Strom, S. E.

English

NASA Technical Reports Server

MODEL ATMOSPHERES FOR RR LYRAE STARS 
S. E. Strom 
July 1968 
(ACCESSION NUMBER) (THRU) 
(CATEGORY) 
Smithsonian Institution 
A st r ophys ical Obse rvato ry 
Cambridge, Massachusetts 021 38 
806 - 1 02 
https://ntrs.nasa.gov/search.jsp?R=19680021962 2020-03-12T10:11:40+00:00Z
MODEL ATMOSPHERES FOR RR LYRAE STARS 
S .  E. Strom 
Smithsonian Astrophysical Observatory and Harvard College Observatory 
Cambridge, Massachusetts 
Re ce ive d 
ABSTRACT 
Model atmospheres have been computed in  the range 6000 5 Teff 5 7500°K 
Convection is found to play a significant 
with 2. 0 5 log g 5 3. 5. 
obtain fo r  stars in  the RR Lyrae gap. 
role in  the influence of the emergent fluxes predicted by these models. Tem- 
perature determinations based on purely radiative models a r e  systematically 
too low by as much as 200" -350"  K; gravity determinations are not affected. 
The method of predicting (B-V), and thus reddening, f rom the strength of 
the Balmer lines is found to give l e s s  than desirable results. 
of line blanketing and departures  f rom LTE on these models is also discussed. 
These parameters  a r e  representative of those that 
The influence 
I. INTRODUCTION 
Oke and Bonsack (1960) and Oke, Giver, and Searle (1962), among others, 
have recently discussed the application of model-atmosphere techniques to 
the study of the physical properties of RR Lyrae  star atmospheres. 
advances have been made since their  work, both in  the accuracy of models 
and in  the hydrogen-line profiles predicted f rom them, so  that a reexamina- 
tion of the problem seems in  order. 
Sufficient 
Moreover, the extremely thorough discussion by Christy (1966) of the 
pulsation mechanism and predicted cyclical atmospheric variations for RR 
Lyrae  variables provides the motivation for a m o r e  careful study of these 
1 
s ta rs .  Specifically, we can now study the influence of convection and 
departures f rom LTE on the observable features of the model as well a s  the 
(small) effects of the most  important metal  opacities. 
computed a detailed grid of model atmospheres that covers most  of the 
range in  T The Paschen 
continuum fluxes, the Balmer discontinuities, and the hydrogen-line profiles 
predicted by these models are discussed in the context of their  effect on the 
choice of Teff and g from observations. 
We have, therefore, 
and g encountered fo r  stars in  the RR Lyrae gap. eff 
11. DETAILS OF THE GRID 
The basic methods outlined by Strom and Avrett (1 965) were used in 
computing the grid,  although some important modifications in  the details of 
the calculations have beenmade by R. Kurucz of the Harvard College 
Observatory. 
him f o r  the IBM 360 and 7000 and the CDC 6000 se r i e s  machines; the details 
of i ts  operation a r e  available on request. Constancy of better than 0. 2 per  
cent throughout the atmosphere is usually obtained for  the flux and the flux 
derivative. 
arising f rom H, H-, H Z ,  SiI, MgI, Rayleigh scattering fo r  atomic H, and 
in  some cases, the Balmer and Lyman lines. 
A new and versatile program, ATLAS, has been written by 
The sources of opacity included in these calculations were those 
t 
Departures f rom LTE f o r  the first s ix  levels of atomic hydrogen and for 
H- were computed by use of the methods already described in  Strom and 
Kalkofen (1966), Strom (1967), and Kalkofen (1968). 
The expressions employed in the computation of the bound-bound and 
bound-free c ross  sections used in  the determination of the H-level populations 
have been described by Strom and Peterson (1968). 
cm sec  
H t H- <= H2 t e was used in the computation of the H- departures. 
