Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~csj/papers/conference/opt_sak.ps Äàòà èçìåíåíèÿ: Fri Feb 2 14:04:58 2001 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 08:51:24 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: messenger

Optical Spectroscopy of V4334 Sgr: 1996­2000
C.S. Jeffery (csj@star.arm.ac.uk)
Armagh Observatory
D. Pollacco (d.pollacco@qub.ac.uk)
Queens University Belfast
The evolution of V4334 Sgr, or Sakurai's object, from its discov­
ery as an early F supergiant in 1996 to its fading as a late K­type
supergiant during 1999 was, in terms of normal stellar behaviour, un­
precedented. That evolution was primarily manifest through gross pho­
tometric changes (Nakano et al., 1996). It was quickly suggested that
V4334Sgr is a rare example of a hot evolved low­mass star, possibly a
white dwarf, in which nuclear reactions in the helium shell have been
reignited, causing the star to expand to giant dimensions (Benetti et
al., 1996b).
From discovery onwards, substantial changes in the optical spectrum
have been apparent. This paper reviews these changes, drawing on pub­
lished and unpublished material. It sets out the measurements neces­
sary for understanding the evolution of the star, and attempts to assess
the quantitative deductions made from the spectroscopic observations.
In the course of other observational work, both authors have ac­
quired a number of spectra of V4334 Sgr. This review presents a number
of these for the first time, including a unique record of the spectral
evolution around Hff during 1996. We have begun independent analyses
of these spectra and of an 'echelle spectrum obtained im 1996 May. Some
preliminary results are included.
Prior to writing this paper, the principal author had not been in­
volved in any completed analysis of V4334 Sgr and he has attempted to
be impartial in reviewing the literature. However his own experience of
modelling stellar atmospheres of peculiar composition and of studying
the spectra presented here have no doubt affected his judgement. He
takes full responsibility for the selection of material to include and
regrets any major omissions.
1. What we want to know and why.
In order to understand the evolution of V4334 Sgr, detailed informa­
tion concerning the stellar surface properties throughout the period
of visibility is of fundamental importance. Most of this information is
provided by the optical spectrum. The following are of interest.
c
fl 2000 Kluwer Academic Publishers. Printed in the Netherlands.
opt—spec.tex; 23/12/2000; 20:38; p.1

2
Spectral Classification. A spectral type provides a model­independent
description of fundamental stellar properties and enables compar­
ative analyses to be carried out objectively and economically. For
these reasons, descriptions of the spectral evolution of V4334 Sgr
from even modest resolution spectrographs can be enormously
helpful for tracing the evolution, particularly during intervals when
high­resolution data are not available.
Photospheric Diagnostics. Where the data is of sufficient quality, opti­
cal spectra provide measurements of effective temperature ( T eff ),
chemical composition and surface gravity ( log g), the latter with
T eff being a proxy for the luminosity to mass ratio (L=M ).
Circumstellar Diagnostics. The optical spectrum also carries informa­
tion concerning material above the stellar photosphere, including
gas in a stellar wind accelerating away from the stellar surface,
dust which may have condensed from the ejected gas several stellar
radii from the surface, and ionized material in a planetary nebula
ejected by the star in an earlier epoch of evolution. This review
deals only with the photospheric diagnostics.
The measurements outlined above may be used to address the follow­
ing questions: What track has V4334 Sgr followed through the Hertz­
sprung­Russell diagram? How has its surface composition changed dur­
ing that evolution? Is V4334Sgr similar to any other stars? What are
the evolutionary origin and fate of V4334 Sgr?
2. Optical Spectroscopy.
2.1. A possible final helium flash.
The outburst of V4334 Sgr was discovered on 1996 Feb 20 (Nakano et
al., 1996). The first published low­resolution spectrum was obtained on
1996 March 8.4 by Duerbeck & Benetti (1996), who found that it most
closely resembled that of an early­F supergiant. However the Balmer
lines were appreciably weaker than in normal F supergiants, whilst
carbon and oxygen appeared to be overabundant. This description cor­
responds precisely with the spectral characteristics of some R Coronae
Borealis (RCrB) stars, although the Balmer lines in V4334Sgr may
have been stronger than in most of the latter. Prompted by the specu­
lation that V4334 Sgr is an example of a ``fast final helium flash object''
(Benetti et al., 1996b, Duerbeck & Pollacco, 1996), the rapid evolu­
tion of V4334Sgr was compared to that of FGSge (van Genderen &
opt—spec.tex; 23/12/2000; 20:38; p.2

