Erratum: "The Fractional Ionization of the Warm Neutral Interstellar Medium" (2013, ApJ, 764, 25)

Some numerical values in Table 3 of the published article are incorrect. There was an error in the code for the program that computed the secondary ionization rates caused by radiation from internal sources (main-sequence stars, active binaries, and white dwarf stars). The most significant changes are in the listed fractional values in the columns for ${{\rm{\Gamma }}}_{s,{{\rm{H}}}^{0}}$, ${{\rm{\Gamma }}}_{s,{\mathrm{He}}^{0}}$, and ${{\rm{\Gamma }}}_{s,{\mathrm{He}}^{+}}$ that apply to the rows for ${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{MS}}$, ${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{AB}}$, and ${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{WD}}$. The numbers for ${\rm{\Gamma }}({\mathrm{He}}^{0})$ and ${\rm{\Gamma }}({{\rm{Ar}}}^{0})$ arising from ${{\rm{\Gamma }}}_{s,{\mathrm{He}}^{0}}$ and ${{\rm{\Gamma }}}_{s,{\mathrm{He}}^{+}}$ for these three internal sources have also changed. After correcting the errors in these relative rates, the total ionization rates changed by amounts that are small and do not have a significant impact on conclusions elsewhere in the paper.

The ionization rates for Ar⁺ are different than before because they now include the additional cross sections for inner shell electrons and somewhat lower rates for the outermost shell (Verner & Yakovlev 1995). Again, these changes do not impact the results expressed elsewhere.

In Table 4, the rate for Total Γ(H⁰) in column (2) should be revised to equal that in the new version of Table 3.

