Measuring stellar rotation periods with Kepler
***Volume Title**ASP Conference Series, Vol. **Volume Number****Author** c (cid:13) **Copyright Year** Astronomical Society of the Pacific Measuring stellar rotation periods with Kepler
M. B. Nielsen , , L. Gizon , , H. Schunker , and C. Karo ff Institut f¨ur Astrophysik, Georg-August-Universit¨at G¨ottingen,Friedrich-Hund-Platz 1, 37077 G¨ottingen, Germany Max-Planck-Institut f¨ur Sonnensystemforschung, Max-Planck-Straße 2,37191 Katlenburg-Lindau, Germany Stellar Astrophysics Centre (SAC), Department of Physics and Astronomy,Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
Abstract.
We measure rotation periods for 12 151 stars in the
Kepler field, basedon the photometric variability caused by stellar activity. Our analysis returns stablerotation periods over at least six out of eight quarters of
Kepler data. This large sampleof stars enables us to study the rotation periods as a function of spectral type. We findgood agreement with previous studies and v sin i measurements for F, G and K stars.Combining rotation periods, B-V color, and gyrochronology relations, we find that thecool stars in our sample are predominantly younger than ∼
1. Introduction
Stellar rotation is a key aspect of stellar evolution, stellar activity, and mass loss throughstellar winds. The spin down experienced by stars during their main sequence lifetimesis also a measure of their ages (e.g. Barnes 2007). The
Kepler mission provides us witha unique opportunity to study stellar rotation over a large and consistent sample of starscovering a wide range of spectral types.Among the high-quality photometric light curves of
Kepler , a significant fractionof stars show periodicities associated with active regions. Using spectral analysis, weextract stable rotation periods from 8 quarters of
Kepler observations. Here we summa-rize the results published by Nielsen et al. (2013) and further comment on the prospectsfor inferring ages of stars through gyrochronology.
2. Method
We use the white-light photometric
Kepler time series, which consist of ∼
90 day seg-ments (quarters). We analyzed quarters 2 to 9 for a total of 192 668 stars. We consid-ered the data processed by PDC MAP reduction pipeline (Smith et al. 2012) and alsothe more recent data from the msMAP pipeline (Thompson et al. 2013) for comparisonpurposes. Periods longer than ∼
21 days are treated di ff erently by the two pipelines andso may lead to di ff erent stellar rotation periods (Garcia private communication, Nielsenet al. 2013). 1 a r X i v : . [ a s t r o - ph . S R ] M a r M. B. Nielsen, L. Gizon, H. Schunker, and C. Karo ff Figure 1. Comparison between the measured PDC MAP rotation periods (thiswork, abscissa) and periods from Reinhold & Reiners (2013) (red), Debosscher et al.(2011) (blue), and McQuillan et al. (2013) (black).
For each star and each quarter we computed the Lomb-Scargle periodogram usingPDC MAP data. We then identified the peak of maximum power in the period range1 - 100 days, discarding periods longer than 30 days (which are potentially subject toinstrumental e ff ects). Detected periods are subjected to a statistically analysis in orderto only extract stable periods, namely at least 6 periods must fall within 2 median ab-solute deviations (MAD), with a maximum MAD of 1 day. These stable periods areadopted as stellar rotation periods.
3. Rotation Periods
The PDC MAP rotation periods for 12 151 stars are published as online material via theCDS . The msMAP data yielded only 9617 stars with measured rotation periods. ThemsMAP tends to suppress long term variability and is therefore ill suited for studyingslow rotators.We compared our results with those of Debosscher et al. (2011) (8654 stars), Rein-hold & Reiners (2013) (24 124 stars), and McQuillan et al. (2013) (1570 stars). In Fig-ure 1 we show periods for the stars in our sample that are also present in each of therespective comparison samples. It is clear that the vast majority ( > ff erent samples. It is also evident that some periodsdi ff er, as seen by the points that lie at twice or half our measured period. Reinhold &Reiners (2013) and McQuillan et al. (2013) consider periods longer than our limit of30 days, this means that a few of our periods above 30 days are likely harmonic peri-ods. Debosscher et al. (2011) use a similar period range as ours, and so it is unclearwhy in some cases their analysis yields what appears to be sub-harmonic to our mea-sured periods. Similarly Reinhold & Reiners (2013) analyzed periods shorter than one http: // cdsarc.u-strasbg.fr / viz-bin / qcat?J / A + A / / L10 easuring stellar rotation with
Kepler Figure 2. Rotation periods (color scale) versus log g and T e ff read from the Kepler
Input Catalog. The open circles denote stars on the red giant branch with log g < . day, giving rise to the scatter of points in the lower part of the figure. The comparisonperiods from Reinhold & Reiners (2013) and Debosscher et al. (2011) that are found athalf our measured period are likely caused be the fact that these studies only consideredone quarter of Kepler data.