3
Gautschy, 1995) and V605 Aql (Seitter, 1987) and with the predictions
of early theoretical models (Iben et al., 1983, Iben, 1984).
2.2. The once and future faint blue star.
The first quantitative analysis of the surface characteristics of V4334 Sgr
was presented by Shetrone & Keane (1997) and based on a high reso­
lution (R = 14 000) spectrum obtained on 1996 April 20, exactly two
months after discovery. Qualitatively, this spectrum also exhibits many
features found in RCrB stars but continues to show much stronger
hydrogen lines. The abundance analysis was carried out using an LTE
spectral synthesis code and Kurucz model atmospheres, leading to
a derivation of the following characteristics: T eff = 7 750 \Sigma 250 K,
log g = 1:0 \Sigma 0:5, [Fe/H]= 0:10 \Sigma 0:22. The hydrogen abundance was
estimated to be ! 20% depleted. The authors were cautious about their
results, doubting the legitimacy of the adopted model atmospheres.
They concluded that, while V4334Sgr might possibly join V854Cen
as a hydrogen­rich RCrB star (Rao & Lambert, 1996), there were im­
portant differences to typical RCrB abundances. However, the authors
took the view that the measurements were acceptably consistent with
the evolution of a final helium flash object -- a faint blue star that
evolves rapidly to become a red giant and will one day contract to
become a faint blue star once more.
2.3. A stellar endgame.
This view was also reflected in a paper by Asplund et al. (1997) in which
high­resolution optical spectra (R ¸ 30 000) obtained on 1996 May 5,6
and October 7 were found to show a 0.7 dex decrease in surface hydro­
gen abundance and 600K decrease in T eff over a five month interval.
These changes were accompanied by an increase of Li and s­process
elements Sr, Y and Zr. Asplund et al. (1997) used hydrogen­deficient
model atmospheres in their analysis. Their conclusion that V4334 Sgr
was 2.3 dex underabundant in H in 1996 May contrasts starkly with
the preliminary result of Shetrone & Keane (1997) (¸ 0:1 dex). An
increase of 0.5 dex in log g in the same five months, corresponding to
a decrease in L by a factor 4 is not consistent with the photometry (or
stellar physics), prompting a suggestion of significant departures from
hydrostatic equilibrium on one (or both) dates of observation.
opt—spec.tex; 23/12/2000; 20:38; p.3

