Skip to main content

Part of the book series: Springer Theses ((Springer Theses))

  • 308 Accesses

Abstract

Stars rotate, but the transport of angular momentum (AM) has been a long standing problem for the study of rotation in stars. The rotation rate of a star can vary on scales of \(0.1-100\) days over the course of their evolution, but the open questions are still how and why it changes. This section is a brief overview of the rotation of stars on: the pre-main-sequence (PMS); the main sequence (MS), focusing on the detailed picture of solar rotation; and finally on what is currently known about radial and latitudinal differential rotation in other stars. This last section also covers rotation on the post-main-sequence as these are some of the few stars for which we have clear signs of radial differential rotation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    A proxy for mass, increasing toward lower (B-V) values.

  2. 2.

    Note that the lack of points in this region of Fig. 1.2 is a selection bias in the chosen catalogs.

  3. 3.

    Traditionally helioseismology only refers to seismology on the Sun, whereas asteroseismology refers to seismology of other stars.

  4. 4.

    Sometimes denoted the \(\eta \)-Earth parameter.

  5. 5.

    Centered on \(\alpha =19\,\mathrm{h} 22\,\mathrm{m} 40\,\mathrm{s}\) \(\delta =+44^{\circ } 30' 00''\), covering part of the Cygnus constellation.

  6. 6.

    https://archive.stsci.edu/kepler/.

  7. 7.

    Often assumed to be the frequency of the \(m=0\) mode.

  8. 8.

    The etymology of the term is unknown but likely connected to the mountaineering pursuit of counting the number of climbed or ‘bagged’ peaks. The term is often falsely credited to Dr. J. Schou who, despite being an avid mountaineer, denies having conceived of the term, but has merely proliferated it.

  9. 9.

    http://dan.iel.fm/emcee/current/.

  10. 10.

    Only recently through the use of asteroseismology, has it become possible to precisely determine the age of a star. This technique requires very high quality data however, and is also not applicable to very active stars.

References

  • M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (1972)

    Google Scholar 

  • C. Aerts, The age and interior rotation of stars from asteroseismology. Astrono. Nachrichten 336, 477 (2015). doi:10.1002/asna.201512177

  • C. Aerts, J. Christensen-Dalsgaard, D.W. Kurtz, Asteroseismology (2010)

    Google Scholar 

  • C. Aerts, A. Thoul, J. Daszyńska, R. Scuflaire, C. Waelkens, M.A. Dupret, E. Niemczura, A. Noels, Asteroseismology of HD 129929: core overshooting and nonrigid rotation. Science 300, 1926–1928 (2003). doi:10.1126/science.1084993

    Article  ADS  Google Scholar 

  • S. Aigrain, J. Llama, T. Ceillier, M.L.d. Chagas, J.R.A. Davenport, R.A. García, K.L. Hay, A.F. Lanza, A. McQuillan, T. Mazeh, J.R. de Medeiros, M.B. Nielsen, T. Reinhold, Testing the recovery of stellar rotation signals from Kepler light curves using a blind hare-and-hounds exercise. MNRAS 450, 3211–3226 (2015). doi:10.1093/mnras/stv853

  • E.R. Anderson, T.L. Duvall, Jr., S.M. Jefferies, Modeling of solar oscillation power spectra. ApJ 364, 699–705 (1990). doi:10.1086/169452

  • R. Angus, S. Aigrain, D. Foreman-Mackey, A. McQuillan, Calibrating gyrochronology using Kepler asteroseismic targets. MNRAS 450, 1787–1798 (2015). doi:10.1093/mnras/stv423

  • T. Appourchaux, On maximum likelihood estimation of averaged power spectra. A & A 412, 903–904 (2003). doi:10.1051/0004-6361:20034401

  • T. Appourchaux, H.M. Antia, W. Ball, O. Creevey, Y. Lebreton, K. Verma, S. Vorontsov, T.L. Campante, G.R. Davies, P. Gaulme, C.Régulo, E. Horch, S. Howell, M. Everett, D. Ciardi, L. Fossati, A. Miglio, J. Montalbán, W.J. Chaplin, R.A. García, L. Gizon, A seismic and gravitationally bound double star observed by Kepler. Implication for the presence of a convective core. A & A 582, A25 (2015). doi:10.1051/0004-6361/201526610

  • T. Appourchaux, E. Michel, M. Auvergne, A. Baglin, T. Toutain, F. Baudin, O. Benomar, W.J. Chaplin, S. Deheuvels, R. Samadi, G.A. Verner, P. Boumier, R.A. García, B. Mosser, J.-C. Hulot, J. Ballot, C. Barban, Y. Elsworth, S. J. Jiménez-Reyes, H. Kjeldsen, C.Régulo, I.W. Roxburgh, CoRoT sounds the stars: p-mode parameters of Sun-like oscillations on HD 49933. A & A 488, 705–714 (2008). doi:10.1051/0004-6361:200810297

