Stellar rotation effects of rotation on colours and line Indices of stars Annamma Mathew [Ph.D Thesis]

Doctor of Philosophy
Indian Institute of Astrophysics, Bangalore 1993

The effect of rotation on colours and line indices of stars has been a subject of
some controversy, though not actually apprecia.ted as such. Empirica} calibra.tions
of broad band and narrow band indices available in the literature have all been
carried out without taking rotation effects into account. (e.g. u v b y and (ß
by Crawford 1978, 1979). The discordant results in this field until 1970 have
been nicely summarised by Collins (1970). The basic reason, that rotation effects
on colours and line indices of stars could not be established firmly, seems to be
due to the smallness of the effect at. ll10dprte rotational velocities. Further, the
effects on observed indices by other such as duplicity, chemical peculiarity,
evolutionary effects and variable interstellar extinction appear to have introduced
a large uncertainity in the determination of rotation effects.
The problem is further complicated by the fact that the effects are a function
of the mass of the stars. Theoretical work especially by Collins and his collaborators
shows that each index is affected differently and very large effects shoud
be observable for the A stars even for moderate rotational velocities. Also, there
is no observable parameter which is not affected by rotation. The problem gets
further confounded by the fact that only V sin. i is observable and there appears
to be no way of determinging l' and i independantly.
We decided therefore to take an approach that would take care of most of
these complications. We eliminated, in each duster, known Be stars, double-lined
binaries and dose visual binaries with Δm<2.0 magnitudes. Only luminosity
dass IV and V stars are considered. Differences between duster and duster would
also not affect the final results as each cluster is analyzed independently . B and
A spectral type stars were analysed independently. For each cluster, two colour
indices were plotted against each other second order polynomial fit was
derived. The observed minus computed (O-C) residuals in each index was determined
and plotted against. Vsin i. These rotation effects determined are relative
a:o both indices are affected by rotation. As interstellar extinction also reddens the stars, the Alpha Persei Cluster
was analysed using both observed and dereddened indices. It, was found that
for Alpha Persei, where non-uniformity of extinction is not large, both reddened
and dereddened indices lead to similar results. However, as suggested by Gray and
Garrison, we used the observed indices for other clusters as dereddening procedures
for A-stars are based on an assumed calibration which may be in error due to
rotational reddening.
Evolutionary effects will introduce a scatter if the cluster members are not
coeval. This is evident from our results for the Scorpio-Centaurus association.
Here the Upper Scorpius members which are younger than the Lower Centaurus
and Upper Centaurus subgroups were found to be separated in all diagrams of
colour excess due to reddening versus V sin i diagrams. Also the scatter for Upper
Scorpius was large where the interstellar extinction is highly non-uniform. The
Upper Centaurus and Lower Centaurus group which are unreddened, consisting
mostly of B2 and B3 type-stars show the reddening effect due to rotation in perfect
agreement with theoretical predictions by Collins & Sonneborn (1977) for stars in
the similar mass range.
We have established firmly the rotation effects for various mass ranges by
analysing a large number of clusters for which sufficient data. was available. As
the predicted effects are a function of the mass, we analysed all clusters grouping
them into three mass ranges corresponding to the spectral type ranges BO-B3, B5-
B9 and A3-FO. The predicted indices for these ranges by Collins and his co-workers
were analysed the same way as we did our observational data,.
In our analysis of the theoretically derived indices we did not assume any
distribution in V or i. Instead, for each value of i (30 0 , 45°, 60° and 90 0 ) we
took sixteen values corresponding to w=O.2, 0.5, 0.8 and 0.9 for the mass range
corresponding to the spectral types from BO-B3, B5-B9 and A3-FO and derived
the rotation effects in different planes (such as ß, Cl; ß (u-b) etc.). We found
that the rotation effects determined from observed data points for clusters, very
closely matched the predictions for the various mass ranges. When this work
was almost completed, Collins, Truax & Cranmer (1991) published the results of
extensive model atmosphere calculations applicahle to rotating early-type stars.
These indices were also analysed the same way as we did f01' Collins and Sonneborn
(1977) models. On an av('rage tll<' predicted theoretical rot.ation effects of the two
models does not difFer apprcciahly. This work establishes very firmly, for t.he first.
time, that. not only rotation effects can be discerned from observa.tions but. also
that the agreement. is good with t,heoretical predictions of Collins & Sonneborn
(1977) and Collins, Tmax & Cranmer (1991) for rigidly rotating stars.
We derived ZRZAMS by two methods. In the first mf'thod we derived the ZRMS of each cluster using observed slopes of rotation effects. These were superposed
to derive ZRZAMS. Similarly theoretical corrections for each star were made
to derive ZRMS for each cluster. These were superposed to derive the ZRZAMS
as derived from theoretical predictions (for i=600 ). The two sets were found to
agree with each other. The absolute magnitudes were corrected only using theoretical
predictions. The ß, Mv relation for ZRZAMS derived by us is in excellent
agreement with the values for the lower envelope of B-stars in the ß, Mv plane
derived by Crawford (1978). This is as expected since the slow rotators in such a
plane would lie along the blue envelope. We have established for the first time the
empirical zero rotation zero age values for the intermediate band indices u v b y
and Hß.
The most dramatic result tha.t we ha.ve obtained is tha.t the blue straggler
phenomenon in young galactic clust.ers can be completely interpreted in terms of
rotation effects in colour magnitude diagrams at least in the large majority of
clusters with ages less than or equal to Hyades.
The effect of rotation on observed colours of stars was considered as a possible
cause for the observed position of blue stragglers in star clusters. We find that
the observed blueness of the blue stragglers which are intrinsic slow rotators, in
the B7-A2 type range can easily be accounted for by such effects. The reddening
caused by rotation shifts the ent.ire cluster main sequence away from the zero
rotation main sequence leaving the slow rota.tors behind. The rotation effect in
(u - b)o index reaches a maximum in the B7 - AO spectra.l type range where all
the slowly rotating blue stragglers are also concentrated. It is also therefore not
surprising that the majority of these A-type stragglers are found to be CP stars.