4
2.4. The chemical composition.
A consequence of the excitement generated by the outburst of V4334 Sgr
was the collection of high­resolution spectra by a large number of ob­
servers (the curent authors being no exception). Kipper & Klochkova
(1997) report the analysis of a spectrum obtained on 1996 July 3 with
R ¸ 20 000. Their qualitiative description again gives a spectral type
of F2­3II, resembling the majority of RCrB stars but with stronger
Hff than most of the latter. A quantitative analysis using hydrogen­
deficient model atmospheres found a 2.4 dex underabundance in H, with
other species broadly similar in abundance to those found by Asplund
et al. (1997).
2.5. The rapid evolution: a retrospective.
Following these early publications, a more measured analysis of the
spectral evolution during 1996 and beyond was presented by Asplund
et al. (1999). High­resolution spectra obtained at five epochs (1996
April 20--25, May 5--9, June 4, July 3, and October 7) were analysed in
a consistent manner, demonstrating the evolution of V4334 Sgr in T eff
and L. Asplund et al. (1999) adopted the same assumptions of plane­
parallel geometry, local thermodynamic and hydrostatic equilibrium
and appropriately hydrogen­deficient model atmospheres as Asplund
et al. (1997).
Both the spectroscopic and photometric records (Duerbeck et al.,
1997) showed a linear decrease in T eff from 7 750 \Sigma 300 K on 1996
April 20 to 6 900 \Sigma 300 K on October 7. Duerbeck et al. (1997) showed
this trend to continue into 1997.
Leaving aside, briefly, the question of chemical evolution, a crucial
question concerns the luminosity of V4334 Sgr over the same interval.
The principal spectroscopic proxy for L is surface gravity; Asplund et
al. (1999) found values from log g = 0:25 \Sigma 0:3 in April, via 0:00 \Sigma 0:3 in
May, to 0:50 \Sigma 0:30 in October. Considering the formal errors alone, the
apparently large variation is consistent either with evolution at constant
luminosity or a linear reduction in luminosity by a factor four over the
six month interval. The apparent contradiction with Duerbeck et al.
(1997) who report a luminosity increase of 30% over the same interval
might be resolved by introducing bolometric corrections appropriate to
the peculiar composition of this star.
As noted already (Asplund et al., 1997), the major problem admitted
in this and all previous analyses is the assumption of hydrostatic equi­
librium. Both Asplund et al. (1999) and Duerbeck et al. (1997) arrive
at the same conclusion. Evidence includes a decrease in microturbulent
velocity ( v t ) from near 10.5km s \Gamma1 in April to 6.5 km s \Gamma1 in October.
opt—spec.tex; 23/12/2000; 20:38; p.4

5
From April to May at least, the luminosity is close to or exceeds
the classical Eddington limit. A trivial calculation is instructive. With
M ¸ 0:8 M fi , log g ¸ 0:3, the stellar radius is ¸ 100 R fi . If the star
reached this radius in 200 days or less at a uniform expansion rate,
the surface expansion velocity would be ¸ 2 km s \Gamma1 which approaches
the sound­speed in the atmosphere of an F supergiant. Consequently,
the interpretation of the earliest spectra, at least, and possibly of all
the spectra, should be treated with circumspection. However, in the
absence of suitable models for expanding atmospheres and, in partic­
ular, any diagnostics with which to reconstruct the structure of the
expanding envelope, the use of plane­parallel LTE models in hydrostatic
equilibrium remains the most powerful tool available.
The most remarkable result arising from the work by Asplund et
al. (1997) and Asplund et al. (1999) is the dramatic change in surface
composition. While the abundances of most elements (He, C, N, O, Ne,
Mg, Al, Si, P, S, K, Ca, Fe, Ni and Cu) remained the same throughout
1996, there were significant changes in H (decrease by 1.0 dex), Li
(increase by 0.6 dex), Sc, Zn, Rb and Y (+0.7 to +1.0 dex) and probably
Ti, Cr, Sr and Zr (+0.5 to +0.7 dex). There are good reasons for
supposing the abundance changes to be real, not least the absence of
changes in the majority of elements.
Although constant, the relative surface abundances of non­varying
elements is far from solar. Large overabundances of He, C (1.2 dex), N
(1.1 dex), O (0.5 dex) and Ne (1.4 dex) point to a surface which has
been heavily processed through hydrogen and helium­burning stages.
Overabundances of Li and s­process elements provide further evidence
of past episodes of nucleosynthesis. Asplund et al. (1999) discuss these
at length; apparent corollaries are found in FGSge (Gonzales et al.,
1998) and RCrB stars (Asplund et al., 2000). The overall metallicity
(relative to solar) is harder to assess because of the carbon problem.
With background opacities defined by C/He=10%, the mean metallicity
is only 0.2 dex below solar, but with C/He=1%, it becomes 0.9 dex
below solar.
The evolution framework considers a post­AGB star in which the
outer layers are already enriched in several species, including C,N and
O, and s­process elements, although not all are manifest at the stellar
photosphere. During and after a final helium­shell flash, H­rich material
(protons) and heavy elements are mixed at high temperatures, possibly
spawning a new episode of nucleosynthesis. As the star expands and
cools, convection in the surface layers dredges both AGB and final­
flash products to the stellar surface. Asplund et al. (1999) propose that
this is the process responsible for the changing surface abundances of
V4334Sgr observed in 1996.
opt—spec.tex; 23/12/2000; 20:38; p.5

