Evaluation Projects for Pulsating Stars Jørgen Christensen-Dalsgaard (29 February, 2016)

Evaluation projects for Pulsating Stars Jørgen Christensen-Dalsgaard (29 February, 2016)

The projects should result in a report of up to around 10 pages, which may be written in Danish or English. Here I expect a description of the general problem considered, and an analysis starting from the references provided, but, as required, taken into account also other references or material. It may be appropriate to present derivations in more detail than provided in the papers. The required papers can in most cases be found through the reprint server ADS, at http://adsabs.harvard.edu/abstract service.html. Also, they are often available as preprints at the arXiv preprint server, at http://xxx.lanl.gov/archive/astro-ph. In some cases, references are given to papers that may be difficult to find; in that case, I shall lend them to you to copy. A few projects also involve simple numerical analyses or calculations; they can be carried out in any language, but I expect the report to include relevant plots of the results. There should be enough suggestions that you can each get your own project. They will be distributed on a first-come first-served basis. When you have chosen a project I ask you to send me an e-mail ([email protected]) with your name, study number (˚arskortnummer) and the number of the project. I shall keep a list of the project numbers that have already been reserved on the home page of the course. The report should similarly be e-mailed to me, as a PDF file. The reports will be graded according to the 12 scale. In the evaluation, I shall give substantial weight to the appropriate combination of results from several sources and/or independent analysis.

1. Helioseismic eﬀect of revision of solar abundances

Although solar models have been found to agree quite well with helioseismic inferences (e.g. Gough et al. 1996), this agreement has been seriously compromised by a recent revision of the solar surface abundances (very recently reviewed by Asplund et al. 2009). These issues were discussed by Basu & Antia (2004), Bahcall et al. (2005) and Christensen-Dalsgaard et al. (2009). Discuss this problem and its possible solution; this should also include a brief review of the relevant analysis techniques, including those presented by Basu & Antia (1997). References: Asplund, M., Grevesse, N., Sauval, A. J. & Scott, P., 2009. [The chemical composition of the Sun]. Annu. Rev. Astron. Astrophys., 47, 481 – 522. Bahcall, J. N., Basu, S., Pinsonneault, M. & Serenelli, A. M., 2005. [Helioseismological implications of recent solar abundance determinations]. Astrophys. J., 618, 1049 – 1056. Basu, S. & Antia, H. M., 1997. [Seismic measurement of the depth of the solar convection zone]. Mon. Not. R. astr. Soc., 287, 189 – 198. Basu, S. & Antia, H. M., 2004. [Constraining solar abundances using helioseismology]. Astrophys. J., 606, L85 – L88. Christensen-Dalsgaard, J., Di Mauro, M. P., Houdek, G. & Pijpers, F., 2009. [On the opacity change required to compensate for the revised solar composition]. Astron. Astrophys., 494, 205 – 208. Gough, D. O., Kosovichev, A. G., Toomre, J., et al., 1996. [The seismic structure of the Sun]. Science, 272, 1296 – 1300.

1 2. Asteroseismic analysis of main-sequence stars based on Kepler data

The Kepler mission has provided detailed frequency spectra for a substantial number of main- sequence stars, and we are just at the beginning of learning how to analyse them in the best possible way. This also involves extensive comparisons of computations using different evolution codes. Based on the examples in the following references discuss what has been learned so far, and how these analyses can be extended and improved. You may include, and possibly criticize, the review provided by Christensen-Dalsgaard (2012). References: Christensen-Dalsgaard, J., 2012. [Stellar model fits and inversions]. Astron. Nachr., 333, 914 – 925. Mathur, S., Metcalfe, T. S., Woitaszek, M., et al., 2012. [A uniform asteroseismic analysis of 22 solar-type stars observed by Kepler]. Astrophys. J., 749, 152-(1 – 14). Metcalfe, T. S., Chaplin, W. J., Appourchaux, T., et al., 2012. [Asteroseismology of the solar analogs 16 Cyg A and B from Kepler observations]. Astrophys. J., 748, L10-(1 – 6). Metcalfe, T. S., Creevey, L. O. & Davies, G. R., 2015. [Asteroseismic modeling of 16 Cyg A & B using the complete Kepler data set]. Astrophys. J., 811, L37-(1 – 5). Silva Aguirre, V., Basu, S., Brandão,I. M., et al., 2013. [Stellar ages and convective cores in field main-sequence stars: first asteroseismic application to two Kepler targets]. Astrophys. J., 769, 141-(1 – 17).

3. Asteroseismic characterization of exoplanet host stars

Asteroseismology based on Kepler data provides a unique possibility for determining the properties stars found by the mission to host extra-solar planets, essentially from the same photometric observations. In particular, the stellar radius and mass are needed to determine radii and masses of the exoplanets, while asteroseismology also provides the possibility to determine the age of the star and its planetary system. The following references give some examples of this type of analysis. You should discuss the potential and the possible problems in determining the stellar properties and the importance for characterizing the exoplanets. You may also ﬁnd other examples of this type of analysis in the literature. References: Christensen-Dalsgaard, J., Kjeldsen, H., Brown, T. M., Gilliland, R. L., Arentoft, T., Frandsen, S., Quirion, P.-O., Borucki, W. J., Koch, D. & Jenkins, J. M., 2010. [Asteroseismic investigation of known planet hosts in the Kepler ﬁeld]. Astrophys. J., 713, L164 – L168. Fogtmann-Schulz, A., Hinrup, B., Van Eylen, V., Christensen-Dalsgaard, J., Kjeldsen, H., Silva Aguirre, V. & Tingley, B., 2014. [Accurate parameters of the oldest known rocky-exoplanet hosting system: Kepler-10 revisited]. Astrophys. J., 781, 67-(1 – 8). Silva Aguirre, V., Davies, G. R., Basu, S., et al., 2015. [Ages and fundamental properties of Kepler exoplanet host stars from asteroseismology]. Mon. Not. R. astr. Soc., 452, 2127 – 2148.

