Photoelectric heating—heating of dust grains by far-ultraviolet photons—has long been recognized as the primary source of heating for the neutral interstellar medium1. Simulations of spiral galaxies2 have shown some indication that photoelectric heating could suppress star formation; however, simulations that include photoelectric heating have typically shown that it has little effect on the rate of star formation in either spiral galaxies3,4 or dwarf galaxies5, which suggests that supernovae are responsible for setting the gas depletion time in galaxies6,7,8. This result is in contrast with recent work9,10,11,12,13 indicating that a star formation law that depends on galaxy metallicity—as is expected with photoelectric heating, but not with supernovae—reproduces the present-day galaxy population better than does a metallicity-independent one. Here we report a series of simulations of dwarf galaxies, the class of galaxy in which the effects of both photoelectric heating and supernovae are expected to be strongest. We simultaneously include space- and time-dependent photoelectric heating in our simulations, and we resolve the energy-conserving phase of every supernova blast wave, which allows us to directly measure the relative importance of feedback by supernovae and photoelectric heating in suppressing star formation. We find that supernovae are unable to account for the observed14 large gas depletion times in dwarf galaxies. Instead, photoelectric heating is the dominant means by which dwarf galaxies regulate their star formation rate at any given time, suppressing the rate by more than an order of magnitude relative to simulations with only supernovae.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Draine, B. T. Photoelectric heating of interstellar gas. Astrophys. J. Suppl. Ser. 36, 595–619 (1978)
Bekki, K. Dust-regulated galaxy formation and evolution: a new chemodynamical model with live dust particles. Mon. Not. R. Astron. Soc. 449, 1625–1649 (2015)
Tasker, E. J. Star formation in disk galaxies. II. The effect of star formation and photoelectric heating on the formation and evolution of giant molecular clouds. Astrophys. J. 730, 11 (2011)
Tasker, E. J., Wadsley, J. & Pudritz, R. Star formation in disk galaxies. III. Does stellar feedback result in cloud death? Astrophys. J. 801, 33 (2015)
Hu, C.-Y., Naab, T., Walch, S., Glover, S. C. O. & Clark, P. C. Star formation and molecular hydrogen in dwarf galaxies: a non-equilibrium view. Mon. Not. R. Astron. Soc. 458, 3528–3553 (2016)
Hopkins, P. F., Quataert, E. & Murray, N. Self-regulated star formation in galaxies via momentum input from massive stars. Mon. Not. R. Astron. Soc. 417, 950–973 (2011)
Hopkins, P. F., Narayanan, D. & Murray, N. The meaning and consequences of star formation criteria in galaxy models with resolved stellar feedback. Mon. Not. R. Astron. Soc. 432, 2647–2653 (2013)
Hayward, C. C. & Hopkins, P. F. How stellar feedback simultaneously regulates star formation and drives outflows. Preprint at http://arxiv.org/abs/1510.05650 (2015)
Krumholz, M. R., McKee, C. F. & Tumlinson, J. The atomic-to-molecular transition in galaxies. II: H i and H2 column densities. Astrophys. J. 693, 216–235 (2009)
Krumholz, M. R. & Dekel, A. Metallicity-dependent quenching of star formation at high redshift in small galaxies. Astrophys. J. 753, 16 (2012)
Christensen, C. et al. Implementing molecular hydrogen in hydrodynamic simulations of galaxy formation. Mon. Not. R. Astron. Soc. 425, 3058–3076 (2012)
Krumholz, M. R. The star formation law in molecule-poor galaxies. Mon. Not. R. Astron. Soc. 436, 2747–2762 (2013)
Makiya, R., Totani, T., Kobayashi, M. A. R., Nagashima, M. & Takeuchi, T. T. Galaxy luminosity function and its cosmological evolution: testing a new feedback model depending on galaxy-scale dust opacity. Mon. Not. R. Astron. Soc. 441, 63–72 (2014)
Hunter, D. A. et al. Little things. Astron. J. 144, 134 (2012)
Bigiel, F. et al. A constant molecular gas depletion time in nearby disk galaxies. Astrophys. J. 730, L13 (2011)
