The estimate of sensitivity for large infrared telescopes based on measured sky brightness and atmospheric extinction

TL;DR

This paper develops a sensitivity model for large infrared telescopes considering atmospheric, instrumental, and detector noise, validated with measurements at specific sites, aiding site selection and instrument design.

Contribution

The paper introduces a comprehensive sensitivity model for large infrared telescopes that accounts for atmospheric and instrumental factors, validated with real site measurements.

Findings

Sky background noise dominates detector noise at optimal conditions.

Limiting magnitudes are approximately 13th magnitude at Ali and Daocheng sites.

Instrument cooling and detector noise levels have minimal impact on sensitivity under ideal conditions.

Abstract

In order to evaluate the ground-based infrared telescope sensitivity affected by the noise from the atmosphere, instruments and detectors, we construct a sensitivity model that can calculate limiting magnitudes and signal-to-noise ratio ($S/N$). The model is tested with tentative measurements of $\rm M'$-band sky brightness and atmospheric extinction obtained at the Ali and Daocheng sites. We find that the noise caused by an excellent scientific detector and instruments at $-135^\circ \rm C$ can be ignored compared to the $\rm M'$-band sky background noise. Thus, when $S/N=3$ and total exposure time is 1 second for 10 m telescopes, the magnitude limited by the atmosphere is $13.01^{\rm m}$ at Ali and $12.96^{\rm m}$ at Daocheng. Even under less-than-ideal circumstances, i.e., the readout noise of a deep cryogenic detector is less than $200e^-$ and the instruments are cooled to below $-87.2^\circ \rm C$, the above magnitudes decrease by $0.056^{\rm m}$ at most. Therefore, according to observational requirements with a large telescope in a given infrared band, astronomers can use this sensitivity model as a tool for guiding site surveys, detector selection and instrumental thermal-control.