Model atmospheric abundance analysis of subdwarf micron Cassiopeia constellatio

Cohen, J. G.

English

Equivalent widths of lines with λ > 4600 Å were measured from a set of 4.5 Å mm^(-1) Palomar plates and were used in performing a model-atmosphere abundance analysis of the mild subdwarf µ Cas. Comparison with the Sun was made by computing abundances from individual solar lines using the same set of transition probabilities as was used for the subdwarf. Results of this analysis show that the iron-peak elements appear to be deficient by a factor of 4, while the α process in µ Cas elements may be enhanced with respect to these elements

Cohen, Judith G.

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The Astrophysical Journal, Vol. 154, October 1968 
ANALYSIS OF F AND G SUBDWARFS. III. AN ABUNDANCE 
ANALYSIS OF THE SUBDWARF p CASSIOPEIA 
Judith G. Cohen* 
Smithsonian Astrophysical Observatory and Harvard College Observatory 
Received August 23,1967; revised April 8, 1968 
ABSTRACT 
Equivalent widths of lines with X > 4600 Â were measured from a set of 4.5 Â mm-1 Palomar plates 
and were used in performing a model-atmosphere abundance analysis of the mild subdwarf p Cas. Com- 
parison with the Sun was made by computing abundances from individual solar lines using the same set 
of transition probabilities as was used for the subdwarf Results of this analysis show that the iron-peak 
elements appear to be deficient by a factor of 4, while the a process in p Cas elements may be enhanced 
with respect to these elements. 
Because of its moderately large ultraviolet excess, b(U — B) = 0.16, ß Cas has been 
identified as a subdwarf by Sandage and Eggen (1959). This star is also an astrometric 
binary (Lippincott and Wyckoff 1964), although only a crude measurement of the sepa- 
ration of the two components is as yet available (Wehinger and Wyckoff 1966). 
Since p Cas has a large parallax, tt = 0''127 ± O''003 (Lippincott and Wyckoff 1964), 
it can be accurately placed on the H-R diagram if its effective temperature is known 
(Strom, Cohen, and Strom 1967, Paper I of this series). Strom and Strom (1967) have 
determined the effective temperature to be 5000° ± 150° K from a comparison of scans 
made in the region 5000-8000 Â with the predictions of model atmospheres. 
Using Wallerstein's (1962) correlation between b(U — B) and metal content, we de- 
duce that p Cas lies less than 0.1 mag above the theoretical zero-age main sequence 
(Faulkner and Iben 1966) appropriate to its metal content. We do not consider this 
difference to be significant, since either small changes in the convective efficiencies or a 
slight error in the computed bólometric magnitude can account for such a difference. 
Unfortunately, no spectroscopic information on the surface gravity is available, and, 
since the separation of the two components has not been measured accurately, the mass 
of the primary is uncertain. We do not expect and do not apparently find p Cas to have 
evolved from the main sequence over a time scale comparable to the age of the Galaxy. 
By using the quasi-homology relations of Faulkner (1967), the computed evolutionary 
tracks of Faulkner and Iben (1966), we can therefore choose (5000, 4.4, 0.03, 0) for our 
initial model. The system for designating models is (Teff, log g, Z/Zo, vt), where Ten is 
effective temperature, g is surface gravity, Z/Zo is metal content relative to the Sun, 
and vt is micro turbulent velocity in km sec“1. All models satisfy radiative equilibrium 
and LTE and have been obtained with Strom’s programs as described in Strom and 
Avrett (1965) and in Paper II (Cohen and Strom 1967). No detailed analysis of p Cas 
has been previously carried out;1 hence the value for Z/Zo is a guess, and the zero 
micro turbulent velocity was chosen to correspond to the results of Wallerstein (1962) 
and Aller and Greenstein (1960) for Population II stars. 
We obtained the equivalent widths from two 4.5 Â mm“1 Palomar plates and calibra- 
tion wedges exposed by Dr. J. B. Oke. The spectra were traced on the David Mann 
* Currently at Department of Astronomy, California Institute of Technology. 
1
 At the time this paper was submitted, a differential curve-of-growth analysis was published by 
Catchpole, Pagel, and Powell (1967). The results of this work are in substantial agreement with the 
model-atmosphere analysis reported here as shown in Table 1. 
