The universal thickness of mid-infrared bubbles

Abstract

Several hundred ring-like structures seen at $8\mu$m in the Spitzer GLIMPSE surveys share a uniform morphology: the shell thickness $\Delta R$ is a nearly constant fraction of the outer radius $R$, $\Delta R/R\sim 0.3$, across a factor of 40 in size and all exciting spectral types. This invariance is unexplained. We ask what sets this thickness and whether its near-constancy is physical or a measurement artifact. We derive analytic constraints on the location, temperature, and heating of the emitting grains, and confront the predicted scaling with radius against the GLIMPSE I and II catalogs (591 objects, 91 with kinematic distances). Grains in radiative equilibrium at the observed radii reach only 20-35 K and fall short of the required $8\mu$m emissivity by more than 20 orders of magnitude; the emission must come from stochastically heated PAHs and very small grains, and therefore from the photon-dominated region, where the ring width is the far-ultraviolet penetration depth. This gives $\Delta R/R=A_V^{\mathrm{PDR}}/A_V^{\mathrm{cloud}}$, independent of radius; a swept-up shell instead predicts $\Delta R/R\propto (R/R_S{)}^{3/2}$, with $R_S$ the initial Strömgren radius. We find a pronounced angular-resolution systematic that inflates the ratio for the smallest bubbles; once this is accounted for, $\Delta R/R=0.217$, with a residual dependence on physical radius of $0.03\pm 0.05$, consistent with zero. A fixed ambient density is excluded at $20\sigma$, the swept-up shell at 9-28$\sigma$. The implied columns are $N_{\mathrm{cloud}}\approx 8.7\times 10^{21}$ cm${}^{-2}$ with only 0.112 dex of scatter. The near-universal appearance of mid-infrared bubbles follows from the ratio of two nearly invariant column densities -- the dust-opacity-fixed far-ultraviolet shielding column and the Larson-like column of the parent molecular cloud -- and requires no reference to stellar winds.

arXiv comment5 pages, 2 figures, 2 tables, accepted for publication in A&A