We present an asteroseismic approach to study the dynamics of the stellar
interior in red-giant stars by asteroseismic inversion of the splittings
induced by the stellar rotation on the oscillation frequencies. We show
preliminary results obtained for the red giant KIC4448777 observed by the space
mission Kepler.Comment: 3 pages, 4 figures, the 40th Liege International Astrophysical
  Colloquium Liac40, 'Ageing low mass stars: from red giants to white dwarfs',
  to be published on EPJ Web of Conference

Beck, P. G.

Bloemen, S.

Cardini, D.

Catanzaro, G.

Christensen-Dalsgaard, J.

Davies, G.

De Smedt, K.

Di Mauro, M. P.

Elsworth, Y.

Garcıa, R. A.

Hekker, S.

Mosser, B.

Stello, D.

Tkachenko, A.

Ventura, R.

EPJ Web of Conferences

English

arXiv

We present an asteroseismic approach to study the dynamics of the stellar interior in red giant stars by asteroseismic inversion of the splittings induced by the stellar rotation on the oscillation frequencies. We show preliminary results obtained for the red giant KIC4448777 observed by the space mission Kepler

Di Mauro, M.P.

Beck, P.G.

García, R.A.

NARCIS 

Internal rotation of red giants by asteroseismology

International Migration, Integration and Social Cohesion online publications

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Internal rotation of red giants by asteroseismologyDi Mauro, M.P.; Cardini, D.; Ventura, R.; Stello, D.; Beck, P.G.; Davies, G.; Elsworth, Y.;García, R.A.; Hekker, S.; Mosser, B.; Christensen-Dalsgaard, J.; Bloemen, S.; Catanzaro, G.;De Smedt, K.; Tkachenko, A.DOI10.1051/epjconf/20134303012Publication date2013Document VersionFinal published versionPublished inEPJ Web of ConferencesLink to publicationCitation for published version (APA):Di Mauro, M. P., Cardini, D., Ventura, R., Stello, D., Beck, P. G., Davies, G., Elsworth, Y.,García, R. A., Hekker, S., Mosser, B., Christensen-Dalsgaard, J., Bloemen, S., Catanzaro, G.,De Smedt, K., & Tkachenko, A. (2013). Internal rotation of red giants by asteroseismology.EPJ Web of Conferences, 43, 03012. https://doi.org/10.1051/epjconf/20134303012General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:26 Jul 2022EPJ Web of Conferences 43, 03012 (2013)DOI: 10.1051/epjconf/20134303012C© Owned by the authors, published by EDP Sciences, 2013Internal rotation of red giants by asteroseismologyM.P. Di Mauroa, D. Cardini1, R. Ventura2, D. Stello3, P.G. Beck4,G. Davies5, Y. Elsworth6, R.A. García5, S. Hekker7, B. Mosser8,J. Christensen-Dalsgaard9, S. Bloemen4, G. Catanzaro2,K. De Smedt4 and A. Tkachenko41INAF-IAPS Roma, Italy2INAF-Osservatorio Astrofisico di Catania, Italy3Sydney Institute for Astronomy, School of Physics, University of Sydney, Australia4Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Belgium5AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/Sap., Centre de Saclay, France6School of Physics and Astronomy, University of Birmingam, UK7Astronomical Institute Anton Pannekoek, University of Amsterdam, The Netherlands8LESLIA, CNRS, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire deParis, Meudon Cedex, France9Department of Physics and Astronomy, Aarhus University, DenmarkAbstract. We present an asteroseismic approach to study the dynamics of the stellar interior in red giantstars by asteroseismic inversion of the splittings induced by the stellar rotation on the oscillation frequencies.We show preliminary results obtained for the red giant KIC4448777 observed by the space mission Kepler.1. ASTEROSEISMIC DATAThe red giant KIC4448777 has been continuously observed by the Kepler satellite for 670 days in longcadence mode (integration time of 30 min). The Fourier analysis of the long time series has showna clear power excess between 180–260  Hz (Fig. 1) and allowed us to identify 58 individual modescharacterized by a mean large frequency separation ν = 16.96 ± 0.03  Hz, a true period spacingP = 90 ± 3 s [1] and a frequency of the maximum amplitude of the smoothed excess power ofνmax = 219.75 ± 1.23  Hz. The observed modes are l = 0 pure acoustic modes, and l = 1, l = 2 andl = 3 modes with mixed gravity–pressure character.2. ROTATIONAL SPLITTINGSRotation breaks the spherical symmetry of the stellar structure and splits the frequencies of normalmodes in (2l + 1) components. Figure 1 shows the