Stellar magnetic cycles in the solar-like stars Kepler-17 and Kepler-63
SStellar magnetic cycles in the solar-like stars Kepler-17 andKepler-63
Raissa Estrela and Adriana Valio
Center for Radio Astronomy and Astrophysics (CRAAM), Mackenzie Presbyterian University, Rua daConsolacao 896, Sao Paulo, SP 01302-907, Brazil [email protected]@craam.mackenzie.br
ABSTRACT
The stellar magnetic field plays a crucial role in the star internal mechanisms, as in theinteractions with its environment. The study of starspots provides information about the stellarmagnetic field, and can characterise the cycle. Moreover, the analysis of solar-type stars is alsouseful to shed light onto the origin of the solar magnetic field. The objective of this work is tocharacterise the magnetic activity of stars. Here, we studied two solar-type stars Kepler-17 andKepler-63 using two methods to estimate the magnetic cycle length. The first one characterisesthe spots (radius, intensity, and location) by fitting the small variations in the light curve of astar caused by the occultation of a spot during a planetary transit. This approach yields thenumber of spots present in the stellar surface and the flux deficit subtracted from the star bytheir presence during each transit. The second method estimates the activity from the excess inthe residuals of the transit lightcurves. This excess is obtained by subtracting a spotless modeltransit from the lightcurve, and then integrating all the residuals during the transit. The presenceof long term periodicity is estimated in both time series. With the first method, we obtained P cycle = 1.12 ± P cycle = 1.27 ± ± ± Subject headings: magnetic activity, magnetic cycles, starspots
1. Introduction
Magnetic fields comparable to that of our Sunappear in the internal regions of all cool, low-masssolar-type stars, in small or higher scales (Lam-mer and Khodachenko 2015). The presence of themagnetic field can affect the evolutionary stagesof a star and is responsible for its magnetic activ-ity. The evidence of the magnetic field presence isthe emergence of dark spots in active regions onthe stellar surface. The number of spots appearingand disappearing in the stellar disk varies in cy-cles. This behaviour observed in the Sun shows an11 year-cycle, but it also happens in other stars.The HK-project using the Mount Wilson Ob-servatory, investigated hundred of stars by observ- ing the Ca II HK lines to find stellar cycles similarto the solar case, with 52 of them showing thisperiodic behaviour (Baliunas et al. 1995). Usingthe Mount Wilson data, Saar and Brandenburg(1999) also studied stellar cycles and multiple cy-cles. From these observations, they estabilishedthe relation between stellar rotation period, P rot ,and magnetic cycle period, P cycle as a functionof the Rossby number, dividing the stars into ac-tive (A) and inactive (I) branches, which were dis-tinguished by the number of rotations per cycleand activity level. Later, several long photometricrecords for a significant sample of stars becameavailable, and other studies of the stellar cycleswere performed (Ol´ah et al. 2009; Messina andGuinan 2002; Lovis et al. 2011).1 a r X i v : . [ a s t r o - ph . S R ] A ug long with the 11 year cycle of the Sun, thereare other short-durations cycles, known as quasi-biennial oscilations (QBO). Fletcher et al. (2010)found a quasi-biennial period of 2 years in thelow-degree solar oscillation frequencies of the Sunafter separating this signal from the influence ofthe dominant 11 year solar cycle. In addition,Bazilevskaya et al. (2014) reported solar QBOswith the time scale of 0.6 − ι Horologii andfound two cycles in (cid:15)
Eridani, one of 2.95 yearsand a long-term cycle of 12.7 years. Egeland et al.(2015) also found a short-period ∼
2. Observations
The stars analysed in the present work, Kepler-17 and Kepler-63, were observed by the Keplersatellite. This mission was responsible for collect-ing data of thousand of stars and planets (Boruckiet al. (2010)). The duration of the mission wasscheduled for 3.5 years, initially planned to finishin 2012 but was extended to 2016 (K2 mission)(see Howell et al. (2014)). The telescope has anaperture of 95 cm and explores about 1 . × stars in a field of 150deg . It was projected to dis-cover Earth size planets located in the habitablezone of stars (dwarfs F to K). To keep the solarpanel towards the Sun, the spacecraft needed torotate about its axis by 90 ◦ every 93 days, thistime interval is known as “quarter”. A total of2,327 planets were confirmed until now and thereare 4706 planet candidates .The lightcurves can be obtained from theMAST ( Mikulski Archive for Space Telescopes )database. The observation of the target stars aremade along sixteen quarters and consists of long(one data point each 29.4 minutes) and short ca-dence data ( ∼ < ≈ . ≈ http://kepler.nasa.gov/, July 2017 http://archive.stci.edu/
3. Spot modelling
