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Centro de Astrofísica da Universidade do Porto

CAUP Researchers: Ahmed Grigahcène, Mário J. P. F. G. Monteiro
Team at CAUP: Origin and Evolution of Stars and Planets
Other Researchers: Victoria Antoci (AT), Luis A. Balona (ZA), G. Catanzaro (IT), Jadwiga Daszyńska-Daszkiewicz (PL), Joyce A. Guzik (US), Gerald Handler (AT), Günter Houdek (AT), Donald W. Kurtz (UK), Marcella Marconi (IT), Andrés Moya Bedón (SP), Vicenzo Ripepi (IT), Juan-Carlos Suárez (SP), Katrien Uytterhoeven (FR), William J. Borucki (US), Timothy M. Brown (US), Jørgen Christensen-Dalsgaard (DK), Ronald L. Gilliland (US), Jon M. Jenkins (US), Hans Kjeldsen (DK), David G. Koch (US), Stefano Bernabei (IT), P. A. Bradley (US), Michel Breger (AT), Marcella Di Criscienzo (IT), Marc-Antoine Dupret (BE), Rafael A. García (FR), Antonio García Hernández (SP), Jason Jackiewicz (US), Alexander Kaiser (AT), Holger Lehmann (DE), Susana Martín-Ruiz (SP), P. Mathias (FR), Joanna Molenda-Żakowicz (PL), James M. Nemec (CA), Janos Nuspl (HU), Margit Paparó (HU), Markus Roth (DE), Robert Szabó (HU), Marian D. Suran (RO), Rita Ventura (IT)

Hybrid γDoradus – δScuti pulsators:
New insights into the physics of the oscillations from Kepler observations
The Astrophysical Journal Letters, Volume 713, pp. L192 (2010)

Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main sequence γ Dor and δ Sct stars with masses 1.2-2.5 M are particularly useful for these studies. The γDor stars pulsate in high-order g modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The δSct stars pulsate in low-order g and p modes with periods of order 2 hours, driven by the κ mechanism operating in the HeII ionization zone. Theory predicts an overlap region in the Hertzsprung-Russell diagram between instability regions, where 'hybrid' stars pulsating in both types of modes should exist. The two types of modes with properties governed by different portions of the stellar interior provide complementary model constraints. Among the known γ Dor and δ Sct stars, only four have been confirmed as hybrids. Now, analysis of combined Quarter 0 and Quarter 1 Kepler data for hundreds of variable stars shows that the frequency spectra are so rich that there are practically no pure δ Sct or γ Dor pulsators, i.e. essentially all of the stars show frequencies in both the δ Sct and γ Dor frequency range. A new observational classification scheme is proposed that takes into account the amplitude as well as the frequency, and is applied to categorize 234 stars as δ Sct, γ Dor, δ Sct/γ Dor or γ Dor/δ Sct hybrids.

Figure 1 | Theoretical Hertzsprung-Russell diagram showing classification of Kepler target stars. Filled red circles represent δ Sct, open pink circles δ Sct/γ Dor, purple crosses γ Dor/δ Sct, and blue plus signs represent γ Dor. The solid lines show the zero-age main sequence, the radial fundamental red and blue edges (1R, 1B), and the fourth overtone radial red and blue edges (4R, 4B) of the δ Sct instability strip. The dashed lines are the red and blue edges of the γ Dor instability strip (l = 1 and mixing length αMLT = 2.0).

In spite of being a somewhat recent branch of Astronomy, asteroseismology already provides astronomers invaluable techniques to probe the interior structure of stars and test the application of theoretical models. Some of the preferred targets for asteroseismology studies are the γ Doradus and δ Scuti stars; these stars are core hydrogen burning, with convective cores, shallow convective envelopes and they often display rapid rotation.

While γ Dor stars pulsate with long periods (0.3-3 days) and present a pulsation constant Q>0.24 days, δ Sct are short-period pulsators (0.014-0.333 days), with Q<0.055 days. Nevertheless, a few stars known to present hybrid pulsation have already been found. As γ Dor pulsate in high-order g-modes (which can be used to probe the stellar core) and δ Sct pulsate in low-order g- and p-modes (which probe the star's envelope) these hybrid stars are especially useful in constraining the stellar structure and internal rotation profiles. While hundreds of δ Sct and several dozen γ Dor stars have been identified, until now, only four stars had been recognized as hybrid pulsators and modeled accordingly.

For this work, we used the Quarter 0 and Quarter 1 Kepler data. With Kepler's reported noise level of 0.001mmag - 10 times better than CoRoT's data - and high sensibility, we soon expect to be able to observe stochastically excited pulsation and perhaps even solar-like pulsations.

From the analysis of Kepler data, it is clear that there aren't almost any pure δ Sct or γ Dor pulsators. This contrasts with ground-based observations, which clearly distinguish between these 2 kinds of pulsators, but this difference is probably due to Kepler's increased precision, allowing the observation of higher degree modes.

However, we want to retain the useful information of δ Sct/γ Dor behavior and, thus, we need to establish criteria that allow one to determine the appropriate category of the pulsating star. If we were to only use mode frequencies, all stars would be classified as hybrids but, adding the amplitude information we can now easily classify the stars in accordance to the following scheme:

  • δ Sct: most of the frequencies are ≥5 day-1, and the lower frequencies are of relatively low amplitude;
  • δ Sct/γ Dor hybrid: most of the frequencies are ≥5 day-1, but there are some lower frequencies which are of comparable amplitude;
  • γ Dor: most of the frequencies are ≤5 day-1, and the higher frequencies are of relatively low amplitude;
  • γ Dor/δ Sct hybrid: most of the frequencies are ≤5 day-1, but there are some higher frequencies which are of comparable amplitude.

We applied this scheme to 234 Kepler targets that present γ Dor or δ Sct frequencies and have an effective temperature which puts them near the instability strips for these types of pulsation. The results were summarized in Table 1 and represented in Figure 1.


ClassNumberPercentage‹log Teff
δ Sct67273.885 ± 0.003
δ Sct/γ Dor32143.883 ± 0.006
γ Dor/δ Sct1993.868 ± 0.006
γ Dor116503.853 ± 0.005
Table 1 | Number of Stars and Percentage in Each Class. For each class, the mean values of the effective temperature are given.

In the future, short-cadence data of hybrid stars should allow us to distinguish short-period modes with closely spaced frequencies.

This project was led by CAUP astronomer Ahmed Grigahcène, who provided the rationale and initial motivation for its preparation, and who was in charge of coordinating the work and writing leading to the publication of the article.

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