  • S.L. Baliunas, R.A. Donahue, W.H. Soon, J.H. Horne, J. Frazer, L. Woodard-Eklund, M. Bradford, L.M. Rao, O.C. Wilson, Q. Zhang, W. Bennett, J. Briggs, S.M. Carroll, D.K. Duncan, D. Figueroa, H.H. Lanning, T. Misch, J. Mueller, R.W. Noyes, D. Poppe, A.C. Porter, C.R. Robinson, J. Russell, J.C. Shelton, T. Soyumer, A.H. Vaughan, J.H. Whitney, Chromospheric variations in main-sequence stars. ApJ 438, 269–287 (1995). doi:10.1086/175072

    Article  ADS  Google Scholar 

  • A. Barekat, J. Schou, L. Gizon, The radial gradient of the near-surface shear layer of the Sun. A & A 570, L12 (2014). doi:10.1051/0004-6361/201424839

  • S.A. Barnes, A simple nonlinear model for the rotation of main-sequence cool stars. I. Introduction, implications for gyrochronology, and color-period diagrams. ApJ 722, 222–234 (2010)

    Google Scholar 

  • S.A. Barnes, Ages for illustrative field stars using gyrochronology: viability, limitations, and errors. ApJ 669, 1167–1189 (2007). doi:10.1086/519295

  • S.A. Barnes, on the rotational evolution of solar- and late-type stars, its magnetic origins, and the possibility of stellar gyrochronology. ApJ 586, 464–479 (2003). doi:10.1086/367639

  • J.R. Barnes, A.C Cameron, J.-F. Donati, D.J. James, S.C. Marsden, P. Petit. The dependence of differential rotation on temperature and rotation. MNRAS 357, L1–L5 (2005). doi:10.1111/j.1745-3933.2005.08587.x

  • S.A. Barnes, J. Weingrill, T. Granzer, F. Spada, K.G. Strassmeier, A color-period diagram for the open cluster M 48 (NGC 2548), and its rotational age. A & A 583, A73 (2015). doi:10.1051/0004-6361/201526129

  • S. Basu, H.M. Antia, Changes in solar dynamics from 1995 to 2002. ApJ 585, 553–565 (2003). doi:10.1086/346020

  • M. Bazot, F. Bouchy, H. Kjeldsen, S. Charpinet, M. Laymand, S. Vauclair, Asteroseismology of \(\alpha \) centauri A. Evidence of rotational splitting. A & A 470, 295–302 (2007). doi:10.1051/0004-6361:20065694

    Article  ADS  Google Scholar 

  • J.G. Beck, A comparison of differential rotation measurements—(Invited Review). Sol. Phys. 191, 47–70 (2000). doi:10.1023/A:1005226402796

  • P.G. Beck, J. Montalban, T. Kallinger, J. De Ridder, C. Aerts, R.A. García, S. Hekker, M.-A. Dupret, B. Mosser, P. Eggenberger, D. Stello, Y. Elsworth, S. Frandsen, F. Carrier, M. Hillen, M. Gruberbauer, J. Christensen-Dalsgaard, A. Miglio, M. Valentini, T.R. Bedding, H. Kjeldsen, F.R. Girouard, J.R. Hall, K.A. Ibrahim, Fast core rotation in red-giant stars as revealed by gravity-dominated mixed modes. Nature 481, 55–57 (2012). doi:10.1038/nature10612

  • E.Böhm-Vitense, Chromospheric activity in G and K main-sequence stars, and what it tells us about stellar dynamos. ApJ 657, 486–493 (2007). doi:10.1086/510482

  • W.J. Borucki, D. Koch, G. Basri, N. Batalha, T. Brown, D. Caldwell, J. Caldwell, J. Christensen-Dalsgaard, W.D. Cochran, E. DeVore, E.W. Dunham, A.K. Dupree, T.N. Gautier, J.C. Geary, R. Gilliland, A. Gould, S.B. Howell, J.M. Jenkins, Y. Kondo, D.W. Latham, G.W. Marcy, S. Meibom, H. Kjeldsen, J.J. Lissauer, D.G. Monet, D. Morrison, D. Sasselov, J. Tarter, A. Boss, D. Brownlee, T. Owen, D. Buzasi, D. Charbonneau, L. Doyle, J. Fortney, E. B. Ford, M.J. Holman, S. Seager, J.H. Steffen, W.F. Welsh, J. Rowe, H. Anderson, L. Buchhave, D. Ciardi, L. Walkowicz, W. Sherry, E. Horch, H. Isaacson, M.E. Everett, D. Fischer, G. Torres, J.A. Johnson, M. Endl, P. MacQueen, S.T. Bryson, J. Dotson, M. Haas, J. Kolodziejczak, J. Van Cleve, H. Chandrasekaran, J.D. Twicken, E.V. Quintana, B.D. Clarke, C. Allen, J. Li, H. Wu, P. Tenenbaum, E. Verner, F. Bruhweiler, J. Barnes, A. Prsa, Kepler planet-detection mission: introduction and first results. Science 327, 977–980 (2010). doi:10.1126/science.1185402

