Diffraction-limited speckle interferometry and modeling of the circumstellar envelope of R CrB at maximum and minimum light

10 Pages·0.45 MB·English

by  K. Ohnaka

Astronomy & Astrophysics manuscript no.
(will be inserted by hand later)
Diffraction-limited speckle interferometry and modeling of the
circumstellar envelope of R CrB at maximum and minimum light
1 2 1 3 1 1 4
2 K. Ohnaka , Y. Balega , T. Bl¨ocker , Y. S. Efimov , K.-H. Hofmann , N. R. Ikhsanov , V. I. Shenavrin ,
1 4
0 G. Weigelt , B. F. Yudin
0
2
1 Max-Planck-Institut fu¨r Radioastronomie, Auf dem Hu¨gel 69, D-53121 Bonn, Germany
n 2 Special Astrophysical Observatory,Nizhnij Arkhyz,Zelenchuk region, 35147 Karachai-Cherkesia, Russia
a 3 Crimean Astrophysical Observatory, Nauchny, 98409, Crimea, Ukraine, and Isaak Newton Institute of Chile,
J
Crimean Branch
4
4 SternbergAstronomical Institute, Universitetskii pr.13, 119899 Moscow, Russia

1
v Received / Accepted
9
4 Abstract. Wepresentthefirstspeckleinterferometric observationsofRCrB,theprototypeofaclass ofpeculiar
0 starswhichundergoirregulardeclinesintheirvisiblelightcurves.Theobservationswerecarriedoutwiththe6m
1
telescopeattheSpecialAstrophysicalObservatorynearmaximumlight(V =7,1996Oct.1)andatminimumlight
0
(V =10.61,1999Sep.28).Aspatialresolutionof75maswasachievedintheK-band.ThedustshellaroundRCrB
2
is partially resolved, and the visibility is approximately 0.8 at a spatial frequency of 10 cycles/arcsec. The two-
0
dimensionalpowerspectraobtainedatbothepochsdonotshowanysignificantdeviationfromcircularsymmetry.
/
h Thevisibilityfunctionandspectralenergydistributionobtainednearmaximumlightcanbesimultaneouslyfitted
p with amodelconsistingof thecentralstarandanoptically thindustshell withdensityproportional tor−2.The
-
o inner boundary of the shell is found to be 82 R⋆ (19 mas) with a temperature of 920 K. However, this simple
r modelfailstosimultaneouslyreproducethevisibilityandspectralenergydistributionobtainedatminimumlight.
st Weshow that this discrepancy can be attributed to thermal emission from a newly formed dust cloud.
a
: Keywords.stars:carbon–stars:circumstellarmatter–stars:mass-loss–stars:individual:RCrB–stars:variable:
v
i general – infrared: stars
X
r
a
1. Introduction troscopic observations as well as theoretical progress on
dust formation suggest that the latter scenario may be
The R Coronae Borealis (RCB) stars are a class of un-
the case (see, e.g. Clayton1996, Feast 1997), however,no
usualobjectscharacterizedbysuddendeclinesintheirvis-
definitive answer is yet available.
ible light curves as deep as ∆V 8. They are extremely
∼
hydrogen-deficient and also carbon-rich (e.g. Asplund et Thespectralenergydistributions(SEDs)ofRCBstars
al. 2000 and references therein). The RCB stars are exhibit infraredemissionpeaks around6 8 µm. The IR
∼
thought to undergo the formation of dust clouds in ran- excess, which accounts for typically 30% of the total flux,
dom directions, and it is believed that a sudden decline is constantly present, regardless of the visual brightness
takes place, only when a dust cloud forms in the line of ofthe centralstar.Therefore,the IRexcessoriginatesnot
sight (Loreta 1934, O’Keefe 1939). A newly formed dust from a single newly formed dust cloud, but mainly from
cloud is expected to be accelerated by radiation pressure agroupofdisperseddustcloudswithtemperaturesofap-
andtomoveaway,expandinganddispersingovermonths, proximately600–900K.Forexample,Walkeretal.(1996)
as the object gradually returns to its maximum visual fit the infrared (spectro)photometric data of R CrB with
brightness. The mechanism of the dust cloud formation a 650 K blackbody. The study of IRAS observations by
and its temporal evolution are, however, still poorly un- Gillett et al. (1986) led to the detection of an additional,
derstood. Especially, the location of dust formation is in very extended “fossil” shell around R CrB, whose diame-
dispute: far from the star, > 20R (e.g. Fadeyev 1986, terisaslargeas18′,withatemperatureof 30K.Walker
1988,Feast1996),orveryclo∼setoth⋆ephotosphere, 2R (1994) found suchfossilshells for atleastf∼our RCB stars.
