Estimating the masses of extra-solar planets
C. A. Watson, S.P. Littlefair, A. Collier Cameron, V. S. Dhillon, E. K. Simpson
aa r X i v : . [ a s t r o - ph . E P ] J un Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 8 November 2018 (MN L A TEX style file v2.2)
Estimating the masses of extra-solar planets
C. A. Watson, ⋆ S. P. Littlefair, A. Collier Cameron, V. S. Dhillon, and E. K. Simpson Astrophysics Research Centre, School of Mathematics & Physics, Queen’s University, University Road, Belfast BT7 1NN, UK Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY19 9SS, UK
Accepted for publication in the Monthly Notices of the Royal Astronomical Society8 November 2018
ABSTRACT
All extra-solar planet masses that have been derived spectroscopically are lowerlimits since the inclination of the orbit to our line-of-sight is unknown except for tran-siting systems. In theory, however, it is possible to determine the inclination angle, i ,between the rotation axis of a star and an observer’s line-of-sight from measurementsof the projected equatorial velocity ( v sin i ), the stellar rotation period ( P rot ) and thestellar radius ( R ∗ ). For stars which host planetary systems this allows the removal ofthe sin i dependency of extra-solar planet masses derived from spectroscopic observa-tions under the assumption that the planetary orbits lie perpendicular to the stellarrotation axis.We have carried out an extensive literature search and present a catalogue of v sin i , P rot , and R ∗ estimates for stars hosting extra-solar planets. In addition, we have usedHipparcos parallaxes and the Barnes-Evans relationship to further supplement the R ∗ estimates obtained from the literature. Using this catalogue, we have obtained sin i estimates using a Markov-chain Monte Carlo analysis. This technique allows proper 1- σ two-tailed confidence limits to be placed on the derived sin i ’s along with the transitprobability for each planet to be determined.While we find that a small proportion of systems yield sin i ’s significantly greaterthan 1, most likely due to poor P rot estimations, the large majority are acceptable. Weare further encouraged by the cases where we have data on transiting systems, as thetechnique indicates inclinations of ∼ ◦ and high transit probabilities. In total, we areable to estimate the true masses of 133 extra-solar planets. Of these 133 extra-solarplanets, only 6 have revised masses that place them above the 13 M J deuterium burn-ing limit; 4 of those 6 extra-solar planet candidates were already suspected to lie abovethe deuterium burning limit before correcting their masses for the sin i dependency.Our work reveals a population of high-mass extra-solar planets with low eccentricitiesand we speculate that these extra-solar planets may represent the signature of differ-ent planetary formation mechanisms at work. Finally, we discuss future observationsthat should improve the robustness of this technique. Key words: planetary systems – stars: fundamental properties – stars: rotation
Over 16 years ago the first planets to be detected outside ofour solar system were discovered around the millisecond pul-sar PSR1257+12 (Wolszcan & Frail 1992). Within 3 years,Mayor & Queloz (1995) announced the first planet orbiting ⋆ E-mail: [email protected] around a main-sequence star, 51 Peg b. Since then, extra-solar planet candidates have been discovered at a phenome-nal rate. At the time of writing, 453 extra-solar planet can-didates have now been identified through a variety of tech-niques including radial velocity studies, transits, microlens-ing events, stellar pulsations as well as pulsar timing.By far the most extra-solar planets have been discoveredby observing the small Doppler wobble of the host star. This c (cid:13) C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson technique, however, only returns a minimum mass M sin i (where M is the mass of the planet, and i is the inclinationof the normal to the planetary orbital plane to the observer’sline-of-sight), which is a firm lower limit to the true plane-tary mass. Indeed, the inclination (and hence true planetarymass) can only be determined accurately for those planetswhich transit their host star. With only ∼
70 transiting plan-ets known, this leaves the vast majority of planets with onlylower-limits placed on their masses. Improving the mass de-terminations of these planets has obvious benefits for planetformation modeling and for studying the planet mass distri-bution.In this paper we present a method for estimating theorbital inclinations and hence true masses of non-transitingextra-solar planets. We then apply this method to the extra-solar planet systems for which there is sufficient data avail-able, and investigate the impact that the corrected masseshave on our knowledge of extra-solar planet properties. Fi-nally, we conclude with a look at the improved measure-ments that should be made to make this technique morerobust.
It is possible to determine the inclination angle, i , betweenthe rotation axis of the extra-solar planet host star and theobserver’s line-of-sight. By combining measurements of thestar’s projected equatorial velocity ( v sin i ), the stellar rota-tion period ( P rot ) and the stellar radius ( R ∗ ) one can deter-mine sin i fromsin i = P rot × v sin i πR ∗ . (1)Indeed, this method has previously been applied byGonzalez (1998) to 7 exoplanet host stars, as well as byCameron & Foing (1997) to determine the inclination of therotation axis of the extensively Doppler-imaged young starAB Dor, for example. Equation 1 can then be used to lift thesin i degeneracy in calculating extra-solar planet masses us-ing spectroscopic observations if it is assumed that the plan-etary orbits lie perpendicular to the host star’s rotation axis.Certainly, this condition holds true for our solar system,which has an angle between the plane of the ecliptic and thesolar equator of around 7 ◦ (Beck & Giles 2005). The degreeof alignment between the stellar spin axis and the planetaryorbit can also be measured for transiting extra-solar planetsusing the Rossiter-McLaughlin effect (e.g. Gaudi & Winn2007). So far this has been carried out for 26 planet sys-tems (see Winn et al. 2005; Winn et al. 2007; Wolf et al.2007; Narita et al. 2007; Johnson et al. 2008; Cochran et al.2008; H´ebrard et al. 2008; Bouchy et al. 2008; Winn et al.2008; Johnson et al. 2009; Winn et al. 2009; Narita et al.2009; Pont et al. 2009; Triaud et al. 2009; Gillon et al.2009; Narita et al. 2010; Anderson et al. 2010; Jenkins et al.2010); Simpson et al. 2010; Queloz et al. 2010; Triaud et al.2010).Of these 26 systems, 7 appear to have appreciable mis-alignment angles. These are HD 80606b, XO-3b, HAT-P-7b,WASP-2b, WASP-8b, WASP-14b, WASP-15b and WASP-17b. However, H´ebrard et al. (2008) suggest that the spin- orbit misalignment measured for XO-3 may be due to asystematic error as a result of the high airmass at whichtheir observations were carried out. We should also notethat at first the spin-orbit misalignment of HD 17156 wasmeasured to be 62 ◦ ± ◦ by Narita et al. (2008), thoughthe more recent work by Cochran et al. (2008) concludedthat the planetary orbital axis is, in fact, very well alignedwith the stellar rotation axis. Pont et al. (2009) have re-ported a ∼ ◦ misalignment in HD 80606. This system isa binary, and the misalignment may well arise through theaction of the Kozai mechanism (e.g. Takeda & Rasio 2005;Malmberg et al. 2007). HD 80606b also exhibits a large or-bital eccentricity, no doubt as a result of the Kozai inter-actions. In addition, WASP-8b is part of a triple system(Queloz et al. 2010) and therefore its mis-alignment angle isalso most likely due to the Kozai mechanism. This leaves 4planetary systems with confirmed mis-alignment angles forwhich no stellar companion is yet known. Whether the Kozaimechanism is a dominant process affecting the orbital evo-lution of exoplanets in non-binary systems is yet to be seen,but obviously some caution must be applied when assumingspin-orbit alignment. For now, however, we will work on thepremise that this assumption is a reasonable one for singlestars.In order to measure the orbital inclination of extra-solarplanets, we can see from equation 1 that we require just 3quantities, v sin i, R ∗ and P rot . The projected stellar equato-rial rotation-velocity, v sin i , can be measured using high res-olution spectroscopy. While the stars targeted by extra-solarplanet hunts are generally slowly rotating (in order to avoidspurious radial velocities introduced by magnetic activitygenerated in rapidly rotating stars), the spectrographs usedfor hunting extra-solar planets are high-resolution instru-ments. Thus most extra-solar planet host stars have theirline-broadening measured. One possible caveat with thesemeasurements is that the stellar rotation may no longer beconsidered the sole line-broadening mechanism and othermechanisms, such as turbulence (see Section 8 for a discus-sion), may have to be taken into account.The radii of the extra-solar planet host stars can be es-timated in a variety of ways. While some stars may havetheir radii measured directly via interferometry, lunar oc-cultations or transits/eclipses (e.g. Fracassini et al. 2001),the majority are estimated using indirect methods. Themost common method is to combine stellar luminositiesderived from bolometric corrections and Hipparcos paral-laxes with effective temperatures (determined from spectralsynthesis modeling) to determine the stellar radii. Indeed,Fischer & Valenti (2005) have done exactly this for a largenumber of extra-solar planet host stars, and quote a medianerror on the radii of ∼ F v ) – colour relationship: F v = 3 . − .
