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Photometric classification of the O-B stars
Photometric Classification of the O-B Stars
J. I-I. BIGAY and R. GA~NIER* Observatoire de Lyon, France
I. INTRODUCTION A. The _Problems Involved in the Measurement o] the Distances o / O - B Stars The 0-]3 stars are excellent indicators for the study of the spiral structure of the Galaxy. They are intrinsically very luminous and are therefore observable at great distances, even through rather dense absorbing clouds. Thus their distance modulus is of great importance, and m a y lead either to a general study of the spiral structure or to more specific studies in certain regions, for instance in cases to which kinematic methods cannot be applied. These results can then also be compared with those supplied b y radio astronomy. The colour diagrams based on the U B V - p h o t o m e t r y p r o v i d e - - b y the application of the standard laws of interstellar absorption, or b y more specific laws applying to the particular stellar r e g i o n - - t h e intrinsic colour indices of stars and, consequently, values of their effective temperatures Te. If, on the other hand, for a certain region the ratio R of the total absorption to the selected absorption is known (for instance R -- 3), then the U B V - p h o t o m e t r y gives the colour excess EB-v of the star, and hence the apparent magnitude V0 it would have if there were no absorbing matter. The problem involved in the determination of the distance modulus of the star is to find its absolute magnitude My. For the (O-B) stars, which are too distant for their trigonometric parallaxes to be measurable, the method of spectroscopic parallaxes is used; but then we are faced with the important problem of calibration.
B. Objectiows to a Calibrations Based on the M K Classification A first approximation assigns to all the O-B stars of a given spectral type and given luminosity class an absolute magnitude derived from a statistical study of stars belonging to galactic clusters or to O-associations, whose distance moduli are known with reasonable accuracy; see Blaauw (1963), Boulon (1963), J u n g (1970), and Lesch (1968). A detailed analysis of the results for stars of a given spectral type and given luminosity class shows t h a t the dispersion of the absolute magnitudes can often reach 0.5 magnitude, and in certain cases can even exceed 0.8 to 1.0 magnitude. * With the collaboration of A. Bernard, G. Paturel and Mlle S. Roux. 165
166
Photometric Classification of the O-B Stars
This dispersion is due to the following causes: (a) The MK classification has the disadvantage to be discontinuous, so t h a t two stars though classified in the same way m a y show small differences in their physical properties, which might lead to appreciable variations in luminosity. This applies particularly to the earliest O- and B-stars, for which the luminosity rapidly decreases with the (U-B) colour index. (b). Some stars are often incorrectly or inconsistently classified. The classifications given in different catalogues for the same star do not always agree, and if a m e a n absolute magnitude for a given group is adopted, the differences in the luminosity for the same star can reach 2.0 magnitudes, or even more. E v e n if the final results m a y have a statistical value when they are based on a great number of stars, the accuracy achieved is insufficient for specific studies.
C. Spectrophotometric Absolute Magnitudes; Application o/ the Barbier-Chalonge-Divan Classification The three-parameter spectral classification (D, 2, Cb), which was developed b y Barbier, Chalonge and Divan (1952), is exclusively based on the spcctrophotometric s t u d y of the continuous spectrum. I t is as yet only partly calibrated in absolute magnitude; t h a t is to say, the function M = / ( 2 , D, qbb) is known only for certain types of stars. This calibration could be based on the knowledge of the trigonometric parallaxes of the nearest F-dwarfs and then extended to the A0 stars, b y the study of stars belonging to galactic clusters of known distances, e.g. the Hyades. But the most efficient method to complete the calibration of the A- and F-stars is based on the precise classification of the components of visual binaries; see Berger (1962). We know exactly the difference A M of the absolute magnitudes of the two components of a system; it is equal to the difference of their apparent magnitude, and we can therefore write:
AM
~M =
- - A ~
~1
1
+
~M dD
AD +
~M
ACb
dqbb
where A21, zJD and Aqbb are the differences of the coordinates of the representative points. The study of a considerable number of systems gives us the partial derivatives dM/O21, (~M/(iD and dM/d~4; the calibration can thus be improved b y successive approximations. The absolute magnitudes obtained with this classification are among the most precise ones we possess, thanks to the homogeneity of the material and also to its being obviously more accurate t h a n the previous Yerkes values. I n the case of normal stars which are situated on the Chalonge surface X, each representative point is inside a curvilinear quadrangle corresponding to a certain symbol in the MK system: but we can find inside each quadrangle, stars having slightly different properties and luminosities, varying in a continuous way. However, this calibration in absolute magnitude, as far as the O - B stars are concerned, has not Y E T been published. I I . I>HOTOMETRICTWO-D~NSmNAL CLASSIFICATION OF THE O - B STARS
A. The Advantage o] a Photometric Classification The accuracy of the Barbier-Chalonge-Divan spectral classification is excellent, but the results hitherto obtained are not yet very extensive for two reasons: (a) The exposure-time for the spectrograms is very long, especially, as in the case of
J. H. BmAr
167
problems of galactic structure, we are mostly concerned with objects faint because of their distance or of interstellar absorption. (b) The necessary very careful evaluation of the plates is most time-consuming. Thus we have been t e m p t e d to seek a multi-dimensional classification of the O-B stars, a classification which is calibrated in absolute magnitude and has properties corresponding to the system of Barbier-Chalonge-Divan. Although photometric methods which refer to a certain spectral region provide far less information on the spectral peculiarities of the individual star, t h e y are nevertheless able to yield a rapid and precise determination of the parameters characterizing the luminosity, and much of this accuracy is maintained in the case of faint stars.
