H i-to-H<sub>2</sub> Transitions in Dust-free Interstellar Gas
A. Sternberg, Alon Gurman, Shmuel Bialy
Abstract
Abstract We present numerical computations and analysis of atomic-to-molecular (H i -to-H 2 ) transitions in cool (∼100 K), low-metallicity, dust-free (primordial) gas in which molecule formation occurs via cosmic-ray-driven negative ion chemistry and removal is by a combination of far-UV photodissociation and cosmic-ray ionization and dissociation. For any gas temperature, the behavior depends on the ratio of the Lyman–Werner (LW) band FUV intensity to gas density, I LW / n , and the ratio of the cosmic-ray ionization rate to the gas density, ζ / n . We present sets of H i -to-H 2 abundance profiles for a wide range of ζ / n and I LW / n for dust-free gas. We determine the conditions for which H 2 absorption-line self-shielding in optically thick clouds enables a transition from atomic to molecular form for ionization-driven chemistry. We also examine the effects of cosmic-ray energy losses on the atomic and molecular density profiles and transition points. For a unit Galactic interstellar FUV field intensity ( I LW = 1) with LW flux 2.07 × 10 7 photons cm −2 s −1 and a uniform cosmic-ray ionization rate ζ = 10 −16 s −1 , an H i -to-H 2 transition occurs at a total hydrogen gas column density of 4 × 10 21 cm −2 , within 3 × 10 7 yr, for a gas volume density of n = 10 6 cm −3 at 100 K. For these parameters, the dust-free limit is reached for a dust-to-gas ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>≲</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:math> , which may be reached for overall metallicities <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msup> <mml:mo>≲</mml:mo> <mml:mn>0.01</mml:mn> </mml:math> relative to Galactic solar values.