  • W.J. Borucki, D.G. Koch, E.W. Dunham, J.M. Jenkins, The kepler mission: a mission to detennine the frequency of inner planets near the habitable zone for a wide range of stars, in Planets Beyond the Solar System and the Next Generation of Space Missions, ed. by D. Soderblom. Astronomical Society of the Pacific Conference Series, vol. 119, p. 153 (1997)

    Google Scholar 

  • J. Bouvier, S.P. Matt, S. Mohanty, A. Scholz, K.G. Stassun, C. Zanni, Angular momentum evolution of young low-mass stars and brown dwarfs: observations and theory. Protostars and Planets VI 433–450 (2014). doi:10.2458/azu_uapress_9780816531240-ch019

  • T.D. Brandt, C.X. Huang, Rotating stellar models can account for the extended main-sequence turnoffs in intermediate-age clusters. ApJ 807, 25 (2015). doi:10.1088/0004-637X/807/1/25

  • M. Briquet, T. Morel, A. Thoul, R. Scuflaire, A. Miglio, J. Montalbán, M.-A. Dupret, C. Aerts, An asteroseismic study of the \(\beta \) Cephei star \(\theta \) Ophiuchi: constraints on global stellar parameters and core overshooting. MNRAS 381, 1482–1488 (2007). doi:10.1111/j.1365-2966.2007.12142.x

  • M. Camenzind, Magnetized disk-winds and the origin of bipolar outflows, in Reviews in Modern Astronomy, ed. by G. Klare. Reviews in Modern Astronomy, vol. 3, pp. 234–265 (1990)

    Google Scholar 

  • A.C. Cameron, Differential rotation on rapidly rotating stars. Astron. Nachrichten 328, 2007 (1030). doi:10.1002/asna.200710880

    Google Scholar 

  • M. Cantiello, C. Mankovich, L. Bildsten, J. Christensen-Dalsgaard, B. Paxton, Angular momentum transport within evolved low-mass stars. ApJ 788, 93 (2014). doi:10.1088/0004-637X/788/1/93

  • W.J. Chaplin, Y. Elsworth, G.R. Isaak, R. Lines, C.P. McLeod, B.A. Miller, R. New, Solar p-mode excitation: further insight from recent low-l BiSON helioseismological data. MNRAS 298, L7–L12 (1998). doi:10.1046/j.1365-8711.1998.01800.x

  • W.J. Chaplin, Y. Elsworth, R. Howe, G.R. Isaak, C.P. McLeod, B.A. Miller, H.B. van der Raay, S.J. Wheeler, R. New, BiSON performance. Sol. Phys. 168, 1–18 (1996). doi:10.1007/BF00145821

    Article  ADS  Google Scholar 

  • P. Charbonneau, Dynamo models of the solar cycle. Living Rev. Sol. Phys. 7 (2010). doi:10.12942/lrsp-2010-3

  • J. L. Christiansen, J.M. Jenkins, D.A. Caldwell, T. Barclay, S.T. Bryson, C.J. Burke, J. Campbell, J. Catanzarite, B.D. Clarke, J.L. Coughlin, F. Girouard, M.R. Haas, K. Ibrahim, T.C. Klaus, J.J. Kolodziejczak, J. Li, S.D. McCauliff, R.L. Morris, F. Mullally, E.V. Quintana, J. Rowe, A. Sabale, S. Seader, J.C. Smith, M.D. Still, P.G. Tenenbaum, S.E. Thompson, J.D. Twicken, A.K. Uddin, Kepler Data Characteristics Handbook (KSCI - 19040 - 004) (2013)

    Google Scholar 

  • M.K. Cowles, B.P. Carlin, Markov chain monte carlo convergence diagnostics: a comparative review. J. Am. Stat. Assoc. 910(434), 883–904 (1996). ISSN 01621459, http://www.jstor.org/stable/2291683

  • G.R. Davies, W.J. Chaplin, W.M. Farr, R.A. García, M.N. Lund, S. Mathis, T.S. Metcalfe, T. Appourchaux, S. Basu, O. Benomar, T.L. Campante, T. Ceillier, Y. Elsworth, R. Handberg, D. Salabert, D. Stello. Asteroseismic inference on rotation, gyrochronology and planetary system dynamics of 16 Cygni. MNRAS 446, 2959–2966 (2015). doi:10.1093/mnras/stu2331

  • S. Deheuvels, R.A. García, W.J. Chaplin, S. Basu, H.M. Antia, T. Appourchaux, O. Benomar, G.R. Davies, Y. Elsworth, L. Gizon, M.J. Goupil, D.R. Reese, C. Regulo, J. Schou, T. Stahn, L. Casagrande, J. Christensen-Dalsgaard, D. Fischer, S. Hekker, H. Kjeldsen, S. Mathur, B. Mosser, M. Pinsonneault, J. Valenti, J.L. Christiansen, K. Kinemuchi, F. Mullally, Seismic evidence for a rapidly rotating core in a lower-giant-branch star observed with kepler. ApJ 756, 19 (2012). doi:10.1088/0004-637X/756/1/19