⋆
∼
(Payne-Gaposchkin 1963). Recent photometric and spec-
Apart from the detection of the fossil shells, most
Send offprint requests to: K. Ohnaka, of the observational results on the circumstellar environ-
e-mail: [email protected] ment around RCB stars were obtained by photometry
2 K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB

12 a 12 b
8 8
c c
se 4 se 4
c c
s/ar 0 s/ar 0
e e
ycl-4 ycl-4
c c
-8 -8
-12 96 Oct. -12 99 Sep.
- 1 2 - 8 - 4 0 4 8 1 2 -1 2 - 8 - 4 0 4 8 1 2
cycles /arcsec cycles /arcsec
1.0 1.0
y y
bilit 0.8 bilit 0.8
si si
d Vi 0.6 d Vi 0.6
e e
z z
ali 0.4 ali 0.4
m c m d
or or
N 0.2 N 0.2
Fig.1. Visual light curve of R CrB based on the AAVSO 96 Oct. 99 Sep.
data. The epochs of the speckle interferometric observa- 0.0 0.0
tions are shown by the arrows 0 2 4 6 8 10 12 0 2 4 6 8 10 12
cycles/arcsec cycles/arcsec
Fig.2. aandbTwo-dimensionalpowerspectraofRCrB
Table 1. Speckle interferometric observations. λ /∆λ:
c
obtained on 1996 October 1 and on 1999 September 28,
central wavelength and FWHM bandwidth of the filters,
respectively.canddAzimuthallyaveragedvisibilityfunc-
NT:numberofspeckleinterferogramsacquiredforthetar-
tions derived from a and b, respectively
get,NR:numberofspeckleinterferogramsacquiredforthe
referencestars,T:exposuretime ofeachframe,S:seeing,
and p: pixel size
2. Speckle interferometric observations
1996 Oct. 1 1999 Sep.28
The K-band speckle interferometric observations were
JD 2450358.2 2451450.2 carried out with the 6 m telescope at the Special
V (mag) 7 10.61 Astrophysical Observatory (SAO) in Russia, using our
λc/∆λ(µm) 2.191/0.411 2.115/0.214 NICMOS-3 camera for the observation in 1996 and our
Reference star HIP80322 HIP77743 HAWAII array speckle camera in 1999. The observations
NT 167 990 are described in Table 1.
NR 198 1044 Fig.1showsthe visuallightcurveofRCrBinthe rel-
T(ms) 150 80
evant periodbased onthe compiled data ofthe American
S(arcsec) 1.4 1.1
Association of Variable Star Observers (AAVSO). The
p(mas) 30.5 26.4
Field of view 8′.′9×8′.′9 5′.′1×5′.′1 data before 1996 were taken from AAVSO Monograph 4
Supplement 1,while J. A. Mattei kindly providedunpub-
lished data for the rest of the period. On 1996 October
1, R CrB was on its final recovery from the 1995-96 deep
minimum and its visual magnitude was around 7 (Mattei
2000). Since V is approximately 6 at maximum light, the
and spectroscopy.Recently, Clayton& Ayres (2001) have starwasslightlyobscuredby∆V =1.On1999September
revealed extended Cii λ1335 emission around two RCB 28,the star wasjust between two sharpdeepminima and
stars, V854 Cen and RY Sgr, by long-slit spectroscopy. had a visual magnitude of 10.61 (see Sect. 3). The star
However, such direct information on the spatial distri- was heavily obscured by ∆V =4.6.
bution of material in the vicinity of the central star has
Fig. 2 shows the two-dimensional power spectra and
been very rare up to now. In this paper, we present high-
azimuthally averaged visibility functions reconstructed
resolutionspeckleinterferometrycarriedoutforRCrBat
with the speckle interferometry method (Labeyrie 1970).
maximumandminimumlight.Thepropertiesofthewarm
The error bars include systematic errors caused by see-
dust shell will be derived by simultaneous fits of the ob-
ing variations as well as speckle noise errors. There is
served visibilities and SEDs using power-law models. We
no significant deviation from circular symmetry in the
will alsodiscuss the possible indication ofa newly formed
two-dimensional power spectra observed at both epochs.
hot dust cloud.
The granular features seen in Fig. 2a are the speckle
noise resulting from the small number of interferograms.