131 ( V − K ) . (2)When combined with the absolute visual magnitude, M v ,the surface brightness parameter F v calculated in equation 2 c (cid:13) , 000–000 stimating the masses of extra-solar planets can be used to determine the radius of the star, in solar radii,using equation 2 of Beuermann et al. (1999): R ∗ = 10 . × [42 . − (10 × F v ) − M v ] . (3)Thus, only the M v of the host star is required, which can becalculated from the V − band magnitude and parallax mea-surements from Hipparcos. We have also taken into accountextinction using the reddening law from Fouque & Gieren(1997): E ( V − K ) = 0 . A v , (4)and the absorption law from di Benedetto & Rabbia (1987): A v = 0 . × − exp ( − × d × | sin b | ) | sin b | , (5)where A v is the visual absorption coefficient, E ( V − K ) the V − K colour extinction, d the distance to the star in kpcand b the galactic latitude. We note that the stellar radiiand associated error bars we derive from the Barnes-Evanstechnique are in excellent agreement with the published stel-lar radii for extra-solar planet host stars showing an rmsscatter of 6.7 per cent. This scatter is largely Gaussian innature, except for a number of notable outliers. Indeed, onclose inspection we find that out of the 373 individual stel-lar radii measurements presented in this work, 11 disagreewith the Barnes-Evans derived radii by 3 − sigma or more.Statistically we would not expect more than 1 or 2 measure-ments to lie beyond 3- σ . On closer inspection, apart fromHD 41004A, all of the outliers (HD 6434, HD 33283 (2 dis-crepant measurements), HD 33564, HD 82943, HD 89744,HD 128311, HD 145675, HD 186427 and HD 216437) haveother radii measurements which agree well with the Barnes-Evans derived radius. We can only surmise that these dis-crepant points are, therefore, due to systematics.This leaves one final quantity, the rotation period of thestar, P rot , to be determined. Unfortunately, for the reasonsstated earlier, the majority of stars targeted in extra-solarplanet hunts are not highly active stars. Therefore, their ro-tation periods generally cannot be measured by tracking oflarge, cool starspots on their surfaces, for example. Theyare often, however, sufficiently active to show Ca ii H andK emission in their spectra. Noyes et al. (1984) derived theratio, R ′ HK , of Ca ii H and K chromospheric emission tothe total bolometric emission for a number of stars whoserotation periods were known from variability in their lightcurves. They found that, as expected from stellar dynamotheory, the mean level of Ca ii H and K emission is cor-related with rotation period. In addition, the emission alsodepends on the spectral type (probably due to convectivezone depth). Noyes et al. (1984) were then able to deter-mine the following rotation period – activity relationshipfor main-sequence stars,log ( P rot /τ ) = 0 . − . y − . y − . y , (6)where y = log(10 R ′ HK ). The value for the convectiveturnover time, τ , can be obtained from the empirical func-tion,log τ = (cid:26) . − . x + 0 . x − . x : x > . − . x : x < x = 1 − ( B − V ). Thus the stellar rotation periodcan be determined from equation 6 if R ′ HK and the B − V colours are known.We are in the fortunate position that many of the ex-trasolar planet hosts have published R ′ HK values, since in-vestigators generally wish to show that the host stars ex-hibit low-level magnetic activity and hence discard activityas the cause of radial velocity variations. Furthermore, mostextra-solar planet hosts are bright stars, of which severalhave been observed by long-term surveys such as the MountWilson H-K survey that started in the mid-1960’s (Wilson1978). Since the level of Ca ii H and K emission may varywith time due to, for example, solar-like activity cycles orrotation of magnetic regions, R ′ HK measurements need tobe averaged over a suitably long ( ∼ decade) baseline. Givena suitable span of observations, Noyes et al. (1984) foundthat they could predict the rotation periods of stars witha reasonably high accuracy. Obviously, for stars where onlya few R ′ HK observations have been made, the error on therotation period may be much higher due to intrinsic vari-ability in the Ca ii H and K emission. This is discussed insection 3.1
In order to calculate the sin i ’s of the extra-solar planethosts, we have conducted an intensive literature anddatabase search to determine the 3 quantities v sin i, R ∗ andlog R ′ HK . The values we have found are presented in Ta-ble 1. Extra-solar planet host stars for which we could notfind estimates of all 3 quantities ( v sin i, R ∗ and log R ′ HK )are not presented in this table. Where identifiable, we haveattempted to remove any duplicate measurements. For ex-ample, many of the v sin i measurements taken from theNASA Stellar Archive and Exoplanet Database (NStED –see http://nsted.ipac.caltech.edu/ ) were found to berounded values from Fischer & Valenti (2005) and havetherefore not been included in Table 1 in these cases.The values in Table 1 have then been used to determine v sin i , R ∗ and P rot for each star in our sample to obtain sin i via equation 1 as follows. We have taken a weighted meanfor the final values of v sin i and R ∗ (the latter includes ourradius estimate derived from the Barnes-Evans technique).Where no error was quoted for a value of v sin i we havetaken it to be 1.0 km s − , which is twice the typical er-ror assumed on v sin i measurements (see the catalogue ofFischer & Valenti 2005, for example). Regarding radii withno associated error estimate, we have taken the error to be10 or 20 per cent of the absolute value. We have chosen10 per cent when the only radius measurement/s availablefor a particular star do not indicate uncertainties. Wherethere is more than one radius estimate for a star, of whichone or more do not include error bars, then we have as-sumed the error bar to be either 10 or 20 per cent. We chosewhether to adopt a 10 or 20 per cent uncertainty such thatradii estimates with associated error bars were given a higherweighting than those without formal error bars in the finalweighted mean. c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson log R ′ HK values and errors The adopted values and error estimates for the log R ′ HK measurements require special mention. A comprehensive lit-erature search has been conducted and for each log R ′ HK measurement reported in Table 1 we have determined, wherepossible, the number of observations and period span overwhich they were carried out. This detailed information issummarised in Table 6. Where details of the log R ′ HK mea-surements are either not present or are ambiguous, we haveassumed that they are from a single observation and haveflagged them as ‘individual?’ . Where available we have alsoquoted any reported variations or error estimations in eitherthe S-index (see Wright et al. 2004 for the definition of S-index, but note that their equation 10 is in error and theleft-hand side should read log C cf ( B − V ) = . . . ) or log R ′ HK measurement. These reported errors should be treated withcaution since in many cases they only represent the mea-surement accuracy and do not sample variations in the CaH & K emission over the course of the stellar rotation and/oractivity cycle.After establishing how well monitored each star was,they were then assigned a grade of P (Poor), O (O.K.), G(Good) or E (Excellent). A grade of ’poor’ was assignedto stars with only a few individual log R ′ HK measurementswhich would not be sufficient to sample the variation of chro-mospheric emission throughout a stellar rotation. ’O’ was as-signed to stars with a few observations spaced over severalmonths where the stellar rotation was probably adequatelysampled, but not the activity cycle. A grade of ’good’ wasassigned to stars with more than 2 years worth of observa-tions where the stellar rotation would be well sampled, butprobably only a portion of any activity cycle present hadbeen covered. Finally, a grade of ’excellent’ was assigned toobjects with over a decade of log R ′ HK measurements avail-able which covered any likely activity cycle.Vaughan et al. (1981) present a study of chromosphericCa H & K variations as a function of stellar rotation for46 lower main sequence field stars. Their results show that,on average, rotation causes the modulation of the S-index(and therefore also the log R ′ HK measurements) by 7.3 percent for F-stars, 9.4 per cent for G-stars, and 13 per cent forK-stars. We refer to these values as the average rotationallymodulated variations or ARMV. In addition, Vaughan et al.(1981) show that modulations due to activity cycles are typ-ically twice that caused by rotation. We have used this toassign general error bars on the log R ′ HK values for our starsdependent upon their spectral type and assigned grade (P,O, G, or E) as follows: • Grade P: 2.0 × the ARMV, • Grade O: 1.5 × the ARMV, • Grade G: 1.0 × the ARMV, • Grade E: 0.5 × the ARMV.Thus, stars with only a few individual observations are as-signed an error that would cover the entire range in Ca H& K variations seen over a typical activity cycle. The errorbars assigned to the other categories are somewhat ad-hoc,but signify an improvement in the reliability of the averagelog R ′ HK as the sampling of the activity cycle is improved.Given the amalgamation of sources for the log R ′ HK obser-vations, we feel this is as robust an error treatment that the data can be given in most cases. For objects with severalindependent log R ′ HK measurements, this error assignmentgenerally covers the observed variations well. In the few caseswhere they do not, we have expanded the error bar to coverthe observed log R ′ HK variations appropriately. Finally, forobjects whose activity cycles have been well monitored andfor which we can define a maximum variation across thecycle, we have taken these limits as representing the 3- σ variation on the average log R ′ HK value. (For example, if awell sampled star has a mean log R ′ HK = -4.9 but variesfrom -4.8 – -5.0, we assigned a 1- σ error = 0.1/3).Where two or more log R ′ HK measurements are availablewe have taken a weighted mean of their values. The weight-ings are based on either how many observations have beentaken, or the time span over which the observations weretaken, depending on what information exists. We have thencalculated the stellar rotational period using the Noyes et al.(1984) relationship and B − V values from the NStEDdatabase. The rotation periods and the associated error barswe have calculated are presented in Tables 2 & 3 and canbe compared to the rotation periods obtained in the litera-ture shown in Table 1. Note, however, that we found severalcases where authors have clearly calculated the rotation pe-riod from log R ′ HK incorrectly (see Appendices A and B). Equation 1 can be thought of as a naive estimator of sin i . Bysimply inputting the derived values for v sin i , R ∗ and P rot for each host star (as discussed earlier) it is possible to obtainan unconstrained distribution of sin i values (i.e. values ofsin i > v sin i , R ∗ and P rot , this naive estimator will, however, occasionallyyield unphysical sin i values greater than 1. Table 2 lists allthe exoplanet host stars which yield a sin i > σ two-tailed confidence limitscan be placed on the derived sin i ’s, as well as allowing theprobability of a transit being observed to be calculated frompurely spectroscopic data. MCMC has been used in severalareas of astronomy, and instead of outlining in detail its op-eration here, we refer the readers to Tegmark et al. (2004),Ford (2006) and Gregory (2007), who have applied MCMCto various astronomical problems including deriving cosmo-logical parameters from the cosmic microwave background,and deriving physical parameters of extra-solar planet sys-tems. In particular, our version of MCMC is modified fromthe code used by Collier Cameron et al. (2007) to identifyextra-solar planet transit candidates.Naturally, values of sin i > i >
1. If, however, we imagine the hypotheticalcase where we have a population of transiting extra-solar c (cid:13) , 000–000 stimating the masses of extra-solar planets planets all with sin i = 1 then, due to measurement errors,on average half of these systems would yield sin i > i = 1 . ± . R ∗ , P rot and v sin i mea-surements leading to sin i >
1. We have, therefore, includedall systems from Table 2 which are within 1- σ of sin i = 1 inour MCMC analysis and have error bars < R ∗ , P rot , v sin i and their associatederror bars, σ R , σ P , σ v , respectively. We assume that the stel-lar inclinations are randomly distributed and hence followa uniform distribution with 0 < x <
1, where x = cos i .For the purposes of calculating the transit probabilities ofthe extra-solar planets, we have also assumed that the stel-lar mass follows the mass-radius relationship M ∗ = R . ∗ (Tingley & Sackett 2005).It is the 3 quantities R ∗ , P rot and x that consti-tute the ‘proposal parameters’ with analogy to the de-scription of the implementation of MCMC outlined byCollier Cameron et al. (2007). We can then perform a ran-dom walk through parameter space by perturbing eachproposal parameter from its previous value by a randomamount: R ∗ ,i = R ∗ ,i − + Gσ R P rot,i = P rot,i − + Gσ P x i = x i − + Gσ x , where G is a Gaussian random number with zero mean andunit variance. The initial value of x = cos i was set to 0.5and given an arbitrary standard deviation σ x = 0.05 whichwas later re-evaluated empirically from the Markov chainsthemselves (see later).After each perturbation, χ was evaluated for the newset of proposal parameters via: χ i = ( R ∗ ,i − R ∗ , ) σ R + ( P rot,i − P rot, ) σ P + (2 πR ∗ ,i p [1 − x i ] /P rot,i − v sin i ) σ v , (8)where p [1 − x i ] = sin i , v sin i is the measured projectedstellar rotation velocity and R ∗ , , P rot, are the measuredstellar radius and rotation period, respectively. For eachjump, if χ i < χ i − then the new parameters were ac-cepted, otherwise the new parameters were accepted withthe acceptance probability given by exp (cid:2) − ( χ i − χ i − ) / (cid:3) (the Metropolis–Hastings rule). The uncertainty σ x was re-computed from the Markov chains themselves every 100 suc-cessful steps by calculating the standard deviation on x overthese 100 jumps.We found that it was necessary to carry out 1,000,000jumps in order for the MCMC to return the maximum like-lihood value of sin i that accurately approached the valueobtained from equation 1. The Markov chains were thenevaluated (after discarding a 1000-step long burn-in phase) in order to determine the 1- σ two-tailed confidence limitson sin i . In addition, for each set of new parameters gen-erated within the Markov chain, we evaluated whether ornot the extra-solar planet (or extra-solar planets in the caseof multiple systems) would transit the host star. Thus ourimplementation of MCMC also returns the transit probabil-ity for each extra-solar planet in the study. We should note,however, that we have assumed that the extra-solar planetsfollow circular orbits, so our calculated transit probabilitiesmay not be accurate for extra-solar planets with highly ec-centric orbits. Furthermore, objects are flagged as transitingif the planets centre crosses the stellar disc – the planetaryradius is not taken into account. The results of the MCMCanalysis are shown in Table 3. While we have already highlighted possible sources of errorarising from, for example, variation of the chromosphericemission due to rotation of active regions or stellar activitycycles, it is pertinent to look into other possible sources ofsystematics. These include potential biases as a result of dif-fering line-of-sight effects, our use of an inhomogeneous setof data from a number of different studies, selection effects,and problems arising due to our ignorance of the physics atwork that affect the measurables in equation 1. We shall dis-cuss possible systematics affecting the estimation of the pa-rameters in the right-hand side of equation 1 (namely P rot , v sin i and R ∗ ) in turn. P rot Most of the stellar rotation periods reported in this pa-per have been estimated from the strength of the chromo-spheric Ca II H & K emission with the exception of a fewthat have been determined photometrically. Rotation pe-riods calculated from analysis of Ca II H & K emissionare, as previously described in detail in section 3.1, im-pacted by variability caused by activity cycles and the tem-poral evolution of magnetic regions. On top of this, how-ever, there may also be line-of-sight geometry effects to con-sider for given starspot or active region distributions. Forinstance, Doppler images of rapidly rotating active stars(e.g. Skelly et al. 2009; Watson et al. 2007; Watson et al.