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THEORETICAL STUDIES OF THE RS CANUM
cH-168549) theoretical STUDIES OF THE
IS JeHATICORUM STARS Final Report, 1
BS CANUH -QQ 1 /nplawate Oniv.)
Jan. 1980 - 31 Dec. 1981 (Delaware
49 p HC A03/HF A01
H 82- 191 16
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
Period: January 1, 1980 - December 31, 1981
Principal Investigator: Dermott J. Mullan
Bartol Research Foundation of The Franklin Institute
University of Delaware, Newark, Delaware 19711
Submitted: February 23, 1982
I. INTRODUCTION AND SUMMARY
The aim of this work has been to improve our theoretical
understanding of activity in RS CVn stars. Specifically, we set
out to develop models for chromospheric structure, and to examine
the role of magnetic fields both in the photosphere as well as in
the chromosphere and upper atmosphere. As an extension of the
work on RS CVn stars, we also wished to examine the case of the
T Tau stars from the same points of view.
In the course of the work done under this grant, we have
made significant progress in using the properties of magnetic
field loops to unify our understanding of atmospheric structure
in RS CVn stars. However, the concepts developed in the case of
these stars now appear to be applicable over a much broader
region of the HR diagram. The key to our new understanding is
the absence of stable magnetic loops in the atmospheres of late-
type giant stars. This is a feature for which our experience
with the solar atmosphere did not prepare us well. If our new
understanding is correct (and we will bring together a broad
diversity of observational facts to support it, see below),
then the atmospheres of RS CVn active components are qualitatively
distinct from the solar atmosphere . This conclusion has an
important bearing on research into the broad area of "solar-
stellar connections": although detailed knowledge of solar
physics and phenomena undoubtedly helps in understanding activity
in certain types of stars (e.g. main sequence G,K, and M stars),
it will be important to resist the temptation to apply all "solar
concepts" universally across the HR diagram.
II. CHROMOSPHERIC MODELS
We have developed a chromospheric modelling code and
applied it to calculate flux profiles of H„ , Hq, and H,, in
stars which lie in the region of the HR diagram occupied by
RS CVn secondaries. The aim is to undertake first of all a
systematic study of Balmer line profiles in order to determine
their usefulness as chromosph-sri c diagnostics in these stars.
Our work has consisted of three parts: (a) code development
for use at Bartol ; (b) specific application to A Andromedae;
and (c) computing a grid of chromospheric models which can serve
not only to interpret RS CVn Balmer Line profiles, but also in a
broader context of understanding the empirical relationship
which is known to exist between the width of H-^ and stellar
1 urn i nos i ty .
(a) Code development
During my stay at Sacramento Peak Observatory in 1978, I
had collaborated with Dr. L. E. Cram in developing a non-LTE
chromospheric code for a six-level hydrogen atom. At that time,
the main interest was to calculate Balmer line profiles in red
dwarfs. The code begins by specifying a photospheric model
from the literature. The highest point in the published model
is taken to be the temperature minimum in the atmosphere, and
we superpose on top of that photosphere a rise in temperature
upwards into the chromosphere. The temperature is supposed to
rise to a value of T (typical of the "top" of the chromosphere)
at a mass loading m_. Usually, T is taken to be 8000 K, since
at that temperature, hydrogen is beginning to ionize appreciably
in the atmosphere, and it becomes difficult for the chromosphere
to keep itself cool in the presence of mechanical energy depos-
ition (whose source we do not specify). Above T^, the tempera-
ture is assumed to rise very rapidly, typically reaching 2 x 10 K
in an interval of only 0.25 in log m. The temperature structure
is taken to be linear in log m between m^. and the temperature
To start the code, a value is chosen for and T^., with
a given photospheric model, An approximate evaluation of the
non-LTE departure coefficients for the two lowest levels of
the hydrogen atom is then used in order to calculate a prelim-
inary solution of the hydrostatic equilibrium chromosphere.
This serves as input for the main program which solves the
radiative transfer (R.T.) problem for a hydrogen atom with
five bound levels plus continuum. In this code, we solve
explicitly for the first three Balmer lines, and for the first
three continua of the hydrogen atom. Radiation temperatures
are assigned to other transitions and continua, except that the
lyman lines are taken to be in detailed balance. No microtur-
bulence is included? these models are strictly static.
Our solutions for red dwarfs had shown that in such cool
stars, essentially no contribution to Hct came from the photo-
sphere. However, this is no longer the case in the stars of
interest to us here. In our present work, there are roughly
comparable contributions from photosphere and chromosphere, at
least in the hotter stars. This requires us to choose our
temperature grid in the chromosphere with some care in order
to avoid convergence problems. As with the red dwarfs, our
code contains an inner iteration (for the RT solution) and an
outer iteration (for hydrostatic equilibrium), because we are
dealing with the principal atmospheric constituent (hydrogen),
and therefore changes in level population which arise from one
converged RT solution to the next can have a serious impact on
the hydrostatic equilibrium. (Such an outer iteration does not
enter into RT calculations of minor species, such as Mg or Ca.)
Once the main RT convergence has satisfied also hydro-
static equilibrium, we then use the converged model as input
to a third program for calculation of detailed flux profiles of
the Balmer lines for purposes of comparison with observations.
Examples of line profiles from some of our converged models
are shown in the Figure l(a)-(f).
The programs were developed first at Sacramento Peak, and
it seemed at first advisable to attempt to convert them to the
Delaware machine for use at Bartol . However, all attempts to
convert the large RT code failed. I therefore submitted a
proposal to Sacramento Peak Observatory requesting time on their
PE-3242 machine, which became accessible for remote job entry
via a dial-up in June 1981, I was granted about 100 hours of
CPU time, and most of the results to be reported here were
obtained in this mode of operation.
(b) X Andromedae: Large Macroturbulence
B. W. Bopp supplied us with four high precision profiles
of Ha in X And, taken at various epochs. The observed line
profiles are broad, and slightly (few %) asymmetric. This star
is especially suitable for study because it is viewed almost
pole on to its orbit, and so rotational broadening can safely
be excluded when we analyze line profiles.
With T =8000 K, we computed several models with log m.
ranging from to -4. as m_ increases, the absorption feature
at Ha deepens and becomes slightly broader at first. But then
emission begins to fill in the central regions of the line, and
eventually the absorption disappears. Thus, there is a maximum
possible broadening of the line in absorption. (We note that
it is because Ha responds in this significant manner to changes
in ni that the Ha profiles can serve as a diagnostic of chromo-
spheric conditions in these stars.)