To characterize the spots, we adopted the tran-sit model proposed by Silva (2003) that uses smalltransit photometry variations to infer the prop-erties of starspots. The passage of the planet infront of the star may occult solar-like spots on thestellar surface, producing a slight increase in theluminosity detected during a short period (min-utes) of the transit. This occurs because the spotis darker (cooler region) than the stellar photo-sphere and causes a smaller decrease in the inten-sity than when it blocks a region without spots.This effect is shown in Figure 1.This model simulates a star with quadratic limbdarkening as a 2D image and the planet is assumedto be a dark disk with radius R p /R star , where R p is the radius of the planet and R star is the radiusof the primary star. For each time interval, theposition of the planet in its orbit is calculated ac-cording to its parameters: inclination angle i andsemi-major axis a . The simulated lightcurve re-sults from the intensity integration of all the pixelsin the image for each planet position during thetransit. All the simulations are performed con-sidering a circular orbit, that is null eccentricity.Applications of such model are described in Silva(2003) for HD 209458, Silva-Valio et al. (2010) andSilva-Valio and Lanza (2011) for the active starCoRoT-2.An example of the application of this model isshown in Fig. 2 for the 120th transit of Kepler-17,where the top panel shows the fit with three spots(red curve), together with the model of a star with-out any spots (yellow curve). The bottom panel ofFig. 2, shows the residuals from the subtraction of the spotless model, where the spots became moreevident, as the three “bumps” seen in the resid-uals. An estimation of the noise presented in theKepler data is given by the CDPP (Combined Dif-ferential Photometric Precision, see Christiansenet al. (2012)), computed for each quarter in thelightcurve. We considered the uncertainty in thedata, σ , as being the average of the CDPP val-ues in all quarters. Only the “bumps” that ex-ceed the detection limit of 10 σ are assumed asspots and modelled. The modelled spots are con-strained within longitude of ± ◦ (dashed lines)to avoid any distortions caused by the ingress andegress branches of the transit. In this region thelightcurve measurements are much less accuratethan in the central part of the transit due to thesteep gradients in intensity. The maximum num-ber of spots modelled per transit was set to 4,with an exception for only one transit of Kepler-17, where it was necessary to fit 5 spots.Fig. 1.— Top : 2D Simulated image of a star withquadratic limb darkening and one spot, and itsplanet, assumed as a dark disk.
Bottom : Result-ing light curve from the transit, with the “bump”due to spot-crossing by the planet.The model assumes that the spots are circu-lar and described by 3 parameters: size (in unitsof planetary radius R p ), intensity with respect tothe surface of the star (in units the maximum in-3 able 1 Observational parameters of the starsKIC Number Mass [ M (cid:12) ] Radius [R (cid:12) ] Age [Gyr] Effective temperature [K] Rotation period [d] ReferenceKepler-17 10619192 1.16 ± ± < ±
80 11.89 ± +0 . − . +0 . − . ±
50 5.401 ± References. (1) Bonomo et al. (2012), (2) D´esert et al. (2011) and (3) Sanchis-Ojeda et al. (2013).
Table 2
Observational parameters of the planetsKIC Number Mass [ M jup ] Radius [ R jup ] Radius [ R star ] Orbital Inclination, i [deg] Semi-major Semi-major ReferencePeriod [d] axis, a [AU] axis, a [ R star ]Kepler-17b 10619192 b 2.45 ± a a ± a a < a a +0 . − . a a a Modified values to obtain a better fit of each transit lightcurve.
References. (1) Bonomo et al. (2012), (2) D´esert et al. (2011) and (3) Sanchis-Ojeda et al. (2013). tensity at disc centre, I c ), and longitude (allowedrange is ± ◦ to avoid distortions of the ingressand egress of the transit). For Kepler-17, wherethe orbital plane is aligned with the stellar equa-tor, the latitude of the spots remains fixed andequal to the planetary transit projection onto thesurface of the star. This latitude is -14 ◦ .6 andcorresponds to an inclination angle of 87.84 ◦ , thatwas arbitrary chosen to be South. Moreover, theforeshortening effect is taken into account for thespots near the limb. Due to the high obliquity ofthe orbit of Kepler-63b, the planet occults severallatitudes of the star from its equator all the wayto the poles.It was necessary to refine the values from thesemi-major axis and planet radius taken from theliterature (D´esert et al. 2011) for Kepler-17b and(Sanchis-Ojeda et al. 2013) for Kepler-63b, to ob-tain a better fit for each transit lightcurve. There-fore, we used 5.729 R star (Kepler-17b) and 19.35 R star (Kepler-63b) for the semi-major axis, whilefor the planet radius we adopted 0.0662 R star and0.138 R star , respectively (see Valio et al. 2016 (tobe submitted) and Netto and Valio, 2016 (submit-ted). These values represent 8% and 6% (radius)and 4% and 1% (semi-major axis) increase, respec-tively for Kepler-17 and Kepler-63, with respect tothe initial values given in (Bonomo et al. 2012) andSanchis-Ojeda et al. (2013).The residuals from each transit lightcurve werefit using this model. We performed initial guessesmanually, for the longitude of the spot, lg spot , ob-tained from the approximate central time of the“bump”, t s (in hours), computed as follows: t s = (cid:26) ◦ − arccos (cid:20) sin( lg s )) cos( lat s ) a (cid:21)(cid:27) P orb ◦ P orb is the orbital period, lat s is the latitudeof the spot in the stellar surface and a is the semimajor axis. The number of spots were determineda priori for each transit. For the radius and inten-sity, we considered initial guesses of 0.5 R p and 0.5 I c . The parameters for the spots are chosen fromthe best fit obtained by the minimization of the χ , calculated using the AMOEBA routine (Presset al. 1992).