B. Which Parameters should be Chosen? I f we consider normal O-B stars only (in the Chalonge-Divan classification) t h e y are positioned in the same region of the surface Z, so t h a t here it is not necessary to use a parameter representing the gradient ~bb. Two unconnected photometric parameters are sufficient to give the characteristics of these stars to a rather good approximation. The construction of models of stellar atmospheres requires three parameters: effective temperature, surface gravity and chemical composition. If we neglect certain classes of peculiar A-stars, i.e. those which are classified as B-stars in the UBV photometry, we can assume t h a t for the O-B stars the effects of the chemical composition are small enough to be neglected. The empirical photometric classification parameters will therefore have to be linked more or less directly with the effective temperature as well as with the surface gravity. (a) The parameter o] e~ective temperature. I n the MK classification, the spectral t y p e approximately corresponds to the effective temperature, and also to the quantity D of the Balmer discontinuity in the Chalonge-Divan classification. Adopting the UBV photom e t r y which is the most frequently used in the case of the above-mentioned stars, either of the two intrinsic colour indices (U - B)0 and (B - V)0 characterizes the effective temperature very well indeed. The index (B - V)0 varies in a uniform manner when we go from the hotter stars to the cooler ones; this is not the case for (U - B)0. Nevertheless, if we limit ourselves to the O-B stars, the quantity (U - B)0 decreases linearly from the O-types to the A0 types stars; and as its variation (1.16 magnitude) is greater t h a n t h a t of (B - V)0, (0 .m32), if we assume equal errors of measurement, the precision in the determination of the index (U - B)0 is better t h a n t h a t obtained for the index (B - V)0. The disadvantage of the choice of one of the intrinsic colour indices in a wide-band p h o t o m e t r y chiefly lies in the fact t h a t these indices are affected b y the interstellar reddening and not directly accessible to measurement, and it is therefore necessary to correct for the reddening, with all the inaccuracy this operation involves. (b) The parameter o/ sur]ace-gravity. I n the Yerkcs Classification the luminosity class corresponds to the electron-pressure which is itself related to the surface gravity. I n the Chalonge System the position of the Balmer 4iscontinuity is essentially a function of the electron pressure--the inter-atomic Stark effect displacing ~1- B y its very definition this parameter 21 is hardly accessible to direct photometric investigation. Instead of ~1, some authors use the quantity nm, i.e. the number of observable Balmer lines. The estimate of nm does not necessitate spectrophotometric measurements; but this advantage loses much of its importance because of the subjective character of this estimate which depends much on the instrument used, and, for the same instrument,
168
Photometric Classification of the O-B Stars
on the observer. Moreover, n m can be expressed only b y an integer, whereas 21 varies continuously. Some detail of such a classification can therefore be lost if n,, is used rather t h a n 21. Moreover, n,, is even less accessible t h a n 21 to photometric techniques. On the other hand, the Stark effect strongly affects certain lines, in particular the hydrogen lines in the case of O-B stars; the intensity of these lines can thus be used as an indicator of surface gravity. H a c k (1953) obtained a classification in good agreement with those due to Chalonge and Morgan b y measuring the apparent central intensity of H)~ on low-dispersion prism spectrograms. Str6mgren (1958) used the total intensity fl of the Hfl line, measuring it photoelectrically. More recently, Crawford (1960-66) gave the values of the p a r a m e t e r fl for m a n y stars. (c) Disturbing e~ects a/leering the total intensity o] hydrogen lines. I n two i m p o r t a n t communications Petrie and Maunsell (1950) and Petrie (1952) gave the distances of a sample of A- and B-stars and drew a diagram (Fig. 1), plotting the absolute magnitudes M v as
M:-% t
6[
-4
• a*~..~ •
A~
.o.
&]k
AA)~
x J<
•x
• xO t ox • xxex
I~:,'0~ • •
~q~l
" I
2
!
4
;
8
10
12
• • ~x
"i 14
a
16
18
""" _~
20 WH~
FIa. 1. A plot of the absolute magnitudes M~ against the equivalent width of H~, derived fore several star clusters and associations. (After Petrie and Maunsell, 1950.) a function of the equivalent width WHy of the Balmer line t I y which was used as a criterion of luminosity; see also Beer (1966). These calibrations of absolute magnitudes with the help of WHy are correct for the types A3-B8, and the types B 7 - 0 9 . Petrie gives a mean curve for each spectral groups and applies a corrections to take into account the influence of the spectral t y p e o n WH~,. We notice t h a t the scatter of the representative points on both sides of the mean curve is considerable; it can reach __+0.57. I n d e p e n d e n t of the Balmcr lines and stars used for this kind of calibration, the dispersion is always of the same order of magnitude. I t s causes can be traced back to several effects.
J. H. BIGAY
169
1. The binary e~ect. H e c k m a n n (1956) noted in his diagram of the M v values, when plotted as a funtion of ( B - V) for the Pleiades cluster t h a t the spectroscopic binaries lie systematically above the normal stars (Fig. 2). I n a calibration of absolute magnitudes we m u s t therefore endeavour to strictly eliminate binaries.
o °
Mv
o
o\ \ o •
\ \\\
\
• 14 •
\ •
eo.o
o'2
\
0;6
0".4
0"8
1;o
1"2
(B-V) FIG. 2. My as a function of (B V), for the Pleiades, showing the exceptional role of spectroscopic binaries: they appear systematically below the normal stars. (After Heckmann, 1956.) -
-
2. The rotation e~ect. Guthrie (1963) showed t h a t the shape and the intensity of Balmer lines are considerably modified b y stellar rotation. I n the case of the O - B stars, which rotate rapidly, the physical conditions are not the same in the neighbourhood of the poles as at the equator, and it follows t h a t if two physically identical (O-B) stars are observed, one pole-on and the other equator-on, the measured p a r a m e t e r fl is not the same in the two cases and thus different absolute magnitudes will be assigned to these
170
Photometric Classification of the OB Stars
two stars. McNamara (1963) reached the same conclusions from his study of the B-stars in the Orion region. 3. The emission e~ect. A large proportion of the B-stars show emission in certain Balmer lines, some of t h e m always, others only occasionally. I f the emission is strong enough, it can affect the lines HE, H~ . . . . . but to a decreasing extent as we progress through the Balmer series. I f we construct a diagram (~ig. 3) showing the values of fl as a function of ~, the emission stars differ strongly from the normal stars.