In Fig. 2b, a slight elongation along the vertical axis of
K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB 3
the figure can be marginally recognized. However, this is
within the error bars, and cannot be regarded as a sig-
nificant feature. Clayton et al. (1997) suggest a bipolar
geometryfor R CrB basedon the wavelengthdependence
ofthe positionangleofpolarization.Ourspeckleobserva-
tions seem to support a rather symmetric distribution of
material.However,adiscortorusmaylieveryclosetothe
star, and therefore, it is premature to rule out a bipolar
geometry completely.
ThereconstructedvisibilityfunctionsshowninFigs.2c
and 2d exhibit no difference larger than the error bars.
The source probably consists of the central star (a point
source) and an extended dust shell. Visibilities observed
for such objects have a plateau at high spatial frequen-
cies resulting from the point source. In the observations
presented here, the angular size of the shell is small, and
therefore, the plateau is not visible within a cut-off fre-
quency of 13 cycles/arcsec. The determination of the
∼
physical parameters of the shell by simultaneous fits to
the observed visibilities and SEDs will be presented in
Sect. 5.
Fig.3. Schematic view of the central star, an obscuring
3. Photometric data
dust cloud, and an optically thin dust shell. The figure is
not to scale
UBVRIJHKLM photometry was carried out on 1999
September29,justonenightafterthespeckleobservation.
Theoptical(UBVRI)datawereobtainedwiththe1.25m resolved with IRAS, therefore, we adopt the point source
telescope at the Crimean Astrophysical Observatory, and processedfluxes for 60 and 100 µm. Long-termvariations
theinfrared(JHKLM)datawiththe1.22mtelescopeat at wavelengths longer than 10 µm are considered to be
the Crimean Laboratory of the Sternberg Astronomical smaller than those in the L- and M-bands. Forrest et al.
Institute. (1972) show that the amplitude at 11 µm is about half
No photometric data, except for the visual magni- as small as those in the L- and M- bands. The varia-
tudes compiled in the AAVSO database, have been pub- tion at wavelengths longer than 11 µm is estimated to be
lished around the date of our speckle observation in 0.75 mag at most.
∼
1996 October. Therefore, we use the data published by The interstellar extinction toward R CrB is E(B
−
Shenavrin et al. (1979), who report a series of photomet- V)= 0.05 (Asplund et al. 1997). The observed fluxes are
ric observations during the 1977 deep minimum. We use dereddened using the method of Savage & Mathis (1979)
theUBVRJHK dataon1978January22(JD2443530.6), with A =3.1E(B V).
V
−
when the visual magnitude was 7.03, almost the same
as that on the date of our speckle observation in 1996
4. Description of the model
October. For the L- and M-bands, we use photomet-
ric data obtained on 1996 June 11 (JD2450246.4) by Thebasicsofthemodelusedherearethesameasadopted
Shenavrin(unpublishedobservation),about4months be- by Gillett et al. (1986). Fig. 3 illustrates the picture con-
foreourspeckleobservation.Itisknownthatthevariation sideredinourmodeling.Itconsistsofthecentralstarand
of the L- and M-band fluxes has no correlation with the an optically thin dust shell responsible for the constant
visual light curve, and that they exhibit a semi-periodic IR excess.As mentioned in Sect. 2, the star was obscured
variation of 1.5 mag with a period of about 1260 days by ∆V = 4.6 (1999 September 28) and ∆V = 1.0 (1996
∼
(e.g. Feast et al. 1997). In fact, the L and M magnitudes October1).Therefore,anadditionalobscuringdustcloud,
on 1996 June 11 are by 1.09 mag and 1.25 mag brighter whichisassumedtobecircular(projectedontotheskyas
thanthoseon1999September29,respectively.TheL-and seenfromthe star),is alsoconsidered,as showninFig.3.
M-bandfluxes measured4months before areexpected to AdoptingMbol andTeff tobe 5.3(Gillettetal.1986)
−
representthevaluesonthedateofthespeckleobservation and6600–6900K(Asplundetal.2000),respectively,the
rather well. radius of the central star is approximately 70 R . We
We also use IRAS observations at 12, 25, 60, and adopt6750K for the effective temperature,andrad⊙iation
100µm. The veryextended “fossil”shellgives riseto flux from the central star is approximately represented by a
excessat60and100µm,whenevaluatedwithalargeaper- blackbody.ThedistancetoRCrBadoptedhereis1.6kpc
ture (Gillett et al. 1986). In this paper, however, we are (Gillettetal.1986),yieldinganangularradiusofthecen-
primarilyinterestedinthe warmdustshellwhichwasnot tral star of 0.23 mas.
