Electron impact ro-vibrational transitions and dissociative recombination of H2+ and HD+ - Rate coefficients and astrophysical implications

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Volume 703 (November 2025)

A&A, 703 (2025) A220

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Table 2

Fitting parameters for DR rate coefficients of $H_{2}^{+}$ $\mathrm{H}_{2}^{+}$ and HD⁺.

Molecule	$v_{i}^{+}$ $v_{i}^{+}$	a₀ (10⁻⁸ cm³ s⁻¹)	a₁	a₂ (K)	a₃ (10⁻⁸ cm³ s⁻¹)	a₄	a₅ (K)	RMS
$H_{2}^{+}$ $\mathrm{H}_{2}^{+}$	0	3.946	−0.8907	5.693	−3.291	−1.368	55.78	0.08937
	1	4.869	−0.5423	−0.1428	−9.517 × 10⁻²	−2.411	59.67	0.2635
	2	2.833	−0.5427	0.3027	5.942 × 10⁻¹⁰	−10.12	139.2	0.1433
	0-2 (Thermal avg.)	3.946	−0.8907	5.693	−3.291	−1.368	55.78	0.08937
	0-2 (Franck-Condon avg.)	2.887	−0.5722	0.1274	7.231 × 10⁻³	−2.608	17.29	0.1087

HD⁺	0	0.8527	−0.3476	−1.089	5.004 × 10⁻²	−1.636	6.182	0.09658
	1	2.582	−0.8402	0.6157	9.247 × 10⁻³	−3.217	34.94	0.2774
	2	2.589	−0.7394	0.4758	4.255 × 10⁻³	−4.704	151.3	0.08529
	0-2 (Thermal avg.)	1.670	−0.5848	0.9308	−0.6311	−1.192	38.97	0.08983

Notes. Parameters correspond to Eq. (10), for the thermally averaged and Franck–Condon averaged rate coefficients of $H_{2}^{+}$ $\mathrm{H}_{2}^{+}$ and HD⁺, for every rotational level $N_{i}^{+}$ $N_{i}^{+}$ with $v_{i}^{+} = 0 - 2$ $v_{i}^{+}=0-2$ , at electron temperatures between 10 and 4000 K. For $H_{2}^{+}$ $\mathrm{H}_{2}^{+}$ , the thermal total average closely follows $v_{i}^{+} = 0$ $v_{i}^{+}=0$ ; therefore the $v_{i}^{+} = 0$ $v_{i}^{+}=0$ fit parameters are used for this row (RMS=0.08937) rather than a direct fit of the average (RMS=0.4577).

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