the last filter, index number 8, which extends out to about 1.8 microns, I extrapolated the zodiacal contribution to the NICMOS background to 1.8 microns while ignoring the instrumental contribution.

First, here is the spectrum of the background sky I've adopted:

# Background sky brightness in space
#    sources: 
#       Bernstein, Freedman and Madore, 2002ApJ...571...56B
#       Bernstein, Freedman and Madore, 2002ApJ...571...85B
#       Leinert et al. 1998A&AS..127....1L
#       NICMOS Instrument handbook, section 4.7
# MWR 4/21/2004
# wavelen   flux: ergs per       flux: ergs per      photons per
#  (Ang)   cm^-s-Ang-sqarcsec     cm^2-s-Ang-sr   cm^2-s-Ang-sqarcsec
  3000.0   5.6411e-19              2.4000e-08      8.5195e-08 
  3175.0   6.8163e-19              2.9000e-08      1.0895e-07 
  3415.0   8.6966e-19              3.7000e-08      1.4951e-07 
  3642.0   9.3548e-19              3.9800e-08      1.7152e-07 
  3844.0   9.4958e-19              4.0400e-08      1.8376e-07 
  4122.0   1.4573e-18              6.2000e-08      3.0240e-07 
  4627.0   1.7158e-18              7.3000e-08      3.9967e-07 
  5145.0   1.5983e-18              6.8000e-08      4.1398e-07 
  5500.0   1.6218e-18              6.9000e-08      4.4905e-07 
  8100.0   1.1282e-18              4.8000e-08      4.6005e-07 
 10000.0   5.1710e-19              2.2000e-08      2.6032e-07 
 12000.0   3.0556e-19              1.3000e-08      1.8459e-07 
 14000.0   2.0684e-19              8.8000e-09      1.4578e-07 
 16000.0   1.4573e-19              6.2000e-09      1.1738e-07 
 18000.0   9.8719e-20              4.2000e-09      8.9455e-08 

Next, the result of convolving this spectrum with the SNAP filters.

  Filter       flux: ergs per     SNAP collects           magnitude per
   index   cm^2-sec-sqarcsec    photons/sec-sqarcsec    sqarcsec below Vega
    0              1.446E-15             10.17                24.02
    1              1.799E-15             14.54                23.58
    2              1.959E-15             18.33                23.19
    3              2.016E-15             21.83                22.82
    4              1.929E-15             24.11                22.55
    5              1.533E-15             22.01                22.53
    6              1.051E-15             17.55                22.63
    7              0.789E-15             15.32                22.55
    8              0.616E-15             13.88                22.41