4 K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB
We consider a spherical shell with an inner radius rin
andouterradiusrout.Theshellisassumedtobeoptically
thin not only in the infrared but also in the optical, since
thereis noevidenceforstrongcircumstellarreddeningfor
RCrB.Asplundetal.(1997)foundthat the observedop-
tical flux at maximum light can be well reproduced by
their line-blanketed model atmospheres without any cir-
cumstellarextinction.Infact,theopticaldepthofthedust
shell in the V-band is < 0.3 in our models presented be-
low. The assumption o∼f spherical symmetry for the shell
is justified, giventhe negative detection ofdeviationfrom
circularsymmetryinthe observedtwo-dimensionalpower
spectra.
The grain number density is assumed to decrease in a
power-law of radius, Fig.4. Temperature distributions derived from the ther-
n(r)=Cr−γ, (1) malbalanceequation.Dottedline:Colangelietal.(1995),
dashedline:Bussolettiet al.(1987),solidline: Rouleau&
where C is a constant which does not affect the shape of Martin (1991) with a=0.01 µm
emergent SEDs, and therefore, should be adjusted to fit
the flux observed on the earth.
not exhibit the contribution of the fossil shell. The varia-
The temperature in an optically thin dust shell is de-
tionofthe25µmfluxisnotavailableintheliterature,but
termined by the thermal balance equation
it is estimated to be smaller than the 0.75 mag at 11 µm.
Z0∞ 4Lπrν2πa2Qabs(a,ν)dν trooutthies sfeatr-tionfbraer∼ed1p.5ar×t1o0f4tRhe⋆,owbsheircvhegdivSeEsDasg,oaosdwmeawtcihll
∞ show below.
2
= 4πa Qabs(a,ν)πBν(T(r))dν, (2) It should be stressed here that the real circumstellar
Z0 environmentaroundRCrBismostlikelymuchmorecom-
whereL istheluminosityofthecentralstaratagivenfre- plex than depicted by the above spherical shell model.
ν
quency,aistheradiusofagrain,Qabs(a,ν)istheabsorp- Since dust ejection in RCB stars presumably occurs in
tionefficiencyofagrain,andB (T(r))isthePlanckfunc- clouds, not in a spherical shell, it is likely that the real
ν
tion. Amorphous carbon is the most probable candidate distribution of material is clumpy or patchy without any
for the circumstellar dust around RCB stars (e.g. Holm clear inner boundary. At large distances, however, it is
et al. 1982, Hecht et al. 1984). In Fig. 4, we show tem- still plausible that a spherical shell model roughly repre-
perature distributions predicted by the thermal balance sents the distribution of material, as long as dust clouds
equation, using the extinction of amorphous carbon ob- are ejected randomly and frequently. There may be some
tained by Bussoletti et al. (1987) (AC2 sample), Rouleau newly formed clouds inside the inner boundary defined in
&Martin(1991)(AC1sample),andColangelietal.(1995) the above spherical model, if the star ejects dust clouds
(ACAR sample). We calculate Qabs from the complex re- frequently, for example, every pulsational cycle (40 – 50
fractive index derivedby Rouleau& Martin (1991) in the days). Without detailed knowledge about the dispersal
Mietheory,assumingasinglegrainsize,a=0.01µm,and processesofclouds,however,itisbeyondthescopeofthis
using the code published by Bohren & Huffman (1983). paper to construct a more detailed model. In the frame-
This grain size is based on the result obtained by Hecht work of our models, we consider only one newly formed
et al. (1984), who analyzedthe UV spectra of R CrB and dust cloud, as Fig. 3 illustrates.
RYSgrandconcludedthatthegrainsizeisbetween0.005 TheobservedSEDs(seeSect.5)demonstratethatthe
and 0.06 µm. As Fig. 4 shows, the temperature distribu- contribution of the central star is not negligible in the
tions agree with one another within 50 K. near-infrared. The flux from the central star was atten-
∼
The flux density observed on the earth from the opti- uated by a dust cloud in front of the star by ∆V 1
∼
cally thin shell described above can be calculated by on 1996 October 1 and ∆V 4.6 on 1999 September 28.