Significantly, all four of Bopp's profiles were much
broader (by at least 50?5) than we could achieve at maximum
absorption strength. Since rotation can be excluded, we tried
to broaden the line by macroturbulence. We then found that
within + 2 A of line center, we could fit the observed line
profiles with surprisingly high precision (+2^), if we used
a macroturbul ent broadening parameter, ?, in the range 30-40
km/sec (see Figure 2). (We assumed a Gaussian distribution of
macroturbul ent velocities.) These velocities seem rather high,
and yet the goodness of fit to the observed profiles suggest
that they are meaningful.
A different approach to broadening the line is to consider
higher pressure chromospheres (i.e. move m to deeper layers).
However, in this case, in order to prevent Ha from going
strongly into emission, we need to reduce T^ to 6500 K. This
was the value used by Baliunas et al . (1979) in deriving a
previous high pressure model of A And, and they claimed they
could fit the line observed by Kraft et al . (1964) for this
star within 10% as regards central intensity and half width.
(However, they did not show an illustration of how good the fit
was to the profile as a whole.) There appears to be no physical
reason for having T^=6500 K, unless the mechanical energy
deposition rate suddenly increases rapidly above those tempera-
tures. (As mentioned above, 8000 K is more reasonable physically
because, with a uniform deposition of mechanical energy, hydrogen
will become more than 50% ionized at typically 8000 K.) Never-
theless, for completeness, we also tried a model with T =6500 K,
and found that indeed, a high pressure model could be calculated
which fitted the observed profiles fairly well, (Not as well,
however, as before: now the precision of fit was only +10% (see
Figure 2)). Thus, in these models, there is no need to intro-
duce macroturbul ent broadening. Our best fits for the X And
profiles turned out to be models with pressures at the top of
the chromosphere, p^, about 0.056 dyn/cm in the low pressure
case (including ?=30-40 km/sec), and p =0.4 dyn/cm in the high
Gan we decide on some other basis between these models?
It turned out, after our calculations were finished, that the
answer may be yes. Certain spectral lines in the UV have the
property that their emission strength ratios are sensitive to
densities in the upper chromosphere and transition region (TR).
It is true that these line ratios are quite difficult to inter-
pret in terms of absolute densities in the chromospheres, but
3 differential comparison of the line intensity ratios in two
stars ought to be quite reliable as an indicator of density in
one of the stars relative to the other. Just such a differential
comparison has recently been completed by Ayres et al. (1982)
for the stars XAnd and a Cen B. For the latter object, a rather
reliable model chromosphere already exists, based on intensities
and profiles of many lines in UV and visible portions of the
spectrum. From the differential comparison, Ayres et al . con-
cluded that p_ in A And probably lies in the range 0.05-0.09
dyn/cm . Our low pressure model, with large ?, lies precisely
in this range, whereas the high pressure model appears to be
excluded (see Mullan and Cram, 1982).
Two other recent studies have appeared in which large
macroturbul ent velocities (45-100 km/sec) were reported in T Tau
stars (Herbig and Scderblom, 1981; Ulrich and Wood, 1981).
The activity in RS CVn itself was first described as "T Tau-like"
(Hall, 1972) and in fact, there may be a close relationship
between T Tau stars and RS CVn stars (see section IV below).
Hence, our conclusion of large macroturbulence in the atmosphere
of an RS CVn star may be less surprising than we first thought.
Moreover, the fact that macroscopical ly large elements move
rapidly through RS CVn atmospheres had been discussed previously
by Weiler (1978) in terms of discrete structures ("prominences")
in the Mg II k line profiles. The "prominences" in Weiler's
data must have been large indeed, since their emission strengths
were at times comparable to the integrated emission from the
rest of the visible disk of the star. Moreover, the "prominences
which he observed were moving at even higher speeds (up to 250
km/sec) than the speeds which we are proposing here.
So we need to confront the basic question: what source
exists for this striking macroturbulence in RS CVn atmospheres?
The work which we have been doing on mass loss (see below)
suggests one possible explanation. We shall argue that the
macroturbul ent "elements" are unstable magnetic flux loops .
We regard the unifying role played by such unstable flux loops
in interpreting a variety of observational data in late-type
giants as the most important conclusion to emerge from the work
of this grant.
(c) Grid of chromospheric models: Ha Width-Luminosity Relation (WLR).
For our grid, we used photospheric models as follows:
T(IO^K), log g = 4,4; 4.3; 4,2; 5,3; 5.2; 6,4; 6.3; 6,2.
For each photospheric model, we have calculated 4 chromospheric
models with and log m„ values as follows: 6500 K, -6;
6500 K, -4; 7500 K, -4; 7500 K, -6. This represents an attempt
to span both "high pressure" and "low pressure" models in our
grid. Examples of Ha profiles at some of the points in our
grid are shown in the Figure 1.
It will now become possible to apply these profiles to
interpret observed Ha profiles in RS CVn stars. However, a
more immediate question can also be addressed with our results,
and this has an important bearing on the overall results of
our work, because it stresses once again the importance of
velocity fields in late-type stars, and the use of Ha as a
diagnostic of chromospheric velocity fields.
The observational relationship between width of Ha and
the stellar luminosity was first pointed out by Kraft et al .
(1964), and verified by LoPresto (1971). The relationship can
be written approximately in the form (where H = half width in A).
log H -0.047 + const (1)
over a range of brighter than about 0 or -2. It is
important to note that the relationship (1) does not extend to
less liiminous stars, nor to M giants and supergiants, but seems
to work only for luminous G and K giants and supergiants.
For G and K stars fainter than the above limit, a separate
width-luminosity relationship (WL%) seems to hold (Kraft et al.,
1964). Part of the difference is that damping wings are
beginning to become noticeable in G dwarfs, and this prevents a
reliable measurement nf the true half-width of the absorption
Now, for our models with = 6000 K, log g = 4 corresponds
to My + 4 (using Iben's tracks, 1 967); while log g = 2 model
corresponds to My -3. Hence, between log g = 4 and 2, equation
(1) suggests that H should increase by a factor of about 2.1.
Results from our models are shown in the Table.
