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Table 4

Measured upper limits to the H2 emission line ratios and theoretical line ratios expected for H2 at LTE, and H2 excited by UV, X-ray, and shocks (Mouri 1994; Tiné et al. 1997; Nomura et al. 2007).


Observed
  HD 97048  <0.20  <0.22
  HD 100546  <0.55  <0.39
LTE
  T = 500 K 0.44 1.8 × 10-5  
  T = 1000 K 0.27 0.005
  T = 2000 K 0.21 0.085
  T = 3000 K 0.18 0.21  
UV pure radiative fluorescencea
  nT = 102 − 104 cm-3
     χ = 1−104 0.38–1.18 0.52–0.58
UV thermal + fluorescenceb
  nT = 105 − 106 cm-3
     χ = 102 − 104 0.27–0.34 0.0062–0.025
X-ray
  Lepp & McCray (1983)c 0.23 0.010
  Draine & Woods (1990)d 0.21–0.20 0.097–0.075
  Tiné et al. (1997)e
    T = 500    K, nH = 105 − 107 cm-3 0.28–0.49 0.01–0.35
    T = 1000 K, nH = 105 − 107 cm-3 0.28–0.29 0.001–0.006
    T = 2000 K, nH = 105 − 107 cm-3 0.21–0.22 0.013–0.082
Shockf 0.23 0.084
Nomura CTTS disk modelsg
  X-ray irradiation 0.23 0.06
  UV irradiation 0.25 0.02
  X-ray+UV irradiation 0.24 0.03

Notes. 

(a)

Models of pure radiative UV fluorescent H2 emission spectra produced in low-density (n ≲ 104 cm-3) cold isothermal photodissociation regions from Black & van Dishoeck (1987).

(b)

Models of H2 infrared emission spectra in dense (n ≳ 104 cm-3) static photodissociation regions exposed to UV radiation that both heats and excites the H2 gas from Sternberg & Dalgarno (1989).

(a,b)

Parameters: nT = the total density of hydrogen atoms and molecules; χ = UV-flux scaling relative to the interstellar radiation field;

(c)

X-ray heating models of Lepp & McCray (1983) assume an X-ray luminosity in the 1–10 keV band of 1035 erg s-1. Here are given the line ratios of their model b.

(d)

X-ray excitation models of Draine & Woods (1990) provide the expected H2 line emissivity efficiencies assuming a rate of absorption of X-ray energy γ = 2 × 10-19 erg s-1, nH = 105 cm-3, and monochromatic X-rays of 100 eV. In the case of the H2 1-0 S(1) line, they obtain efficiencies of 9.1 × 10-3,7.9 × 10-3, and 4.8 × 10-3 for an X-ray energy absorbed per H nucleus of 1, 10, and 62.3 eV respectively. In HD 97048 and HD 100546, we measured H2 1-0 S(1) luminosities of 1.9 × 1029 and 3.4 × 1028 erg s-1 respectively. Using the Draine & Woods (1990) H2 1-0 S(1) line efficiencies, these H2 1-0 S(1) luminosities would imply a LX from 1030 to 1031 erg s-1, somewhat brighter than the LX ∼ 1029.5 measured in Herbig Ae stars (Telleschi et al. 2007).

(e)

Tiné et al. (1997) models do not prescribe a specific X-ray input luminosity. They assume electrons of 30 eV and use as input parameters the ionization rate ζ (10-8 to 10-17 s-1), nH(10 − 107 cm-3), and T = 500,1000,2000 K (see Tables 8 and 9 of Tiné et al. 1997). These models include, in addition to the effects of X-rays, the effects of collision processes of H2, with H2, H, and He on the resulting H2 emission spectrum.

(f)

Brand et al. (1989).

(g)

Nomura et al. (2007) CTTS models assume a LX ∼ 1030 erg s-1 and LFUV ∼ 1031 erg s-1. Here are given the line ratios of the models with maximum grain radii amax = 10   μm.

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