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Suppression of star formation in dwarf galaxies by photoelectric grain heating feedback


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.

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Figure 1: The morphology of the gas.
Figure 2: The star formation rates of the simulations.
Figure 3: The photoelectric heating rate.
Figure 4: The effect of photoelectric heating.


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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.

Author information




J.C.F. and N.J.G. developed modifications to the publicly available Enzo code used in this work. The code was run and the results were analysed by J.C.F. The manuscript was written by J.C.F. and edited by all authors. The work was supervised and routinely advised by M.R.K. and A.D.

Corresponding author

Correspondence to John C. Forbes.

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The authors declare no competing financial interests.

Additional information

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

Extended Data Figure 1 Supernovae are well-resolved.

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.

Source data

Extended Data Figure 2 Comparison to observations.

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.

Source data

Extended Data Figure 3 A resolution study.

ad, 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.

Extended Data Figure 4 Phase diagrams after 90 Myr of evolution.

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.

Source data

Extended Data Table 1 Parameters for a fit

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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).

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