4. Spots physical parameters
Using the model transit lightcurve proposed bySilva (2003) and described in the previous sec-tion, we analysed each transit separately and thesmall variations in the luminosity detected dur-ing the transit were interpreted as the presenceof a spot occulted by the planet. A total of507 transits for Kepler-17 and 122 for Kepler-63showed “bumps” in the lightcurve residuals abovethe adopted threshold of 10 CDPP. From the anal-ysis of these “bumps”, we obtained a total of 1069spots (Kepler-17) and 297 (Kepler-63) and esti-mated their average parameters (radius, intensityand longitude). Furthermore, from the relativespot intensity it is possible to estimate its temper-ature by considering that both the photosphereand the spots radiate like a blackbody, accordingto the equation: I spot I star = e hν/K B T eff − e hν/K B T − +70°+70° Fig. 2.— The 120th transit from Kepler-17 illustrates a typical example of the spot fit by the model developedby Silva (2003).
Top : Transit lightcurve with the model of a spotless star overplotted (yellow).
Bottom :Residuals of the transit lightcurve after subtraction of a spotless star model. The red curve shows the fit tothe data “bumps” on both panels.from which we obtain the temperature of thespots: T = K b hν ln (cid:0) f i (cid:0) e hν/KT eff − (cid:1) + 1 (cid:1) (3)where K b and h are the Boltzmann and Planckconstants, respectively, and ν is the frequency as-sociated with a wavelength of 600 nm , f i is thefraction of spot intensity with respect to the cen-tral stellar intensity I c obtained from the fit, and T eff is the effective temperature of the star. Con-sidering an effective temperature of 5781 K forKepler-17 and 5576 K for Kepler-63, we found anaverage spot temperature of 5000 ± K and4800 ± K , respectively, for both stars.These results are summarized in Table 3. The distributions of the parameters are presented inFigure 3 and Figure 4. In the case of Kepler-63,we can observe that the radii of the spots are be-tween the range 0.3 up to 2.0 R p . For the intensity,we have a variation from 0.1 to 0.8 I c . The tem-perature varies from 3000K to 5400K. The longi-tude varies from -50 to +50 ◦ . For the other star,Kepler-17, the variation of the spots parametersare the following: 0.1 to 2.0 R p for the radius,0.1 to 1.0 I c for intensity, 2000K to 6000K for thetemperature, and ± ◦ is the range for the longi-tude. Note that in Kepler-17 the longitude of thespots are concentrated preferentially in the cen-ter of the transit, and for this reason, there is adecrease when the values approach ± ◦ , howeverthe same does not happen for Kepler-63, due to thefact that the orbit of the planet crosses several lat-5 ◦ )0.0000.0020.0040.0060.0080.0100.012 Fig. 3.— Histograms of the spots parameters forKepler-17: spots intensity (in units of I c ) ( top ),spots radius (in units of R p ) ( middle ), and tem-perature ( bottom ).itudes. For further details of the spot modelling,see Valio et al. (2016) (to be submitted) and Netto& Valio (2016) (submitted) for Kepler-63.
60 40 20 0 20 40 60Longitude ( ◦ )0.0000.0020.0040.0060.0080.0100.0120.0140.016 Fig. 4.— Same as Fig. 3 for Kepler-63.
Table 3
Average values for the parameters of the spotsKepler-17 Kepler-63Radius [ R p ] 0.6 ± ± ± × (33 ± × Intensity [ I c ] 0.54 ± ± ±
600 4800 ± ◦ ] -3 ±
30 -7 ± . Stellar magnetic activity Our aim is to characterize the magnetic cyclesof Kepler-17 and Kepler-63. For this purpose weadopted two different methods as proxies for thestellar activity: (1) number and flux deficit of thespots modelled in the previous section and (2) esti-mate of the excess residuals during transits. Theseprocedures were applied to a total of 583 transitsfor Kepler-17 and 131 transits for Kepler-63. De-tails and results from both methods are describedbelow.
