Number of photons per sq.cm. per sec in V-band from a V=7.6 star is
10^6 photons -0.4*7.6
N(star) = --------------- * 10
sec * cm^2
photons
= 912 --------------
sec * cm^2
Number of photons collected per second in V-band is
912 photons
N(coll) = ------------- * pi * (180 cm)^2
sec * cm^2
~ 10^8 photons / sec
In order to see a feature of depth 10^(-6), one must exceed
the Poisson noise in the starlight.
1
starlight noise = ------------------------
sqrt(number of photons)
Therefore, the number of photons collected must be
N(coll) > (starlight noise)^(-1/2)
> [ 10^(-4) ]^(-1/2)
> 10^(8)
How long should this take?
10^(8) photons
exptime = -----------------------
10^(8) photons/sec
= 1 sec
How long _did_ they actually expose?
Three nights, several hours per night
Why the difference?
They broke up the light into spectra, instead of adding
up all the light within a broadband filter.
V-band filter bandpass width approx 900 Angstroms
spectroscopy "bandpass" width approx 0.5 Angstroms