The implications of the 10 micron polarization of the Orion Nebula were re-examined. The polarization was produced by preferential extinction in one of the well studied regions of the Kleinman-Low Nebula and/or its surroundings. In particular, the need for abnormally low temperatures in the polarizing medium was obviated. The most likely candidate for the polarizing medium was the extended region surrounding the Kleinman-Low Nebula. The degree of polarization produced by emission in the far infrared was estimated to be as large as 8 percent, although other factors could reduce the observable value

Dennison, B.

English

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jN6rP• ^3 •D/4•/^/4
ON THE INFRARED POLARIZATION
OF THE ORION NEBULA*
(NASA-CR-149366) ON THE INFRARED N77-14963
POLARIZATION OF THE ORION WEBULA (Virginia
Polytechnic Inst. and State Univ.) 	 16 p HC
A02/.MF A01 CSCL 03A Unclas
G3/89	 583.50
Brian Dennison
Department of Physics
" Virginia Polytechnic Institute
f*
and State University
ikR'GA	('
Blacksburg, Virginia
3+24061
Portiors of this work were completed at Cornell University, Ithaca,
New Yoik, and are contained in the author's Ph.D. dissertation.
7( Q^ASA... BRAN
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•	 47
A ,
ABSTRACT
i
i
The implications of the 10 micron polarization of the Orion Nebula
are re-examined, and it is concluded that the polarization is produced
by preferential extinction in one of the well studied regions of the
Kleinman-Low Nebula and/or its surroundings. In particular, the need
for abnormally low temperatures (-,6°K) in the polarizing medium is ob-
viated. The most likely candidate for the polarizing medium is the
extended region surrounding the Kleinman-Low Nebula.
The degree of polarization produced by emission in the far infrared
(-,100 microns) is estimated to be as large as 8 percent, although other
factors could reduce the observable value.
d
f
s
3I. INTRODUCTION
Recent observations have uncovered significant linear polarization
in the 3-13 micron radiation from the Orion Nebula (Dyck, et al., 1913;
Dyck and Beichman, 1974). The observations of Dyck and Beichman (DB)
were made throughout the KleinmanT -)w Nebula (KL), including observations
centered on the Becklin-Neugebauer object (BN). KL is known to consist
of a number of compact objects, and a diffuse component (Rieke, et al.,
1973). The observed polarization direction is roughly uniform over the
angular extent of the observations	 The degree of linear polariza-
tion is correlated with the 10 micron silicate absorption feature, reach-
ing as much as 15 percent in the band. Over the observed wavelength
range the polarization direction does not appear to change significantly.
These features led DB to propose that this polarization is caused by pre-
ferential extinction by aligned dust particles. At these wavelengths the
cooler absorbing medium does not radiate appreciably.
Application of the theory of grain alignment by paramagnetic relaxa-
tion (Davis and Greenstein, 1951; Jones and Spitzer, 1967; Cugnon, 1971;
"and Purcell and Spitzer, 1971) yielded grain temperatures ,,6°K (DB). In
§II this is re-examined under the probable assumption that the i0 micron
optical depth to BN is larger than that used by DB (Aitken.and Jones,	 i
1973; and Gillett, et al., 1975).
The 1.0 micron polarization has led to some observational interest
regarding the polarization of the Orion Nebula at much longer wavelengths
(ti100 microns). Upper limits have been reported (Dennison, et al., 1977)
	