Bryan, G. L. et al. ENZO: an adaptive mesh refinement code for astrophysics. Astrophys. J. Suppl. Ser. 211, 19 (2014)
Papastergis, E., Cattaneo, A., Huang, S., Giovanelli, R. & Hanes, M. P. A direct measurement of the baryonic mass function of galaxies and implications for the galactic baryon fraction. Astrophys. J. 759, 138 (2012)
Okamoto, T., Gao, L. & Theuns, T. Mass loss of galaxies due to an ultraviolet background. Mon. Not. R. Astron. Soc. 390, 920–928 (2008)
Dekel, A. & Silk, J. The origin of dwarf galaxies, cold dark matter, and biased galaxy formation. Astrophys. J. 303, 39–55 (1986)
Janowiecki, S. et al. (Almost) dark HI Sources in the ALFALFA survey: the intriguing case of HI1232+20. Astrophys. J. 801, 96 (2015)
Broeils, A. H. & Rhee, M.-H. Short 21-cm WSRT observations of spiral and irregular galaxies. H i properties. Astron. Astrophys. 324, 877–887 (1997)
Katz, N. Dissipational galaxy formation. II. Effects of star formation. Astrophys. J. 391, 502–517 (1992)
Turk, M. J. et al. yt: a multi-code analysis toolkit for astrophysical simulation data. Astrophys. J. Suppl. Ser. 192, 9 (2011)
Cannon, J. M. et al. The ALFALFA “Almost Darks” campaign: pilot VLA H i observations of five high mass-to-light ratio systems. Astron. J. 149, 72 (2015)
Davé, R., Finlator, K. & Oppenheimer, B. D. An analytic model for the evolution of the stellar, gas and metal content of galaxies. Mon. Not. R. Astron. Soc. 421, 98–107 (2012)
Lilly, S. J., Carollo, C. M., Pipino, A., Renzini, A. & Peng, Y. Gas regulation of galaxies: the evolution of the cosmic specific star formation rate, the metallicity-mass-star-formation rate relation, and the stellar content of halos. Astrophys. J. 772, 119 (2013)
Forbes, J. C., Krumholz, M. R., Burkert, A. & Dekel, A. On the origin of the fundamental metallicity relation and the scatter in galaxy scaling relations. Mon. Not. R. Astron. Soc. 443, 168–185 (2014)
Goldbaum, N. J., Krumholz, M. R. & Forbes, J. C. Mass transport and turbulence in gravitationally unstable disk galaxies. I. The case of pure self-gravity. Astrophys. J. 814, 131 (2015)
Springel, V. & White, S. D. M. Tidal tails in cold dark matter cosmologies. Mon. Not. R. Astron. Soc. 307, 162–178 (1999)
Leitherer, C. et al. Starburst99: synthesis models for galaxies with active star formation. Astrophys. J. Suppl. Ser. 123, 3–40 (1999)
Chabrier, G. Galactic stellar and substellar initial mass function. Publ. Astron. Soc. Pac. 115, 763–795 (2003)
Thornton, K., Gaudlitz, M., Janka, H.-T. & Steinmetz, M. Energy input and mass redistribution by supernovae in the interstellar medium. Astrophys. J. 500, 95–119 (1998)
Geha, M. et al. The stellar initial mass function of ultra-faint dwarf galaxies: evidence for IMF variations with galactic environment. Astrophys. J. 771, 29 (2013)
Habing, H. J. The interstellar radiation density between 912 Å and 2400 Å. Bull. Astron. Inst. Netherlands 19, 421–431 (1968)
Wolfire, M. G., McKee, C. F., Hollenbach, D. & Tielens, A. G. G. M. Neutral atomic phases of the interstellar medium in the galaxy. Astrophys. J. 587, 278–311 (2003)
Kim, J.-h. et al. The AGORA high-resolution galaxy simulations comparison project. Astrophys. J. Suppl. Ser. 210, 14 (2014)
The Grackle Library. https://grackle.readthedocs.org/
Oñorbe, J. et al. Forged in FIRE: cusps, cores and baryons in low-mass dwarf galaxies. Mon. Not. R. Astron. Soc. 454, 2092–2106 (2015)
Bekki, K. Formation of ultra-compact blue dwarf galaxies and their evolution into nucleated dwarfs. Astrophys. J. 812, L14 (2015)
Bekki, K. Formation of emission line dots and extremely metal-deficient dwarfs from almost dark galaxies. Mon. Not. R. Astron. Soc. 454, L41–L45 (2015)
Truelove, J. K. et al. Self-gravitational hydrodynamics with three-dimensional adaptive mesh refinement: methodology and applications to molecular cloud collapse and fragmentation. Astrophys. J. 495, 821–852 (1998)
Krumholz, M. R. & Tan, J. C. Slow star formation in dense gas: evidence and implications. Astrophys. J. 654, 304–315 (2007)
