Helen Roberts University of Manchester Deuterated H3+ as a probe of isotope fractionation in star-forming regions. Helen Roberts University of Manchester

T = 10 K n(H2) = 104 cm-3 u.v. radiation HCO+ H2 H3+ HC11N H2CO NH3 CO CH3OH u.v. radiation

T = 10 K n(H2) = 104 cm-3 H2 + c.r.  H2+ + e- H2+ + H2  H3+ + H H3+ + CO  HCO+ + H2 H3+ + N2  N2H+ + H2 H3+ + HD  H2D+ + H2 H3+ + e-  H + H + H; H2 + H Cosmic rays

We can run chemical models which evolve the chemistry over time: >100 species; several thousand reactions physical conditions are constant gas-grain interactions are neglected, so steady-state is reached H3+ e- H3+ abundance depends on the cosmic ray ionisation rate, and on the rate of destruction by neutral species. The fractional abundance of H3+ depends on the density. ζ n(H2) n(H3+) = kCO n(CO)

H3+ + HD  H2D+ + H2 T = 10 K n(H2) = 104 cm-3 Cosmic rays H2 + c.r.  H2+ + e- H2+ + H2  H3+ + H H3+ + CO  HCO+ + H2 H3+ + N2  N2H+ + H2 H3+ + HD  H2D+ + H2 H3+ + e-  H + H + H; H2 + H Cosmic rays

Underlying D/H ratio ~ 10-5 H3+ + HD H2D+ + H2 + 230K H2D+ + HD D2H+ + H2 + 187K D2H+ + HD D3+ + H2 + 234K CH3+ + HD CH2D+ + H2 + 370K C2H2+ + HD C2HD+ + H2 + 550K H3+ + CO HCO+ + H2 k cm3s-1 H2D+ + CO HCO+ + HD 2/3 k cm3s-1 DCO+ + H2 1/3 k cm3s-1

In TMC-1: NH2D/NH3 = 0.01; DCO+/HCO+ = 0.02 H2,H HD,H2 D,H HD,D2,D,H D2,D e- H2 H3+ H2D+ D2H+ D3+ HD CO,N2,O DCO+,HCO+,N2D+, N2H+,OD+,OH+ HCO+,N2H+,OH+ DCO+,N2D+,OD+ In dark clouds CO and electrons are the major destroyers of H3+ and H2D+. At steady-state H2D+/H3+ ~ 0.1, so other D/H ratios are ~ a few percent. In TMC-1: NH2D/NH3 = 0.01; DCO+/HCO+ = 0.02

Steady-state molecular D/H ratios: H2D+ N2D+ DCO+

kr + [CO]kCO + [e-]ke + [HD]kHD Steady-state approximation for H2D+ fractionation: [H2D+] [H3+] kf kr + [CO]kCO + [e-]ke + [HD]kHD [HD] [H2] = H3+ + HD  H2D+ + H2 kf cm3s-1 H2D+ + H2  H3+ + HD kr cm3s-1 ~ 0 at 10K

kr + [CO]kCO + [e-]ke + [HD]kHD kf kr + [CO]kCO + [e-]ke + [HD]kHD [HD] [H2] = So the H2D+/H3+ ratio can depend on the ionisation fraction – a parameter we want to know. As it is difficult to directly determine the H2D+ fractionation in dark clouds, DCO+ and/or N2D+ are used instead (e.g. Williams et al. 1998; Caselli et al. 1998) BUT: we do need to know kf , ke and [CO]. In dark clouds the gas-phase models predict [CO] ~ 10-4, its canonical value, but there is increasing evidence that CO is depleted in many regions….

