Hello, everybody!
If you still get trouble to deal with the flux, magnitude, error of the catalog you get (Mostly, the catalog are created by SExtractor). This file must be helpful for you. Just give you all the equations about how the photometric system works.
If You still have question about these, please leave me a message, I will be quite pleasant to help you. You will be the nest astronomer!
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Magnitude systems
STMAG
ZEROPTsecond = -2.5 * log10(PHOTFLAM) + PHOTZPTZEROPTexptime = -2.5 * log10(PHOTFLAM) + PHOTZPT + 2.5 * log10(exptime)
PHOTZPT = -21.1 (always)
mstmag = -2.5 * log10(counts/exptime) + ZEROPTexptime
mstmag = -2.5 * log10(counts/sec) + ZEROPTseconds
mstmag = -2.5 * log10( PHOTFLAM * DN / EXPTIME) + PHOTZPT
mstmag = -2.5 * log10(counts/exptime) + ZEROPTexptime
mstmag = -2.5 * log10(counts/sec) + ZEROPTseconds
mstmag = -2.5 * log10( PHOTFLAM * DN / EXPTIME) + PHOTZPT
AB mag
mAB = -2.5 log10( Fluxnu ) - 48.594where fluxnu is in ergs cm-2 s-1 HZ-1
mAB = -2.5 log10( Fluxlambda ) - 2.402 - 5.0 * log10( lambda )
where fluxlambda is in ergs cm-2 s-1 A-1
and lambda in A
Fnu = flambda * lambda2 / c
flam = 3x10^18 * fnu / lam^2
fnu = (lam^2 * flam) / 3x10^18
fnu = (lam^2 * flam) / 3x10^18
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Converting an image to flux
flux = DN * PHOTFLAM / exposure_timewhere flux is in erg cm-2s-1A-1
flux = DN * PHOTFLAM / exposure_time * PHOTPLAM**2 / 2.9972E18 * 1E+23
where flux is in Jy
JANSKY
1 Jy = 1.0 * 10-26 (W/m2/Hz) = 1.0E-23 erg/s/cm2/HzFWHM
seeing_fwhm = 1.22 * (photplam / 24000000000.0 ) * 206264.806247
seeing_fwhm = math.sqrt( (seeing_fwhm * seeing_fwhm) + (pixscale[chip] * pixscale[chip]) )
24000000000.0 = size of the mirror
206264.806247 = 180 * 3600. / pi
$diameter=2.4e10; #diameter of the telescope
$arc_rad = 206264.8; #number of arcsec/rad
$rayleigh=1.22*$photplam * $arc_rad / $diameter; #1.22 * lambda/D
$resolution = sqrt( ($rayleigh**2) + ($pixscale**2))
CVORES
cvosres = (( photplam / 10.0E10 ) / 2.4 ) * (2.063 * (10**5)) cvonyqr = cvosres / pixscale[chip] cvosres = cvosres / 3600.0 The Nyquist ratio (spatial_resolution/spatial_sample). Values less than 2.5 are undersampled.equations
# [Y ABnu] = -2.5 * log([X ergs/cm^2/s/Hz]) - 48.594# [Y ABnu] = -2.5 * log([X ergs/cm^2/s/A]) - 2.402 - 5.0 * log(lambda A)
# [Y ABnu] = -2.5 * log([X W/m^2/Hz]) - 56.094
# [Y ABnu] = -2.5 * log([X photon/cm^2/s/A]) + 16.852 - 2.5 * log(lambda A)
# [Y ABnu] = -2.5 * log([X photon/cm^2/s/um]) + 16.852 - 2.5 * log(lambda um)
[Y Jy] = 1.0E+23 * [X erg/cm^2/s/Hz]
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Daniel Durand, April 2004
Alberto Micol, September 2004
Photometric systems: zeropoints and formulae
Generic: m = -2.5 * log10( DN/EXPTIME ) + ZEROPOINT
ST sys: mst = -2.5 * log10( Flambda ) - 21.10
AB sys: mAB = -2.5 * log10( Fnu ) - 48.60
where Flambda is in erg/cm2/sec/A
and Fnu in erg/cm2/sec/Hz
Flambda = countRate * PHOTFLAM
Fnu = Flambda * lambda2 / c
= countRate * PHOTFLAM * PHOTPLAM2 / c
where:
- counteRate is the number of counts diveded by the exptime
- PHOTFLAM is the flux of a source with constant flux per unit wavelength
(in erg/cm2/sec/A) which produces a count rate of 1DN/sec.
Note: Obviously a change of GAIN will have repercussions on PHOTFLAM
- c must be given in A/sec, that is: 2.99792E+18 A/sec
since PHOTPLAM is in A, and PHOTFLAM in erg/cm2/sec/A.
Hence,
mst = -2.5 * log10( countRate * PHOTFLAM ) - 21.10
= -2.5 * log10( countRate ) -2.5*log10( PHOTFLAM ) - 21.10
= -2.5 * log10( count ) -2.5*log10( PHOTFLAM ) - 21.10 + 2.5 * log10( EXPTIME )
mAB = -2.5 * log10( countRate * PHOTFLAM * PHOTPLAM2 / c ) - 48.60
= -2.5 * log10( countRate ) -2.5*log10(PHOTFLAM*PHOTPLAM2/c) - 48.60
= -2.5 * log10( count ) -2.5*log10(PHOTFLAM*PHOTPLAM2/c) - 48.60 + 2.5*log10( EXPTIME )
Effective Gain
The effective gain is to be used within PIPE only when running SExtractor,that is, when the noise of the image must be computed.
The effective gain is g for the noise of an single image.
The effective gain is g for the noise of an coadded image (pure sum).
The effective gain is N * g for the noise of an averaged image.
That's because the poissonian noise can be computed only from the Total number of electrons,
not from the average number of electrons; and
the total number of electrons is N * g * the number of counts
of an averaged image.
All the formulae to do with gain
FLUX COMPUTATIONFor a source which has 1DN/sec in an image with gain g,
the flux is PHOTFLAM, where PHOTFLAM is to be scaled to g7 or g15.
Flux(erg/cm2/sec/A) = NDN/exptime * PHOTFLAM(g=g7 or g15)
For an averaged image, whose members are images at g=g7,
the flux is computed this way:
Flux = Total Ne / g7 / Total Exptime * PHOTFLAM(g7)
= N * g7 * Mp / g7 / Total Exptime * PHOTFLAM(g7)
= N/Total Exptime * Mp * PHOTFLAM(g7)
= Mp / AVGExpTime * PHOTFLAM(g7)
For a summed image, whose members are images at g=g7,
the flux is computed this way:
Flux = Total Ne / g7 / Total Exptime * PHOTFLAM(g7)
= g7 * Tp / g7 / Total Exptime * PHOTFLAM(g7)
= Tp / Total Exptime * PHOTFLAM(g7)
SExtractor outputs always FLUXes as counts;
hence,
a SExtractor run onto an averaged image, will return the average counts;
a SExtractor run on a total image will return the total number of counts.
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PS: This is from an quite old document, but the idea will not change.
From:
http://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/hst/wfpc2/wfpc2_r2_processing.html
in units of erg cm-2 s-1 Å-1 that produces 1 count per second in the HST observing mode (PHOTMODE) used for the observation. If the F