  • V. Domingo, B. Fleck, A.I. Poland, The SOHO mission: an overview. Sol. Phys. 162, 1–37 (1995). doi:10.1007/BF00733425

    Article  ADS  Google Scholar 

  • J.-F. Donati, A.C. Cameron, Differential rotation and magnetic polarity patterns on AB Doradus. MNRAS 291, 1–19 (1997). doi:10.1093/mnras/291.1.1

  • J.-F. Donati, A. Collier Cameron, M. Semel, G.A.J. Hussain, P. Petit, B.D. Carter, S.C. Marsden, M. Mengel, A. López Ariste, S.V. Jeffers, and D.E. Rees, Dynamo processes and activity cycles of the active stars AB Doradus, LQ Hydrae and HR 1099. MNRAS 345, 1145–1186 (2003). doi:10.1046/j.1365-2966.2003.07031.x

  • J.-F. Donati, C. Moutou, R. Farès, D. Bohlender, C. Catala, M. Deleuil, E. Shkolnik, A. Collier Cameron, M.M. Jardine, G.A.H. Walker, Magnetic cycles of the planet-hosting star \(\tau \) Bootis. MNRAS 385, 1179–1185 (2008). doi:10.1111/j.1365-2966.2008.12946.x

  • B.R. Durney, D. Mihalas, R.D. Robinson, A preliminary interpretation of stellar chromospheric CA II emission variations within the framework of stellar dynamo theory. PASP 93, 537–543 (1981). doi:10.1086/130878

  • T.L. Duvall, Jr., J.W. Harvey, Solar Doppler shifts: sources of continuous spectra, in NATO Advanced Science Institutes (ASI) Series C, ed. by D.O. Gough. NATO Advanced Science Institutes (ASI) Series C, vol. 169, pp. 105–116 (1986)

    Google Scholar 

  • P. Eggenberger, J. Montalbán, A. Miglio, Angular momentum transport in stellar interiors constrained by rotational splittings of mixed modes in red giants. A & A 544, L4 (2012). doi:10.1051/0004-6361/201219729

  • R. Fares, J.-F. Donati, C. Moutou, D. Bohlender, C. Catala, M. Deleuil, E. Shkolnik, A. Collier Cameron, M.M. Jardine, G.A.H. Walker, Magnetic cycles of the planet-hosting star \(\tau \) Bootis—II. A second magnetic polarity reversal. MNRAS 398, 1383–1391 (2009). doi:10.1111/j.1365-2966.2009.15303.x

  • D. Foreman-Mackey, D.W. Hogg, D. Lang, J. Goodman, emcee: The MCMC Hammer. PASP 125, 306–312 (2013). doi:10.1086/670067

  • S. Frandsen, A. Jones, H. Kjeldsen, M. Viskum, J. Hjorth, N.H. Andersen, B. Thomsen, CCD photometry of the \(\delta \)-Scuti star \(\kappa \) \(^{}2^{}\) Bootis. A & A 301, 123 (1995)

    Google Scholar 

  • H.-E. Fröhlich, M.Küker, A.P. Hatzes, K.G. Strassmeier, On the differential rotation of CoRoT-2a. A & A 506, 263–268 (2009). doi:10.1051/0004-6361/200911895

  • R.A. García, T. Ceillier, D. Salabert, S. Mathur, J.L. van Saders, M. Pinsonneault, J. Ballot, P.G. Beck, S. Bloemen, T.L. Campante, G.R. Davies, J.-D. do Nascimento, Jr., S. Mathis, T.S. Metcalfe, M.B. Nielsen, J.C. Suárez, W.J. Chaplin, A. Jiménez, C. Karoff, Rotation and magnetism of Kepler pulsating solar-like stars. Towards asteroseismically calibrated age-rotation relations. A & A 572, A34 (2014). doi:10.1051/0004-6361/201423888

  • S. Geman, D. Geman, Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-60(6), 721–741 (1984). ISSN 0162-8828. doi:10.1109/TPAMI.1984.4767596

  • L. Gizon, S.K. Solanki, Determining the inclination of the rotation axis of a sun-like star. ApJ 589, 1009–1019 (2003). doi:10.1086/374715

  • L. Gizon, J. Ballot, E. Michel, T. Stahn, G. Vauclair, H. Bruntt, P.-O. Quirion, O. Benomar, S. Vauclair, T. Appourchaux, M. Auvergne, A. Baglin, C. Barban, F. Baudin, M. Bazot, T. Campante, C. Catala, W. Chaplin, O. Creevey, S. Deheuvels, N. Dolez, Y. Elsworth, R. Garcia, P. Gaulme, S. Mathis, S. Mathur, B. Mosser, C. Regulo, I. Roxburgh, D. Salabert, R. Samadi, K. Sato, G. Verner, S. Hanasoge, K.R. Sreenivasan, Seismic constraints on rotation of Sun-like star and mass of exoplanet. Proc. Nat. Acad. Sci. 110, 13267–13271 (2013). doi:10.1073/pnas.1303291110

