RESEARCH ARTICLE

ASTROPHYSICS 2016 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed Precise stellar surface gravities from the under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). time scales of convectively driven 10.1126/sciadv.1500654 brightness variations

Thomas Kallinger,1* Saskia Hekker,2,3 Rafael A. García,4 Daniel Huber,5,6,3 Jaymie M. Matthews7

A significant part of the intrinsic brightness variations in cool of low and intermediate mass arises from surface convection (seen as granulation) and acoustic oscillations (p-mode pulsations). The characteristics of these phenome- na are largely determined by the stars’ g. Detailed photometric measurements of either signal can yield an accurate value of g. However, even with ultraprecise photometry from NASA’s Kepler mission, many stars are too

faint for current methods or only moderate accuracy can be achieved in a limited range of stellar evolutionary stages. Downloaded from This means that many of the stars in the Kepler sample, including exoplanet hosts, are not sufficiently characterized to fully describe the sample and exoplanet properties. We present a novel way to measure surface gravities with accura- cies of about 4%. Our technique exploits the tight relation between g and the characteristic time scale of the combined granulation and p-mode oscillation signal. It is applicable to all stars with a convective envelope, including active stars. It can measure g in stars for which no other analysis is now possible. Because it depends on the time scale (and no other properties) of the signal, our technique is largely independent of the type of measurement (for example, photometry or radial velocity measurements) and the calibration of the instrumentation used. However, the oscillation signal must be temporally resolved; thus, it cannot be applied to dwarf stars observed by Kepler in its long-cadence mode. http://advances.sciencemag.org/

INTRODUCTION on similar scales. They can, however, be disentangled (3) to measure For spherical bodies such as stars, surface gravity g is proportional to their individual properties, from which g canbeinferredinvariousways mass divided by radius squared. Usually expressed as log g (where log (3, 8). Most precise surface gravities can be obtained by the analysis of a denotes the decadic logarithm), it plays a key role in many aspects of as- ’s global oscillations (that is, asteroseismology), which can yield g trophysics, from knowing stellar properties such as mass and radius to with typical uncertainties better than 2% (8). Although powerful, as- knowing the size of an exoplanet and whether it orbits in its star’shabitable teroseismology is now limited to relatively bright stars and underlying zone. Usually, g is difficult to measure accurately, but a tight relation (1–3) scaling relations about which there remain unanswered questions (2, 3). between g and the properties of surface convection should allow for a Determination of more reliable surface gravities in a larger sample of precise inference of surface gravity for stars with a convective envelope. stars calls for new strategies. An elegant method to estimate g from Kepler Gas in a convective cell travels a vertical distance proportional to the pres- photometry (9) was recently established by directly measuring the ampli- sure scale height (Hp) at the speed of sound (cs), where Hp is the charac- tude of the brightness variations due to granulation and acoustic oscillations on January 1, 2016 teristic length scale of the variation of pressure. For an ideal gas of uniform in the light curves (10). The advantage here is that instead of disentangling −1 −1 chemical composition in a hydrostatic equilibrium, Hp = P(rg) º Tg , granulation from oscillations and measuring their individual characteristics, where P, r,andT are pressure, density, and temperature, respectively. In the method uses the combined signal, which can be up to four times as ½ an adiabatic environment, cs º T , so the typical time scale of convection strong as the oscillation signal alone (3). This “8-hour flicker amplitude” [just like the acoustic cutoff frequency for pulsations (4)] is expected to method (using the root mean square of variations at time scales shorter − be proportional to T½g 1 (1, 2). This time scale is in turn associated with than 8 hours) was introduced to separate power from g-dependent and g- the properties of granulation (the visible signature of convection on a independent sources. When applied to a large sample of Kepler targets, the star’s surface) and also sets the typical time scale of acoustic oscillations flicker method produced a large set of g estimates; however, it has drawbacks: (resonantly driven by the turbulent motions in the convective envelope). a) Granulation and oscillation amplitudes are not determined solely In stars with a convective envelope, brightness variations arising by g (2, 3). from a combination of phenomena that are gravity-dependent [granu- b) The fixed frequency limit of the 8-hour filter suppresses an lation and acoustic oscillations (5, 6)] and gravity-independent [for increasing fraction of stellar signal as stars evolve up the giant branch, example, rotation and magnetic activity (7)] are usually observed. where the variability time scales rapidly increase. For stars with oscillation Granulation and oscillations are both tied to convection and thus act power peaking at 35 mHz, which corresponds to a time scale of about 8 hours (that is, basically all stars that are more luminous than about 1Institute of Astrophysics, University of Vienna, Türkenschanzstrasse 17, Vienna 1180, Austria. 30 to 40 times the Sun), most of the brightness variations are filtered 2Max-Planck-Institute für Sonnensystemforschung, Justus-von-Liebig-Weg 3, Göttingen out. For even more evolved stars, the flicker method eventually breaks 37077, Germany. 3Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, Aarhus C 8000, Denmark. 4Laboratoire AIM, CEA/ down because essentially only photon noise remains to be measured. DSM–CNRS, Université Paris Diderot–IRFU/SAp,CentredeSaclay, Gif-sur-Yvette Cedex c) Toward the Zero Age Main Sequence, the 8-hour filter admits 91191, France. 5Sydney Institute for Astronomy, School of Physics, University of Sydney, more power from gravity-independent sources such as rotation and 6 Sydney, New South Wales 2006, Australia. SETI Institute, 189 Bernardo Avenue, Mountain activity, which adds significant uncertainty. View, CA 94043, USA. 7Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada. d) Always part of the 8-hour flicker amplitude is photon noise, *Corresponding author. E-mail: [email protected] which needs to be evaluated on a case-by-case basis.