-9 The value C- = 1.3 X 1 0  
3 -1 estimated by Dalgarno and Browne (1967) for  the reaction 
2 
The influence of convective energy transport  was estimated by use of a 
mixing-length theory and the temperature- correction procedure already 
described by Mihalas (1965). 
his equation (32) fo r  y ,  we find that, while convergence is slowed, the 
resulting temperature corrections and f l u x  e r r o r s  a r e  considerably smoother 
than those found by Mihalas. 
By eliminating the derivative t e rms  in  
In Table 1, we indicate the models computed for this study. The notation 
represents,  i n  compact fo rm Teff, log g, [(metal/H) model/(metal/H) sun]. 
Space requirements preclude publication of the model details. However, 
such desiderata as temperature structures,  predicted fluxes, and Balmer 
profiles a r e  available from the author upon request. 
111. THE RESULTS 
The effective temperature of a n  R R  Lyrae s t a r  is usually determined 
from some measure of the slope of the Paschen continuum o r  from a Balmer- 
line profile o r  equivalent width. 
comparison of the observed and computed Balmer discontinuities f o r  a model 
of the appropriate T 
The surface gravity is then chosen by a 
eff' 
With these typical procedures in mind, we plot in Figure 1 the relation 
between DB, the Balmer discontinuity, and S 
tinuum, predicted by our  models. W e  define 
the slope of the Paschen con- 
P' 
DB = -2.5 log[Fy(3650-)/Fy(3650t)] 
and 
S = -2. 5 log[Fv(4100)/F (5800)l . P 1) 
The solid and dashed lines in  this figure represent the relation found f o r  
purely radiative models and that f o r  convective models having I / h  = 1, 
respectively. 
vective models with I / h  = 2. 
1 
In Figure 2, the dashed line represents the relation for con- 
We f ind  that the I / h  = 2 models most closely 
3 
match the models computed by means of methods that average the influence 
of upward and downward moving elements (e. g. , Latham 1964 and Parsons  
1966). A purely local velocity is used in  the Mihalas (1 965) formulation. 
the extent that the fo rmer  models match reality, the l / h  = 2 models give 
more  likely estimates of the behavior of the atmosphere in the region of flux 
formation. 
Figures  1 and 2: 
To 
In any case, we note two basic conclusions we can reach f rom 
1) The choice of g is not influenced by the effects of convection. 
2)  The temperatures  estimated f rom purely radiative models are too 
small by perhaps as much as 200"-350" K near  7500°K and 50"-100" K 
at 6000" K. 
In Figure 3, we plot W(Hy), the equivalent width of Hy a s  computed 
f rom the mos t  recent Griem (1967) theory, against S 
radiative models. 
models with 1 / h  values of 1. 
as predicted f rom the 
P 
The relation is essentially unchanged for  the convective 
We conclude f rom Figure 3: 
1)  F o r  stars with log g 5 3 in  this Teff range, an e r r o r  of f10 per cent in 
W(Hy) results in  an e r r o r  of about fO. 06 mag in  S 
such as (b-y) and (B-V). Therefore, in this range we must be cautious in  
determining reddening corrections based on observations of W(Hy) and on 
the associated S 
this method, see Searle and Oke 1962. ) 
2)  At leas t  a crude estimate of g must be obtained before S 
dicted accurately f r o m  W(Hy). 
o r  analogous quantities 
P 
values predicted f rom models. (Fo r  a discussion of 
P 
can be pre- 
P 
In Figure 4, the dashed lines represent  D plotted against S fo r  some 
Again, 
B P 
representative models in which we allow fo r  departures  f rom LTE. 
the solid lines represent the results obtained with the purely radiative 
models. 
than for  the L T E  models. 
( in  the usual way) bn as  the ratio of the true population predicted by the 
Saha-Boltzmann equation, we find for  all models considered here  that 
b2 < 1 and b 
is smaller fo r  the non-LTE models p' DB We note that for  a g i v e n s  
This can be understood as follows: If we define 
> 1 fo r  n < 3. Since the second level is underpopulated and n 
4 
the third and higher levels overpopulated, i t  follows that the atmosphere is 
more  transparent in the Balmer continuum and l e s s  transparent in the Paschen 
and higher continua than is the case in LTE. 
l a rge r  emergent f l u x  in  the Balmer continuum and a smaller  flux in the 
Paschen and higher continua, and therefore a smaller  Balmer discontinuity. 