6
If the onset of convection is responsible for the abundance changes,
the proposed framework raises both questions and problems. One ques­
tion concerns how much dredged­up material was produced in the final
shell flash and how much during preceding shell flashes on the AGB.
A problem concerns the efficiency of convective dredge­up; Bl¨ocker
(2000) shows that for a theoretical post­AGB star undergoing a late
thermal pulse (a final flash when the star is on the constant luminosity
segment of the post­AGB track), dredge­up only starts after the star
reaches minimum effective temperature (¸ 6 700 K). A very late ther­
mal pulse (FF on the white dwarf cooling track) produces stars that
are already H­deficient before they reach maximum radius (Herwig et
al., 1999). The ramifications of these evolution models are discussed
elsewhere (Herwig, 2000), but neither fits the observations of V4334 Sgr
particularly well.
2.6. The development of the molecular absorption
spectrum.
By October 1996, the Swan bands of C 2 had become detectable as T eff
dropped below 7 000 kelvin, and proceeded to strengthen through 1997
and 1998. Asplund et al. (1999) showed how line crowding increased
dramatically over the same period. making continuum placement and
the measurement of accurate abundances increasingly difficult. Strong
CN bands (red and violet) were also seen to develop. Pavlenko et
al. (2000) succeeded in modelling the increasingly complex molecu­
lar spectrum from a grid of hydrogen­deficient and carbon­rich model
atmospheres, and deduced T eff ú 5 500 K in 1997, April. This is ¸
500 K lower than indicated by Duerbeck et al. (1997) from photometry,
and below the linear trend indicated througout 1996. Although the
spectroscopic measurement may be realistic, the model atmosphere
calculations are still in their infancy.
A comparison with the FAST stellar spectral atlas (URL: http://cfa­
www.harvard.edu/¸pberlind/atlas/atframes.html) shows the 1997 April
spectrum of V4334 Sgr to approximately resemble the carbon star HD­
182040, with spectral type C­R2. With T eff ¸ 4 500 K, this assignment
may be too late for V4334 Sgr; a more precise classification is required.
In early 1998, V4334Sgr started to show a large­amplitude decrease
in brightness (Duerbeck et al., 2000) likened, initially, to an RCrB­type
fading event (Liller et al., 1998a, Liller et al., 1998b). The formation
of obscuring dust was evident from an increasing infrared excess, but,
unlike RCrBs, the optical extinction continued to increase, exceeding
11 magnitudes by mid 1999 (Duerbeck et al., 2000) and from which it
opt—spec.tex; 23/12/2000; 20:38; p.6

7
Figure 1. Evolution of the optical spectrum of V4334 Sgr during 1996. The date of
each observation is shown on the left (yy mm dd); all spectra are shown normalized
and offset. Selected aborption lines are identified.
has not recovered. Under these circumstances, high­resolution optical
spectroscopy has all but ceased.
3. The Isaac Newton Telescope Record.
Following the discovery of V4334Sgr on 1996 February 20, one of us
(DLP) began to obtain optical spectroscopy from the La Palma Ob­
opt—spec.tex; 23/12/2000; 20:38; p.7

8
Figure 2. Model spectra with varying hydrogen abundance (nH ) and T eff = 8000 K,
compared with the spectrum of V4334 Sgr on 1996 March 1 (heavy line). The carbon
abundance is nC = 0:01.
servatory, mostly with the intermediate dispersion spectrograph on the
Isaac Newton Telescope but also partly with ISIS on the William Her­
schel Telescope. Various resolutions up to ¸ 5 000 were used, mostly in
the optical red. The record begins on 1996 March 1 (the first spectrum
to be obtained following discovery) and continues with a frequency of
at least one observation per month (Sun permitting) up to the deep
decline of 1999.
The spectral evolution around Hff from 1996 March to 1996 October
is illustrated in Fig. 1. Note in particular the changing ratio of the C ii
and C i line strengths.
Preliminary attempts have been made to simulate the evolution of
the spectrum, with limited success. Model atmospheres with RCrB
mixtures (C/He=1%) computed for analysis of RCrB stars (Asplund
et al., 2000) were kindly made available by Martin Asplund. These
were used as input to Kurucz' spectral synthesis code synthe in the
opt—spec.tex; 23/12/2000; 20:38; p.8

