 X-ray effective area

X-ray effective area is the area that converts an incident photon arrival rate per unit area into an accepted count rate. For a fixed direction and a sufficiently narrow energy interval, writeHere $A_{\mathrm{geom}}$ is projected geometric area, $T$ is transmittance through windows or optics, $\eta$ is quantum efficiency, ${ϵ}_s$ is the probability that a detected source event passes event selection, and $t$ is live observing time. $N_s$ is an expected value, not a guarantee of an integer count. Multiplication follows by counting incident photons over area and time, then applying the successive conditional acceptance probabilities. Live time already excludes intervals when the instrument cannot record events; multiplying by a live-time fraction again would count the same loss twice.

For an invented narrow-band example, choose $A_{\mathrm{geom}}=40\mathrm{c}{\mathrm{m}}^2$, $T=0.8$, $\eta =0.75$, and ${ϵ}_s=5/6$. Then $A_{\mathrm{eff}}=20\mathrm{c}{\mathrm{m}}^2$. A source with $F=0.30\mathrm{photons}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ observed for $t=100\mathrm{s}$ gives $N_s=600$. $F$ here counts photons; converting it into observed radiative flux requires their energies. If all have energy $E_0$, the corresponding radiative flux is $E_{0}F$.

A broad spectrum instead requireswhere $F_E$ is the differential photon arrival rate per area and energy. A single band-averaged X-ray effective area depends on the assumed spectrum. This is why a count rate alone cannot give an assumption-free radiative flux.