In all cases,  b the departure coefficient f o r  H- is greater  than unity, although 
not large enough to be more than of academic interest. 
As a consequence, we predict a 
- 
In concrete terms,  the effect of departures f rom LTE is to force us to 
choose lower values of g by about 0.25 dex than in  the case with the LTE 
models. 
For  a few points on our grid, the effects of Balmer- and Lyman-line 
opacities on the models were estimated and found to be negligible. 
effects on the resul ts  of varying the metal  abundances a r e  a lso negligible. 
The 
These results allow us  to estimate the effects of the recent changes in 
the absolute calibration of spectrophotometric observations proposed by 
Hayes (1967). His new calibration decreases  S by 0.11 mag, compared to 
the calibration suggested by Oke (1964). In this range of S value, the Hayes 
calibration also increases  D by 0. 06 mag. As a consequence, the values of 
Teff 
if we adopt the calibration of Hayes. Also, as a net result, g is chosen 
smaller  for  Oke's calibration by 0. 5 dex. 
P 
P 
B 
found from Oke's calibration a r e  about 300" K smaller  than is the case 
We can a l so  cornment on the helium content of RR Lyrae s t a r s ,  following 
Christy 's  (1966) work. According to his computations, the location of the 
high Teff boundary of the instability s t r ip  is a function of the atmospheric 
helium content; the higher the helium content, the higher the value of Teff 
at the high Teff boundary. Since both the new model atmospheres presented 
here  and the recently proposed Hayes calibration ac t  to raise Teff (by more 
than 300" K),  we must revise upward any estimates of the atmospheric helium 
content of these stars (by more than 0. 09 by m a s s  fraction). 
5 
IV. SUMMARY 
The basic results of this work suggest that: 
If we ignore the influence of convection on RR Lyrae atmospheres, 
Teff 
estimated by as much as 200" -350" K. 
The gravities chosen f rom the Balmer discontinuity a r e  unaffected by 
convection. 
The effects of departures f rom LTE act in the direction of decreasing 
(by a s  much a s  0.25 dex) the values of g chosen f rom the Balmer dis- 
continuity. 
as estimated from the slope of the Paschen continuum may be under- 
The values of Paschen continuum slopes estimated f rom the observed 
Hy equivalent widths a r e  in e r r o r  by a s  much a s  fO. 06 mag i f  the 
equivalent widths a r e  known to f l 0  per cent. 
The helium content of RR Lyrae s t a r s  is  somewhat higher than that 
estimated f rom previous models and observations. 
We wish to thank R. L. Kuruce and D. M. Peterson f o r  many useful 
discussions and assistance in  some of the computational details. Dr .  I. J. 
Danziger has a lso provided some valuable comments. 
gratitude the support of NASA grant NGR 22-024-001. 
We acknowledge with 
/ 
6 
REFERENCES 
Christy, R. F. 
Dalgarno, A., andBrowne, J. C. 1967, Ap. J., 149, 231. 
Griem, H. R. 1967, Ap. J., 147, 1092. 
Hayes, D. S. 1967, unpublished Ph. D. thesis, University of California, 
1966, Ap. J., *, 108. 
:uinc 
..uJ--- 
Los Angeles. 
Kalkofen, W. 
Latham, D. W. 
Mihalas, D. 1965, Ap. J., 141 564. 
Oke, J. B. 1964, Ap. J., 140, 689. 
Oke, J. B., and Bonsack, S. J. 
Oke, J. B., Giver, L. P., and Searle, L. 1962, Ap. J., 136, 393. 
Parsons,  S. 
Searle, L. , and Oke, J. B. 
Strom, S. E. 1967, Ap. J., 150 637. 
w-’ 
Strom, S .  E., and Avrett, E. H. 
