Point Source

If we consider for example a point source with a uniform emission of magnitude 20 in the band B, at 0 days from new moon, being the sky airmass 1.2, and a seeing of 0.5, using a slit width of 2 arcsec, in standard resolution, slow read out mode, grism GRIS-600B inserted, no polarimetry for an integration time of 60 seconds, we get:

$$M_{B}=20\Longrightarrow Z_{B}=7.1804\Longrightarrow F=6.60085207\cdot 10^{-16} ~J\cdot s^{-1}\cdot m^{-2}\cdot \mu m^{-1}$$

where we have used data in Tab. 2.3 and eq. (2.5), (2.6) and expressed the result in Joule units.

Using eq. (2.7):

$$P=\frac{h\cdot c}{\lambda}=4.51\overline{36}\cdot10^{-20} J\slash ph\hbox{ at $\lambda=0.44~\mu m$}$$

$$\displaystyle\left(\frac{F}{P}\right)_{Obj}=1.46567163444\cdot 10^{3}~ph\cdot s^{-1}\cdot m^{-2}\cdot\mu m^{-1}$$

$$\Delta_{S}=1.2\cdot 10^{-3} ~\mu m\slash bin$$

S=51.5676726123  m²

T=60  s

E=0.1171

With the previously specified parameter we can get from formulae in Tab. 2.1:

$$N_{Obj}=\frac{F\cdot \Delta\cdot T\cdot E\cdot S}{P}= 63.5829033247 ~cnts\slash bin$$ (2.13)

The ETC for FORS1 with the input parameter as specified above predicts N_ETC=63 cntsbin.