Efficiency of Interstellar Nanodust Heating: Accurate Bottom-up Calculations of Nanosilicate Specific Heat Capacities

Abstract

Ultrasmall nanosized silicate grains are likely to be highly abundant in the interstellar medium. From sporadically absorbing energy from ultraviolet photons, these nanosilicates are subjected to significant instantaneous temperature fluctuations. These stochastically heated nanograins subsequently emit in the infrared. Previous estimates of the extent of the heating and emission have relied on empirical fits to bulk silicate heat capacities. The heat capacity of a system depends on the range of available vibrational modes, which for nanosized solids is dramatically affected by the constraints of finite size. Although experimental vibrational spectra of nanosilicates is not yet available, we directly take these finite size effects into account by using accurate vibrational spectra of low-energy nanosilicate structures from quantum chemical density functional theory calculations. Our results indicate that the heat capacities of ultrasmall nanosilicates are smaller than previously estimated, which would lead to a higher temperature and more intense infrared emission during stochastic heating. Specifically, we find that stochastically heated grains ultrasmall nanosilicates could be up to 35-80 K hotter than previously predicted. Our results could help to improve the understanding of infrared emission from ultrasmall nanosilicates in the ISM, which could be observed by the James Webb Space Telescope.

Figure 1

Left: Comparison of the cumulative vibrational mode spectra of pyroxene (blue, upper) and olivine (red, lower) dimers with respect to the corresponding BFM silicate vibrational spectra (green). Right: Differences in number of modes between the DFT and BFM spectra with respect to binned frequency in ranges of 100 cm^–1. Positive (negative) differences indicate that the DFT-derived spectra have more (fewer) vibrational modes in that bin. Atom color code: red, oxygen; blue, magnesium; yellow, silicon.

Figure 2

Left: Comparison between the cumulative vibrational spectra of the global minimum pyroxene dimer (blue) and the averaged spectra of three pyroxene dimer isomers (green). Right: The respective difference in the number of modes in each bin (i.e., global minimum vs average). A positive (negative) number of modes difference indicates that the averaged spectrum has more (fewer) vibrational modes in that bin.

Figure 3

Left: Comparison between the cumulative vibrational spectra of the global minimum olivine dimer (red) and the averaged spectra of three olivine dimer isomers (green). Right: The respective difference in the number of modes in each bin (i.e., global minimum vs average). A positive (negative) number of modes difference indicates that the averaged spectrum has relatively more (fewer) vibrational modes in that bin.

Figure 4

Left: Comparison of the cumulative vibrational mode spectra of pyroxene (blue) and olivine (red) nanosilicates containing 35 (upper) and 70 atoms (lower) with respect to the corresponding BFM vibrational spectra (green). Right: Differences in number of modes between the DFT and BFM spectra with respect to binned frequency ranges of 100 cm^–1. Positive (negative) differences indicate that the DFT-derived spectra have more (fewer) vibrational modes in that bin. Atom color code as in Figure 1.

Figure 5

Specific heat capacity for pyroxene (left) and olivine (right) dimers compared with BFM (green). Inset plots show the heat capacity difference between the two respective C(T) curves.

Figure 6

Specific heat capacity for pyroxene (blue) and olivine (red) nanosilicates with 35 (left) and 70 atoms (right) compared with BFM (green). Inset plots show the difference between the two respective C(T) curves.

Figure 7

Temperature vs average energy plots for nanosilicates derived from DFT-calculated vibrational spectra (pyroxenes, blue; olivines, red) and from the BFM vibrational spectra (green) for different sizes. Insets show the difference between the DFT-derived values and the BFM-derived values (pyroxenes, blue; olivines, red).

Figure 8

Comparison of the low-temperature BFM-like fitted C(T) used in refs ^and (black solid line) and our DFT-derived C(T) values for 70-atom pyroxene (left) and olivine (right) nanosilicates (blue data points). We include an approximate fit to our data (green solid line) for comparison with the BFM-like fit.