To determine the required observation time, we need to consider the signal-to-noise ratio (SNR) and the exposure time.
The SNR is given by the formula:
SNR = (flux of the object) / (sqrt(flux of the sky background) + sqrt(flux due to read noise))
In this case, the flux of the object (galaxy) is given by the magnitude difference:
flux of the object = 10^((V_mag - V_star)/2.5)
where V_mag is the magnitude of the galaxy and V_star is the magnitude of the reference star.
The flux of the sky background is given by the magnitude of the sky glow:
flux of the sky background = 10^((V_sky - V_star)/2.5)
where V_sky is the magnitude of the sky background.
Assuming the spectrograph spreads the photons received evenly across the V-filter bandpass, the total flux for the galaxy signal would be distributed across the V-filter bandpass.
Given that the SNR per nanometer is 25, we can use this information to obtain the exposure time required to achieve the desired SNR. Let's assume the V-filter bandpass is 100 nm wide.
SNR = (flux of the object per nanometer) / (sqrt(flux of the sky background per nanometer) + sqrt(flux due to read noise))
The flux of the object per nanometer is given by:
flux of the object per nanometer = (flux of the object) / 100
The flux of the sky background per nanometer is given by:
flux of the sky background per nanometer = (flux of the sky background) / 100
Rearranging the SNR equation, we get:
SNR = (flux of the object per nanometer) / (sqrt(flux of the sky background per nanometer) + sqrt(flux due to read noise))
Solving for the exposure time (t):
t = (SNR^2 * (flux of the sky background per nanometer) + SNR * sqrt(flux of the sky background per nanometer)) / flux of the object per nanometer
Substituting the magnitude values and calculating the flux values using the aforementioned formulas, we can find the required observation time.
Imaging from the Earth's surface causes a problem when even on a clear night the atmosphere emits a faint glow, equivalent to a V
21 star everywhere you look.On such a night, how long would you need to observe on the a 8.2m telescope to obtain an optical spectrum of a V
20 magnitude elliptical galaxy where the signal to noise ratio per nanometer is 25 ?Assume the spectrograph spreads the photons received evenly across the V-filter bandpass.
1 answer