In an extension of Fischera & Martin (2012a) and Heitsch (2013), two aspects of the evolution of externally pressurized, hydrostatic filaments are discussed. (a) The free-fall accretion of gas onto such a filament will lead to filament parameters (specifically, FWHM--column density relations) inconsistent with the observations of Arzoumanian et al. (2011), except for two cases: For low-mass, isothermal filaments, agreement is found as in the analysis by Fischera & Martin (2012b). Magnetized cases, for which the field scales weakly with the density as $Bpropto n^{1/2}$, also reproduce observed parameters. (b) Realistically, the filaments will be embedded not only in gas of non-zero pressure, but also of non-zero density. Thus, the appearance of sheet-embedded filaments is explored. Generating a grid of filament models and comparing the resulting column density ratios and profile shapes with observations suggests that the three-dimensional filament profiles are intrinsically flatter than isothermal, beyond projection and evolution effects.
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