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

Material type: TextPublication details: Bangalore Indian Institute of Astrophysics 1993Description: xi,137pSubject(s): Online resources: Dissertation note: Doctor of Philosophy Indian Institute of Astrophysics, Bangalore 1993 Summary: 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.Item type | Current library | Shelving location | Call number | Status | Date due | Barcode |
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Thesis & Dissertations | IIA Library-Bangalore | General Stacks | 043:524.3-54/ MAT (Browse shelf(Opens below)) | Available | 11638 |

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.

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