Table 3.  Ionization Rates from Known Sources^a

Ionization	Rate	Relative Contributionb
Sourcec	(${10}^{-17}\,{{\rm{s}}}^{-1}$)	${{\rm{\Gamma }}}_{p}$	${{\rm{\Gamma }}}_{s,{{\rm{H}}}^{0}}$	${{\rm{\Gamma }}}_{s,{\mathrm{He}}^{0}}$	${{\rm{\Gamma }}}_{s,{\mathrm{He}}^{+}}$	${{\rm{\Gamma }}}_{{s}^{{\prime} }}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)
${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{ext}.}$	5.36	0.20	0.22	0.52	0.013	0.048
${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{MS}}$	2.53	0.69	0.12	0.15	1.9e-3	0.033
${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{AB}}$	0.202	0.11	0.050	0.17	4.5e-3	0.67
${\rm{\Gamma }}{({{\rm{H}}}^{0})}_{\mathrm{WD}}$	2.09	0.96	0.033	4.6e-3	4.2e-5	1.0e-5
${{\rm{\Gamma }}}_{{\mathrm{He}}^{+}}({{\rm{H}}}^{0})$	0.166	⋯	⋯	⋯	⋯	⋯
${{\rm{\Gamma }}}_{{\mathrm{He}}^{0}}({{\rm{H}}}^{0})$	4.60	⋯	⋯	⋯	⋯	⋯
${\zeta }_{\mathrm{CR}}({{\rm{H}}}^{0})$	12.4	⋯	⋯	⋯	⋯	⋯
Total Γ(H0)	27.4	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{He}}^{0})}_{\mathrm{ext}.}$	31.5	0.87	0.037	0.088	2.3e-3	7.5e-3
${\rm{\Gamma }}{({\mathrm{He}}^{0})}_{\mathrm{MS}}$	21.4	0.96	0.015	0.019	2.2e-4	3.6e-3
${\rm{\Gamma }}{({\mathrm{He}}^{0})}_{\mathrm{AB}}$	0.449	0.63	0.022	0.071	1.9e-3	0.27
${\rm{\Gamma }}{({\mathrm{He}}^{0})}_{\mathrm{WD}}$	16.9	0.99	4.8e-3	6.1e-4	5.6e-6	1.2e-6
${{\rm{\Gamma }}}_{{\mathrm{He}}^{+}}({\mathrm{He}}^{0})$	0.912	⋯	⋯	⋯	⋯	⋯
${{\rm{\Gamma }}}_{{\mathrm{He}}^{0}}({\mathrm{He}}^{0})$	6.61	⋯	⋯	⋯	⋯	⋯
${\zeta }_{\mathrm{CR}}({\mathrm{He}}^{0})$	14.4	⋯	⋯	⋯	⋯	⋯
Total ${\rm{\Gamma }}({\mathrm{He}}^{0})$	92.2	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{He}}^{+})}_{\mathrm{ext}.}$	16.9	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{He}}^{+})}_{\mathrm{MS}}$	8.31	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{He}}^{+})}_{\mathrm{AB}}$	0.0977	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{He}}^{+})}_{\mathrm{WD}}$	0.224	⋯	⋯	⋯	⋯	⋯
${{\rm{\Gamma }}}_{{\mathrm{He}}^{+}}({\mathrm{He}}^{+})$	0.316	⋯	⋯	⋯	⋯	⋯
Total Γ(He+)d	25.8	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{Ar}}^{0})}_{\mathrm{ext}.}$	250.0	0.93	0.018	0.043	1.1e-3	3.9e- 3
${\rm{\Gamma }}{({\mathrm{Ar}}^{0})}_{\mathrm{MS}}$	66.0	0.95	0.018	0.022	2.7e-4	4.9e-3
${\rm{\Gamma }}{({\mathrm{Ar}}^{0})}_{\mathrm{AB}}$	8.77	0.92	4.4e-3	0.015	4.0e-4	0.059
${\rm{\Gamma }}{({\mathrm{Ar}}^{0})}_{\mathrm{WD}}$	44.8	0.99	5.9e-3	8.2e-4	7.5e-6	1.8e-6
${{\rm{\Gamma }}}_{{\mathrm{He}}^{+}}({\mathrm{Ar}}^{0})$	1.35	⋯	⋯	⋯	⋯	⋯
${{\rm{\Gamma }}}_{{\mathrm{He}}^{0}}({\mathrm{Ar}}^{0})$	87.1	⋯	⋯	⋯	⋯	⋯
${\zeta }_{\mathrm{CR}}({\mathrm{Ar}}^{0})$	113.0	⋯	⋯	⋯	⋯	⋯
Total ${\rm{\Gamma }}({\mathrm{Ar}}^{0})$	571.0	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{Ar}}^{+})}_{\mathrm{ext}.}$	207.0	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{Ar}}^{+})}_{\mathrm{MS}}$	44.3	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{Ar}}^{+})}_{\mathrm{AB}}$	8.98	⋯	⋯	⋯	⋯	⋯
${\rm{\Gamma }}{({\mathrm{Ar}}^{+})}_{\mathrm{WD}}$	6.87	⋯	⋯	⋯	⋯	⋯
${{\rm{\Gamma }}}_{{\mathrm{He}}^{+}}({\mathrm{Ar}}^{+})$	0.925	⋯	⋯	⋯	⋯	⋯
Total Γ(Ar+)d	305.6	⋯	⋯	⋯	⋯	⋯

Notes.

^aThe internal rates (with subscripts MS, AB, and WD) are based on a volume density $n({{\rm{H}}}_{\mathrm{tot}})=0.5\,{\mathrm{cm}}^{-3}$. Such rates scale inversely with density (although not exactly so, because the secondary ionization efficiencies change when x_e changes). ^bFractions of the values shown in column (2). See Equations (6), (A1), (A2), (A3), and (A4). ^cMeaning of the subscripts that follow the different forms of Γ: ext. = external X-ray background radiation (Section 7.1), MS = embedded main-sequence stars (Section 7.2.1), AB = embedded active binary stars (Section 7.2.2), and WD = embedded WD stars (Section 7.2.3). ^dThe total ionization rates for the ions He⁺ and Ar⁺ do not include the ionizations from secondary electrons or cosmic rays. Hence, these totals underestimate the true rates.

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