Transit mapping of a starspot on CoRoT-2 - Probing a stellar surface by planetary transits
U. Wolter, J.H.M.M. Schmitt, K.F. Huber, S. Czesla, H.M. Mueller, E.W. Guenther, A.P. Hatzes
aa r X i v : . [ a s t r o - ph . S R ] J un Astronomy&Astrophysicsmanuscript no. Exo2˙AA2008˙prefinalXArchiv c (cid:13)
ESO 2018October 24, 2018
Transit mapping of a starspot on CoRoT-2
Probing a stellar surface by planetary transits
U. Wolter , J.H.M.M. Schmitt , K.F. Huber , S. Czesla , H.M. M¨uller , E.W. Guenther and A.P. Hatzes Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germanye-mail: [email protected], [email protected] Th¨uringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenburg, Germanye-mail: [email protected], [email protected]
Received ... / Accepted ...
ABSTRACT
We analyze variations in the transit lightcurves of CoRoT-2b, a massive hot Jupiter orbiting a highly active G star. We use one transitlightcurve to eclipse-map a photospheric spot occulted by the planet. In this case study we determine the size and longitude of theeclipsed portion of the starspot and systematically study the corresponding uncertainties. We determine a spot radius between 4 . ◦ and 10 . ◦ on the stellar surface and the spot longitude with a precision of about ± Key words. stars: planetary systems – activity – late-type – imaging – stars: individual: CoRoT-2
1. Introduction
The atmosphere of the Sun shows inhomogeneities down to thesmallest scales currently accessible to solar observations whichare of the order of 50 km (e.g. Scharmer et al. 2002). Such in-tricate fine structure can also be expected in the atmospheres ofother active stars. However, the best currently available stellarobservations only resolve surface features down to the size of afew degrees on the surface, corresponding to several 10000 kmon a main sequence star.The increasing number of known transiting extrasolar plan-ets o ff ers an outstanding opportunity to study surface inhomo-geneities of their host stars with an unprecedented surface res-olution. As an example of this new technique, we present theanalysis of one transit lightcurve of the planetary system CoRoT-2, recently detected by the CoRoT satellite (Rouan et al., 1998).Our study indicates that under favourable conditions the CoRoTlightcurves allow the study of e.g. starspots and / or faculae downto a sub-degree scale on the stellar surface.Deformations of planetary transit lightcurves, attributableto dark spots, have been observed for several systems:HD 189733, Pont et al. 2007; HD 209458, Silva-Valio 2008;Tres-1, Rabus et al. 2009 and CoRoT-2, Lanza et al. 2009.Especially, Pont et al.’s study, based on HST data, for the firsttime showed that low-noise transit photometry of exoplanets canyield detailed information about surface features of their hoststar. We present a systematic analysis of the spot locations andextensions, including their uncertainties, that can be deducedfrom transit lightcurves.CoRoT-2a (GSC 00465-01282) is an apparently younglate G-dwarf star (Alonso et al. 2008, AL08 in the fol-lowing); it is unsually active and intrinsically variable Send o ff print requests to : U. Wolter,e-mail: [email protected] among the presently known planetary host stars. Its rota-tion period of P ∗ = . ± . d (Lanza et al. 2009) amountsto less than three times the planetary orbit period P orb :13 · P orb = . · P ∗ . Densely sampled high-precision photom-etry in combination with spectroscopic measurements makethe transit geometry of CoRoT-2b exceptionally well known(AL08, Bouchy et al. 2008): The planet is on a nearly circu-lar orbit ( e = . ± . i = . ± . ◦ ) and approximately oriented perpendicular tothe stellar rotation axis (deviating by λ = . ± . ◦ ).These attributes turn the planetary disk into an extremelywell-defined probe which periodically scans a band on the stellarsurface covering 20 ◦ in latitude. The orbital period of CoRoT-2btranslates into an orbital angular velocity of 0.002 deg / s. As aresult, close to the center of the stellar disk, the planet moves ≈ .
2. Observations and data analysis
The CoRoT (Auvergne et al., 2009) lightcurve of CoRoT-2 ob-served from 2007 May 16 to 2007 October 15 continuously sam-ples 31 stellar rotations. After five days of observations the satel-lite’s sampling cadence of CoRoT-2 was switched from 512 s to32 s, resulting in a lightcurve that covers 79 planetary transits atthis high time resolution.Our analysis started out from the lightcurve data as deliveredby the CoRoT pipeline. The pipeline sorts out defective data (e.g.due to crossings of the South Atlantic Anomaly, SAA) and per-forms a background subtraction. As a first step we added up allthree CoRoT photometry channels (red-green-blue) into a singlelightcurve, because the individual channels are more a ff ected byinstrumental instabilities than their summed-up signal. Wolter, Schmitt et al.: Transit mapping of a starspot on CoRoT-2
Fig. 1.