    Article  ADS  Google Scholar 

  • J. Goodman, J. Weare, Ensemble samplers with affine invariance. Commun. Appl. Mathe. Comput. Sci. 5, 65–80 (2010). doi:10.2140/camcos.2010.5.65

    Article  MathSciNet  MATH  Google Scholar 

  • R. Handberg, T.L. Campante, Bayesian peak-bagging of solar-like oscillators using MCMC: a comprehensive guide. A & A 527, A56 (2011). doi:10.1051/0004-6361/201015451

  • J.D. Hartman, G.Á. Bakos, G. Kovács, R.W, Noyes, A large sample of photometric rotation periods for FGK Pleiades stars. MNRAS 408, 475–489 (2010). doi:10.1111/j.1365-2966.2010.17147.x

  • L. Hartmann, R. Hewett, S. Stahler, R.D. Mathieu, Rotational and radial velocities of T Tauri stars. ApJ 309, 275–293 (1986). doi:10.1086/164599

  • J. Harvey. High-resolution helioseismology, in Future Missions in Solar, Heliospheric & Space Plasma Physics, vol. 235, ed. by E. Rolfe, B. Battrick (ESA Special Publication, 1985), pp. 199–208

    Google Scholar 

  • J.W. Harvey, F. Hill, J.R. Kennedy, J.W. Leibacher, W.C. Livingston, The global oscillation network group (GONG). Adv. Space Res. 8, 117–120 (1988). doi:10.1016/0273-1177(88)90304-3

    Article  ADS  Google Scholar 

  • W.K. Hastings, Monte carlo sampling methods using markov chains and their applications. Biometrika 57, 97–109 (1970). doi:10.2307/2334940

  • W. Herbst, J.F. Booth, D.L. Koret, G.V. Zajtseva, H.I. Shakhovskaya, F.J. Vrba, E. Covino, L. Terranegra, A. Vittone, D. Hoff, L. Kelsey, R. Lines, W. Barksdale, Photometric variations of Orion population stars. V—A search for periodicities. AJ 94, 137–149 (1987). doi:10.1086/114456

  • W. Herbst, J. Eislöffel, R. Mundt, A. Scholz, The rotation of young low-mass stars and brown dwarfs. Protostars and Planets V 297–311 (2007)

    Google Scholar 

  • R. Howard, J. Harvey, Spectroscopic determinations of solar rotation. Sol. Phys. 12, 23–51 (1970). doi:10.1007/BF02276562

    Article  ADS  Google Scholar 

  • R. Howe, Solar interior rotation and its variation. Living Rev. Sol. Phys. 6 (2009). doi:10.12942/lrsp-2009-1

  • S.V. Jeffers, J.-F. Donati, E. Alecian, S.C. Marsden, Observations of non-solar-type dynamo processes in stars with shallow convective zones. MNRAS 411, 1301–1312 (2011). doi:10.1111/j.1365-2966.2010.17762.x

  • T. Kallinger, J. De Ridder, S. Hekker, S. Mathur, B. Mosser, M. Gruberbauer, R.A. García, C. Karoff, J. Ballot, The connection between stellar granulation and oscillation as seen by the Kepler mission. A & A 570, A41 (2014). doi10.1051/0004-6361/201424313

  • T. Kallinger, B. Mosser, S. Hekker, D. Huber, D. Stello, S. Mathur, S. Basu, T.R. Bedding, W.J. Chaplin, J. De Ridder, Y.P. Elsworth, S. Frandsen, R.A. García, M. Gruberbauer, J.M. Matthews, W.J. Borucki, H. Bruntt, J. Christensen-Dalsgaard, R.L. Gilliland, H. Kjeldsen, D.G. Koch, Asteroseismology of red giants from the first four months of Kepler data: fundamental stellar parameters. A & A 522, A1 (2010). doi:10.1051/0004-6361/201015263

  • C. Karoff, T.S. Metcalfe, W.J. Chaplin, S. Frandsen, F. Grundahl, H. Kjeldsen, J. Christensen-Dalsgaard, M.B. Nielsen, S. Frimann, A.O. Thygesen, T. Arentoft, T.M. Amby, S.G. Sousa, D.L. Buzasi, Sounding stellar cycles with Kepler—II. Ground-based observations. MNRAS 433, 3227–3238 (2013). doi:10.1093/mnras/stt964

    Article  ADS  Google Scholar 

  • S.D. Kawaler, Angular momentum loss in low-mass stars. ApJ 333, 236–247 (1988). doi:10.1086/166740

  • R. Kippenhahn, A. Weigert, A. Weiss, Stellar Struct. Evol. (2012). doi:10.1007/978-3-642-30304-3

  • H. Kjeldsen. Ph.D. thesis, University of Aarhus, Denmark, 1992

    Google Scholar 

  • A. Koenigl, Disk accretion onto magnetic T Tauri stars. ApJ 370, L39–L43 (1991). doi:10.1086/185972

