Rotation and differential rotation of active Kepler stars
TL;DR: In this paper, the Lomb-Scargle periodogram was used to detect different periods in the light curves, and the most dominant periods from the fit were associated to different surface rotation periods.
Abstract: Context. The Kepler space telescope monitors more than 160 000 stars with an unprecedented precision providing the opportunity to study the rotation of thousands of stars. Aims. We present rotation periods for thousands of active stars in the Kepler field derived from Q3 data. In most cases a second period close to the rotation period was detected that we interpreted as surface differential rotation (DR). We show how the absolute and relative shear (ΔΩ and α = ΔΩ/Ω, respectively) correlate with rotation period and effective temperature.Methods. Active stars were selected from the whole sample using the range of the variability amplitude. To detect different periods in the light curves we used the Lomb-Scargle periodogram in a pre-whitening approach to achieve parameters for a global sine fit. The most dominant periods from the fit were associated to different surface rotation periods. Our purely mathematical approach is capable of detecting different periods but cannot distinguish between the physical origins of periodicity. We ascribe the existence of different periods to DR, but spot evolution could also play a role. Because of the large number of stars the period errors are estimated statistically. We thus cannot exclude the existence of false positives among our periods. Results. In our sample of 40 661 active stars we found 24 124 rotation periods P 1 between 0.5 and 45 days, with a mean of ⟨P 1 ⟩ = 16.3 days. The distribution of stars with 0.5 − V 2 within ±30% of the rotation period P 1 was found in 18 616 stars (77.2%). Attributing these two periods to DR we found that for active stars other than the Sun the relative shear α increases with rotation period, and slightly decreases with effective temperature. The absolute shear ΔΩ slightly increases from ΔΩ = 0.079 rad d-1 at T eff = 3500 K to ΔΩ = 0.096 rad d-1 at T eff = 6000 K. Above 6000 K, ΔΩ shows much larger scatter. The dependence of ΔΩ on rotation period is weak over a large period range. Conclusions. Latitudinal differential rotation measured for the first time in more than 18 000 stars provides a comprehensive picture of stellar surface shear. This picture is consistent with major predictions from mean-field theory, and seems to support these models. To what extent our observations are prone to false positives and selection bias has not been fully explored, and needs to be addressed using other data, including the full Kepler time coverage.
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TL;DR: In this article, the authors analyzed three years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. They found typically higher amplitudes for shorter periods and lower effective temperatures, with an excess of low-amplitude stars above ∼5400 K.
Abstract: We analyzed three years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. Our automated autocorrelation-based method detected rotation periods between 0.2 and 70 days for 34,030 (25.6%) of the 133,030 main-sequence Kepler targets (excluding known eclipsing binaries and Kepler Objects of Interest), making this the largest sample of stellar rotation periods to date. In this paper we consider the detailed features of the now well-populated period-temperature distribution and demonstrate that the period bimodality, first seen by McQuillan et al. in the M-dwarf sample, persists to higher masses, becoming less visible above 0.6 M {sub ☉}. We show that these results are globally consistent with the existing ground-based rotation-period data and find that the upper envelope of the period distribution is broadly consistent with a gyrochronological age of 4.5 Gyr, based on the isochrones of Barnes, Mamajek, and Hillenbrand and Meibom et al. We also performed a detailed comparison of our results to those of Reinhold et al. and Nielsen et al., who measured rotation periods of field stars observed by Kepler. We examined the amplitude of periodic variability for the stars with detection rotation periods, and found a typical range betweenmore » ∼950 ppm (5th percentile) and ∼22,700 ppm (95th percentile), with a median of ∼5600 ppm. We found typically higher amplitudes for shorter periods and lower effective temperatures, with an excess of low-amplitude stars above ∼5400 K.« less
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01 May 2011TL;DR: In this paper, the authors present an overview of the solar system and its evolution, including the formation and evolution of stars, asteroids, and free-floating planets, as well as their internal and external structures.
Abstract: 1. Introduction 2. Radial velocities 3. Astrometry 4. Timing 5. Microlensing 6. Transits 7. Imaging 8. Host stars 9. Brown dwarfs and free-floating planets 10. Formation and evolution 11. Interiors and atmospheres 12. The Solar System Appendixes References Index.
