ee a
in interstellar space, but we shall not discuss them. Interstellar absorption lines
can be distinguished from stellar ab-
2.0-
.
T
4
i
t
T
i
Theoretical Spectra from Models
t
When the first model atmospheres
were constructed, the radiation-block-
sorption lines by the fact that, in a
multiplet, only the component that
arises from the ground state is observed. The dilute radiation and low
particle density in interstellar space
cannot excite atoms and ions even by
0.01 ev.
ing effects of the strong stellar lines
in the ultraviolet spectral region were
ignored. These models, for stars of
types O to B2, predicted a rather
bright continuous spectrum in the ultraviolet spectral region (Fig. 1). Even
so, it may be seen that only stars of
“
LOR
-
=
aad
In the case of normal dwarf or mainsequence stars, the geometric extent of
the layers through which the line spectrum is formed is smail in comparison
to the radius of the star. Consequently
it is sufficient to consider that the steilar atmosphere consists of plane parallel layers of gas in hydrostatic equilibrium under the local acceleration of
gravity. On the surface of a mainsequence star, gravity is about 104
centimeters per square second. The
composition of the stellar atmosphere
is constant throughout the relevant layers. The theoretical spectra to be presented have been computed for models
having a fractional abundance, by
weight, of hydrogen equal to 0.68;
of helium, 0.32. The fractional abun-
dance by weight of all other elements
is small (1.41 x 10—-+* for Fe, for in-
stance), and it is usually neglected
when a model is constructed. When
the line spectrum is computed, a representative abundance, relative to hydrogen, for each element is adopted
according to the results of abundance
analyses of stellar spectra.
The condition that hydrostatic equilibrium should exist gives a relation between gas pressure and geometrical
depth in the atmosphere. The relation
between temperature and depth in the
atmosphere is found by requiring that
a constant flux of energy flow through
the model. As the radiation field in alt
frequencies from 0 to « passes through
each layer of the model, no energy is
lost or gained, but the energy is re-
distributed in frequency as a result of
the interactions with the atoms and ions
in the atmosphere. In principle this
redistribution may be followed by solution of an equation of radiative transfer appropriate to the physical situation encountered. In practice these interactions
between
atoms,
ions,
and
radiation are represented in a somewhat schematic manner that is complex enough to describe the major
1274
spectral types O to B4 will produce a
-
Models of Stellar Atmospheres
=t
a
5
©.0}-
E
4
2
a
Zz
=z
=
[ |,
S000A 2500A
o
!
2
i]
4
4
|. 3
250A
1
6
1.
8
{
wave number (2!)
WwW
|
TA
!
count; only O-type stars will produce
f
2
'|4
Fig. 1. The continuous spectrum of OB
stars, predicted without attention to the
blocking of radiation by the ultraviolet
lines. The unit of flux is 10° erg per
square
centimeter
frequency interval.
per
second
per
unit
simple enough for expeditious handling
by a large computer.
Preliminary studies have indicated
that only stars classified, according to
empirically selected spectroscopic criteria, types O or B may be expected
to produce an ultraviolet flux of energy comparable to that in the normally
observed spectral region; they are
among the hottest known, Consequent-
ly the results we present have been
calculated with equations suitable for
atmospheres in which the electron
temperature varies between 8000° and
60,000°K.
brief,
the
monochromatic
flux
emerging from the stellar surface has
been calculated by use of the MilneEddington transfer equation. This equation represents the postulates that the
radiation is removed from the beam
by absorption in the continua of H,
H-, He I, and He II and in lines,
and as a result of coherent isotropic
scattering by electrons; and that energy
is returned to the beam by reemission,
as though the gas were in thermodynamic equilibrium at the local elec-
tron temperature, and as a result of
coherent isotropic
a significant flux of energy at wavelengths shorter than the Lyman limit.
A few models have been constructed
that take into account the line blanketing (3). An example of the resultant
changes in the overall intensity distribution of the emergent spectrum ap-
trends of the processes that occur but
In
greater flux between 3000 and 911.6
A than they produce in the spectral
region observed with ground-based instruments (2). The predicted ultraviolet
fluxes below 1500 A will be reduced
considerably when the absorption by
the ultraviolet lines is taken into ac-
scattering by the
electrons. The methods of constructing
model stellar atmospheres and of computing the line and continuous spectrum have been described (J).
pears in Fig. 2; both models shown
may be classified type B1.5 according
to the size of the Balmer jump. For
main-sequence B-type stars a singlevalued empirical relation exists between
spectral type and the intensity jump
at the Balmer limit of hydrogen; since
this relation is rather insensitive to
gravity and to the electron pressure
in the atmosphere, it may be used to
obtain a first approximation of the
equivalent spectral type of a model
atmosphere. In practice, spectral types
are assigned to stars according to the
relative intensity of a few empirically
selected strong absorption lines.
Including the strong lines in the procedure for constructing the model is
physically more correct than ignoring
them. One result is that the effective
temperature is reduced by about 10
percent from its value in an unblanket-
ed model having the same Balmer jump
and thus nominal spectral type. The
temperature-pressure structure is not
significantly changed in the deeper layers of a blanketed model from that in
an unblanketed model of the same
spectral type. However, in the extreme
outer layers of a blanketed model, the
temperature for a given value of the
pressure is lowered from its value in
an unblanketed model. This difference
between models having the same nomi-
nal spectral type will be important only
for interpretation of lines so strong
that they are formed effectively in the
SCIENCE, VOL. 158