  • R.P. Kraft, Stellar Rotat. 385 (1970)

    Google Scholar 

  • M. Küker, G. Rüdiger, Differential rotation of main sequence F stars. A & A 433, 1023–1030 (2005). doi:10.1051/0004-6361:20041987

  • D.W. Kurtz, H. Saio, M. Takata, H. Shibahashi, S.J. Murphy, T. Sekii, Asteroseismic measurement of surface-to-core rotation in a main-sequence A star, KIC 11145123. MNRAS 444, 102–116 (2014). doi:10.1093/mnras/stu1329

  • A.F. Lanza, M.L. Das Chagas, J.R. De Medeiros, Measuring stellar differential rotation with high-precision space-borne photometry. A & A 564, A50 (2014). doi:10.1051/0004-6361/201323172

  • T.P. Larson, J. Schou, Improved helioseismic analysis of medium-\(l\) data from the michelson doppler imager. Sol. Phys. 290, 3221–3256 (2015). doi:10.1007/s11207-015-0792-y

  • N.R. Lomb, Least-squares frequency analysis of unequally spaced data. APSS 39, 447–462 (1976). doi:10.1007/BF00648343

  • M. Long, M.M. Romanova, R.V.E. Lovelace, Locking of the rotation of disk-accreting magnetized stars. ApJ 634, 1214–1222 (2005). doi:10.1086/497000

  • M.N. Lund, M. Lundkvist, V. Silva Aguirre, G. Houdek, L. Casagrande, V. Van Eylen, T.L. Campante, C. Karoff, H. Kjeldsen, S. Albrecht, W.J. Chaplin, M.B. Nielsen, P. Degroote, G.R. Davies, R. Handberg, Asteroseismic inference on the spin-orbit misalignment and stellar parameters of HAT-P-7. A & A 570, A54 (2014a). doi:10.1051/0004-6361/201424326

  • A. Maeder, G. Meynet, Stellar evolution with rotation and magnetic fields. II. General equations for the transport by Tayler-Spruit dynamo. A & A 422, 225–237 (2004). doi:10.1051/0004-6361:20034583

  • A. Maeder, G. Meynet, ARA & A 38, 143–190 (2000). doi:10.1146/annurev.astro.38.1.143

    Article  ADS  Google Scholar 

  • E.E. Mamajek, L.A. Hillenbrand, Improved age estimation for solar-type dwarfs using activity-rotation diagnostics. ApJ 687, 1264–1293 (2008). doi:10.1086/591785

  • J.P. Marques, M.J. Goupil, Y. Lebreton, S. Talon, A. Palacios, K. Belkacem, R.-M. Ouazzani, B. Mosser, A. Moya, P. Morel, B. Pichon, S. Mathis, J.-P. Zahn, S. Turck-Chièze, P.A.P. Nghiem, Seismic diagnostics for transport of angular momentum in stars. I. Rotational splittings from the pre-main sequence to the red-giant branch. A & A 549, A74 (2013). doi:10.1051/0004-6361/201220211

  • S.P. Matt, K.B. MacGregor, M.H. Pinsonneault, T.P. Greene, Magnetic braking formulation for sun-like stars: dependence on dipole field strength and rotation rate. ApJ 754, L26 (2012). doi:10.1088/2041-8205/754/2/L26

  • A. Mazumdar, M.J.P.F.G. Monteiro, J. Ballot, H.M. Antia, S. Basu, G. Houdek, S. Mathur, M.S. Cunha, V. Silva Aguirre, R.A. García, D. Salabert, G.A. Verner, J. Christensen-Dalsgaard, T.S. Metcalfe, D.T. Sanderfer, S.E. Seader, J.C. Smith, W.J. Chaplin, Measurement of acoustic glitches in solar-type stars from oscillation frequencies observed by kepler. ApJ 782, 18 (2014). doi:10.1088/0004-637X/782/1/18

  • A. McQuillan, T. Mazeh, S. Aigrain, Rotation periods of 34,030 kepler main-sequence stars: the full autocorrelation sample. ApJS 211 24 (2014). doi:10.1088/0067-0049/211/2/24

  • S. Meibom, S.A. Barnes, I. Platais, R.L. Gilliland, D.W. Latham, R.D. Mathieu, A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster. Nature 517, 589–591 (2015). doi:10.1038/nature14118

  • L. Mestel, Angular momentum loss during pre-main sequence contraction, in Cool Stars, Stellar Systems, and the Sun, ed by S.L. Baliunas, L. Hartmann. Lecture Notes in Physics, vol. 193 (Springer, Berlin, 1984), p. 49. doi:10.1007/3-540-12907-3_179

  • L. Mestel, Magnetic braking by a stellar wind-I. MNRAS 138, 359 (1968). doi:10.1093/mnras/138.3.359