179 
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180 JUDITH G. COHEN Vol. 154 
microphotometer of the Harvard College Observatory. The transformation of the trans- 
mission versus position data into intensities versus wavelength and then to equivalent 
widths was carried out on a CDC 6400 computer. Approximately 250 lines were chosen 
(in the wavelength regions 4650-4900 Â and 5100-6250 Â) for analysis, and a table of 
equivalent widths is available from the author upon request. Errors of no more than + 20 
per cent in W\ are expected. 
Lines falling at shorter wavelengths have been used in most previous detailed analy- 
ses. As a result, many errors in the normalization of the scales of transition probabilities 
for lines with X > 5000 Â have not yet been discussed. Furthermore, since we have used 
a selection of transition probabilities from the recent literature, the absolute scale of 
our ^/-values is in many cases different from that used by Goldberg, Müller, and Aller 
(1960) (hereinafter called “GMA”) in their study of the Sun. Since we wish to obtain 
abundances in p Cas relative to the Sun as well as to determine the absolute metal-to- 
hydrogen ratios, the normalization of the ¿/-values is critical. We have therefore adopted 
a procedure that preserves the advantages of a detailed model atmospheric analysis 
(Strom, Gingerich, and Strom 1966) and also insures the validity of comparisons with 
the solar abundances. For each element, the solar equivalent widths for lines corre- 
sponding to those observed in p Cas were obtained from the revised Rowland tables 
(Moore, Minnaert, and Houtgast 1966). If more than ten lines of an element were ob- 
served in p Cas, a random selection from the subdwarf lines was made. We then used 
the same transition probabilities as had been used for the subdwarf analysis and per- 
formed the identical analysis for the Sun, using the Utrecht reference model (URM) 
(Heintze, Hubenet, and de Jager 1964) assuming a constant micro turbulent velocity of 
1.4 km sec“1 throughout the solar atmosphere. Although the solar equivalent widths in 
the revised Rowland tables are reported for the center of the disk, we have treated them 
as if they were identical to those that would be obtained from the integrated disk; the 
errors thus introduced will generally not be large, as can be seen by comparing the 
widths for various values of cos 6 given by Withbroe (1967). We shall call the abun- 
dances obtained using our transition probabilities, the equivalent widths determined as 
above, and the URM the new “reference-Sun” abundances. 
Sometimes the same abundance for a given element is not deduced from each ioniza- 
tion stage even though the photospheric structure for the Sun is rather well known in the 
region of formation of the weak lines. We therefore assume that the difference in abun- 
dance between two ionization stages for the solar analysis is caused solely by errors in the 
scale of the ¿/-values. We then proceed to choose the appropriate model for p Cas by 
adjusting the atmospheric parameters until the same difference in abundance is achieved 
for the two ion states in question. We stress that the abundances listed in the column 
“Reference Sun” of Table 1 are not suggested revisions of the GMA solar abundances. 
Rather, they indicate (1) differences and possible errors in the absolute scale of the 
transition probabilities for this particular wavelength region and for this selection of 
lines, (2) possible errors in the model solar atmosphere, or (3) systematic errors in the 
solar equivalent widths given by Moore, et al. (1966). In all but a few cases, the first 
contribution is undoubtedly the largest. 
The final model for p Cas (5100, 4.2, 0.2, 3) was chosen to produce the correct ioniza- 
tion equilibrium and a constant deduced abundance as a function of both W\ and x> the 
excitation potential of the lower level, for Fe i lines. Note the rather high value of the 
micro turbulent velocity (vt = 3 km sec“1), which disagrees with previous results on 
other subdwarfs (Wallerstein 1962) and the result of vt= 1.5 km sec“1 obtained by 
Catchpole et al. (1967). A possible source of this disagreement is discussed in Paper II. 
We see in Figure 1, which shows deduced abundance as a function of equivalent width 
for Fe i lines, that the final model gives quite consistent results. We have eliminated all 
lines that fall on the damping part of the curve of growth in making this plot. Owing to 
the lack of accurate damping constants (ten times the classical value was used through- 
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No. 1, 1968 F AND G SUBDWARFS 181 
out this analysis), lines with equivalent widths greater than 160 mÂ were not used in 
the abundance analysis. 