∼
In order to estimate the attenuated flux from the star in
fs(λ)= 4πmDd2κλC Z routBλ(T(r))r2−γdr, (3) thenear-infrared,theextinctioncurveofthedustcloudis
rin empiricallyderivedfromphotometryintheoptical,where
emissionfromthedustshellisnegligible.Theeffectofthe
where md and κλ is the mass and mass absorption coef-
obscuration due to a dust cloud is expressed as
ficient of a grain, respectively, and D is the distance to
the star. The constant C is adjusted so that the flux pre- max cl
f (λ)=f (λ)exp( τ (λ)), (4)
dictedfromthemodelscanreproducetheobservedfluxat ⋆ ⋆ −
25 µm, since its long-term variation mentioned in Sect. 3 where f (λ) and fmax(λ) denote fluxes observed at any
⋆ ⋆
is expected to be minimal, and at the same time, it does giventimeandatmaximumlight,respectively,andτcl(λ)
K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB 5
the ratio of total to selective extinction (A /E(B V))
V
−
duringdeclineeventsforRCrBandanotherRCBstar,RY
Sgr, and suggested that rather large glassy carbon parti-
cleswithradiifrom0.075to0.15µmmightberesponsible
for the nearly neutral extinction seen at the very bottom
ofminimumlight.Thesesizesaresignificantlylargerthan
the 0.01µmweadoptfora singlegrainsize,butitshould
be noted that we adopt 0.01 µm as the grain size in the
optically thin dust shell,while the largegrainsmentioned
above are claimed to be present in a newly formed op-
tically thick dust cloud. For the temporal change of the
extinctionatthe risephasefromminimumlight,Hechtet
al. (1984) proposed shattering of large grains as a possi-
ble mechanism. Efimov (1990) also proposed that the ob-
served temporal variation of colors and polarization can
be accounted for by the change of grain sizes, but assum-
ing graphite grains instead of amorphous carbon. In any
case,the spectralindexofthedustcloudapproaches1,as
the clouddispersesandbecomespartofthe opticallythin
dust shell. Therefore, the dust properties in the optically
thin shell may presumably remain constant.
The lack of detailed knowledge about the properties
of dust grains formed in R CrB and of their tempo-
ral variation forces us to adopt an empirical extinction
law. As Fig. 5 shows, the extinction due to a dust cloud
Fig.5. Extinction curves of a dust cloud and its tem-
can be approximated by τcl(λ) (1/λ)p. At the bot-
poral variation. The open symbols represent the extinc- ∝
tom of minimum light, p is approximately 0, and changes
tion curves derived from the observations covering the
to 1, as the star returns to maximum light. By the
1983minimumobtainedbyGoncharova(1992).Opencir- ∼
least square fit for the extinction curves shown in Fig. 5,
cles: 1983 Oct. 17 (JD2445625.21), open squares: 1984
we derive logτcl(λ) = 0.52 0.47logλ(µm) when the
Jan.16(JD2445715.60),and opentriangles:1984May 22 V magnitude of the star is−10.61, while logτcl(λ) =
(JD2445843.43). The filled squares represent the extinc-
0.18 0.84logλ(µm)whentheV magnitudeis7.03.The
tion derived for 1999 Sep. 29. The filled triangles repre- − −
extinction at longer wavelengths is then estimated by ex-
senttheextinctionderivedfromthedataobtainedon1978
trapolation. Obviously this procedure is not optimal, but
Jan. 22 by Shenavrin et al. (1979). The visual magnitude
with no alternatives at hand for disentangling the contri-
at each epoch is also given. The extinction characterized
butions of the central star and the dust shell for the data
by 1/λ is plotted with the dotted line for reference
studied here, we are forced to adopt this method.
Assuming a blackbody for the flux of the central star,
the flux density observed on the earth from the obscured
is the optical depth of the dust cloud in front of the star. central star is
Notethattheeffectofinterstellarextinction,thoughsmall
2
ffomraRx(λC)rBby, ctahnecsealsmoeuatm, boeucnatu.se it affects both f⋆(λ) and f⋆(λ)=(cid:18)RD⋆(cid:19) πBλ(Teff)×exp(−τcl(λ)−τs(λ)), (5)
⋆
Fig. 5 shows the temporal change of the optical depth whereτs(λ)istheopticaldepthofthedustshellalongthe
of a dust cloud during the 1983 minimum in the U, B,
radial direction.
V, R, and I bands. The optical depth in each band was
The flux density observed towardR CrB is, therefore,
derived using the photometric data in the decline and at
the sum of the flux from the central star obscured by a
maximum light obtained by Goncharova (1992). We also
dustcloudandslightlydimmed bythe opticallythin dust
plottheextinctioncurvesderivedforthephotometricdata
shell (equation (5)), thermal emission from the optically
discussed in Sect. 3. The figure illustrates that the ex-
thindustshell(equation(3)),andthethermalemissionof
tinction is almost independent of the wavelength at the
anewlyformed(thereforepresumablystillopticallythick)
very bottom of the deep minimum (V = 14.19). As the
dust cloud given by
starstartsits finalrecovery,the extinctioncurvestartsto
steepen. Pugach (1984) proposed that the neutral extinc- 2
Rcl s
tion observed during the initial drop to minimum light fcl(λ)= πBλ(Tcl) exp( τ (λ)), (6)
(cid:18) D (cid:19) × −
can be explained by an optically very thick dust cloud
whose coverage over the stellar disk varies with time. On where Rcl and Tcl are the radius and the temperature of
theotherhand,Hechtetal.(1984)analyzedthechangeof the newly formed dust cloud, respectively.