spectrum of KIC4448777 which is characterized bythe presence of 15 rotational splittings for l = 1. As it has been noticed by [2], the observed rotationalsplittings are not constant for consecutive dipole modes (see lower panel of Fig. 1): they are larger formodes with larger gravity component which probes better the core. This indicates that the core of thisstar is rotating faster than the upper layers. In order to quantify the internal rotation it is possible to invertae-mail: maria.dimauro@inaf.itThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20134303012EPJ Web of ConferencesFigure 1. The upper panel shows theoscillation spectrum of KIC4448777. Theharmonic degree of the observed modes(l = 0, 1, 2, 3) are indicated. Multipletsdue to rotation are visible for l = 1.The lower panel shows the values of theobserved rotational splitting for individuall = 1 modes.000022223 3 31 1 1 1 1 1 111 1 1 1 1 1 1Table 1. Atmospheric parameters.Mv 11.56Teff (K) 4750 ± 250log g (dex) 3.5 ± 0.5[F e/H ] 0.23 ± 0.12v sin i (km/s) <5Table 2. Parameters of the best fitting models.Model 1 Model 2M/M 1.02 1.13Teff (K) 4800 4735log g (dex) 3.26 3.27R/R 3.94 4.08L/L 7.39 7.50(Z/X)i 0.022 0.032the following equation, obtained by applying a standard perturbation theory to the eigenfrequencies,relating the splittings νn,l to the internal rotation (r):νn,l =∫ R0Kn,l(r)(r)2dr (1)where Kn,l(r) are the mode kernel functions calculated on the unperturbed eigenfunctions for the modes(n, l) of the ‘best’ model of the star and R is the photospheric stellar radius.3. RESULTS AND CONCLUSIONThe theoretical structure models which better reproduce the identified pulsational frequencies have beencalculated with the ASTEC evolution code [3] assuming the basic atmospheric parameters given in the03012-p.2Ageing Low Mass Stars: From Red Giants to White DwarfsFigure 2. Evolutionary tracks plotted in aH-R diagram. Black dots indicate two mod-els which best reproduce the observations.Figure 3. Echelle diagrams for Model 1 (on the left) and Model 2 (on the right) of Table 2. The filled symbolsshow the observed frequencies. The open symbols show the computed frequencies. Circles are used for modes withl = 0, triangles for l = 1, squares for l = 2, diamonds for l = 3.Table 1. These parameters have been obtained by the analysis of the spectra taken with the Hermesspectograph [4] mounted on the 1.2 m Mercator telescope located in the Canary Islands. Adiabaticoscillation frequencies have been calculated with the ADIPLS code [5] and corrected for the surfaceeffect by using the relation proposed by [6]. The mass, the effective temperature, the gravity, the surfaceradius, the luminosity and the initial metallicity of the two models which best fit the observations aregiven in Table 2. These values indicate that this star is in the hydrogen-shell burning phase (see Fig. 2),as predictable from the period spacing.Figure 3 shows the echelle diagram obtained for one of the best fitting models. In a close futurewe plant to invert Eq. (1) by using both the OLA (Optimally localized Averaging) and the SOLA(Subtractive Optimally Localized Averaging) techniques which were successfully applied to the Sun(see e.g. [7]; [8]). These techniques allow to estimate a localized weighted average of (r) makingattempts to fit the averaging kernels to a function of fixed width and centered at a chosen value of theradius. Results will thus give us quantitative information on the differential rotation of the interior of theexamined star.03012-p.3EPJ Web of ConferencesReferences[1] T.R. Bedding, B. Mosser, D. Huber et al. Nature 471, (2011) 608-611[2] P.G. Beck, J. Montalban, T. Kallinger, J. De Ridder et al., Nature 481, (2012) 55-57[3] J. Christensen-Dalsgaard, ApSS 316, (2008) 13-24[4] G. Raskin, H. van Winckel, H. Hensberge, et al., A&A 526, (2011) 69-81[5] J. Christensen-Dalsgaard, ApSS 316, (2008) 113-120[6] H. Kjeldsen, T.R. Bedding, J. Christensen-Dalsgaard, ApJ 683, (2008) L175-L178[7] L. Paternó, S. Sofia, M.P. Di Mauro, A&A 314, (1996) 940-946[8] M.P. Di Mauro and W.A. Dziembowski, Mem. Sait 69, (1998) 559-56203012-p.4

Di Mauro, Maria Pia

Stello, Dennis

Davies, Guy R.

Elsworth, Yvonne P.

Garcia, Rafael A.

Hekker, Saskia

Mosser, Benoît

Christensen-Dalsgaard, Jörgen

Bloemen, Steven

de Smedt, K.

