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Sebastia Barcelo Forteza SONG 2018 24 October 2018 0 / 12
The envelope of the power spectra of
over a thousand δ Scuti stars
Sebastia Barcelo Forteza
24 October 2018
Contents
1 Introduction
2 Data & Methods
3 Results
4 Conclusions & Future Work
Sebastia Barcelo Forteza SONG 2018 24 October 2018 1 / 12
Introduction The envelope
The envelope
Definition:
Power spectrum structure → modes → M, R , Teff
νmax, Aenv, δνenv, α
Aenv
env
i
How to calculate:
1 Gaussian fit
2 Kallinger et al. (2010):
νmax =∑
Aiνi∑Ai
Envelope of the red giant KIC 5701829.
Sebastia Barcelo Forteza SONG 2018 24 October 2018 2 / 12
Introduction The envelope
The envelope
Solar-like pulsators:
Kjeldsen & Bedding (1995): νmax ∝ MR−2T−0.5eff
Kallinger et al. (2010): α .3%
Aenv
env
i
How to calculate:
1 Gaussian fit
2 Kallinger et al. (2010):
νmax =∑
Aiνi∑Ai
Envelope of the red giant KIC 5701829.
Sebastia Barcelo Forteza SONG 2018 24 October 2018 2 / 12
Introduction The envelope
The envelope
δ Scuti stars:
κ-mechanism (Chevalier 1971; Xiong et al. 2016)
M ∈ [1.5, 2.5] M⊙
Teff ∈ [6000, 9000] K
Ω . ΩK
ν ∈ [60, 930] µHz
Scaling relation?
1 Dziembowski (1997):Teff ∝ νi
2 Kallinger et al. (2010):
νmax =∑
Aiνi∑Ai
Excited modes of a δ Scuti model from Dziembowski (1997).
Sebastia Barcelo Forteza SONG 2018 24 October 2018 3 / 12
Introduction The envelope
The envelope
δ Scuti stars:
κ-mechanism (Chevalier 1971; Xiong et al. 2016)
M ∈ [1.5, 2.5] M⊙
Teff ∈ [6000, 9000] K
Ω . ΩK
ν ∈ [60, 930] µHz
Scaling relation?
Teff ∝ νmax
Excited modes of a δ Scuti model from Dziembowski (1997).
Sebastia Barcelo Forteza SONG 2018 24 October 2018 3 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
Rotation
geff (i) ≈ g − R(i)Ω2 sin2i
Teff (i) ∝ gβ/4eff
(i) → β ≈ 1 (von Zeipel 1924)
δTeff (i) ≡(
Teff(i)− Teff
)
/Teff
Sebastia Barcelo Forteza SONG 2018 24 October 2018 4 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
Rotation
geff (i) ≈ g − R(i)Ω2 sin2i
Teff (i) ∝ gβ/4eff
(i) → β ≈ 1 (von Zeipel 1924)
δTeff (i) ≡(
Teff(i)− Teff
)
/Teff
Ω/ΩK = 0
|δTeff (i)| = 0 %
Sebastia Barcelo Forteza SONG 2018 24 October 2018 4 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
Rotation
geff (i) ≈ g − R(i)Ω2 sin2i
Teff (i) ∝ gβ/4eff
(i) → β ≈ 1 (von Zeipel 1924)
δTeff (i) ≡(
Teff(i)− Teff
)
/Teff
Ω/ΩK = 0
|δTeff (i)| = 0 %
Ω/ΩK = 0.7
|δTeff (i)| . 4.1 %
Sebastia Barcelo Forteza SONG 2018 24 October 2018 4 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
Rotation
geff (i) ≈ g − R(i)Ω2 sin2i
Teff (i) ∝ gβ/4eff
(i) → β ≈ 1 (von Zeipel 1924)
δTeff (i) ≡(
Teff(i)− Teff
)
/Teff
Ω/ΩK = 0
|δTeff (i)| = 0 %
Ω/ΩK = 0.7
|δTeff (i)| . 4.1 %
Ω/ΩK = 1
|δTeff (i)| . 12.4 %
Sebastia Barcelo Forteza SONG 2018 24 October 2018 4 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
i ≈ 90
Ω/ΩK = 0
δTeff (i) = 0 %
Ω/ΩK = 0.7
δTeff (i) ≈ −2.4 %
Ω/ΩK = 1
δTeff (i) ≈ −12.4 %
Sebastia Barcelo Forteza SONG 2018 24 October 2018 5 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
i ≈ 0
Ω/ΩK = 0
δTeff (i) = 0 %
Ω/ΩK = 0.7
δTeff (i) ≈ 4.1 %
Ω/ΩK = 1
δTeff (i) ≈ 9.4 %
Sebastia Barcelo Forteza SONG 2018 24 October 2018 5 / 12
Introduction Gravity-darkening effect
Gravity-darkening effect
i ≈ 55
Ω/ΩK = 0
δTeff (i) = 0 %
Ω/ΩK = 0.7
δTeff (i) ≈ 0 %
Ω/ΩK = 1
δTeff (i) ≈ 0 %
Sebastia Barcelo Forteza SONG 2018 24 October 2018 5 / 12
Introduction Teff − νmax diagram
Teff − νmax diagram
Barcelo Forteza et al. (2018)
Teff = Teff(1 + δTeff(i))
1 νmax → Teff
2 δTeff(i) → Ω
ΩK, i
Predicted temperatures of over 5000 δ Scuti star models with ∀ νmax,Ω
ΩK, i including the Kepler ETeff ≈ 250 K
Sebastia Barcelo Forteza SONG 2018 24 October 2018 6 / 12
Data & Methods Data sources
Data sources
νmax,Teff
νmax → δSBF pipeline
Teff → CATALOGUES
Brown et al. (2011)
Debosscher et al. (2009)
Measured νmax,Teff values of over a thousand δ Scuti stars.