s
based upon observations carried out with the NASA Lear Jet 30-cm telescope.
i
,i
4More detailed investigations involving larger apertures are in progress
(Harwit, 1976). In §III the far infrared polarization is estimated, based
upon the conclusions obtained in §II.
II. THE POLARIZING MEDIUM
DB employ a picket fence model to represent the absorbing medium
with f = fraction of totally aligned grains, G = geometrical cross sec-
tion of a grain, N = number density of grains, and L = path length in
the medium. The optical depth in the two fundamental perpendicular di-
rections x and y is
Tx'y = 7[(l+f)Q jl ^ l + (1-f )Q, 11]GNL
where Q,, ,
-
,
-
 are the grain extinction efficiencies parallel and perpen-
dicular to the symmetry axis. Some simplification results if we defii.e
T E 2( Tx+Ty ) and AT E T X-Ty . Then
T = 2 {Q I 1+90GNL and AT = f(Q, I -Q1)GNL	 (la,b)
The polarization produced by absorption is
-T -T
x	 y
P = 
e	 e	
-tanh (AT) 
•	 (2)
a	 -T	 -T	 2
e x+e y
By convention P is negative indicating polarization by absorption. DB
a
were able to fit their data with a model involving prolate spheroids with
an axis ratio of til/5, and f = 1/4. This involved the assumption that the
or)tical depth to BN in the silicate absorption feature is T10u = 1.4.
However, Aitken and Jones (1973) and Gillett et al. (1975) favor inter-
pretations of the absorption spectra which give T1011 = 3.3. The degree of
polarization at 10 microns fixes the value of AT lop (Equation 2). From
REPR,C)DUCIBILITY UF THE
R a^I^^Ia PA.C'E is PO4R
. 'i
3
5Equations (la,b) we see that assuming T10u = 3.3 implies f = 1/10, pro-
vided that we do not alter the shape of the grains.
DB argue in favor of paramagnetic relaxation (Davis and Greenstein,
1951) as the grain alignment mechanism. For this mechanism to be effec-
tive the timescale for magnetic damping of the grains' angular momentum,
TB , must be shorter than the timescale for randomizing of the angular
momentum by collisions with the gas, T gas , i.e., T 
gas 
/TB = 6 > 1 (DB;
Jones and Spitzer, 1967; Cugnon, 1971; and Purcell and Spitzer, 1971).
DB show that the parameter 6 can be related to f through the polarization
reduction factor, R, (Greenberg, 1968) which is twice the fractional align-
ment, £. Greenberg (1968) gives R(C), where
2 - 1+6(T dust /T gas )
1+6
and 
Tdust is the dust temperature, and Tgas is the gas temperature. .
Alignment can occur only if the gas anddust temperatures are somewhat
different. If Tdust < T gas' then 0<E<l; and since alignment requires
6>1, then Tdust < ^ 2T gas ' For f = 1/4 DB show that E 2 = 0.084. For the
70°K average gas temperatures th,Lt are thought to exist in KL, this im-
plies that Tdust S 6°K. As they point out this is at least several degrees
.cooler than tre lowest temperatures that can be expected in the densest
clouds (Greenberg, 1971). Since the dust in and around KL is known to be
substantially hotter than this from its far infrared emission (Forrest
et al., 1976; Houck et-al., 1974;,Ward.et al., 1976; a-id Werner et al.,
1976), DB argue that the polarizing medium lies in front of this region.
_However, it is likely that at this distance from the center of KL the
gas is even cooler than 70°K, thus restricting further the value of
Tdust' Also, a major fraction of the optical 'depth to BN must be in this
{
6polarizing medium, rather than KL and the surrounding warm dust. However,
Forrest et al. (1976) found that the optical depth to the center of KL is
unity at ti28 microns. When scaled to 10 microns this gives roughly the
10 micron optical depth to BN proposed by Aitken and Jones (1973) and Gil-
lett et al. (1975) (Forrest, 1976), using Lunar silicate 12065 as a model
(Perry et al., 1972). This is consistent with BN being located near the
center of KL, and tends to confirm that T lop = 3.3, with virtually all of
this optical depth attributable to KL, and its surroundings.
We now examine the consequences of this. As was shown, we now have
f ,= 1/10, then R = 2/10, and from Greenberg (1968) 0.4 s E 2 S 0.5. This
then allows a much more reasonable dust temperature. For example, if Tgas
70°K, then Tdust < 35°K,. The magnetic field required to produce alignment,
B, varies as Tdust Tgas 61/2. For Tdust
	
