Sky

With the configuration previously specified, in the J band the sky magnitude is 13 so:

$$M_{K}=13\Longrightarrow Z_{K}=9.4367\Longrightarrow F=2.3083... ...} ~J\cdot s^{-1}\cdot m^{-2}\cdot \mu m^{-1}\cdot arcsec^{-2}$$

$$\displaystyle\left(\frac{F}{P}\right)_{Obj}=2.55707482586\cdo... ...{3}~ph\cdot s^{-1}\cdot m^{-2}\cdot\mu m^{-1}\cdot arcsec^{-2}$$

Using the dispersion value $\Delta _{S}$, the telescope surface S, the exposure time T and the efficiency E as specified before, and taking in count theat the plate scale is 0.29 arcsecpix and the slit width is 2 arcsec, we get

$$\Omega=0.58~arcsec^{2}$$

So we get

$$N_{Sky}=\frac{F\cdot \Delta_{S}\cdot T\cdot E\cdot S\cdot\Omega}{P}= 1.99974246804\cdot 10^{3} ~cnts\slash bin$$ (2.12)

The ETC for FORS1 with the input parameter as specified above predicts $N_{ETC}=1.75\cdot 10^{3}$ cntsbin.