In the case of the Sun, the number of spots onthe solar surface is the most common proxy of itsactivity cycle and displays a periodic variation ev-ery 11 years or so. Similarly, the number of spotsthat appears at the surface of a star varies in ac-cordance with the stellar magnetic cycle. Thusby monitoring the number of spots, during theapproximate 4 years of observation of the Keplerstars, it is in principle possible to detect stellarcycles. N u m b e r o f s p o t s Kepler-17 T o t a l f l u x d e f i c i t Kepler-17
Fig. 5.— Number of spots (
Top ) and total fluxdeficit ( bottom ) caused by the spots in Kepler-17 derived from the transits analysed with themethod described in Sections 3 and 4. N u m b e r o f s p o t s Kepler-63 T o t a l f l u x d e f i c i t Kepler-63
Fig. 6.— Number of spots (Top) and total fluxdeficit ( bottom ) in Kepler-63.Another way to estimate stellar activity is cal-culating the flux deficit resulting from the presenceof spots on the star surface. The spots contrast istaken to be 1 − f i , where f i is the relative intensityof the spot with respect to the disk center intensity I c . A value of f i = 1 means that there is no spot atall. The relative flux deficit of a single spot is theproduct of the spot contrast and its area, thus foreach transit the total flux deficit associated withspots was calculated by summing all individualsspots: F ≈ (cid:88) (1 − f i )( R spot ) (4)To the resulting flux deficit and spot numberwe apply a running mean over a range of five datapoints. Note that due to this process, the numberof spots may have non-integer values. Also, to re-move possible aperiodic or long duration trends inthese time series, we applied a quadratic polyno-mial fit to the data and then subtracted it. Dueto this procedure, the number of spots and theflux deficit can be negative. Figures 5 and 6 showthese treated results for the number of spots (top,in blue) obtained from modelling each transit andthe total flux deficit (bottom, in green) for bothstars.7 .000 0.005 0.010 0.015 0.020Frequency (1/days)051015202530354045 L o m b - S c a r g l e P o w e r Kepler-17 Periodogram number of spotsflux deficit -16 -14 -12 -10 -8 -6 -4 -2 L o c a l p - v a l u e σ σ Fig. 7.— (
Top ) Power spectrum indicating the periodicity of the spots number (blue) and of the flux deficit(green) for Kepler-17. The highest peak is indicated by the vertical dashed lines and is 410 ±
60 days forthe spot number and 410 ±
50 days for the spot flux. (
Bottom ) P-values associated to each frequency fromthe periodogram, the significance level is assumed to be 3 σ . L o m b - S c a r g l e P o w e r Kepler-63 Periodogram number of spotsflux deficit -7 -6 -5 -4 -3 -2 -1 L o c a l p - v a l u e σ σ Fig. 8.— Power spectrum indicating the periodicity of the spots number ( top ) and of the flux deficit ( bottom )for Kepler-63. The highest peak is indicated by the dashed lines and is 460 ±
60 days for the spot numberand 460 ±
50 days for the spot flux.A Lomb Scargle periodogram (LS) (Scargle1982) is perfomed on these time series to obtainthe period related to the magnetic cycle. In addi-tion, we applied a significance test to quantify thesignificance of the peaks from the LS periodogram.For this, we assumed the null hypothesis as: (a) there is no periodicity in the data, and (b) thenoise has a Gaussian distribution, thus the peri-odogram power spectrum in any frequency of thedata will be exponentially distributed. The sta-tistical significance associated to each frequencyin the periodogram is determined by the p-value8
50 100 150 200 250 300 350 400 450Time (days)1.51.00.50.00.51.01.52.0 N u m b e r o f s p o t s Kepler-17 T o t a l f l u x d e f i c i t Fig. 9.— Three folded data of Kepler-17 for both spot number and total flux deficit, the 410 days periodicityclearly showing.(p). The smaller the p-value, the larger the sig-nificance of the peak. The corresponding valuesfor p-value in critical values are given by z = (cid:112) (2)erf − (1 − α as being 3 σ (p ± ±
60 days (number of spots)and 410 ±
50 days (flux deficit). There is also another significant periodicity in ∼
104 days ( f = 0.0096 days − ) appearing in both cases. Thispeak might be a harmonic, because it is approxi-mately four times the value of the frequency fromthe main peak ( f = 0.0024 days − , P = 410 days).However, as we are interested only in long term pe-riodicities, we adopted P cycle = 410 days as beingthe most relevant peak for our case. This yields amagnetic cycle of approximately 1.12 yr.Kepler-63 shows a periodicity of 460 ±
60 daystaking into account the total number of spots, and460 ±
50 days for the flux deficit, as shown inFig. 8. This corresponds to a cycle of about 1.27 ± ∼
100 200 300 400 500Time (days)2.01.51.00.50.00.51.01.5 N u m b e r o f s p o t s Kepler-63 T o t a l f l u x d e f i c i t Fig. 10.— Same as Fig.9 for Kepler-63, indicating the periodicity of 460 days of the spot data.total flux deficit by the dominant period obtainedin the periodograms. These results are presentedin Figures 9 (Kepler-17) and 10 (Kepler-63), andin both cases we obtained three periods duringthe time of observation of the stars (1240 days forKepler-17 and 1400 days for Kepler-63).