Kallinger et al. Sci. Adv. 2016;2:e1500654 1 January 2016 1of6 RESEARCH ARTICLE

Drawbacks (b) and (c) exclude fast rotators (that is, young dwarf variations in a star but on the typical time scale of those variations. stars but also M dwarfs of a wide range of ages) and a large number of The method applies a self-adapting filter to time-series data to isolate red giants (basically all stars with log g < 2.5). Even within the valid the gravity-dependent signal (that is, granulation and oscillations) evolutionary range, the method gives surface gravities of only moder- from slower gravity-independent stellar (that is, activity and rotation) ate accuracy (about 25%). Drawback (d) can be mitigated to some ex- and instrumental effects. The typical time scale of the residual signal tent for Kepler targets, but the sensitivity to photon noise means that can be determined directly from the autocorrelation function (ACF) of the flicker method will not work (without major modifications) for the filtered time-series data (see Fig. 1 for three examples of time- very faint stars (for example, M dwarfs, where the intrinsic brightness series and ACF analysis results). The ACF quantifies the temporal variations are typically much smaller than the photon noise) or on correlation of the observed brightness fluctuations and therefore also most of the targets from missions such as Microvariability and Oscil- reveals the intrinsic nature of the signal. In case of coherent harmonic lations of STars (MOST) (11) and BRIght Target Explorer (BRITE) variations from a classical pulsator such as a d Scuti star (13), the ACF (12),whereitismoredifficulttoseparatethecontributionofphoton is periodic, even for multiperiodic variations. The damped and sto- noise from those of other sources of instrumental noise. chastically re-excited signal that originates from granulation and solar-like oscillations, however, results in an ACF that approximates a sinc function (that is, approaches zero correlation toward larger time Downloaded from RESULTS lags; Fig. 1, insets to lower panels). These quite different ACF shapes allow us to identify stars with both granulation and solar-like oscilla- The time scale technique tion signals. The typical ACF time scale is then defined as the width of Here, we present a method to determine surface gravity, which avoids the sinc function fitted to the ACF of the filtered time series (Supple- the above drawbacks, based not on the amplitude of brightness mentary Materials). http://advances.sciencemag.org/ on January 1, 2016

Fig. 1. Examples of the Kepler light curves (top) of stars at different evolutionary stages (from left to right: upper main sequence, lower giant branch, and upper giant branch) and the corresponding power density spectra (bottom). (Top) Gray symbols represent relative intensity measure- ments as a function of time, and the red curves represent boxcar smoothings of the data. (Insets) Shorter segments of the light curves (as solid points) after high-pass filtering, where the black curves represent three-point running means and the spacings of the vertical red lines represent the dominant variability time scales measured from the ACF. (Bottom) The gray and black curves represent the power density spectra of the original and filtered data, respectively. The solid colored curves represent global model fits to the original spectra, and the dashed curves represent the components of these −1 models (3). A long arrow points to the typical ACF frequency (nACF = tACF ) in each panel. Each inset shows the squared ACF of the filtered time series (solid points) along with the fit (red curve) from which we estimate the typical ACF time scale tACF (vertical dashed line).

Kallinger et al. Sci. Adv. 2016;2:e1500654 1 January 2016 2of6 RESEARCH ARTICLE

The ACF time scale represents the characteristic time scale of the variability are inherently better correlated with surface gravity than combined granulation and oscillation variability and therefore should their amplitudes, and (ii) the ACF is relatively insensitive to uncorre- tightly scale with surface gravity. To calibrate the relation, we mea- lated noise (and instrumental perturbations) in the time-series data, sured ACF time scales of about 1300 stars from their Kepler corrected which does contribute to the 8-hour flicker amplitude. light curves (14) and correlated them (Fig. 2) with surface gravities derived from an asteroseismic analysis of their acoustic oscillations Limitations of the time scale technique (3, 8). The sample covers a wide range of stellar masses and evolution- A disadvantage of the time scale method is that the observations re- ary stages (including about five active stars with a strong rotational- quire sufficient temporal resolution. The flicker method is designed to ly modulated signal) [details of the observations may be found in estimate the surface gravity g of main sequence stars and subgiant stars Kallinger et al. (3)]. The residuals from a low-order polynomial fit (with the oscillations acting in a time scale range from a few minutes to (Supplementary Materials) show that a measure of the ACF time scale tens of minutes) from their Kepler long-cadence observations (15). gives g with an average precision of about 4%. The improvement in For the time scale method to be effective, it must temporally resolve precision by a factor of about 6 over the flicker method is partly at- the oscillations, and hence the high-frequency tail of the granulation tributable to the fact that the use of a self-adapting filter in the time signal, even though the signals can be below the formal detection limit scale technique reliably separates the gravity-dependent signal from the in the Fourier spectrum. This implies that we can measure g for main Downloaded from magnetic/rotation component, minimizing contamination of the astro- sequence stars only from their Kepler short-cadence data. This is, physical relation between g and the ACF time scale. Other contribut- however, specific to Kepler and not relevant to future missions such ing factors are as follows: (i) the time scales of granulation and oscillation as Transiting Exoplanet Survey Satellite (TESS) (16)andPLAnetary Transits and Oscillations of stars (PLATO) (17) with planned sampling intervals of minutes and seconds. In fact, the time scale method will make it possible to characterize a much larger sample of stars observed

by those missions than will be possible by any other method. http://advances.sciencemag.org/