6 K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB
The intensity distribution for the central star and the
dust shell can be written as
cl s
I (b) = B (T )exp( τ (λ) τ (λ)) circ(b/R )
λ λ ⋆ ⋆
− − ×
√ro2ut−b2
+ 2mdκλ n(r)Bλ(T(r))dz
Z
zmin
s
+ Bλ(Tcl)exp( τ (λ)) circ(b/Rcl), (7)
− ×
where b is the impact parameter and z = √r2 b2. The
−
function circ(b/R ) takes a value of 1 for b < R and
⋆ ⋆
| |
0 elsewhere. The lower limit of the integration is zmin =
0 for b rin, while zmin = ri2n b2 for b < rin. The
≥ −
visibilityiscalculatedbytakinpgthemodulusoftheFourier
transform of the intensity distribution.
5. Simultaneous fit of observed visibilities and
SEDs
5.1. Model fitting without thermal emission from a
dust cloud
We first try to fit the observed SEDs and visibilities us-
ing models without thermal emission from a dust cloud,
namely, neglecting the term given by equation (6). We
adoptγ =2,appropriatefor a constantmass loss andex-
pansion velocity. The sensitiveness of the near- and mid-
infraredpartsofemergentSEDs toTin allowsus todeter-
mine it by fitting the observed SEDs. The visibility func-
tions,whichdirectlyreflectthe spatialextentofthe shell,
enable us to examine the validity of the models described Fig.6. Simultaneous fit of the SED and visibility of R
above. CrB observed on 1996 October 1, using the models dis-
Figs. 6 and 7 show the fit of the observed SEDs and cussed in Sect. 5.1. a The open squares,filled circles, and
visibilityfunctionsatthe twoepochsofourspeckleobser- filled triangles represent the photometric data obtained
vations. The SEDs and visibilities are calculated with the byShenavrinetal.(1979),Shenavrin(unpublishedobser-
opacities of amorphous carbon obtained by Bussoletti et vation), and IRAS, respectively. The three curves repre-
al. (1987) (AC2 sample), Rouleau & Martin (1991) (AC1 sent the SEDs predicted from models. CO represents the
sample),andColangelietal.(1995)(ACARsample).The model with the data derived by Colangeli et al. (1995),
corresponding temperature distributions shown in Fig. 4 RM with those derived by Rouleau & Martin (1991), and
areusedinthe calculations.Figs.6aand 6bdemonstrate BU with those derived by Bussoletti et al. (1987). b The
that the SED and visibility for the 1996 data are well re- filled circles represent the observed visibility, while the
produced with rin = 76 – 90 R⋆ and Tin = 900 – 950 K. three curves represent the visibilities predicted from the
Foragivenopacitydataset,the uncertaintyofTin isesti- models.cNormalizedintensityprofile(λ=2.2µm)ofthe
mated to be 100 K, translating to an uncertainty of rin BU model
±
of 20 R⋆. Taking the average of the Tin and rin derived
±
withthreedifferentopacitiesandaddingtheuncertainties
resulting from the fitting, we derive Tin = 920 103 K with the observed SED. The observed SED can be well
±
and rin = 82 23 R⋆. Fig. 6c illustrates the normalized fitted using the models with Tin = 700 – 800 K and rin =
±
intensity profile of the best fit model for the 1996 data. 116 – 172 R , but the visibilities predicted from these
⋆
It consists of the central star and a ring-like structure models are too low as compared with the observation.