The second method adopted in this work con-sists in subtracting from the transit lightcurves amodelled lightcurve of a star without spots. Theresult from this subtraction is the residual. An ex-ample of this method is shown in Figure 11 for the100th transit of Kepler-17. An excess during thetransit is clearly seen and is due to the presence ofspots occulted by the planet. Next we integratedall residuals excess within ± ◦ longitude of thestar (delimited by the dashed lines of Fig. 11) thusobtaining another proxy for the stellar activity.This residual excess resulting from all transits is plotted in Fig. 12, and is seen to oscillate duringthe period of observation.A quadratic polynomial fit was also applied tothis time series and subtracted, removing any pos-sible trends. Its Lomb Scargle periodogram isshown in Fig. 13, where a noticeable peak is seenat 490 ±
100 days (1.35 ± ±
40 days (1.27 ± σ significance level, confirming their significance.The value obtained for Kepler-63 is similar to thatfrom the first approach, and corresponds to a 1.27year-cycle. There is also a notable peak at ∼ f = 0.00485 days − ), but this peak does notappear in the first approach (neither for spot num-ber or flux deficit), thus we do not consider it. Thethree folded data with the obtained periodicity isshown in Figure 14 for Kepler-17 and Kepler-63.On the other hand, the cycle period estimate forKepler-17 agree within the uncertainty, as shown10ig. 11.— Top : 100th transit lightcurve of Kepler-17, overplotted is a simulated lightcurve without spots(solid curve).
Bottom : Residuals of the subtracted light curve. The dashed vertical lines correspond tolongitudes ± ◦ . R e s i d u a l s e x c e ss Kepler-17 R e s i d u a l s e x c e ss Kepler-63
Fig. 12.— Activity level from the integration of alllightcurve residuals excess during transits as de-scribed in Sect. 5.2 for Kepler-17 ( top ) and Kepler-63 ( bottom ).in Figure 15. All the results for the magnetic cycleobtained with the two methods are listed in Table4.
6. Discussion
We have estimated the period of the mag-netic cycle, P cycle , for two active solar-type stars,Kepler-17 and Kepler-63, by applying two newmethods: spot modelling and transit residuals ex-cess. The results obtained from both methods arepresented in Table 4. For Kepler-63, we foundthe same result in the different approaches. Theother star, Kepler-17, however, has a P cycle ob-tained with the second method that is within theuncertainty range from the first approach. Con-sidering that, we confirm that the results in bothmethods agree with each other and assure the ro-bustness of the methods. Next, we compare ourresults to those stars, with their magnetic cycle, P cycle , reported in the literature. The observa-tional data from Saar and Brandenburg (1999) andLorente and Montesinos (2005) are the records ofthe CaII H&K emission fluxes of the stars observedat the Mount Wilson Observatory and also anal-ysed by Baliunas et al. (1995). Ol´ah et al. (2009)studied multi-decadal variability in a sample ofactive stars with photometric and spectroscopicdata observed during several decades. Messinaand Guinan (2002) performed long-term photo-metric monitoring of solar analogues. Lovis et al.(2011) took a sample of solar-type stars observed11 .000 0.005 0.010 0.015 0.020Frequency (1/days)0510152025 L o m b - S c a r g l e P o w e r Kepler-17 Periodogram - Transit residuals excess -7 -6 -5 -4 -3 -2 -1 L o c a l p - v a l u e σ σ σ σ L o m b - S c a r g l e P o w e r Kepler-63 Periodogram - Transit residuals excess -5 -4 -3 -2 -1 L o c a l p - v a l u e σ σ Fig. 13.— Lomb Scargle periodogram applied to the integrated transit residuals excess of Kepler-17 ( top )and Kepler-63 ( bottom ). The highest peak, indicated by a dashed line, corresponds to a periodicity of 494 ±
100 days for Kepler-17 and 465 ±
40 days for Kepler-63.