No wavelength dependence greater than 0.15 in the logarithm of the average abun- 
dance for lines in the two regions 4650-4900 Â and 5100-6250 Â has been observed for 
elements having a sufficient number of lines to make such a test (Fe i, Ti i, Ni i, and 
V i). This suggests that the reference-Sun and GMA abundances should agree for these 
elements. We shall see that this holds, except for titanium. 
Fig 1.—Deduced abundance for Fe i lines in p Cas as a function of equivalent width for the model 
(5100, 4.2, 0.2, 3). 
In Table 1 we present the abundances log (Nei/Nn) for y, Cas for the final model and 
the number of lines in p Cas for each element, the GMA and the reference-Sun abun- 
dances, and the number of lines that were used to construct the reference-Sun abun- 
dances. The results of Catchpole et al. (1967) are also displayed, normalized to our 
Fe i abundance. Some comments on, the individual elements are given below: 
Ba ii.—We have used the Corliss and Bozman (1962) transition probabilities (herein- 
after abbreviated as “CB”). Garstang and HilFs (1966) ^/-values have the same ratio 
for these two lines, although the absolute scale is different. 
C I.—All the lines in p Cas are quite weak. The only line in the long-wavelength 
region under study here gives an abundance of —3.5. It is possible, though not probable, 
that the three lines measured near 4800 Â are misidentified. However, we note that in 
Groombridge 1830, a slightly more metal-deficient subdwarf of almost the same reff, 
these three carbon lines are also enhanced (Greenstein 1966). From comparison of CH 
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182 JUDITH G. COHEN Vol. 154 
and C i abundances, we feel that the g/-scale (Griem 1964) is satisfactorily normalized. 
Ce ii.—The value given here for the Sun is that of Allen (1963). 
Cr i and Cr n.—Note the poor ionization equilibrium obtained for the Sun, which 
seems to indicate an error in the normalization of the absolute g/-values for these two 
ionization stages. 
Cu I.—There appears to be a large difference between the g/-scale of CB and that used 
by GMA for the two lines observed in Cas, as has been noticed by Aller (1965). 
Fe i and Fe it.—The agreement between our abundance and that of GMA is good. 
TABLE 1 
Average Abundances for m Cas for the Final Model (5100, 4.2, 0.01, 3) 
' Compared to Catchpole, Pagel, and Powell (1967) 
Element Reference Sun 
Number of 
Lines GMA 
Subdwarf 
Abundance 
Number of 
Lines 
Abundances of 
Catchpole et al 
C I 
Na I 
Mg I 
Al i 
Si i 
Si 
Ca I 
Sc I 
Sc II 
Ti I 
Ti II 
Y I 
Cr I 
Cr II 
Mn I 
Fe I 
Fe II 
Co I 
Ni I 
Cu I 
Zn I 
Y I 
Y II 
Zr I 
Mo I 
Ba II 
Ce II 
Nd II 
- 3 
5 
4 
6 
4 
5 
5 
21 
70 
58 
12 
60 
06 
97 
8 69 
8 80 
7 67 
7 14 
8 29 
6 92 
59 
07 
45 
34 
6 
7 
5 
5 
7 77 
33 
15 
32 
8 94 
9 49 
8 71 
10 92 
58 
28 
8 29 
4 
5 
2 
1 
9 
3 
10 
6 
18 
4 
10 
8 
6 
9 
9 
9 
11 
14 
2 
1 
1 
2 
4 
1 
2 
3 
4 
7 
6 
6 
7 
9 
9 
10 
9 
10 
10 
28 
70 
60 
80 
70 
50 
85 
18 
7 32 
8 30 
6 64 
7 10 
5 43 
36 
09 
94 
60 
75 
77 
10 
90 
4 
5 
- 3 
6 
5 
6 
4 
4 
6 
9 
9 
01 
46 
17 
81 
97 
90 
44 
35 
27 
8 07 
7 68 
8 62 
7 60 
7 02 
7 93 
6 02 
5 90 
8 30 
7 10 
8 95 
10 
62 
6 
9 
10 10 
9 05 
11 96 
10 41 
9 88 
- 8 87 
4 
5 
2 
1 
9 
3 
10 
6 
10 
23 
4 
23 
20 
7 
17 
62 
9 
11 
28 
2 
1 
1 
4 
4 
1 
2 
3 
5 
34 
88 
9 
99 
6 11 
9 22 
8 02 
7 48 
8 81 
7 57 
92 
91 
8 33 
88 
02 
78 
10 05 
8 76* 
10 35 
- 8 6F 
* Upper limit owing to weakness of lines observed by Catchpole et al (1967) 
Nd ii.—The value given here for the Sun is that of Allen (1963). 