-0.8
-0.6
-0.4
-0.2
-0.0
oj
oo ~o
8
o2
-0.2
-0.4
-0.6 % -0.8
- 1.0
FIG. 3. The intensity of Hc¢ plotted against the Hfl values. C. One Parameter Only, Indicating the Intensity o/.Lines, is Inadequate to Characterize the Absolute Magnitude The study of the (B - V)o/Vo and (B - V)o/(U - B)o diagrams for the stars given in the literature as belonging to the I Lacertae Association permits us to select a sample of those stars of which we are rather certain t h a t they are members of the Association. B y assuming the distance modulus 8.m9 (generally adopted for this Association) it has been possible to determine their absolute magnitudes. The diagram (U - B)o/fl is given in Fig. 4 for these selected stars, and near to each representative point its corresponding absolute magnitude has been marked. ~ o r an equal index fl we note t h a t the stars of the upper p a r t of this diagram are as a rule intrinsically less luminous t h a n those of the lower part. This observation is typical for all the stars later t h a n B2 and it does not seem t h a t different values of v sin i could explain it. Moreover, it is normal to expect t h a t of two stars with identical indices the one having the larger (U - B)0 index will be the more luminous, which means t h a t the spectral-type corrections described b y Petrie are inadequate and t h a t actually two parameters are necessary to characterize the luminosity.
3. H. Bmxr
171
(U.B).I 11"1.32
11,1.21 11.0.32
-0.2
• 1.0011 11"0.89 11,0.96 -0.2511
11.0.78
• 0.6111 l | `0.42 IB+0.64 11-0.12 11,0.22
-0.4
11,001
.oo ~ l "°°°!o,.
-0.6
-0.77
.2.601111-2.70 -1.5811 .2.02111
-0.8
-1.5211 11-1.67
• 0J89 - "
n-o.85
-2.7411 11-1.80 -2.7211 11-2.40 -3.0211 11-2.98 II-3.63 II -4.01
-1.0
, ,22
2.500
2.7
2.8
2.9
P
Fro. 4. The relationship between ( U - B) 0 and fl for stars belonging to the Association I Lacertae; the absolute magnitudes are indicated.
III. THE (U -- B)o/~ CLASSIFICATION OF THE O - B STARS
A. Representation o/the Points on a Plane Each star is represented b y a point M of coordinates fl and (U - B)0 (Fig. 5). Within this plane two families of curves have been drawn: curves which separate the spectral type, and curves which are approximately orthogonal to the curves of the first family and which separate the Yerkes luminosity classes. Thus each curvilinear quadrangle corresponds to a definite symbol of the M K classification. While the subdivision into Yerkes spectral types is good, t h a t into luminosity classes is far less clear, especially for the classes I I I , I V and V. This arises in p a r t from the fact t h a t the M K classification is not very satisfactory for these luminosity classes. B. Comparison between the (U - B)o/fl and the D/21 Classifications F o r the stars for which we have both a ( U - B)o/~ classification and another in the Chalonge system D]Az, the two diagrams are represented in Fig. 5 and Fig. 6. The analogy is evident and the two systems of classification have obviously the same properties. This is not surprising if we consider the definition of the parameters (U - B)0 and D on the one hand, and of/~ and A1 on the other.
172
Photometric Classification of the O-B Stars
(U-B)j
IV, V
-0.0
o II , III
la
o
-0.2
oo
-0.4
o o~ /
%,"
-0.6
-0.8
IV,V
•
I1,111 0
o=
IbA la •
-1.00
06 2.500
I
2.6
I
2.7
I
2.8
I
2.900
FIG. 5. The (U -- B)o/fl diagram for 0-B stars. 1. T h e correlation between D and ( U - B)o. I n spite of the disadvantage resulting from the fact t h a t the U filter of the UBV system lies across the Balmer discontinuity, the colour index (U - B)0 shows the size of the discontinuity rather clearly. Crawford (1960) has demonstrated existence of a linear relation between D and (U - B)0. Figure 7 shows this relation for those O- and B-stars which are common to Crawford and ChalongeDivan. Indeed the relation is linear and the correlation excellent. 2. T h e correlation between ~z and ft. Figure 8 shows the correlation between Chalonge's 21 p a r a m e t e r and StrSmgren's fl index for stars having about the same Balmer discontinuity.
IV. PROBLEMS OF EVOLUTION
AND
GALACTIC STRUCTURE
I t can be expected t h a t the results deduced from Chalonge's (D, ,~1) diagram (Chalonge, 1966) can, as far as clusters and associations are concerned, also be seen in the ( U - B)o/fl diagram. I n particular, since the parameters (U - B)0 and fl, represent (in the same w a y as ~1 and D) the intrinsic characteristic of the stars, we can expect to obtain a diagram which is v e r y similar to the colour magnitude diagrams which are used in the study of problems of evolution.
J . H. B I o ~ r
173
0.6-
Ib
0.50.4 0.3
0.2 0.1 0.0 0
i
I
I
l
I
I
I
10
20
30
40
50
60
70
v
/~ - 3 7 0 0
FIG. 6. Chalonge's
D/21 diagram.
0 0 0 O0 0
aoo~
80oO°O
Oo o
o
oo
o
0.4
0
o°.°oOo'o 0
0 0
ooo
o
O0
0¢~0
0.2
o
0 o
0
o
~8 ¢ °°°°°Oo O°o
0.0 i
I
(~_B)o-l.O
i
i
-o.8
i
i
-o.6
i
s
-o.4
i
i
I
-0.2
FIG. 7. Plot of the values of the Balmer discontinuity D against the colour index (U -- B) o for O - B stars.