527 citations
TL;DR: In this paper, the authors analyzed 3 years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. Their automated autocorrelation-based method detected rotation periods between 0.2 and 70 days for 34,030 (25.6%) of the 133,030 Kepler targets (excluding known eclipsing binaries and Kepler Objects of Interest).
Abstract: We analyzed 3 years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. Our automated autocorrelation-based method detected rotation periods between 0.2 and 70 days for 34,030 (25.6%) of the 133,030 main-sequence Kepler targets (excluding known eclipsing binaries and Kepler Objects of Interest), making this the largest sample of stellar rotation periods to date. In this paper we consider the detailed features of the now well-populated period-temperature distribution and demonstrate that the period bimodality, first seen by McQuillan, Aigrain & Mazeh (2013) in the M-dwarf sample, persists to higher masses, becoming less visible above 0.6 M_sun. We show that these results are globally consistent with the existing ground-based rotation-period data and find that the upper envelope of the period distribution is broadly consistent with a gyrochronological age of 4.5 Gyrs, based on the isochrones of Barnes (2007), Mamajek & Hillenbrand (2008) and Meibom et al. (2009). We also performed a detailed comparison of our results to those of Reinhold et al. (2013) and Nielsen et al. (2013), who have measured rotation periods of field stars observed by Kepler. We examined the amplitude of periodic variability for the stars with detected rotation periods, and found a typical range between ~950 ppm (5th percentile) and ~22,700 ppm (95th percentile), with a median of ~5,600 ppm. We found typically higher amplitudes for shorter periods and lower effective temperatures, with an excess of low-amplitude stars above ~5400 K.
432 citations
Cites background or methods or result from "Rotation and differential rotation ..."
...To directly compare our periods with those detected by Reinhold et al. (2013) and Nielsen et al. (2013), for the stars where both methods report periods, we plotted their periods versus ours in Figure 7....
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...We then compared our results to those of Reinhold et al. (2013) and Nielsen et al. (2013) who have also performed rotation period studies of the Kepler sample....
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...Two previous studies focussing on the broader Kepler sample are those of Reinhold et al. (2013), with an emphasis on differential rotation, who derive ∼ 24, 000 periods using Q3, and Nielsen et al. (2013), who measured ∼ 12, 000 periods from Q2–Q9, and compare to previous spectroscopic studies....
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...For the alternative methods there are ∼ 85 cases where AutoACF detects a short period and Reinhold et al. (2013) or Nielsen et al. (2013) detect a considerably longer period....
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...The panels show AutoACF compared to Reinhold et al. (2013) (R13, left) and Nielsen et al. (2013) (N13, right), with the number of stars in each group denoted as N ....
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TL;DR: In this paper, the authors studied the surface rotation and photometric magnetic activity of a subset of 540 solar-like stars on the main-sequence and the subgiant branch for which stellar pulsations have been measured.
Abstract: Kepler ultra-high precision photometry of long and continuous observations provides a unique dataset in which surface rotation and variability can be studied for thousands of stars. Because many of these old field stars also have independently measured asteroseismic ages, measurements of rotation and activity are particularly interesting in the context of age-rotation-activity relations. In particular, age-rotation relations generally lack good calibrators at old ages, a problem that this Kepler sample of old-field stars is uniquely suited to address. We study the surface rotation and photometric magnetic activity of a subset of 540 solar-like stars on the main-sequence and the subgiant branch for which stellar pulsations have been measured. The rotation period was determined by comparing the results from two different analysis methods: i) the projection onto the frequency domain of the time-period analysis, and ii) the autocorrelation function of the light curves. Reliable surface rotation rates were then extracted by comparing the results from two different sets of calibrated data and from the two complementary analyses. General photometric levels of magnetic activity in this sample of stars were also extracted by using a photometric activity index, which takes into account the rotation period of the stars. We report rotation periods for 310 out of 540 targets (excluding known binaries and candidate planet-host stars); our measurements span a range of 1 to 100 days. The photometric magnetic activity levels of these stars were computed, and for 61.5% of the dwarfs, this level is similar to the range, from minimum to maximum, of the solar magnetic activity. We demonstrate that hot dwarfs, cool dwarfs, and subgiants have very different rotation-age relationships, highlighting the importance of separating out distinct populations when interpreting stellar rotation periods. Our sample of cool dwarf stars with age and metallicity data of the highest quality is consistent with gyrochronology relations reported in the literature.
