The spatial distribution of 11 micron radiation from omicron Ceti was observed at various phases of its light cycle using a stellar interferometer. Changes were seen which can be attributed to variation in the strength of thermal emission from circumstellar dust relative to the stellar continuum at 11 microns. These changes are shown to be correlated with the changes in luminosity of micron Ceti in such a way that dust grain emission at 11 microns was increased more than the continuum during the period of maximum luminosity. The degree of the change in dust grain emission implies that the maximum dust temperature is in the range of 500 K to 700 K during minimum stellar luminosity

Spears, D. L.

Storey, J. W. V.

Sutton, E. C.

Townes, C. H.

English

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1.
VARIATIONS IN THE SPATIAL DISTRIBUTION OF 11 MICRON
RADIATION FROM OMICRON CETI* boe,.
E.C. Sutton, J.W.V. Storey, and C.H.
	
Townes N H co
Department of Physics 3 0
En
University of California, Berkeley Ft
z° m IQ n
and 3031
3psLQ,t^ ^HnoD.L. Spears a ^
Lincoln Laboratory MAY 1978
a °°
kn
Massachusetts Institute of Technology
Lexington, Massachusetts ^[GEI\tE9 w ^
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-	 ABSTRACT `^GLl^15Y' z H
c ^f m
The spatial	 distribution of 11 micron radiation from o'Ceti has
been observed at various phases of its light cycle using a stellar
r.
H y
t ^ ^ oa.a .^{, v rn^+zs; ^. 1v	 ^.r3,u.^5'na1^7^.n'.vcxnc F^{:uu.u^y:3s7MSt-A'hp4FY.wPf^^,^..c3 :F^Sit?'t vn,^rcpw `rya 7 a^i TJLCY^
interferometer.	 Changes have been seen 'which can be attributed to r z
n w0+A W
` variation in the strength of thermal emission from circumstellar dust nm o ^—
li
relative to the stellar continuum at 11 microns.
	 These changes are W" N
shown to be cor:-elated with the changes in luminosity of o Ceti in Wi
s
such away that dust grain emission at ll microns was increased more to
than the continuum during the period of maximum luminosity. 	 The de-
z
o , gree of the change in dust grain emission implies that the 'maximum
C+ 0
r
com	
f
Ndust temperature is in the range of 500 K to 700 K during minimum
w
-.stellar luminosity.
: * This work was supported in ,part by the National Aeronautics and S-ice
s
Administration under grant N9L-0.5=003-V.?—and in part by the National
Science Foundation under grant AST 77-12256.
2.
9
I INTRODUCTION
Long-period variable stars commonly are surrounded by circumstellar
dust shells. Variations in, the luminosities of these stars will oreatly
change the radiative environment of the dust grains; thus it is expected
that variations will be seen in the thermal emission from these grains.
I	 Conventional techniques which might detect such variations include mea-
surements of broad-band infrared colors and also narrow-band spectro-
photometry in the 8-14p region. Forrest, Gillett, and Stein (1975) have
reported such measurements on o Ceti and several other long-period
variables. They found no evidence for large changes in the strength of
emission from circumstellar material.-" The work reported in this Letter
shows that there are changes in the dust grain emission which can be
I^
"	 seen using rather different techniques. These variations are consistent
with the limits set by Forrest,. Gillett, and Stein.
Interferometric techniques in the infrared may be use ld to determine
tJ	 directly the relative brightness of circumstellar emission with respect
to the stellar continuum and also the sizes of these regions of circum-
stellar emission (Sutton et al. 1977; McCarthy, Low, and Howell, 1977).
For this, waielengths near 11 microns are of particular importance due
to the spectral feature attributed to silicate grains. Spatial resolu-
tions of existing instruments at this wavelength are of the order of l°
which is an appropriate scale for examining many circumstellar dust
shells. ' It is thus possible to examine variations in thermal emission
from dust around-long-period variables in more detail than previous_
techniques have allowed.
iI OBSERVATIONS
The interferometer used in these observations makes use of the
/	
1	
r
i
4
3.
McMath auxiliary telescopes at Kitt Peak Nat i onal Observatory.** The
equipment and techniques used have been described by Sutton et al, (1977).
During these observations the sensitivities of the heterodyne receivers
were approximately 3 x 10-15 watts/ 3Hi for an infrared bandwidth of
0.1 cm 1 at 11.106p.
Observations were made of o Ceti from February 1977 through February
1978, which represents slightly more than one cycle of the visible
light curve. No observations were possible for several months before
and after May 1977 during which time o Ceti was in the daytime sky.
The overall instrumental calibration,'originally based on Tabora-
	