Tkachenko, Andrew

Hal-Diderot

HAL-INSU

We present an asteroseismic approach to study the dynamics of the stellar interior in red-giant stars by asteroseismic inversion of the splittings induced by the stellar rotation on the oscillation frequencies. We show preliminary results obtained for the red giant KIC4448777 observed by the space mission Kepler.3 pages, 4 figures, the 40th Liege International Astrophysical
  Colloquium Liac40, 'Ageing low mass stars: from red giants to white dwarfs',
  to be published on EPJ Web of Conferencesstatus: publishe

Di Mauro, MP

Cardini, D

Ventura, R

Stello, D

Beck, Paul

Davies, G

Elsworth, Y

Garcia, RA

Hekker, S

Mosser, B

Christensen-Dalsgaard, J

Catanzaro, G

De Smedt, Kenneth

Lirias

M.P. Di Mauro

D. Cardini

R. Ventura

D. Stello

P.G. Beck

G. Davies

Y. Elsworth

R.A. García

S. Hekker

B. Mosser

J. Christensen-Dalsgaard

S. Bloemen

G. Catanzaro

K. De Smedt

A. Tkachenko

Crossref

EDP Sciences OAI-PMH repository (1.2.0)

HAL-OBSPM

We present an asteroseismic approach to study the dynamics of the stellar interior in red giant stars by asteroseismic inversion of the splittings induced by the stellar rotation on the oscillation frequencies. We show preliminary results obtained for the red giant KIC4448777 observed by the space mission Kepler.</p

García, R. A.

