Lecture 9
Interstellar molecules
• Destruction of H2
• Formation of H2
• Gas phase formation
• Formation on grain surfaces
• Chemistry in diffuse clouds
• Ex.: Formation of OH
• The equilibrium abundance of H in molecular clouds
• The formation and destruction of CO in molecular clouds
Destruction of H2
• H2 molecules can be destroyed via:
• Collisions. Requires T > 4000K. Collisions with HI → H2 excited to unbound v > 13
vibrational states.
• Photoionisation:
• H2 + hν(15.5eV) → H2+ + e-
(hν > 15.5eV (λ < 804Å) regime)
• Photodissociation (by UV photons)
• Direct photodissociation:
• H2 (X1Σg+) + hν(14.7eV) → H + H
(hν > 14.7eV (λ < 850Å) regime)
• HI ionisation (hν > 13.6eV) has much higher cross section
Example
ofhas
scattering
also
larger cross section
• H2 photoionisation (hν > 15.5eV, see above)
• Thus, direct photodissociation can occur but is very rare
Destruction of H2
• Indirect photodissociation:
• 2-step process. Also called Solomon
process
• 1) Absorption of UV photons by ground
state (X1Σg+) → two possible electronic
excited states (Lyman and Werner bands
of H2). Only hν = 11-13eV allowed.
• 2) …followed by radiative de-excitation
into electronic ground state (X1Σg+)
‘vibrational continuum’ with v > 13 →
molecule dissociates into H + H (in
12% of cases)
Dominant mechanism for H2 destruction
Example of scattering
Formation of H2: gas-phase formation
• In principle there are three primary ways that H2 can form in the gas-phase:
• 1) Radiative association:
• 2) Three body reaction:
Ignore 1) since: when two free H atoms, both in the ground electronic state, approach each other, by
symmetry there is no electric dipole moment → no electric dipole radiation to remove excess energy
and leave the two H atoms in a bound state. Only ‘forbidden’ electric quadrupole transitions (small
A Einstein coefficients) → the molecule is more likely to dissociate before it relaxes.
Example of scattering
Ignore 2) since: the rate for this three-body reaction is negligible at typical ISM (and IGM) densities.
Although, at the high densities in proto-planetary disk (or proto-star) H2 is able to form via this
reaction.
Formation of H2: gas-phase formation
• 3) Radiative association + associative detachment:
reaction rates
, slow:
, faster:
(exothermic ion-molecule reaction)
• Formation rate of H2 ∝ n(H-)
• n(H-) tends to be low in diffuse regions since rad. assoc.
is slow and assoc. det. is fast (see above). Also, H- is
destroyed via reactions with p+, positive ions or by photo
detachment:
must compete with Hdestroying reactions
Example
of scattering
,
,
,
Formation of H2: grain catalysis
• Grain-Surface Catalysis:
• H atom collides with dust grain:
• ‘Stickyness’-factor (Tgrain-dependent)
• H-atom random walk on grain surface until:
• Chemisorption (valence forces)
• Physisorption (van der Waals forces)
• Encounter with another H-atom
• H2 forms and 4.5eV of binding energy is released:
• Heating of the dust grain
Example of scattering
• Breaking the ‘Activation barrier’ and ejecting the newly formed H2 (desorption)
• Internal vibrational energy (excited ground states), subsequently radiated away as rot-vib
emission lines
• The dominant H2 formation process in our Milky Way and in other galaxies.
Formation of H2: grain catalysis
• The rate of dust-catalysed H2 formation is:
Stickyness-factor: fraction
of grain-colliding H atoms
that depart from grain as H2
Factor of 2 is because
two H atoms are
required to form H2
• Remember that the quantity πa2Qextngr is related to extinction (Lecture 6), and if we assume Qext=1,
and typical ISM grain parameters, then πa2Qextngr =3×10-23n [m-1], where n = nH + 2n(H2). And
for a typical gas temperature of 100K, we get:
• When comparing this formation rate with the destruction
rates, of
onescattering
finds that εgr ~ 0.1 - 1. So H2
Example
formation on grains has to be very efficient (nearly all H atoms hitting grains end up in H2).
• Average ISM V-band extinction is 1.6mag per kpc. This means that for a path length of l = 1kpc =
3×1019m and an average ISM H number density of 106m-3, the optical depth is: τ~2. Remember
that τ = πa2Qextngr l ( which in this case ~2 ). For Qext~1 this gives πa2ngr ~ n × 0.3×10-19m-1.