Infra-red ISO SWS spectrum (Whittet et al. 1996) Evidence for ice mantles and freeze-out of molecules in the ISM: SOLID STATE OBSERVATIONS Infra-red ISO SWS spectrum (Whittet et al. 1996) Observations from Caselli et al. (1999) showing CO depletion across the prestellar core L1544 GAS-PHASE OBSERVATIONS

kr + [CO]kCO + [e-]ke + [HD]kHD Prestellar core: T = 8-10K; n(H2) ~ 106 cm-3 [CO] is lower; [e-] is lower. [H2D+] [H3+] kf kr + [CO]kCO + [e-]ke + [HD]kHD [HD] [H2] = H2,H HD,H2 D,H HD,D2,D,H D2,D e- H2 H3+ H2D+ D2H+ D3+ HD CO,N2,O DCO+,HCO+,N2D+, N2H+,OD+,OH+ HCO+,N2H+,OH+ DCO+,N2D+,OD+

[H2D+] [H3+] [D2H+] [H2D+] kf [e-]ke + [HD]kHD [HD] [H2] ~ ~ [D3+] Eventually all heavy species will disappear: H2,H HD,H2 D,H HD,D2,D,H D2,D e- H2 H3+ H2D+ D2H+ D3+ HD [H2D+] [H3+] [D2H+] [H2D+] kf [e-]ke + [HD]kHD [HD] [H2] ~ ~ [D3+] [H2D+] kf [e-]ke [HD] [H2] ~ (n.b. this approximation assumes rate coefficients are the same for all isotopologues)

~ 1 ~ 20 [H2D+] [H3+] kf [e-]ke + [HD]kHD [HD] [H2] ~ [D2H+] [D3+] Eventually all heavy species will disappear: H2,H HD,H2 D,H HD,D2,D,H D2,D e- H2 H3+ H2D+ D2H+ D3+ HD [H2D+] [H3+] kf [e-]ke + [HD]kHD [HD] [H2] ~ [D2H+] ~ 1 [D3+] [e-]ke ~ 20 Observing molecular line profiles can give unique information. H2D+ and D2H+ are, therefore, important tracers of the physical conditions at the centre of a prestellar core in the last stage before star formation.

Abundances evolving over time in a model which includes freeze-out Predictions from a `one-point’ prestellar core model: Accretion of heavy species onto grains is now included. Thermal desorption is included, but is very inefficient Abundances evolving over time in a model which includes freeze-out Molecular D/H ratios increasing as CO and other heavy species disappear from the gas-phase.

Molecular abundance distributions (Tafalla et al. 2002) From observations of L1544: Physical conditions and abundances as a function of distance from the core centre. Temperature and density profiles: Tafalla et al. 2002; Evans et al. 2001. Molecular abundance distributions (Tafalla et al. 2002) We now run a set of models (points show fit) at different physical conditions to try and reproduce abundance distributions and column densities.

Predicted molecular abundance distributions from the model of L1544: (using flattened density profile from Tafalla et al. 2002) After 1000 years After 30,000 years CO CO Abundances still constant across the core. CO and CS are freezing out at the centre, but are not completely gone.

Predicted abundances after 105 yr: CO is completely frozen out at the core centre; N2H+ and NH3 are depleted. D3+ is the most abundant deuterated species AND the most abundant ion.

Predicted deuterium fractionation across the core Beam-averaged column densities assuming a 15 arcsec beam) (cm-2) Predicted deuterium fractionation across the core Predicted Observed CO 4.2(+17) 9.0(+17) H2D+ 4.7(+13) 5.0(+13) D2H+ 4.4(+13) --- D3+ 2.2(+14) HCO+ 2.5(+13) 1.0(+14) DCO+ 2.5(+12) 4.0(+12) N2H+ 3.9(+12) 2.0(+13) N2D+ 5.0(+12) H2CO 1.5(+15) D2CO 1.6(+12) 9.0(+11) HNC 7.9(+14) 9.0(+13) DNC 4.2(+13) 3.0(+12) Molecular D/H ratios increase as CO freezes out. D2CO/H2CO close to the centre ~0.1, higher than that observed. BUT: the ratio of the column densities is 0.001 - much lower! N(H2D+) and N(CO) are in good agreement, though. Refs: Bacmann et al. 2001,2002; Caselli et al. 2003; Caselli et al. 2001,2002; Hirota et al. 2002

We can look at the effects of changing parameters on the model results: Rate coefficients: use slower fractionation rates (Gerlich et al. 2002; Roueff et al. 2005) Density profile: density may continue increasing towards the core centre rather than flattening off (Young et al. 2001; van der Tak et al. 2005) Gas-grain interaction: we currently include thermal desorption (inefficient at 10K), but molecules could also be formed on the grain surfaces and then returned to the gas-phase. Other authors have concentrated on different cases: the effects of grain size distribution on the H3+ fractionation, and the resulting ortho-para ratios (Flower et al. 2004, Walmsley et al 2004); Aikawa et al. (2003,2004) have a detailed collapse model with grain-surface chemistry.