Ni i.—The same shift is found for lines in the visible, as discussed in Paper II. We 
used Corliss’ (1965) g/-values. 
S I.—The solar lines and those in /z Cas are quite weak, so that the difference between 
the reference-Sun abundance, obtained with g/-values given by Kohl (1964), and the 
GMA abundance may not be meaningful. 
Sc.—There appears to be a difference in the absolute normalization of the CB and 
the GMA scales of transition probabilities. 
Ti.—We have used CB values for Ti i and two of the four Ti n lines. Transition 
probabilities for the other two Ti n lines were taken from Tatum (1961). His scale ap- 
pears to differ from the CB normalization by 0.5-0.8 in the logarithm. 
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No. 1, 1968 F AND G SUBDWARFS 183 
Y.—There appears to be an error in the normalization of the CB scale. We have 
noticed a similar problem for Y i and Y n lines in the visual. 
Zr I.—These lines are so weak that the identifications are doubtful (the largest W\ of 
the four lines in the Sun is 3.5 mÂ). If the identifications are correct, there must be a 
large change in normalization. We have used the CB scale for this element. 
Note that for cerium, molybdenum, neodymium, and zinc no accurate partition func- 
tions were available. The same value for each element has been adopted in analyzing p 
Cas and the Sun. Thus, errors in the partition function will appear as errors in the 
absolute value of the abundances if the atom is partially ionized, but we feel that relative 
abundances of the subdwarf as compared to the reference Sun should be largely unaf- 
fected. 
Such uncertainties in the absolute scale of transition probabilities make it difficult to 
ascertain the absolute deficiencies of elements representing the various processes of 
nucleosynthesis. We have used the reference-Sun abundances deduced with the same 
set of transition probabilities as were used in the analysis of p Cas to construct Table 2, 
which displays the average deficiencies of a-, e-, and ^-process elements. Since the abun- 
dance of zirconium is so uncertain, it has been omitted in obtaining the average, as have 
TABLE 2 
Average Process Deficiencies in Cas 
with Respect to the Reference Sun 
Process Deficiency 
a -o 32 
a, excluding sulfur 48 
e .58 
5 . . -0 65 
all elements with only one observed line. Although the scatter is larger than any of the 
differences between the average deficiencies, it is clear that metals in p Cas are deficient 
by about a factor of 4, and it is possible that the a-process elements are slightly en- 
hanced, while the ^-process elements are slightly more deficient than the iron-peak ele- 
ments. The agreement between our results and those of Catchpole et al. (1967), using a 
differential curve-of-growth analysis, is rather striking considering that the equivalent 
widths and model parameters were separately determined for each investigation. 
We note that errors in the absolute calibration of Vega affect our choice of effective 
temperature for p Cas from the scans. Calculations of ionization equilibrium at various 
values of Teu and log g show that in this temperature range, if we increase Teü by 250° K, 
we must increase log g by 0.4 to preserve ionization equilibrium. Thus, in order to obtain 
agreement between the spectroscopic determination of log g = 4.2 for p Cas and a de- 
termination based on the mass-luminosity relationship given in Catchpole et al. (1967) 
of 4.4, we must have underestimated Teu as determined from the scans by ^150° K. 
Recent results on the recalibration of Vega by Hayes (1967) suggest that the slope of that 
star’s Paschen continuum must be increased. By using this new calibration, the values 
of Teff for the subdwarfs must then be increased by about 200° K, in close agreement with 
the spectroscopic conclusions. 