(2006); Cameron & Donati 2002) have revealed the presenceof high-latitude and even polar spots covering a significantfraction of the stellar surface. This is in stark contrast to ourSun where spots are rarely observed at latitudes > ◦ andseldomly cover more that ∼ c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson viewed at low inclinations. This, in turn, would lead to sys-tematically shorter P rot estimates for rapidly-rotating, lowinclination stars and (from equation 1) drive the estimatedsin i to even lower values. Conversely, rapidly rotating starsviewed at high inclinations would, presumably, have sin i estimates systematically biased towards higher values. Un-fortunately, we are largely ignorant of the exact interplaybetween spot numbers, sizes and distributions and the cor-responding Ca II H & K emission which makes the estima-tion of the magnitude of this effect beyond the scope of thispaper. This is further exasperated by our lack of detailedunderstanding of how stellar activity varies as a function ofspectral-type and stellar age (or, equivalently, rotation rate).In addition, the majority of exoplanet host stars are,by selection, relatively inactive and therefore exhibit low CaII H & K emission. For these stars there may be a possiblebias towards measurements of higher R ′ hk values, since itshould be easier to detect their Ca II H & K emission at thepeak of their activity. This would cause the estimated stellarrotation rates to be too fast, skewing our sin i distributionto low values. v sin i ’s The v sin i values quoted in this work come from a variety ofsources and are not from a homogeneous sample. For manyexoplanet discovery papers the value of the rotational broad-ening of the host star is often reported with little discussionas to how this was determined. This is of little surprise, sincethe authors are largely preoccupied with characterising theplanet rather than the parent star. However, it raises thequestion of whether the reported v sin i values are accurateand, in addition, also correct relative to one another.The observed stellar line broadening is a function ofthe intrinsic line-profile width, convolved with the rotation-ally broadened profile and the instrumental profile. Thus,to first approximation the observed line-profile full-width athalf maximum (∆ obs ) is given by∆ obs = q ( α × v sin i ) + ξ + ∆ inst , (9)where α is an arbitrary scaling constant to convert v sin i toa full-width half maximum, ξ in the intrinsic line-profile full-width half maximum, and ∆ inst is the instrumental profile.If the instrumental profile and/or intrinsic line-profile are ig-nored then the derived v sin i will be an overestimate. Thiswould drive the sin i distribution towards high values. Fur-thermore, this systematic bias would be more profound forslow rotators and also for systems seen at low inclinations.If the intrinsic line-profile, ξ , is not properly treated in theestimation of v sin i then, since hotter stars have broaderintrinsic line-profile widths, the problem will also becomeprogressively worse for earlier spectral-type stars. Clearlymany of these potential systematic biases could be allevi-ated if the data were taken from a homogeneous set andanalysed in a consistent manner. R ∗ Most of the stellar radii presented in this work have beencalculated by comparison of theoretical stellar atmospheremodels to observed high-resolution spectra. As outlined by (Brown 2010), this yields small formal errors on the radius(often better than 2 per cent), but is heavily model depen-dent. Brown (2010) compared the results of this techniquewith a group of well calibrated eclipsing binaries, as wellas single stars for which good fundamental parameters wereknown from asteroseismology investigations. While the re-sults of the models compare accurately with the slowly ro-tating, inactive, single stars in the asteroseismic sample, adiscrepancy occurs when applied to the stellar componentsin the eclipsing binary sample. Indeed, for this sample amass-dependent underestimate of the stellar radius by ∼ ∼ M ⊙ ,was found.The explanation for this underestimation is that themore rapidly rotating active stars have their radii inflateddue to blocking of energy transport in the outer convectionregions by star spots. Since spots do not affect the core lu-minosity, the stars response to the appearance of spots isto inflate the stellar radius and/or increase the tempera-ture of the non-spotted regions in the photosphere. Thus,more rapidly rotating stars in our sample are likely to havetheir radii underestimated, leading to a skew to high sin i ’s.Given that most of exoplanet host stars are (by selection)slowly rotating, we don’t expect this to be a dominant sourceof systematic error. There are, however, a few cases wherestars have several radii estimates available in the literaturefrom different sources which differ quite dramatically. Weare unable to offer any reasonable explanation for these dis-crepancies (highlighted in Section 2). In the Markov-chain Monte Carlo analysis performed in Sec-tion 4 we have assumed that the errors on the stellar radius,rotation period and v sin i measurements are Gaussian innature. This assumption, however, may not be true, espe-cially given the range of systematic errors that may existas discussed above. While we could, technically, inject non-Gaussian errors and assume modified probability distribu-tions for each of the parameters in our MCMC analysis, anysuch probability distribution would have to be guessed at.We feel that, given the complexity and interplay arising dueto the systematics discusses above, any such attempt mightbe just as misleading as our assumption of Gaussianity. The transiting planets included in our literature search aresummarised in Table 4 and provide a good test of how ac-curate our method is, since all these systems should havesin i ∼
1. Indeed, 6 out of the 11 transiting systems havesin i ’s > − σ of sin i = 1.The notable exception is OGLE-TR-111, which yields awildly discrepant value of sin i = 4.518, probably due to sys-tematic errors in measuring the stellar parameters due to itsfaintness (see Appendix A for more details). This probablyalso explains why we obtain a relatively low sin i = 0.763for OGLE-TR-113. In addition, the extra-solar planet hoststar HAT-P-1 gives a low sin i = 0.747, but in this case it c (cid:13) , 000–000 stimating the masses of extra-solar planets is actually the member of a binary system and no B − V value is available for the individual host star. We calculateda B − V value using T eff = 5975K from Bakos et al. (2007)and the relationship log T eff = 3.908 - 0.234 ( B − V ) fromNoyes et al. (1984). It is, therefore, probable that the rota-tion period we have calculated from log R ′ HK and our esti-mated ( B − V ) colour is incorrect. Finally, we find a low sin i of 0.754 +0 . − . for the transiting system HD 17156. This in-fers a misalignment angle between the spin-axis of the hoststar and the orbit of the planet of 41 ◦ +13 − . We note that thisis consistent with the misalignment angle of 62 ◦ ± ◦ mea-sured by Narita et al. (2008) from the Rossiter-McLaughlineffect. This, however, has been more recently revised to9.4 ◦ ± ◦ by Cochran et al. (2008). It would be interest-ing to confirm these observations.The remainder of the transiting extra-solar planet hoststars, however, all yield sin i ’s close to 1, with the TrEScandidates providing particularly encouraging results. It iscomforting to find that 8 of the known transiting extra-solarplanets in our sample (excluding OGLE-TR-111b, HAT-P-1b and HD 17156 for the reasons outlined earlier) lie withinthe top 20 transiting candidates as determined from ourMCMC analysis. Furthermore, the technique flagged theknown transiting extra-solar planet OGLE-TR-56b as themost likely to transit. This suggests that the use of MCMCcould be an efficient tool in identifying extra-solar planettransit candidates from spectroscopic analysis of the hoststars.In Table 5 we have listed the top 20 spectroscopicallydiscovered extra-solar planets with the highest transit prob-abilities as determined from the MCMC analysis. Naturallythere is a bias for extra-solar planets with short orbitalperiods to be flagged as more probable transit candidateson account of their close proximity to the host star. Thismeans that any long-period extra-solar planet that has a rel-atively high transit probability is worthy of mention, sincesuch planets are more likely to have been overlooked in tar-geted transit searches. From Table 5, HD117176b is perhapsthe most interesting candidate. With an orbital period of116.689 days it would be of no surprise if transits had beenmissed. For the purposes of this paper, we have adopted the WorkingGroup on Extra-solar Planets definition of a planet to be anobject below the limiting mass for thermonuclear fusion ofdeuterium, currently calculated to be 13 M J . It is comfort-ing, therefore, to find that only 6 extra-solar planet candi-dates in our sample have calculated masses that place themover this deuterium burning limit. These are HD 81040b(17.1 M J ), HD 136118b (14.5 M J ), HD 141937b (17.6 M J ),HD 162020b (147.8 M J ), HD 168443c (18.1 M J ) and HD202206b (17.7 M J ). Of these 6, HD 168443c and HD 202206balready had minimum masses calculated to be > M J .Of the remainder, only HD 162020b has a revised mass thatputs it significantly above the 13 M J cut-off for planetarystatus and, with a calculated true mass of 148 M J , we sug-gest that the companion is most likely an ∼ M4 dwarf. In-cluding the errors on sin i , we find a possible minimum mass(at the 1- σ level) of 67 M J , and thus the possibility of a brown dwarf companion cannot be ruled out. We believethat a companion mass much larger than 148 M J is unlikelysince it would have a clear spectral signature. Interestingly,Udry et al. (2002) use tidal dissipation arguments to con-clude that the companion to HD 162020 is probably a browndwarf, although they could also not rule out a low-mass star,in agreement with our results.Fig. 1 shows a histogram of the cos i values ob-tained from the MCMC analysis for the spectroscopically-discovered systems in our catalogue. This shows a peak athigh inclinations where the systems with naive estimatorsof sin i > i = 1 in the subsequent MCMCanalysis. Given an isotropic distribution of stellar rotationinclination angles, one would expect the cos i distributionto be flat. However, since the amplitude of a planets’ radialvelocity signal decreases with sin i then we would expectplanet detectability to also drop off towards low sin i . Theredoes, however, seem to be a slight excess of low inclinationsystems, with a general decrease in the number of systemspopulating higher inclinations (ignoring the pile-up). We in-terpret this overall shape of the distribution to be due to sys-tematic errors pushing high and moderately inclined starsinto the cos i = 0 ‘spike’. Indeed, one could envisage redis-tributing the cos i ∼ i estimates greater than 1- σ above sin i = 1 isreasonable. Inclusion of more objects with naive estimatesof sin i > i very close to 1 and verysmall sin i uncertainties on account of enforcing our priorknowledge that sin <
1. For these reasons, inclusion of theseobjects would be questionable as it is likely that the errorshave been underestimated in for these objects, or they areaffected by systematics.A summary of our findings are presented in Fig. 2, whichshows both the minimum extra-solar planet masses and‘true’ masses versus properties such as number frequency,orbital semi-major axis, orbital eccentricity and host starmetallicity. In order to make the comparison fair, we onlyplot the minimum extra-solar planet masses for those plan-ets which have been included in the MCMC analysis (i.e.only those systems presented in Table 3).Comparing the results of the minimum and true extra-solar planet masses versus number frequency (top panel,Fig. 2), we still find that lower mass extra-solar planetsare more common, with a tail of high-mass companions.This mass distribution can be roughly characterised by thepower-law dN/dM ∝ M − . (Butler et al. 2006), and doesnot change appreciably once the sin i dependency has beenremoved. This has previously been noted in a purely statis-tical analysis of extra-solar planet masses by Jorissen et al.(2001). It is often cited (e.g. Jorissen et al. 2001) that thenumber of planets with minimum masses above 10 M J isessentially zero – suggesting that planetary formation is adistinct process from that which forms low-mass and sub-stellar (e.g. brown dwarf) objects. When considering theirtrue masses, the planet frequency appears to drop to zeroaround a slightly higher limit of ∼ M J . Interestingly, thiscorresponds to the adopted upper mass-limit for a planetat the planet/brown dwarf boundary. Given the low num-ber of extra-solar planets in this mass range, however, it c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson is difficult to definitively place a higher mass ‘cut-off’ forextra-solar planets.Figs. 2c & d show the extra-solar planet minimummasses and true masses versus orbital eccentricity, respec-tively. It can be seen that when considering just the extra-solar planet minimum masses, there is a dearth of low ec-centricity ( e < .
