An algorithm for the random walk problem of multiple elastic collisions between newly formed non-thermal neutral cometary radicals and the outflowing cometary molecules was incorporated into the Monte Carlo particle-trajectory model. Preliminary model analysis has shown that the effects of collision on the observed spatial distribution of cometary radicals becomes important for the larger bright comets, especially at smaller values of the helicocentric distance. The model and early results are discussed herein

Combi, M. R.

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(1IS1-CH-175485) CCBZTIRT ITBOSPRERES:
DUELING ISE SPITIIL DIS22IBOTI01 OF
OBSERVED 1EOTBII 11DICILS Interim Report,
Dec. 1984 - Feb. 1965 (Itsoapheric and
Environmental BesEarch) 8 F BC 102/!!l 101
M85-21098
Onclar
t^91 15185
Cometary Atmospheres:
Modeling the Spatial Distribution of Observed Neutral Radicals
Michael R. Combi
Atmospheric and Environmental Research, Inc.
840 Memorial Drive
Cambridge, MA 02139
February 1985
Interim Report for the Period
December 1, 1984 to February 28, 1985
Prepared for
NASA Headquarters
IN
IECNNICAL REPORT STANDARD TITLE PAGE
1. Report Me. 2. Govetnment Accession Pie. 3. Recipient's Catalog Me.
4. Toile and	 lit a 5, Rtp*tt Dove
February 1985
Cometary Atmospheres:	 Modeling the ;aatial
6. Perlorming O.gonisetion CedeDistribution of Observed Neutral Radicals
7. Auther(a) S. Perforating Oryeniletion Report No.
Michael R. Combi
9. Performing Orgenisetren Home and Address 10. Wer4 Unit No.
Atmospheric and Environmental Research, Inc.
It. Contract er Grant Me.
NASW-3950840 Memorial Drive
Cambridge, MA	 02139
13. Tree of Report and Period Covered
Interim Report12. Sponsoring Agency Name and Address
NASA Headquarters December 1984-Fehnkary1985
Headquarters Contract Division 14. sponsoring Agency Cede
Washington, DC	 20546
1S. Supplementary Notes
16. A►stract
An algorithm for the random walk problem of multiple elastic
collisions	 between	 newly	 formed	 nor..-thermal	 neutral	 cometary
radicals	 and	 the	 outflowing	 cometary	 molecules	 has	 been
incorporated	 into
	