Surface gravities from noisy light curves The time scale technique delivers results of high accuracy for all our test stars. It gives results of reasonable accuracy even for very noisy light curves, where asteroseismology is not possible [that is, the os- cillation modes are barely visible (or undetectable) in the Fourier spectrum of the time series]. Mathematically, the ACF of a time se- ries is equivalent to the Fourier transform of its Fourier transform or, put simply, the ACF averages the signal shape over time and frequen- cy. Given that and the fact that the combined granulation and oscil- lation signal is up to four times larger than the oscillation signal alone (3), it is not surprising that the time scale technique is able to re-

construct g for stars whose oscillations are not detectable in the on January 1, 2016 Fourier spectrum. To demonstrate this, we apply the time scale tech- nique to the ~1300-day-long time series of the planet-hosting star Kepler 22 (18), where we have removed the transit signal. In these data, the oscillation signal is buried in the Fourier noise (Fig. 3) such that asteroseismic measurement of the surface gravity is unreliable. Despite the high Fourier noise, we extract a clear ACF signal corre- sponding to log g = 4.39 ± 0.04, consistent with the spectroscopic de- Fig. 2. Relation between asteroseismically determined surface gravity termination for this star. Tests on Kepler data (Supplementary Materials) suggest that reliable (log g) and ACF time scale (tACF) for a sample of Kepler light curves. Red dots represent long-cadence data (sampled every 29.4 min) for ~1200 results are possible for red giants as faint as V ~14 and for main se- red giants, whereas blue dots represent short-cadence data (59-s sampling) quence stars as faint as V ~12.5, even with light curves as short as 2 for 75 main sequence stars and subgiant stars. The solid black curve repre- months. The ACF time scales measured from the space-based light sents a second-order polynomial fit, deviating from linearity (dashed curve) curve and ground-based radial velocity (RV) curve of e Ophiuchi [the because of a weak correlation between surface gravity and surface tem- only pulsating red giant for which both types of sufficiently precise time perature and the fact that stars cool as they evolve up the giant branch. series exist (19, 20)] are comparable (Fig. 2, upper right inset). This Error boxes represent typical uncertainties of g measured by photometric suggeststhatthetimescaletechniquewillgiveaccuratemeasurements colors [ph (25)] ~100%; spectroscopy [sp (26)] ~50%; flicker method [fl (10)] of surface gravity when applied to RV data from ground-based net- ~25%;timescaletechnique(ts)~4%;asteroseismology[as(8)] ~2%. (Top right inset) The same relation for stars observed with other instruments workssuchastheStellarObservationsNetworkGroup(SONG)(21). (Supplementary Materials). Cnc, Cancri; Cyg, ; Oph, Ophiuchi. (Bottom left inset) The correlation improves for main sequence stars when correcting Surface gravities of active stars for the temperature trend with log g. Empty circles represent original mea- Another advantage of the time scale technique is that it is largely inde- ½ surements of tACF, whereas filled circles represent tACF(Teff/TSun) ,where pendent of the activity level of a star. To demonstrate this, we show in TSun = 5777 K. For more details on the insets, see Supplementary Materials. Fig. 4 the and power density spectrum of KIC 6508366—

Kallinger et al. Sci. Adv. 2016;2:e1500654 1 January 2016 3of6 RESEARCH ARTICLE

µ Downloaded from

µ http://advances.sciencemag.org/ Fig. 3. Example of a “noisy” star. Same as in the bottom panels of Fig. 1 but for a star with significantly more photon noise. The gray and black curves represent the original and heavily smoothed power density spectra of the ~1300-day-long Kepler photometry of the planet-hosting star Kepler 22. The red horizontal bar indicates the expected position of oscillation power µ excess. (Inset) The ACF computed from the time series (where the symbols Fig. 4. Example of an active star. Same as in Fig. 1 but for a star with a are the same as in Fig. 1). strong rotation and/or magnetic activity signal. (Top) A 200-day-long subset of the Kepler short-cadence photometry showing a strong quasi-periodic signal one of the stars in our main sequence sample exhibiting a strong low- with a time scale of about 4 days. (Bottom) Original spectrum (light gray) of frequency signal, presumably resulting from rotational modulation the full (~1030 days) Kepler time series. The dark-gray and black curves show due to spots. The dominant signal (frequency, ~3 mHz; period, ~4 days) heavily smoothed versions of the original spectrum before and after filtering, respectively. The solid colored curves represent global model fits to the inthelightcurveofthisbrightF6IVstarisroughly104 times stronger original spectrum. The 8-hour flicker amplitude roughly measures the sig- (in power) than the granulation signal and leaks significant power into nal between the vertical dashed lines, indicating the 8-hour filter cut (left) on January 1, 2016 the frequency range where the flicker amplitude is measured. As a re- and the long-cadence Nyquist frequency (right). (Inset)TheACFcomputed sult, the flicker amplitude is significantly overestimated, leading to a fromthetimeseries(wherethesymbolsarethesameasinFigs.1and3). log g estimate of about 2.94, which is considerably lower than the as- teroseismic reference value (3.880 ± 0.005). The time scale technique, on the other hand, filters the light curve at a frequency (~200 mHz) high understood stars, which will lead to better characterization of exo- enough to suppress any rotational signal and recovers log g =3.864± planetary systems both individually and statistically. 0.015, consistent with the asteroseismic measurement. The methodology established here is based on Kepler photometry, for which clear oscillation signatures were detected in the data. We will, however, extend our tests to the 1500 or more targets from the short- cadence survey phase with no measureable oscillation signal and to K2 DISCUSSION targets (in particular, short-cadence observations of known exoplanet We have demonstrated that the typical time scale of the combined host stars) (22). Other potential applications include the still incomplete granulation and oscillation variability is a reliable tracer of stellar surface characterization of all COnvection ROtation and planetary Transits gravity for stars with masses 0.8 to 3 times the mass of the Sun across a (CoRoT) (23) and MOST targets and future TESS mission data, for wide evolutionary range—from main sequence stars with granulation which the shorter time series and the smaller signal-to-noise ratios rel- time scales of minutes to hours to red giants with granulation time ative to Kepler will require a new generation of improved techniques. scales of days, including luminous red giants with time scales of weeks. The technique we present here is the first of that new generation. We have tested this for a well-defined subsample of the Kepler catalog and found it to maintain a high accuracy, about six times better than that of the flicker method. In addition, it is more noise-tolerant than MATERIALS AND METHODS asteroseismology and gives a reasonably accurate surface gravity g for stars that are too faint for a reliable asteroseismic analysis. Therefore, This work was based on data from the Kepler space telescope, which thetimescaletechniquemakesitpossibletostudyotherwisepoorly was launched in March 2009 with the primary goal of searching for

