Period - radius relation

for semiregular and

Mira stars

poster on JENAM 2003 Astroseismology minisymposium

Károly Szatmáry

Department of Experimental Physics and Astronomical Observatory
k.szatmary@physx.u-szeged.hu, http://astro.u-szeged.hu




Fernie (1992), Laney et al. (2002), Turner and Burke (2002) and others studied a log P vs log R relation for radially pulsating variable stars. This relation might serve to test whether the pulsation is radial or nonradial, similarly to the log P vs log g relation (Szatmáry and Kiss, 2002). Furthermore, if the observed period and radius did not fit the relation but the pulsation is evidently radial, the shift from the relation would indicate the presence of overtone pulsation. There is a possibility of mode discrimination and mass estimation based on this relation.

The mentioned analyses covered wide period range from the delta Scuti stars (0.06 days) to the classical Cepheids (120 days). The main goal of our study is to extend the relation into the domain of semiregular and Mira variables. For this, we have collected a few tens of long period pulsators with published radii. Radii were determined by Baade-Wesselink analysis, surface-brightness method and infrared interferometry. We present here some earlier results and a new log P - log R diagram for 233 pulsating variables from delta Scuti stars to Miras.

There are some problems to determine radius of red giant SR and Mira stars:

- pulsational phase-dependent radius
- wavelength-dependent limb darkening
- strong molecular absorption in IR bands
- gas and dust envelopes around the star
- shape distortion from the spherical symmetry
- duplicity


(from Reid and Goldston 2002)

A Mira variable is dimmest when it is largest. As the pulsing, oxigen-rich star expands and cools, thick,
light-absorbing titanium oxide vapor forms in its atmosphere and blocks our view of the glowing star below
(from Sky&Tel. 2001 Nov, based on Reid and Goldston 2002).


(from Andersen et al. 2002)


Some earlier P-R relations:

(from Demarque and Percy 1965)

(from Tsvetkov 1988)


(from Tsvetkov 1988)


(from Feast 1996)
 


(from van Leeuwen et al. 1999)

Fig. 1. Radius vs. period for the Miras observed. Open diamonds are for Miras with K-[12] excess between +0.0 and +1.25, indicating less dusty mass loss, and filled triangles are for Miras with K-[12] excess >1.75 indicating more mass loss. Comparing fit lines for the lower and higher mass loss Miras (solid and dotted lines, respectively), the Miras with greater dusty mass loss appear on average 120 Ro larger. The fundamental and first-overtone regions are derived from the period-radius relationships found in Ostlie & Cox (1986).
(from van Belle et al. 2002)
Our work:
233 star data
ps file in Comm. Astroseism. (submitted version)
jpg file in Comm. Astroseism. 145, p. 60 (published version)

fitted line: log R = 0.6286 log P + 1.0819 (R [Ro], P [day])
(colors noted in data file)

References:

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Bono G., Caputo F., Marconi M.: 1998, On the period-radius relation of classical Cepheids, Astrophys. J. 497, L43

Demarque P., Percy J.R.: 1965, On Fernie's period-radius-mass relation for variable stars, Astrophys J. 142, 1082

Dumm T., Schild H.: 1998, Stellar radii of M giants, New Astronomy 3, 137

ESA: 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200

Feast M.W.: 1996, The pulsation, temperatures and metallicities of Mira and semiregular variables in different stellar systems, Mon. Not. R. Astron. Soc. 278, 11

Fernie J.D.: 1992, A new approach to the Cepheid period-luminosity law: d Scuti stars as small cepheids, Astron. J. 103, 1647

Gieren W.P., Moffett T.J., Barnes T.G.: 1999, Calibrating the Cepheid period-radius relation with galactic and Magellanic Cloud Cepheids, Astrophys. J. 512, 553

Haniff C.A., Scholz M., Tuthill P.G.: 1995, New diameter measurements for 10 Mira variables: Implications for effective temperatures, atmospheric structure and pulsation modes, Mon. Not. R. Astron. Soc. 276, 640

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