2) extra-solar planets for minimum massesgreater than ∼ M J , as already noted by several other au-thors (e.g. Butler et al. 2006). When one considers the truemasses, however, we find 6 extra-solar planets with masses inthe range 6 − M J , along with one brown dwarf companion(all indicated by triangular markers), with e ∼ . M J , rejectingobjects above 13 M J . This returns a 55 per cent probabilitythat the eccentricity distribution is not unimodal and may,therefore, be indicative of two different populations ofexoplanets. A larger sample of extra-solar planets in the > M J mass range is needed before any firm conclusionsabout the significance of these HMLE extra-solar planetscan be drawn. A larger sample of high mass extra-solarplanets would also help to establish whether the gap inorbital eccentricities between e = 0.2 – 0.3 for high massextra-solar planets apparent in Fig. 2d is real. If confirmed,however, the presence of these HMLE extra-solar planets,and the gap in orbital eccentricities between e = 0.2 – 0.3,hints at a distinct evolution and/or formation process forthese extra-solar planets.Studies of brown dwarfs and spectroscopic binarieshave shown that they exhibit a similar eccentricity distri-bution to the higher-mass extra-solar planets (extra-solarplanets exhibit a trend of increasing mean orbital eccen-tricity with increasing mass, as mentioned earlier). Thishas led Ribas & Miralda-Escud´e (2007) to suggest that theeccentricity-mass distribution of extra-solar planets mayprovide a signature of different extra-solar planet formationmechanisms. They hypothesize that there are two forma-tion scenarios for extra-solar planets. The first is that thelow-mass population forms by gas accretion onto an ice-rockcore within the circumstellar disk, and initially form in circu-lar orbits and grow their eccentricities by varying amountslater. The second is that the high-mass population formsdirectly from fragmentation of the pre-stellar cloud (in thesame manner as brown dwarfs and binaries) and would ini-tially be located in far larger orbits. The subsequent long-distance migration required to bring them to their currentpositions is then postulated to drive these higher mass extra-solar planets to much larger eccentricities.If Ribas & Miralda-Escud´e (2007) are correct then thismight suggest that the candidates we have identified asHMLE extra-solar planets in Fig. 2 have formed along the same route as the low-mass planets, i.e. through gas ac-cretion onto a rock-ice core rather than via fragmentation.In order to form such massive planets by gas accretion,we might expect the host stars to have higher metallici-ties. Figs. 2g & h show host star metallicity [Fe/H] versus M sin i and true mass, respectively, with the HMLE extra-solar planets indicated by triangles. We note that 5 of theHMLEs are indeed around host stars with high metallicitiesbut the remaining HMLE candidate happens to be aroundone of the most metal poor host stars in our selection. Theanonymous referee has pointed out that the conclusion thatthe HMLEs should have higher metallicities is not the onlypossibility, and that formation in a high-mass disc could sup-ply the right environmental conditions as well. Obviously,the true masses of more extra-solar planets need to be cal-culated before any sound conclusions as to whether theseHMLEs truly constitute a distinct population, and the cluesthey may give us about planetary formation, can be made. Under the assumption that the rotation axes of extra-solarplanet host stars are aligned perpendicularly to the planes ofthe extra-solar planetary orbits, we have used measurementsof R ∗ , v sin i and P rot to remove the sin i dependency from133 spectroscopically-determined extra-solar planet massdeterminations. We find that, bar two problematic cases,the inclination angles of all the known transiting extra-solarplanets in our sample are commensurate with sin i = 1, asexpected. Using a Markov-chain Monte Carlo analysis, wehave also computed the transit probabilities of all 133 extra-solar planets from purely spectroscopic measurements. Wefind that all 8 known transiting extra-solar planets with reli-able parameter determinations lie in the top 20 most proba-ble transiting candidates. This gives us some confidence thatnot only can the technique outlined in this paper be usedto correctly estimate the true masses of extra-solar planets,but also that MCMC can reliably identify extra-solar planettransit candidates from spectroscopic measurements.We find that only 6 out of the 133 extra-solar plan-ets have masses that place them over the standard 13 M J upper limit for planets, which indicates that the vast major-ity of extra-solar planet candidates found by spectroscopicmeans are truly planetary in nature. We also find evidencefor a population of high-mass extra-solar planets with loworbital eccentricities that is not apparent when only extra-solar planet minimum masses are considered. It is possiblethat these extra-solar planets may have formed along a dif-ferent path to the other high-mass extra-solar planets. Thissuggests that, while some high-mass planets may well formthrough fragmentation resulting in high eccentricity orbitsas suggested by Ribas & Miralda-Escud´e (2007), not all highmass planets form in this way.Only by calculating the true masses of more extra-solarplanets can such distributions, and their impact on our un-derstanding of both planet and brown dwarf formation, beproperly studied. With 453 extra-solar planet candidates,there are still over 300 extra-solar planets for which wecould not find the necessary data to determine sin i , or forwhich the data were unreliable and yielded sin i ’s signifi-cantly greater than 1. There are several observational prob- c (cid:13) , 000–000 stimating the masses of extra-solar planets lems to overcome. In order to calculate the rotation periodof the star we generally must rely on measurements of thestrength of the chromospheric Ca ii H & K lines and applythe chromospheric-emission / rotation law of Noyes et al.(1984). The Noyes et al. (1984) relation has obvious draw-backs (i.e. it is not a direct measurement of the stellar rota-tion period), and the Ca ii H & K emission in these stars maybe variable over long-time scales due to, for example, mag-netic activity cycles like the 11-year solar cycle. Thus mea-surements of Ca ii H & K need to be averaged over a suitablylong time-span in order to derive a reliable rotation-period.Whilst we are in the fortunate position that large Ca ii H &K surveys like the Mt. Wilson survey have observed manyextra-solar planet host stars for several decades now, thereare still many host stars where only one brief ‘snapshot’ ofthe chromospheric emission is available from the planet dis-covery paper. We plan to commence the targeted monitoringof chromospheric emission from extra-solar planet host stars,not only to obtain a long-term average of the chromosphericemission from these stars, but also to see if variations in theindicators over the actual rotation period of the star can beidentified. This would give a direct measure of the stellarrotation period.The next observational problem is the determination ofthe projected stellar equatorial velocity, v sin i . Again, thenature of the hunt for extra-solar planets means that thehost stars are almost always observed with high-resolutionechelle spectrographs from which the line-broadening can bemeasured. Due to the low (typically ∼ − ) rotationvelocities of these stars, rotational broadening is no longerthe dominant line-broadening mechanism, and other mech-anisms such as thermal broadening and turbulence need tobe taken into account. Many of the quoted v sin i measure-ments in the literature do not fully account for these effects,which require the use of stellar atmosphere models to esti-mate the true level of broadening due to rotation. We planto systematically analyse the spectra of extra-solar planethost stars to produce accurate v sin i measurements takinginto account other broadening mechanisms.Finally, we note that the inclination of the rota-tion axis of stars can be measured using asteroseismology.Gizon & Solanki (2003) present a technique which deter-mines the stellar axial inclination from observations of low-degree non-radial oscillations which are strong functions of i .They find that the inclination angle can be measured usingthis method to within ∼ ◦ when i > ◦ . One conditionfor this technique to work, however, is that the star musthave a high rotation rate, and this restricts the technique tostars that rotate at least twice as fast as the Sun. Since