Fermi LAT Sensitivity: Estimating Spectral Flux in Jy

[zhermes]

I'm trying to figure out the sensitivity of the Fermi LAT, in units of spectral flux---e.g. Jansky, or a limiting magnitude which could easily be converted. I've only found sensitivity in traditional high-energy terms, e.g:
$$4\times10^{-6} \textrm{ photons/s/cm}^2$$
for photons above 100 MeV, with a photon spectral index of -2.1
from http://arxiv.org/abs/1003.1436" .

The published spectral range of the LAT is 20 MeV to 300 GeV, thus for a spectral index of -2.1, I find that the average photon energy (above 100 MeV) should be about 606 MeV.
This gives a sensitivity of about $$3.9\times10^{-9} \textrm{ ergs/s/cm}^2$$ That seems fair.

Now, to get spectral flux, one needs to divide by the bandpass to yield units of ergs/s/cm^2/Hz, and then 1 Jy = 10^-23 erg/s/cm^2/Hz (wikipedia).

Dividing by a bandpass of 300 GeV (~7e25 Hz) gives a sensitivity of ~$$5\times10^{-12} \textrm{ Jy}$$! That can't be right! This would correspond to a limiting magnitude of 37!

What am I doing wrong?
Thanks!
Z

EDIT: This value is for an integration of 100s --- not very long.

 

[lippyka]

I'm also not sure how to account for the energy resolution/window of the LAT, which is typically ~10%.It looks like you need to take into account the energy resolution of the LAT when calculating the spectral flux. The energy resolution is about 10%, so that means that only 10% of the energy of the photons in the range of 100 MeV to 300 GeV will actually be detected by the LAT. So if your average photon energy is 606 MeV, then the effective energy of the photons detected by the LAT will be more like 600 MeV. Using this revised energy value and dividing by the bandpass of 300 GeV (~7e25 Hz) gives a sensitivity of ~6\times10^{-11} \textrm{Jy}. This corresponds to a limiting magnitude of ~29, which is much more realistic.