Table 4
Magnetic activity cycle periodsSpot Modelling Transit residuals excess(Number of spots) (Spot Flux)Kepler-17 1.12 ± ± ± ± ± ± spectrograph and used the mag-nitude and timescale of the Ca II H&K variabilityto identify activity cycles.Two distinct branches were reported for the cy-cling stars (Saar and Brandenburg 1999; B¨ohm-Vitense 2007): the active (blue line) and inactive High Accuracy Radial velocity Planet Searcher (green line), classified according to their activitylevel and number of rotations per cycle (plotted inFig. 16). The majority of the stars analysed byLovis et al. (2011) falls in the inactive branch, theSun, however, with its 11 year-cycle appears in be-tween the two branches. In Figure 16 we observethe relation between P cycle (stellar cycle period)and P rot (stellar rotation period) for all selected12
100 200 300 400 500Time (days)0.080.060.040.020.000.020.040.060.080.10 R e s i d u a l s e x c e ss Kepler-17 R e s i d u a l s e x c e ss Kepler-63
Fig. 14.— Activity level data folded three times with the resulting periodicity.
Top : Kepler-17 (490 days)and bottom : Kepler-63 (460 days). -16 -14 -12 -10 -8 -6 -4 -2 L o c a l p - v a l u e Fig. 15.— Comparison between the peak significance obtained from the first method for the flux deficit(green) and the second method (purple). The frequency peak obtained in the second method falls inside theuncertainty from the first approach. 13
Fig. 16.— Activity cycle periods, P cycle , versus stellar rotation period, P rot , for a sample of stars cited in theliterature. The dashed vertical lines connect different periods found for the same stars, i.e: stars exhibitingtwo cycles.samples, first studied by Baliunas et al. (1996).The vertical dashed line joins data for the samestar (stars with multiple periodicities detected).Kepler-63 (blue star in Fig. 16) is an active starand in the rotational period-cycle relation followsthe trend set by stars in the active branch. Onthe other hand, Kepler-17 (blue star) lies close tothe inactive stars branch, but shows a cycle periodquite close to the short-period cycle obtained byEgeland et al. (2015) for the active star HD 30495,of P cycle ∼ P rot = 11 days, and the oneanalysed by Salabert et al. (2016) for the youngsolar analog KIC 10644253 ( P cycle ∼ P rot = 10.91 days).
7. Conclusions
In the present work we applied two new meth-ods to investigate the existence of a magnetic cy-cle: spot modelling and transit residuals excess.Two active solar-type stars were analysed, Kepler-17 ( P rot = 11.89 days and age < P rot = 5.40 days and age = 0.2 Gyr).With the first method, we obtained P cycle = 1.12 ± P cycle = 1.27 ± P cycle = 1.35 ± P cycle = 1.27 ± ∼ ∼
12 years, thatagrees well with the active branch. As observedpreviously by B¨ohm-Vitense (2007), some starsthat are located in the active branch, could alsoshow short cycles falling in the inactive branch.This might be the case of Kepler-17, that is alsoan active star, showing a spots area coverage of6%, much higher than the Sun, where it is lessthan 1%, and may also have a long cycle peri-odicity. Unfortunately, as we are constrained bythe period of observation ( ≤ P cycle of the young star Kepler-63, fits well withinthe active stars branch. Morever, Metcalfe et al.(2010) found a 1.6 year magnetic cycle for the ex-oplanet host star ι Horologii observed during 2008and 2009, that seems to be in between Kepler-17and Kepler-63 in the cycle-rotation relation.14he intensity of a magnetic field is controlledby the dynamo process, and associated with dif-ferential rotation. Our analysis to identify activitycycle periods is essential for a deep investigationabout how stellar dynamos work. B¨ohm-Vitense(2007) and Durney et al. (1981) suggest that thetwo branches of stars in the P rot − P cycle diagramare possibly ruled by different kinds of dynamo,exhibiting different ratios for P cycle /P rot . In ad-dition, B¨ohm-Vitense brings up that the activebranch can be driven by a dynamo operating in thenear-surface shear layer, while in the inactive starsbranch, the shear layer of the dynamo is locatedat the base of the convection zone. This combina-tion between the analysis of the time variation inthe stellar activity and the stellar rotation periodscan also be crucial to determine the differential ro-tation rates of the star, which is fundamental togenerate the magnetic field in the stellar interiors.All these indicate that activity cycles play a keyrole in understanding the evolution of stars.This work has been supported by grant fromthe Brazilian agency FAPESP ( EFERENCES
Baliunas, S. ´a., Donahue, R., Soon, W., Horne,J., Frazer, J., Woodard-Eklund, L., Bradford,M., Rao, L., Wilson, O., Zhang, Q., et al.(1995). Chromospheric variations in main-sequence stars.
ApJ , 438:269–287.Baliunas, S. L., Nesme-Ribes, E., Sokoloff, D., andSoon, W. H. (1996). A Dynamo Interpretationof Stellar Activity Cycles.
ApJ , 460:848.Bazilevskaya, G., Broomhall, A.-M., Elsworth, Y.,and Nakariakov, V. M. (2014). A CombinedAnalysis of the Observational Aspects of theQuasi-biennial Oscillation in Solar MagneticActivity.