thehost stars of extra-solar planets are generally slow rotators(selected in order to avoid ‘jitter’ in the radial velocity mea-surements caused by magnetic activity which is enhanced formore rapidly rotating stars), this technique will not be ableto access a substantial portion of these stars. We thereforebelieve that, for the foreseeable future at least, the techniqueoutlined in this paper will remain the main way in which toremove the sin i degeneracy in spectroscopically-determinedextra-solar planet masses. c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 1: Published data on the properties of 154 extra-solar planet hoststars. Columns 1 and 2 give the HD and HIP catalogue number of thehost star, respectively, and column 3 gives any other common name thatthe star may be known as. Published v sin i measurements and the asso-ciated error bar, σ v , are given in columns 4 and 5, respectively. Column6 lists the measured log R ′ HK found from the literature, and columns 7and 8 list any stellar rotation periods and corresponding errors that arequoted. Note that the stellar rotation period may not correspond to thelog R ′ HK on the same line. Actual observed rotation periods are indicatedwith an asterisk next to the measurement. The final two columns give thepublished values and error bars for the stellar radius. References for thevalues are indicated by the numbers in superscript and can be found atthe end of the table. We have also included the radii we have calculatedfor each star from the Barnes-Evans relationship (reference number 93).Where rotation periods do not have an associated reference number, theyhave been calculated using the adjacent P rot value and the Noyes et al.(1984) chromospheric emission – rotation period relationship along with( B − V ) values taken from the NStED database.Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)142........ 522 10.350 ... -4.440 ... 0.940 ... -4.270 ... 0.850 ...5.030 ... -4.340 ...... ... ... ... ... 1.224 ... -4.820 ... 1.010 ...... ... ... ... ... 0.917 ... 0.920 ... 0.870 * ... 0.879 ... 0.866 ... 1.560 ... 1.330 ... 1.000 ... -5.050 ...... ... ... ... ... 1.023 ... -4.890 ... 1.000 ... ... 18.600 ... 0.570 ...... ... ... ... ... 1.078 ... 1.400 υ And 9.620 ... 1.620 ... -4.700 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)10697.... 8159 109 Psc 2.480 ... 1.840 ... -4.990 ... 1.460 ... 2.160 ... 1.280 ... 1.124 ...... ... ... ... ... 1.155 ... 0.770 ... -4.640 ... ... 30.000 ... 0.800 ... 1.520 ... 1.404 ... 1.156 ... 1.154 ... 1.470 ... 1.810 ... -4.770 ... 1.685 ... ... ... ... 1.795 ... -4.500 ... 1.170 ... ... ... ... 1.210 ...... ... ... ... ... 1.202 ... -4.850 ǫ Eri 2.450 * 0.600 0.740 ... 0.895 ...... ... -4.950 ... 1.630 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)27442.... 19921 2.800 ...2.900 ...... ... ... ... ... 4.500 ... -4.900 ... 0.900 ...... ... ... ... ... 0.836 ... -4.990 ... 1.030 ...1.820 ... -4.829 ... -5.600 ... 1.930 ... -4.950 ...... ... ... ... ... 1.533 ... 1.010 ... 0.980 c ... 3.080 π Men 3.140 ...... ... ... ... ... 1.153 ... 1.230 ... -4.660 ... 0.800 ...1.220 ... ... ... ... 1.122 ... 1.390 ... 1.130 ... 1.030 c ... 1.550 ... 1.100 ... 1.149 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)3.880 ... ... ... ... 1.096 ...... ... ... ... ... 1.135 ... 1.290 ... -5.020 ... 1.255 β Gem 1.600 ∗ ... 8.800 .. ... ... ... 8.067 ... -4.530 ... 0.720 ...... ... ... ... ... 0.780 ... 1.270 ... 0.870 ... ... 0.874 ... ... 3.296 * ... 0.839 ...13.600 ... ... ... ... ... ...70642.... 40952 0.300 ... 1.460 c ... -4.490 ... 1.010 ... ... 13.970 ... 0.890 ...3.560 ... ... ... ... 0.900 ...... ... ... ... ... 0.975 ... 1.640 ... 1.300 ... 1.040 ... 0.947 ... 1.040 ... 1.250 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)1.700 ... -4.920 ... 1.125 ... 0.887 ... 1.190 ... -4.850 ... 1.037 ... 1.540 ...... ... ... ... ... 2.113 ... 1.050 ... 2.190 ... -5.120 * ... 1.100 ...... ... ... ... ... 2.140 ...... ... ... ... ... 2.080 ...... ... ... ... ... 2.079 ... 1.150 ... -5.050 ... 0.993 ... ... 1.074 ... -5.020 ... 0.890 ... 1.220 ... -5.020 ... 1.230 ...2.800 ... 1.219 ... 1.220 ... ... ... ... 1.055 ...... ... ... ... ... 0.813 ... 1.230 ... -4.990 ... 0.950 ... 1.470 ... -5.030 ... -4.560 ...... ... ... ... ... 11.000 ...... ... ... ... ... 11.686 ... 1.100 ... 1.093 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)... ... ... ... ... 1.119 ... 1.290 ... ... ... ... 1.160 ... 1.220 ... -4.720 ... 1.350 c ... -5.040 ... 1.280 ... -4.980 ... 0.870 ... ... ... ... 0.899 ... 1.380 c ... 1.870 ... 1.860 ... 1.095 ... 1.250 τ Boo 14.980 ... 1.430 * ... ... ...15.600 ... -4.730 ... 1.220 ... -4.570 ... 1.190 ... -4.850 ... 1.020 ... 0.780 c ... 0.850 ... -4.780 ... 0.833 ... 1.330 ... 1.204 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)136118.. 74948 7.330 ... 1.670 ... 1.738 ... 1.070 ... -4.650 ... 1.056 ... -4.970 ... -5.010 ...... ... ... ... ... 1.088 ... 1.080 ... -4.660 ρ CrB 1.560 ... 1.260 ... 1.340 * ... 1.319 ... 1.380 ... 1.130 < ... -5.070 c ... 0.895 ... 0.970 ...... ... ... 4.700 ... 0.934 ... 1.490 ... ... ... ... 1.610 ... -4.570 ... 0.950 ...2.900 µ Ara 3.120 ... 1.440 ... -5.020 ... ... ... ... 0.707 ... 1.040 ... ... ... ... 0.900 ...... ... ... ... ... 0.948 ... 1.660 ... -5.120 ... 1.560 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)... ... -4.800 ... 1.593 ... 1.150 ... ... ... ... 1.116 ... ... ... ... 1.137 ... 1.810 ... -4.820 ... 1.844 ... 1.480 ... 1.220 ... 3.800 ... 2.990 ... 1.140 ... 1.210 ... 1.330 ... -5.140 ... 1.910 ... 1.170 ... 1.650 ... 1.154 ... 1.230 ... 1.173 ... 0.770 ... -4.537 ... 2.490 ... 1.190 ... 2.350 ...... ... ... ... ... 1.145 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)190647.. 99115 1.000 ... -5.090 ... 1.660 ... 0.790 ... -4.350 ... 0.800 ... 1.500 ... 1.382 ... 1.440 ... -5.040 ... 1.380 ... 1.180 ... 1.122 ... 1.160 ... 1.070 ...... ... ... ... ... 1.079 ... -4.840 ... 1.190 ... ... ... ... 1.020 ...... ... ... ... ... 1.186 ... 1.570 τ Gruis 5.780 ρ Ind 3.130 ... 1.560 ... -5.030 ...... ... ... ... ... 1.456 ... -4.920 ... 1.120 ... -4.840 ...1.040 ... ... ... ... 0.981 ... 1.180 ... 1.138 ... 1.160 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 1 – continued
Alternative v sin i σ v log R ′ HK P rot σ P R ∗ σ R HD HIP Name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)2.000 ... -5.040 ... 1.950 ... ... ... ... 1.804 ... -4.590 ... 1.100 γ Cep 1.500 ... 1.140 ... -5.150 ... 2.030 ... 1.350 ... 1.280 ...... ... ... ... ... 0.922 ... ... 0.850 < ... -4.812 Saffe et al. (2005), Butler et al. (2006), Fischer & Valenti (2005), NStED, Barnes et al. (2001), Coralie, Geneva, Coravel, Nordstr¨om et al. (2004), Moutou et al. (2005), Fracassini et al. (2001), Pizzolato et al. (2003), Wright et al. (2004), Barnes (2007), California & Carnegie Planet Search Team, Valenti & Fischer (2005), Udry et al. (2006), Mayor et al. (2004), Perrier et al. (2003), Fuhrmann et al. (1998), Bernkopf et al. (2001), Fischer et al. (2007), Fischer et al. (2001), Saar & Osten (1997), Reiners & Schmitt (2003), Jones et al. (2006), O’Toole et al. (2007), Johnson et al. (2006), Galland et al. (2005), Acke & Waelkens (2004), Santos et al. (2002), Fischer et al. (2002), Hatzes et al. (2006), de Medeiros & Mayor (1999), Lovis et al. (2006), Lowrance et al.(2005), Messina et al. (2001), Henry et al. (1996), Udry et al. (2003), Naef et al. (2004), Naef et al. (2001), Sozzetti et al. (2006), Bernacca & Perinotto (1970), Korzennik et al. (2000), Lovis et al. (2005), Fuhrmann et al.(1997), Naef et al. (2007), Ge et al. (2006), Melo et al. (2007), Sato et al. (2003), Fischer et al. (2006), Vogt et al.(2002), Udry et al. (2002), Eggenberger et al. (2006), Soderblom (1982), Benz & Mayor (1984), Bakos et al.(2007), Da Silva et al. (2006), Santos et al. (2004), Pepe et al. (2002), Johnson et al. (2007), Johnson et al.(2006), Bouchy et al. (2005), Melo et al. (2006), Masana et al. (2006), Naef et al. (2003), Henry et al. (2002), Santos et al. (2000), Mazeh et al. (2000) Fuhrmann (1998), Lo Curto et al. (2006), Pepe et al. (2004), Alonso et al.(2004), Sozzetti et al. (2004), Narita et al. (2007), Laughlin et al. (2005), Sozzetti et al. (2007), Bakos et al.