= X-ray effective area
{c}
{title2=$A_{\mathrm{eff}}$}
<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, write
$$
A_{\mathrm{eff}}=A_{\mathrm{geom}}T\eta\epsilon_s,\qquad N_s=F A_{\mathrm{eff}}t.
$$
Here $A_{\mathrm{geom}}$ is projected geometric area, $T$ is <transmittance> through windows or optics, $\eta$ is <quantum efficiency>, $\epsilon_s$ 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 $A_{\mathrm{geom}}=40\,\mathrm{cm^2}$, $T=0.8$, $\eta=0.75$, and $\epsilon_s=5/6$. Then $A_{\mathrm{eff}}=20\,\mathrm{cm^2}$. A source with $F=0.30\,\mathrm{photons\,cm^{-2}\,s^{-1}}$ 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 $E_0F$.
A broad <spectrum> instead requires
$$
N_s=t\int F_E(E)A_{\mathrm{eff}}(E)\,\mathrm{d}E,
$$
where $F_E$ 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>.
Back to article page