Formation of H2: grain catalysis
• The rate of dust-catalysed H2 formation (accounting for H velocity and grain size distribution) is:
• The effective rate coefficient (which depends on Tk and Tgr and the sticky-factor) is:
• Consider the total grain surface area per H nucleon:
• Then the sticky-factor averaged over the grain surface area is:
Example of scattering
• Then we can write the effective rate coefficient as:
Formation of H2: grain catalysis
• FUV spectroscopy (in Lyman-Werner bands) of diffuse clouds (with Tk ~ 70K) along the line of
sight towards nearby stars find Rgr ~ 1-3×10-17cm3s-1, consistent with the above. This also implies a
sticky fraction of <εgr> ~ 0.06-0.08.
• However, from the H2 destruction we require high εgr (~0.1-1). This discrepancy is likely due to a
very low εgr for small grains/PAHs but εgr > 0.5 for large grains (0.01µm).
• While small grains have most of the grain surface area, they are expected to be less efficient as H2
formation sites. Most H2 formation takes place on larger grains.
• This is not surprising, as H-grain collision time-scales are much larger for small grains:
Example of scattering
• tHI ~ photon absorption time-scale.
• H2 formation on small grains is also suppressed by stochastic heating of small grains (large
variations on T → ejection of one or both H atoms before before H2 is formed).
Formation of H2: grain catalysis
• The time-scale for H2 formation on dust grains is:
• Typical interstellar clouds: n ~ 104cm-3 → possible to convert most of the HI into H2 in as little as
105yrs.
• Interstellar shocks: denser and warmer gas → more rapid H2 formation (provided the shocks do not
destroy the grains or the newly formed molecules).
• Evidence that H2 forms on grains:
Example
of scattering
• Ejected H2 are kinematically and internally (ro-vib)
excited
• H2 molecules heat the gas through collisions
• More high-J H2 observed than expected for ~80K gas (H2 is formed in high-J state)
• H2 absorption in v=3 is seen (weakly) in HST UV spectra
H2 formation on dust grains populates high v-states
Chemistry in diffuse clouds
• Diffuse clouds are pervaded by interstellar UV light → many molecules are photodissociated, even
for hν < 13.6eV. For example:
• Ex.: what’s the lifetime of a molecule in the diffuse ISM ~10pc from B star and exposed to a
typical UV flux of ~1010 photons m-3s-1nm-1?
• Assume photodissociation cross section of ~10-21m2
• So the loss rate of the molecule due to photodissociation (adopting a 10nm bandwidth) is:
• ~1010m-3s-1nm-1×10-21m2×10nm ~ 10-10s-1
• And so the lifetime of the molecule is: ~300yrs
Example of scattering
• Most molecules are destroyed on this time-scale → must be replaced by chemical reactions
• Shielding by dusty can lengthen the life-time of molecules by a factor of exp(-τ)
• Examples of molecules observed in diffuse clouds: H2, CH, CH+, OH, CN, CO, NH, SH, HCO+
Chemistry in diffuse clouds
• Ex.: what is the abundance of OH in a diffuse cloud with n(H2) = 108m-3?
• Assume a photodissociation rate of OH of βOH = 10-10s-1:
• Assume every CR ionisation of H2 leads to the formation of one OH molecule through:
• Then in equilibrium:
Example of scattering
By measuring nOH/nH2 we
can determine ζ in diffuse
clouds. Such observations
give ζ ~ 10-17s-1.
Equilibrium abundance of H in molecular clouds
• The four reactions governing the H abundance in molecular clouds
• In equilibrium:
(A)
Example of scattering
(B)
(C)
Equilibrium abundance of H in molecular clouds
• From (B) and (C):
(D)
• Substituting (D) into (A), we get:
Since n ~ 2nH2 in all
Example of scatteringmolecular clouds. Also
assumed ζ = 10-17s-1.
• For a molecular cloud with nH2 ~ 103-104cm-3:
So nH is almost independent
go nH2. Instead it is largely set
by ζ, the CR ionisation rate
Formation and destruction of CO in molecular clouds
• CO is the most abundant molecule after H2 in molecular clouds.
• Main formation reactions
• From H2+:
• From H2+:
(slow)
Example of scattering
Formation and destruction of CO in molecular clouds
• The formation reactions are balanced by destruction reactions
• Main destruction reactions:
Note the prominence of
HCO+ in these reactions.
HCO+ is an abundant
species.
where He+ comes from CR ionisation of He.
• Also CO photo-dissociation by UV photons (but only in less shielded diffuse cloud regions).
Example of scattering