A star’s surface temperature is among the most important features that can be deduced from its light. We have made measurements to see how reliably we could determine the surface temperatures of some A to K stars using Wien’s Displacement Law. We took spectra, corrected them for atmospheric extinction and instrumental response, found the wavelengths of their intensity maxima, and then from Wien’s law found the surface temperatures of the observed stars. For F to early K stars, our results agree with temperatures determined in other ways. For A and later K stars, the agreement is poor because the spectra are appreciably different from ideal blackbody spectra and because our equipment responds poorly to the deep red and blue wavelengths where the spectra of these stars have their peak intensities. This paper points out several interesting concepts in and outside the astrophysical domain that can be instructive for undergraduate students.
REFERENCES
1.
Here and in the following we approximate all temperatures to the nearest 50 K (see Sec. V for an explanation of this choice).
2.
Stellar spectra are usually classified according to a so-called Spectral Classification (Harvard scheme): there are seven main spectral classes, labelled by the capital letters O, B, A, F, G, K and M and ordered from higher to lower surface temperature. O stars are the hottest, with temperatures up to 30 000 K or higher, and M stars are the coldest, down to 3000 K; F and G stars have intermediate temperatures with values around 6000–7000 K. Each class is further divided into ten types labeled by the numbers 0, 1, 2, … , 9. Once astronomers thought that stars evolved cooling down, and they spoke of “early” (hotter) or “late” (colder) spectral classes. Even within one class, they spoke of “early” and “late” types: for example K1 is an early K-type, and K8 a late one. Such ideas about evolution were discarded decades ago, but this terminology is still used. Moreover, for a given temperature, luminosity is related to radius, and in the subsequent MK classification scheme stars were given a “luminosity class” (indicated by a roman numeral I, II, etc.) according to their luminosity or dimension. To wit, class I stars are the largest, or supergiants, while class V stars are the much smaller main sequence stars. For elaboration on this point, see
, Fundamental Astronomy
edited by H.
Karttunen
, P.
Kröger
, H.
Oja
, M.
Poutanen
, and K. J.
Donner
, 3rd ed. (Springer
, Berlin/Heidelberg/New York
, 1996
) pp. 236
–240
.3.
About the concept of stellar magnitude, see Karttunen et al. (
1996
) cited in Ref. 2, pp. 97
–101
. The B and V filters are filters centered on the blue (B) and yellow-green (V for visible) part of the spectrum.4.
The paper is
D.
Cenadelli
and M.
Zeni
, “Measuring stellar temperatures: An astrophysical laboratory for undergraduate students
,” Eur. J. Phys.
29
, 113
–121
(2008
).The method is based upon the concept of equivalent width, for which see also
R. C.
Smith
, Observational Astrophysics
(Cambridge U.P.
, Cambridge
, 1995
), p. 182
, orK.
Robinson
, Spectroscopy: The Key to the Stars
(Springer
, London
, 2007
), pp. 52
–57
.5.
G. H.
Jacoby
, D. A.
Hunter
, and C. A.
Christian
, “A library of stellar spectra
,” Astrophys. J., Suppl. Ser.
56
, 257
–281
(1984
). Another reference book that gives full account of the science of stellar spectroscopy is
R. O.
Gray
and C. J.
Corbally
, Stellar Spectral Classification
(Princeton U.P.
, Princeton
, 2009
).6.
Data about the stars (spectral classes and temperatures) here and in what follows are taken from Internet-available resources like the SIMBAD database or the site of Prof. James B. Kaler (Professor Emeritus of Astronomy, University of Illinois): <stars.astro.illinois.edu/sow/sowlist.html> (accessed June 2011). Capella is a well-known double; as both stars have similar spectra and brightness we kept it under consideration and when speaking of temperature, we mean the average temperature of the two stars.
7.
There also exists reddening due to interstellar matter. However, it only becomes significant for distances of more than a thousand light years or so, and the stars we observed are closer than a few hundred light years, so we can neglect interstellar reddening in our case.
8.
See
J. M.
Picone
, A. E.
Hedin
, D. P.
Drob
and A. C.
Aikin
, “NRL-MSISE-00 Empirical model of the atmosphere: Statistical comparisons and scientific issues
,” J. Geophys. Res.
107
, 1468
–1483
, doi: (2002
).9.
10.
F. A.
Jenkins
and H. E.
White
, Fundamentals of Optics
, 4th ed. (McGraw-Hill
, New York
, 1981
).11.
The star is located 148 light years away and interstellar reddening can be safely neglected.
12.
We carried out this interpolation via the website <www.arachnoid.com/polysolve/index.html> by Paul Lutus (accessed June
2011
).13.
All data are taken (as said in Ref. 6) from the SIMBAD database or the site of Prof. Kaler, except the temperature of Albireo A (HD 183915), that is taken from
T.
ten Brummelaar
, B. D.
Mason
, H. A.
McAlister
, L. C.
Roberts
Jr., N. H.
Turner
, W. I.
Hartkopf
, and W. G.
Bagnuolo
Jr., “Binary star differential photometry using the adaptive optics system at Mount Wilson Observatory
,” Astron. J.
119
, 2403
–2414
(2000
).14.
Not all the spectral classes of our stars are present in Ref. 1, but when this is the case, there is always a “very similar” spectrum we can resort to. This is the case for Albireo A (for which we utilized as a reference a K3III spectrum), for Arcturus (K2III) and Vega (A1V).
© 2012 American Association of Physics Teachers.
2012
American Association of Physics Teachers
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