174
Photometric Classification of the O-B Stars
70
60
50
40
30
•
0.34 ~ D
O
0.23 ~: D ~
~ 0.38 0.25
•
0.13 ~ D ~
0.15
/~.
0.04 ~D~
0.06
20
10 / 0 2.5
I 2.6
I 2.7
I 2,8
.~_
FIG. 8. Relationship between Chalonge's parameter 21 and StrSmgren's index fl for stars with essentially the same value of the Balmer discontinuity.
A. Use o/the Diagram (U - B)o/fl /or Stars in Clusters or Associations L e t us recall t h a t the m e m b e r s of these stellar groups h a v e the same age a n d the same initial chemical composition. Our selected star groups are the Pleiades, ~ Persei, I Orionis, I Lacertae, h a n d Z Persei. All these stars are indicated on Fig. 9, as Chalonge (1966) showed t h a t the evolution of a star close to the zero-age m e a n sequence (ZAMS) can be represented in a precise w a y in a diagram of the D/21 type, or in this particular case b y (U - B)o/fl. The older m e m b e r s of these stellar groups permit us to determine again the zero-age sequence (see Fig. 10). The members which have more rapidly evoled (more massive stars) are on lateral branches.
B. Possible Uses o] these Data (a) Calibration o] the Z A M S in years. (b) Calibration o/the diagram (U - B)o/fl in absolute magnitude.
J . H. BIGAY
175
CU-B)o .,'//
~0
/°
~
° o. o~ . , , •~. o
-0.2
o
o
-0.4
-O,q " ~ ' e e Ir'%T.
/~/
~( Per. • 1 ori.e Ple'J'ades
-0-I
o
] Lac. h&X
Pe[
•
-1.0 /
-1.2 I
2.500
I
2.6
I
I
2.7
I
I
a
2.8
FIG. 9. The (U - - B)0/~ diagram for stars in clusters a n d associations.
I
2.9
176
Photometric Classification of the O - B Stars
(U-B)o,
f~
0.0 i ll
/ / / j l
-0,2
1
I
i
I 1
/ I/
-0.6
tI
-
ii
I
i
z
I
/
7111~
/
h&X Pe III/P ii /I
-0.4
/ i
i
~,
~ ~
!
I ~
Lac.
~~7
-0-8
-1.0
-1.2
7 I
2.500
I
2.6
I
I
2.7
I
I
2.8
I
I
2.9
FIo. 10. The ( U - - B)o/fl values of Fig. 9 plotted relative to the position of the zero-age sequence (ZAMS).
J. H. BIGAY
177
REFERENCES
BARBIER,D., CHALONGE,D. and DIVAN, L. (1952) Ann. Astrophys. 15, 201. BEE~, A. (1966) Symposium No. 24 o] the I.A.U. (1964, SaltsjSbaden), p. 322. BERGER, J. (1962) Ann. Astrophys. 25. BLAA~W, A. (1963) Basic astronomical data, in Stars and Stellar Systems (ed. K. AA. STR~rD) Vo|. 3, Section 20, p. 383 (KUIPEI~-MIDDLEnuI~ST),Chicago. BOULON, J. (1963) Thesis, J. Observateurs, l~Iarseflle, 46, 225. CRALO~GE, D. (1966) Sym2osium 270. 24 o] the I.A.U. (1964, SaltsjSbaden), p. 77. CRAWFORD,D. L. (1960) Astrophys. J. 188, 843. CRAWFORD,D. L. (1960) Astrolghys. J. 188, 860. CRAWFORD,D. L. (1963~Astro~hys. J. 187, 523. C~AWFOI~D,D. L. (1963) Astro2hys. J. 187, 530. CRAWFORD,D. L. (1966)JKitt Peak 27at. Obs. Contr. No. 110. CI~AWFORD,D. L. and BARNES, J. V. (1967) Kitt Peak Nat. Obs. Cont. No. 192. C~AW~ORD, D. L. and BARNES, J. V. (1969) Kitt Peak Nat. Obs. Cont. No. 432. CRAWFORD,D. L., BAR~ES, J. V., FAURE,B. Q., GOLSOlV,J. C. and PIeR,Y, C. L. (1966) Kitt Peak Nat. Obs. Contr. No. 195. CI~AWFOI~D,D. L. and MA~D]~R,J. (1966) Kitt Peak 27at. Obs. Cont. No. 145. CRAWFORD,D. L. and PERRY, C. L. (1966) Kitt Peak Nat. Obs. Cont. I~o. 147. CRAWFOR1),D. L. and STR5~GREN, B. (1966) Kitt Peak 27at. Obs. Cont. No. 82. DryAd, L. (1966) ~.%~mposium27o. 24 o/the I.A.U. (1964, SaltsjSbaden), p. 311. GUTHRIE, B. N. G. (1963) Publ. B. Obs. Edinburgh 3, 83. HACK, M. (1953) Ann. Astro~hys. 16, 417. HECXMANN, 0. (1956) AstroThys. J. 124, 477. JOHNSON, H. L. and IRIARTE,B. (1958) Lowell Obs. Bull. 4, 47. JuNG, J. (1970) Thesis and Astr. Astrophys. 4, 53. LESCH, J. R. (1968) Thesis and Astrophys. J. Suppl. 17, 371. MCN~ARA, D. H. (1963) Astro~hys. J. 187, 317. PETRIE, R. M. and MAU~SELL,C. D. (1950) Publ. Dora. Astro~hys. Obs. Victoria 8, 253. PETRIE, R. M. (1952) Publ. Dom. Astrophys. Obs. Victoria 9, 251. PETRIE, R. M. (1966) SymTosium 27o. 24 o/the I.A.U. (1964, Saltsj5baden), p. 304. STRO~GBE~, B. (1958) Observatory 78, 137.