characteristicofanopticallythinshell.Notethatthepre- Regarding this discrepancy, we first examine the approx-
dicted visibilities become plateau-like at spatial frequen- imations adopted in our models. The line-blanketing ef-
cies > 20 cycles/arcsec in Fig. 6b. This plateau results fect in the atmosphere of RCB stars is very prominent as
from∼the unresolved central star. It should also be noted Asplund et al. (1997) show, but the use of line-blanketed
thatthegoodmatchinthewavelengthrangeshorterthan atmospheres instead of the blackbody would lower Tin by
1 µm is simply due to the adoption of the empirical ex- only 50 K. The effect of the uncertainty of the effec-
∼
tinction for a dust cloud, as described in Sect. 4. tive temperature is also minor.A decreaseof the effective
Figs. 7a and 7b reveal that the visibility observed temperatureby500Kleadstoadecreaseofthedusttem-
at minimum light cannot be reproduced simultaneously peratureby 60Kat 100R .Combiningtheseeffects,
⋆
∼ ∼
K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB 7
Fig.7.SimultaneousfitoftheSEDandvisibilityofRCrB
observed on 1999 September 28, using the models with-
out thermal emission from the newly formed dust cloud,
as discussed in Sect. 5.1. a The filled circles representthe
photometricdataobtainedonenightafterthe speckleob-
servation. The IRAS data are represented by the filled
triangles. The three curves represent the SEDs predicted
from models. See also the legend to Fig. 6. b The filled
circles represent the observed visibility, while the three
curvesrepresentthe visibilitiespredictedfromthe models Fig.8. Simultaneous fit of the SED and visibility of R
CrB observed on 1999 September 28, using an extinction
curve different from that extrapolated. a See the legend
thedusttemperatureintheshellcanbeby 100Klower to Fig. 7a for the reference of the symbols. b The filled
∼
than those used in the fitting above. We tried to fit the circles represent the observed visibility. c The solid line
observedSEDandvisibilityusingsuchatemperaturedis- represents an extinction curve for the dust cloud with a
tribution, but it has turned out that the match to the change of the spectral index at 1.4 µm. The dashed line
observations is not much improved. represents the extinction curve derived by extrapolation
One concern is the estimation of the K-band flux of from the optical depth shortward of 1 µm, as discussed
the central star obscured by the dust cloud. As described in Sect. 4. The filled squares represent the optical depths
in Sect. 4, the extinction of the dust cloud in the K-band derived from the observations as shown in Fig. 5
is derived by extrapolation from the region shortward of
1 µm. However, the actual extinction curve of the dust
cloud could become steeper longward of 1 µm and ap-
5.2. Thermal emission from a newly formed dust cloud
proach the usual extinction curve of amorphous carbon,
which is characterized by a spectral index of 1.3 (Le We show an alternative to interpret the data obtained at
∼
Bertre 1997). We find that the observed SED and visibil- minimum light. We propose that the inconsistency found
ity can be simultaneously fitted by adopting an extinc- for the 1999 data set may be attributed to the thermal
tion curve for the obscuring dust cloud such as shown emission of a newly formed optically thick dust cloud in
in Fig. 8c. The extinction curve bends at 1.4 µm and the front of the star. The newly formed dust cloud is suppos-
spectralindexchangesfrom0.47to1.3.Figs.8aand 8bre- edly still rather close to the star and its angular size is
vealthatthe observedSEDandvisibility arefairlyrepro- not yet large enough to be resolved with the 6 m tele-
duced.Itshouldbestressedthatthephysicalunderstand- scope. This assumption may be reasonable, because the
ing of such an extinction curve is still unclear, and that 1999speckleobservationwascarriedoutinadeclinewhen
theexactshapeoftheextinctioncurvecannotbeuniquely thestarwasobscuredby∆V =4.6.Thesizeandthetem-
determinedbythefittingpresentedhere.However,theun- perature of such a dust cloud are by no means obvious,
usual properties of grains in the newly formed dust cloud but the temperature (Tcl) should not exceed 1500 K,
∼
maybe responsibleforthediscrepancyfoundforthe min- otherwise the thermal emission of the cloud would be too
imum light data. prominent and would lead to a poorer match to the ob-
8 K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB
Fig.10. Simultaneous fit of the SED and visibility of
R CrB observed on 1996 October 1, using models with
thermal emission from a newly formed dust cloud out of
the line of sight, as discussed in Sect. 5.2. A cloud with
Rcl = 4.5 R⋆ and Tcl = 1200 K is placed out of the line
of sight,20R (5 mas)offsetfrom the centralstar.a The
⋆
three curves represent the SEDs predicted from the mod-
els. CO, RM, and BU denote the opacities of amorphous
carbon obtained by Colangeli et al. (1995), Rouleau &
Fig.9.SimultaneousfitoftheSEDandvisibilityofRCrB
Martin (1991), and Bussoletti et al. (1987), respectively.
observed on 1999 September 28, using models with ther-
Thecontributionofthe newlyformeddustcloudisshown
malemissionfromanewlyformeddustcloud,asdiscussed
withthedash-dottedlinefortheBUmodel.Seethelegend
in Sect. 5.2. a Three models with different data sets for to Fig. 6a for the reference of the symbols. b The filled
the opacity of amorphous carbon are plotted. The radius
circles represent the observed visibility
and the temperature of a newly formed dust cloud are
4.5R and1200K,respectively.CO,RM,andBUdenote
⋆
the opacities of amorphous carbon obtained by Colangeli shows the normalized intensity profile of a model consist-
et al. (1995), Rouleau & Martin (1991), and Bussoletti ing of the central star, an optically thin dust shell, and a
et al. (1987), respectively. The contribution of the newly thermally emitting optically thick dust cloud, whose pa-
formed dust cloud is shown with the dash-dotted line for rameters will be derived below.