5°K and 6 = 73, DB find that B=7
milligauss for a reasonable choice of grain parameters. Although the larger
upper limit on 
Tdust proposed here leads to a v2.5 increase in the field
strength for the same value of 6, B need not be larger since 6 is by no means
fixed. In fact, the larger limit on 
Tdust may even make plausible somewhat
weaker magnetic fields since smaller valuits of 6 can be obtained without de-
pressing 
Tdust to abnormally low temperatures.
It is also possible that reverse alignment could occur if T dust >Tgas
Jones and Spitzer (1967) use an alignment parameter, F, (different from f),
for which
F -	
q(E2-1)q(Y-1)
where Y is a shape dependent factor and q(x) is given by these authors. Ob-
servations of the degree of polarization and specification of the extinction
efficiencies of the grains, and the optical depth fixes the magnitude of F
i
7(Capps and Knacke, 1976). Thus, the magnitude but not the sign of q(^2-1)
is fixed. From Jones and Spitzer (1967) q(--!)=.096, which assumes normal
alignment. From their tabulation we have q(1.2) = -.096, corresponding to
reverse alignment. This gives C 2=2.2 or 3.4 Tgas > Tdust > 2.2 Tgas' for
6 > 1. For reverse alignment the field would have to be at least ti2.1 times
greater than that for normal alignment for a fixed value of 6.
To possibly choose between normal and reverse alignment we consider
several other factors. The possibly slightly stronger magnetic field re-
quired for reverse alignment does not necessarily vitiate this possibility.
The gas temperature of 70°K is an average value for a 1' region centered on
KL. Within the central 1/2' of this region n H >106 cm 3 , and the gas and
2
dust should be coupled so that Tdust gas=T
	 (Zuckerman and Palmer, 1975;
Goldreich and Kwan, 1974 a, b). Indeed, far infrared spectral observations
give 70°K < Tdust < 100°K (Forrest et al., 1976; Ward et al., 1976; Werner
et al., 1976; Houck et al., 1974). Extending outwards from the center of
KL, the dust temperature is expected to decline slowly, with Tdust 
°C 
r-0.4'
and this appears to be confirmed (Werner et al., 1976; Forrest et al., 1975).
The dust density gradients around KL are quite steep, perhaps varying as
r-1.5 or r-2 (Westerbrook et al., 1976). For constant dust to gas mass racia,
-the gas density also declines rapidly with radius, and the gas should quickly
decouple from the dust, such that 
T
gzs < Tdust. Apparently we may have nH
2
=2x104
 cm 3 in this extended region (Zuckerman and Palmer, 1975). In this
case the condition, 
Tdust ^ 2.2 Tgas' may be satisfied (Goldreich and Kwan,
1974a), thus allowing reverse alignment in this extended region.
To polarize effectively, this region must possess a significant frac-
tion of the optical depth to BN. Very far infrared map, at wavelengths at
which the nebula is optically thin may provide some indication. Although the
data of Westerbrook et al., (1976) have an angular resolution n l'", it appears
that this extended region may have sufficient optical depth.
.
r,
HNormal alignment of the grains is a possibility that cannot be com-
pletely ruled out yet. However, the requirement that T 	 T	 isdust	 2 gas 
not consistent with the theoretical picture presented here. Normal
alignment may occur well within KL where existing observations do not
possess adequate resolution (<l') to rule out large values of T 	 31 orgas
lar€- optical depths.
In this section we have shown that the 10 micron polarization can
be accounted for in a much more plausible way, which is consistent with
what is known about the Orion Nebula. The most likely candidate for the
polarizing medium appears to be the extended region surrounding KL, which
is reverse aligned. No recourse to unseen, abnormally cold regions is
needed. The similarity of these conclusions to a discussion on somewhat
different grounds by Zuckerman and Palmer (1975) is noted.
Finally it is important to mention the possibility of other align-
ment mechanisms being operative. Of particular interest is superpara-
magnetism (Jones and Spitzer, 1967) which requires considerably smaller
magnetic fields to produce the alignment discussed in this section.
III. FAR INFRARED POLARIZATION
•
	