4. Rotation vs. spectral type
Nielsen et al. (2013) presented an additional comparison with v sin i measurements fromthe Gł (cid:44) ebocki & Gnaci´nski (2005) catalog. Using radii from the Kepler
Input Cata-log, we converted the starspot periods into equatorial velocities and found a very goodagreement between the two samples for spectral types F, G and K. For later type stars(late-K and M dwarfs), the rotational velocities from
Kepler photometry are lower by upto an order of magnitude than implied by the v sin i catalog, which predominantly con-tains younger stars in open clusters. For earlier type stars, there is also a disagreement,likely due to incorrect KIC radii.Figure 2 shows a (log g , T e ff )-diagram of the stars for which we measure a rotationperiod. A strong change in rotation period with temperature along the main sequence isimmediately evident around 6000 K. This indicates the transition from cool stars withouter convective envelopes to hotter stars with only a shallow convective shell. M. B. Nielsen, L. Gizon, H. Schunker, and C. Karo ff Figure 3. Measured rotation periods as a function of spectral type. The spectraltype is derived from the g-r color indexes available from the
Kepler
Input Catalog, theshaded area represents the ± ff erent ages.
5. Toward age determination
Stars rotate slower as they age because of magnetic braking. Cool stars with a deep con-vective zone exhibit stronger magnetic fields and so lose angular momentum faster viastellar winds. This spin down is described by the relationship between stellar rotationperiod, stellar age, and B-V color index (Barnes 2007). Three isochrones (250 Myr,500 Myr, and 1 Gyr) are plotted as a function of rotation period and spectral type(Fig. 3). By comparison with the starspot rotation periods, some information aboutstellar ages can be obtained. The isochrones indicate that the stars in our sample covera range of ages up to about 1 Gyr, thus confirming that they are predominantly youngactive stars.
Acknowledgments.
M.N., L.G., and H.S. acknowledge research funding by theDeutsche Forschungsgemeinschaft (DFG) under grant SFB 963 / Kepler mission. Funding for the
Kepler mission is pro-vided by the NASA Science Mission directorate. Some of the data presented in thispaper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScIis operated by the Association of Universities for Research in Astronomy, Inc. underNASA contract NAS5-26555. Support for MAST for non-HST data is provided by easuring stellar rotation with
Kepler ffi ce of Space Science via grant NNX09AF08G and by other grants andcontracts. References
Barnes, S. A. 2007, ApJ, 669, 1167Debosscher, J., Blomme, J., Aerts, C., & De Ridder, J. 2011, A&A, 529, A89Gł (cid:44) ebocki, R., & Gnaci´nski, P. 2005, VizieR Online Data Catalog, 3244, 0Kjeldsen, H., & Bedding, T. R. 2011, A&A, 529, L8McQuillan, A., Aigrain, S., & Mazeh, T. 2013, MNRAS, 432, 1203Nielsen, M., Gizon, L., Schunker, H., & Karo ff , C. 2013, arXiv preprint: 1305.5721Reinhold, T., & Reiners, A. 2013, arXiv preprint:1306.2176Smith, J. C., Stumpe, M. C., Van Cleve, J., Jenkins, J. M., Barclay, T. S., Fanelli, M. N.,Girouard, F. R., Kolodziejczak, J. J., McCauli ff , S. D., Morris, R. L., & Twicken, J. D.2012, PASP, 124, 1000. arXiv:1203.1383v1 , URL http://arxiv.org/abs/1203.1383http://arxiv.org/abs/1203.1383