Reliability of In-band and Broadband Spectral Index Measurement: Systematic Study of the Effect of Signal-to-noise Ratio for uGMRT Data

Abstract

Abstract Low-radio-frequency spectral index measurements are a powerful tool for distinguishing between different emission mechanisms and, in turn, understanding the nature of the sources. Besides the standard method of estimating the “broadband” spectral index of sources from observations in two different frequency “bands,” if the observations were made with large instantaneous bandwidth, the “in-band” spectral index can be determined, either using images of emission at multiple frequency ranges within a band or using the novel Multi Term-Multi Frequency Synthesis (MT-MFS) imaging algorithm. Here, using simulated upgraded Giant Metrewave Radio Telescope (uGMRT) data, we have systematically studied the reliability of various methods of spectral index estimation for sources with a wide range of signal-to-noise ratios (S/Ns). It is found that for synthetic uGMRT point-source data, the MT-MFS imaging algorithm produces in-band spectral indices for S/N ≲ 100 that have errors ≳0.2, making them unreliable. However, at a similar S/N, the sub-band splitting method produces errors ≲0.2, which are more accurate and unbiased than the in-band spectral indices. The broadband spectral indices produce errors ≲0.2 even for S/N ≳ 15, and hence they are most reliable if there are no higher-order variations in the spectral index. These results may be used to improve the uGMRT observation and data analysis strategies, depending on the brightness of the target source.