	
Since the polarizing medium has been tentatively identified with the
regions surrounding KL, it is appropriate to estimate the degree of
polarization seen in emission at longer wavelengths. The polarization by
emission is
a
P _ 
(he Tx) -Ty) - sinh(.ZT)	 (3)
e	
(1-e x ) + (1-e y)
y)	
eT-cosh(ZT)
By definition Z . T < T. Pe is positive indicating a 90° rotation with re
spect to 'the absorption , polarization AT can 'be related to T through equa-
Fk
t
• 9
tions (la) and (lb) giving
Q1 -L .	 (4)2T = T f Q
11	 Q L
For the j th axis of an ellipsoidal grain it can be shown that (van de
Hulst,	 1957)
QJ	
-	 X	 [(L.(e'-
3
1)+l)2 + (L a.11)2
J	 J
. where
e'+ie" = m2
m = complex refractive index
i
L. = shape factor for the jth axis.
J
r
For the prolate spheroids used by DB L 1 	0.056 and L 2=L3	0.472 (van de
Hulst, 1957).	 The lunar dust studies	 (Perry et al., 1972) suggest that at
long wavelengths (a k 40 microns) the optical constants may take on the
simple behavior:	 e' = constant between 4 and 7, e" = 501	 Taking
f = 10 , we obtain AT = .06 T for e' = 4, and 2T = .08 T for e' = 7.	 The
f
optical depth in Equation (3) corresponds to a substantial fraction of the
" depth of the source, and the results of Forrest,et al.,	 (1976) suggest
that T(40u) = 1.	 For Q - X-2 ' .the resulting polarization is given in
Figure 1 for e' = 4 and e' = 7. 	 Several features of the curves can be
i
` readily understood. 	 For short wavelengths the source is becoming onticall)
I
thick and the polarization decreases.	 At long wavelengths, T-*O, and in
this limit we have
OT/2
P e =	
T	
,
-^
neglecting terms of order T	 or high-, r.	 For the more optimistic case (e'=>)
F,
g
f
_
s
_
rf
l10
we have Pe=.08 in the long wavelength limit. These estimates are subject
to depth effects and beam size effects. If the source is optically thin
at long wavelengths, then grain alignment must be maintained through the
entire depth of the source, not just down to the hot 10 micron source
seen by DB. The long wavelength source would appear more extended than
the 1/2' studied by DB, and over a larger angular size cancellation ef-
fects may occur.
As was pointed out, the polarization by emission is orthogonal to the
10 micron absorption polarization. However, the latter was observed only
over the central 1/2' of the region. For far infrared observations in-
volving larger beam areas and small optical depths, the emission polari-
zation arises in a more extended region in which the grain alignment may
vary. Therefore, the observed emission polarization may not bear such a
simple relationship (as orthogonality) to the absorption polarization.
As discussed in III the core of KL may not be aligned, and thus the
radiation emitted from this region is largely unpolarized. When seen
through the surrounding cloud of aligned, grains, the core will appear
polarized by absorption. This may tend to cancell the polarization by
emission along the same line of sight, because of the core's greater volume
• emissivity due to its higher density, and slightly higher temperature.. The
degree of polarization by absorption can be estimated from Equation (2). As
we have seen 2T	 (0.7+0.1)T. From Forrest et al., (1976) the optical depth
to the core is T = ( 2 Xu ) 2 , assuming Q-X 2 . This gives 
Pa core= ( )2 for
a>30 microns. Thus, at long wavelengths, polarization by absorption is ex-
pected to be small. Along a ray passing through the core of KL, the total
observed polarization will be small, since in this direction the flux is
dominated-by the denser unaligned central region. This dilution, when
averaged over the entire source, should not be too severe, since about 31)
percent of the total far infrared flux comes from the central l' of the
source (Werner et al., 1976).
The alternative discussed in §II, normal alignment in the core of KL,
could also yield far infrared polarization. In this case the polarization
would be confined to the core region, and would be of similar magnitude to
that predicted by Equation (3). Depending upon the beam size, the outer
regions of KL may dilute the polarized signal.
A first attempt (Dennison et al., 1977) did not detect polarization
at 85 microns. The beam size used was r-6', and the cancellation and di-
lution effects discussed above, may have reduced the polarization averaged
over the beam. Higher resolution studies may prove to be more definitive
(Harwit, 1976).
V
IV. CONCLUSIONS
The medium producing the infrared polarization of the Orion Nebula is
tentatively identified with the extended regions surrounding KL. This
identification permits dust temperatures which are consistent with both
theoretical expectations and observations.
The extended regions of KL may emit polarized radiation in the far
-infrared (ti100 microns). In the absence of cancellation and dilution ef-
fects, up to r-8 percent polarization is estimated.
Determining the lccation of the polarizing medium is important, since
this also applies to the derived magnetic fields. L.Dcalizing the estimated
magnetic fields is necessary for making comparisons co magnetic fields de-
rived by other means, which are applicable to distinct regions (Zuckerman
and Palmer, 1975), and for understanding the physics of regions of star
	 a
s
formation.
_a
i
1•	 12	 1
a
This work has been primarily supported by NASA vontract NGR 33-010-346.
I thank my thesis advisor, Dr. M. Harwit, and Drs. W. Forrest, B. Turner,
	
and D. Ward for valuable discussions. 	 1
r
13
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Telesco, C. M., and Throi
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M. G., Lo, K. Y., and Ne
BRIAN DENNISON: Department o
State University, Blacksburg,
•
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s
15
FIGURE CAPTION
Figure 1 - Theoretical polarization of aligned region in Orion. Solid
curve corresponds to c' = 4, and dashed curve to e' = 7.
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On the infrared polarization of the Orion Nebula

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