A systematic bias in fitting the surface-density profiles of interstellar filaments

TL;DR

The paper reveals a systematic bias in fitting the surface-density profiles of interstellar filaments, showing that averaging along the filament length can underestimate the true Plummer exponent, especially for steeper profiles.

Contribution

It demonstrates how averaging observational data biases the estimated Plummer profile exponent, highlighting a significant factor in analyzing filament density profiles.

Findings

Averaging along filaments reduces the estimated Plummer exponent.

Bias increases with the true exponent and the range of scale-lengths.

The effect is minor for p_intrinsic=2 but substantial for p_intrinsic=4.

Abstract

The surface-density profiles of dense filaments, in particular those traced by dust emission, appear to be well fit with Plummer profiles, i.e. Sigma(b)=Sigma_B+Sigma_O{1+[b/w_O]^2}^{[1-p]/2}. Here Sigma_B is the background surface-density; Sigma_B+Sigma_O is the surface-density on the filament spine; b is the impact parameter of the line-of-sight relative to the filament spine; w_O is the Plummer scale-length (which for fixed p is exactly proportional to the full-width at half-maximum, w_O=FWHM/2{2^{2/[p-1]}-1}^{1/2}); and p is the Plummer exponent (which reflects the slope of the surface-density profile away from the spine).} In order to improve signal-to-noise it is standard practice to average the observed surface-densities along a section of the filament, or even along its whole length, before fitting the profile. We show that, if filaments do indeed have intrinsic Plummer profiles with exponent p_INTRINSIC, but there is a range of w_O values along the length of the filament (and secondarily a range of Sigma_B values), the value of the Plummer exponent, p_FIT, estimated by fitting the averaged profile, may be significantly less than p_INTRINSIC. The decrease, Delta p = p_INTRINSIC - p_FIT, increases monotonically with increasing p_INTRINSIC; with increasing range of w_O values; and -- if, but only if, there is a finite range of w_O values -- with increasing range of Sigma_B values. For typical filament parameters the decrease is insignificant if p_INTRINSIC = 2 (0.05 <~ Delta p <~ 0.10), but for p_INTRINSIC =3 it is larger (0.18 <~ Delta p <~ 0.50), and for p_INTRINSIC =4 it is substantial (0.50 <~ Delta p <~ 1.15). On its own this effect is probably insufficient to support a value of p_INTRINSIC much greater than p_FIT ~ 2, but it could be important in combination with other effects.