274 citations
Yale University1, Massachusetts Institute of Technology2, University of Chicago3, University of Turin4, Heidelberg University5, University of Cambridge6, University of Copenhagen7, University of Turku8, University of Hawaii9, Hungarian Academy of Sciences10, Eötvös Loránd University11, Spanish National Research Council12, University of La Laguna13, University of Texas at Austin14, Polish Academy of Sciences15, University of Bern16, Ames Research Center17, Adler Planetarium18, Cornell University19, University of Helsinki20, University of Oxford21, Finnish Meteorological Institute22, ETH Zurich23, California Institute of Technology24
TL;DR: In this paper, the authors made use of data from the first public release of the WASP data (Butters et al. 2010) as provided by the NASA Exoplanet Archive, which is operated by the California Institute of Technology under contract with the National Aeronautics and Space Administration under the ERC grant number 279973.
Abstract: TSB acknowledges support provided through NASA grant ADAP12-0172 and ADAP14-0245. MCW and GMK acknowledge the support of the European Union through ERC grant number 279973. The authors acknowledge support from the Hungarian Research Grants OTKA K-109276, OTKA K-113117, the Lendulet-2009 and Lendulet-2012 Program (LP2012-31) of the Hungarian Academy of Sciences, the Hungarian National Research, Development and Innovation Office – NKFIH K-115709, and the ESA PECS Contract No. 4000110889/14/NL/NDe. This work was supported by the Momentum grant of the MTA CSFK Lendulet Disc Research Group. GH acknowledges support by the Polish NCN grant 2011/01/B/ST9/05448. Based on observations made with the NOT, operated by the Nordic Optical Telescope Scientific Association at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofisica de Canarias. This research made use of The DASCH project; we are also grateful for partial support from NSF grants AST-0407380, AST-0909073, and AST-1313370. The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreements no. 269194 (IRSES/ASK) and no. 312844 (SPACEINN). We thank Scott Dahm, Julie Rivera, and the Keck Observatory staff for their assistance with these observations. This research was supported in part by NSF grant AST-0909222 awarded to M. Liu. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. KS gratefully acknowledges support from Swiss National Science Foundation Grant PP00P2_138979/1. HJD and DN acknowledge support by grant AYA2012-39346-C02-02 of the Spanish Secretary of State for R&D&i (MINECO). This paper makes use of data from the first public release of the WASP data (Butters et al. 2010) as provided by the WASP consortium and services at the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, and NEOWISE, which is a project of the Jet Propulsion Laboratory/California Institute of Technology. WISE and NEOWISE are funded by the National Aeronautics and Space Administration. This research made use of the SIMBAD and VIZIER Astronomical Databases, operated at CDS, Strasbourg, France (http://cdsweb.u-strasbg.fr/), and of NASA's Astrophysics Data System.
265 citations
Additional excerpts
...%) for F-type stars (Reinhold et al. 2013)....
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References
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1,732 citations
TL;DR: The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves as discussed by the authors, and it can be used to detect eccentric orbits of exoplanets.
Abstract: The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights (χ 2 fitting). Compared to the Lomb-Scargle periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the date-compensated discrete Fourier transform, the floating-mean periodogram, and the “spectral significance” estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian periodogram that searches for the period of the best-fitting Keplerian orbit to radial velocity data. The systematic and non-random algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.
1,367 citations
"Rotation and differential rotation ..." refers methods in this paper
...To detect periods in a light curve we used the generalized Lomb-Scargle periodogram (Zechmeister & Kürster 2009)....
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...Our analysis method is based on the LombScargle periodogram (Zechmeister & Kürster 2009) which has been successfully used to measure rotation periods for several CoRoT stars (Affer et al. 2012)....
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TL;DR: In this article, the authors developed an improved way of using a rotating star as a clock, set it using the Sun, and demonstrate that it keeps time well, using only their rotation periods and colors.