Space Sci. Rev. , 186:359–386.B¨ohm-Vitense, E. (2007). Chromospheric Activityin G and K Main-Sequence Stars, and What ItTells Us about Stellar Dynamos.
ApJ , 657:486–493.Bonomo, A. S., H´ebrard, G., Santerne, A., Santos,N. C., Deleuil, M., Almenara, J., Bouchy, F.,D´ıaz, R. F., Moutou, C., and Vanhuysse, M.(2012). SOPHIE velocimetry of Kepler tran-sit candidates. V. The three hot Jupiters KOI-135b, KOI-204b, and KOI-203b (alias Kepler-17b).
A&A , 538:A96.Bonomo, A. S. and Lanza, A. F. (2012). Starspotactivity and rotation of the planet-hosting starKepler-17.
A&A , 547:A37.Borucki, W. J., Koch, D., Basri, G., Batalha,N., Brown, T., Caldwell, D., Caldwell, J.,Christensen-Dalsgaard, J., Cochran, W. D.,DeVore, E., Dunham, E. W., Dupree, A. K.,Gautier, T. N., Geary, J. C., Gilliland, R.,Gould, A., Howell, S. B., Jenkins, J. M., Kondo,Y., Latham, D. W., Marcy, G. W., Meibom,S., Kjeldsen, H., Lissauer, J. J., Monet, D. G.,Morrison, D., Sasselov, D., Tarter, J., Boss,A., Brownlee, D., Owen, T., Buzasi, D., Char-bonneau, D., Doyle, L., Fortney, J., Ford,E. B., Holman, M. J., Seager, S., Steffen, J. H.,Welsh, W. F., Rowe, J., Anderson, H., Buch-have, L., Ciardi, D., Walkowicz, L., Sherry,W., Horch, E., Isaacson, H., Everett, M. E.,Fischer, D., Torres, G., Johnson, J. A., Endl,M., MacQueen, P., Bryson, S. T., Dotson, J.,Haas, M., Kolodziejczak, J., Van Cleve, J., Chandrasekaran, H., Twicken, J. D., Quintana,E. V., Clarke, B. D., Allen, C., Li, J., Wu,H., Tenenbaum, P., Verner, E., Bruhweiler, F.,Barnes, J., and Prsa, A. (2010). Kepler Planet-Detection Mission: Introduction and First Re-sults.
Science , 327:977.Christiansen, J. L., Jenkins, J. M., Caldwell,D. A., Burke, C. J., Tenenbaum, P., Seader,S., Thompson, S. E., Barclay, T. S., Clarke,B. D., Li, J., Smith, J. C., Stumpe, M. C.,Twicken, J. D., and Van Cleve, J. (2012). TheDerivation, Properties, and Value of Kepler’sCombined Differential Photometric Precision.
PASP , 124:1279–1287.Davenport, J. R. A., Hebb, L., and Hawley, S.(2015). Using Transiting Exoplanets to StudyStarspots with Kepler.
IAU General Assembly ,22:2257832.D´esert, J.-M., Charbonneau, D., Demory, B.-O., Ballard, S., Carter, J. A., Fortney, J. J.,Cochran, W. D., Endl, M., Quinn, S. N.,Isaacson, H. T., Fressin, F., Buchhave, L. A.,Latham, D. W., Knutson, H. A., Bryson, S. T.,Torres, G., Rowe, J. F., Batalha, N. M.,Borucki, W. J., Brown, T. M., Caldwell, D. A.,Christiansen, J. L., Deming, D., Fabrycky,D. C., Ford, E. B., Gilliland, R. L., Gillon,M., Haas, M. R., Jenkins, J. M., Kinemuchi,K., Koch, D., Lissauer, J. J., Lucas, P., Mul-lally, F., MacQueen, P. J., Marcy, G. W., Sas-selov, D. D., Seager, S., Still, M., Tenenbaum,P., Uddin, K., and Winn, J. N. (2011). TheHot-Jupiter Kepler-17b: Discovery, Obliquityfrom Stroboscopic Starspots, and AtmosphericCharacterization.
ApJS , 197:14.Durney, B. R., Mihalas, D., and Robinson, R. D.(1981). A preliminary interpretation of stellarchromospheric CA II emission variations withinthe framework of stellar dynamo theory.
PASP ,93:537–543.Egeland, R., Metcalfe, T. S., Hall, J. C., andHenry, G. W. (2015). Sun-like Magnetic Cyclesin the Rapidly-rotating Young Solar Analog HD30495.
ApJ , 812:12.Fletcher, S. T., Broomhall, A.-M., Salabert, D.,Basu, S., Chaplin, W. J., Elsworth, Y., Garcia,16. A., and New, R. (2010). A Seismic Signatureof a Second Dynamo?
