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

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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.

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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)

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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

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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

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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

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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

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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

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