(2007), Pont et al. (2007), Santos et al. (2006), Queloz et al. (2000), Bouchy et al. (2004), Konacki et al. (2004), Torres et al. (2008), Konacki et al. (2005), Irwin et al. (2008), Henry et al. (2002), Strassmeier et al. (2000), Butler et al. (2003), Butler et al. (2000), Santos et al. (2001), Jenkins et al. (2006), Derived from the Barnes-Evansrelationship of Fouque & Gieren (1997) c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 2: Adopted parameters and sin i estimates for all extra-solar planethost stars with sin i > R ′ HK ’s listed in Table 1, and column 5gives the error bar adopted from the scatter measured for the Ca ii H & Kemission – rotation period relationship of Noyes et al. (1984). Columns6 and 7 give the radii and associated error bar adopted from Table 1.See Section 3 for an in-depth discussion of how the adopted values wereobtained. The final two columns give the resulting sin i value and corre-sponding error bar which have been calculated using equation 1 and aformal error propagation. Sub-giants are indicated with an asterisk.HD or v sin i σ v P rot σ P R ∗ σ R sin i ± Alt. name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9)142* 10.349 0.500 10.524 0.599 1.389 0.018 1.548 0.1172039* 3.250 0.500 25.487 2.34 1.256 0.097 1.302 0.2473651 1.149 0.500 44.000 9.793 0.878 0.008 1.137 0.5558574 4.327 0.386 17.073 0.884 1.383 0.029 1.054 0.1119826 9.482 0.362 11.910 1.18 1.586 0.017 1.406 0.13211506 5.000 0.447 18.300 0.696 1.397 0.046 1.293 0.13211964* 2.700 0.500 50.492 2.553 2.032 0.045 1.325 0.25613445 2.259 0.179 27.240 6.203 0.823 0.003 1.477 0.35619994 8.511 0.408 10.783 1.682 1.698 0.028 1.067 0.17523127 3.299 0.500 32.034 2.285 1.574 0.071 1.326 0.23023596 3.956 0.381 21.251 1.108 1.583 0.048 1.049 0.11927442* 2.873 0.257 89.184 15.674 4.335 0.427 1.167 0.25727894 1.500 1.000 44.449 4.177 0.844 0.031 1.559 1.05128185 2.484 0.461 29.976 2.685 1.062 0.031 1.384 0.28830177 2.959 0.500 45.399 2.896 1.152 0.028 2.303 0.41933283 3.360 0.447 58.678 6.985 1.306 0.049 2.981 0.54433564 12.390 0.937 6.802 0.429 1.503 0.024 1.107 0.11033636 3.080 0.500 16.697 0.966 1.003 0.022 1.012 0.17638529 3.899 0.500 37.761 2.210 2.750 0.079 1.057 0.15250499 4.209 0.500 22.160 1.146 1.428 0.027 1.289 0.16852265 4.775 0.447 15.791 1.191 1.275 0.022 1.168 0.14263454 1.899 1.000 20.251 5.316 0.744 0.024 1.021 0.60168988 2.839 0.500 26.459 0.926 1.182 0.037 1.255 0.22873526 2.620 0.500 35.643 2.433 1.505 0.077 1.225 0.25675289 4.139 0.500 16.839 1.201 1.271 0.016 1.083 0.15275732 2.467 0.447 46.791 3.800 0.953 0.009 2.392 0.47580606 1.431 0.384 42.254 2.62 0.941 0.192 1.268 0.43286081 4.200 0.500 24.838 1.683 1.295 0.079 1.590 0.23888133* 2.185 0.353 49.838 3.263 2.080 0.113 1.033 0.18999109* 1.891 0.447 48.485 3.252 1.081 0.048 1.675 0.41899492 1.379 0.353 46.585 3.923 0.789 0.031 1.609 0.438100777 1.800 1.000 40.084 1.433 1.133 0.061 1.258 0.703102195 3.226 0.069 18.429 10.979 0.835 0.013 1.405 0.838108874 2.220 0.500 40.610 1.401 1.246 0.070 1.429 0.335109749 2.399 0.447 27.091 1.810 1.243 0.075 1.032 0.213111232 2.600 1.000 30.437 2.263 0.899 0.017 1.737 0.681117176 2.827 0.249 35.463 3.4 1.825 0.025 1.085 0.133128311 3.649 0.500 10.778 2.714 0.769 0.011 1.009 0.289130322 1.667 0.447 29.377 19.924 0.824 0.026 1.173 0.856134987 2.169 0.500 33.778 1.649 1.225 0.018 1.181 0.278142022A 2.100 1.000 42.052 2.368 1.085 0.028 1.607 0.772145675 1.560 0.500 48.500 1.137 0.984 0.009 1.519 0.488149143* 3.979 0.447 26.703 2.31 1.487 0.055 1.411 0.198160691 3.662 0.182 32.157 2.172 1.322 0.018 1.758 0.149164922 1.808 0.447 44.192 1.547 0.980 0.013 1.610 0.402 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 2 – continued
HD or v sin i σ v P rot σ P R ∗ σ R sin i ± Alt. name (km s − ) (days) ( R ⊙ )(1) (2) (3) (4) (5) (6) (7) (8) (9)168443 2.100 0.447 38.606 0.675 1.595 0.030 1.004 0.215177830* 2.540 0.500 65.711 6.921 3.129 0.105 1.053 0.237178911B 1.939 0.500 36.250 2.24 1.130 0.183 1.229 0.381185269* 5.679 0.447 21.458 1.382 1.890 0.054 1.273 0.134186427 2.253 0.315 29.343 0.767 1.167 0.009 1.119 0.159187085 5.099 0.500 14.349 1.206 1.331 0.045 1.085 0.145190360 2.320 0.447 35.807 0.621 1.151 0.013 1.425 0.276190647 1.969 0.832 40.977 1.410 1.496 0.061 1.065 0.453192263 2.501 0.447 20.773 12.259 0.775 0.014 1.324 0.817196050 3.235 0.447 23.282 7.293 1.321 0.039 1.126 0.387196885* 7.750 0.500 12.306 0.672 1.387 0.027 1.358 0.117209458 4.280 0.367 14.914 0.629 1.150 0.029 1.096 0.108210277 1.839 0.447 40.141 1.849 1.081 0.012 1.349 0.334212301 6.220 1.000 11.340 0.492 1.172 0.030 1.188 0.200216435* 5.780 0.500 21.299 1.567 1.768 0.031 1.375 0.158216437* 3.004 0.447 26.985 1.857 1.470 0.019 1.088 0.179216770 1.813 1.000 38.656 5.99 0.997 0.027 1.388 0.788217014 2.178 0.367 29.467 0.766 1.159 0.010 1.093 0.187219828 3.450 1.000 28.476 1.439 1.842 0.128 1.053 0.318222582 2.290 0.500 25.032 1.786 1.128 0.030 1.003 0.232224693* 3.799 0.447 29.735 1.487 1.831 0.148 1.218 0.184OGLE-TR-56 3.200 1.000 26.312 2.204 1.234 0.042 1.347 0.438OGLE-TR-111 5.000 1.000 37.964 6.118 0.829 0.020 4.518 1.165 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 3: Adopted parameters and sin i estimates for extra-solar planethost stars for which we have carried out a Markov-chain Monte Carloanalysis. Extra-solar planets with sin i values more than 1- σ greater than1 (see Table 2) were excluded from this analysis. Columns 1–7 are de-scribed in Table 2. For stars with multiple planets, the first row gives thefull planet name, and subsequent planets are indicated in the followingrows by their designated letter only (e.g. ‘c’, ‘d’, etc.). Sub-giants areindicated with an asterisk. Column 8 lists the calculated sin i ’s for eachstar given the adopted v sin i, P rot and R ∗ , and columns 9 & 10 list thetwo-tailed 1- σ error bars on sin i . Column 11 lists the exoplanet mass (inJupiter masses) after applying the sin i correction in column 8. Finally,column 12 gives the transit probability for each extra-solar planet, where1 indicates a 100% probability that the system shows transits.HD or v sin i σ v P rot σ P R ∗ σ R sin i σ − σ + Mass prob.Alt. Name (km s − ) (days) ( R ⊙ ) ( M J )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)1237 5.510 1.000 4.314 3.213 0.901 0.014 0.527 0.365 0.413 6.295 0.0042638 1.100 1.000 38.832 4.626 0.926 0.057 0.905 0.153 0.094 0.530 0.0554203 1.229 0.500 43.015 1.550 1.403 0.075 0.744 0.211 0.213 2.215 0.0024308 0.400 0.447 22.524 2.12 1.029 0.009 0.174 0.172 0.306 0.269 0.0006434 2.149 1.000 17.235 1.620 0.910 0.031 0.811 0.176 0.166 0.591 0.0138574 4.327 0.386 17.073 0.884 1.383 0.029 0.999 0.049 0.000 2.230 0.00910647 5.464 0.447 7.669 1.38 1.101 0.014 0.756 0.155 0.160 1.203 0.00110697 2.479 0.500 34.273 1.181 1.791 0.032 0.941 0.069 0.058 6.502 0.00212661 1.300 0.500 37.253 2.457 1.145 0.025 0.834 0.142 0.151 2.755 0.003c . . . . . . . . . 1.881 0.00116141 1.743 0.447 31.839 1.554 1.453 0.043 0.754 0.187 0.194 0.305 0.00617051 5.599 0.304 7.921 1.626 1.156 0.012 0.756 0.180 0.191 2.565 0.00217156 2.600 0.500 22.138 1.118 1.504 0.056 0.754 0.165 0.177 4.123 0.01119994 8.511 0.408 10.783 1.682 1.698 0.028 0.999 0.066 0.000 2.001 0.00620367 3.290 1.000 5.465 1.497 1.200 0.025 0.293 0.135 0.184 3.650 0.00020782 2.391 0.447 20.462 1.980 1.124 0.021 0.864 0.118 0.118 2.083 0.00222049 1.898 0.257 11.679 6.801 0.721 0.007 0.588 0.295 0.359 2.632 0.00123079 2.990 0.500 17.117 1.182 1.128 0.014 0.895 0.091 0.094 2.914 0.00223596 3.956 0.381 21.251 1.108 1.583 0.048 0.999 0.055 0.000 7.191 0.00327442* 2.873 0.257 89.184 15.674 4.335 0.427 0.999 0.080 0.000 1.280 0.01033564 12.390 0.937 6.802 0.429 1.503 0.024 0.999 0.037 0.000 9.100 0.00833636 3.080 0.500 16.697 0.966 1.003 0.022 0.999 0.094 0.000 9.282 0.00137124 1.219 0.500 27.311 0.650 1.006 0.027 0.645 0.258 0.278 0.946 0.003c . . . . . . . . . 1.059 0.000d . . . . . . . . . 0.930 0.00138529 3.899 0.500 37.761 2.210 2.750 0.079 0.999 0.068 0.000 0.780 0.079c . . . . . . . . . 12.705 0.00239091 3.140 0.500 17.328 1.583 1.161 0.010 0.924 0.067 0.074 11.193 0.00140979 7.429 0.500 7.896 0.948 1.205 0.020 0.964 0.047 0.035 3.443 0.00541004A 1.609 1.000 26.897 6.627 1.016 0.045 0.833 0.136 0.160 2.759 0.00145350 1.370 0.500 39.402 1.921 1.299 0.035 0.818 0.155 0.160 2.187 0.00146375 0.859 0.500 43.876 3.514 1.024 0.027 0.738 0.233 0.223 0.337 0.05849674 0.419 0.500 27.226 1.740 0.974 0.025 0.241 0.239 0.467 0.477 0.00750554 3.675 0.356 14.665 0.474 1.134 0.021 0.939 0.056 0.056 5.217 0.00262509 1.331 0.668 135.000 13.500 8.738 0.098 0.392 0.329 0.523 7.393 0.00469830 0.700 0.353 36.452 1.929 0.892 0.010 0.554 0.311 0.339 0.060 0.015c . . . . . . . . . 0.069 0.006d . . . . . . . . . 0.105 0.00270573 12.300 1.000 3.295 31.226 0.846 0.251 0.991 0.244 0.000 6.155 0.00270642 0.299 0.500 28.829 3.276 1.016 0.013 0.167 0.166 0.520 11.932 0.00072659 2.209 0.500 20.731 0.759 1.458 0.043 0.616 0.177 0.191 4.798 0.00073256 3.260 1.000 13.912 3.897 0.966 0.025 0.921 0.113 0.078 2.029 0.07773526 2.620 0.500 35.643 2.433 1.505 0.077 0.999 0.083 0.000 2.900 0.009c . . . . . . . . . 2.500 0.00574156 4.217 0.389 18.202 0.891 1.627 0.063 0.935 0.061 0.059 2.011 0.016 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 3 – continued