2 4. A detailed example of asteroseismic model ﬁtting

Lebreton & Goupil (2014) gave a very detailed and illustrative analysis of a star observed by the CoRoT mission, comparing the results of using diﬀerent combinations of asteroseismic and ‘classical’ constraints. Also, the provided extensive tables of additional properties of the models, allowing further investigations of how these properties are related and constrained by the data. In this project you should discuss the analysis in the paper and try to carry it further by using the data provided in connection with the paper. I hope that this can provide additional insight for you (and me!) on how the properties of the models depend on the assumed physics etc. References:

Lebreton, Y. & Goupil, M. J., 2014. [Asteroseismology for “`ala carte” stellar age-dating and weighing. Age and mass of the CoRoT exoplanet host HD 52265]. Astron. Astrophys., 569, A21-(1 – 24).

5. Asteroseismic analysis of the α Centauri system

Solar-like oscillations have been detected in both main components of the α Cen binary system. The masses of these components span the solar mass; furthermore, the properties of the stars are known with unusually good precision due to their proximity, and from analysis of the binary motion. Thus the system provides excellent opportunities for asteroseismology. The references discuss observations of the system and attempts at analysing the results. In the project, discuss the observational data and the modelling, and the conclusions reached so far. What will be required to improve both observations and models? References:

Bedding, T. R., Kjeldsen, H., Butler, R. P., McCarthy, C., Marcy, G. W., O’Toole, S. J., Tinney, C. G. & Wright, J. T., 2004. [Oscillation frequencies and mode lifetimes in α Centauri A]. Astrophys. J., 614, 380 – 385. Bouchy, F. & Carrier, F., 2002. [The acoustic spectrum of α Cen A]. Astron. Astrophys., 390, 205 – 212. Carrier, F. & Bourban, G., 2003. [Solar-like oscillations in the K1 dwarf star α Cen B]. Astron. Astrophys., 406, L23 – L26. de Meulenaer, P., Carrier, F., Miglio, A., Bedding, T. R., Campante, T. L., Eggenberger, P., Kjeldsen, H. & Montalb´an,J., 2010. [Core properties of α Centauri A using asteroseismology]. Astron. Astrophys., 523, A54-(1 – 8). Eggenberger, P., Charbonnel, C., Talon, S., Meynet, G., Maeder, A., Carrier, F. & Bourban, G., 2004. [Analysis of α Centauri AB including seismic constraints]. Astron. Astrophys., 417, 235 – 246. Kjeldsen, H., Bedding, T. R., Butler, R. P., Christensen-Dalsgaard, J., Kiss, L. L., McCarthy, C., Marcy, G. W., Tinney, C. G. & Wright, J. T., 2005. [Solar-like oscillations in α Centauri B]. Astrophys. J., 635, 1281 – 1290. Miglio, A. & Montalb´an,J., 2005. [Constraining fundamental stellar parameters using seismology. Application to α Centauri AB]. Astron. Astrophys., 441, 615 – 629.

3 6. Asteroseismic diagnostics of subgiant stars

Subgiants, i.e., stars in the hydrogen shell-burning phase evolving towards the red-giant branch, are very interesting from an asteroseismic point of view. They typically show mixed modes, with great diagnostic potential, and they have somewhat larger amplitudes, owing to their larger luminosity, than stars on the main sequence. Here we consider examples of asteroseismic diagnostics of such stars based on CoRoT and Kepler observations. References: Metcalfe, T. S., Monteiro, M. J. P. F. G., Thompson, M. J., et al., 2010. [A precise asteroseismic age and radius for the evolved Sun-like star KIC 11026764]. Astrophys. J., 723, 1583 – 1598. Deheuvels, S. & Michel, E., 2011. [Constraints on the structure of the core of subgiants via mixed modes: the case of HD 49385]. Astron. Astrophys., 535, A91-(1 – 19). Di Mauro, M. P., Cardini, D., Catanzaro, G., et al., 2011. [Solar-like oscillations from the depths of the red-giant star KIC 4351319 observed with Kepler]. Mon. Not. R. astr. Soc., 415, 3783 – 3797. Do˘gan,G., Metcalfe, T. S., Deheuvels, S., et al., 2013. [Characterizing two solar-type Kepler subgiants with asteroseismology: KIC 10920273 and KIC 11395018]. Astrophys. J., 763, 19-(1 – 10).

7. Inversion for solar internal rotation

We now have very extensive data on rotational splittings of solar oscillations. As a result, rotation in much of the solar interior has been determined, although there remain some uncertainties. In the project, a discussion should be made of the various techniques used for the inversion and of the results. In particular, consider the remaining problems, in the limitations to the parts of the Sun that can be studied and the remaining inconsistencies between different datasets. References: Larsen, R. M., Christensen-Dalsgaard, J., Kosovichev, A. G. & Schou, J., 1998. [Improved SOLA inversions of MDI data]. In Structure and dynamics of the interior of the Sun and Sun-like stars; Proc. SOHO 6/GONG 98 Workshop, eds S.G. Korzennik & A. Wilson, ESA SP-418, ESA Publications Division, Noordwijk, The Netherlands, p. 813 – 818. Schou, J., Antia, H. M., Basu, S., et al., 1998. [Helioseismic studies of differential rotation in the solar envelope by the Solar Oscillations Investigation using the Michelson Doppler Imager]. Astrophys. J., 505, 390 – 417. Schou, J., Howe, R., Basu, S., Christensen-Dalsgaard, J., Corbard, T., Hill, F., Larsen, R. M., Rabello-Soares, M. C. & Thompson, M. J., 2002. [A comparison of solar p-mode parameters from the Michelson Doppler Imager and the Global Oscillation Network Group: splitting coefficients and rotation inversions]. Astrophys. J., 567, 1234 – 1249.