J. I-I. BIGAY and R. GA~NIER* Observatoire de Lyon, France
I. INTRODUCTION A. The _Problems Involved in the Measurement o] the Distances o / O - B Stars The 0-]3 stars are excellent indicators for the study of the spiral structure of the Galaxy. They are intrinsically very luminous and are therefore observable at great distances, even through rather dense absorbing clouds. Thus their distance modulus is of great importance, and m a y lead either to a general study of the spiral structure or to more specific studies in certain regions, for instance in cases to which kinematic methods cannot be applied. These results can then also be compared with those supplied b y radio astronomy. The colour diagrams based on the U B V - p h o t o m e t r y p r o v i d e - - b y the application of the standard laws of interstellar absorption, or b y more specific laws applying to the particular stellar r e g i o n - - t h e intrinsic colour indices of stars and, consequently, values of their effective temperatures Te. If, on the other hand, for a certain region the ratio R of the total absorption to the selected absorption is known (for instance R -- 3), then the U B V - p h o t o m e t r y gives the colour excess EB-v of the star, and hence the apparent magnitude V0 it would have if there were no absorbing matter. The problem involved in the determination of the distance modulus of the star is to find its absolute magnitude My. For the (O-B) stars, which are too distant for their trigonometric parallaxes to be measurable, the method of spectroscopic parallaxes is used; but then we are faced with the important problem of calibration.
B. Objectiows to a Calibrations Based on the M K Classification A first approximation assigns to all the O-B stars of a given spectral type and given luminosity class an absolute magnitude derived from a statistical study of stars belonging to galactic clusters or to O-associations, whose distance moduli are known with reasonable accuracy; see Blaauw (1963), Boulon (1963), J u n g (1970), and Lesch (1968). A detailed analysis of the results for stars of a given spectral type and given luminosity class shows t h a t the dispersion of the absolute magnitudes can often reach 0.5 magnitude, and in certain cases can even exceed 0.8 to 1.0 magnitude. * With the collaboration of A. Bernard, G. Paturel and Mlle S. Roux. 165
166
Photometric Classification of the O-B Stars
This dispersion is due to the following causes: (a) The MK classification has the disadvantage to be discontinuous, so t h a t two stars though classified in the same way m a y show small differences in their physical properties, which might lead to appreciable variations in luminosity. This applies particularly to the earliest O- and B-stars, for which the luminosity rapidly decreases with the (U-B) colour index. (b). Some stars are often incorrectly or inconsistently classified. The classifications given in different catalogues for the same star do not always agree, and if a m e a n absolute magnitude for a given group is adopted, the differences in the luminosity for the same star can reach 2.0 magnitudes, or even more. E v e n if the final results m a y have a statistical value when they are based on a great number of stars, the accuracy achieved is insufficient for specific studies.
C. Spectrophotometric Absolute Magnitudes; Application o/ the Barbier-Chalonge-Divan Classification The three-parameter spectral classification (D, 2, Cb), which was developed b y Barbier, Chalonge and Divan (1952), is exclusively based on the spcctrophotometric s t u d y of the continuous spectrum. I t is as yet only partly calibrated in absolute magnitude; t h a t is to say, the function M = / ( 2 , D, qbb) is known only for certain types of stars. This calibration could be based on the knowledge of the trigonometric parallaxes of the nearest F-dwarfs and then extended to the A0 stars, b y the study of stars belonging to galactic clusters of known distances, e.g. the Hyades. But the most efficient method to complete the calibration of the A- and F-stars is based on the precise classification of the components of visual binaries; see Berger (1962). We know exactly the difference A M of the absolute magnitudes of the two components of a system; it is equal to the difference of their apparent magnitude, and we can therefore write:
AM
~M =
- - A ~
~1
1
+
~M dD
AD +
~M
ACb
dqbb
where A21, zJD and Aqbb are the differences of the coordinates of the representative points. The study of a considerable number of systems gives us the partial derivatives dM/O21, (~M/(iD and dM/d~4; the calibration can thus be improved b y successive approximations. The absolute magnitudes obtained with this classification are among the most precise ones we possess, thanks to the homogeneity of the material and also to its being obviously more accurate t h a n the previous Yerkes values. I n the case of normal stars which are situated on the Chalonge surface X, each representative point is inside a curvilinear quadrangle corresponding to a certain symbol in the MK system: but we can find inside each quadrangle, stars having slightly different properties and luminosities, varying in a continuous way. However, this calibration in absolute magnitude, as far as the O - B stars are concerned, has not Y E T been published. I I . I>HOTOMETRICTWO-D~NSmNAL CLASSIFICATION OF THE O - B STARS
A. The Advantage o] a Photometric Classification The accuracy of the Barbier-Chalonge-Divan spectral classification is excellent, but the results hitherto obtained are not yet very extensive for two reasons: (a) The exposure-time for the spectrograms is very long, especially, as in the case of
J. H. BmAr
167
problems of galactic structure, we are mostly concerned with objects faint because of their distance or of interstellar absorption. (b) The necessary very careful evaluation of the plates is most time-consuming. Thus we have been t e m p t e d to seek a multi-dimensional classification of the O-B stars, a classification which is calibrated in absolute magnitude and has properties corresponding to the system of Barbier-Chalonge-Divan. Although photometric methods which refer to a certain spectral region provide far less information on the spectral peculiarities of the individual star, t h e y are nevertheless able to yield a rapid and precise determination of the parameters characterizing the luminosity, and much of this accuracy is maintained in the case of faint stars.
