CHAI system temperature

The CCAT Heterodyne Array Instrument (CHAI) is being built for the CCAT Observatory. It covers the frequency ranges between 460 and 500 GHz and 780 and 820 GHz. It is set-up to cover channel spacings from 61 kHz to 4 GHz. It has a receiver temperature of 100 K for the lower frequency range and 200 K for the higher frequency range. (See Barrueto et al. 2023 for more details.) CHAI is a single polarisation instrument and so \(n_\mathrm{pol}\) should be set to 1 when using it.

Here in the AtLAST sensitivity calculator, we use it as an exemplar of a heterodyne instrument capable of working at these frequencies.

In this module, we calculate the system temperature used in the overall sensitivity equation. For a CHAI like system, the system temperature is calculated as:

\[T_{sys} = \frac{1+g}{\eta_\mathrm{eff} \mathfrak{t}} \times [T_\mathrm{rx} + (\eta_\mathrm{eff} T_\mathrm{sky}) + (1-\eta_\mathrm{eff}) O(\nu, T_\mathrm{amb})]\]

where

  • \(g\) is the sideband ratio, which is 1 for CHAI as it is a dual sideband instrument

  • \(\eta_\mathrm{eff}\) is the forward efficiency of the telescope

  • \(\mathfrak{t}\) is the atmospheric transmittance, defined as \(\mathfrak{t} = \textrm{exp}^{(-\tau_{atm})}\)

  • \(T_\mathrm{rx}\) is the receiver temperature

  • \(T_\mathrm{sky}\) is the sky temperature (in terms of a Rayleigh-Jeans brightness temperature) calculated from the model grid described in Weather Calculations

  • \(T_\mathrm{amb}\) is the ambient temperature

Here, \(O(\nu, T)\) converts a physical temperature to a Rayleigh-Jeans brightness temperature

\[O(\nu, T) = T\frac{h\nu/kT}{\exp(h\nu/kT)-1}.\]

Through consultation with the developers of the CHAI instrument, we assume a constant receiver temperature across each sub-band the receivers are sensitive to:

\[\begin{split}T_{rx} = \left\{ \begin{array}{rcl} 100\,\mbox{K} & \mbox{for} & 460<\nu<500\,\mbox{GHz} \\ 200\,\mbox{K} & \mbox{for} & 780<\nu<820\,\mbox{GHz} \end{array}\right.\end{split}\]

These values are used in the \(T_{sys}\) equation above, which is in turn used to calculate the System Equivalent Flux Density used in the overall sensitivity (or integration time) calculation.