4 8. Rotation of the solar core

In most of the Sun the rotation rate has been determined with quite good precision. However, the rotation of the central parts of the Sun is still rather uncertain. This partly results from the fact that few oscillations are sensitive to this region, partly from small influence of the core on the rotational splitting of the oscillation frequencies owing to the small extent of the core. Consequently there are several partly conflicting observations of the relevant oscillations of low degree, from ground- based networks of observatories and from the GOLF instrument on SOHO, observing the Sun in integrated light. The project consists in discussing the different observations and the problems arising in the determination of the rotational splitting, as well as the problems involved in the inversions to determine rotation of the central parts of the Sun. This should also include a critical comparison and discussion of the results. References: Elsworth, Y., Howe, R., Isaak, G. R., McLeod, C. P., Miller, B. A., New, R., Wheeler, S. J. & Gough, D. O., 1995. [Slow rotation of the Sun’s interior]. Nature, 376, 669 – 672. Chaplin, W. J., Elsworth, Y., Isaak, G. R., Marchenkov, K. I., Miller, B. A. & New, R., 2001. [Rigid rotation of the solar core? On the reliable extraction of low-` rotational p-mode splittings from full-disc observations of the Sun]. Mon. Not. R. astr. Soc., 327, 1127 – 1136. Chaplin, W. J., Christensen-Dalsgaard, J., Elsworth, Y., Howe, R., Isaak, G. R., Larsen, R. M., New, R., Schou, J., Thompson, M. J. & Tomczyk, S., 1999. [Rotation of the solar core from BiSON and LOWL frequency observations]. Mon. Not. R. astr. Soc., 308, 405 – 414. Eff-Darwich, A. & Korzennik, S. G., 2013. [The dynamics of the solar radiative zone]. Solar Phys., 287, 43 – 56. Eff-Darwich, A., Korzennik, S. G., Jiménez-Reyes, S. J. & Garc´ıa,R. A., 2008. [Analysis of the sensitivity of solar rotation to helioseismic data from GONG, GOLF, and MDI observations]. Astrophys. J., 679, 1636 – 1643.

5 9. Solar rotation and the solar cycle

It has been found that the solar angular velocity changes systematically during the solar cycle, in a manner that appears closely related to the varying number and location of the sunspots. The observational evidence is very clear and indicates that the variation occurs in a large fraction of the solar convection zone, but the physical origin and the relation to the generation of the solar magnetic ﬁeld are still not fully understood. In the project, discuss the observations and characterize the observed variations. A particularly interesting aspect is the relation to the last apparently anomalous solar activity minimum (Howe et al. 2009). References: Basu, S., Broomhall, A.-M., Chaplin, W. J. & Elsworth, Y., 2012. [Thinning of the Sun’s magnetic layer: the peculiar solar minimum could have been predicted]. Astrophys. J., 758, 43-(1 – 6). Howe, R., Christensen-Dalsgaard, J., Hill, F., Komm, R. W., Larsen, R. M., Schou, J., Thompson, M. J. & Toomre, J., 2000. [Deeply penetrating banded zonal ﬂows in the solar convection zone]. Astrophys. J., 533, L163 – L166. Howe, R., Christensen-Dalsgaard, J., Komm, R., Schou, J. & Thompson, M. J., 2005. [Solar convection-zone dynamics, 1995–2004]. Astrophys. J., 634, 1405 – 1415. Howe, R., Rempel, M., Christensen-Dalsgaard, J., Hill, F., Komm, R., Larsen, R. M., Schou, J. & Thompson, M. J., 2006. [Solar Convection Zone Dynamics: How sensitive are inversions to subtle dynamo features?]. Astrophys. J., 649, 1155 – 1168. Howe, R., Jain, K., Bogart, R. S., Haber, D. A. & Baldner, C. S., 2012. [Two-dimensional helioseismic power, phase and coherence spectra of Solar Dynamics Observatory photospheric and chromospheric observables]. Solar Phys., 281, 533 – 549. Howe, R., Christensen-Dalsgaard, J., Hill, F., Komm, R., Larson, T. P., Rempel, M., Schou, J. & Thompson, M. J., 2013. [The high-latitude branch of the solar torsional oscillation in the rising phase of cycle 24]. Astrophys. J., 767, L20-(1 – 4).

6 10. Global properties of oscillating red giants

Solar-like oscillations have been observed in literally thousands of red giants. The global properties of the stars are determined from the large frequency separation and the frequency at maximum power, allowing ensemble analysis of the stars. This shows clear patterns in the oscillation properties but also detailed scaling relations that are so far not fully understood. Discuss some of these issues, including possible problems with the inferences. References:

Huber, D., Bedding, T. R., Stello, D., Mosser, B., Mathur, S., Kallinger, T., Hekker, S., Elsworth, Y. P., Buzasi, D. L., De Ridder, J., Gilliland, R. L., Kjeldsen, H., Chaplin, W. J., Garc´ıa,R. A., Hale, S. J., Preston, H. L., White, T. R., Borucki, W. J., Christensen-Dalsgaard, J., Clarke, B. D., Jenkins, J. M. & Koch, D., 2010. [Asteroseismology of red giants from the ﬁrst four months of Kepler data: global oscillation parameters for 800 stars]. Astrophys. J., 723, 1607 – 1617. Mosser, B., Belkacem, K., Goupil, M. J., Michel, E., Elsworth, Y., Barban, C., Kallinger, T., Hekker, S., De Ridder, J., Samadi, R., Baudin, F., Pinheiro, F. J. G., Auvergne, M., Baglin, A. & Catala, C., 2011. [The universal red-giant oscillation pattern. An automated determination with CoRoT data]. Astron. Astrophys., 525, L9-(1 – 4). Huber, D., Bedding, T. R., Stello, D., et al., 2011. [Testing scaling relations for solar-like oscillations from the main-sequence to red giants using Kepler data]. Astrophys. J., 743, 143-(1 – 10). Basu, S., Grundahl, F., Stello, D., et al., 2011. [Sounding open clusters: asteroseismic constraints from Kepler on the properties of NGC 6791 and NGC 6819]. Astrophys. J., 729, L10-(1 – 6).