ApJ , 718:L19–L22.Howell, S. B., Sobeck, C., Haas, M., Still, M., Bar-clay, T., Mullally, F., Troeltzsch, J., Aigrain, S.,Bryson, S. T., Caldwell, D., Chaplin, W. J.,Cochran, W. D., Huber, D., Marcy, G. W.,Miglio, A., Najita, J. R., Smith, M., Twicken,J. D., and Fortney, J. J. (2014). The K2Mission: Characterization and Early Results.
PASP , 126:398–408.Lammer, H. and Khodachenko, M., editors (2015).
Characterizing Stellar and Exoplanetary En-vironments , volume 411 of
Astrophysics andSpace Science Library .Lorente, R. and Montesinos, B. (2005). Predictingthe Length of Magnetic Cycles in Late-TypeStars.
ApJ , 632:1104–1112.Lovis, C., Dumusque, X., Santos, N. C., Bouchy,F., Mayor, M., Pepe, F., Queloz, D., S´egransan,D., and Udry, S. (2011). The HARPS search forsouthern extra-solar planets. XXXI. Magneticactivity cycles in solar-type stars: statistics andimpact on precise radial velocities.
ArXiv e-prints .Messina, S. and Guinan, E. F. (2002). Mag-netic activity of six young solar analogues I.Starspot cycles from long-term photometry.
A&A , 393:225–237.Metcalfe, T. S., Basu, S., Henry, T. J., Soderblom,D. R., Judge, P. G., Kn¨olker, M., Mathur, S.,and Rempel, M. (2010). Discovery of a 1.6 YearMagnetic Activity Cycle in the Exoplanet HostStar ι Horologii.
ApJ , 723:L213–L217.Nutzman, P. A., Fabrycky, D. C., and Fortney,J. J. (2011). Using Star Spots to Measurethe Spin-orbit Alignment of Transiting Planets.
ApJ , 740:L10.Ol´ah, K., Koll´ath, Z., Granzer, T., Strassmeier,K. G., Lanza, A. F., J¨arvinen, S., Korhonen,H., Baliunas, S. L., Soon, W., Messina, S.,and Cutispoto, G. (2009). Multiple and chang-ing cycles of active stars. II. Results.
A&A ,501:703–713.Oshagh, M., Boisse, I., Bou´e, G., Montalto, M.,Santos, N. C., Bonfils, X., and Haghighipour, N. (2013). SOAP-T: a tool to study the lightcurve and radial velocity of a system with atransiting planet and a rotating spotted star.
A&A , 549:A35.Press, W. H., Teukolsky, S. A., Vetterling, W. T.,and Flannery, B. P. (1992). Numerical recipes:The art of scientific computing (cambridge.Saar, S. H. and Brandenburg, A. (1999). TimeEvolution of the Magnetic Activity Cycle Pe-riod. II. Results for an Expanded Stellar Sam-ple.
ApJ , 524:295–310.Salabert, D., R´egulo, C., Garc´ıa, R. A., Beck,P. G., Ballot, J., Creevey, O. L., P´erezHern´andez, F., do Nascimento, Jr., J.-D., Cor-saro, E., Egeland, R., Mathur, S., Metcalfe,T. S., Bigot, L., Ceillier, T., and Pall´e, P. L.(2016). Magnetic variability in the young so-lar analog KIC 10644253. Observations fromthe Kepler satellite and the HERMES spectro-graph.
A&A , 589:A118.Sanchis-Ojeda, R. and Winn, J. N. (2011).Starspots, Spin-Orbit Misalignment, and Ac-tive Latitudes in the HAT-P-11 ExoplanetarySystem.
ApJ , 743:61.Sanchis-Ojeda, R., Winn, J. N., Marcy, G. W.,Howard, A. W., Isaacson, H., Johnson, J. A.,Torres, G., Albrecht, S., Campante, T. L.,Chaplin, W. J., Davies, G. R., Lund, M. N.,Carter, J. A., Dawson, R. I., Buchhave, L. A.,Everett, M. E., Fischer, D. A., Geary, J. C.,Gilliland, R. L., Horch, E. P., Howell, S. B.,and Latham, D. W. (2013). Kepler-63b: A Gi-ant Planet in a Polar Orbit around a YoungSun-like Star.
ApJ , 775:54.Scargle, J. D. (1982). Studies in astronomical timeseries analysis. II - Statistical aspects of spectralanalysis of unevenly spaced data.
ApJ , 263:835–853.Silva, A. V. (2003). Method for spot detectionon solar-like stars.
The Astrophysical JournalLetters , 585(2):L147.Silva-Valio, A., Lanza, A., Alonso, R., and Barge,P. (2010). Properties of starspots on corot-2.
Astronomy & Astrophysics , 510:A25.17ilva-Valio, A. and Lanza, A. F. (2011). Timeevolution and rotation of starspots on CoRoT-2 from the modelling of transit photometry.
A&A , 529:A36.