September 8 2000
Cornelis de Jager (1), Alex Lobel (2), Garik Israelian (3) and
Hans Nieuwenhuijzen (1)
(1) SRON Laboratory for Space Research, Sorbonnelaan 2, 3584 CA
Utrecht, NL
(2) CfA, 60 Garden Street, Cambridge MA, 02138 1516, USA
(3) IAC, Obs. del Teide, via Lactea, E 38200 La Laguna, Spain
WILL HR 8752 BECOME A P CYGNI TYPE STAR?
Abstract: As long as the yellow hypergiant HR8752 has been
observed spectroscopically it has shown erratic and significant
fluctuations in its effective temperature. But an impressive
and hitherto never observed rise in its temperature started
around 1988. Since that time T_eff rose from 4600 K to 7900 K.
Regular further observations are needed to see if and when
this rise will stop, and what will happen thereafter.
The instability is related to to the fact that in its
evolution the star has entered the Yellow Evolutionary Void,
this being a region in the Hertzsprung-Russell diagram where
blueward evolving supergiants are dynamically unstable. In
that region the values of , averaged over the whole
of the star is smaller than the critical value of 4/3, and
the atmospheric values of g_eff are negative.
Already for at least the last 30 years , averaged
over the atmosphere of HR8752 is far below 4/3, while
recently the atmospheric effective acceleration has decreased
to below zero. This star is the first object where stellar
dynamic instability can be studied observationally in great
detail. We hypothize that HR8752 will traverse the Void and
thereafter, entering the "blue" region of dynamic instability,
may become a star like P Cygni.
1. The Yellow Evolutionary Void.
The Yellow Evolutionary Void (Figure 1) is a part of the
Hertzsprung-Russell diagram where evolved supergiants,
moving blueward in the HR-diagram become unstable
(Nieuwenhuijzen and de Jager, 1995; de Jager, 1998). In this
region the atmospheric effective acceleration in the
line-forming region is negative. Moreover, in this region
- and in a larger area of lower temperatures as well - the
atmospheric values of the logarithmic (P,rho) gradient,
Gamma_1, fall below the critical value of 4/3.
There also exists another, slightly less well defined area
of instability, at higher temperatures, where the same two
criteria are fullfilled. We called that area the 'Blue
Instability Region'.
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Fig. 1: The upper part of the Hertzsprung-Russell diagram.
The central line-bordered area is the Yellow Void; the
upper-left bordered area is the Blue Instability Region.
Large dots and circles are hypergiants; small dots are
supergiants. The temperature excursions of IRC+10420, Rho
Cas and HR8752 are shown by horizontal lines. From de Jager
(1988).
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From a determination of masses for well-studied yellow
hypergiants, Nieuwenhuijzen and De Jager (2000) found
that the hypergiant HR8752 is a post-red blueward evolving
supergiant, such in view of its chemical composition and
its low mass. The same applies to the related hypergiant
IRC10420. There seems little doubt that the same applies
to the hypergiant Rho Cas and to the other yellow
hypergiants in the same part of the HR-diagram.
Independently of our studies, Stothers and Chin (1995)
found similar results that agree with ours in broad outline.
They derived the value of , averaged over the
whole star, for a set of models of evolved supergiants,
and found that is smaller than 4/3 in two parts
of the HR-diagram. They called these areas the "first and
second phase of dynamic instability". We note that their
first phase area includes the Yellow Void (actually, the
high temperature borders agree fairly well) but that it
extends to lower temperatures than the Void. That latter
result does not imply a disagreement because the Void was
defined after two criteria: atmospheric Gamma_1 < 4/3 and
negative g_eff values. The area where the first condition
is fulfilled is larger that that where both are satisfied.
Stothers (1999) found that the average value
should be calculated by weighing the local Gamma_1 values
according to the local volume (d(r^3)) and pressure. He
stressed that the average should be taken over the whole
of the star, particularly when the mean value of Gamma_1
is close to 4/3 (examples in Stothers, 1999). Although
this is basically correct, there is the empirical fact
(Nieuwenhuijzen and de Jager, 1995, cf. also de Jager,
1998) that those regions where the atmospheric Gamma_1
< 4/3 coincide reasonably well with those where the stellar
value (as calculated by Stothers and Chin) does so too.