11. Excitation of solar-like oscillations: a relation between νmax and νac?

With increasing understanding of the processes exciting and damping the oscillations, and the extensive Kepler data, the distribution of power in solar-like oscillations provides an important diagnostics of stellar properties. In particular, the frequency νmax at maximum power has proven very useful in the determination of stellar mass and radius, through a claimed relation to the acoustic cut-oﬀ frequency νac. Discuss the excitation of solar-like oscillations and in particular argue whether or not Belkacem et al. (2011) provide a convincing physical explanation for the relation between νac and νmax. References:

Houdek, G., 2012. In Proceedings of the 61st Fujihara Seminar: Progress in solar/stellar physics with helio- and asteroseismology. H. Shibahashi, M. Takata & A. E. Lynas-Gray,eds, ASP Conf. Ser., vol. 462, 7 – 18. Chaplin, W. J., Houdek, G., Elsworth, Y., Gough, D. O., Isaak, G. R. & New, R., 2005. [On model predictions of the power spectral density of radial solar p modes]. Mon. Not. R. astr. Soc., 360, 859 – 868. Belkacem, K., Goupil, M. J., Dupret, M. A., Samadi, R., Baudin, F., Noels, A. & Mosser, B., 2011. [The underlying physical meaning of the νmax − νc relation]. Astron. Astrophys., 530, A142-(1 – 8).

7 12. Probing the core of red giants with g modes

One of the wonderful surprises of the Kepler mission has been the richness of the observed oscillations of red giants. This potentially allows detailed investigations of the properties of their cores. This project considers the properties of the oscillations in red giants and the initial diagnostics that have been obtained. An important issue is the selection of modes expected to be visible in these stars, discussed by Dupret et al. (2009) and Grosjean et al. (2014). Discuss the results that have already been obtained from the Kepler and CoRoT data, and the potential for further information from continuing analysis of the available data. References: Dupret, M.-A., Belkacem, K., Samadi, R., Montalban, J., Moreira, O., Miglio, A., Godart, M., Ventura, P., Ludwig, H.-G., Grigahcène,A., Goupil, M.-J., Noels, A. & Caffau, E., 2009. [Theoretical amplitudes and lifetimes of non-radial solar-like oscillations in red giants]. Astron. Astrophys., 506, 57 – 67. Grosjean, M., Dupret, M.-A., Belkacem, K., Montalban, J., Samadi, R. & Mosser, B., 2014. [The- oretical power spectra of mixed modes in low-mass red giant stars]. Astron. Astrophys., 572, A11-(1 – 13). Bedding, T. R., Mosser, B., Huber, D., et al., 2011. [Gravity modes as a way to distinguish between hydrogen- and helium-burning red giant stars]. Nature, 471, 608 – 611. Mosser, B., Barban, C., Montalbán,J., Beck, P. G., Miglio, A., Belkacem, K., Goupil, M. J., Hekker, S., De Ridder, J., Dupret, M. A., Elsworth, Y., Noels, A., Baudin, F., Michel, E., Samadi, R., Auvergne, M., Baglin, A. & Catala, C., 2011. [Mixed modes in red-giant stars observed with CoRoT]. Astron. Astrophys., 532, A86-(1 – 8). Bildsten, L., Paxton, B., Moore, K. & Macias, P. J., 2012. [Acoustic signatures of the helium core flash]. Astrophys. J., 744, L6-(1 – 5).

8 13. Internal rotation of evolved stars from Kepler observations

The Kepler data reached a duration where the rotational splitting could be measured in a number of stars. Since our understanding of the evolution of stellar rotation is extremely limited, such information is very important. In this project we consider two cases: red giants and a subgiant star. Discuss (possibly critically) the analysis and the results and relate this to how the stars might have reached the observed state. References: Beck, P. G., Montalban, J., Kallinger, T., et al., 2012. [Fast core rotation in red-giant stars as revealed by gravity-dominated mixed modes]. Nature 481, 55 – 57. Cantiello, M., Mankovich, C., Bildsten, L., Christensen-Dalsgaard, J. & Paxton, B., 2014. [Angular momentum transport within evolved low-mass stars]. Astrophys. J., 788, 93-(1 – 7). Deheuvels, S., Garc´ıa,R. A., Chaplin, W. J., et al., 2012. [Seismic evidence for a rapidly rotating core in a lower-giant-branch star observed with Kepler]. Astrophys. J., 756, 19-(1 – 16). Deheuvels, S., Do˘gan,G., Goupil, M. J., et al., 2014. [Seismic constraints on the radial dependence of the internal rotation proﬁles of six Kepler subgiants and young red giants]. Astron. Astrophys., in the press. [arXiv:arXiv:1401.3096 [astro-ph]] Eggenberger, P., Montalb´an,J. & Miglio, A., 2012. [Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants]. Astron. Astrophys., 544, L4-(1 – 4). Goupil, M. J., Mosser, B., Marques, J. P., Ouazzani, R. M., Belkacem, K., Lebreton, Y. & Samadi, R., 2013. [Seismic diagnostics for transport of angular momentum in stars. II. Interpreting observed rotational splittings of slowly rotating red giant stars]. Astron. Astrophys., 549, A75-(1 – 13). Mosser, B., Goupil, M. J., Belkacem, K., Marques, J. P., Beck, P. G., Bloemen, S., De Ridder, J., Barban, C., Deheuvels, S., Elsworth, Y., Hekker, S., Kallinger, T., Ouazzani, R. M., Pinson- neault, M., Samadi, R., Stello, D., Garc´ıa,R. A., Klaus, T. C., Li, J., Mathur, S. & Morris, R. L., 2012. [Spin down of the core rotation in red giants]. Astron. Astrophys., 548, A10-(1 – 14).