i
i
tory measurements, was verified by observing the star a Her which has
=:been_-seen to-ha ve--n-o
 s--i.gnifican-t till-i-ca-te =emi-ss?on=- I_M.rr111 .-w . ,^.d (Zte1S^-
I
1976). Thus a Her should behave as a point source since its diameter
is at least an order of magnitude smaller than 0.4°. which was the
finest lobe spacing used. Three observations were made yielding an
average fringe visibility of 0.95 ± 0.08. Since this result was con-
sistent with unit visibility, no further correction was applied to the
visibility scale. As a secondary standard, a Ori was observed with
maximum resolution within a few days of each observation of o Ceti.
The observations of a Ori were internally consistent.
Figure 1 presents the measured fringe visibilities for n Ceti.
The phase quoted is with respect to the visible li g ht curve with $ = 0
representing maximum light. Vote that Figure lc contains data from two
separate cycles but at nearly the same phase. Figure 2 shows a compar-
ison set of observations on a Ori which indicate the flatness of the
instrumental response.
** Operated by the Association of Universities for 'Research in Astrononw,
 ,
Inc., under contract with the National Science Foundation.
4.
!,I
j
III RESULTS
The observations have been fitted with a two-component model of
the brightness distribution in which one component is spatially unre-
solved and emits a fraction, f, of the flux at llp. The other compo-
nent, which contains the remainin g
 1-f of t1,e flux, was assumed to have
a Gaussian spatial distribution with a full-width to 1/e intensity
given by the parameter e 9 . The curves drawn in Figure 1 are the best
fits to the data using this model, and the values of f and e 9 used to
make these fits are listed in Table 1.
This two-component model was chosen because it was k9own that
s
there would be contributions to the llp flux both from the stellar
conti nuum
 and-from oust grain=emi»ion: Tile°diameter- of the photo-
	 ^
spher-e of o Ceti is sufficiently small that the region of stellar con-
tinuum emission should appear point-like at these resolutions (Labeyrie
et al., 1977). This is demonstrated by the flatness of the visibility
curves in Figure 1 at high resolution. The component representing dust
i
g rain emission was arbitrarily assumed to have a simple Gaussian spatial
distribution. None of the results presented here are greatly affected
by ttic detailed shape ofthis distribution.
The most noticeable variation shown in Table 1 is in the parameter
f• Since l-f is the fraction of the 11 micron flux contributed by dust
emission,it is seen that this dust emission is strongest relative to
	
1i41
the stellar continuum near a phase of 0.10 or sli ghtly later. This
phase also corresponds to maximum .stellar luminosity indicating that
	
r
the dust grain temperatures are raised by the increased stellar radiation.
The data in Table '1 also suggest some variation in the spatial ex-
tent of the re i ar of it t t 11
	 d t'	 TV, d'	 tg,	 c	 c^m5 a	 ar us	 emission. a	 lame er, eg,
a
r	 ^,
iI.	 a,	 ,
t
5.
seems to increase together with the strength of dust emission, indicating
that it also may be related to the increased stellar luminosity.
Changes in stellar luminosity may be caused by changes in either.
effective temperature or size. The effective temperature of o Ceti is
thought to undergo a periodic variation from about 2300 K to 2800 K
(Strecker, 1973). This alone predicts a factor of 2.2 change in the
total stellar luminosity. Small diameter changes may also be present,
but Strecker calculates that the luminosity change is still about a
factor of 2.2. Although this calculation is subject to a number of
uncertainties, it is in good agreement with the factor of 2.5 variation
in bolometric magnitude observed by Pettit and Nicholson (1933). The
maximum in luminosity as well - as the maxima of the-31 . 5 1.,
 and 11p-1igh*_
curves fall at a phase of approximately 0.15 after visible maximum.
Thus the chan ges in luminosity are of the correct phase to explain the
variations in dust grain emission.
The strength of dust emission at 11 microns relative to the
stellar continuum is seen from Table 1 to vary by a factor of 1.8. As
the stellar temperature varies from 2300 K to 2800 K, the 11 micron
stellar continuum will itself increase by a factor of 1.3. Thus, the
overall change in dust emission is a factor of 2.3. This is to be
compared with the calculated effect of changes in stellar luminosity
on the strength of dust emission.
The expected magnitude of the variation in dust emission depends
on the temperature of the grains. It is likely that emission is seen
from dust at a variety of distances from the star and hence at a va-
riety of temperatures. The maximum temperature prr,ent P, limited by
the condensation temperature of the grains, which is approximately
6.
1000 K for silicate materials (Salpeter, 1977). The actual temperaturei
of the hottest grains may be considerably lower if grain formation is
j	 inhibited due to difficulties in nucleation. The lowest temperature of
t
interest is 250 K since dust grains cooler than this will not radiate
Istrongly at llu. Grains at 1000 K and 250 K e^11 change in brightness
by factors of 1.4 and 2.6 respectively when subjected to a factor of
2.2 change in stellar luminosity. The expected variation in brightness
1
for the entire dust shell should lie between these extremes and thus
j	 is consistent with the observed factor of 2.3 variation in dust emission.
The observations further indicate that the'radiation must come predom-
inantly from grains near the cooler end of this range of temperatures.
Detailed calculations have been made for the brightness variation
of an optically thin dust region using several models. It was assumed
that the dust region has an inner radius characterized by some maximum
temperature for grains in radiative equilibrium and that the dust
density follows a power-law distribution, r-n ,
 