9
Figure 3. As Fig. 2 but with T eff = 7500 K and the spectrum of 1996 May 23.
implementation described by Jeffery et al. (1997). A grid of high­
resolution model spectra was generated with T eff = 5 000 \Gamma 8 000 K,
log g = 0:0 \Gamma 1:5 (cgs) and nH = 0:0001 \Gamma 0:4. These were binned to
match the resolution of the INT spectra (Figs. 2 to 4).
The model spectra do not yet account correctly for the C ii lines,
so the carbon abundance will need to be examined. Significant changes
will be necesssary in order to reconcile the 1996 October spectrum
with the hydrogen abundance ( nH = 0:004) reported by Asplund et al.
(1999). In our models, such a low abundance leads to a line spectrum
very much stronger than observed. We expect that increasing the C
abundance and, hence, the background opacity in the input models
will resolve this problem.
The behaviour of Hff is interesting. In our 1996 March 1 spectrum,
it is too weak compared with any theoretical models. It remains weak
through March (spectra from March 27 and 31 are not sufficiently
resolved), beginning to strengthen around April 1. The central intensity
opt—spec.tex; 23/12/2000; 20:38; p.9

10
Figure 4. As Fig. 2 but with T eff = 6500 K and the spectrum of 1996 Oct 28.
approaches that of the LTE hydrostatic models by July. It is clear that
this line cannot be simulated with equilibrium models during the first
few months of evolution, as already concluded by Asplund et al. (1999).
4. Echelle spectroscopy
A high­resolution spectrum was obtained (by CSJ) with the UCL 'echelle
spectrograph at the Anglo­Australian Telescope on 1996 May 15 with
wavelength coverage 3800 ­ 5050 š A. In parallel with our analysis of
the INT record, we have begun an analysis of this spectrum using an
independent set of hydrogen­deficient model atmospheres. Complete
details of the model atmosphere and spectrum synthesis codes may
be found elsewhere (e.g. Jeffery & Heber, 1992, Jeffery et al., 2001).
For this investigation, new model atmospheres have been computed
on the grid T eff = 6 000(500)8 000(1 000)10 000 K, log g = 0:0(0:5)1:0,
nH = 0:01; 0:05, nC = 0:005; 0:03; 0:10.
opt—spec.tex; 23/12/2000; 20:38; p.10

11
Figure 5. AAT 'echelle spectrum of V4334 Sgr (bold histogram) obtained on 1996
May 15, together with best­fit synthetic spectrum (smooth curve) in the region of
Hfl.
The region of the spectrum around Hfl is shown in Fig. 5, together
with the best fit synthetic spectrum so far obtained from an iterative
ü 2 ­minimization procedure. Because of the large number of degrees of
freedom, the procedure is fragile and improvements will no doubt be
made. Significant problems currently include incompleteness and inac­
curacies in the atomic linelists, where we have considered approximately
2 500 lines in the interval 4 200­4 500 š A.
To derive the basic parameters T eff , log g, nH , nC , and v t , a 5­
dimensional grid of synthetic spectra was computed from the model
atmosphere grid. Best­fit solutions were obtained within this grid for up
to five simultaneous independent parameters, including the rotational
broadening v sin i. Thus the hydrogen abundance was deduced from
opt—spec.tex; 23/12/2000; 20:38; p.11