9 14. Detailed properties of mixed modes in red giants

The properties of mixed modes with predominantly g-mode character in red giants are quite com- plex, but they are important for a full understanding of the diagnostic potential of the modes, such as the observed period spacings. Discuss these properties and their diagnostic implications. A simple analysis is provided in Section 4.2 of Christensen-Dalsgaard (2012); it should be compared with the more detailed analysis by Mosser et al. (2012) and Goupil et al. (2013). References: Christensen-Dalsgaard, J., 2012. [Kepler asteroseismology of red-giant stars]. In Proceedings of the 61st Fujihara Seminar: Progress in solar/stellar physics with helio- and asteroseismology. H. Shibahashi, M. Takata & A. E. Lynas-Gray, eds, ASP Conf. Ser., 462, p. 505 – 524. Goupil, M. J., Mosser, B., Marques, J. P., Ouazzani, R. M., Belkacem, K., Lebreton, Y. & Samadi, R., 2013. [Seismic diagnostics for transport of angular momentum in stars. II. Interpreting observed rotational splittings of slowly rotating red giant stars]. Astron. Astrophys., 549, A75-(1 – 13). Mosser, B., Goupil, M. J., Belkacem, K., Michel, E., Stello, D., Marques, J. P., Elsworth, Y., Barban, C., Beck, P. G., Bedding, T. R., De Ridder, J., Garc´ıa,R. A., Hekker, S., Kallinger, T., Samadi, R., Stumpe, M. C., Barclay, T. & Burke, C. J., 2012. [Probing the core structure and evolution of red giants using gravity-dominated mixed modes observed with Kepler]. Astron. Astrophys., 540, A143-(1 – 11). Stello, D., 2012 [Non-radial modes in cool stars]. In Proceedings of the 61st Fujihara Seminar: Progress in solar/stellar physics with helio- and asteroseismology. H. Shibahashi, M. Takata & A. E. Lynas-Gray, eds, ASP Conf. Ser., 462, p. 200 – 209.

15. Suppressed dipolar modes and magnetic ﬁelds in red-giant stars

In some red giants the dipolar (l = 1) modes have very low amplitudes, compared with modes of other degrees. This has for some time been a major mystery in the study of red-giant asteroseismology. In very recent analyses combining observational and theoretical considerations this has been linked to a possible magnetic field in the core of these stars, which scatters and hence damps the modes, selectively for l = 1. In addition to solving an interesting puzzle, this also may provide a unique way to study the evolution of magnetic fields in these stars In the project you should discuss the observational evidence (Mosser et al. 2012, Garc´ıaet al. 2014, Stello et al. 2016) and the model proposed by Fuller et al. (2015). You might also consider the more detailed model analysis provided by Cantiello et al. (2016). References: Cantiello, M., Fuller, J. & Bildsten, L., 2016. [Asteroseismic signatures of evolving internal stellar magnetic fields]. Submitted to Astrophys. J.. [arXiv:1602.03056 [astro-ph.SR]]. Fuller, J., Cantiello, M., Stello, D., Garcia, R. & Bildsten, L., 2015. [Asteroseismology can reveal strong internal magnetic fields in red giant stars]. Science, 350, 423 – 426. Garc´ıa,R. A., PérezHernández,F., Benomar, O., et al., 2014. [Study of KIC 8561221 observed by Kepler: an early red giant showing depressed dipolar modes]. Astron. Astrophys., 563, A84-(1 – 17). Mosser, B., Elsworth, Y., Hekker, S., et al., 2012. [Characterization of the power excess of solar-like oscillations in red giants with Kepler]. Astron. Astrophys., 537, A30-(1 – 15).

10 Stello, D., Cantiello, M., Fuller, J., Huber, D., Garc´ıa, R. A., Bedding, T. R., Bildsten, L. & Silva Aguirre, V., 2016. [A prevalence of dynamo-generated magnetic ﬁelds in the cores of intermediate-mass stars]. Nature, 529, 364 – 367.

16. Eﬀects on frequencies of sharp features in the model

‘Sharp’ features (i.e., features that vary on a scale shorter than the wavelength of the eigenfunctions) cause oscillations in the frequencies as functions of the mode order. Examples are the boundaries of convection zones and the ionization zone of helium. By analysing the eﬀect on the frequencies, information about the feature can be obtained. This is discussed in some detail in Problems in Asteroseismology, Problem 4.4, following Mon- teiro et al. (1994). In this project, carry through the analysis in Problem 4.4 (neglecting point viii)) and discuss, following Monteiro et al., the investigation of the base of the solar convection zone based on the oscillations in the frequencies. You may also consider the possibilities for such analyses for other stars, following Monteiro et al. (2000). References: Monteiro, M. J. P. F. G., Christensen-Dalsgaard, J. & Thompson, M. J., 1994. [Seismic study of overshoot at the base of the solar convective envelope]. Astron. Astrophys., 283, 247 – 262. Monteiro, M. J. P. F. G., Christensen-Dalsgaard, J. & Thompson, M. J., 2000. [Seismic study of stellar convective regions: the base of convective envelopes in low-mass stars]. Mon. Not. R. astr. Soc., 316, 165 – 172. Christensen-Dalsgaard, J., Monteiro, M. J. P. F. G., Rempel, M. & Thompson, M. J., 2011. [A more realistic representation of overshoot at the base of the solar convective envelope as seen by helioseismology]. Mon. Not. R. astr. Soc., 414, 1158 – 1174.