Kallinger et al. Sci. Adv. 2016;2:e1500654 1 January 2016 4of6 RESEARCH ARTICLE transiting Earth-sized planets in and near the habitable zones of Sun- 8. S. Hekker, Y. Elsworth, B. Mosser, T. Kallinger, S. Basu, W. J. Chaplin, D. Stello, Asteroseismic like stars. Kepler houses a 95-cm aperture telescope that points at a surface gravity for evolved stars. Astron. Astrophys. 556, A59 (2013). 9. W. J. Borucki, D. Koch, G. Basri, N. Batalha, T. Brown, D. Caldwell, J. Caldwell, J. Christensen-Dalsgaard, single field in the Cygnus and Lyra, feeding a photom- W. D. Cochran, E. DeVore, E. W. Dunham, A. K. Dupree, T. N. Gautier III, J. C. Geary, R. Gilliland, 2 eter with a 115-deg field of view to continuously monitor the bright- A.Gould,S.B.Howell,J.M.Jenkins,Y.Kondo,D.W.Latham,G.W.Marcy,S.Meibom,H.Kjeldsen, ness of more than 145,000 stars. Kepler observations are subdivided J. J. Lissauer, D. G. Monet, D. Morrison, D. Sasselov, J. Tarter, A. Boss, D. Brownlee, T. Owen, into quarters, starting with the initial commissioning run (10 days, 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, Q0) then followed by a short first quarter (34 days, Q1) and the sub- H. Isaacson, M. E. Everett, D. Fischer, G. Torres, J. A. Johnson, M. Endl, P. MacQueen, S. T. Bryson, sequent full quarters 90 days long. Photometry of most of the stars is J. Dotson, M. Haas, J. Kolodziejczak, J. Van Cleve, H. Chandrasekaran, J. D. Twicken, E. V. Quintana, conducted at a long cadence of 29.42 min, but a subset of up to 512 B.D.Clarke,C.Allen,J.Li,H.Wu,P.Tenenbaum,E.Verner,F.Bruhweiler,J.Barnes,A.Prsa,Kepler stars can be observed at a short cadence of 58.82 s. planet-detection mission: Introduction and first results. Science 327, 977–980 (2010). 10. F. A. Bastien, K. G. Stassun, G. Basri, J. Pepper, An observational correlation between stellar Our studies were based on long-cadence data for red giants span- brightness variations and surface gravity. Nature 500, 427–430 (2013). ning from Q0 to Q13 (~1140 days of continuous observations) and on 11. G. Walker, J. Matthews, R. Kuschnig, R. Johnson, S. Rucinski, J. Pazder, G. Burley, A. Walker, short-cadence data obtained between Q5 and Q8 spanning at least one K.Skaret,R.Zee,S.Grocott,K.Carroll,P.Sinclair,D.Sturgeon,J.Harron,TheMOST asteroseis- full quarter of observations for subgiants and main sequence stars. The mology mission: Ultraprecise photometry from space. Publ. Astron. Soc. Pac. 115, 1023–1035 Kepler raw data were reduced in the manner of Kallinger et al. (3)and (2003). Downloaded from 12. W. W. Weiss, S. M. Rucinski, A. F. J. Moffat, A. Schwarzenberg-Czerny, O. F. Koudelka, C. C. Grant, García et al. (14) and subsequently smoothed with a triangular filter to R. E. Zee, R. Kuschnig, St. Mochnacki, J. M. Matthews, P. Orleanski, A. Pamyatnykh, A. Pigulski, suppress residual instrumental long-term trends with time scales lon- J. Alves, M. Guedel, G. Handler, G. A. Wade, K. Zwintz; CCD and Photometry Tiger Teams, ger than about 40 days. To calibrate the time scale technique, we used BRITE-: Nanosatellites for precision photometry of bright stars. Publ. Astron. Soc. Pac. the Bayesian inference tool MULTINEST (24). All fits and more de- 126, 573–585 (2014). 13. S. J. Murphy, Investigating A-Type Stars Using Kepler Data (Springer-Verlag, Berlin, 2015); tails about the methods are given in the Supplementary Materials. http://adsabs.harvard.edu/abs/2015iats.book.....M 14. R.A.García,S.Hekker,D.Stello,J.Gutiérrez-Soto,R.Handberg,D.Huber,C.Karoff,K.Uytterhoeven,