12
Table I. Provisional atmospheric parameters for V4334 Sgr derived from an AAT
'echelle spectrum obtained on 1996 May 15. Abundances are given as log n + c,
normalized such that
P log ¯n = 12:15. These preliminary values are compared
with May 5--9 results for V4334 Sgr (Asplund et al., 1999) and the Sun (Grevesse
& Sauval, 1998). Values marked `:' are uncertain. Velocities are in km s \Gamma1 .
1996 1996 Sun 1996 1996 Sun
May 15 May 5--9 May 15 May 5--9
T eff / K 8300 7500 H/He 0.07
log g 0.50 0.00 C/He 0.05 0.10
v t 7.50 8.0 v sin i 17
H 10.3 9.7 12.00 Sc 3.7 3.1 3.17
He 11.2 11.4 10.93 Ti 4.3 4.1 5.02
C 10.3 9.7 8.52 V 3.1 4.00
N 7.9 8.9 7.92 Cr 4.3 4.5 5.67
O 7.9: 9.5 8.83 Mn 4.8 5.39
Mg 7.2 6.6 7.58 Fe 6.6 6.4 7.50
Al 6.4 6.6 6.47 Ni 6.5 6.1 6.25
Si 7.3 7.1 7.55 Sr 4.9 4.9: 2.97
P 5.4: 6.2 5.45 Y 3.2 3.3 2.24
S 7.1 6.6 7.33 Zr 2.1 3.0 2.60
Ce 1.0 1.58
models with carbon abundances nC = 0:005; 0:03 and 0.10, giving
nH = 0:07 \Sigma 0:01. The carbon abundance was then deduced from the
best fit in a grid with nH fixed. Note that this takes into account
the overall effect of carbon on the absorption spectrum, including its
contribution to the continuous opacity.
Having established the basic parameters, a new model atmosphere
was computed and used as input to a second ü 2 ­minimization proce­
dure. This computes synthetic spectra in which one or more elemental
abundances and v t are free parameters.
As with all quantitative analyses of spectra in which the dominant
opacity source is not well defined, the overall procedure from model
atmosphere to derived abundances is intensively iterative. The results
presented here (Table I) require further iteration in order to ensure the
correct composition of the input model atmospheres. They are currently
based on only 300 out of a possible 1200 š A of spectrum. The results are
therefore presented as provisional and without error estimates.
There are significant differences to the analysis of spectra obtained
6 to 10 days previously and reported by Asplund et al. (1999). The
opt—spec.tex; 23/12/2000; 20:38; p.12

13
most obvious are in T eff and log g; these can probably be accounted
for by differences in the opacities used in constructing the model at­
mospheres. Our analysis gives higher abundances for both hydrogen
and carbon by a factor four which may be significant. In general the
results for other abundances are similar for both the May 5--9 and May
15 spectra, despite the difference in analysis methods. However we find
that compared with Asplund et al. (1999) i) V4334Sgr is not so nitrogen
rich, ii) other light elements (Mg, Al, Si, P, S) follow the solar values
more closely, iii) V4334 Sgr may be richer in iron­group elements (Sc
-- Ni) and iv) light s­process elements Sr and Y are confirmed to be
overabundant, but not Zr. Since the data, models, and methods are all
completely independent it will eventually be instructive to study the
systematics of these differences in greater detail.
5. Future model atmosphere requirements for V4334 Sgr
The object of constructing model atmospheres for V4334Sgr is to be
able to deduce the physical properties of the star from the observed
spectrum. As described elsewhere in these proceedings, existing models
have already succeeded in describing many of the gross properties of
V4334Sgr during 1996. Consequently we know that model atmospheres
must be valid for a parameter space defined by effective temperature:
T eff ¸ 5 000 \Gamma 9 000 K, surface gravity: log g ! ¸ 1 (cgs), hydrogen abun­
dance: nH ! ¸ 10% (by number) and carbon abundance: nC ? ¸ 1 \Gamma 10%
(by number).
Thus it is clear already that models must be able to treat very
low surface gravities and unusual compositions. To a good approxima­
tion, these are all problems which have been dealt with using classical
assumptions of plane­parallel geometry, local thermodynamic, hydro­
static and radiative equilibrium, and contemporary methods for the
calculation of continuous and line opacities.
As a contribution to the closing discussion, the principal author
was asked to suggest directions future model atmospheres calculations
might take. There are three drivers for this. One is to introduce greater
physical realism, the second is to solve problems that cannot be treated
under classical approximations and the third is to make predictive
models to facilitate tests of stellar evolution theories.
The major problems encountered during existing analyses of the
spectral evolution through 1996 concern the treatment of opacities.
The carbon problem is extensively discussed by Asplund et al. (1999),
but there are signs that it may now be reaching a resolution (Kipper,
private communication). The combination of low effective temperature
opt—spec.tex; 23/12/2000; 20:38; p.13

