Dark Cloud Modeling of the Abundance Ratio of Ortho-to-Para Cyclic C 3 H 2 In Hee Park & Eric Herbst The Ohio State University Yusuke Morisawa & Takamasa Momose Kyoto University

Dark Clouds Low Temperature (10 K) High Density (10 4 cm -3 ) Rich in Chemistry Birth place of stars Gas(H 2 ) + Dust Ion-molecule reaction induced by cosmic-ray Inhomogeneity (Cores) Lifetime ~ yr

Characteristics of C 3 H 2 C CC HH CCC H H c-C 3 H 2 l-C 3 H 2 Widely distributed organic ring molecule in the ISM Large dipole moment  well detected! n(C 3 H 2 )/ n(H 2 ) = Cyclic / linear isomers  info on physical conditions Ortho/para isomers  correlation with evolution

o/p Abundance Ratio (analogy with H 2 ) Energy released during the formation of ortho and para-H 2 n(o-H 2 ) = (2J+1) 3 exp(-E/T) / Q n(p-H 2 ) = (2J+1) 1 exp(-E/T) / Q Formation energy » ∆ E (o ↔ p interconversion) p-H 2 + H + ↔ o-H 2 + H K (0.015 eV) cf) Bond energy of H 2 = K (4.48 eV) Statistical o/p-ratio of 3 at high temperatures (T  ∞) n(o-H 2 )/n(p-H 2 )= 3 Deviation from 3 at low temperatures (T = 10 K) n(o-H 2 )/n(p-H 2 )= 9 exp(-170.5/T) at LTE at 10 K n(o-H 2 )/n(p-H 2 ) = 3.5 x 10 -7

o/p Ratio as a Function of Temperature (LTE) Ortho-to-para abundance ratio at LTE ~ 9 exp(-∆ E / 10 K) ∆ E(p-H 2 ↔ o-H 2 ) ∆ E(p-H 2 CO ↔ o-H 2 CO) ∆ E(p-C 3 H 2 ↔ o-C 3 H 2 ) ~ 170 K ~ 15 K ~ 9 K 1e o/p-H2o/p-H2CO o/p-C3H2 at 10 K

TMC-1 Ridge Well-studied dense regions of TMC-1 cores Inhomogeneous characteristics in variations of –physical (temperature, density…) –chemical (molecular abundance) Hanawa et al. ApJ, 420, 318 (1994)

o/p-C 3 H 2 Observations for Cores in TMC-1 TMC-1A ( ) TMC-1B ( ) TMC-1C ( ) TMC-1CP ( ) TMC-1D ( ) TMC-1E ( ) (1950) NH 3 -Peak NW SE (1950) CP-Peak Morisawa et al. ApJ, in prep (2005)

+ HX + 67% + e 100% + C 3 H + 67% o-C 3 H 2 p-C 3 H 2 33% 100% 50% 33% 100% + Y + Z + + e products | C 3 H + H | C 2 H 2 + CH | o-H 2 p-H 2 + e | C 3 H + H | C 2 H 2 + CH | p-C 3 H 3 + o-C 3 H 3 + Branching Ratios o-C 3 H 3 + p-C 3 H 3 +

o-C 3 H 2 + HX +  o-C 3 H 3 + : p-C 3 H 3 + I 1 = 1 I 2 =1/2 I= 3/2 I=1/2 D 1 x D 1/2 = D 3/2 + D 1/2 (2I + 1 = 4 ) : (2I + 1 = 2 ) 67% 33% p-C 3 H 2 + HX +  o-C 3 H 3 + : p-C 3 H 3 + I 1 = 1/2 I 2 =1/2 I= 3/2 I=1/2 D 1/2 x D 1/2 = D 1 + D 1/2 0% 100% Ortho, Para Conversion Branching Ratio

Description of models Model Parameter 1 C/O ratio 2 Metal depletion 3 Cosmic-ray ionization 4 Gas-density 5 Branching ratio 6 Combine above o-C 3 H 3 + e HX C, O, | S, Si product e C 3 H + H 2 o-C 3 H 2 p-C 3 H 2 C + | S +, Si + product 12 C 3 H + + p-H 2 p-C 3 H 3 + Ortho-para C 3 H 2 models

Initial Conditions & Variations Low-Metallic elemental abundance condition : C, O, N, H 2, and Metals (S, Si, Fe, Mg, Na, P, Cl) Cosmic-ray ionization rate = 1.3 x s -1 Gas-density = 10 4 cm -3 Equivalent branching ratio C 3 H e  C 3 H 2 + H 50%  C 3 H + H 2 50% Temperature = 10 K [1] Depletion of initial abundance of C and/or O by factors of 2 [2] Depletion of initial elemental metal abundances by orders of 2 [3] Cosmic-ray ionization rate < 1.3 x s -1 < [4] 10 3 < n H =10 4 cm -3 < 10 6 [5] 50:50 < C 3 H 2 : C 3 H < 100:0

Minor Parameters [model 1-4] Highest o/p-ratio with minor parameters   C/O ratio < 0.2  Metal depletion by 2 orders of mag. than LM  Density < 10 5 cm -3  Zeta = 1.3 x s -1 Observations A B E C D CP

Branching Ratios [model 5] Highest o/p-ratio with major parameter   Extreme branching ratio of C 3 H e  C 3 H 2 : C 3 H  C 3 H 2 neutral channel should be dominant! Observations A B E C CP D Models 1-4 Model Model Model Model

Combined Models [model 6] Highest o/p-ratio   Can be enhance only up to 2.1 Observations A B E C CP D Models 1-5 Model Model Model Model Model

Summary of Model Results TMC-1 o/p-C 3 H 2 Comparison A B E C CP D Cannot reproduce The large o/p-C3H2 ratio more or less 3 Less evolved  More evolved o/p-C 3 H 2 : 3 C/O ratio : 0.4  0.2 Metal abund. : LM  2 order less than LM Standard cosmic-ray ionization rate Density : 10 4 cm -3  10 5 cm -3 Branching ratio two channels C 3 H 2 : C 3 H: 50%:50%  100%:0% Time : 10 5 yr  10 6 yr (steady-state) MORE EVOLVED LESS EVOLVED

Conclusion o/p-C 3 H 2 is a probe of degree of evolution of dense cloud cores Variations of parameters and those effect on the ratio are consistent with gradient of physical conditions of TMC-1 ridge Lower abundance of C 3 H by an order of magnitude than C 3 H 2 might support the dominant branching ratio of C 3 H 2 over C 3 H Still need to reproduce the more evolved cores Similar modeling attempt for the o, p-molecules (e.g. H 2 CO, H 2 ) would be helpful to confirm the spin conversion branching fraction