University of Birmingham Research Portal

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Internal rotation of red giants by asteroseismologyDi Mauro, M.P.; Cardini, D.; Ventura, R.; Stello, D.; Beck, P.G.; Davies, G.; Elsworth, Y.;García, R.A.; Hekker, S.; Mosser, B.; Christensen-Dalsgaard, J.; Bloemen, S.; Catanzaro, G.;De Smedt, K.; Tkachenko, A.DOI10.1051/epjconf/20134303012Publication date2013Document VersionFinal published versionPublished inEPJ Web of ConferencesLink to publicationCitation for published version (APA):Di Mauro, M. P., Cardini, D., Ventura, R., Stello, D., Beck, P. G., Davies, G., Elsworth, Y.,García, R. A., Hekker, S., Mosser, B., Christensen-Dalsgaard, J., Bloemen, S., Catanzaro, G.,De Smedt, K., & Tkachenko, A. (2013). Internal rotation of red giants by asteroseismology.EPJ Web of Conferences, 43, 03012. https://doi.org/10.1051/epjconf/20134303012General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:15 Apr 2023EPJ Web of Conferences 43, 03012 (2013)DOI: 10.1051/epjconf/20134303012C© Owned by the authors, published by EDP Sciences, 2013Internal rotation of red giants by asteroseismologyM.P. Di Mauroa, D. Cardini1, R. Ventura2, D. Stello3, P.G. Beck4,G. Davies5, Y. Elsworth6, R.A. García5, S. Hekker7, B. Mosser8,J. Christensen-Dalsgaard9, S. Bloemen4, G. Catanzaro2,K. De Smedt4 and A. Tkachenko41INAF-IAPS Roma, Italy2INAF-Osservatorio Astrofisico di Catania, Italy3Sydney Institute for Astronomy, School of Physics, University of Sydney, Australia4Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Belgium5AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/Sap., Centre de Saclay, France6School of Physics and Astronomy, University of Birmingam, UK7Astronomical Institute Anton Pannekoek, University of Amsterdam, The Netherlands8LESLIA, CNRS, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire deParis, Meudon Cedex, France9Department of Physics and Astronomy, Aarhus University, DenmarkAbstract. We present an asteroseismic approach to study the dynamics of the stellar interior in red giantstars by asteroseismic inversion of the splittings induced by the stellar rotation on the oscillation frequencies.We show preliminary results obtained for the red giant KIC4448777 observed by the space mission Kepler.1. ASTEROSEISMIC DATAThe red giant KIC4448777 has been continuously observed by the Kepler satellite for 670 days in longcadence mode (integration time of 30 min). The Fourier analysis of the long time series has showna clear power excess between 180–260  Hz (Fig. 1) and allowed us to identify 58 individual modescharacterized by a mean large frequency separation ν = 16.96 ± 0.03  Hz, a true period spacingP = 90 ± 3 s [1] and a frequency of the maximum amplitude of the smoothed excess power ofνmax = 219.75 ± 1.23  Hz. The observed modes are l = 0 pure acoustic modes, and l = 1, l = 2 andl = 3 modes with mixed gravity–pressure character.2. ROTATIONAL SPLITTINGSRotation breaks the spherical symmetry of the stellar structure and splits the frequencies of normalmodes in (2l + 1) components. Figure 1 shows the spectrum of KIC4448777 which is characterized bythe presence of 15 rotational splittings for l = 1. As it has been noticed by [2], the observed rotationalsplittings are not constant for consecutive dipole modes (see lower panel of Fig. 1): they are larger formodes with larger gravity component which probes better the core. This indicates that the core of thisstar is rotating faster than the upper layers. In order to quantify the internal rotation it is possible to invertae-mail: maria.dimauro@inaf.itThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20134303012EPJ Web of ConferencesFigure 1. The upper panel shows theoscillation spectrum of KIC4448777. Theharmonic degree of the observed modes(l = 0, 1, 2, 3) are indicated. Multipletsdue to rotation are visible for l = 1.The lower panel shows the values of theobserved rotational splitting for individuall = 1 modes.000022223 3 31 1 1 1 1 1 111 1 1 1 1 1 1Table 1. Atmospheric parameters.Mv 11.56Teff (K) 4750 ± 250log g (dex) 3.5 ± 0.5[F e/H ] 0.23 ± 0.12v sin i (km/s) <5Table 2. Parameters of the best fitting models.Model 1 Model 2M/M 1.02 1.13Teff (K) 4800 4735log g (dex) 3.26 3.27R/R 3.94 4.08L/L 7.39 7.50(Z/X)i 0.022 0.032the following equation, obtained by applying a standard perturbation theory to the eigenfrequencies,relating the splittings νn,l to the internal rotation (r):νn,l =∫ R0Kn,l(r)(r)2dr (1)where Kn,l(r) are the mode kernel functions calculated on the unperturbed eigenfunctions for the modes(n, l) of the ‘best’ model of the star and R is the photospheric stellar radius.3. RESULTS AND CONCLUSIONThe theoretical structure models which better reproduce the identified pulsational frequencies have beencalculated with the ASTEC evolution code [3] assuming the basic atmospheric parameters given in the03012-p.2Ageing Low Mass Stars: From Red Giants to White DwarfsFigure 2. Evolutionary tracks plotted in aH-R diagram. Black dots indicate two mod-els which best reproduce the observations.Figure 3. Echelle diagrams for Model 1 (on the left) and Model 2 (on the right) of Table 2. The filled symbolsshow the observed frequencies. The open symbols show the computed frequencies. Circles are used for modes withl = 0, triangles for l = 1, squares for l = 2, diamonds for l = 3.Table 1. These parameters have been obtained by the analysis of the spectra taken with the Hermesspectograph [4] mounted on the 1.2 m Mercator telescope located in the Canary Islands. Adiabaticoscillation frequencies have been calculated with the ADIPLS code [5] and corrected for the surfaceeffect by using the relation proposed by [6]. The mass, the effective temperature, the gravity, the surfaceradius, the luminosity and the initial metallicity of the two models which best fit the observations aregiven in Table 2. These values indicate that this star is in the hydrogen-shell burning phase (see Fig. 2),as predictable from the period spacing.Figure 3 shows the echelle diagram obtained for one of the best fitting models. In a close futurewe plant to invert Eq. (1) by using both the OLA (Optimally localized Averaging) and the SOLA(Subtractive Optimally Localized Averaging) techniques which were successfully applied to the Sun(see e.g. [7]; [8]). These techniques allow to estimate a localized weighted average of (r) makingattempts to fit the averaging kernels to a function of fixed width and centered at a chosen value of theradius. Results will thus give us quantitative information on the differential rotation of the interior of theexamined star.03012-p.3EPJ Web of ConferencesReferences[1] T.R. Bedding, B. Mosser, D. Huber et al. Nature 471, (2011) 608-611[2] P.G. Beck, J. Montalban, T. Kallinger, J. De Ridder et al., Nature 481, (2012) 55-57[3] J. Christensen-Dalsgaard, ApSS 316, (2008) 13-24[4] G. Raskin, H. van Winckel, H. Hensberge, et al., A&A 526, (2011) 69-81[5] J. Christensen-Dalsgaard, ApSS 316, (2008) 113-120[6] H. Kjeldsen, T.R. Bedding, J. Christensen-Dalsgaard, ApJ 683, (2008) L175-L178[7] L. Paternó, S. Sofia, M.P. Di Mauro, A&A 314, (1996) 940-946[8] M.P. Di Mauro and W.A. Dziembowski, Mem. Sait 69, (1998) 559-56203012-p.4

Internal rotation of red giants by asteroseismology

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Lirias

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EDP Sciences OAI-PMH repository (1.2.0)

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University of Birmingham Research Portal

International Migration, Integration and Social Cohesion online publications