Abstract
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, $\, \Sigma _{{\rm B}}$ 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, $w_{{\rm O}}=\rm{\small fwhm}/2\lbrace 2^{2/[p-1]}-1\rbrace ^{1/2}$); 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.
Highlights
We label B the secondary parameter, because a finite range of B values only produces a reduction in pFIT when there is a finite range of wO values
The reduction associated with the range of B values tends to saturate at large σ B We label O the null parameter, because whatever the range of O values it has no effect on pFIT
We have shown that averaging filament profiles can reduce the fitted Plummer exponent, pFIT below its intrinsic value, pINTRINSIC, i.e. it artificially reduces the slope of the SDS at large distance from the spine. (It is tempting to speculate that this effect operates even if the intrinsic SDP is not well fit by a Plummer profile, but we have not proven this.)
Summary
It has become clear that filaments play a critical role in assembling the material to form stars (e.g. Schneider & Elmegreen 1979; Bally et al 1987; Abergel et al 1994; Cambresy 1999; Myers 2009; Hacar & Tafalla 2011; Peretto et al 2012; Hacar et al 2013; Palmeirim et al 2013; Peretto et al 2013; Alves de Oliveira et al 2014; Andreet al. 2014; Konyves et al 2015; Marsh et al 2016; Hacar, Tafalla & Alves 2017; Ward-Thompson et al 2017; Hacar et al 2018; Williams et al 2018; Watkins et al 2019; Ladjelate et al 2020; Arzoumanian et al 2021). ΚF, of dust at λF is known (and universal), one can convert a map of τ F into a map of the surface density of dust, D = τ F/κF. If the fraction of dust by mass, ZD is known (and universal), one can convert this map into a map of the total surface density (hereafter ‘the surface density’), = D/ZD. With X = 0.70 this reduces to NH2 = 4.4 × 1019 cm−2 M pc−2 This last conversion neglects the fact that on most lines of sight a significant fraction of the hydrogen is not molecular. In the sequel, we prefer to present our analysis in terms of
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