Issue 
A&A
Volume 547, November 2012



Article Number  L3  
Number of page(s)  5  
Section  Letters  
DOI  https://doi.org/10.1051/00046361/201220330  
Published online  07 November 2012 
Online material
Appendix A: Linewidth of recombination lines
RLs are broadened by several mechanisms: a natural broadening from the quantum uncertainty ΔE of the energy level E, a thermal/microturbulence Gaussian broadening from the motions of the emitting particles and of parcels of gas that are much smaller than the beam, the Stark (or “pressure”) broadening from the perturbation of the atomic energy levels by the electric field of neighboring charged particles, and a dynamical broadening from bulk flows (e.g., infall, rotation, outflow) in the gas. A detailed discussion of these processes and the physics of RLs can be found in Gordon & Sorochenko (2002).
For n > 20 (where Hnα is a n + 1 → n transition), the natural linewidth in velocity units is (A.1)where c is the speed of light. For H30α and H53α, Δv_{N} is 1.3 × 10^{3} km s^{1} and 0.5 × 10^{3} km s^{1}, respectively. The natural broadening is negligible for radio and (sub)mm RLs.
The thermal distributions of velocities of both the individual particles and small pockets of gas (“microturbulence”) produce a Gaussian contribution to the broadening. Neglecting microturbulence, the thermal FWHM is (A.2)where k_{B} is the Boltzmann constant, m_{H} is the hydrogenatom mass, and it is assumed that all the gas is thermalized to the electron temperature T_{e}. For a purehydrogen gas with T_{e} = 9000 K, Δv_{th} = 20.3 km s^{1}.
The pressure broadening has a Lorentzian shape, and it increases with density and quantum number. Collisions with ions and electrons make different contributions. The contribution from ions has the form (Gordon & Sorochenko 2002) (A.3)where γ_{i} = 6−2.7 × 10^{5} T_{e}−0.13(n + 1)/100. For T_{e} = 9000 K and N_{i} = 10^{7} cm^{3}, the H30α line is virtually free from ion broadening (0.04 km s^{1}, and decreases close to linearly with decreasing T_{e}), whereas the H53α line is broadened by 5.1 km s^{1}.
The collisions with electrons dominate the collisions with ions under most conditions. They produce a broadening of width (Smirnov et al. 1984): (A.4)For N_{e} = 10^{7} cm^{3}, the electron broadenings for the H53α and H30α are ≈ 37.3 km s^{1} and 0.6 km s^{1}, respectively.
Finally, the last source of broadening is bulk motions (Δv_{dy}) of the ionized gas, which may be in the form of outflows/winds, infall/accretion, and/or rotation. For unresolved observations, the method outlined here permits estimating the magnitude of these motions from the nonthermal linewidth of the line that is free of pressure broadening. Of course, ideally one wishes to spatially resolve these motions. ALMA in its Cycle 1 is now able to resolve the ionizedgas motions in sources as faint as ~10 mJy at the line peak at subarcsecond resolution.
Including all the contributions to the broadening, the total linewidth will have a Voigt profile with FWHM given by Eq. (1) in the text.
Appendix B: Cm and (sub)mm recombination lines
Here we discuss the advantages and limitations that cm and (sub)mm RLs have compared to each other. The cm lines are intrinsically fainter and optically thicker, and can be partially absorbed by the relatively high continuum opacity at their wavelengths (see e.g., Wilson et al. 2009). A possible drawback of (sub)mm RLs is that the freefree continuum may be contaminated by dust emission. Another problem is that they are out of LTE more easily than cm lines, so their interpretation may require careful modeling (e.g., JiménezSerra et al. 2011; Peters et al. 2012). As shown below, our simple LTE interpretation seems to be reasonable, but it is possible that a significant fraction of the 1.3mm continuum comes from dust in the line of sight.
Let b_{n} be the ratio of the population of level n to its LTE population. Then the actual line absorption coefficient κ_{L} is related to the LTE coefficient κ_{L,LTE} by (Gordon & Sorochenko 2002) (B.1)with (B.2)While 0 < b_{n} < 1 expresses the nonLTE level depopulation, β_{n} can be negative when there are conditions for maser amplification.
In the opticallythin case (τ_{C,1.3mm} ~ 0.08 from the data), the nonLTE corrected line intensity I_{L} is (Gordon & Sorochenko 2002) (B.3)Using the tabulated values in the calculations of Walmsley (1990), b_{30} ≈ 0.98 and β_{30} ~−1.5 for a density N_{e} = 10^{7} cm^{3}. Therefore, the intensity of the H30α line is only amplified by ~3%. The H53α is even closer to LTE, with b_{53} ≈ 0.999 and β_{53} ~ 0.5.
Sub(mm) RLs are more opticaly thin and intrinsically brighter than cm RLs. For a given T_{e} and N_{e}, and in the RayleighJeans regime (hν ≪ k_{B}T_{e}), the line absorption coefficient decreases linearly with frequency κ_{L} ∝ ν^{1}, so the LTE line emission coefficient j_{L} = κ_{L}B_{ν}(T_{e}) ∝ ν. Similarly, the continuum absorption coefficient κ_{C} ∝ ν^{2.1}, so the LTE continuum emissivity j_{C} ∝ ν^{0.1}. Therefore, in the optically thin regime, the linetocontinuum ratio increases almost linearly with frequency S_{L}Δv/S_{C} ∝ ν^{1.1}. Under these assumptions, the expected ratio of the H30α to H53α linetocontinuum ratios is 6.4. However, the observed value is 1.6. If we assume that only ~32 mJy of the 1.3mm continuum are due to freefree then the linetocontinuum ratio would increase to the expected value. This suggests that dust contributes a significant fraction to the (sub)mm continuum of BN. However, it is known (and we have confirmed this with the ALMA data set) that BN is not embedded in dense molecular gas. Therefore, it is unlikely that this lineofsight dust arises in a dense core around BN.
© ESO, 2012
Current usage metrics show cumulative count of Article Views (fulltext article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 4896 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.