14
and very low surface gravity together with an unusually carbon­rich
chemistry and forests of molecular lines creates a substantial demand
for molecular data and new methods to include these in spectral syn­
thesis calculations. Pavlenko et al. (2000) are making progress in this
area. However there remain important issues to address.
5.1. Non­local thermodynamic equilibrium
As is common in supergiant atmospheres, the combination of very low
density and high luminosity means that atomic and molecular level
populations may not be fully thermalized. Some effort should be made
to measure the extent to which departures from LTE are important.
5.2. Spherical geometry
A cursory inspection of the geometrical extent of a plane­parallel LTE
model atmosphere for a normal F­supergiant ( T eff =8 000 K, log g=0.5,
nH =0.90) is instructive. Between optical depths Ü = 10 \Gamma3 ; 10 \Gamma1 and
unity lie distances of 59 and 34 R fi respectively. A low­opacity hydrogen­
deficient atmosphere is even more extended. These depths are to be
compared with a stellar radius (M = 0:8 M fi ) of ¸ 100 R fi . Under such
circumstances, the plane­parallel approximation may be untenable.
5.3. Expansion, Rotation, and Turbulence
During 1996, V4334Sgr expanded from white dwarf dimensions to
¸ 100 R fi in approximately one year. If the surface had been propelled
outward at uniform velocity, this would correspond to a surface expan­
sion velocity ¸ 2 km s \Gamma1 . The outer atmosphere would be expanding
at least twice this rate. To first order, the differential expansion of the
atmosphere represents a negligible departure from hydrostatic equi­
librium. For example, there is no evidence of expansion­induced line
asymmetry in the optical 'echelle spectrogram from May 1996.
If the outer layers of a rotating star are rapidly propelled to larger
radii, conservation of angular momentum demands that their rota­
tion velocities decrease as a function of radius, and hence, in the case
of V4334 Sgr, of time. Given its extent, differential rotation will also
affect the radiative layers of the atmosphere. However, by the time
V4334Sgr was discovered, its rotation velocity was already small (we
found v sin i ¸ 17 km s \Gamma1 ) so the effects of rotational deceleration and
differential rotation on the spectrum will be modest.
The sound speed in the atmospheres of F supergiants is ! ¸ 5 km s \Gamma1 .
The boundary between the expanding atmosphere and the local inter­
stellar medium may thus constitute a mild shock front. The supersonic
opt—spec.tex; 23/12/2000; 20:38; p.14

15
dust
1997
photosphere
HeI 10830?
IR/mm
optical/IR
00000
00000
00000
11111
11111
11111
2030?
1996 1997
2000?
a. Extended atmosphere in 2000 b. Evolution through HR diagram
Figure 6. Schematic representations of (a) the extended envelope of V4334 Sgr,
illustrating where different observed features may originate, and and (b) its visible
evolution to low effective temperature, its possible current location obscured by dust
and its possible future evolution.
microturbulent velocity v t ¸ 8 km s \Gamma1 (Asplund et al., 1999) also points
to a turbulent atmosphere, possibly disrupted by local instabilities or
shocks. Other evidence of disruption is provided by evidence for Hff
emission discussed above.
5.4. Dust
During and after 1997, the formation of dust poses a whole new series
of problems for modelling the atmosphere which now consists of several
components. The classical photosphere, where the previously visible op­
tical spectrum would have been formed and now with T eff ¸ 5\Gamma7 000 K,
can no longer be seen (Fig. 6a). In its place, an infrared continuum
formed by condensed dust at much lower temperatures is seen. Super­
imposed on this IR continuum is an emission line due to Hei 10830 š A.
What is the extent of coupling between the original photosphere and
the newly formed dust cloud? Where is the Hei line formed and what
does it tell us about the physics of the extended atmosphere? New
models will have to deal with all of these problems.
6. The future evolution of V4334 Sgr
Both stellar evolution theory and historical precedent suggest that
V4334Sgr will eventually start to contract and once again become first
a hot planetary nebula central star and then a white dwarf. As it heats,
ultraviolet radiation will dissociate, disperse and ionize the dust cloud
now surrounding the star, so that clumps of hydrogen­deficient gas
and dust may be seen within the existing planetary nebula. How long
it will be before that occurs is contentious; theoretical models suggest
opt—spec.tex; 23/12/2000; 20:38; p.15