Sebastia Barcelo Forteza SONG 2018 24 October 2018 7 / 12
Data & Methods δSBF
δ Scuti Basics Finder
Barcelo Forteza et al. (2015)
F (t) → νi ,Ai , φi → νmax
Detail of the light curve of CID 546. Different colours point to the observed and estimated data
Accuracy of νmax determination using δSBF for different run length and duty cycle from Moya et al. (submitted)
Sebastia Barcelo Forteza SONG 2018 24 October 2018 8 / 12
Results Linear fit
Method 1: Linear fit
Teff ≈ a · νmax + b
a (K/µHz) 3.8 ± 0.2 σ (%) 6.67b (K) 6800 ± 40 Nin (%) 97R 0.964 Nout (%) 3
Sebastia Barcelo Forteza SONG 2018 24 October 2018 9 / 12
Results Linear fit
Method 1: Linear fit
Teff ≈ a · νmax + b
a (K/µHz) 3.8 ± 0.2 σ (%) 6.67b (K) 6800 ± 40 Nin (%) 97R 0.964 Nout (%) 3
Sebastia Barcelo Forteza SONG 2018 24 October 2018 9 / 12
Results Known δ Scuti stars
Method 2: Known δ Scuti stars
Teff ,Ω
Ωk, i → Teff
Teff ≈ a · νmax + b
a (K/µHz) 2.5 ± 0.6
b (K) 7090 ± 120∣
∣
∣
Teff−Teff,M
Teff,M
∣
∣
∣. ETeff
R 0.882
Sebastia Barcelo Forteza SONG 2018 24 October 2018 10 / 12
Conclusions & Future Work
Conclusions
We suggest a new scaling relation non dependent of Ω
Ωk, i
We suggest a new method to constrain Ω
Ωk, i
Future work
Improve Teff − νmax with more data
Improve Teff − νmax with known δ Scuti stars
6= between photometric and spectroscopic data
TESS
CHEOPS
SONG
Sebastia Barcelo Forteza SONG 2018 24 October 2018 11 / 12
Acknowledgements
Thanks for your attention!
Acknowledgements
P.L. Palle, T. Roca Cortes, R. A. Garcıa
J.A. Caballero, E. Solano, A. Moya
Sebastia Barcelo Forteza SONG 2018 24 October 2018 12 / 12
Acknowledgements
Barcelo Forteza, S., Michel, E., Roca Cortes, T., & Garcıa, R. A.2015, A&A, 579, A133
Barcelo Forteza, S., Roca Cortes, T., & Garcıa, R. A. 2018, A&A,614, A46
Brown, T. M., Latham, D. W., Everett, M. E., & Esquerdo, G. A.2011, AJ, 142, 112
Chevalier, C. 1971, A&A, 14, 24
Debosscher, J., Sarro, L. M., Lopez, M., et al. 2009, A&A, 506, 519
Dziembowski, W. 1997, in IAU Symposium, Vol. 181, Sounding Solarand Stellar Interiors, ed. J. Provost & F.-X. Schmider, 317
Kallinger, T., Mosser, B., Hekker, S., et al. 2010, A&A, 522, A1
Kjeldsen, H. & Bedding, T. R. 1995, A&A, 293, 87
von Zeipel, H. 1924, MNRAS, 84, 684
Xiong, D. R., Deng, L., Zhang, C., & Wang, K. 2016, MNRAS, 457,3163
Sebastia Barcelo Forteza SONG 2018 24 October 2018 12 / 12
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