outside of this radius.
I
For grains with a 1/a emissivity spectrum and a maximum temperature of
	
	 {
i
1000 K  power-law given by n = 1.5 is needed to produce the observed
variation. This particular result does not depend strongly on the dust
spectrum. The more likely density dependence n = 2 requires a lower
maximum temperature between 500 K and 700 K. Models with grain density
dropping off slower than r-1 '5 or with still lower temperature dust are
ruled out in all cases since the emphasis on cooler grains would produce	 i
r	
variations in the 11µ shell brightness with stellar phase much larger
than those observed.
The observed shell diameter allows a rough determination to W.- mddr
of the grain emissivity spectrum. The temperature of grains at the inner
7.
i
	
^^	 i	
4	
r	 E	 r	 r^	
t
boundary of the shell has been shown to be between 500 K and 700 K.
The grain emissivity spectrum determines the distance from the star at
which the grains will be in equilibrium at this temperature. The ob-
served diameter of 0.7" fits the brightness distribution of a model
with an emissivity spectrum of approximately 1/a.
The diameter of the shelf appears to change somewhat with stellar
phase. Such a change is the result of the fact that the cool grains
change lln brightness faster than hotter grains as the stellarJ uminos-
ity incrP',ses. Thus emission at larger distances from the star is em-
phasized
-
as the dust is heated, The model with a maximum grain tempera-
ture of 500 K to 700 K, an r_ 2 
 density dependence, and a x -1 grain
emissivity spectrum predicts a 20% increase in diameter from minimum
to maximum stellar luminosity. This increase is consistent with the
observed variation within the rather large errors. This apparent size
change need not involve any physical redistribution of the dust itself.'
Such redistribution is possible although unlikely within the timescales
involved here.
The optical de ^th of the dust shell can be derived from the bright-
ness of the circuntellar shell, but it is dependent on all of the param-
eters of the model. The result for the model indicated hefa is an
optical depth at 11 microns of approximately 0.02.
Since the properties of this dust model depend rather strongly on
the observed variation in dust brightness, it is important to consider
other more conventional measurements which may be able to detect this
variation, For example, the 8-1411 spectrum of o Ceti should show a
more pronounced silicate emission feature at phases near maximum lumi-
nosity. Such a variation is suggested in the data of Forrest, Gillett,
i,
and Stein (1975). However, this should be interpreted with caution
since their single spectrum near maximum light predated their other
spectra by several years. In addition, it is possible that such spec-
tra may have been distorted due to phase-dependent changes in the
strength of Si0 absorption bands at Bµ such as those changes detected
by Nnkle et al. (1976) in the first overtone bands of Si0 at 41j. 1`f
so, as maximum light was approached the Bp absorption may have weakened
at the same time as silicate emission near llp was getting strorger.
Thus the shape of the spectrum over this narrow region may have remained
relatively unchanged. Nevertheless, further investigation of the 8-1411
spectra of long-period variables at various phases may prove fruitful.
Broadband infrared color measurements provide additional-informs=	
i;
tion. The observations of Forrest, Gillett, and Stein show a variation
of approximately 0.e in [11 1 ] - [8.411] with the Up band being re-
latively brightest at phases between 0.0 and 0.25. As with the spectro
photometric measurements the effect of Si0 absorption near 8p may be
such as to mask an inherently much larger variation in 01p] - [8.411].
Similarly the quantity [llp] - [ 3,5p] is contaminated by the H2O absorp-
tion band at 2.7p. Forrest, Gillett, and Stein observed virtually no
variation in this color as a function of phase. Yet considering the
1.3m amplitude of the 2.7p light curve observed by Maran et al. (1977)
and the width of the absorption in this region as shown by the data of
Merrill and Stein (1976), it is to be expected that there would be a
variation in [3.5p] of approximately 0.3 m solely due to changes in H2O
absorption. This effect masks variations in [1111] - r3.5 11 1 which may
be prevent due to increased dust emission. Thus the broadband photo-
metric measurements are consistent with the observed increased dust
9.	 1
emission at phases near 0.10 although by themselves they are not
F	 sufficient to demonstrate such an increase. 	 i
IV SUMMARY
The observed variations in the 11 micron brightness distribution
of o Ceti indicate an increase in both the relative brightness and
the apparent size of the circumstellar dust shell occurring during
W	 the period of maximum stellar luminosity. These variations can be
understood in terms of changes in the temperature of the dust grains
produced by the known variation in luminosity of o Ceti.
f;
The authors especially wish to thank L Greenberg and A. Harris for
	 1
their assistance in making these observations and A. Betz for his help
with the equipment.
	 r
i
:r
4 ^^ TABLE 1
PARAMETERS !JSED TO FIT FRINGE VISIBILITY MEASUREMENTS
P'nure Phase f eg
la 0.75 0.54 t 0.02
lb 0.90 0.54 t 0.02 e62 ± 0.08
lc 0.11 0.40 ± 0.01 0"77 ± 0.14
r
- —	 ---
* Undetermined due to the lack of measurements at low spatial
i
resolution.
s
3
3
t
S
3
j
C	
11
It	 MIr	
L1.
FIGURE CAPTIONS
,. o
Figure 1: Fringe visibility measurements of sr Ceti at 4 different
e
phases of its light cycle. Curves drawn are fits using
the parameters of Table 1 as discussed in the text. The
graphs are in order of increasing phase centered about
0.
	