B. Which Parameters should be Chosen? I f we consider normal O-B stars only (in the Chalonge-Divan classification) t h e y are positioned in the same region of the surface Z, so t h a t here it is not necessary to use a parameter representing the gradient ~bb. Two unconnected photometric parameters are sufficient to give the characteristics of these stars to a rather good approximation. The construction of models of stellar atmospheres requires three parameters: effective temperature, surface gravity and chemical composition. If we neglect certain classes of peculiar A-stars, i.e. those which are classified as B-stars in the UBV photometry, we can assume t h a t for the O-B stars the effects of the chemical composition are small enough to be neglected. The empirical photometric classification parameters will therefore have to be linked more or less directly with the effective temperature as well as with the surface gravity. (a) The parameter o] e~ective temperature. I n the MK classification, the spectral t y p e approximately corresponds to the effective temperature, and also to the quantity D of the Balmer discontinuity in the Chalonge-Divan classification. Adopting the UBV photom e t r y which is the most frequently used in the case of the above-mentioned stars, either of the two intrinsic colour indices (U - B)0 and (B - V)0 characterizes the effective temperature very well indeed. The index (B - V)0 varies in a uniform manner when we go from the hotter stars to the cooler ones; this is not the case for (U - B)0. Nevertheless, if we limit ourselves to the O-B stars, the quantity (U - B)0 decreases linearly from the O-types to the A0 types stars; and as its variation (1.16 magnitude) is greater t h a n t h a t of (B - V)0, (0 .m32), if we assume equal errors of measurement, the precision in the determination of the index (U - B)0 is better t h a n t h a t obtained for the index (B - V)0. The disadvantage of the choice of one of the intrinsic colour indices in a wide-band p h o t o m e t r y chiefly lies in the fact t h a t these indices are affected b y the interstellar reddening and not directly accessible to measurement, and it is therefore necessary to correct for the reddening, with all the inaccuracy this operation involves. (b) The parameter o/ sur]ace-gravity. I n the Yerkcs Classification the luminosity class corresponds to the electron-pressure which is itself related to the surface gravity. I n the Chalonge System the position of the Balmer 4iscontinuity is essentially a function of the electron pressure--the inter-atomic Stark effect displacing ~1- B y its very definition this parameter 21 is hardly accessible to direct photometric investigation. Instead of ~1, some authors use the quantity nm, i.e. the number of observable Balmer lines. The estimate of nm does not necessitate spectrophotometric measurements; but this advantage loses much of its importance because of the subjective character of this estimate which depends much on the instrument used, and, for the same instrument,
168
Photometric Classification of the O-B Stars
on the observer. Moreover, n m can be expressed only b y an integer, whereas 21 varies continuously. Some detail of such a classification can therefore be lost if n,, is used rather t h a n 21. Moreover, n,, is even less accessible t h a n 21 to photometric techniques. On the other hand, the Stark effect strongly affects certain lines, in particular the hydrogen lines in the case of O-B stars; the intensity of these lines can thus be used as an indicator of surface gravity. H a c k (1953) obtained a classification in good agreement with those due to Chalonge and Morgan b y measuring the apparent central intensity of H)~ on low-dispersion prism spectrograms. Str6mgren (1958) used the total intensity fl of the Hfl line, measuring it photoelectrically. More recently, Crawford (1960-66) gave the values of the p a r a m e t e r fl for m a n y stars. (c) Disturbing e~ects a/leering the total intensity o] hydrogen lines. I n two i m p o r t a n t communications Petrie and Maunsell (1950) and Petrie (1952) gave the distances of a sample of A- and B-stars and drew a diagram (Fig. 1), plotting the absolute magnitudes M v as
M:-% t
6[
-4
• a*~..~ •
A~
.o.
&]k
AA)~
x J<
•x
• xO t ox • xxex
I~:,'0~ • •
~q~l
" I
2
!
4
;
8
10
12
• • ~x
"i 14
a
16
18
""" _~
20 WH~
FIa. 1. A plot of the absolute magnitudes M~ against the equivalent width of H~, derived fore several star clusters and associations. (After Petrie and Maunsell, 1950.) a function of the equivalent width WHy of the Balmer line t I y which was used as a criterion of luminosity; see also Beer (1966). These calibrations of absolute magnitudes with the help of WHy are correct for the types A3-B8, and the types B 7 - 0 9 . Petrie gives a mean curve for each spectral groups and applies a corrections to take into account the influence of the spectral t y p e o n WH~,. We notice t h a t the scatter of the representative points on both sides of the mean curve is considerable; it can reach __+0.57. I n d e p e n d e n t of the Balmcr lines and stars used for this kind of calibration, the dispersion is always of the same order of magnitude. I t s causes can be traced back to several effects.
J. H. BIGAY
169
1. The binary e~ect. H e c k m a n n (1956) noted in his diagram of the M v values, when plotted as a funtion of ( B - V) for the Pleiades cluster t h a t the spectroscopic binaries lie systematically above the normal stars (Fig. 2). I n a calibration of absolute magnitudes we m u s t therefore endeavour to strictly eliminate binaries.
o °
Mv
o
o\ \ o •
\ \\\
\
• 14 •
\ •
eo.o
o'2
\
0;6
0".4
0"8
1;o
1"2
(B-V) FIG. 2. My as a function of (B V), for the Pleiades, showing the exceptional role of spectroscopic binaries: they appear systematically below the normal stars. (After Heckmann, 1956.) -
-
2. The rotation e~ect. Guthrie (1963) showed t h a t the shape and the intensity of Balmer lines are considerably modified b y stellar rotation. I n the case of the O - B stars, which rotate rapidly, the physical conditions are not the same in the neighbourhood of the poles as at the equator, and it follows t h a t if two physically identical (O-B) stars are observed, one pole-on and the other equator-on, the measured p a r a m e t e r fl is not the same in the two cases and thus different absolute magnitudes will be assigned to these
170
Photometric Classification of the OB Stars
two stars. McNamara (1963) reached the same conclusions from his study of the B-stars in the Orion region. 3. The emission e~ect. A large proportion of the B-stars show emission in certain Balmer lines, some of t h e m always, others only occasionally. I f the emission is strong enough, it can affect the lines HE, H~ . . . . . but to a decreasing extent as we progress through the Balmer series. I f we construct a diagram (~ig. 3) showing the values of fl as a function of ~, the emission stars differ strongly from the normal stars.