17. Determination of the depth of the solar convection zone

An important property of the Sun is the depth to which the outer convection zone extends. The properties of the convection zone are likely crucial for the generation of the solar magnetic ﬁeld, and mixing throughout the convection zone is important for the surface abundance of the Sun, particularly for elements like lithium which are destroyed by nuclear reactions at relatively low temperature. Thus a determination of the depth of the convection zone was an early goal of helioseismology, which was achieved with considerable success. In the project, discuss the determination of the convection-zone depth based on the references given. It would be interesting to consider the likely reliability of these determinations; good marks will be given for constructive criticism! References: Basu, S. & Antia, H. M., 1997. [Seismic measurement of the depth of the solar convection zone]. Mon. Not. R. astr. Soc., 287, 189 – 198. Christensen-Dalsgaard, J., Gough, D. O. & Thompson, M. J., 1991. [The depth of the solar convection zone]. Astrophys. J., 378, 413 – 437.

11 18. Helium abundance and equation of state from helioseismology

Analyses of solar oscillation frequencies offer the hope to determine the abundance of helium in the solar envelope. In addition, the frequencies are sensitive to the detailed properties of the equation of state in the Sun; this is the background for trying to use the Sun as a ‘laboratory’ for studying the thermodynamical properties of matter under solar conditions. Obviously there may be difficulties in separating the effects of errors in the equation of state from errors in the helium abundance. In the project, discuss these determinations on the basis of the references provided. It would be interesting to consider how one might separate effects of uncertainties in composition and equation of state and whether such a separation is always possible. References:

Basu, S. & Christensen-Dalsgaard, J., 1997. [Equation of state and helioseismic inversions]. Astron. Astrophys., 322, L5 – L8. Basu, S., D¨appen, W. & Nayfonov, A., 1999. [Helioseismic analysis of the hydrogen partition function in the solar interior]. Astrophys. J., 518, 985 – 993. Di Mauro, M. P., Christensen-Dalsgaard, J., Rabello-Soares, M. C. & Basu, S., 2002. [Inferences on the solar envelope with high-degree modes]. Astron. Astrophys., 384, 666 – 677. Elliott, J. R. & Kosovichev, A. G., 1998. [The adiabatic exponent in the solar core]. Astrophys. J., 500, L199 – L202.

19. Seismic constraints on the solar (and stellar?) helium abundance and age

One of the important goals of asteroseismology is to determine stellar ages. Also, an important result of helioseismology has been to constrain the solar envelope helium content. However, in both cases the determination is sensitive to other uncertainties in the model parameters. Houdek & Gough (2007ab, 2011) have made a careful analysis of these issues in the solar case (where of course we have independent determination of the age). In this project you should discuss the analysis of Houdek & Gough and possibly consider the observational requirements that must be met before it can be applied to other solar-like stars. A preliminary analysis can be found in Mazumdar et al. (2014). References:

Houdek, G. & Gough, D. O., 2007a. [An asteroseismic signature of helium ionization]. Mon. Not. R. astr. Soc., 375, 861 – 880. Houdek, G. & Gough, D. O., 2007b. [On the seismic age of the Sun]. In Stancliﬀe R. J., Dewi J., Houdek G., Martin R. G., Tout C.A., eds, AIP Conf. Proc. vol. 948, Unsolved Problems in Stellar Physics. American Institute of Physics, Melville, p. 219 – 224. [arXiv:0710.0762 [astro-ph]] Houdek, G. & Gough, D. O., 2011. [On the seismic age and heavy-element abundance of the Sun]. Mon. Not. R. astr. Soc., 418, 1217 – 1230. Mazumdar, A., Monteiro, M. J. P. F. G., Ballot, J., et al., 2014. [Measurement of acoustic glitches in solar-type stars from oscillation frequencies observed by Kepler]. Astrophys. J., 782, 18-(1 – 17).

12 20. Oscillations of subdwarf B stars

A very interesting class of pulsating stars was discovered around 1996: the pulsating subdwarf B stars which are at the hot end of the horizontal branch. Amazingly, they were independently predicted theoretically and detected observationally, at the same time. A few years later the detection was extended to longer periods and slightly cooler effective temperatures. Fontaine et al. (2003) provided a detailed analysis of the instability mechanisms likely causing the pulsations. In the project, provide an overview of the properties of these stars and their pulsations. Try also to investigate the likely asteroseismic use that can be made of these objects. References: Brassard, P., Fontaine, G., Billères,M., Charpinet, S., Liebert, J. & Saffer, R. A., 2001. [Discovery and asteroseismological analysis of the pulsating sdB star PG 0014+067]. Astrophys. J., 563, 1013 – 1030. Fontaine, G., Brassard, P., Charpinet, S., Green, E. M., Chayer, P., Billères,M. & Randall, S. K., 2003. [A driving mechanism for the newly discovered long-period pulsating subdwarf B stars]. Astrophys. J., 597, 518 – 534. Fontaine, G., Brassard, P., Charpinet, S. & Chayer, P., 2006. [The need for radiative levitation for understanding the properties of pulsating sdB stars]. Mem. Soc. Astron. Ital., 77, 49 – 52. Charpinet, S., Van Grootel, V., Fontaine, G., Green, E. M., Brassard, P., Randall, S. K., Silvotti, R., Østensen, R. H., Kjeldsen, H., Christensen-Dalsgaard, J., Kawaler, S. D., Clarke, B. D., Li, J. & Wohler, B., 2011. [Deep asteroseismic sounding of the compact hot B subdwarf pulsator KIC02697388 from Kepler time series photometry]. Astron. Astrophys., 530, A3-(1 – 20).