Our standard prestellar model: Using slower fractionation rates: Molecular abundance distributions are not significantly affected (as we expect), but we do still get [D3+] ~ [e-] at the centre. The relative abundances of H3+ and analogues are changed.

standard prestellar model: slower fractionation rates: Molecular D/H ratios in the outer envelope are lower, but still become highly enhanced within ~6000 AU. Under the conditions where the major destroyer of H3+, H2D+ and D2H+ is HD, D3+ is still the end of the chain. But the slower formation rates mean D3+/H3+ at the core centre is lower.

Molecular abundance distributions (Tafalla et al. 2002) We also have an alternate density profile: …van der Tak et al. (2005) suggest this based on the observed H2D+ line profile Temperature and density profiles: Tafalla et al. 2002; Evans et al. 2001. Molecular abundance distributions (Tafalla et al. 2002)

Our standard prestellar model: Centrally peaked density profile: Lower density in outer cloud means freeze-out is slower, but is very rapid at the centre. The very high central density causes a drop in [e-] at the very centre of the core.

standard prestellar model: centrally peaked profile: Molecular D/H ratios change much more across the core. The fractionation becomes very high at the centre due to the drop in electron abundance.

Our standard prestellar model: cosmic-ray desorption from grains: When we include a continuous desorption mechanism, the heavier species never freeze out completely.

standard prestellar model: Cosmic-ray desorption: Unsurprisingly, we now do not get the enormous molecular D/H ratios that are caused by depletion. Several ratios (e.g. DCO+/HCO+, H2D+/H3+, N2D+/N2H+) still reach 1 at the core centre.

A comparison with observed molecular D/H ratios: Norm. Slow Peak CRD H2D+/H3+ 1 0.5 DCO+/HCO+ 0.1 0.03 N2D+/N2H+ 0.8 D2CO/H2CO 0.001 0.0002 DNC/HNC 0.05 0.025 0.04 Obs. ~1 0.04 0.3 0.03 These averaged ratios are not dramatically different for the different models. One could argue that the slow fractionation rates give the best overall agreement, but they are the worst for D2CO. BUT: the D2CO fractionation is ALWAYS too low. CRD seems to be too fast, but there may be other desorption mechanisms we could try: e.g. spot heating by cosmic-rays (Shen et al. 2004); desorption caused by molecule formation (Garrod, Herbst et al. in prep).

Using deuterated H3+ to determine the ionisation fraction: This is most straightforward when we can assume that [D3+] ~ [e-] Norm. Slow Peak (CRD) H2D+/H3+ ~1 0.5 (0.5) D2H+/H2D+ 0.33 0.6 D3+/D2H+ 5 6 3 (0.8) D2H+/H2D+ is the only ratio we can directly measure. So observations may not be accurate enough to choose between these different models. BUT: the latest generation of models also predict molecular line profiles: these should be sensitive to the prestellar core structure.

Summary: deuterium fractionation is interesting because it is such an enormous effect (orders of magnitude) observations of deuterated molecules are most useful, though, when they are giving us information about the core: chemistry and physical conditions. column density ratios can give an indication of the ionisation fraction, but predicted line profiles will be even more useful. gas-grain interaction is key: freeze-out causes these high ratios, and surface chemistry plus desorption may be important for others (CH3OH, D2CO).

Acknowledgements: Co-workers: Funding: T.J. Millar (Queens University Belfast) Eric Herbst (Ohio State University) Funding: PPARC