-0.8
-0.6
-0.4
-0.2
-0.0
oj
oo ~o
8
o2
-0.2
-0.4
-0.6 % -0.8
- 1.0
FIG. 3. The intensity of Hc¢ plotted against the Hfl values. C. One Parameter Only, Indicating the Intensity o/.Lines, is Inadequate to Characterize the Absolute Magnitude The study of the (B - V)o/Vo and (B - V)o/(U - B)o diagrams for the stars given in the literature as belonging to the I Lacertae Association permits us to select a sample of those stars of which we are rather certain t h a t they are members of the Association. B y assuming the distance modulus 8.m9 (generally adopted for this Association) it has been possible to determine their absolute magnitudes. The diagram (U - B)o/fl is given in Fig. 4 for these selected stars, and near to each representative point its corresponding absolute magnitude has been marked. ~ o r an equal index fl we note t h a t the stars of the upper p a r t of this diagram are as a rule intrinsically less luminous t h a n those of the lower part. This observation is typical for all the stars later t h a n B2 and it does not seem t h a t different values of v sin i could explain it. Moreover, it is normal to expect t h a t of two stars with identical indices the one having the larger (U - B)0 index will be the more luminous, which means t h a t the spectral-type corrections described b y Petrie are inadequate and t h a t actually two parameters are necessary to characterize the luminosity.
3. H. Bmxr
171
(U.B).I 11"1.32
11,1.21 11.0.32
-0.2
• 1.0011 11"0.89 11,0.96 -0.2511
11.0.78
• 0.6111 l | `0.42 IB+0.64 11-0.12 11,0.22
-0.4
11,001
.oo ~ l "°°°!o,.
-0.6
-0.77
.2.601111-2.70 -1.5811 .2.02111
-0.8
-1.5211 11-1.67
• 0J89 - "
n-o.85
-2.7411 11-1.80 -2.7211 11-2.40 -3.0211 11-2.98 II-3.63 II -4.01
-1.0
, ,22
2.500
2.7
2.8
2.9
P
Fro. 4. The relationship between ( U - B) 0 and fl for stars belonging to the Association I Lacertae; the absolute magnitudes are indicated.
III. THE (U -- B)o/~ CLASSIFICATION OF THE O - B STARS
A. Representation o/the Points on a Plane Each star is represented b y a point M of coordinates fl and (U - B)0 (Fig. 5). Within this plane two families of curves have been drawn: curves which separate the spectral type, and curves which are approximately orthogonal to the curves of the first family and which separate the Yerkes luminosity classes. Thus each curvilinear quadrangle corresponds to a definite symbol of the M K classification. While the subdivision into Yerkes spectral types is good, t h a t into luminosity classes is far less clear, especially for the classes I I I , I V and V. This arises in p a r t from the fact t h a t the M K classification is not very satisfactory for these luminosity classes. B. Comparison between the (U - B)o/fl and the D/21 Classifications F o r the stars for which we have both a ( U - B)o/~ classification and another in the Chalonge system D]Az, the two diagrams are represented in Fig. 5 and Fig. 6. The analogy is evident and the two systems of classification have obviously the same properties. This is not surprising if we consider the definition of the parameters (U - B)0 and D on the one hand, and of/~ and A1 on the other.
172
Photometric Classification of the O-B Stars
(U-B)j
IV, V
-0.0
o II , III
la
o
-0.2
oo
-0.4
o o~ /
%,"
-0.6
-0.8
IV,V
•
I1,111 0
o=
IbA la •
-1.00
06 2.500
I
2.6
I
2.7
I
2.8
I
2.900
FIG. 5. The (U -- B)o/fl diagram for 0-B stars. 1. T h e correlation between D and ( U - B)o. I n spite of the disadvantage resulting from the fact t h a t the U filter of the UBV system lies across the Balmer discontinuity, the colour index (U - B)0 shows the size of the discontinuity rather clearly. Crawford (1960) has demonstrated existence of a linear relation between D and (U - B)0. Figure 7 shows this relation for those O- and B-stars which are common to Crawford and ChalongeDivan. Indeed the relation is linear and the correlation excellent. 2. T h e correlation between ~z and ft. Figure 8 shows the correlation between Chalonge's 21 p a r a m e t e r and StrSmgren's fl index for stars having about the same Balmer discontinuity.
IV. PROBLEMS OF EVOLUTION
AND
GALACTIC STRUCTURE
I t can be expected t h a t the results deduced from Chalonge's (D, ,~1) diagram (Chalonge, 1966) can, as far as clusters and associations are concerned, also be seen in the ( U - B)o/fl diagram. I n particular, since the parameters (U - B)0 and fl, represent (in the same w a y as ~1 and D) the intrinsic characteristic of the stars, we can expect to obtain a diagram which is v e r y similar to the colour magnitude diagrams which are used in the study of problems of evolution.
J . H. B I o ~ r
173
0.6-
Ib
0.50.4 0.3
0.2 0.1 0.0 0
i
I
I
l
I
I
I
10
20
30
40
50
60
70
v
/~ - 3 7 0 0
FIG. 6. Chalonge's
D/21 diagram.
0 0 0 O0 0
aoo~
80oO°O
Oo o
o
oo
o
0.4
0
o°.°oOo'o 0
0 0
ooo
o
O0
0¢~0
0.2
o
0 o
0
o
~8 ¢ °°°°°Oo O°o
0.0 i
I
(~_B)o-l.O
i
i
-o.8
i
i
-o.6
i
s
-o.4
i
i
I
-0.2
FIG. 7. Plot of the values of the Balmer discontinuity D against the colour index (U -- B) o for O - B stars.