Strom, S. E., and Kalkofen, W. 1966, Ap. J., 144, 76. 
Strom, S .  E. .) and Peterson, D. M. Ap. J., 196,8 (in press). 
1968, Ap. J., El, 317. 
1964, SmithsonianAstrophys. Obs. Spec. Rep. No. E, 199. 
b.w--’ 
F- 
1960, Ap. J., s, 417. -
1968, unpublished Ph. D. thesis,  University of California, Berkeley. 
I 1962, Ap. J., E, 790. 
1965, Ap. J. Suppl., 12, 103. -
7 
TABLE 1 
SUMMARY OF MODEL ATMOSPI 
Radiative models 
(6000, 3 , l )  
(6000, 3,O. 1) 
(6000,2. 5,O. 1) 
(6000,2,1) 
(6000,2,0.1) 
(6000,2,0.01) 
(6000, 3,O. 1)NLTE 
(6000,2,0.1)NLTE 
(6500,3,1) 
(6500,3,0. 1) 
(6500,2,1) 
(6500,2,0.1) 
(6500,2,0,01) 
Radiative models 
(7000, 3 , l )  
(7000, 3,O. 1) 
(7000,2,1) 
(7000,2,0.1) 
(7000,2,0.01) 
(7000,3,0.1)NLTE 
(70O0,2,O01)NLTE 
(7500, 3 , l )  
(7500,3,0.1) 
(7500,2,1) 
(7500,2,0.1) 
(7500,3,0.1)NLTE 
(7500,2,0.1)NLTE 
3RES USED IN THIS 
Convective models 
( l / h  = 1) 
(6000, 3,O. 1) 
(6000,2. 5,O. 1) 
( ~ o o o , ~ ,  0.1) 
(6500,3,0. 1) 
(6500,2. 5,O. 1)  
(6500,2, 0.1) 
(7000, 3,O. 1) 
(7000,2. 5, 0.1) 
(7000,2, 0.1) 
(7500, 3, 0.1) 
(7500,2. 5,O. 1) 
(7500,2,0.1) 
WES TIGA TION 
Convective models 
( l / h  = 2) 
(6500,2. 5,O. 1) 
(6500,2. 5. 0. 01) 
(7000,3,0.1) 
(7500,3,0.1) 
8 
1.80 
1.60 
1.40 
OB 1.20 
1.00 
0.80 
0.60 
1 1 1 1 1 1 1 
- 0.20 -0.10 0.00 0.1 0 0.20 0.30 0.40 0.50 
s P  
Fig. 1. - The relation between DB, the Balmer discontinuity, and Sp, 
the slope of the Paschen continuum predicted by our models. 
for  definitions of DB and Sp. ) 
have l / h  = 1. 
(See text 
The convective models illustrated in this figure 
9 
I .80 
I .60 
I .40 
1.20 
I .oo 
0.80 
0.60 
1 1 1 1 1 1 1 
( 7500) 
- 0.20 -0.10 0.00 0.10 0.20 0.30 0.40 0.50 
S P  
Fig. 2. - The relation between DB, the Balmer discontinuity, and Sp, 
the slope of the Paschen continuum predicted by our models. 
for definitions of DB and Sp. ) 
have l / h  = 2. 
(See text 
The convective models illustrated in this figure 
10 
16 I I I 1 I I 1 
d / h  = I  
PURE RADIATIVE 
--- 
A 
h 
I - 8 -  - 
3 
4 -  
Fig. 3. - The equivalent width of Hy, W(Hy) plotted against S Both W(Hy) and Sp have been computed f rom the pure radiative models. P' 
11 
NON - LTE 
LTE 
--- 
-0.20 - 0.1 0 0.00 0.10 0.20 0.30 0.40 0.50 
S P  
Fig. 4. - A  plot of DB against Sp for  LTE (dashed lines) and non-LTE 
models (solid lines). 
12 


Model atmospheres for RR Lyrae stars

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server