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\IBVShead{4707}{14 May 1999}

\IBVStitle{The Dust Shell Around Sakurai's Object}


\IBVSauth{T.~KIPPER}

\IBVSinsto{Tartu Observatory, T\~oravere, 61602, Estonia, e-mail: tk@aai.ee}

\SIMBADobj{V4334 Sgr}
\IBVStyp{ R CrB }
\IBVSkey{photometry}
\IBVSabs{The published optical and near-IR photometric data of Sakurai's}
\IBVSabs{object are analyzed in the framework of circumstellar dust envelope.}
\IBVSabs{The temperature of the dust is found to be around 1200 K and the}
\IBVSabs{dust consists of small grains with diameter of 0.05 micrometers}
\IBVSabs{in 1997 and additional large grains for 1998 and 1999.}

\begintext

In our recent paper (Kipper \& Klochkova 1999) we analysed the spectra
of the born--again giant Sakurai's object (V4334~Sgr) whose evolution
has been extraordinarily rapid.  We found that the effective
temperatures of the object derived using spectral and photometric
methods were quite consistent until March 1997.  Later results diverge
noticeably. The natural explanation for that is the increased
circumstellar reddening and an extra radiation from hot dust clouds as
the star starts to show R~CrB--type brightness drops.
In this note we try to model this situation.

The most comprehensive photometric data for June, September and October of 1997 in $UBVJHK LM$ colours were obtained from Arkhipova et al.\ (1998).
Further data for May, 1997 in $JHK$ were taken from Kamath \& Ashok (1999)
and from the near--IR spectrum figures of Eyres et al.\ (1998) for April
and July, 1997. Shorter wavelength data $(UBVRi)$ for April, 1997 were taken from Duerbeck et al.\ (1997). For dereddening the $E(B-V)=0.53$
(Duerbeck \& Benetti 1996) and for the flux calibration the zero point
fluxes by Strai\v{z}ys (1977) were used. The derived fluxes are plotted
in Fig.~1. As could be seen, the data for near--IR deviate from each
other quite noticeably. This reflects both the large observation errors
and the variability as the plotted data cover the half a year time
span.

For modelling the dust shell the publicly available code DUSTY, developed
by Ivezi\'c, Nenkova \& Elizur (1997), was used.

For the input radiation from the central star the model spectra 
of H--deficient stars were used. Particularly for June 1997 and later  we chose the model with $T_{\rm eff}=5750$~K, $\log g=0.3$ and ${\rm C/He}= 0.1$. This was the model giving the best fit for the C$_2$ bands in
1998 spectra of Sakurai's object. We have earlier found that the line spectrum had not changed from 1997 (Kipper \& Klochkova 1999). With assumed stellar mass of 0.8~$M_{\odot}$ this corresponds to $\log L/L_{\odot}=4.03$ and $R_{\ast}=104~R_{\odot}$.
 
According to Zubko (1997) the most probable grain type acting in R~CrB
stars envelopes are the graphite grains. We used the optical properties
of graphite grains by Draine  \& Lee (1984). In the course of modelling
we found that only single size grains with radii around
$a\approx 0.055$~$\mu$m allow to explain $UBV$ observations
of 1997. This is in accord with Zubko's (1997) findings that in the case of R~CrB stars the size distributions of dust grains have peak--like form with typical sizes $0.02\div0.07$~$\mu$m. The constant dust density in quite narrow shell thickness $\Delta R/R_{\rm in}=0.25$ was adopted as the shell formed during very short time.

The dust temperature $T_{\rm d}$ at the inner shell boundary $R_{\rm in}$ was estimated
from the observed spectral shape and the location of the peak in
near--IR region.