H = Half-width of Ha in chromospheric models (Tg=6000 K)
Our models certainly do not behave in the way the observations
indicate: in no case do we find Ha increasing in width by a
factor of 2,1 between log g = 4 and log g = 2. It is true that
there may be systematic variations of m with gravity (Kelch
et al . , 1978), but these are not sufficient to alter the ratios
of H(2)/H(4) to a value as large as 2.1. A similar conclusion
emerges from our models with T^ = 4000 K. We cannot explain
the empirical WLR by our static chromospheres, by, e.g. varying
the depth of the chromosphere (i.e. m^,). This conclusion is in
striking contrast to the explanation which Ayres (1979) has
proposed for the WLR in Ca K emission: there, the WLR is due
to systematic effects in m_, rather than in any velocity-related
Our conclusion therefore seems to be that depth of the
chromosphere is not the controlling influence in the Ha WLR.
What else can be responsible then, other than velocity fields
in the chromosphere? In this regard, the success which we had
in using macroturbulence in RS CVn stars comes to mind, and we
wonder about applicability of macroturbulence over more general
areas of the HR diagram (such as is covered by the sample of
Kraft et al.). In this cnnection, it is worth noting a further
important difference between the WLR in Ca K and the WLR in Ha:
the former applies essentially in a single-valued way over the
entire range of whereas the latter does not. Kraft et al.
point out that the linear relationship in (1) above applies only
to brighter stars, and a different relationship apparently
holds for fainter stars. The break between the two separate
relationships occurs close to 0 or -2. Interestingly,
values of macroturbulence also show a distinct break at almost
the same value of the luminosity (Smith and Dominy, 1979). At
lower luminosities, c is small for photospheric lines, while
for higher luminosities, there is an almost discontinuous jump
to larger values of c. Now, there seems tobearather close link
between velocity fields in the photospheres and chromospheres
of late-type stars (Imhoff, 1977), and so we are led to suspect
that the jump seen by Smith and Dominy 1n the photospheric
velocity fields may be related to the discontinuity 1n the MLR
reported many years pr&vlously by Kraft et al . , 1,e. a discon-
tinuity In a chromospheric velocity parameter.
Me are led to the conclusion therefore that Ha profiles
in late-type giants may serve as useful diagnostics of chromo-
spheric macro-velocity fields.
ni. MAGNETIC ACTIVITY AND MASS LOSS
Mhen we started work on this grant, it had just been
discovered from lUE and Einstein data that rapid mass loss in
cool giants sets In across a certain boundary line in the HR
diagram, which also serves to separate stars with detectable
steady X-rays from those with no detectable steady X-rays.
During the course of our work in the last two years, It has
emerged that this boundary also serves to segregate stars accord-
ing to other criteria as well. Among these, v/e wish to draw
particular attention to C-13 richness in the atmosphere (indica-
tive of dredge-up processes from deep inside the star), and the
behavior of the He 10830 A line. Thus, the mass-loss boundary
which we (Stencel and Mullan, 1980) discovered in the HR
diagram, has turned out to be an intensely interesting area
for research in several areas of stellar astrophysics.
The feature which had drawn my attention originally to the
RS CVn stars was that the mass loss boundary passed through the
sub-giants at spectral types KO-Kl . Now, it had been known for
many years (without any explanation for the fact) that active
secondary stars in many RS CVn systems were subgiants of just
these spectral classes (Popper, 1970). This suggested
to us a possible connection between rapid mass loss in cool
giants and activity. As we shall describe here, this suggestion
has turned out to be a fruitful area for research.
(i) Non-thermally driven mass loss
It is important that mass loss becomes rapid among just
those giant stars where the X-ray flux (time-averaged) becomes
too weak to be detected by Einstein. This forces us to conclude
that thermal pressure is not responsible for driving mass loss
in late-type stars. Parker's concept of a steady, spherically
symmetric wind, with thermal conduction dominating in the energy
transport, would lead one to predict that mass-loss rate is
very sensitive to coronal temperature: if the temperature drops
noticeably (as it appears to do, when one observes giants of
later and later spectral types), then, if anything, the mass
loss rate ought to be dramatically reduced in going to later
spectral types (other things being equal). Precisely the opposite
behavior, however, is indicated by the observations. A non-
thermal source of the wind must be. identi f i ed .
During the first month of the grant period, I decided to
examine the scenario which is shown in Figure 3. Consider a
magnetic loop emerging at a stellar surface (due, e.g. to dynamo
activity in the sub-surface gas, which is convective in all late-
type giants, and therefore highly conducive to dynamo activity).
The way in which such a loop will evolve depends on the proper-
ties of both the loop itself (its length, magnetic flux, etc) as
well as the properties of the ambient atmosphere into which it
emerges. Under certain conditions, it will certainly be possible
for such a loop to find a static equilibrium in the atmosphere,
in which case, we are no longer interested in the loop. However,
it is also possible for the loop to become unstable, e.g. to
a ballooning instability (Low, 1981). In that case, the loop
will become greatly distended upwards. Pinching near the base
will help to drive magnetic reconnection there, and ultimately a
bubble’ of material will be severed from the star, and ejected
as a mass loss "event".
When I presented this concept at the first Cambridge Cool
Star workshop. Dr. I. A. Ahmad pointed out that there was already
some solar evidence for this type of mass loss process. He and
I therefore began a collaborative study of the non-thermal
sources of the solar wind.
(ii) Solar wind: magnetic driving?
Skylab data have demonstrated conclusively that the Parker
concept for the solar wind is definitely inadequate: the wind is
not steady, not spherically symmetric, and certainly is not
fastest where the temperatures were highest (coronal holes are
cool). Neither can the energy fluxes in the high speed streams
be provided by conduction: the conductive energy flux in
coronal holes is too small to provide the kinetic energy flux
in the streams emerging from the holes. Additional, non-thermal
energy is required to drive the solar wind (cf. Brueckner et al . ,
Ahmad and Webb (1978) studied X-ray images from Skylab, and
examined X-ray bright points (XBP) at the bases of plumes in the
solar polar coronal holes. They found that the plumes are the
sites of upward flowing material, with substantial mass flux.
In fact, taking into account the total number of XBP in the polar
holes (there are typically 5-10 XBP (plumes) per polar hole),
they showed that the mass flux was sufficient to explain the
entire mass flux in the solar wind. According to Ahmad and Webb,
then, the solar wind comes from a small number of discrete
sources, any one of which lasts only a relatively short time
(less than 1 day, typically), Hence, the solar wind is intrinsi-
cally unsteady on a time scale of order one day, and is expected
to fluctuate in mass flux by at least 20-305S (assuming a total
number, of 10-20 "sources" which evolve independently). Statis-
tical confirmation of their hypothesis has been provided recently
(during the period of this grant) by Davis (1980), who found a
good positive correlation between numbers of X-ray bright points
in coronal holes and the mass flux in the solar wind.