Section of the CoRoT lightcurve of CoRoT-2, purged of outlying values (see Sect. 2). The transits appear as recurrent dipsoverlying the modulation by the stellar rotation. Transits are numbered from the beginning of the CoRoT observations, our analysisfocusses on transit no. 56.Similar to AL08, we then removed outlier points which showa pronounced non-normal distribution. To this end we computedthe standard deviation σ in several narrow intervals, yielding σ ≈ σ froma boxcar-smoothed copy of the lightcurve, thus rejecting nearly2% of all points. Finally, also following AL08, we corrected forthe 5 .
6% contamination by a neighbouring object; a subintervalof the resulting lightcurve is shown in Fig. 1.The transits occur during di ff erent stellar rotation phases, i.e.at di ff erent levels and slopes of the lightcurve. In order to com-pare the transit lightcurves, it is convenient to normalize themto a common level. To this end, we carried out a linear interpo-lation of points adjacent to each transit and divided all transitlightcurves by their interpolating function. One lightcurve nor-malized in this way is shown in Fig. 2.We note that this procedure introduces a systematic error thatdepends on the spot coverage of the stellar disk visible during thetransit. If, e.g., the disk is covered by dark spots not occulted bythe planet, the transit depth will not yield the true ratio of radii R planet / R ∗ . Instead, the stellar radius R ∗ will be underestimatedrelative to the planet, because part of the stellar disk is dark andessentially invisible. Given the typical amplitude of CoRoT-2’slightcurve of about 4% peak-to-peak, this introduces a compa-rable uncertainty for the planetary radius deduced from a sin-gle transit. Consequently, this uncertainty also a ff ects our spotsize estimate of the next section. We will discuss the influenceof activity-induced lightcurve variations on the determination ofplanetary parameters in a forthcoming paper.
3. Transit lightcurve modelling
To determine a spot configuration compatible with the deforma-tions of a transit lightcurve, we selected one particular transitoccuring close to JD 2454335.0 and referred to as “transit 56”.Rendered in Fig. 2, it shows the most pronounced and isolated“bump” of the whole time series of CoRoT-2, suggesting a rela-tively narrow spot occulted close to the disk center. Additionally,the symmetry of the bump indicates a spot geometry that islargely symmetric in longitude.
To model a transit lightcurve we decompose the stellar surfaceinto roughly square elements. The integrated stellar flux is com-puted by summing up the fluxes of all visible elements, respect-ing their projected area and the limb darkening (e.g. Wolter et al.2005). To model the planetary transit, all surface elements oc-
Fig. 2.
Normalized lightcurve during “transit 56”, as a func-tion of time from the transit center. Gray symbols indicate theunbinned measurements, the red line shows them averaged in224 sec time bins with 1 σ -errors indicated. The vertical linesdelimit the time interval used for our spot model; the lightcurvefit resulting from our model is drawn black (model “BN” inTable 1). The blue line shows the transit model for an unspottedstar for comparison. The shallow deformation left of the transitcenter is caused by another spot not included in our model.culted by the planetary disk at a given phase are removed fromthe sum, thus treating the planet as a circular disk without anyintrinsic emission. The surface resolution needs to be su ffi cientto analyze the densely sampled movement of the planetary diskover the stellar surface. We choose a surface grid with 750 el-ements at the equator, yielding 178 868 elements in total and asurface resolution of roughly 0 . ◦ near the equator. Also, thishigh resolution is required to compute lightcurve models su ffi -ciently free of jitter, not exceeding a few 10 − in our models.Next, we adjusted the limb darkening to optimize the fit tothe transit ingress and egress as well as to a tentative lower enve-lope of transit 56 and the surrounding transits. We adopt a linearlimb-darkening law with ǫ = .
6; we note, however, that this haslittle influence on our determined spot parameters since the spotoccultation in transit 56 occurs close to the disk center.We compute the position of the planetary disk on the stellardisk and the corresponding stellar rotation phase using the or-bital parameters and planetary size given by AL08, as well asa stellar rotation period of P ∗ = . olter, Schmitt et al.: Transit mapping of a starspot on CoRoT-2 3 Fig. 3.
