Point Source

If we consider for example a point source with a uniform emission of magnitude 15, in K band, being the sky airmass 1.2, and a seeing of 0.5, using a slit width of 2 arcsec, in low resolution, with the red grism inserted, and the large field, for an integration time, we could get:

$$M_{K}=15\Longrightarrow Z_{K}=9.4367\Longrightarrow F=3.65847422794\cdot 10^{-16} ~J\cdot s^{-1}\cdot m^{-2}\cdot \mu m^{-1}$$

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):

$$P=\frac{h\cdot c}{\lambda}=0.90\overline{27}\cdot10^{-20} J\slash ph\hbox{ at $\lambda=2.2~\mu m$}$$

$$\displaystyle\left(\frac{F}{P}\right)_{Obj}=4.05269048412\cdot 10^{3} ~ph\cdot s^{-1}\cdot m^{-2}\cdot\mu m^{-1}$$

$$\Delta_{S}=1.01\cdot 10^{-3} ~\mu m\slash bin$$

S=8.9  m²

T=60  s

E=0.25

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

$$N_{Obj}=\frac{F\cdot \Delta_{S}\cdot T\cdot E\cdot S}{P}= 546.444521425 ~cnts\slash bin$$ (2.11)

The ETC for FORS1 with the input parameter as specified above predicts N_ETC=515 cntsbin.