The neglect of convection is a possible source of error in this analysis. However, we 
expect that, in this mildly metal-deficient subdwarf, the flattening of the temperature 
gradient will occur only at depths greater than the line-forming region. It is possible 
that our difficulties with zirconium and carbon are due to the change in temperature 
structure at the comparatively large optical depths, where these very weak lines are 
formed. 
In summary, the problems of line blending in stars with Teu < 5500° K force one to 
© American Astronomical Society • Provided by the NASA Astrophysics Data System 
184 JUDITH G. COHEN 
use spectral lines at longer wavelengths for detailed abundance analyses. Uncertainties 
in the calibration of g/-values for X > 5000 Â are large and cannot be neglected. Bearing 
in mind these differences between our transition probabilities and those used by GMA, 
we obtain a metal deficiency of a factor of 4 for jjl Cas as compared with the Sun. Com- 
parison of the results of Catchpole et al. (1967) and the present analysis for p Cas gives 
convincing evidence of the validity of the methods employed in each investigation and 
the accuracy of the final results. 
I would like to thank Dr. J. B. Oke for the use of his plates, Dr. W. Parkinson of 
Harvard College Observatory for permission to use the David Mann microphotometer, 
Dr. Stephen Strom and Mr. R. Kurucz for the use of their programs and for helpful 
discussion. 
This research has been supported in part by grant NGR 22-024 001 from the Na- 
tional Aeronautics and Space Administration. 
REFERENCES 
Allen, C. W. 1963, Astrophysical Quantities (2d ed ; London: Athlone Press). 
Aller, L. H. 1965, Adv. Astr and Ap , 3, 1. 
Aller, L. H., and Greenstein, J L. 1960, Ap. J. Suppl., 5, 139. 
Catchpole, R M., Pagel, B E. J., and Powell, A. L. T. 1967, M.N.R.A S., 136, 403 
Cohen, J. G., and Strom, S. E. 1967, Ap. J., 151, 623 (Paper II). 
Corliss, C. H 1965, N.B S. J. Res. , 69A, 87. 
Corliss, C. H , and Bozman, W. R. 1962, N.B S. Monog , No. 53 (Washington, D.C : Government Print- 
ing Office). 
Faulkner, J. 1967, Ap. J., 147, 617. 
Faulkner, J , and Iben, I., Jr , 1966, Ap J , 144, 995. 
Garstang, R. H., and Hill, S J. 1966, Pub. A S P ,78, 70. 
Goldberg, L., Müller, E. A , and Aller, L. H 1960, Ap J. Suppl., 5, 1. 
Griem, M R 1964, Plasma Spectroscopy (New York: McGraw-Hill). 
Greenstein, J. L. 1966, unpublished 
Hayes, D. 1967, unpublished Ph D thesis, University of California at Los Angeles 
Heintze, J. R. W., Hubenet, M., and de Jager, C. 1964, Smithsonian Ap Obs. Spec. Rept No. 167, p 239. 
Kohl, K. 1964, Zs.f. Ap., 60, 115 
Lippincott, S L., and Wyckofï, S. 1964, A J., 69, 471. 
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Sandage, A. R., and Eggen, O J. 1959, M.N R.A S., 119, 278. 
Strom, S. E., and Avrett, E. M 1965, Ap. J. Suppl, 12, 1. 
Strom, S E., Cohen, J G., and Strom, K M. 1967, Ap. J., 147, 1038 (Paper I). 
Strom, S. E., Gingerich, O. J., and Strom, K M 1966, Ap. J., 146, 880. 
Strom, S. E., and Strom, K. M. 1967, Ap. J, 150, 501. 
Tatum, J. B. 1961, Com. U. London Obs., No 41. 
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Wehinger, P., and Wyckofï, S. 1966, A.J., 71, 185. 
Withbroe, G. L. 1967, Ap.J., 147, 1117. 
Copyright 1968 The University of Chicago Printed in U.S A 
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Analysis of F and G Subdwarfs. III. An Abundance Analysis of the Subdwarf μ Cassiopeia

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Analysis of F and G subdwarfs. 3 - An abundance analysis of the subdwarf mu Cassiopeia

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