T. Appourchaux, W. J. Chaplin, Y. Elsworth, S. Mathur, J. Ballot, J. Christensen-Dalsgaard, http://advances.sciencemag.org/ SUPPLEMENTARY MATERIALS R. L. Gilliland, G. Houdek, J. M. Jenkins, H. Kjeldsen, S. McCauliff, T. Metcalfe, C. K. Middour, J. Molenda-Zakowicz, M. J. P. F. G. Monteiro, J. C. Smith, M. J. Thompson, Preparation of Kepler Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ light curves for asteroseismic analyses. Mon. Not. R. Astron. Soc. 414,L6–L10 (2011). content/full/2/1/e1500654/DC1 15. J. M. Jenkins, D. A. Caldwell, H. Chandrasekaran, J. D. Twicken, S. T. Bryson, E. V. Quintana, Materials and Methods B. D. Clarke, J. Li, C. Allen, Overview of the Kepler science processing pipeline. Astrophys. J. Lett. Fig. S1. Improving filter frequency. 713,L87–L91 (2010). Fig. S2. Normalized squared ACFs for about 250 stars (gray dots) in the sample. 16. G.R.Ricker,J.N.Winn,R.Vanderspek,D.W.Latham,G.Á.Bakos,J.L.Bean,Z.K.Berta-Thompson, t n Fig. S3. Robustness of the ACF time scale ( ACF) with respect to filter frequency ( filter). T.M.Brown,L.Buchhave,N.R.Butler,R.P.Butler,W.J.Chaplin,D.Charbonneau, Fig. S4. Relation between asteroseismic surface gravity and ACF time scale, including stars with J. Christensen-Dalsgaard, M. Clampin, D. Deming, J. Doty, N. De Lee, C. Dressing, E. W. Dunham, suppressed dipole modes (black circles). M. Endl, F. Fressin, J. Ge, T. Henning, M. J. Holman, A. W. Howard, S. Ida, J. Jenkins, G. Jernigan, Fig. S5. Performance of the time scale method with different lengths of and noise levels in J. A. Johnson, L. Kaltenegger, N. Kawai, H. Kjeldsen, G. Laughlin, A. M. Levine, D. Lin, J. J. Lissauer, time series. P. MacQueen, G. Marcy, P. R. McCullough, T. D. Morton, N. Narita, M. Paegert, E. Palle, F. Pepe, Table S1. Reference (log gref) and time scale technique gravities (log gACF) for our independent J. Pepper, A. Quirrenbach, S. A. Rinehart, D. Sasselov, B. Sato, S. Seager, A. Sozzetti, K. G. Stassun, calibration sample. P. Sullivan, A. Szentgyorgyi, G. Torres, S. Udry, J. Villasenor, The Transiting Exoplanet Survey – References (27 39) Satellite (TESS). Proc. SPIE 9143, 914320 (2014).

17.H.Rauer,C.Catala,C.Aerts,T.Appourchaux,W.Benz,A.Brandeker,J.Christensen-Dalsgaard, on January 1, 2016 M. Deleuil, L. Gizon, M.-J. Goupil, M. Güdel, E. Janot-Pacheco, M. Mas-Hesse, I. Pagano, G. Piotto, REFERENCES AND NOTES D. Pollacco, Ċ. Santos, A. Smith, J.-C. Suárez, R. Szabó, S. Udry, V. Adibekyan, Y. Alibert, J.-M. Almenara, P. Amaro-Seoane, M. Ammler-von Eiff, M. Asplund, E. Antonello, S. Barnes, 1. H. Kjeldsen, T. R. Bedding, Amplitudes of solar-like oscillations: A new scaling relation. F.Baudin,K.Belkacem,M.Bergemann,G.Bihain,A.C.Birch,X.Bonfils,I.Boisse,A.S.Bonomo, Astron. Astrophys. 529, L8 (2011). F. Borsa, I. M. Brandão, E. Brocato, S. Brun, M. Burleigh, R. Burston, J. Cabrera, S. Cassisi, 2. R. Samadi, K. Belkacem, H.-G. Ludwig, E. Caffau, T. L. Campante, G. R. Davies, T. Kallinger, W. Chaplin, S. Charpinet, C. Chiappini, R. P. Church, Sz. Csizmadia, M. Cunha, M. Damasso, M. N. Lund, B. Mosser, A. Baglin, S. Mathur, R. A. Garcia, Stellar granulation as seen in M. B. Davies, H. J. Deeg, R. F. Díaz, S. Dreizler, C. Dreyer, P. Eggenberger, D. Ehrenreich, P. Eigmüller, disk-integrated intensity. II. Theoretical scaling relations compared with observations. A. Erikson, R. Farmer, S. Feltzing, F. de Oliveira Fialho, P. Figueira, T. Forveille, M. Fridlund, Astron. Astrophys. 