\vfill
\eject

\IBVSfig{8.0cm}{4707-f1.ps}{Modelling of circumstellar dust shell around
Sakurai's object in 1997. Triangles -- Arkhipova et al.\ (1998) for June; 
diamonds -- ibid., for September and October; asterisks -- Duerbeck et al.\
(1997) for April; squares -- Kamath \& Ashok (1999) for May;
slanted crosses -- Eyres et al.\ (1998) for March, crosses -- ibid.\ for
July. The model spectra for June and July of 1997 are plotted with
lines: full line -- total emerging flux, dotted line -- contribution of
the attenuated input radiation, dashed line -- contribution of the
scattered radiation, dash--dotted line -- dust emission, and dash--dot--dot
line -- input stellar photospheric spectrum}

\IBVSfig{8.0cm}{4707-f2.ps}{The same as in Fig.~1 but the model
spectra are plotted for April 1997}

\IBVSfig{8.0cm}{4707-f3.ps}{Modelling of circumstellar dust shell around
Sakurai's object
in 1998 and 1999. Triangles -- Jacoby \& De Marco (1998)
and Kaeufl (1998) (near--IR) for June 1998; crosses -- Lynch et al.\ (1998)
for March 1888; asterisks -- Jacoby (1999) for March 1999.
Full line -- model total flux for March -- July 1998,
dashed line -- model flux for March 1999}

In that way for June and July of 1997 the following model was found:
visual optical depth, $\tau_V=0.95$, dust temperature, $T_{\rm d}(R_{\rm in})=1200$~K, inner radius of dust shell, $R_{\rm in}=68~R_{\ast}$. This model is plotted also in Fig.~1. In this modelling the data by Arkhipova et al.\ (1998) was given the highest weight.

For April 1997 higher stellar temperature, $T_{\rm eff}=6000$~K, smaller
grain size, $a=0.04$~$\mu$m, visual optical depth, $\tau_V=0.6$, and
rather high dust temperature, $T_{\rm d}=2500$~K 
at $R_{\rm in}=8~R_{\ast}$ were needed (Fig.~2).
The speed of the changes in the envelope parameters 
between these  two dates is in the order of the time--scale of gas
acceleration found by Fadeyev (1988) for R CrB dust envelopes.

For the autumn of 1997 the model with spherical
distribution of dust is impossible as both optical and near--IR flux have
risen. The fit is possible only if the luminosity of the star was higher by
about 20\% or there was a hole in dust towards the observer with smaller
extinction. It should be noted that, according to AAVSO data, the observed $V$ magnitudes vary rather erratically up to 0\fmm5.

In 1998 the star suffered deeper brightness drops. At the end of February
the weakening in $V$ amounted to 2\mm, but the star almost recovered by the
end of July when another, much deeper weakening started. For the first
weakening the photometry by Jacoby \& De Marco (1998), Kaeufl (1998) and
Lynch et al.\ (1998) is plotted in Fig.~3. These observations could be 
approximated with the model having $\tau_V=3.5$, $T_{\rm d}=1250$~K. In this case in addition larger grains up to $a= 0.15$~$\mu$m 
with standard IS distribution, $n(a)\propto a^{-3.5}$, and larger relative
thickness of the shell $\Delta R/R_{\rm in}=10$ are needed. Inclusion of
larger grains allows to model much flatter output spectrum at the shorter
wavelengths. Larger relative thickness gives better fit in near--IR 
region. The luminosity of the star should be higher by 20\% 
compared to July 1997.

The weakening which started in July 1998 has not yet stopped and by
March 1999 the star was already as weak as $V=20.08$ (Jacoby 1999).
These last data could be approximated with the model having 
$\tau_V=11.0$ and $T_{\rm d}$ not higher than 900~K. The (1023--2230) colour
alone corresponds to a blackbody
with temperature of 1285~K (Jacoby 1999). This very deep and longlasting
minimum indicates that Sakurai's object could share the fate of another
final helium shell flash star V605~Aql which after four years of fadings
and brightenings disappeared from the sky (Clayton \& De Marco 1997).

The presented models follow from very crude approximations.
The state of the system is not steady but highly dynamical.
The outpuffs of dust are probably
related to a pulsational cycle of the central star. This means that the
input stellar radiation rapidly changes. The gas in which the dust
grains condense is ejected rather in cones with semi-angle of about
$20\deg$ (Feast 1986) than in spherical symmetry. Nevertheless, such
modelling allows to explain why the effective temperatures of the star
determined from colours and spectral data do not coincide
and the spectral energy distribution of the system for 1997 and later
could be explained with the constant effective temperature of
central star, $T_{\rm eff}=5750$~K.

\medskip
{\it Acknowledgements.} The work on this note was supported by Estonian Science Foundation grant 3166. We have used, and acknowledge with thanks, the data from the AAVSO International Database.

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% Original: Kaeufl, H.U., 1998, {it IAU Circ.}, No.\,6896
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