qu ••	 ,	 ^i _
 measuremen ts fllr ^,. Or On15-.,_.	 _ r7 gore c: -iU,^ar-iwrrringe visib l4i_,,t,- e..	 _
idaaM
lL.
REFERENCES;
t
S
i
Forrest, W.J., Gillett,
	
F.C.,	 and Stein, W.A.	 1975, Ap.J.,	 195, 423.
a
Hinkle,	 K.H., Barnes, T.G., Lambert, 	 D.L. and Beer, R. 1976, Ap.J.	 (Letters),
210,	 L141.
Labeyrie, A.,	 Koechlin, L., Bonneau,	 D.,	 Blazit,	 A., and Foy,	 R.	 1977, Y
Ap.J.	 (Letters),	 218,	 L75. ;R
Maran,	 S.P., Heinsheimer, T.F., 	 Stocker, T.L., Anand, S.P.S., Chapman, 1
R.D.,	 Hobbs,	 R.W.,	 Michalitsanos,	 A.G.,	 Wright,	 F.H.,	 Kipp,	 S.L.	 1977, y '.j
a
Infrared Phys., 17,	 565. l.i r
a
--
	
McCarthy, D,_W., Lo_w_, F.J., and Howell. R-_1977,-Ap,,l (Letters 1 	 21,4, L-35. $
Merrill,	 K.M.	 and Stein, W.A.	 1976,	 Pub.A.$ P.,	 88,	 285.
a
Pettit,	 E.	 and Nicholson, S.B.	 1933, Ap.J., 78, 320.
v
Salpeter,	 E.E. 1977, Ann.	 Rev.	 Astron.	 Astrophys., 15, 267.
Strecker,	 D.W. 1973,	 Ph.D. Thesis, University of Minnesota.
4 i
Sutton,	 E.C., Storey, J.W.V., Betz, A.L., Townes, C.H.,	 and Spears,	 D.L l
1977, Ap.J.	 (Letters), '11, L97. k
I
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spollal Ire(Imoncy, 10 rr:(J
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'DT I
0.75 12 15 Seplund)er 1977
oL
ti
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0*2 0.90 2.4	 wbot 1977
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0,2	 0.11 7 12 J	 I'M
•	 0.10 IS I t Inuat ?
 1977
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0.24 21 1 t-fawa, 1"711
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Variations in the spatial distribution of 11 Micron radiation from omicron Ceti

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