1. The abundances of gaseous H 2 O and O 2 in dense cloud cores Eric Herbst & Helen Roberts The Ohio State University

2. Successes for quiescent cores: (1)Reproduces 80% of abundances including ions, radicals, isomers (2)Predicts strong deuterium fractionation

3. 10 6 sites

4. TYPES OF SURFACE REACTIONS REACTANTS: MAINLY MOBILE ATOMS AND RADICALS A + B  AB association H + H  H 2 H + X  XH (X = O, C, N, CO, etc.) WHICH CONVERTS O  OH  H 2 O C  CH  CH 2  CH 3  CH 4 N  NH  NH 2  NH 3 CO  HCO  H 2 CO  H 3 CO  CH 3 OH X + Y  XY ??????????

5. MODELLING DIFFUSIVE SURFACE CHEMISTRY Rate Equations

6. Rates of Diffusion Standard astrochemical (e.g. Hasegawa et al. 1991) for silicates Versions for amorphous carbon and for water ice Slow H (P1): H slowed down to olivine (carbon) value of Pirronello et al. (1997) Slow (P2): all other species slowed proportionally All networks contain evaporation and cosmic-ray desorption; some contain photo processes

7. MORE ACCURATE METHODS FOR SURFACE RATES Modified rate approach – available but semi-empirical; used here and by a few other groups. Stochastic methods – soon to be available

8. STOCHASTIC METHODS Based on solution of master equation, which is a kinetic-type equation in which one calculates not concentrations but probabilities that certain numbers of species are present. Can solve directly (Hartquist, Biham) or via Monte Carlo realization (Charnley). Current status: not yet programmed for large models

9. Some predicted gas-phase abundances (10 K; 10 4 cm -3 ) P2 Energies

10. Some predicted surface abundances (10 K; 10 4 cm -3 )

11. TMC-1

12. SWAS UPPER LIMITS WRT H 2 H 2 O O 2 7.0(-08) 3.2(-06) (Odin claims 7.7(-08) towards ammonia)

13. Overall and particular agreement: pure gas-phase (low metals)

14. Same but with C/O = 1

15. Percentage agreement for gas- grain models 2 nd peak despite depletion

16. Agreement for specific species Is late-time CO depletion serious???

17. L134N

18. SWAS UPPER LIMITS WRT H 2 H 2 O O 2 3.0(-07) 3.4(-06) (Odin claims 1.7(-07) towards ammonia)

19. Percentage agreement for gas-grain models

20. Ageement for specific species

21. Source:  Oph

22. SWAS VALUES WRT H 2 H 2 O O 2 3.0(-09) <3(-07) (Odin claims <9.3(-08) towards a)

23. Gas-phase abundances for P2, 20 K, 10 5 cm -3 P1 similar at 15 K

24. Specific agreement

25. Same with amorphous carbon grains

26. CONCLUSIONS Current generation of our gas-grain models gives best agreement for water and oxygen at long times for 10 K sources Chemistry and physics of desorption critical and poorly known Depletion at long times from gas in agreement with results on pre-stellar cores including deuterium fractionation