Krumholz, M. R., Dekel, A. & McKee, C. F. A universal, local star formation law in galactic clouds, nearby galaxies, high-redshift disks, and starbursts. Astrophys. J. 745, 69 (2012)
Chomiuk, L. & Povich, M. S. Toward a unification of star formation rate determinations in the Milky Way and other galaxies. Astron. J. 142, 197 (2011)
J.C.F. and M.R.K. acknowledge support from Hubble Archival Research grant HST-AR-13909. This work was also supported by NSF grants AST-09553300 and AST-1405962, NASA ATP grant NNX13AB84G and NASA TCAN grant NNX14AB52G (J.C.F., M.R.K. and N.J.G.), and by Australian Research Council grant DP160100695. A.D. acknowledges support from the grants ISF 124/12, I-CORE Program of the PBC/ISF 1829/12, BSF 2014-273 and NSF AST-1405962. Simulations were carried out on NASA Pleiades and the UCSC supercomputer Hyades, supported by NSF grant AST-1229745.
The authors declare no competing financial interests.
Reviewer Information Nature thanks R. Makiya and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
The cumulative distribution of the density of cells in which supernovae explode is shown in red, and that in which stars form is shown in blue. The thin lines show these distributions in different 10-Myr intervals, while the thick lines show the cumulative density function over the entire simulation. The vertical dashed line indicates the density at which a supernova remnant would radiate all of its energy before it expanded to the size of a single cell (10 pc) in the simulation, assuming solar metallicity. Nearly every supernova in the simulation occurs to the left of this line, indicating that the simulation does not suffer from the overcooling problem.
a, b, Star formation properties (a, depletion time; b, star formation rate (SFR)) for a heterogeneous set14,20,24 of galaxies are shown as a function of gas mass MHI. Upper and lower limits are indicated with arrows. Boxes representing the range of values covered by our simulations are over-plotted. The vertical range of the box is determined by the final snapshot for each simulation; the high (low) SFR extremum represents the 1-kpc (5-kpc) disk. No ‘SN only’ simulation was run for the 1-kpc case, so the blue box is not closed. Only simulations that include photoelectric heating agree with the depletion times observed for bulk of galaxies in the mass range we simulated. See Methods section ‘Comparison to observations’ for more details.
a–d, The depletion time of all 12 simulations with 5-kpc gas scale-length is plotted over time. The four feedback models are shown (a, ‘no feedback’, grey; b, ‘PE only’, red; c, ‘SN only’, blue; d, ‘SN + PE’, black), with the line style indicating the result for different resolutions (see legend). The orange lines show the depletion time when the measurement is carried out in a cylinder with 1-kpc radius; the other lines use a 9-kpc radius. Regardless of the aperture, the simulations quickly converge; differences between simulations with factor-of-two differences in resolution are small compared to the differences resulting from changing the physics.
Runs with different feedback models and 5-kpc gas scale-length are shown, all at 10-pc resolution. The light blue diagonal lines show the threshold for star formation, at which the gas becomes Jeans unstable on the highest refinement level. The black lines trace where the net cooling rate is zero, assuming different values for the volumetric heating rate, from 10−26 erg s−1 (highest line) to 10−29 erg s−1 (lowest line). Photoelectric heating raises the typical temperature of gas near the star formation threshold such that moderate star formation can stabilize nearby gas against collapse.
About this article
Cite this article
Forbes, J., Krumholz, M., Goldbaum, N. et al. Suppression of star formation in dwarf galaxies by photoelectric grain heating feedback. Nature 535, 523–525 (2016). https://doi.org/10.1038/nature18292
Nature Physics (2016)