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

The surface-density profiles (SDPs) 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 SDP 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 (i) with increasing p(INTRINSIC); (ii) with increasing range of w(O) values; and (iii) 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 less than or similar to Delta p less than or similar to 0.10), but for p(INTRINSIC )= 3, it is larger (0.18 less than or similar to Delta p less than or similar to 0.50), and for p(INTRINSIC) = 4, it is substantial (0.50 less than or similar to Delta p less than or similar to 1.15). On its own, this effect is probably insufficient to support a value of p(INTRINSIC) much greater than p(FIT) similar or equal to 2, but it could be important in combination with other effects.

Automated summary

The surface-density profiles of dense filaments, especially those traced by dust emission, can be well fit with Plummer profiles. However, variations in the Plummer scale-length and background surface density along the filament length can lead to significant discrepancies between the estimated Plummer exponent and the intrinsic value. This discrepancy increases with the intrinsic Plummer exponent, range of scale-length values, and in cases with a range of background surface density values.