559, A40 (2013). R. A. García, P. Giommi, G. Giuffrida, M. Godolt, J. Gomes da Silva, T. Granzer, J. L. Grenfell, 3. T. Kallinger, J. De Ridder, S. Hekker, S. Mathur, B. Mosser, M. Gruberbauer, R. A. García, C. Karoff, A. Grotsch-Noels, E. Günther, C. A. Haswell, A. P. Hatzes, G. Hébrard, S. Hekker, R. Helled, J. Ballot, The connection between stellar granulation and oscillation as seen by the Kepler K. Heng, J. M. Jenkins, A. Johansen, M. L. Khodachenko, K. G. Kislyakova, W. Kley, U. Kolb, mission. Astron. Astrophys. 570, A41 (2014). N. Krivova, F. Kupka, H. Lammer, A. F. Lanza, Y. Lebreton, D. Magrin, P. Marcos-Arenal, P. M. Marrese, 4. T. M. Brown, R. L. Gilliland, R. W. Noyes, L. W. Ramsey, Detection of possible p-mode oscillations J. P. Marques, J. Martins, S. Mathis, S. Mathur, S. Messina, A. Miglio, J. Montalban, M. Montalto, on Procyon. Astrophys. J. 368,599–609 (1991). M. J. P. F. G. Monteiro, H. Moradi, E. Moravveji, C. Mordasini, T. Morel, A. Mortier, V. Nascimbeni, 5. S. Mathur, S. Hekker, R. Trampedach, J. Ballot, T. Kallinger, D. Buzasi, R. A. García, D. Huber, R. P. Nelson, M. B. Nielsen, L. Noack, A. J. Norton, A. Ofir, M. Oshagh, R.-M. Ouazzani, P. Pápics, A. Jiménez, B. Mosser, T. R. Bedding, Y. Elsworth, C. Régulo, D. Stello, W. J. Chaplin, J. De Ridder, V. C. Parro, P. Petit, B. Plez, E. Poretti, A. Quirrenbach, R. Ragazzoni, G. Raimondo, M. Rainer, S. J. Hale, K. Kinemuchi, H. Kjeldsen, F. Mullally, S. E. Thompson, Granulation in red giants: D. R. Reese, R. Redmer, S. Reffert, B. Rojas-Ayala, I. W. Roxburgh, S. Salmon, A. Santerne, J. Schneider, Observations by the Kepler mission and three-dimensional convection simulations. Astrophys. J. J. Schou, S. Schuh, H. Schunker, A. Silva-Valio, R. Silvotti, I. Skillen, I. Snellen, F. Sohl, S. G. Sousa, 741, 119 (2011). A. Sozzetti, D. Stello, K. G. Strassmeier, M. Švanda, Gy. M. Szabó, A. Tkachenko, D. Valencia, 6. S. Hekker, Y. Elsworth, B. Mosser, T. Kallinger, W. J. Chaplin, J. De Ridder, R. A. García, D. Stello, V. Van Grootel, S. D. Vauclair, P. Ventura, F. W. Wagner, N. A. Walton, J. Weingrill, S. C. Werner, B. D. Clarke, J. R. Hall, K. A. Ibrahim, Solar-like oscillations in red giants observed with Kepler: P. J. Wheatley, K. Zwintz, The PLATO 2.0 mission. Exp. Astron. 38,249–330 (2014). Influence of increased timespan on global oscillation parameters. Astron. Astrophys. 544, A90 18. W. J. Borucki, D. G. Koch, N. Batalha, S. T. Bryson, J. Rowe, F. Fressin, G. Torres, D. A. Caldwell, (2012). J. Christensen-Dalsgaard, W. D. Cochran, E. DeVore, T. N. Gautier, J. C. Geary, R. Gilliland, A. Gould, 7.R.A.García,T.Ceillier,D.Salabert,S.Mathur,J.L.vanSaders,M.Pinsonneault,J.Ballot, S. B. Howell, J. M. Jenkins, D. W. Latham, J. J. Lissauer, G. W. Marcy, D. Sasselov, A. Boss, P.G.Beck,S.Bloemen,T.L.Campante,G.R.Davies,J.-D.doNascimentoJr.,S.Mathis, D.Charbonneau,D.Ciardi,L.Kaltenegger,L.Doyle,A.K.Dupree,E.B.Ford,J.Fortney,M.J.Holman, T.S.Metcalfe,M.B.Nielsen,J.C.Suárez,W.J.Chaplin,A.Jiménez,C.Karoff,Rotation J. H. Steffen, F. Mullally, M. Still, J. Tarter, S. Ballard, L. A. Buchhave, J. Carter, J. L. Christiansen, and magnetism of Kepler pulsating solar-like stars. Towards asteroseismically calibrated age- B.-O. Demory, J.-M. Désert, C. Dressing, M. Endl, D. Fabrycky, D. Fischer, M. R. Haas, C. Henze, rotation relations. Astron. Astrophys. 572, A34 (2014). E. Horch, A. W. Howard, H. Isaacson, H. Kjeldsen, J. A. Johnson, T. Klaus, J. Kolodziejczak,