the	 Monte	 Carlo	 particle-trajectory	 model.
Preliminary model analysis has shown that the effects of collision
on the observed spatial distribution of cometary radicals becomes
important	 for	 the	 larger	 bright	 comets,	 especially	 at	 smaller
values of the heliocentric distance.	 The model and early results
are discussed herein.
17. Key words (Selected toy Author(s)) 18. Distribution .' - emant
comets
19. Security Classlf. (of this report) 20. Security Clessif. (of this page) 21. No. of Peges 22. Price•
Unclassified Unclassified 7
*For sale by the tararialthatrse for Frdrrsl %cientific end Technical Information, Sftrinitheld, Virginia 22151.
i
Program of Research in the Third Quarter
During this past quarter, research activities have concentrated on
development of the algorithm for including collisions in the Monte Carlo
particle -trajectory model.
Multiple Collisions in Cometary Atmospheres
Models of neutral cometary comae have generally dealt with the two 	 t
extreme cases: one where the densities are high enough so that all neutral
species are thermalized and are characterized by a bulk radial flow away from
the nucleus, and the other where the densities are so low that essentially no
collisions occur. A characteristic distance from the nucleus separating these
two regions has been defined where the mean free path for a collision is equal
to the distance from the nucleus. Whipple and Huebner (1976), for example,
express this collision radius as
r c 	 4wv	 f
where	 Q = molecular production rate	 r
a = cross-section for elastic scattering -10 -15 cm2
v = molecular outflow velocity.
The value of rc
 varies from -104 km for a bright comet like Kohoutek near
perihelion, down to -10 2 km for a small short period comet like PJEncke at
1 AU.
In reality, though, there is no clear separation between the two zones.
In order for a typical radical (CN, C 21 OH) which has been emitted from its
parent with some exothermic velocity to be truly thermalize3, it needs on Lhe
order of 10 collisions with outflowing water molecules. On the other hand,
many radicals produced outside of r c will be subjected to at least 1 to 5
collisions, thus questioning the true applicability of a free flow model.
What we truly have, then, is a large regime on the order of 0.2 r c to 5 r.
where partial thermalization will occur.
The true random walk nature of the elastic scattering problem is modeled
in a straightforward manner in the Monte Carlo particle-trajectory model
(MCPTM). Kitamura et al. (1983) have included collisions in a Monte Carlo
^7
2
ate-
1* 1
model essentially based on our original model (Combi and Delsemme 1980a).
Since they followed the correct procedure, we have adopted a similar
algorithm. There is one problem with their procedure which involves the
expression they assume for the density of outflowing molecules with which the
modeled neutral radicals are colliding. They assume a Haser-like description
for the density which is
nH2O (r)	 exp(-r/vzH2O)
where	 Q, v are as above
r = distance from the nucleus
t H2
 0 ' photochemical lifetime for H2O.
Strictly speaking, this is the correct density distribution for H2O molecules,
but as the H 2O molecules dissociate, they produce OH and H, which still
provide targets with which radicals collide. Since the effective cross-
sectional area for the fragments is larger than the parent H2O but their
outflow velocity is, on the average, larger, a better approximation would be
to simply drop the exponential term in the density expression. This yields
nH2O(r) 44 .
For the simple case of no radiation pressure, this yields a closed form
algebraic expression for the collision length of an arbitrarily moving neutral
species, in place of the integral found by Kitamura et al.
The random walk algorithm begins with the production of a neutral radical
by its parent with a given velocity vector. From this location and velocity
vector, a collision length is given by assumed values for the collision cross
section, the molecular (H 20) production rate, and a random number. The
neutral is then displaced this distance, scattered elastically off a moving
water molecule and continued on for another collision. The trajectory
proceeds this way until the observation time snap-shot.
Preliminary model runs have been performed for the case of CN produced by
the photodissociation of HCN (Combi and Delsemme 1980b). We have chosen
parameters appropriate for the photochemical lifetimes at 1 AU and have
neglected radiation presuure, which is of less importance at 1 AU, for the
3
4i
r
purpose of simplifying the preliminary analysis. Subsequent models will test
both processes simultaneously. The physical parameters of the coma models are
listed in Table 1.
Models were run for cases of general molecular production rates from
1 x 1028 s-1 to 1 x 10 30 8-1 . The collision statistics from these model runs
are summarized in Table 2. As can be seen, for larger gas production rates,
only half of the CN radicals produced are in a true free—flow regime.
Furthermore, the effect collisions bave on the determination of radical
production rates is also evident in these model runs. For the case of the
largest gas production rate, if one neglects collisions in the model, an
underestimate of 11% to 15% in the determination of radical production rate
would be made, depending upon the size of the photometer aperture used. The
systematic error13, when reducing data for even smaller heliocentric distances
(rH — 0.5 AU), should be quite important in bright comets such as P/Halley,
since at these distances the collisional effects are compounded by larger gas
production rates and smaller radical parent scale lengths.
Program of Research for the Fourth Quarter
Research efforts in the last quarter will concentrate on (1) model
analysis of the effect of collisions on the spatial distributions of the
neutral radicals, (2) evaluation of newly published brightness profiles of
C2 (Cochran 1985), (3) incorporation cf time dependent production rates and 	
.-I
lifetimes into the model code, and (4) preliminary model runs for OH, C2
and C3.
References
Cochran, A. (1985) Astrophys. J. 289, 388.
Combi, M.R. and A.H. Delsemme (1980a) Astrophys. J. 237 9 633.
Combi, M.R. and A.H. Delsemme (1980b) Astrophys. J. 237, 641.
Kitamura, Y., 0. Ashihara and T. Yamamoto (1983) ISAS Research Note 153.
Whipple, F.L. and W.F. Huebner (1976) Ann. Rev. Astron. Astrophys. 14, 143.
It
.r
5
--laws
Table 1
CN Radical Coma Model Parameters
rH - IAU
T(HCN) - 9 x 104 s
T(CN) - 2.75 x 10 5 s
v(varent) - 0.58 km/s
ve (CN) - 1.02 km/s
cscattering - 1 x 10
15 cm-2
6
Table 2
Collision. Statistico fc^r the CN Model at 1 AU
Fraction of Radicals Undergoing n Collisions
0 1-2 3-5 6-10 >10
.723
.272
.0042
.0005
.0003
.705
.283
.0094
.0023
.0005
.681
.2)6
.0160
.0055
.0009
.653
.3.1
.0247
.0101
.0016
.576
.343
.0503
.0252
.0055
.503
.355
.0852
.0459
.0147
QH20	
n
1 x 10za
5 x 1028
1 x 1029
2 x 1029
5 x 1029
1 x 1030
I
7 b


Cometary atmospheres: Modeling the spatial distribution of observed neutral radicals

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