Relating dust, gas, and the rate of star formation in M 31

Max-Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany e-mail: tabataba@mpifr-bonn.mpg.de

Received: 3 November 2009
Accepted: 26 April 2010

Abstract

Aims. We investigate the relationships between dust and gas, and study the star formation law in M 31.

Methods. We have derived distributions of dust temperature and dust opacity across M 31 at 45 resolution using the Spitzer data. With the opacity map and a standard dust model we de-reddened the Hα emission yielding the first Hα map of M 31 corrected for extinction. We compared the emissions from dust, Hα, HI, and H₂ by means of radial distributions, pixel-to-pixel correlations, and wavelet cross-correlations. We calculated the star formation rate and star formation efficiency from the de-reddened Hα emission.

Results. The dust temperature steeply decreases from 30 K near the center to 15 K at large radii. The mean dust optical depth at the Hα wavelength along the line of sight is about 0.7. The radial decrease in the dust-to-gas ratio is similar to that of the oxygen abundance. Extinction is nearly linearly correlated with the total gas surface density within limited radial intervals. On scales <2 kpc, cold dust emission is best correlated with that of neutral gas, and warm dust emission with that of ionized gas. The Hα emission is slightly better correlated with emission at 70 μm than at 24 μm. The star formation rate in M 31 is low. In the area 6 kpc < R < 17 kpc, the total SFR is 0.3  yr^-1. A linear relationship exists between surface densities of SFR and H₂. The Kennicutt-Schmidt law between SFR and total gas has a power-law index of 1.30 ± 0.05 in the radial range of R = 7–11 kpc increasing by about 0.3 for R = 11–13 kpc.

Conclusions. The better 70 μm–Hα than 24 μm–Hα correlation plus an excess in the 24 μm/70 μm intensity ratio indicates that other sources than dust grains, e.g. those of stellar origin, contribute to the 24 μm emission. The lack of H₂ in the central region could be related to the lack of HI and the low opacity/high temperature of the dust. Since neither SFR nor SFE is well correlated with the surface density of H₂ or total gas, other factors than gas density must play an important role in the formation of massive stars in M 31. The molecular depletion time scale of 1.1 Gyr indicates that M 31 is about three times less efficient in forming young massive stars than M 33.