  • T.S. Metcalfe, O.L. Creevey, G. Doğan, S. Mathur, H. Xu, T.R. Bedding, W.J. Chaplin, J. Christensen-Dalsgaard, C. Karoff, R. Trampedach, O. Benomar, B.P. Brown, D.L. Buzasi, T.L. Campante, Z. Çelik, M.S. Cunha, G.R. Davies, S. Deheuvels, A. Derekas, M.P. Di Mauro, R.A. García, J.A. Guzik, R. Howe, K.B. MacGregor, A. Mazumdar, J. Montalbán, M.J.P.F.G. Monteiro, D. Salabert, A. Serenelli, D. Stello, Steşacute, M. licki, M.D. Suran, M.Yıldız, C. Aksoy, Y. Elsworth, M. Gruberbauer, D.B. Guenther, Y. Lebreton, K. Molaverdikhani, D. Pricopi, R. Simoniello, T.R. White, Properties of 42 Solar-type Kepler Targets from the Asteroseismic Modeling Portal. ApJS 214, 27 (2014). doi:10.1088/0067-0049/214/2/27

  • N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, Equation of state calculations by fast computing machines. J Chem. Phys. 21, 1953 (1087). doi:10.1063/1.1699114

    Google Scholar 

  • G. Meynet, P. Eggenberger, N. Mowlavi, A. Maeder, Models for Pop I stars: implications for age determinations, in The Ages of Stars, ed. by E.E. Mamajek, D.R. Soderblom, R.F.G. Wyse. IAU Symposium, vol. 258, pp. 177–188 (2009). doi:10.1017/S1743921309031834

  • M.S. Miesch, Large-scale dynamics of the convection zone and tachocline. Living Rev. Sol. Phys. 2 (2005). doi:10.12942/lrsp-2005-1

  • B. Mosser, M.J. Goupil, K. Belkacem, J.P. Marques, P.G. Beck, S. Bloemen, J. De Ridder, C. Barban, S. Deheuvels, Y. Elsworth, S. Hekker, T. Kallinger, R.M. Ouazzani, M. Pinonneault, R. Samadi, D. Stello, R.A. García, T.C. Klaus, J. Li, S. Mathur, R.L. Morris, Spin down of the core rotation in red giants. A & A 548, A10 (2012). doi:10.1051/0004-6361/201220106

  • J.A. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 70(4), 308–313 (1965). doi:10.1093/comjnl/7.4.308

  • A.A. Pamyatnykh, G. Handler, W.A. Dziembowski, Asteroseismology of the \(\beta \) Cephei star \(\nu \) Eridani: interpretation and applications of the oscillation spectrum. MNRAS 350, 1022–1028 (2004). doi:10.1111/j.1365-2966.2004.07721.x

  • E.N. Parker, Dynamics of the interplanetary gas and magnetic fields. ApJ 128, 664 (1958). doi:10.1086/146579

  • W.D. Pesnell, B.J. Thompson, P.C. Chamberlin, The solar dynamics observatory (SDO). Sol. Phys. 275, 3–15 (2012). doi:10.1007/s11207-011-9841-3

  • M.J.D. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 70(2), 155–162 (1964). doi:10.1093/comjnl/7.2.155

  • A. Reiners, N. Joshi, B. Goldman, A catalog of rotation and activity in Early-M stars. AJ 143, 93 (2012). doi:10.1088/0004-6256/143/4/93

  • A. Reiners, J.H.M.M. Schmitt, On the feasibility of the detection of differential rotation in stellar absorption profiles. A & A 384, 155–162 (2002). doi:10.1051/0004-6361:20011801

  • A. Reiners. Rotation- and temperature-dependence of stellar latitudinal differential rotation. A & A 446, 267–277 (2006). doi:10.1051/0004-6361:20053911

  • T. Reinhold, A. Reiners, Fast and reliable method for measuring stellar differential rotation from photometric data. A & A 557, A11 (2013). doi:10.1051/0004-6361/201321161

  • M. Rempel, R. Schlichenmaier, Sunspot modeling: from simplified models to radiative mhd simulations. Living Rev. Sol. Phys. 80(3) (2011). doi:10.1007/lrsp-2011-3

  • A.E. Rydgren, F.J. Vrba, Periodic light variations in four pre-main-sequence K stars. ApJ 267, 191–198 (1983). doi:10.1086/160858

  • J.D. Scargle, Studies in astronomical time series analysis. II—Statistical aspects of spectral analysis of unevenly spaced data. ApJ 263, 835–853 (1982). doi:10.1086/160554

  • E. Schatzman. A theory of the role of magnetic activity during star formation. Ann. d’Astrophysique 25, 18 (1962)

    Google Scholar 

  • J. Schou, H.M. Antia, S. Basu, R.S. Bogart, R.I. Bush, S.M. Chitre, J. Christensen-Dalsgaard, M.P. Di Mauro, W.A. Dziembowski, A. Eff-Darwich, D.O. Gough, D.A. Haber, J.T. Hoeksema, R. Howe, S.G. Korzennik, A.G. Kosovichev, R.M. Larsen, F.P. Pijpers, P.H. Scherrer, T. Sekii, T.D. Tarbell, A.M. Title, M.J. Thompson, J. Toomre, Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the michelson doppler imager. ApJ 505, 390–417 (1998). doi:10.1086/306146

