1. Impulsive spot heating and chemical explosion of interstellar grains revisited Alexei Ivlev Thomas Röcker, Anton Vasyunin, Paola Caselli Max-Planck-Institut für extraterrestrische Physik

2. Freeze-out In cold ( T ~10 K), dense ( n H >~10 4 cm –3 ), and dark ( A V >~10 mag) molecular cloud cores, the timescale of freeze-out of molecular species is much shorter than the lifetime of the cores (e.g., Myers et al. 1987). Hence, “non-thermal” desorption mechanisms of the icy mantles are required to maintain the observed gas-phase abundances of species (e.g., Tafalla et al. 2004, Caselli et al. 2012). The recent discovery of, e.g., complex organic molecules (e.g., Bacmann et al. 2012, Cernicharo et al. 2012) in the cold gas is the further evidence for non-thermal processing of icy mantles.

3. Origin of “non-thermal” desorption Various kinds of impulsive heating: Cosmic rays X rays UV photons Mutual dust collisions … Question: How does the non-thermal desorption occur? Herbst 2014

4. Regimes of desorption: sublimation vs. explosion Sublimation: The deposited energy E dep is removed from dust in a form of the latent heat E sub, leading to temperature decrease. The number of desorbed molecules is N sub ~E dep /E sub. Explosion: The deposited energy stimulates exothermic reactions between radicals frozen in the icy mantle. This may trigger runaway temperature growth and chemical explosion, leading to the ejection of the entire mantle off the grain. Conventional view: The timescale of thermal diffusion in dust, ~a 2 / , is very short (less than ~10 –8 s for a ~0.1  m). Therefore, it is usually assumed that the deposited energy is instantaneously redistributed over the whole volume (whole grain heating). Two extreme regimes are then possible:

5. Conventional view: Explosion due to whole grain heating Due to a slight temperature increase, chemistry in the mantle is exponentially accelerated. The explosion occurs if the surface cooling (sublimation and radiation) cannot balance the chemical heating. cosmic ray sublimation and radiation Leger et al. 1985, Schutte & Greenberg 1991, Shen et al. 2004, …

6. Evolution after impulsive heating heating “cooling” cosmic ray stopping power S CR The temperature along the CR path falls off as T(0,t)  T 0 (t)  t –1

7. Dimensionless units The problem is governed by a single dimensionless number: We introduce the dimensionless units: temperature  =k B T/E, coordinate  =r/r * and time  =t/t * (r * and t * are certain combinations of the physical parameters). heat of reaction  A  B N  E r CR stopping power thermal conductivity  c   diffusion energy E diff heat capacity

8. Explosive solutions Explosion when  > 9.94 Explosion Whole grain heating

9. Explosion condition Thus, iron CRs (with  ~1 MeV/nucleon) are certainly able to trigger the chemical explosion of icy mantles, while the heating by CR protons is insufficient for that. Abundances  i =N i /N of the reactive species are derived from the MONACO simulations of contracting clouds (Vasyunin&Herbst 2013). The major radicals are CO and OH, with  CO  OH ~ 3  10 –4. We assume typical dust properties, and substitute the maximum S CR for Fe ions:

10. Desorption rates Let us estimate the minimum value of the explosion rate 1/t expl (per grain): The desorption rate 1/t des of molecules into the gas scales as  a 3 /t expl  a 5. For CO molecules and large grains ( a ~ 0.1  m) we get: This is comparable to the rates of “conventional” desorption (sublimation and explosion due to whole grain heating, Shen et al. 2004, Herbst&Cuppen 2006).

11. Conclusions We have developed a rigorous theory describing the localized spot heating of a reactive medium. This allows us to determine the universal explosion threshold of icy mantles. Heavy CR species, such as iron ions, are able to trigger the explosion, while the stopping power of the most abundant CR protons is insufficient for that. The resulting desorption rates (estimated for CO) are comparable to the rates due to “conventional” desorption mechanisms.

12. Conclusions When the deposited energy is below the threshold, it is quickly redistributed over the entire grain volume (whole-grain heating scenario). The explosion is unlikely in this case, since the sublimation cooling from the grain surface turns out to be very efficient. Open question: It is unclear whether the mantle is completely evaporated due to chemical explosion, or a part of it is ejected off the grain in a form of tiny ice pieces…

14. Abundance of radicals Evolution of abundances  i =N i /N of the reactive species in the icy mantles (from the MONACO simulations of contracting clouds, Vasyunin&Herbst 2013). The major radicals are CO and OH, with  CO  OH ~3  10 –4.

15. Stopping power of CRs The stopping power scales with the ion charge (roughly) as S CR  z 2, so for iron CRs ( z =26 ) the deposited energy is ~10 2 times higher than for protons. We get S CR max ~10 –10 J/cm for H, and S CR max ~10 –8 J/cm for Fe. Paul et al. 1991

16. Local energy spectra of CRs In molecular cloud cores, the CR spectra are heavily modified due to energy loss in collisions with molecules. The local spectra strongly depend on the assumption about the low-energy part of the interstellar spectra. The relative abundance of low-energy Fe ions in the local CR spectra is unknown (to the best of our knowledge…). CR protons: “Maximum” modelCR protons: “Minimum” model Padovani et al. 2009

17. Explosion due to whole grain heating The deposited energy is rapidly redistributed over the whole grain, leading to exponential amplification of the chemical heating in the mantle. It has been argued that there is a critical temperature of the whole-grain heating, above which the explosion must be triggered (d’Hendecourt et al. 1982, Shalabiea&Greenberg 1994, Shen et al. 2004,…). The thermal stability is determined by the ”global” balance between the chemical (volume) heating and the (surface) cooling due to thermal radiation and sublimation (e.g., Leger et al. 1985, Schutte&Greenberg 1991,Cuppen et al. 2006). cosmic ray radiation and sublimation

18. Heating and cooling Chemical reactions between radicals in the icy mantle generate the heat P heat. The heat is removed from the surface via radiation and sublimation; at T > 25-30 K, the cooling P cool is dominated by sublimation. saturated vapor pressure sublimation heat We use the same parameters as before, and (following Vasyunin&Herbst 2013 and Garrod 2013) assume E diff  E sub. The thermal explosion due to whole grain heating is very unlikely. Explosion when: (i) P heat > P cool (ii) E diff >  E sub For CO molecules, this yields P heat /P cool ~10 –4. diffusion energy

19. Saturated pressure Hama&Watanabe 2013

20. What is flame front?