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

Whitworth, A. P., Priestley, F. D. and Arzoumanian, D. 2021. A systematic bias in fitting the surface-density profiles of interstellar filaments. Monthly Notices of the Royal Astronomical Society 508 (2) , 2736–2742. 10.1093/mnras/stab2782

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Abstract

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. Σ(b) = ΣB + ΣO{1 + [b/wO]2}[1 − p]/2. Here, ΣB is the background surface density;  ΣB + ΣO is the surface density on the filament spine;  b is the impact parameter of the line-of-sight relative to the filament spine;  wO is the Plummer scale-length (which for fixed p is exactly proportional to the full width at half-maximum, wO=fwhm/2{22/[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 pINTRINSIC, but there is a range of wO values along the length of the filament (and secondarily a range of ΣB values), the value of the Plummer exponent, pFIT, estimated by fitting the averaged profile, may be significantly less than pINTRINSIC. The decrease, Δp = pINTRINSIC − pFIT, increases monotonically (i) with increasing pINTRINSIC; (ii) with increasing range of wO values; and (iii) if (but only if) there is a finite range of wO values, with increasing range of ΣB values. For typical filament parameters, the decrease is insignificant if pINTRINSIC = 2 (0.05 ≲ Δp ≲ 0.10), but for pINTRINSIC = 3, it is larger (0.18 ≲ Δp ≲ 0.50), and for pINTRINSIC = 4, it is substantial (0.50 ≲ Δp ≲ 1.15). On its own, this effect is probably insufficient to support a value of pINTRINSIC much greater than pFIT ≃ 2, but it could be important in combination with other effects.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Physics and Astronomy
Publisher: Royal Astronomical Society
ISSN: 0035-8711
Date of First Compliant Deposit: 1 December 2021
Date of Acceptance: 21 September 2021
Last Modified: 01 Dec 2021 10:15
URI: https://orca.cardiff.ac.uk/id/eprint/145761

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