  • A. Skumanich. Time scales for CA II emission decay, rotational braking, and lithium depletion. ApJ 171, 565 (1972). doi:10.1086/151310

  • J.C. Smith, M.C. Stumpe, J.E. Van Cleve, J.M. Jenkins, T.S. Barclay, M.N. Fanelli, F.R. Girouard, J.J. Kolodziejczak, S.D. McCauliff, R.L. Morris, J.D. Twicken, Kepler presearch data conditioning II—a bayesian approach to systematic error correction. PASP 124, 1000–1014 (2012). doi:10.1086/667697

  • H.B. Snodgrass, R.K. Ulrich, Rotation of Doppler features in the solar photosphere. ApJ 351, 309–316 (1990). doi:10.1086/168467

  • S.K. Solanki, Sunspots: an overview. A & A Rev. 11, 153–286 (2003). doi:10.1007/s00159-003-0018-4

  • T. Stahn, Analysis of time series of solar-like oscillations—Applications to the Sun and HD 52265. Ph.D. thesis, Göttingen University, Germany, 2010

    Google Scholar 

  • M.C. Stumpe, J.C. Smith, J.E. Van Cleve, J.D. Twicken, T.S. Barclay, M.N. Fanelli, F.R. Girouard, J.M. Jenkins, J.J. Kolodziejczak, S.D. McCauliff, R.L. Morris, Kepler presearch data conditioning I—architecture and algorithms for error correction in kepler light curves. PASP 124, 985–999 (2012). doi:10.1086/667698

  • M.J. Thompson, J. Christensen-Dalsgaard, M.S. Miesch, J. Toomre. The internal rotation of the sun. ARA & A 41, 599–643 (2003). doi:10.1146/annurev.astro.41.011802.094848

  • S.A. Triana, E. Moravveji, P.I. Pápics, C. Aerts, S.D. Kawaler, J. Christensen-Dalsgaard, The internal rotation profile of the B-type star KIC 10526294 from frequency inversion of its dipole gravity modes. ApJ 810, 16 (2015). doi:10.1088/0004-637X/810/1/16

  • J.L. van Saders, T. Ceillier, T.S. Metcalfe, V.S. Aguirre, M.H. Pinsonneault, R.A. García, S. Mathur, G.R. Davies, Weakened magnetic braking as the origin of anomalously rapid rotation in old field stars. Nature, 529, 181–184 (2016). doi:10.1038/nature16168

  • A.H. Vaughan, G.W. Preston, A survey of chromospheric CA II H and K emission in field stars of the solar neighborhood. PASP 92, 385–391 (1980). doi:10.1086/130683

  • H. Vázquez Ramió, T. Roca Cortés, C.Régulo, Background solar irradiance spectrum at high and low phases of the solar activity cycle, in Solar Variability: From Core to Outer Frontiers, ed. by A. Wilson. ESA Special Publication, vol. 506, pp. 897–900 (2002)

    Google Scholar 

  • S.N. Vogel, L.V. Kuhi, Rotational velocities of pre-main-sequence stars. ApJ 245, 960–976 (1981). doi:10.1086/158872

    Article  ADS  Google Scholar 

  • H. von Zeipel, The radiative equilibrium of a rotating system of gaseous masses. MNRAS 84, 665–683 (1924). doi:10.1093/mnras/84.9.665

  • L.M. Walkowicz, G.S. Basri, Rotation periods, variability properties and ages for Kepler exoplanet candidate host stars. MNRAS 436, 1883–1895 (2013). doi:10.1093/mnras/stt1700

  • E.J. Weber, L. Davis, Jr., The angular momentum of the solar wind. ApJ 148, 217–227 (1967). doi:10.1086/149138

  • O.C. Wilson, Flux measurements at the centers of stellar h- and K-Lines. ApJ 153, 221 (1968). doi:10.1086/149652

  • B.E. Wood, Astrospheres and solar-like stellar winds. Living Rev. Sol. Phys. 1(2) (2004). doi:10.1007/lrsp-2004-2

  • M.F. Woodard, Short-Period Oscillations in the Total Solar Irradiance. Ph.D. thesis, University of California, San Diego, 1984

    Google Scholar 

  • K.T. Wraight, L. Fossati, M. Netopil, E. Paunzen, M. Rode-Paunzen, D. Bewsher, A.J. Norton, G.J. White, A photometric study of chemically peculiar stars with the STEREO satellites—I. Magnetic chemically peculiar stars. MNRAS 420, 757–772 (2012). doi:10.1111/j.1365-2966.2011.20090.x

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Martin Bo Nielsen .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Nielsen, M.B. (2017). Introduction. In: Differential Rotation in Sun-like Stars from Surface Variability and Asteroseismology. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-50989-1_1

Download citation

Publish with us

Policies and ethics