In a study of detailed models of evolved supergiants
Stothers and Chin (2000b, in press) confirmed that yellow
hypergiants are dynamically unstable post-red supergiants.
They also calculated the high-temperature border of the
Yellow Void; it appears to be situated at about 9000 K,
with small uncertainty dependent on the choise of the
convection parameter.
The approach of Stothers and Chin has been criticized
by Glatzel and Kiriakidis (1998; references to other
authors in Stothers, 1999)). The latter remark that a
nonadiabatic correction has to be applied to sigma, the
eigenfrequency of the slowest mode of oscillation. To
this, Stothers (1999; cf. also Stothers and Chin, 1993)
replies that the remark may apply to pulsational
instability, but not to dynamic. Dynamic instability is
a strictly adiabatic phenomenon, as was shown already by
Jeans (1929) and by Baker (1966).
As to the calculation of the local value of Gamma_1 one
of us (Lobel, 1997, p. 97) remarked that its value should
be calculated including microscopic processes such as
thermal and photo-ionisation, radiation pressure, non-LTE
excitation and ionization. This remark naturally applies
particularly to atmospheric regions, where such effects
are more important than in the interior. A paper on this
more complete calculation of Gamma_1 is presently in
preparation (Lobel, 2001). We note that the atmospheric
Gamma_1 values derived by us in the present paper are
already based on the still unpublished extended expression.
2. HR8752, a hypergiant running into instability
HR8752 is a yellow hypergiant. The hypergiant classification
(spectral luminosity type Ia+) signifies that supergiant
criteria such as mass loss and strong turbulence are
spectrally more pronounced than is the case for 'normal'
supergiants (for a discussion of the hypergiant criterion
and earlier references cf. de Jager, 1980, p. 18ff). The
effective temperature of HR8752 has been determined from
spectral data since the years '60. Table 1, based on
Nieuwenhuijzen and de Jager, 2000) lists those T_eff data
that were derived from studies of high-resolution spectra;
we consider these the most reliable ones.
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Table 1: Input data for HR8752. Here, g_K is the Kurucz
g-value, deduced from a comparison of spectral line
profiles with data calculated for Kurucz models; zeta_t
is the microturbulence (km/s).
References: ILS = Israelian et al. (1999); NdJ:
Nieuwenhuijzen and de Jager (2000).
yr and mo
of obs. T_eff log g_K zeta_t ref
_____________________________________________________
1969/09 5250 - 0.5 10 ILS
1973/08 4930 - 1.8 5.3 NdJ
1978/08 5540 0.15 11.3 NdJ
1984/07 4570 - 6 ?? 4.9 NdJ
1995/04 7170 - 0.18 13.2 NdJ
1998/08 7900 1.1 11 ILS
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Figure 2 presents the T_eff data against time. The Figure
includes also temperatures estimated from color
observations (open circles). The hatched areas along the
abscissa are periods for which Smolinski (1989) noted
excessive mass loss. These data present a fairly complete
picture of the life history of this star during the past
half century, although one would wish that more observations
had been taken during that period. It leads to a scenario
in which T_eff decreased around 1970, after a first period
of large mass loss, which was followed by stellar
contraction as one deduces from the higher T_eff. After
the periods of large mass loss around 1980 T_eff decreased
again but since 1987 it has been rising steadily. The
consequent radius of the star (assuming constant bolometric
luminosity) decreased in this period from 900 to 335 solar
radii, which means an average shrinking spreed of 0.8 km/s.
This behaviour shows great similarity to one of the
theoretical models derived by Stothers (1999). His Figure 2
presents the shrinking of of a dynamically unstable and
pulsationally stable star. His model has Log (L/Lo) = 6
and log T_eff = 4. For that model = 1.330.