Fit quality of our transit lightcurve models as a functionof spot longitude, shown for the models BC (blue stars), BN (redplus symbols) and DS (black curve), of Table 1. Our adoptedlimiting value of χ = . R ∗ with their origin at the center ofthe star and the observer located on the x -axis. The stellar rota-tion axis is assumed to coincide with the z -axis, while the axisof the planetary orbit is tilted by 90 ◦ − i = . ◦ in the xz -plane.Both, the stellar rotation and the planetary orbit are adopted asright-handed around the z -axis.Using these coordinates, z pl and y pl describe the position ofthe center of the planetary disk projected onto the stellar diskvisible at the stellar rotation phase φ . The following relationsapply: z pl = cos i · a / R ∗ (1)where i and a describe the inclination and the semimajor axis ofthe planetary orbit, respectively. φ − φ cen = y pl y IV · τ trans P ∗ (2)where φ cen is the stellar rotation phase at transit center, while τ trans and P ∗ give the transit duration (first to last contact) and thestellar rotation period, respectively. τ trans = y IV describesthe lateral planet position at last contact y IV = r(cid:16) + R pl / R ∗ (cid:17) − z pl (3)with R pl giving the planetary radius. Note that Eq. 2 is onlystrictly valid for R ∗ ≪ a ; however, the error is of the orderof ( R ∗ / a ) and can be neglected for our analysis. In addition,Eq. 1 does not include the projected angle between the stellarrotation axis and the planetary orbital axis λ . However, givenBouchy et al. (2008)’s value of λ ≈ ◦ and the proximity of themodelled spot to the disk center, this introduces an uncertaintyof less than 2 ◦ for the spot latitude. Our initial tests showed that the given transit lightcurves donot significantly constrain the spot shape and contrast. Hencewe limit our models to circular spots or circle segments.Furthermore, we tentatively adopt two values for the spot-to-photosphere contrast: As a “dark spot” scenario we choose a spotflux of 30% of the photospheric flux. Based on Bouchy et al.(2008)’s e ff ective temperature of CoRoT-2a of 5625 K and Fig. 4.
Fit quality χ of our transit lightcurve models as a func-tion of the spot radius and its center colatitude. The upper panel describes the “bright spot” scenario (models BC, BN and BS ofTable 1), while the lower panel applies to the “dark spot” so-lutions (models DN and DS). Subsequent contours mark levelsof χ = , , ,
10 and 20; the adopted limiting contour, χ = χ -contours, only colatitudes in the upper half of the transit bandare shown. See text for discussion.Planck’s law at a wavelength of 6000 Å, this corresponds to aspot approximately 1200 K cooler than the photosphere. This ismotivated by spot temperatures found for other highly active Gand K stars (e.g. Strassmeier & Rice 1998, O’Neal et al. 2004).As a “bright spot” we adopt a value of 75% of the photosphericflux. This roughly represents the average contrast of large spotgroups on the Sun at visible wavelengths (Walton et al. 2003,Albregtsen et al. 1984). Our two spot contrast scenarios are com-parable to those adopted for CoRoT-2a by Lanza et al. (2009).Defining the spot contrast and shape in this way, three freeparameters describe a given spot, namely the spot radius r aswell as its central longitude ϕ and colatitude θ . However, as il-lustrated by Fig. 3, the longitude is closely confined by the transitlightcurve, irrespective of the spot contrast and colatitude. Thisis due to the well defined maximum of the transit bump. Thusonly two undetermined parameters remain to optimize the fit oftransit 56’s lightcurve: r and θ . We calculated model lightcurvesfor grids in these two parameters, the resulting goodness-of-fit χ is shown in Fig. 4.To calculate χ we rebinned the lightcurve into 224 sec bins,and estimated the resulting errors σ j assuming Gaussian er-ror propagation: χ = / ( N − M ) · P Nj = (cid:16) F obs , j − F model , j (cid:17) /σ j .Here, M = N = Wolter, Schmitt et al.: Transit mapping of a starspot on CoRoT-2
Table 1.
Parameters of characteristic spot solutions dis-cussed in the text, longitudes and colatitudes are given forthe spot center.
Model a Long. Colat. Radius Flux b χ Area c BC 216 . ◦ . ◦ . ◦ .
75 0.8 0.45%BN 216 . ◦ . ◦ . ◦ .
75 1.4 0.55%BS 216 . ◦ . ◦ . ◦ .