13 21. Period changes in white dwarfs

In some compact pulsators changes resulting from stellar evolution are so fast that the effects on the pulsation periods can be measured. Of course, this is greatly helped by the extreme precision to which the periods can be determined. A very interesting aspect is the fact that during parts of the evolution the cooling is to a large extent the result of neutrino emission. In the project, give a discussion of the observational possibilities for determining the period changes for such stars, and in particular how the precision depends on the period of time over which period determinations are available. In addition, discuss the physical effects of the changes in the models on the periods. References: Kawaler, S. D. & Bradley, P. A., 1994. [Precision asteroseismology of pulsating PG 1159 stars]. Astrophys. J., 427, 415 – 428. O’Brien, M. S., Vauclair, G., Kawaler, S. D., et al., 1998. [Asteroseismology of a Star Cooled by Neutrino Emission: The Pulsating Pre–White Dwarf PG 0122+200]. Astrophys. J., 495, 458 – 467. Costa, J. E. S., Kepler, S. O. & Winget, D. E., 1999. [Direct measurement of a secular pulsation period change in the pulsating hot pre-white dwarf PG 1159–035]. Astrophys. J., 522, 973 – 982. O’Brien, M. S. & Kawaler, S. D., 2000. [The predicted signature of neutrino emission in observations of pulsating pre-white dwarfs]. Astrophys. J., 539, 372 – 378. Winget, D. E., Sullivan, D. J., Metcalfe, T. S., Kawaler, S. D. & Montgomery, M. H., 2004. [A strong test of electroweak theory using pulsating DB white dwarf stars as plasmon neutrino detectors]. Astrophys. J., 602, L109 – L112. Vauclair, G., Fu, J.-N., Solheim, J.-E., Kim, S.-L., Dolez, N., Chevreton, M., Chen, L., Wood, M. A., Silver, I. M., Bognár,Zs., Paparó,M. & Córsico,A. H., 2011. Astron. Astrophys., 528, A5-(1 – 10).

14 22. A diamond in the sky? Eﬀects of white-dwarf crystallization

A press release on St Valentine’s day announced the detection of a diamond core in a white dwarf. This was based on analysis of the oscillation frequencies which showed the star to be partly crystallized. The story also made it into the Danish media. The analysis was published by Metcalfe et al. (2004). In the project, discuss the analysis of the oscillation frequencies and the resulting conclusions, including the basis for postulating this as evidence for diamond structure (it would be interesting also to consider brieﬂy the hype surrounding the announcement; try to look for diamond and Met- calfe with Google!) Consider also the analysis technique (the so-called genetic algorithm; Metcalfe & Charbonneau 2003) used in the investigation. Finally, note that the interpretation by Metcalfe et al. has been questioned by Brassard & Fontaine (2005). References: Brassard, P. & Fontaine, G., 2005. [Asteroseismology of the crystallized ZZ Ceti star BPM 37093: a diﬀerent view]. Astrophys. J., 622, 572 – 576. Metcalfe, T. S. & Charbonneau, P., 2003. [Stellar structure modeling using a parallel genetic algorithm for objective global optimization]. J. Comp. Phys., 185, 176 – 193. Metcalfe, T. S., Montgomery, M. H. & Kanaan, A., 2004. [Testing white dwarf crystallization theory with asteroseismology of the massive pulsating DA star BPM 37093]. Astrophys. J., 605, L133 – L136.

23. Constraints on nuclear reactions from white-dwarf asteroseismology?

The structure of a white dwarf depends on the evolution leading up to the formation of the white dwarf, including the helium burning phase. This in particular determines the relative fraction of carbon and oxygen in the white dwarf, since helium burning produces both 12C and 16O, in amounts that also depend on the relevant reaction rates. In this project we consider whether asteroseismic constraints on the structure of a white dwarf can be used to determine the reaction rate of the 12C(4He, γ)16O reaction. References: Fontaine, G. & Brassard, P., 2002. [Can white dwarf asteroseismology really constrain the 12C(α, γ)16O reaction rate?]. Astrophys. J., 581, L33 – L37. Kepler, S. O., Costa, J. E. S., Castanheira, B. G., Winget, D. E., Mullally, F., Nather, R. E., Kilic, M., von Hippel, T., Mukadam, A. S. & Sullivan, D. J., 2005. [Measuring the evolution of the most stable optical clock G 117-B15A]. Astrophys. J., 634, 1311 – 1318. Metcalfe, T. S., 2003. [White dwarf asteroseismology and the 12C(α, γ)16O rate]. Astrophys. J., 587, L43 – L46. Metcalfe, T. S., Salaris, M. & Winget, D. E., 2002. [Measuring 12C(α, γ)16O from white dwarf asteroseismology]. Astrophys. J., 573, 803 – 811.