(But note that the time scale of the model's shrinking is
about one year, ten times smaller that the observed values).
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Fig. 2: Effective temperatures of HR8752 during the past half
century. Filled dots are values derived from high-resolution
spectra and open circles are derived from colors. The hatched
areas along the abscissa are period of enhanced mass loss.
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One wonders how this process will continue. In any case, it
has been agreed during the Armagh Workshop to henceforth
secure one spectrum monthly, in order to obtain detailed
information about the future behaviour of this remarkable
object.
3. The photosphere
For obtaining some information about the possible reasons
for this strong instability we have derived photospheric
models, based on Kurucz models and fitted to the observed
photospheric parameters as given in Table 1. We took a
stellar mass of 18.8 M_o (Nieuwenhuijzen and de Jager,
2000), a luminosity log (LO/L_o) = 5.6, and a rate of mass
loss log(M-dot) = -4.7 (de Jager, 1998). For these models
we have derived by integrating over the
atmosphere, generally between optical depths of 0.001 and
100. We also calculated the various contributions to the
acceleration (Newtonian, wind, turbulence and radiation)
and summed them up to find g_eff. As a rule the Newtonian
and turbulent accelerations are the largest in absolute
numbers. The results are given in Table 2.
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Table 2: The atmospheric value of , (delta-R)/R
and g_eff at three op-tical deepths, for the six sets of
observed photospheric parameters given in Table 1. Here
(delta-R)/R is the fraction of the radius over which the
integration leading to has been made.
________________________________________________________
g_eff at tau_Ross =
..... ..... ......... ..........
data T_eff (delta-R)/R 0.01 0.1 1.5
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69/09 5250 1.153 .15 -.25 -.17 1.82
73/08 4930 1.197 .23 .85 .14 1.34
78/08 5540 1.140 .05 -2.63 -2.26 4.21
87/04 4570 1.151 .14 .10 .11 .98
95/04 7170 1.066 .24 .20 .31 5.81
98/08 7895 1.168 .02 -10.4 -7.76 18.46
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While appears to be far below 4/3 for all dates of
observations, the g_eff value in the outer part of the
photosphere was negative at three instants. The first
occurred in 1969, thereafter in 1978 and again in 1998.
It is perhaps not fortuitous that the first two periods of
enhanced mass loss occurred in 1970 and in 1979-1983, both
times after the periods during which the upper-atmospheric
acceleration was negative. Following that line one might
speculate that soon after 1998 one might again have met a
period of enhanced mass loss, followed by a downfall of
T_eff to values below 5000. This has yet to be seen, dependent
on spectra taken since 1998. Much has to be hoped for from
new spectral observations.
4. Speculations on the possible further evolution of HR8752.
What follows are speculations.
Sooner or later, after having bounced various times against
the border of the Yellow Void, the star may have lost that
much of his outer envelope that it will be possible to
'jump over' the Void to arrive in the region of higher
temperature, above 9000 K. (We do not yet have reliable
estimates how long this 'jumping over' may take). From
there on the initial evolution should be fairly quiet until
the star enters the 'second phase of dynamic instability'
or (in other terms:) the 'Blue Instability Region'. Then it
may become a star like P Cyg.
We think that P Cyg and the other S Dor stars (alternatively
called LBV's) are evolved objects, as follows from the high
atmospheric He/H contents of the envelopes of well-studied
S Dor's (Stothers and Chin, 2000b; for a further discussion
of P Cyg in that connection, cf. de Jager, 2001). during the
next dynamically unstable stage HR8752 might therefore be an
S Dor star, like P Cyg. Let us note that these ideas are also
found in a recent paper by Stothers and Chin (2000b).
If this speculation is correct then we may consider the yellow
hypergiants precursors of S Dor stars. The evolutionary scenario
might then be: main sequence O supergiant (mass about 60 solar)
-- red supergiant -- yellow hypergiant star (mass about 20
solar) -- S Dor star -- WR star or supernova.
Acknowledgment: Thanks are due to Dr R. Stothers for
enlightening discussions and useful information.
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