the BU model. See the legend to Fig. 7a for the reference Figs. 9a and 9b show a simultaneous fit using models
ofthe symbols.b The filled circles representthe observed with thermal emission from a newly formed dust cloud.
visibility. c Normalized intensity profile (λ = 2.1 µm) of TheobservedSEDandvisibilityarenowfairlyreproduced
the BU model. The model consists of the central star, a with models consisting of the central star, an optically
newlyformedopticallythickdustcloudwithRcl =4.5R⋆ thin dust shellwith aninner radius ofrin = 150– 193 R⋆
(1.0 mas) and Tcl = 1200 K, and an optically thin dust (average172 R⋆) and Tin = 650– 720K (average685K),
shell with rin = 180 R⋆ (41 mas) and Tin = 650 K and an optically thick dust cloud with Rcl = 4.5 R⋆ and
Tcl =1200K.Thefitshouldberegardedastentative.The
uncertainties of Tin and rin are estimated to be 100 K
±
served SED. We assume a circular cloud (projected onto and 20 R⋆, respectively, while those of Tcl and Rcl are
±
the sky as seen from the star) with a radius of Rcl be- about 100 K and 1 R⋆, respectively.
± ±
tween 1 R⋆ and 10 R⋆. As shown in Fig. 3, Rcl denotes Thedifferenceofrinderivedforthe1996and1999data
theradiusofanindividualclouditself,notthedistancebe- may indicate a variation of the dust ejection frequency.
tweenthecloudandthecentralstar.As1R corresponds If the star experiences dust ejection less frequently, the
⋆
to 0.23 mas, even a cloud with a radius of 10 R can well inner boundary is expected to become larger, and the IR
⋆
be treated as a point source for our speckle interferome- excess is expected to decrease. In fact, as mentioned in
try.Thethermalemissionofthecloudisapproximatedby Sect.3,theLandM magnitudesdecreasedmonotonically
the blackbody radiation,as givenby equation(6). Fig.9c by 1 magfrom1996to1999.Thisisconsistentwiththe
∼
K. Ohnakaet al.: Diffraction-limited speckle interferometry of R CrB 9
trendfoundforrin derivedforthetwoepochs,butfurther a newly formeddust cloudas hotas1200K witha radius
observations are required to confirm this correlation. of4–5R isinferred,togetherwithanopticallythindust
⋆
Now we apply the thermally emitting cloud models to shell with rin 170 R⋆ and Tin 690 K. Furthermore,
∼ ∼
the data obtainednear maximumlight as wellfor the fol- the SEDandvisibilityobtainednearmaximumlightwere
lowing reason. Fig. 1 shows that R CrB started its final showntobefittedalsousingamodelwithanewlyformed
recoveryfromthe1995-96deepminimumabout6months dust cloudout of the line ofsight.However,we havealso
before our speckle observation on 1996 October 1. If dust discussed that the discrepancy found for the minimum
ejection occurs rather frequently, for example, every pul- light data may be attributed to the unusual extinction
sational cycle (40 – 50 days), we can expect that the star curve of the obscuring dust cloud. Observations during
underwent dust ejection out of the line of sight during the very bottom of a deep minimum, when the contribu-
these 6 months.It is likely thatnewly formeddust clouds tion of the central star is truly negligible, are crucial for
out of the line of sight existed on 1996 October 1, in ad- investigating the dust shell and dust clouds.
dition to the dust cloud in front of the star responsible
for an obscuration of ∆V 1. The latter cloud may al-
∼ Acknowledgements. We have used, and acknowledge with
ready be regardedas part of the optically thin dust shell,
thanks, data from the AAVSO International Database, based
because τKcl =0.34is derivedfor this cloud by the extrap- on observations submitted to the AAVSO by variable star
olationdescribedinSect.4.Therefore,fornearmaximum observers worldwide. N.R.I. acknowledges the support of
light, we consider a model with the central star dimmed the Long-Term Cooperation program of the Alexander von
by ∆V 1, thermal emission from an optically thin dust Humboldt Foundation.
∼
shell, and that from a newly formed optically thick dust
cloud out of the line of sight. Fig. 10 shows the SED and
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