16
that contraction times for final­flash stars are ¸ 10 times the expansion
times (Bl¨ocker & Sch¨onberner, 1997), so it may be 10--30 years before
V4334Sgr reappears from behind its obscuring cocoon (Fig. 6b).
In the meantime, the only data which tells us about the chemical evo­
lution of the stellar surface as V4334 Sgr approached maximum radius
is contained in those optical spectra obtained between 1996 February
and 1998 April. It is essential that this brief record be preserved, and
every effort made to apply the best theoretical models to ascertain how
the stellar surface responded to the flash event.
References
Asplund M., Gustafsson B., Lambert D.L., Rao N.K., 1997. A&A 321, L17
Asplund M., Lambert D.L., Kipper T., Pollacco D., Shetrone M.D., 1999, A&A 343,
507
Asplund M., Gustafsson B., Lambert D.L., Rao N.K., 2000. A&A 353, 287
Benetti S., Duerbeck H.W., Seitter W.C., Harrison T., 1996, IAU Circ., 6325
Bl¨ocker T., Sch¨onberner D., 1997, A&A 324, 991
Bl¨ocker T., 2000, preprint
Duerbeck H.W., Pollacco D., 1996, IAU Circ., 6328
Duerbeck H.W., Benetti S., 1996, ApJ 468, L111
Duerbeck H.W., Benetti S., Gautschy A., et al., 2000, AJ 114, 1657
Duerbeck H.W., Liller W., Sterken C., et al., 2000, AJ 119, 2360
Grevesse N., Sauval A.J., 1998, Space Sci. Rev. 85, 161
Gonzales G., Lambert D.L., Wallerstein G. Kameswara Rao N., Smith V.V.,
McCarthy J.K., 1998, ApJS 114, 133
Herwig F., Bl¨ocker T., Langer N., Driebe T., 1999, A&A 349, L5
Herwig F., 2000, these proceedings
Iben I., Jr., 1984, ApJ 277 333
Iben I., Jr., Kaler J.B., Truran J.W., Renzini A., 1983, ApJ 264, 605
Jeffery C.S., Heber U., 1992, A&A 260, 133
Jeffery C.S., Short C.I., Lester J.B., 1997, CCP7 Newsletter No. 24, 13
Jeffery C.S., Woolf V., Pollacco D., 2001, A&A in preparation.
Kipper T., Klochkova V.G., 1997, A&A 324, L65
Liller W., Duerbeck H.W., van der Meer A., van Genderen A.M., 1998b, IAU Circ.
7049
Liller W., Janson M., Duerbeck H.W., van Genderen A.M., 1998a, IAU Circ. 6825
Nakano S., Benetti S., Duerbeck H.W., 1996, IAU Circ., 6322
Pavlenko Ya.V., Yakovina L.A., Duerbeck H.W., 2000, A&A 354, 229
Rao N.K., Lambert D.L., 1996, ASP Conf., 96, 43
Seitter W.C., 1987, ESO Messenger 50, 14
Shetrone M.D., Keane M., 1998, in '3rd Confrence on Faint Blue Stars', ed. Davis­
Philip A.G., L.Davis Press, Schenectady.
van Genderen A.M., Gautschy A., 1995, A&A 294, 453
opt—spec.tex; 23/12/2000; 20:38; p.16