This led me to consider the scenario in Figure 3 in more
detail in collaboration with Ahmad. We were led to consider
a magnetic driver for the mass loss events because (i) XBP are
known to be wel 1 -correl ated with bipolar emerging magnetic
flux loops, and (ii) the fact that they are bright in .X-rays
indicates that energetic processes are already at work in those
magnetic loops, presumably related to releasing some magnetic
energy in the form of heat. It seemed to us natural to consider
tapping some of this released magnetic energy in the form of
mass loss. Since reconnection had already bt^en discussed as a
possible source of the energy release in XBP (Parker, 1975;
Habbal and Withbroe, 1981), and it is well-known that magnetic
reconnection leads to ejection of high speed flows (Vasyliunas,
1975), it seemed natural to consider the reconnection process
in the evolution shown in Figure 3 as a source of energy for
mass ejection. We were able to show that conditions in a loop
are capable of leading to a ballorvis.|[ 1drt>t:il1ty to start with,
and so the upward distending proye>f^^i^ with what
can happen in the solar atmosphere. derived time scales
and mass ejection rates, as well as for dissolution of
magnetic bubbles, which were all consi'^ten. with solar wind
data (Mullan and Ahmad, 1982). At presont, the most important
aspect of the scenario which requires further research, is just how a
loop evolves in a stellar corona subject to a ballooning instability.
This is a complicated dynamical problem, rev, ing numerical MHD
modelling. However, it is of sufficiently tj;sneral interest for
the mass loss process from all late-type stars (see below), that
it requires detailed attention. The post-doctoral fellow who
was hired under this grant (Dr. Wayne Waldron), has been using his
plasma physics and astrophysics backgrounds to construct a 2-D
MHD code to examine this question.
The major conclusion which has emerged from the work with
Ahmad has been the radical re-appraisal to which we have been
led for the source(s) of the solar wind. According to this
scenario, the sun loses mass in a series of discrete events,
each one of which is accompanied by release of sufficient energy
to cause local X-ray brightening. Since release of magnetic
energy is traditionally considered as the most likely candidate
for "magnetic activity" of all kinds, we have here an intimate
connection between activity and mass loss . It was precisely
such a connection which led us to embark on RS CVn studies, and
so the implications of applying what we have learned in the solar
case to the stellar case are obvious,
(Hi) Solar and stellar coronaej essential distinctions
The key to the scenario for solar mass loss described above is
the ballooning instability. It is crucial to note that in the
sun, not all magnetic loops are subject to such an instability.
Quite the contrary. When a new loop emerges into the solar
atmosphere from beneath the surface, it is more likely to enter
a long-lived phase of relative stability; closed, quiescent loops
are observed to emit X-rays at an essentially unchanging level
for days on end in the sun. This is a very important point which
our long familiarity with the sun may cause us to overlook.
Evidently, the footpoints of a loop are pushed around by the
constantly changing convective turbulence near the photosphere,
and so in strictness, a magnetic loop evolves according to the
MHD equations in time. And yet, most loops can apparently find
an almost force-free state, or series of states, through which
they evolve in a quasi-steady manner (tow, 1982). At any given
time, the loops give the appearance of being stable, because the
atmospheric structure is such that they can remain static. It
is in this sense that one is led to the basic concept of "build-
ing blocks" of the solar corona (Vaiana and Rosner, 1978), i.e.
individual loops which remain in existence for long periods of
time, and contain essentially all of the coronal emission in
X-rays. The term "building block" itself carries a basic
connotation of a stable structure. However, when we discuss
other stars, it will not be appropriate to carry over the concept
of "building blocks" for the magnetic loops, unless these stellar
loops can be shown to be stable . The latter is a crucial proviso,
as we shall argue below.
In the sun, the fact that coronal loops can be long-lived
and essentially stable, leads to a conclusion which, although
obvious, is worth making explicitly in view of what we shall
discuss below for other stars; enhanced coronal emission is well
correlated with enhanced chromospheric emission. In contrast, if
corona! loops are not stable, then there is no a priori reason
why chromospheric emission should be positively correlated with
coronal emission. In this regard, the following point must be
stressed: the boundary in the HR diagram where coronal properties
undergo striking alterations (e.g. rapid mass loss, disappearance
of steady X-rays), is not accompanied by any sensible alteration
in the chromospheric emission strengths of the stars (Mullan, 1981;
Mullan and Stencel , 1982). As mentioned above, it is important
to prevent solar prejudices from making us overlook the possibility
that chromospheric and coronal emission in late-type stars need
not be correlated. In fact, just such a lack of correlation has
emerged strikingly from He 10830 work by Zirin (1982). The
strength of He 10830 absorption is a measure of coronal X-ray
flux (because the lower level of the transition is populated via
X-ray processes; cf. Zirin, 1975). This strength has been found
to be well correlated with the strength of Ca K emission (i.e.
chromospheric emission) in G-type stars: our experience with the
sun leads us to find this as no surprise. The surprise comes
with the K and M stars: for these stars, Zirin finds that the
correlation between coronal and chromospheric emissions becomes
very poor, essentially non-existent: suggesting that (in Zirin's
words) "the late stars of relatively high K-line intensity may
indeed have active regions [on their surfaces], but [they]
cannot keep the corona from flying away in the stellar wind".
(iv) Helmet streamer stability: solar corona
Pneuman's (1968) work on helmet streamers provides a con-
venient starting point for analyzing the stability of closed
magnetic loops in the solar corona. Helmet streamers are regions
of closed field lines near their base, with open field lines
surrounding the closed fields. The closed field lines reach out
to a maximum radial extent of r|^, while solar wind can flow out
along the open field lines, passing through a sonic point at a
radial distance of r^ . Pneuman analyzed the steady state case, in
which magnetohydrostatic equilibrium obtains in the close field
region, and a thermally driven wind exists on the open field lines.
Making several simplifying assumptions, in order to keep the dis-
cussion analytic, Pneuman derived a simple relation between r|^
'•h = <2)
I have re-done Pneuman's calculations, relaxing the various sim-
plifying assumptions which he made, in order to determine how
(2) is altered from the simplest case. I have found that the
relationship in (2) holds over a considerably broader range of
conditions than Pneuman assumed, although it is true that the
numerical value of the denominator may need to be increased
somewhat. Nevertheless, to much better than an order of magnitude,
(2) can serve as a useful approximation.