Name or v sin i σ v P rot σ P R ∗ σ R sin i σ − σ + Mass prob.Alt. Name (km s − ) (days) ( R ⊙ ) ( M J )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)c . . . . . . . . . 8.588 0.001d . . . . . . . . . 0.424 0.00475289 4.139 0.500 16.839 1.201 1.271 0.016 0.999 0.063 0.000 0.410 0.14876700 1.350 0.500 36.599 4.721 1.372 0.031 0.709 0.215 0.238 0.277 0.04980606 1.431 0.384 42.254 2.62 0.941 0.192 0.999 0.128 0.000 3.410 0.00881040 2.000 1.000 9.085 2.12 0.887 0.033 0.400 0.290 0.368 17.136 0.00082943 1.420 0.447 21.892 1.912 1.098 0.018 0.566 0.250 0.254 3.090 0.001c . . . . . . . . . 3.550 0.00183443 1.303 0.447 35.999 4.37 1.058 0.024 0.868 0.105 0.127 0.460 0.06988133* 2.185 0.353 49.838 3.263 2.080 0.113 0.999 0.093 0.000 0.220 0.16689307 2.879 0.500 17.155 1.369 1.075 0.024 0.909 0.086 0.084 3.001 0.00189744 9.208 0.447 9.000 6.785 2.126 0.041 0.763 0.191 0.212 10.461 0.00692788 0.567 0.447 33.611 1.702 1.049 0.020 0.375 0.369 0.427 10.276 0.00193083 0.900 1.000 48.549 3.434 0.874 0.026 0.990 0.233 0.009 0.374 0.00495128 2.830 0.231 21.113 0.373 1.220 0.012 0.969 0.033 0.030 2.681 0.002c . . . . . . . . . 0.474 0.002101930 0.699 1.000 46.575 3.485 0.907 0.028 0.710 0.238 0.253 0.422 0.007102117 1.004 0.447 37.555 1.342 1.314 0.026 0.580 0.320 0.298 0.296 0.009104985 2.699 1.100 120.982 29.627 10.273 1.176 0.635 0.256 0.299 9.913 0.010106252 1.778 0.223 20.523 0.812 1.107 0.022 0.647 0.092 0.102 10.517 0.000107148 0.705 0.447 32.451 1.660 1.186 0.034 0.385 0.369 0.371 0.545 0.002108147 5.939 0.447 8.867 1.267 1.220 0.019 0.855 0.117 0.117 0.468 0.032109749 2.399 0.447 27.091 1.810 1.243 0.075 0.999 0.103 0.000 0.280 0.077114386 0.589 0.500 35.568 3.658 0.778 0.021 0.545 0.380 0.375 1.815 0.001114729 2.290 0.500 18.836 0.333 1.439 0.029 0.590 0.161 0.166 1.389 0.000114783 0.869 0.500 45.202 2.447 0.807 0.011 0.968 0.181 0.031 1.022 0.002117176 2.827 0.249 35.463 3.4 1.825 0.025 0.999 0.052 0.000 7.440 0.017117207 1.050 0.500 37.238 1.296 1.128 0.024 0.687 0.260 0.259 2.997 0.001120136 14.735 0.173 4.000 0.400 1.426 0.016 0.777 0.020 0.221 5.015 0.109121504 3.299 1.000 11.397 2.162 1.196 0.045 0.626 0.245 0.282 1.421 0.004125612 2.680 0.447 17.625 0.965 1.030 0.040 0.911 0.091 0.082 3.510 0.002128311 3.649 0.500 10.778 2.714 0.769 0.011 0.999 0.127 0.000 2.180 0.002c . . . . . . . . . 3.210 0.002134987 2.169 0.500 33.778 1.649 1.225 0.018 0.999 0.106 0.000 1.580 0.005136118 7.330 0.500 9.845 1.148 1.744 0.044 0.818 0.125 0.131 14.536 0.001141937 1.923 0.447 15.533 2.300 1.079 0.036 0.550 0.201 0.233 17.636 0.000142415 3.403 0.447 12.344 2.567 1.039 0.022 0.806 0.159 0.158 2.010 0.002143761 1.420 0.300 17.000 7.223 1.328 0.015 0.350 0.232 0.331 2.969 0.001145675 1.560 0.500 48.500 1.137 0.984 0.009 0.999 0.138 0.000 4.640 0.001147506 19.800 1.600 4.045 0.373 1.600 0.117 0.989 0.069 0.010 8.709 0.104147513 1.475 0.353 8.525 2.233 0.947 0.011 0.259 0.099 0.130 3.849 0.000150706 3.650 0.325 9.428 2.195 0.959 0.012 0.691 0.191 0.242 1.446 0.002154857 1.439 0.500 31.520 2.162 2.466 0.101 0.358 0.140 0.157 5.023 0.000159868 2.100 0.500 35.537 2.426 1.888 0.072 0.775 0.165 0.181 2.191 0.001162020 2.235 0.447 1.620 1.27 0.746 0.025 0.093 0.080 0.112 147.849 0.000168443 2.100 0.447 38.606 0.675 1.595 0.030 0.999 0.117 0.000 8.021 0.016c . . . . . . . . . 18.101 0.002168746 0.500 0.408 34.774 1.738 1.132 0.027 0.294 0.287 0.391 0.780 0.004169830 3.724 0.447 9.625 1.810 1.838 0.036 0.384 0.089 0.102 7.497 0.000c . . . . . . . . . 10.517 0.000170469 1.699 0.500 31.518 1.86 1.302 0.042 0.821 0.165 0.152 0.815 0.001175541 2.899 0.500 58.171 1.324 3.800 0.008 0.880 0.109 0.102 0.693 0.006177830* 2.540 0.500 65.711 6.921 3.129 0.105 0.999 0.111 0.000 1.280 0.006178911B 1.939 0.500 36.250 2.24 1.130 0.183 0.999 0.126 0.000 6.294 0.012179949 7.019 0.500 7.700 0.486 1.227 0.020 0.868 0.088 0.097 1.094 0.065183263 1.560 0.500 28.001 1.367 1.236 0.046 0.695 0.222 0.235 5.302 0.001186427 2.253 0.315 29.343 0.767 1.167 0.009 0.999 0.063 0.000 1.680 0.003187085 5.099 0.500 14.349 1.206 1.331 0.045 0.999 0.057 0.000 0.750 0.003 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 3 – continued
Name or v sin i σ v P rot σ P R ∗ σ R sin i σ − σ + Mass prob.Alt. Name (km s − ) (days) ( R ⊙ ) ( M J )(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)187123 2.149 0.500 26.804 1.375 1.185 0.023 0.962 0.098 0.037 0.540 0.095c . . . . . . . . . 2.025 0.001189733 2.730 0.832 13.230 5.338 0.760 0.011 0.938 0.131 0.061 1.226 0.075190228 1.850 0.500 47.970 3.216 2.473 0.083 0.708 0.211 0.221 7.047 0.001190647 1.969 0.832 40.977 1.410 1.496 0.061 0.999 0.180 0.000 1.900 0.002192699 1.899 0.500 59.813 2.888 3.923 0.058 0.574 0.186 0.185 4.351 0.000195019 2.470 0.500 29.074 2.488 1.464 0.035 0.969 0.096 0.030 3.818 0.029196050 3.235 0.447 23.282 7.293 1.321 0.039 0.999 0.120 0.000 3.001 0.002196885* 7.750 0.500 12.306 0.672 1.387 0.027 0.999 0.017 0.000 2.960 0.005202206 2.299 0.500 22.980 3.585 1.064 0.032 0.984 0.125 0.015 17.674 0.004c . . . . . . . . . 2.478 0.001208487 4.610 0.500 12.412 1.134 1.150 0.035 0.983 0.069 0.016 0.457 0.009209458 4.280 0.367 14.914 0.629 1.150 0.029 0.999 0.040 0.000 0.690 0.186210702 1.699 0.500 69.061 5.140 4.449 0.069 0.527 0.216 0.215 3.793 0.000212301 6.220 1.000 11.340 0.492 1.172 0.030 0.999 0.067 0.000 0.450 0.182213240 3.969 0.609 17.022 4.748 1.536 0.036 0.867 0.110 0.122 5.185 0.002216437* 3.004 0.447 26.985 1.857 1.470 0.019 0.999 0.077 0.000 2.100 0.002217014 2.178 0.367 29.467 0.766 1.159 0.010 0.999 0.081 0.000 0.468 0.106219828 3.450 1.000 28.476 1.439 1.842 0.128 0.999 0.145 0.000 0.066 0.110221287 5.607 0.832 4.586 0.424 1.126 0.033 0.452 0.085 0.090 6.830 0.000222404 1.500 1.000 68.020 4.626 4.511 0.527 0.454 0.394 0.411 3.522 0.001222582 2.290 0.500 25.032 1.786 1.128 0.030 0.996 0.119 0.003 5.129 0.003231701 4.000 0.500 10.276 0.383 1.372 0.131 0.594 0.112 0.124 2.995 0.000330075 0.699 0.200 47.365 3.209 1.008 0.062 0.649 0.231 0.250 1.171 0.028TrES-1 1.195 0.169 33.528 5.968 0.824 0.015 0.970 0.091 0.029 0.629 0.081TrES-2 2.000 1.000 24.783 1.622 1.000 0.035 0.986 0.188 0.013 1.214 0.081HAT-P-1 2.200 0.200 19.711 1.44 1.149 0.100 0.747 0.123 0.141 0.701 0.014OGLE-TR-10 3.000 2.000 15.836 1.925 1.143 0.042 0.809 0.154 0.178 0.778 0.068OGLE-TR-56 3.200 1.000 26.312 2.204 1.234 0.042 0.999 0.136 0.000 1.290 0.218OGLE-TR-113 9.000 3.000 3.244 0.748 0.765 0.025 0.763 0.191 0.201 1.730 0.082 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 4.
Summary of known transiting planets. All the listedsin i ’s are from the Markov-chain Monte Carlo analysis, exceptOGLE-TR-111b which was not included in the MCMC analysison account of its discrepant sin i value. The two-tailed 1- σ errorbars on sin i , σ − and σ + are also listed. The final column indicatesthe transit probability as calculated from the MCMC analysis,where available.Name sin i σ − σ + Trans. prob.HAT-P-1b 0.747 0.123 0.141 0.014HAT-P-2b 0.989 0.069 0.010 0.104HD17156 0.754 0.165 0.177 0.011HD189733b 0.933 0.131 0.061 0.075HD209458b 0.999 0.040 0.000 0.186OGLE-TR-10b 0.809 0.154 0.178 0.068OGLE-TR-56b 0.999 0.134 0.000 0.219OGLE-TR-111b 4.518 1.165 1.165 ...OGLE-TR-113b 0.763 0.191 0.201 0.082TrES-1b 0.970 0.091 0.029 0.081TrES-2b 0.986 0.188 0.013 0.081
Table 5.
The 20 most probable transiting extra-solar planetsas determined from spectroscopic data and the MCMC analysis.Only spectroscopically-discovered planets are included in this ta-ble. Column 1 gives the common name for the extra-solar planet,column 2 the extra-solar planet’s orbital period in days, and col-umn 3 the transit probability as determined from the MCMCanalysisName P orb (days) Trans. prob.HD 212301b 2.457 0.182HD 88133b 3.41 0.166HD 75289b 3.51 0.148HD 219828b 3.8335 0.110 τ Boo-b 3.3135 0.10951 Peg 4.23077 0.106HD 187123b 3.097 0.095HD 38529b 14.309 0.079CS Pyx-b 2.54858 0.077HD 109749b 5.24 0.077HD 83443b 2.985625 0.069HD 179949b 3.0925 0.065HD 46375b 3.024 0.058HD 2638b 3.4442 0.055HD 76700b 3.971 0.049HD 108147b 10.901 0.032HD 195019 18.20163 0.029HD 330075b 3.369 0.028HD 117176 116.689 0.017HD 74156 51.65 0.016
ACKNOWLEDGMENTS
Much of this work was carried out while CAW was sup-ported by a PPARC/STFC Postdoctoral Fellowship. SPLacknowledges the support of an RCUK fellowship. The au-thors would also like to thank the anonymous referee whosedetailed and valuable comments helped substantially im-prove the quality of this paper.
Figure 1.
