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.
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 ---------------------------------------------------------
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 ------------------------------------------------------
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 ----------------------------------------------------------------------------