Pneuman found that his steady state situation could exist
only as long as the coronal temperature was less than T„,„. The
numerical value of T_,„ turned out to vary (slowly) with an area
parameter, 8 (= ratio of area of closed field lines to area of
open field lines). Pneuman had no means of deciding on the
correct value of S, because of his simplifications. Over a broad
range in 6, (factor of 10^), he found in the range from 0.8
to 3.6 X 10® K. For T > (once 8 is prescribed), no static
solution of the helmet streamer exists: all field lines presumably
become open. I have tried to make this conclusion more definitive
by collaborating with Dr. R. S. Steinolfson (UC, Irvine), who has
a 2-D MHO code for the study of coronal transients. In this applica-
tion, one starts the code with a dipole magnetic field at the center
of the sun, and then at t=0, impose a Parker-type solar wind flow.
The flow interacts with the field, and vice versa, and eventually
approaches a steady state with some field lines closed, some field
lines open, and the ratio 0 is determined by the steady state solu-
tion, rather than being a free parameter. For low values of T
(coronal temperature), some closed field lines do indeed survive,
and equation (2) is satisfied to better than a factor of 2. More-
over, as T increases, a value is eventually reached (between 4 and
4.5 X 10® K), such that at higher temperatures, the steady state
solution contains no closed field lines above the solar surface.
This is valuable confirmation of the general validity of Pneuman's
(v) Helmet streamer stability: stellar coronae
In the sun, the only way to force a helmet streamer towards
instability is essentially to allow T to increase. However, in
other stars, we can also use the gravity to approach instability.
That is what I have done in an application of Pneuman's results to
the stellar case in general. I used empirical chromospheric
pressures as pressures at the base of the stellar coronae (Kelch
et al . , 1978), and then I assumed the minimum flux coronal concept
(Hearn, 1975). With these, I could ask the question: where in the
HR diagram is the condition r^ = 2r* satisfied? The results are
shown in Figure 4, where I have used Paczynski's (1970) evolution-
ary tracks to convert masses and radii to points on the HR diagram.
The striking result is that r^ = 2 r* along the Mg mass loss
boundary, such that stars which are losing mass rapidly have
r^ < 2 r^, while stars which do not show rapid mass loss, have
Ts > 2 r*.
The significance of this emerges from considering equation
(2). Stars with r^ > 2r* have rj^ > r* , just as the sun does, and
so closed loops (and steady helmet streamers) may exist in stable
conditions in the atmospheres of such stars. Hence, they can be
strong in X-rays, low in mass loss rate, and show good correlation
between coronal and chromospheric emissions. However, if a star
is above the mass loss boundary, it has r^ < r*, i.e. the last
closed field line is inside the star . If dynamo action causes
a new magnetic loop to emerge at the surface of the star, then
the radial extent of that loop already violates the condition
for the last closed field line of a static helmet streamer.
Therefore, in such a star, an emerging loop cannot exist in a
static helmet streamer type of configuration . Hence, no closed
steady loops exist in the atmospheres of such stars. This seems
to explain naturally why X-rays from such stars are at a very low
level. Furthermore, if closed loops cannot be stable, what can
they do when they emerge into the atmosphere? They must evolve
dynamically, and this immedia’ely reminds us of the scenario discussed
above for mass loss in coronal XBP: we expect that dynamical evolu-
tion will enter a ballooning phase, and field loops in late-type
giants will be distended upwards in the atmosphere (cf. Fig. 3(b), (c)).
In this regard, it is important to remark that greatly distended
loops play a major role in interpreting X-ray and lUE data of RS CVn
coronae (Walter et al . , 1980; Swank et al . , 1981: Simon et al . , 1980),
for entirely independent reasons from the ones which we are discussing
here.' And as a support of our finding that the onset of extended cor-
onal loops occurs among subgiants at early K type, we may cite recent evidence
of X-ray eclipses in the RS CVn system AR Lac, consisting of an
early 6 subgiant and an early K subgiant. The details of the X-ray
light curve in the immediate vicinity of both primary and secondary
eclipse in this system are such that the X-ray emission around the
G star must be confined to a thin corona close to the stellar sur-
face, whereas the K subgiant must have an extended corona, reaching
out to radial distances of order 2R(star) (Walter et al., 1981).
This system is therefore particularly interesting in the present
context since it happens to contain one star on one side of MTTL, (see below)
and a second star on the other side of the MTTL, both of which are
in a position to eclipse (at least partially) the other.
What eventually happens to a loop which is balloon unstable?
So far, a definitive answer cannot be given. However, according to
the scenario in Figure 3, magnetic reconnection may ultimately sever
the connection with the stellar surface, and a bubble of material
will be ejected from the star. In this scenario, then, mass loss
among late-type giants is an intrinsically episodic process, with
discrete mass ejection events each time a new flux loop emerges at
the stellar surface. In this view, the Mg mass loss boundary
corresponds to a transition in the overall magnetic topology in
the stellar atmosphere from mainly closed to mainly open . Because
of that, we call this the "Magnetic Topology Transition Locus" (MTTL).
Above MTTL, mass loss is considered to be driven by magnetic reconnec-
tion processes. Since these are generally responsible for magnetic activity
also, we propose that magnetic reconnection in unstable loops provide the causal
link between activity and mass loss which first drew our attention to RS CVn
stars. This is an important point, because if mass loss is being driven by
an energetic process of the kind we propose, then transient (non-thermal ) X-rays
should be observed from time to time in late-type giants. The X-rays may be
hard, depending on how strong the reconnecting magnetic fields are (e.g. in
RS CVn stars). In fact, rather energetic processes must be occurring in RS CVn
atmospheres in order to explain the non-thermal radio outbursts, and the hard
X-rays which seem to set the RS CVn systems apart as an especially powerful
class of active stars: the hard X-rays from RS CVn systems cannot be easily
understood in terms of solar analogies (Garcia et al . , 1980). Thus, we make a
distinction between quasi-steady (thermal) X-rays which may characterize long-
lived loops in solar-like atmospheres, and the intrinsically variable (perhaps
hard, probably non-thermal) X-rays which characterize the mass-ejection events
in cool giants. In this regard, it is worth noting that the hard X-rays in
RS CVn systems are indeed highly variable in time (Swank et al . , 1981).
