The accretion luminosity of Class I protostars

TL;DR

This study develops and tests a method to measure protostellar accretion luminosity in Class I objects using mid-infrared hydrogen recombination lines, anchored to empirical Class II line ratios and L$_{\rm acc}$–line relations. By deriving extinction from line ratios and applying Class II correlations, the authors estimate L$_{\rm acc}$ for a sample in Taurus and ρ-Ophiuchus, finding accretion-dominated luminosity for the most embedded sources and a sharp decrease as bolometric temperature rises past ~$700$ K. The results qualitatively agree with non-ideal MHD simulations of star formation, supporting an evolutionary transition from accretion-dominated to internally powered luminosity. The work highlights critical caveats, notably the extinction law and geometric effects, and argues for larger samples and JWST data to refine the method and constrain dust properties in protostellar envelopes.

Abstract

The value of the accretion luminosity during the early phases of star formation is a crucial information which helps us understand how stars form, yet it is still very difficult to obtain. We develop a new methodology to measure accretion luminosity using mid-infrared hydrogen recombination lines, and apply it to a limited sample of Class~I protostars in the Taurus and Ophiuchus star forming regions. We adopt the commonly used assumption that the properties of disk-protostar accretion in Class I objects is similar to the disk-star accretion in Class II objects. Using simultaneous observations of three hydrogen recombination lines Brg, Pfg, and Bra, we derive the mean intrinsic line ratios, and we verified that these are constant across the probed range of photospheric and accretion properties. We establish correlations between the line luminosities and accretion luminosity. We measure the extinction towards the line emission regions in Class I protostars comparing the observed line ratios to the Class II mean values. We then derive the Class I accretion luminosities from the established Class II correlations. We find that the accretion luminosity dominates the bolometric luminosity for the more embedded protostars, corresponding to lower values of the bolometric temperature. As the bolometric temperature increases above ~700K, there is a sharp drop of the contribution of the accretion from the bolometric luminosity. Our finding are in qualitative agreement with numerical simulations of star formation. We suggest that this methodology should be applied to larger and more statistically significant samples of Class I objects, for a more detailed comparison. Our results also suggest that by combining multiple infrared line ratios, it will be possible to derive a more detailed description of the dust extinction law in protostellar envelopes.

Figures (14)

• Figure 1: Top panel: Ratio of the de-reddened Br$\alpha$ and Br$\gamma$ fluxes of Class II sources shown as a function of L$_{\star}$ (left), L$_{\mathrm {acc}}$, computed from the Br$_\gamma$ luminosity (center; see Sec. \ref{['sec:ClassII_lline']}), and the extinction in the K band (right). Bottom panel: Same but for the ratio of Pf$_\gamma$ to Br$_\gamma$ fluxes. The values of the ratios are shown by filled dots; the 3$\sigma$ upper limits are indicated by arrows. When not visible, the errors are smaller than the dots. In both sets of panels, the mean values of the ratios and their uncertainties are shown in orange.
• Figure 2: Accretion luminosity, L$_{\mathrm {acc}}$, derived from the Br$_\gamma$ luminosity (eq.(1)) plotted as a function of the line luminosity for Br$_\alpha$ (left panel) and Pf$_\gamma$ (right panel), respectively. The orange line and shadowed area show the best-fitting correlation and their uncertainty (see eq.(2) and (3)).
• Figure 3: Top panel: Values of the accretion luminosity, L$_{\mathrm {acc}}$, derived from L(Br$_\alpha$) as a function of L$_{\mathrm {acc}}$ derived from L(Br$_\gamma$). Bottom panel: Same but for L$_{\mathrm {acc}}$ derived from L(Pf$_\gamma$). The line of equal values is shown in orange in each panel.
• Figure 4: Accretion luminosity computed from Pf$_\gamma$ shown as a function of the accretion luminosity computed from Br$_\alpha$ for Class I objects. In the first case, the extinction is derived from the ratio Pf$_\gamma$/Br$_\gamma$, and in the second it is from Br$_\alpha$/Br$_\gamma$ (see Sect. \ref{['sec:extinction']}). Dark blue dots are objects in Ophiuchus; light blue dots are objects in Taurus. Light blue squares are Taurus objects from 2007AJ....133.1673B. The green dashed line shows the locus of equal values.
• Figure 5: Extinction in the K band computed from the ratio Pf$_\gamma$/Br$_\gamma$ is shown versus the value derived from the Br$_\alpha$/Br$_\gamma$ ratio ( see Sect. \ref{['sec:extinction']}). Symbols are as in Fig. \ref{['fig:f_AKbra_AKpfg']}. The green dashed line shows the locus of equal values.