Variation of Dense Gas Mass–Luminosity Conversion Factor with Metallicity in the Milky Way

Abstract HCN and HCO + are the most common dense gas tracers used both in the Milky Way and external galaxies. The luminosity of HCN and HCO + J = 1 → 0 lines are converted to a dense gas mass by the conversion factor, α Q . Traditionally, this α Q has been considered constant throughout the Galaxy and in other galaxies, regardless of the environment. We analyzed 17 outer Galaxy clouds and five inner Galaxy clouds with metallicities ranging from 0.38 Z ⊙ to 1.29 Z ⊙ . Our analysis indicates that α Q is not constant; instead, it varies with metallicity. The metallicity-corrected α Q derived from the HCN luminosity of the entire cloud is almost three times higher in the outer Galaxy than in the inner Galaxy. In contrast, HCO + seems less sensitive to metallicity. We recommend using the metallicity-corrected dense gas conversion factors <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mrow> <mml:mi>tot,</mml:mi> <mml:mi>gas</mml:mi> </mml:mrow> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>HCN</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>19</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>5</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>5.6</mml:mn> </mml:mrow> </mml:msubsup> <mml:msup> <mml:mi>Z</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.53</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.59</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mrow> <mml:mi>tot,</mml:mi> <mml:mi>gas</mml:mi> </mml:mrow> <mml:mo>′</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mi>HCO</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mn>21</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>4</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>5.5</mml:mn> </mml:mrow> </mml:msubsup> <mml:msup> <mml:mi>Z</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.32</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.55</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:math> for extragalactic studies. Radiation from nearby stars has an effect on the conversion factor of a similar magnitude as that of the metallicity. If we extend the metallicity-corrected scaling relation for HCN to the Central Molecular Zone (CMZ), the value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">HCN</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> becomes one-third to one-half of the local values. This effect could partially account for the low star formation rate per dense gas mass observed in the CMZ.