The fact that a source of transient X-rays exists (in our
scenario) in cool giants from time to time has an important bearing
on the excitation of the He 10830 A line. This line becomes stronger
in absorption, the larger the coronal X-ray flux becomes (Zirin, 1975).
In general, therefore, it is expected that in crossing the boundary
where mass loss becomes rapid, and (steady) X-rays die away, the
He 10830 A absorption should also die away. In a broad sense, that
turns out to be true (Zirin, 1982): He 10830 weakens monotonically in
going from G to K to M stars of all luminosity classes from I to IV
(dwarfs do not show this behavior), at least when one averages over
broad spectral classes. However, Zirin (1982) has noted that in finer
detail, the decline is not monotonic, but shows a peak at K3 among
the giants. He o fers no explanation for the fact, but he also points
out something which has a bearing in the present context: variability
in the profiles (i.e. what Zirin calls "activity") also is most
prominent at K3 among the giants. The puzzle of He 10830 excitation
in cool giants has been discussed in some detail by Simon et a1.
(1982), and they also cannot provide an explanation for why the line
should be so strong in stars where, on average, the X-ray coronal
flux ought to be negligible.
Our scenario provides a natural interpretation: transient
X-rays from mass ejection phenomena excite variable He 10830 absorption,
and the more pronounced the activity, the more pronounced the He
absorption can become. The low photospheric temperatures of late-
type giants have the effect that He 10830 absorption is very sensitive
to coronal X-ray flux (more so than solar).
(vi) Discrete mass ejection
The He 10830 data also provide evidence which has a bearing
on episodic mass ejection. Zirin (1982) has shown that the 10830
line cannot go into emission when seen against a stellar disk without
at the same time violating other observational constraints. There-
fore, when He 10830 appears in emission (which it does from time to
time in some of Zirin's 455 program stars), it must be created in a
detached shell of material around the star. Presumably, the shell
indicates an episode of mass ejection. As many as 4 discrete mass
ejection events can be traced in the records of He 10830 in certain
stars (Zirin, 1982), in the course of 10-15 years. Hence, discrete
mass ejections seem to be rather common events in stars which have
evolved across the MTTL., as our scenario requires.
Unstable magnetic flux loops provide a natural explanation
for macroturbulent line broadenifig in the chromosphere of a late
type star. If an emerging loop were stable, then it would contribute
little or nothing to macroturbulent velocity fields. Therefore, it
is an essential part of the current picture that the magnetic flux
loops in RS CVn stars and late type giants are unstable, moving
upwards rapidly through the stellar chromosphere, with material
draining down along both legs for at least some time during the
evolution. The macroturbulent velocity parameter is, in this scen-
ario, to be interpreted as related to the rise velocity of the
unstable loops. In this regard- the sun provides a useful calibra-
tion: young active regions, where new flux loops are continually
emerging, have been found to be the site of large macroturbulence
(Shine and Linsky, 1973), and the value of the macroturbulence
broadening parameter, t;, in the brightest active regions
(C aj 10 km/sec) agrees quantitatively with the upward velocity
of rising flux loops (Bruzek and Currant, 1977). Older active
regions show much reduced ? (Shine and Linsky, 1973), and in these,
loops are no longer emerging.
In our scenario, the interpretation of line broadening
in a stellar profile in terms of macroturbulent broadening requires
a large number of macroscopi cal ly large elements on the surface of
the star. Recently, various authors have made estimates of the
numbers of loops which are present in the visible atmosphere of
RS CVn stars, using a scaling relation which was originally derived
for static loops in the solar corona (Walter et al . , 1980; Swank
et al . , 1981). These authors have found that the numbers of loops
required on the visible hemisphere to explain the observed X-ray
emission from RS CVn stars are large, 10^-10^. Now, application of
static loop scaling relations cannot be quantitatively accurate if
our scenario of non-static loops holds true. Thus, we cannot
interpret these loop numbers as literally accurate. However, they
are large enough to suggest that even if the condition of static
loops were relaxed, the numbers of loops would still be large.
We are therefore led to propose that the macroturbulent
"elemen<is" which give rise to the large line broadening in X And
and other late-type stars are to be identified with unstable magnetic
flux loops. Each loop would contain an essentially distinct
"chromosphere", shielded by the magnetic field lines from the ambient
medium through which it was passing. Hence, there is no difficulty
with the fact that the macroturbulence velocities which we have
been discussing (30-40 km/sec) are highly supersonic in the chromo-
sphere: the magnetic field will shield the "chromosphere" in the
rising loop from the effects of supersonic turbulent dissipation
in the ambient medium.
If macroturbulence is determined by flux loops, it follows
that the broadening parameter, is intrinsictlly time-dependent.
With a value which depends on the immediate pre-history of flux loop
emergence prior to the time of observation. At times, the number
of loops will be small, in which case, it is expected that a line
profile might break up into separate components, one from each loop.
In fact, the Ca K line profile shows this kind of behavior (Baliunas
and Dupree, 1979): at times it is flat topped (implying large
numbers of rapidly moving macroturbulence elements), and at other
times, a strong central absorption develops, indicating that the
macroturbul ence broadening has dropped to a small value.
The existence of a finite number of loops on the surface also
results in some asymmetry in the line profiles. From purely statis-
tical arguments, we can estimv\te that with 10 -10^ loops on the
visible disk at any one time, the variations due to random changes
in numbers of flux loops are expected to be of order 1-3^. Asym-
metries of just this order are known to occur both in Ca K emission
and in the Ha line profile in X And (Baliunas and Dupree, 1979;
Mullan and Cram, 1982) .
(viii) The magnetic key; RS CVn stars
Our proposal for mass loss in cool giants rests on the
assumption that there are magnetic fields in these stars. Nothing
in the literature, however, forces us to believe unambiguously that
late-type giants and supergiants have magnetic fields on the magni-
tude required to drive rapid mass loss in a series of discrete
reconnection events. On the other hand, it seems rather likely
that magnetic fields will exist in cool giants because of dynamo
action in their convection zones. However, in order to put our
proposal on a firm footing, we need to find a group of stars in
which the proposed mechanism is at wv.rk, and which are known from
other reasons to possess magnetic fields in their atmospheres.