Abstract: We here develop an improved way of using a rotating star as a clock, set it using the Sun, and demonstrate that it keeps time well. This technique, called gyrochronology, derives ages for low-mass main-sequence stars using only their rotation periods and colors. The technique is developed here and used to derive ages for illustrative groups of nearby field stars with measured rotation periods. We first demonstrate the reality of the interface sequence, the unifying feature of the rotational observations of cluster and field stars that makes the technique possible, and extend it beyond the proposal of Skumanich by specifying the mass dependence of rotation for these stars. We delineate which stars it cannot currently be used on. We then calibrate the age dependence using the Sun. The errors are propagated to understand their dependence on color and period. Representative age errors associated with the technique are estimated at ~15% (plus possible systematic errors) for late F, G, K, and early M stars. Gyro ages for the Mount Wilson stars are shown to be in good agreement with chromospheric ages for all but the bluest stars, and probably superior. Gyro ages are then calculated for each of the active main-sequence field stars studied by Strassmeier and collaborators. These are shown to have a median age of 365 Myr. The sample of single field stars assembled by Pizzolato and collaborators is then assessed and shown to have gyro ages ranging from under 100 Myr to several Gyr, with a median age of 1.2 Gyr. Finally, we demonstrate that the individual components of the three wide binaries ξ Boo AB, 61 Cyg AB, and α Cen AB yield substantially the same gyro ages.
851 citations
"Rotation and differential rotation ..." refers background or methods in this paper
...Nowadays, a method called gyrochronology (Barnes 2007) is being developed using the above Skumanich’s relation in the opposite way to infer stellar ages from the rotation rate....
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...Barnes (2007) empirically found a relation between B − V , age t, and rotation period P (B − V, t) = 0.7725 (B − V − 0.4)0.601 t0....
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TL;DR: In this article, a Bayesian maximum a posteriori (MAP) approach is presented, where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set, which is in turn used to establish a range of "reasonable" robust fit parameters.
Abstract: With the unprecedented photometric precision of the Kepler spacecraft, significant systematic and stochastic errors on transit signal levels are observable in the Kepler photometric data. These errors, which include discontinuities, outliers, systematic trends, and other instrumental signatures, obscure astrophysical signals. The presearch data conditioning (PDC) module of the Kepler data analysis pipeline tries to remove these errors while preserving planet transits and other astrophysically interesting signals. The completely new noise and stellar vari- ability regime observed inKepler data poses a significant problem to standard cotrending methods. Variable stars are often of particular astrophysical interest, so the preservation of their signals is of significant importance to the astrophysical community. We present a Bayesian maximum a posteriori (MAP) approach, where a subset of highly correlated and quiet stars is used to generate a cotrending basis vector set, which is in turn used to establish a range of "reasonable" robust fit parameters. These robust fit parameters are then used to generate a Bayesian prior and a Bayesian posterior probability distribution function (PDF) which, when maximized, finds the best fit that simulta- neously removes systematic effects while reducing the signal distortion and noise injection that commonly afflicts simple least-squares (LS) fitting. A numerical and empirical approach is taken where the Bayesian prior PDFs are generated from fits to the light-curve distributions themselves.
721 citations
TL;DR: In this paper, the authors investigate the extent to which the Palomar-Green (PG) Bright Quasar Survey (BQS) is complete and representative of the general quasar population by comparing it with imaging and spectroscopy from the Sloan Digital Sky Survey (SDSS).
Abstract: We investigate the extent to which the Palomar-Green (PG) Bright Quasar Survey (BQS) is complete and representative of the general quasar population by comparing it with imaging and spectroscopy from the Sloan Digital Sky Survey (SDSS). A comparison of SDSS and PG photometry of both stars and quasars reveals the need to apply a color and magnitude recalibration to the PG data. Using the SDSS photometric catalog, we define the PG's parent sample of objects that are not main-sequence stars and simulate the selection of objects from this parent sample using the PG photometric criteria and errors. This simulation shows that the effective U - B cut in the PG survey is U - B 0.5 are inherently rare in bright surveys in any case). We find no evidence for any other systematic incompleteness when comparing the distributions in color, redshift, and FIRST radio properties of the BQS and a BQS-like subsample of the SDSS quasar sample. However, the application of a bright magnitude limit biases the BQS toward the inclusion of objects that are blue in g - i, in particular compared to the full range of g - i colors found among the i-band limited SDSS quasars, and even at i-band magnitudes comparable to those of the BQS objects.
676 citations
"Rotation and differential rotation ..." refers methods in this paper
...For the Kepler stars we used the relation between g − r and B − V from Jester et al. (2005)....
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