174
Photometric Classification of the O-B Stars
70
60
50
40
30
•
0.34 ~ D
O
0.23 ~: D ~
~ 0.38 0.25
•
0.13 ~ D ~
0.15
/~.
0.04 ~D~
0.06
20
10 / 0 2.5
I 2.6
I 2.7
I 2,8
.~_
FIG. 8. Relationship between Chalonge's parameter 21 and StrSmgren's index fl for stars with essentially the same value of the Balmer discontinuity.
A. Use o/the Diagram (U - B)o/fl /or Stars in Clusters or Associations L e t us recall t h a t the m e m b e r s of these stellar groups h a v e the same age a n d the same initial chemical composition. Our selected star groups are the Pleiades, ~ Persei, I Orionis, I Lacertae, h a n d Z Persei. All these stars are indicated on Fig. 9, as Chalonge (1966) showed t h a t the evolution of a star close to the zero-age m e a n sequence (ZAMS) can be represented in a precise w a y in a diagram of the D/21 type, or in this particular case b y (U - B)o/fl. The older m e m b e r s of these stellar groups permit us to determine again the zero-age sequence (see Fig. 10). The members which have more rapidly evoled (more massive stars) are on lateral branches.
B. Possible Uses o] these Data (a) Calibration o] the Z A M S in years. (b) Calibration o/the diagram (U - B)o/fl in absolute magnitude.
J . H. BIGAY
175
CU-B)o .,'//
~0
/°
~
° o. o~ . , , •~. o
-0.2
o
o
-0.4
-O,q " ~ ' e e Ir'%T.
/~/
~( Per. • 1 ori.e Ple'J'ades
-0-I
o
] Lac. h&X
Pe[
•
-1.0 /
-1.2 I
2.500
I
2.6
I
I
2.7
I
I
a
2.8
FIG. 9. The (U - - B)0/~ diagram for stars in clusters a n d associations.
I
2.9
176
Photometric Classification of the O - B Stars
(U-B)o,
f~
0.0 i ll
/ / / j l
-0,2
1
I
i
I 1
/ I/
-0.6
tI
-
ii
I
i
z
I
/
7111~
/
h&X Pe III/P ii /I
-0.4
/ i
i
~,
~ ~
!
I ~
Lac.
~~7
-0-8
-1.0
-1.2
7 I
2.500
I
2.6
I
I
2.7
I
I
2.8
I
I
2.9
FIo. 10. The ( U - - B)o/fl values of Fig. 9 plotted relative to the position of the zero-age sequence (ZAMS).
J. H. BIGAY
177
REFERENCES
BARBIER,D., CHALONGE,D. and DIVAN, L. (1952) Ann. Astrophys. 15, 201. BEE~, A. (1966) Symposium No. 24 o] the I.A.U. (1964, SaltsjSbaden), p. 322. BERGER, J. (1962) Ann. Astrophys. 25. BLAA~W, A. (1963) Basic astronomical data, in Stars and Stellar Systems (ed. K. AA. STR~rD) Vo|. 3, Section 20, p. 383 (KUIPEI~-MIDDLEnuI~ST),Chicago. BOULON, J. (1963) Thesis, J. Observateurs, l~Iarseflle, 46, 225. CRALO~GE, D. (1966) Sym2osium 270. 24 o] the I.A.U. (1964, SaltsjSbaden), p. 77. CRAWFORD,D. L. (1960) Astrophys. J. 188, 843. CRAWFORD,D. L. (1960) Astrolghys. J. 188, 860. CRAWFORD,D. L. (1963~Astro~hys. J. 187, 523. C~AWFOI~D,D. L. (1963) Astro2hys. J. 187, 530. CRAWFORD,D. L. (1966)JKitt Peak 27at. Obs. Contr. No. 110. CI~AWFORD,D. L. and BARNES, J. V. (1967) Kitt Peak Nat. Obs. Cont. No. 192. C~AW~ORD, D. L. and BARNES, J. V. (1969) Kitt Peak Nat. Obs. Cont. No. 432. CRAWFORD,D. L., BAR~ES, J. V., FAURE,B. Q., GOLSOlV,J. C. and PIeR,Y, C. L. (1966) Kitt Peak Nat. Obs. Contr. No. 195. CI~AWFOI~D,D. L. and MA~D]~R,J. (1966) Kitt Peak 27at. Obs. Cont. No. 145. CRAWFORD,D. L. and PERRY, C. L. (1966) Kitt Peak Nat. Obs. Cont. I~o. 147. CRAWFOR1),D. L. and STR5~GREN, B. (1966) Kitt Peak 27at. Obs. Cont. No. 82. DryAd, L. (1966) ~.%~mposium27o. 24 o/the I.A.U. (1964, SaltsjSbaden), p. 311. GUTHRIE, B. N. G. (1963) Publ. B. Obs. Edinburgh 3, 83. HACK, M. (1953) Ann. Astro~hys. 16, 417. HECXMANN, 0. (1956) AstroThys. J. 124, 477. JOHNSON, H. L. and IRIARTE,B. (1958) Lowell Obs. Bull. 4, 47. JuNG, J. (1970) Thesis and Astr. Astrophys. 4, 53. LESCH, J. R. (1968) Thesis and Astrophys. J. Suppl. 17, 371. MCN~ARA, D. H. (1963) Astro~hys. J. 187, 317. PETRIE, R. M. and MAU~SELL,C. D. (1950) Publ. Dora. Astro~hys. Obs. Victoria 8, 253. PETRIE, R. M. (1952) Publ. Dom. Astrophys. Obs. Victoria 9, 251. PETRIE, R. M. (1966) SymTosium 27o. 24 o/the I.A.U. (1964, Saltsj5baden), p. 304. STRO~GBE~, B. (1958) Observatory 78, 137.