RS CVn active secondaries satisfy this requirement: circular
polarization in their radio emission, and large starspots on their
surfaces, provide strong circumstantial evidence for magnetic
fields. The various pieces of evidence which have been accumulated
in many spectral regions for these systems suggest flaring activity
is in progress. Estimates of current rates of mass loss (Walter
et al , 1978; DeCampli and Baliunas, 1979) seems at first sight to
bf small (few times 10 •^sun^^'^^* However, it is important to
realize that the average rate of mass loss and/or exchange between
components over evolutionary time scales must be much smaller than
this (10“^^ ^sun^’^’^’ Ulrich, 1 977). Hence, the current
mass loss process cannot have been in existence for more than about
]% of the stellar lifetime: i.e. it is a very recent development.
This is consistent with our discovery that active secondary stars
in RS CVn systems lie very close to the mass-loss boundary (as seen
in Mg II h and k; Mullan, 1981).
Thus, all of the ingredients (flaring activity, recent mass
loss, magnetic fields) appear to be present in the RS CVn stars,
and therefore consider these systems as the key to understanding
the relationship between rapid mass loss in cool giants and magnetic
activity. The RS CVn systems even provide evidence for discrete
ejections of mass (Pfeiffer, 1979).
The reason that the RS CVn stars stand out against the back-
ground of all other late-type giant stars is that they have magnetic
fields which are strong enough to make magnetic activity detectable
at Earth. (Membership in a binary probably helps to make the mag-
netic fields strong by means of tidal action; Mullan, 1975). We
propose that other late-type giant stars also have magnetic fields
in their atmosphere, not strong enough in general to produce magnetic
activity at a high enough level to be detectable readily at earth,
but still strong enough to have a dominant dynamic effect on mass
loss from that atmosphere. And although the flaring activity in
these other late-type stars is not as prominent as in RS CVn systems,
nevertheless, evidence is beginning to accumulate which shows that
some activity is indeed in progress in late-type giants (cf.
Wischnewski and Wendker, 1981; Boice et al., 1981; Baliunas et al . ,
1981; Mullan and Stencel , 1982).
Perhaps the most interesting feature to emerge in the dis-
cussion of "boundary lines" in the HR diagram in recent months
involves the heavy isotope of carbon, C'". This isotope is created
by GNO burning inside massive stars. During evolution of these objects
it must presumably be dredged up from oeep within the star if it is
ever to appear in the atmosphere in r“punts which exceed the "normal"
abundance (i.e. the interstellar medium abundance of about 1/89
of C ). There are severe problems with most of the mechanisms which
have been devised so far to explain the required mixing, not only of
C isotopes, but also of other elements (cf, Iben, 1981; Scalo, 1981).
After a long discussion of many possible mixing scenarios, Scalo
(1981) concludes "our understanding of the advanced stages of stellar
evolution is seriously incomplete, a stochastic mixing process is
at work" (Scalo, 1981, p. 104),
It is with this in mind that we draw attention to an impor-
tant feature of C' rich stars: they show a strong preponderance to
lie on the rapid mass loss side of the Mg boundary discovered by
Stencel and Mullan (1980). Thus, in a sample of stars studied by
Lambert and Ries (1981) for C abundance, 18 stars overlap with our
sample of mass loss stars. Of these, 11 show S/L > 1 in our data
(no rapid mass loss),, and 7 show S/L <1. Of the former, 9 have
S/L > 1 in our Mg data (i.e. solar-like atmospheres, no rapid mass
loss), while of the latter, 5 have S/L < 1, while the other 2 have
S/L % 1 . Thus , C richness appears to be rather highly correlated
with rapid mass loss.
How can this be fitted into our scenario of unstable mag-
netic loops? Obviously, the unstable loops are dredging up material
from deep within the star, wherever ^he dynamo action is occurring.
It is believed (Rosner, 1980) that dynamo activity occurs rather
deep inside many stars, namely, beneath the convection zone. In
red giants, this would place the dynamo region certainly deep enough
to have access to CNO-processed material. In fact, magnetic mixing
has already been proposed as an explanation for elemental composition
in one of the stars where mass loss is rapid (Arcturus: Hubbard and
Dearborn, 1980), and Scalo (1981) mentions magnetic fields as a
possible candidate for mixing of elements in peculiar giants in
general. The characteristic of stochasti city required for the mixing
processes (Scalo; quoted above) is obviously well satisfied by a
magnetic loop mechanism, since loops are known to appear at the
surface in a chaotic fashion in time.
IV. T TAURI STARS
I have used empirical estimates of pressures in T Tau
chromospheres (Cram, private communication) to estimate that these
stars lie close to the MTTL, just as active secondaries of RS CVn
stars do. However, there is one important distinction: RS CVn stars
are evolving across the MTTL from left to right (they are older
stars, 10^ years old, on the basis of tidal synchronization;
Mullan, 1981) while T Tau stars are young and are evolving in the
opposite direction. Thus, there seems to be no difficulty in ascrib-
ing high macroturbulence, activity and mass outflow rates in T Tau
stars to the same physical mechanism as in RS CVn stars i.e.
unstable magnetic loops.
The distinction about the direction of evolution, however.
makes for some differences between RS CVn stars and T Tau stars.
For example, C richness ought not to be a characteristic of rapid
mass loss in T Tau stars, according to our' scenario , since, evolution
has not yet been able to proceed through CNO burning in T Tau stars.
Moreover, since the T Tau stars are moving from right to left across
the MTTL, they are moving in the direction of having magnetic loops
become stable (rather than unstable). Hence, we expect that some
loops, rather than breaking away from the star, may evolve outwards
for a time, and then be restrained by the stellar gravity, and become
a stable loop. Then, upward motion would cease, and only material
draining back down along the loop legs would be visible in the spec-
trum, and material would be observed to be falling into the star.
Thus, T Tau stars ought to be characterized by both outflow and
inflow of material, depending on whether the loop is on the unstable
side of MTTL, or on the stable side. If most T Tau stars are on
average above MTTL, then the lack of correlation between chromospheric
and coronal emission reported by several authors (e.g. Walter and
Kuhi, 1981) can be understood in terms of the arguments given
above (section III (iii)).
Unstable emerging magnetic flux loops have emerged as a
unifying factor in our study of RS CVn systems. However, although
the idea is most strongly supported among the RS CVn systems, the idea
appears to have much broader application, namely, it may be appli-
cable to most late-type giants which are losing mass rapidly. We
have been able to use the concept of unstable loops to account for
rapid mass loss, episodic mass loss, flaring activity, high macro-
turbulence in chromospheres , He 10830 A line data (i.e. maximum
strength correlated with maximum activity), and richness
in rapid mass loss stars.