15 24. The properties of the hottest pulsating stars

The oscillations observed in stars about to become white dwarfs, including central stars in planetary nebulae, have for a long time been incompletely understood. Major progress in this area was made by Quirion et al. (2007). The goal of this project is to discuss the properties of these so-called GW Virginis stars, including the excitation of the oscillations and the dependence on the stellar properties, based on the papers by Quirion et al. and possibly other relevant papers. References: Quirion, P.-O., Fontaine, G. & Brassard, P., 2007. [Mapping the instability domains of GW Vir stars in the eﬀective temperature–surface gravity diagram]. Astrophys. J. Suppl., 171, 219 – 248. Quirion, P.-O., Fontaine, G. & Brassard, P., 2009. [Nonadiabatic asteroseismology of GW Vir stars]. In Proc. 16th European White Dwarfs Workshop, J. Phys.: Conf. Ser., 172, 12077-(1–4). Quirion, P.-O., Fontaine, G. & Brassard, P., 2012. [Wind competing against settling: a coherent model of the GW Virginis instability domain]. Astrophys. J., 755, 182-(1 – 10).

25. Asteroseismic investigations of main-sequence B stars

Asteroseismology of B stars is very interesting, since this extends the investigations to fairly massive stars which, e.g., are precursors of supernovae. One problem is that the pulsation periods are quite long and the frequencies closely spaced, requiring very extended observing campaigns to determine the oscillation properties. A major effort in this direction has been carried out by Conny Aerts, Leuven, and her collaborators; examples are provided in the references given. In the project, summarize the oscillation properties of ν Eri, as obtained in these observing campaigns, and the analysis that has been carried out. You may also discuss the problems involved in observing this type of stars. References: Aerts, C., De Cat, P., Handler, G., et al., 2004. [Asteroseismology of the β Cephei star ν Eridani – II. Spectroscopic observations and pulsational frequency analysis]. Mon. Not. R. astr. Soc., 347, 463 – 470. Ausseloos, M., Scuflaire, R., Thoul, A. & Aerts, C., 2004. [Asteroseismology of the β Cephei star ν Eridani: massive exploration of standard and non-standard stellar models to fit the oscillation data]. Mon. Not. R. astr. Soc., 355, 352 – 358. De Ridder, J., Telting, J. H., Balona, L. A., et al., 2004. [Asteroseismology of the β Cephei star ν Eridani – III. Extended frequency analysis and mode identification]. Mon. Not. R. astr. Soc., 351, 324 – 332. Dziembowski, W. A. & Pamyatnykh, A. A., 2008. [The two hybrid B-type pulsators: ν Eridani and 12 Lacertae]. Mon. Not. R. astr. Soc., 385, 2061 – 2068. Handler, G., Shobbrook, R. R., Jerzykiewicz, M., et al., 2004. [Asteroseismology of the β Cephei star ν Eridani – I. Photometric observations and pulsational frequency analysis]. Mon. Not. R. astr. Soc., 347, 454 – 462. Pamyatnykh, A. A., Handler, G. & Dziembowski, W. A., 2004. [Asteroseismology of the β Cephei star ν Eridani: Interpretation and applications of the oscillation spectrum]. Mon. Not. R. astr. Soc., 350, 1022 – 1028.

16 26. Propagation of rays in a realistic solar model (computational)

Solve Problems in Asteroseismology, Problem 3.1, to derive the equation for rays in a simpliﬁed plane-parallel model. The main goal of the project is to make plots of rays in a realistic (spherically symmetric) model of the Sun, based on a stellar-evolution calculation. Such a model is provided at the site http://astro.phys.au.dk/∼jcd/solar models/; see in particular the ﬁle http://astro.phys.au.dk/∼jcd/solar models/cptrho.l5bi.d.15c (under Limited set of vari- ables for Model S). Write a programme to calculate and plot the rays in this case, and illustrate the variation of the behaviour of the rays with well-chosen examples. You may test the programme by applying it also to the simple case of Problem 3.1.

27. Approximate behaviour of trapped g modes (computational)

Problems in Asteroseismology, Problems 2.1 and 3.2 are closely related, as representing the properties of gravity waves or g modes in a region of the star where the composition is varying rapidly. In Problem 2.1 the discontinuity in density may be assumed to arise from a discontinuity in composition. In this project the goal is to solve these two problems, with the addition given below. In problem 3.2, question ix), the numerical solution should be carried out; it is straightforward in IDL or MATLAB. You may also try to relate the results of this project to the discussion by Dziembowski & Pamyatnykh (1991) and Bildsten & Cumming (1998). Addition to Problem 3.2 We now consider the case of a peak in the buoyancy frequency corresponding to a sharp change in density ρ. We assume that ρ = ρ1 is constant for r < r1 and ρ = ρ2 is constant for r > r2, and that ln ρ varies linearly with r for r1 ≤ r ≤ r2. Also, we neglect the variation in pressure and gravity in the region considered. x) Show that N 2 has the form given in Eq. (32), with 2 g ρ1 g ρ1 − ρ2 Nm = ln ' 2 , r2 − r1 ρ2 r2 − r1 ρ1 + ρ2 where the last approximation is valid when the change in ρ is small. 2 We keep kh and ρ1, ρ2 ﬁxed but let ∆ → 0, so that Nm → ∞.

xi) Show that for suﬃciently small ∆, Eq. (36) has one solution β = β0 for which √ ˜ β0 = ∆ β0 ' 2∆ , ˜ as well as the sequence of solutions βn ' nπ in Eq. (37). ˜ 2 xii) Show that for the solutions βn, ω → 0 for ∆ → 0. ˜ xiii) Show that for the solution β0, 2 1 ρ1 ρ1 − ρ2 ω → gkh ln ' gkh for ∆ → 0 . 2 ρ2 ρ1 + ρ2 Does this look familiar? References: Dziembowski, W. A. & Pamyatnykh, A. A., 1991. [A potential asteroseismological test for convective overshooting theories]. Astron. Astrophys., 248, L11 – L14. Bildsten, L. & Cumming, A., 1998. [Hydrogen electron capture in accreting neutron stars and the resulting g-mode oscillation spectrum]. Astrophys. J., 506, 842 – 862.