The volumetric star formation law in the Milky Way

¹ Dipartimento di Fisica e Astronomia, Università di Bologna, Via P. Gobetti 93/2, 40129 Bologna, Italy
e-mail: cecilia.bacchini@unibo.it
² Kapteyn Astronomical Institute, University of Groningen, Postbus 800, 9700 Groningen, The Netherlands
³ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
⁴ Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland
⁵ ASTRON, Netherlands Institute for Radio Astronomy, Oude Hoogeveensedijk 4, 7991 Dwingeloo, The Netherlands
⁶ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

Received: 23 August 2019
Accepted: 5 November 2019

Abstract

Several open questions on galaxy formation and evolution have their roots in the lack of a universal star formation law that could univocally link the gas properties, such as its density, to the star formation rate (SFR) density. In a recent paper we used a sample of nearby disc galaxies to infer the volumetric star formation (VSF) law, a tight correlation between the gas and the SFR volume densities derived under the assumption of hydrostatic equilibrium for the gas disc. However, due to the dearth of information about the vertical distribution of the SFR in these galaxies, we could not find a unique slope for the VSF law, but two alternative values. In this paper, we use the scale height of the SFR density distribution in our Galaxy adopting classical Cepheids (age ≲200 Myr) as tracers of star formation. We show that this latter is fully compatible with the flaring scale height expected from gas in hydrostatic equilibrium. These scale heights allowed us to convert the observed surface densities of gas and SFR into the corresponding volume densities. Our results indicate that the VSF law ρ_SFR ∝ ρ^α_gas with α ≈ 2 is valid in the Milky Way as well as in nearby disc galaxies.