The work which has been done in the course of this grant
has opened up several avenues for future research, avenues which
have an impact on the way in which we will approach not only the
question of mass-loss and activity, but also the '!solar-stel lar
connection" in general.
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Figure 1. Examples of Ha flux profiles from various stellar model
chromospheres. The photospheric model is specified in
the lower left corner. 6 denotes that it is model of
Gingerich (Carbon and Gingerich, 1969), the first three
numbers denote T^^^/IO, and the last three are 100 log g.
The four curves for each photospheric model refer to four
chromospheres, with T , log m. values as follows:
6500, -6; 6500, -4; 7500, -4 ;
7500, -6. In the model with T^^^ =6000 K,
log g = 2.00, thci peculiar behavior in one curve is due
to data drop out during plotting.
Figure 2. Observed and theoretical line profiles of Ha in X And.
Observations refer to 2 of 4 epochs provided to us by
Bopp and Smith (1980). Model 1 is our low pressure
chromosphere, broadening by macroturbulence; Model 2
is a high pressure chromosphere, without turbulence.
The observed profiles have been extracted from the data
of Bopp and Smith within 2A of line center: the observed
line is somewhat asymmetric, and is not completely smooth;
we have chosen the smoother side of line center to
extract the half profiles shown here.
Figure 3. Scenario for magnetically driven mass loss. A new flux
loop emerges at time t^ from beneath the stellar surface,
and balloons upwards. Reconnection near the base even-
tually leads to a severing of the magnetic link with
the star, and a bubble of material is ejected. Each
new flux loop which becomes unstable contributes a new
mass loss episode in this scenario.
Figure 4. Survey of chromospheric velocity fields in the HR
diagram shows a dividing line (VDL=vel oci ty dividing
line) between stars where mass loss is rapid (X) from
those where mass loss rates are small (o) (Data from
Stencel and Mullan, 1980). TDL denotes temperature
dividing line (Linsky and Haisch, 1979; see also Simon
et al., 1982 for further confirmation of the existence
of TDL.) Note that cool coronae set in at essentially
the same place where mass loss becomes rapid. Circled
P's and tt's denote STL (supersonic transition locus;
Mullan, 1978) and MTTL (magnetic topology transition
locus; Mullan, 1981, 1982) according to evolutionary
tracks of Paczynski ( 1 970). Note that MTTL. and VDL
are essentially coincident, i.e. mass loss becomes rapid
in those stars where static closed loops of magnetic
flux can no longer exist.
During the period of this grant, Dr. Wayne Waldron was
appointed as a post-doctoral fellow at Bartol. Dr. Waldron has a
master's degree in Plasma physics from Ohio State University, a
master's degree in plasma physics from University of Wisconsin, and
a Ph.D. in Astrophysics from the University of Wisconsin. His Ph.D.
work was on winds from hot stars, the effects of hot coronae, and
how these affect the radiatively driven winds in these stars. His
work has involved an important new step in analyzing X-rays from
hot stars, for his model allows one to follow the transfer of X-rays
outwards from a base corona through a wind. Thus, he has been
able to include an energy equation to follow how the effects of
recombination and photo- ioni zati on control the temperature structure
of the wind. His detailed knowledge of stellar winds, and also
of MHD effects in plasma physics, make him an ideal person to under-
take the problem described in this report on magnetically driven
mass loss from stellar coronae. He has been working to develop a
2-D MHD code to study the ballooning instability of a flux loop
emerging into a stratified atmosphere.
PAPERS PRESENTED AT MEETINGS:
1. "Non-thermal Stellar Winds in Cool Stars", presented by D. J.
Mullan at Cool Star Workshop, Cambridge, MA, January 31, 1980.
2. "Mass Loss from Warm Giants: Magnetic Effects", presented by
D. J. Mullan, Erice Workshop on Physical Processes in Red
Giants, September 3-13, 1980.
3. "Variable Mass Loss and Magnetic Topology in Cool Giant Stars",
by D. J. Mullan and R. E. Stencel , presented by D. J. MuVlan,
American Astronomical Society Meeting, Calgary, June-July 1981.
4. "Large Maqroturbul ence in the Chromosphere of an RS CVn Star",
by L. E. Cram and D. J. Mullan, presented by D. J. Mullan,
American Astronomical Society Meeting, Calgary, June-July, 1981.
5. "Are discrepant asymmetry red giants necessarily hybrid stars?"
D. J. Mullan and R. E. Stencel , presented at American Astronomical
Society Meeting, Boulder, January 1982.
6. "Discrepant Asymmetry Stars: the Role of Unsteady Magnetic Flux
Loops in the Atmospheres of Late-Type Giant Stars", 0. J. Mullan
and R. E. Stencel, to be presented at "Four Years of lUE",
7. "Static and Non-Static Helmet Streamers in Stellar Atmospheres:
Effects on Mass Loss in Cool Stars", D. J. Mullan, to be presented
at lAU Symposium No. 102,' "Solar and Stellar Magnetic Fields:
Origins and Coronal Effects", Zurich, August 1982.
PAPERS PUBLISHED AND IN PRESS
1. Non-thermal Stellar Winds in Cool Stars, by D. J. Mullan, in
Cool Stars, Stellar Systems, and the Sun , ed. A. K. Dupree,
Smithsonian Ap. Obs. Spec. Rep. #389, p. 189 (1980).
2. Mass Loss from Warm Giants: Magnetic Effects, by D. 0. Mullan,
in Physical Processes in Red Giants , eds . I. Iben and
A. Renzini, (Dordrecht: Reidel), p. 355 (1981).
3. Heating of Chromospheres and Coronae in Cool Stars, by D. J.
Mullan, Irish Astron. 0. 14, 73 (dated 1979; published 1981).
4. Coronal Holes: Mass Loss driven by Magnetic Reconnection, by
D. J. Mullan and I. A. Ahmad, Solar Phys. 75_, 347 (1982).
5. Onset of Rapid Mass Loss in Cool Giant Stars: Magnetic Field
Effects, by D. J. Mullan, Astron. & Astrophys. (in press).
6. Model Chromospheres of RS CVn Stars: Balmer Line Profiles in
Andromedae, by D. 0. Mullan and L. E. Cram, Astron. &
Astrophys. (in press).
7. Caution: High Winds Beyond This Point, by D. J. Mullan,
Astronomy, 10, 74, 1982.
8. Corona-Warm Wind Model for the X-ray Emission from Of Stars
and OB Supergiants, by W. L. Waldron, submitted to Astrophysical
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