Molecular hydrogen emission as a density and temperature indicator

Transcription

1 Molecular hydrogen emission as a density and temperature indicator Xiang Wang University of Kentucky

2 Collaborators: Gary Ferland University of Kentucky Jack Baldwin Michigan State University Edwin Loh Michigan State University David Flower Durham University Andrew Fabian Cambridge University Robin Williams AWE

3 Introduction Strong H 2 emission from cool-core clusters and Crab Nebula filaments Consider hydrogen only excited by collisions with thermal particles Consider regions predominantly atomic or molecular Examine level excitation diagrams Discuss the relation between LTE and three different kinds of densities Compare the computational results to the observational results

4 Radiative and collisional rates

5 Level excitation diagram (Master plot) Atomic case: quasithermal behavior gives temperature indicator Molecular case: discontinuous behavior across vibrational manifolds used as possible density diagnostic Low density cases are similar to fluorescent or shock excitations Density needed to get to LTE larger than the critical density

6 Low density limit Excited levels are mainly populated from the ground states Both Sum A ul and q ug are roughly constant for the atomic case Level populations are proportional to the Boltzmann factor So the population is quasi-thermal

7 Low density limit Excited levels are mainly populated from the ground states Both Sum A ul and q ug are roughly constant for the atomic case Level populations are proportional to the Boltzmann factor So the population is quasi-thermal

8 Low density limit Excited levels are mainly populated from the ground states (This is true only for the atomic case) Both Sum A ul and q ug are roughly constant for the atomic case Level populations are proportional to the Boltzmann factor So the population is quasi-thermal

9 Mass estimates from the µm line Departure coefficient of the upper level of a line: Convert luminosity to mass: So the departure coefficient is the inverse of the factor by which the H 2 mass will be underestimated if LTE is assumed Departure coefficient vs density

10 Density needed to get to LTE for a line density required for the µm line to be within a factor of two of its LTE value Densities below those shown in this figure will lead to more than a factor of two error in the mass estimate For molecular case this density is much higher than the critical density Minimum density required to achieve b n 0.5

11 Comparison with observation ---- Abell 2597 Observation: Oonk+ (2010)

12 Comparison with observation ---- Crab Nebula Observation: Loh+ (2012)

13 Optimization results (Abell 2597) Original study (Oonk+ 2010): n 10 6 cm -3 nt cm -3 K X-ray study (Tremblay+ 2012): nt cm -3 K Our results: ² Atomic case: n 10 2 cm -3 nt cm -3 K ² Molecular case: n 10 8 cm -3 nt cm -3 K

14 Optimization results (Crab Nebula) Original study (Loh+ 2012, by using [S II] lines): n ~ cm -3 nt ~ cm -3 K Our results: ² Atomic case: n 10 2 cm -3 nt cm -3 K ² Molecular case: n 10 4 cm -3 nt cm -3 K

15 Conclusions At T=2000K for the atomic case the H 2 levels of v=1, 2 are quasi-thermal and indicate approximate temperature for low densities. At low densities for the molecular case, the discontinuous behavior between different vibrational manifolds could be used as a density diagnostic. We describe three different densities. (1) the density where collisional and radiative de-excitation rates are equal. (2) the density that makes a vibrational manifold have a quasi-thermal population. (3) the density required for a the level population to be in LTE relative to the molecule. The first density is not the best parameter for discussing the behavior of the level populations. The mass in H 2 would be underestimated, sometimes by large factors, if LTE were assumed to convert a line luminosity into a mass. It is not easy to determine the density of the gas by using the excitation diagram if not enough lines could be observed. The real deviations could be misinterpreted as observational errors.