Kallinger et al. Sci. Adv. 2016;2:e1500654 1 January 2016 5of6 RESEARCH ARTICLE

T.Barclay,J.Li,S.Meibom,A.Prsa,S.N.Quinn,E.V.Quintana,P.Robertson,W.Sherry, 34. L. Bigot, D. Mourard, P. Berio, F. Thévenin, R. Ligi, I. Tallon-Bosc, O. Chesneau, O. Delaa, N. Nardetto, A. Shporer, P. Tenenbaum, S. E. Thompson, J. D. Twicken, J. Van Cleve, W. F. Welsh, S. Basu, K. Perraut, Ph. Stee, T. Boyajian, P. Morel, B. Pichon, P. Kervella, F. X. Schmider, H. McAlister, W. Chaplin, A. Miglio, S. D. Kawaler, T. Arentoft, D. Stello, T. S. Metcalfe, G. A. Verner, C. Karoff, T. ten Brummelaar, S. T. Ridgway, J. Sturmann, L. Sturmann, N. Turner, C. Farrington, P. J. Goldfinger, M. Lundkvist, M. N. Lund, R. Handberg, Y. Elsworth, S. Hekker, D. Huber, T. R. Bedding, W. Rapin, The diameter of the CoRoT target HD 49933. Combining the 3D limb darkening, asteroseis- Kepler-22b: A 2.4 Earth-radius planet in the habitable zone of a Sun-like star. Astrophys. J. 745, mology, and interferometry. Astron. Astrophys. 534, L3 (2011). 120 (2012). 35. T. Kallinger, M. Gruberbauer, D. B. Guenther, L. Fossati, W. W. Weiss, The nature of p-modes 19. T. Kallinger, D. B. Guenther, J. M. Matthews, W. W. Weiss, D. Huber, R. Kuschnig, A. F. J. Moffat, and granulation in HD 49933 observed by CoRoT. Astron. Astrophys. 510, A106 (2010). S. M. Rucinski, D. Sasselov, Nonradial p-modes in the G9.5 giant e Ophiuchi? Pulsation model 36. T. S. Metcalfe, W. J. Chaplin, T. Appourchaux, R. A. García, S. Basu, I. Brandão, O. L. Creevey, fits to MOST photometry. Astron. Astrophys. 478, 497–505 (2008). S. Deheuvels, G. Doğan, P. Eggenberger, C. Karoff, A. Miglio, D. Stello, M. Yıldız, Z. Çelik, H. M. Antia, 20. J. De Ridder, C. Barban, F. Carrier, A. Mazumdar, P. Eggenberger, C. Aerts, S. Deruyter, O. Benomar, R. Howe, C. Régulo, D. Salabert, T. Stahn, T. R. Bedding, G. R. Davies, Y. Elsworth, J. Vanautgaerden, Discovery of solar-like oscillations in the red giant ɛ Ophiuchi. Astron. Astrophys. L. Gizon, S. Hekker, S. Mathur, B. Mosser, S. T. Bryson, M. D. Still, J. Christensen-Dalsgaard, 448,689–695 (2006). R. L. Gilliland, S. D. Kawaler, H. Kjeldsen, K. A. Ibrahim, T. C. Klaus, J. Li, Asteroseismology of 21. F. Grundahl, J. Christensen-Dalsgaard, H. Kjeldsen, S. Frandsen, T. Arentoft, P. Kjaergaard, the solar analogs 16 Cyg A and B from Kepler observations. Astrophys. J. Lett. 748, L10 U. G. Jørgensen, SONG Stellar Observations Network Group. Proc. Int. Astron. Union 252, (2012). 465–466 (2008). 37. T. R. White, D. Huber, V. Maestro, T. R. Bedding, M. J. Ireland, F. Baron, T. S. Boyajian, X. Che, 22. S. B. Howell, C. Sobeck, M. Haas, M. Still, T. Barclay, F. Mullally, J. Troeltzsch, S. Aigrain, S. T. Bryson, J.D.Monnier,B.J.S.Pope,R.M.Roettenbacher,D.Stello,P.G.Tuthill,C.D.Farrington,P.J.Goldfinger, D. Caldwell, W. J. Chaplin, W. D. Cochran, D. Huber, G. W. Marcy, A. Miglio, J. R. Najita, M. Smith, H. A. McAlister, G. H. Schaefer, J. Sturmann, L. Sturmann, T. A. ten Brummelaar, N. H. Turner, J. D. Twicken, J. J. Fortney, The K2 mission: Characterization and early results. Publ. Astron. Soc. Pac. Interferometric radii of bright Kepler stars with the CHARA Array: q Cygni and A and Downloaded from 126,398–408 (2014). B. Mon. Not. R. Astron. Soc. 433, 1262–1270 (2013). 23. A. Baglin, M. Auvergne, P. Barge, M. Deleuil, C. Catala, E. Michel, W. Weiss; COROT Team, 38. S. Frandsen, H. Lehmann, S. Hekker, J. Southworth, J. Debosscher, P. Beck, M. Hartmann, A. Pigulski, Scientific objectives for a Minisat: CoRoT. Proc. CoRoT Mission Pre-Launch Status Stellar Seismol. G. Kopacki, Z. Kołaczkowski, M. Stęślicki, A. O. Thygesen, K. Brogaard, Y. Elsworth, KIC 8410637: A Planet Finding 1306, 33 (2006). 408-day period eclipsing binary containing a pulsating giant star. Astron. Astrophys. 556,A138 24. F. Feroz, M. P. Hobson, M. Bridges, MULTINEST: An efficient and robust Bayesian inference (2013). tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009). 39. S. Basu, S. Basu, F. Grundahl, D. Stello, T. Kallinger, S. Hekker, B. Mosser, R. A. García, S. Mathur, 25. T. M. Brown, D. W. Latham, M. E. Everett, G. A. Esquerdo, Kepler input catalog: Photometric K.Brogaard,H.Bruntt,W.J.Chaplin,N.Gai,Y.Elsworth,L.Esch,J.Ballot,T.R.Bedding, calibration and . Astron. J. 142, 112 (2011). M. Gruberbauer, D. Huber, A. Miglio, M. Yildiz, H. Kjeldsen, J. Christensen-Dalsgaard, R. L. Gilliland, 26. J. A. Valenti, D. A. Fischer, Spectroscopic properties of cool stars (SPOCS). I. 1040 F, G, and K dwarfs M. M. Fanelli, K. A. Ibrahim, J. C. Smith, Sounding open clusters: Asteroseismic constraints from http://advances.sciencemag.org/ from Keck, Lick, and AAT planet search programs. Astrophys. J. Suppl. Ser. 159,141–166 (2005). Kepler on the properties of NGC 6791 and NGC 6819. Astrophys. J. Lett. 729, L10 (2011). 27. R. A. García, F. Pérez Hernández, O. Benomar, V. Silva Aguirre, J. Ballot, G. R. Davies, G. Doğan, D. Stello, J. Christensen-Dalsgaard, G. Houdek, F. Lignières, S. Mathur, M. Takata, T. Ceillier, Acknowledgments: We acknowledge M. Mooij for useful discussions that improved the manu- W. J. Chaplin, S. Mathis, B. Mosser, R. M. Ouazzani, M. H. Pinsonneault, D. R. Reese, C. Régulo, script significantly. Funding: The research leading to the presented results received funding from D. Salabert, M. J. Thompson, J. L. van Saders, C. Neiner, J. De Ridder, Study of KIC 8561221 the European Research Council under the European Community’s Seventh Framework Program observed by Kepler: An early red giant showing depressed dipolar modes. Astron. Astrophys. (FP7/2007-2013)/European Research Council grant agreement 338251 (StellarAges). T.K. acknowl- 563, A84 (2014). edges financial support from the Austrian Science Fund (FWF P23608). S.H. acknowledges 28. B. Mosser, Y. Elsworth, S. Hekker, D. Huber, T. Kallinger, S. Mathur, K. Belkacem, M. J. Goupil, support from the Deutsche Forschungsgemeinschaft under grant SFB 963/1 (“Astrophysical flow R. Samadi, C. Barban, T. R. Bedding, W. J. Chaplin, R. A. García, D. Stello, J. De Ridder, C. K. Middour, instabilities and turbulence”). D.H. acknowledges support from the National Aeronautics and Space R. L. Morris, E. V. Quintana, Characterization of the power excess of solar-like oscillations in red Administration under grant NNX14AB92G issued through the Kepler Participating Scientist giants with Kepler. Astron. Astrophys. 537, A30 (2012). Program and support from the Australian Research Council’s Discovery Projects funding scheme 29. W. J. Chaplin, T. R. Bedding, A. Bonanno, A.-M. Broomhall, R. A. García, S. Hekker, D. Huber, (project number DE140101364). R.A.G. acknowledges funding of the Centre national d’études G.A.Verner,S.Basu,Y.Elsworth,G.Houdek,S.Mathur,B.Mosser,R.New,I.R.Stevens, spatiales grant by the Commissariat à l’énergie atomique et aux énergies alternatives, as well T. Appourchaux, C. Karoff, T. S. Metcalfe, J. Molenda-Żakowicz, M. J. P. F. G. Monteiro, as the Agence Nationale de la Recherche (France) program “Interaction Des Etoiles et des M. J. Thompson, J. Christensen-Dalsgaard, R. L. Gilliland, S. D. Kawaler, H. Kjeldsen, J. Ballot, Exoplanetes” (ANR-12-BS05-0008). Author contributions: T.K. developed the idea and performed

