The Effect of Noise on the Dust Temperature-Spectral Index Correlation

Abstract

We investigate how uncertainties in flux measurements affect the results from modified blackbody spectral energy distribution (SED) fits. We show that an inverse correlation between the dust temperature T and spectral index β naturally arises from least-squares fits due to the uncertainties, even for sources with a single T and \(\beta\). Fitting SEDs to noisy fluxes solely in the Rayleigh–Jeans regime produces unreliable T and \(\beta\) estimates. Thus, for long wavelength observations \((\lambda > \sim 200 \mu m)\), or for warm sources \((T >\sim 60 K)\), it becomes difficult to distinguish sources with different temperatures. We assess the role of noise in recent observational results that indicate an inverse and continuously varying \(T –\beta\) relation. Though an inverse and continuous \(T –\beta\) correlation may be a physical property of dust in the interstellar medium, we find that the observed inverse correlation may be primarily due to noise.