Exposure Time Calculator

The proposed Exposure Time Calculator is preliminary. It assumes targets are main-sequence stars with tabulated color indexes as in Table 5 of Pecaut & Mamajek 2013. No instrument background nor airmass treatment is included. It is based on zero-point calculations with instrumental efficiency and detector characteristics that will be refined with on-sky tests. The sky effective magnitude is a way to take into account the sky continuous background below the emission lines. The presently used list of these characteristics is the following:

RON 5 electrons
DC 0.05 electron/s
Sky effective magnitudes (night) Y:18.6 J:18.4 H:18.3 K:17.5
Velocity bin 2.28 km/s
Individual exposure time 5.4 s
Extracted pixels 35
Efficiency Y:4% J:7% H:14% K:13%
Zero points (10-9 W/m2/micron) Y: 9.38 J: 2.45 H: 1.06 K: 0.33
adjusted from from Hewett et al (table 7)

The ETC can be used both ways: 1) to calculate the SNR per 2-km/s spectral bin form a set of magnitude, star temperature, seeing, and total integration time (left example below) or 2) to estimate the exposure time needed to reach a given SNR per 2-km/s bin in the H band (right example below). In the final implementation, the ETC will give the spectral format, an SNR/bin and photon count (of target and sky) per order, and allow to use stellar templates as input. The dotted line in the left example below is the SNR distribution obtained by the final ETC (still being implemented with a library of various spectra). Regions of low SNR correspond to low-transmission bands of the Earth.



The way the SNR translates into effective radial-velocity precision depends on many parameters:

- the signal-to-noise ratio per velocity bin (as calculated with the tool described above)
- the spectral line content of the spectrum : see for instance Figueira et al, 2016
- the completeness of LSD or CCF masks of line properties in different types of stars (in development by the SPIRou science group)
- the projected rotational velocity of the star: see for instance Artigau et al 2014
- the magnetic field of the star (through Zeeman broadening): see Reiners et al 2013
- the actual performances of the SPIRou instrument and detector cosmetics, both of which are not known as of April 2017.

Theoretical predictions as those cited above, and SNR estimates, allow us to foresee the following performance in terms of radial-velocity accuracy. "Removing" and "correcting" tellurics refer to methods 2 and 3, respectively, of Figueira et al, 2016.
Again, such performances will be refined and validated when SPIRou gets on-sky data.