O. Benomar, E. Corsaro, T. L. Campante, P. Gaulme, S. J. Hale, R. Handberg, E. Jarvis, C. Régulo, all computations and tests. S.H. seeded the idea initially as well as in further discussions and on January 1, 2016 I. W. Roxburgh, D. Salabert, D. Stello, F. Mullally, J. Li, W. Wohler, Evidence for the impact of contributed significantly to the writing of this manuscript. All authors discussed the results and stellar activity on the detectability of solar-like oscillations observed by Kepler. Astrophys. J. Lett. commented on the manuscript. Competing interests: The authors declare that they have no 732,L5(2011). competing interests. Data and materials availability: All data needed to evaluate the 30. D. Dragomir, J. M. Matthews, J. N. Winn, J. F. Rowe, New MOST photometry of the 55 Cancri conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional system. Proc. Int. Astron. Union 293,52–57 (2014). data related to this paper may be requested from the authors. This work used data obtained 31. K. von Braun, T. S. Boyajian, T. A. ten Brummelaar, S. R. Kane, G. T. van Belle, D. R. Ciardi, by the NASA Kepler space mission, which are publicly available through the online database S. N. Raymond, M. López-Morales, H. A. McAlister, G. Schaefer, S. T. Ridgway, L. Sturmann, Mikulski Archive for Space Telescopes (https://archive.stsci.edu/). J. Sturmann, R. White, N. H. Turner, C. Farrington, P. J. Goldfinger, 55 Cancri: Stellar as- trophysical parameters, a planet in the habitable zone, and implications for the radius of a transiting super-Earth. Astrophys. J. 740,49(2011). Submitted 21 May 2015 32. G. Schaefer, H. E. Bond, M. Barstow, M. Burleigh, R. L. Gilliland, T. M. Girard, D. H. Gudehus, Accepted 4 November 2015 J. B. Holberg, E. Nelan, HST observations of astrophysically important visual binaries. Bull. Published 1 January 2016 Am. Astron. Soc. 209, 1104 (2006). 10.1126/sciadv.1500654 33. D. B. Guenther, T. Kallinger, M. Gruberbauer, D. Huber, W. W. Weiss, R. Kuschnig, P. Demarque, F. Robinson, J. M. Matthews, A. F. J. Moffat, S. M. Rucinski, D. Sasselov, G. A. H. Walker, The Citation: T. Kallinger, S. Hekker, R. A. García, D. Huber, J. M. Matthews, Precise stellar surface nature of p-modes and granulation in Procyon: New MOST photometry and new Yale con- gravities from the time scales of convectively driven brightness variations. Sci. Adv. 2, vection models. Astrophys. J. 687,1448–1459 (2008). e1500654 (2016).

Kallinger et al. Sci. Adv. 2016;2:e1500654 1 January 2016 6of6 Precise stellar surface gravities from the time scales of convectively driven brightness variations Thomas Kallinger, Saskia Hekker, Rafael A. García, Daniel Huber and Jaymie M. Matthews (January 1, 2016) Sci Adv 2016, 2:. doi: 10.1126/sciadv.1500654

This article is publisher under a Creative Commons license. The specific license under which this article is published is noted on the first page.

For articles published under CC BY licenses, you may freely distribute, adapt, or reuse the article, including for commercial purposes, provided you give proper attribution. Downloaded from

For articles published under CC BY-NC licenses, you may distribute, adapt, or reuse the article for non-commerical purposes. Commercial use requires prior permission from the American Association for the Advancement of Science (AAAS). You may request permission by clicking here.

The following resources related to this article are available online at http://advances.sciencemag.org. (This information is current as of January 1, 2016): http://advances.sciencemag.org/

Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://advances.sciencemag.org/content/2/1/e1500654.full

Supporting Online Material can be found at: http://advances.sciencemag.org/content/suppl/2015/12/28/2.1.e1500654.DC1

This article cites 38 articles,3 of which you can be accessed free: http://advances.sciencemag.org/content/2/1/e1500654#BIBL on January 1, 2016

Science Advances (ISSN 2375-2548) publishes new articles weekly. The journal is published by the American Association for the Advancement of Science (AAAS), 1200 New York Avenue NW, Washington, DC 20005. Copyright is held by the Authors unless stated otherwise. AAAS is the exclusive licensee. The title Science Advances is a registered trademark of AAAS