The photometric error is estimated from poisson statistics (when the confusion noise is low), as follows.
where zero is the zero calibration magnitude and sum is the integral (sum) of all pixel values located within some radius of center.
mag_err = 1.0857 * znoise / sum
where
Negative Integrated Flux and Upper Limits
For the record, future deliveries of the bandfill module (within GALWORKS) will apply the following formulae to handle "negative" flux and upper limits. I realize that we may want to change this at a later date, but I do need to go with something now, so I decided to use the given formulae to minimize the impact upon the database manager. -tj
"Negative flux"
Case in which the integrated flux within the standard circular aperture is less than zero.
quoted mag = 99.0 - [ ZERO_CAL - 2.5 log10( | integ. flux | ) ]
where ZERO_CAL is the zero calibration magnitude;
e.g., suppose the integrated flux is -15.5 DN, then for a ZERO_CAL = 19.93 (typical value for K band), we get
mag = 82.05
(a) if int. flux >= 0.0 DN AND int. flux < 0.01 DN
then quoted mag = ZERO_CAL - 2.5 log10( 0.01 )
e.g., suppose the int. flux = 0.0005 DN, then then for a ZERO_CAL = 19.93, we get
mag = 24.93
(b) if int. flux >= -0.01 DN AND int. flux < 0.0 DN
then quoted mag = 99.0 - [ ZERO_CAL - 2.5 log10( 0.01 ) ]
i.e., treat as a "negative flux" near zero
e.g., suppose the int. flux = -0.0005 DN, then then for a ZERO_CAL = 19.93, we get
mag = 74.07
upperlim flux = int. flux + (2 * noise)
where the noise in this case means the "local noise", computed as follows (using the DAOPHOT algorithm):
noise = sqrt[ (error1 + error2) + error3 ]
where
npix = number of pixels in the aperture skyvar = the variance (square of the standard deviation) of the sky brightness
error2 == photon noise ,br> = int. flux * Gain
error3 == (skyvar/nsky) * (npix ** 2)
nsky = number pixels in sky annulus
(skyvar/nsky) = square of the standard error of the
mean sky brightness
where
noise = sqrt[ error1 + error3 ]