75 1.2 0.47%DN 216 . ◦ . ◦ . ◦ . . ◦ . ◦ . ◦ . . ◦ . ◦ . ◦ . a BC, BN and BS stand for ’bright central’, ’bright north’ and’bright south’, respectively. They describe spots with colatitudesclose to the center of the planetary disk. DN and DS stand for’north’ and ’south’ dark spot solutions, respectively; DEQ repre-sents a “dark” spot centered below the equator. b Relative to the photosphere c Fraction of total stellar surface time bins used to constrain the modelled spot, see the intervallimits indicated in Fig. 2.Reducing χ in this way is non-unique because of the signif-icant correlation of the spot radius and colatitude, illustrated bythe slanted contours of Fig. 4. Tentatively we choose a limit of χ ≤ . χ = . As the χ -contours in the upper panel of Fig. 4 show, for the“bright spot” scenario, the central spot colatitude is confinedto θ = ± ◦ , i.e. inside the stellar surface belt transited by theplanet. The spot radii are slightly smaller than, or comparable to,the size of the planetary disk: r = . ◦ . . . . ◦ . This scenario isillustrated by Fig. 5 and the exemplary solutions BN, BC and BS(“bright north, central and south ”) of Table 1.For the “dark spot” scenario, on the other hand, only spotcenters away from the center of the transit belt yield proper fits tothe transit lightcurve: θ ≤ ◦ and θ ≥ ◦ . This is illustrated bythe lower panel of Fig. 4 which also shows that the resulting spotradii are smaller than in the “bright spot” case ( r = . ◦ . . . . ◦ ).Also spots with centers outside the transit band yield feasi-ble solutions. An example is illustrated by the red arc in Fig. 5,showing solution DEQ of Table 1. As illustrated by the figure,concerning area and longitude extent they do not di ff er signif-icantly from solutions with centers inside the band. We do notdiscuss them further since their radii do not describe the tran-sited extension and area of the spot appropriately.
4. Discussion
The shape of the transit lightcurves of CoRoT-2 exhibits highlysignificant variations between di ff erent transits. This indicates aubiquitous presence of starspots in the surface regions transitedby the planet. Furthermore, as illustrated by Fig. 1 and the analy-sis of Lanza et al. (2009) the overall lightcurve of CoRoT-2 con-tinuously changes in amplitude during the complete CoRoT ob-servations. This shows that the stellar surface of CoRoT-2a per-sistently evolves on timescales shorter than its rotation period.Such a fast spot evolution is interesting physically and makesCoRoT-2a a favourable case for the study of stellar activity, po-tentially a landmark system. Fig. 5.
A starspot on CoRoT-2a occulted by the planet duringtransit 56, as reconstructed by transit mapping. The black andgray circles represent the planetary disk and the spot for our“bright spot” scenario, i.e. adopting a spot flux of 75% relativeto the photosphere. The purple arcs illustrate the northern- andsouthernmost solutions for this spot flux. The red arc illustratesa “dark spot” solution (DEQ in Table 1), see text for discussion.We concentrate our analysis on a single planetary transitwhose lightcurve shows a pronounced and isolated bump closeto the transit center. Assuming this bump is caused by a circu-lar starspot, we determine parameter ranges for this spot whichreproduce the observed transit lightcurve.While, similar to Pont et al.’s analysis of HD189733, thespot contrast is only weakly constrained, the spot longitude andradius are closely confined by the transit lightcurve. The spotthus reconstructed on CoRoT-2b is comparable in extent withlarge spot groups on the Sun which cover up to about 1% of thesolar surface (Baumann & Solanki, 2005; Norman, 2005).Given the nearly 90 ◦ inclination of CoRoT-2b’s orbit, thetransit-covered belt on its surface lies close to the equator. Ouranalysis proves that CoRoT-2a, like the Sun, exhibits spots inthis region. Such well-constrained latitude measurements nearthe equator are di ffi cult or impossible with other surface recon-struction methods like Doppler imaging. Using long-term tran-sit observations, this may allow to study activity cycles analogto the solar butterfly diagram. Also, concerning possible indica-tions of di ff erential rotation on CoRoT-2a (Lanza et al., 2009),the spots in the transit-covered belt could supply additional in-formation.Solar umbrae have diameters up to about 10 Mm, corre-sponding to one degree in heliographic coordinates; penumbraereach approximately twice this size. Our study indicates that asurface resolution of potentially better than one degree can beachieved for host stars of eclipsing planets when applying transitmapping to low-noise and fast-sampled lightcurves. Thus, suchobservations o ff er a new opportunity to study “solar-like” sur-face structures on other stars, they may for example allow tomeasure the umbra / penumbra contrasts of their spots. Acknowledgements.
U.W. acknowledges financial support from DLR, project50 OR 0105.
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