A logarithmic histogram of the cos i values for thespectroscopically-discovered extra-solar planet systems in oursample. APPENDIX A: NOTES ON SPECIFIC SYSTEMSWITH SIN I GREATER THAN 1
From Tables 2 and 3 we can see that out of a total of 154extra-solar planet hosts with sufficient data, 119 (77 percent) yield sin i < σ of sin i = 1. In thisSection we discuss why some systems have calculated sin i ’ssignificantly (i.e. more than 1- σ ) greater than 1. Sub-giants
Of the 35 extra-solar planet host stars with sin i signifi-cantly greater than 1, ten are classified as sub-giants. Sincethe Noyes et al. (1984) chromospheric index – rotation raterelationship is calibrated for main-sequence stars only, webelieve that the rotation periods of these stars determinedfrom R ′ HK measurements may be incorrect. We have indi-cated the sub-giants with asterisks in Table 2. Other systemswhere we can highlight potential problems which may resultin values of sin i > In addition to being classified as a sub-giant, the ( B − V )colour of this star may be contaminated by a nearby com-panion as reported by the NStED database. HD 11506
We note that Fischer et al. (2007) quote the stellar rota-tion period determined from the log R ′ HK measurements is12.6 days. We, however, derive a longer rotation period of18.3 days using the log R ′ HK value reported by Fischer et al.(2007) and the relationship from Noyes et al. (1984). Wetherefore believe the rotation period quoted by Fischer et al.(2007) has been calculated incorrectly. HD 13445
There seems to be some confusion over the v sin i value forthis star. Fischer & Valenti (2005) quote 2.37 km s − , whileSaar & Osten (1997) place an upper limit of 0.7 km s − .Assuming a v sin i of 2.37 km s − results in a large sin i ∼ c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Figure 2.
Top panel: a histogram of the number of extra-solar planets with a) observed minimum masses M sin i and (b) their calculatedtrue masses, M (both in units of Jupiter masses, M J ). The solid line indicates a mass distribution characterised by the power-law dN/dM ∝ M − . . Figures c) and d) plot the orbital eccentricity versus the minimum extra-solar planet mass and their calculated truemasses, respectively. A number of relatively high mass, low eccentricity ( e < .
25) planets discussed in Section 7 have been indicatedusing triangular markers. Figures 2e and f are the same as c) and d), but against extra-solar planet semi-major axis. Finally, figures g)and h) plot the host star metallicity [Fe/H] versus M sin i and true mass. The horizontal dashed line represents solar metallicity.c (cid:13) , 000–000 stimating the masses of extra-solar planets − gives sin i ∼ v sin i for this star we have deemedthis measurement to be suspect. HD 27442
There is considerable doubt over the radius of this star, withestimates ranging from 3.48–6.60 R ⊙ . Furthermore, this staris classified as a sub-giant, hence the rotation period derivedfrom the log R ′ HK measurements is also likely to be inaccu-rate. HD 27894
This has an uncertain v sin i , with only an upper limit of 1.5km s − from Moutou et al. (2005). HD 28185
This has an uncertain v sin i , with estimates ranging from1.82 – 3.00 km s − . While v sin i = 1.82 km s − gives sin i =1, we feel there is too much uncertainty in the v sin i values,and hence have taken a weighted mean, placing HD 28185in the sin i significantly greater than 1 category. HD 75732
The calculated rotational period of the star from log R ′ HK measurements (42–47 days) is possibly related to the orbitof one of its planets, 55 Cnc c, which has a measured orbitalperiod of 43.93 days (see Marcy et al. 2002). HD 86081
We note that Johnson et al. (2006) derived a stellar rotationperiod of 40.1 days from their measured log R ′ HK using thecalibration of Noyes et al. (1984). Employing the same B − V colour and log R ′ HK quoted by Johnson et al. (2006) wedetermine a far shorter rotation period of 27.7 days via thesame relationship, and 24.83 days if we take the value of B − V = 0.641 from the NStED database. We thereforeconclude that the rotation period derived by Johnson et al.(2006) is incorrect but, despite the shorter rotation periodwe have calculated, we still determine sin i = 1.590. HD 145675
While Fischer & Valenti (2005) quote a v sin i = 1.56 kms − , Naef et al. (2004) quote an upper limit of v sin i < − . This upper limit would yield sin i < v sin i we have decided to place thisobject in the sin i significantly greater than 1 category. HD 216435
Jones et al. (2003) have noted a discrepancy between theassigned spectral-type of HD 216435 in the literature, whichis either quoted as G0V or G3IV. They find that HD 216435lies 1 magnitude above the main sequence, and hence thisstar is most likely a sub-giant. The rotation period deter-mined from log R ′ HK is therefore suspect. OGLE-TR-111
While the OGLE extra-solar planets are all transiting sys-tems, published data for OGLE-TR-111 yields a sin i =4 . ± .
486 and is one of the most discrepant systems foundin this work. We believe that this is undoubtedly due to thefaintness of the OGLE targets (all OGLE extra-solar planethosts have
I >
14 whereas most extra-solar planet hosts typ-ically have V − band magnitudes around 8 – 9), which meansthat accurate spectroscopic follow-up is difficult. In addition,none of these systems have a long baseline of R ′ HK measure-ments, which means that the rotation periods are also notwell known. For these reasons, we believe that systematicerrors in one or more of the measurements have contributedto the highly discrepant sin i obtained for OGLR-TR-111. Summary
In total, we can find plausible reasons explaining why 18of the extra-solar planet host stars yield sin i ’s significantlygreater than 1. This still leaves 17 systems for which noexplanation can be given for their high sin i values. APPENDIX B: NOTES ON SPECIFIC SYSTEMSWITH SIN I LESS THAN 1
In this Section we highlight any published data on stars thatappears incorrect, and justify any decisions that have beenmade regarding the rejection of any published parametersfrom our analysis. Any other special cases that apply arealso indicated here, such as the use of actual observed stel-lar rotation rates from photometry instead of rotation ratesderived from log R ′ HK measurements, for example. HD 1237
The value of P rot = 12.6 days quoted on the GenevaObservatory web-page and apparently derived from theNoyes et al. (1984) relationship appears to be wrong. Usingthe Geneva Observatory’s values of log R ′ HK = -4.27 and B − V = 0.749, we derive P rot = 4.01 days. We note thatBarnes (2001) use the same B − V value, but a weaker chro-mospheric activity index of log R ′ HK = -4.44 and derivea rotation period of 10.4 days. Using the values of Barnes(2001), we also derive 10.4 days, and thus conclude that theGeneva P rot is quoted incorrectly. HD 6434
The Extrasolar Planets Encyclopedia quote the radius ofHD 6434 as 0.57 R ⊙ (from Fracassini et al. 2001) and itsspectral type as G3 IV. The NStED database quotes thespectral type as G2–3 V. Given the spectral type, we findit highly unlikely that the radius is actually 0.57 R ⊙ , andinstead use the value of 1.0 R ⊙ from the NStED database. HD 16141
The Extrasolar Planets Encyclopedia quotes a radius for HD16141 of 1 R ⊙ but provides no reference for this figure. Giventhis, and that the radius is discrepant from other estimates c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson obtained from the literature (1.4 and 1.52 R ⊙ ), we haverejected this radius estimate from Table 1. HD 142022A
Eggenberger et al. (2006) determined an upper limit of 48days to the rotation period of HD 142022A by combiningtheir measured v sin i with the radius of the star estimatedfrom evolutionary models. Despite measuring log R ′ HK , theydid not calculate the rotation period using the Noyes et al.(1984) relationship. Using Eggenberger et al. (2006)’s valuesfor log R ′ HK = -4.97 and B − V = 0.790 we determine arotation period of 39 days. HD 170469
Fischer et al. (2007) quote a log R ′ HK = -5.06 and determinethe rotation period to be 13 days. Using the same value oflog R ′ HK , we determine the rotation period to be 30 days.Our period agrees closely with that of Wright et al. (2004),who find a rotation period of 31 days from a very similarmeasurement of log R ′ HK = -5.09. We therefore assume thatFischer et al. (2007) have calculated the rotation period in-correctly. HD 217014
The rotation period of 21.9 days has been used since thisis a measured rotation period from variability in the lightcurve, rather than one estimated from log R ′ HK . c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 6: Compilation of chromospheric indices (log R ′ HK ) for the starsin Table 1. The spectral type of the host star is given in column 2.Entries in bold give the grade assigned to each star (P = Poor, O =O.K., G = Good, and E = Excellent) followed by the weighted meanof the log R ′ HK measurements and adopted error bar (see section 3.1 fordetails). Reference numbers are identical to those used in Table 1.Name Type log R’ HK Observations Ref.HD 142 F7 -5.020 average of 2 individual points 1-4.950 individual on 2001 Aug 04 92 (P) Adopted value: -4.997 ± HD 1237 G6 -4.440 1992 individual 5-4.270 61 obs in 2 years 6-4.340 average of above + extra individual 1 (G) Adopted value: -4.273 ± HD 2039 G2/3 -4.980 average of 2 individuals 1-4.890 individual on 2001 Aug 04 92 (P) Adopted value: -4.950 ± HD 2638 K1 -4.820 28 HARPS spectra over 434 days, Oct 2003 –Jan 2005 10 (O) Adopted value: -4.820 ± HD 3651 K0 -5.020 34 obs in 18 month bins. Report σ = 2.56% 13-4.991 1966 – 1991. Shows quite large variation over cycle,estimate peak variation of log R ′ hk -5.06 – -4.83 fromFig. 1f of Baliunas et al. (1995) 14 (E) Adopted value: -4.994 ± HD 4203 G5 -5.180 19 obs in 10 month bins. Report σ = 1.84% 13-5.130 14 obs from JD 2450757.1224 – 2451187.9624 (431 days) 52 (G) Adopted value: -5.159 ± HD 4308 G5 -4.930 41 HARPS spectra from JD 2452899.77052 –2453579.83685 (680 days) 17-5.050 1 obs on UT 11/12/1993 38 (G) Adopted value: -4.933 ± HD 6434 G2/3 -4.890 individual 5 (P) Adopted value: -4.890 ± HD 8574 F8 -5.070 11 obs in 8 month bins. Report σ = 0.81% 13 (P) Adopted value: -5.070 ± HD 9826 G0 -5.040 48 obs in 6 month bins 13-4.927 obs in 1991 & from mid-1996 – 1999 (seeFig. 2 of Henry et al. 2000). Shows variable activity level.Report σ s = 4.7% 87 (G) Adopted value: -4.950 ± HD 10647 F8 -4.680 individual? 6-4.700 individual on 2001 Aug 04 92 (P) Adopted value: -4.690 ± HD 10697 G5 -5.080 57 obs in 25 month bins. Report σ = 2.53% 13 (G) Adopted value: -5.080 ± HD 11506 G0 -4.990 19 Keck spectra from JD 2453014.73505 –2454286.11838 (1271 days) 22 (G) Adopted value: -4.990 ± HD 11964 G8 -5.160 33 obs in 21 month bins. Report σ = 1.66% 13 (O) Adopted value: -5.160 ± HD 12661 K0 -5.120 individual? 5-5.080 52 obs in 16 month bins. Report σ = 1.44% 13 (O) Adopted value: -5.082 ± HD 13445 K1 -4.740 individual 5-4.640 individual on 2001 Aug 04 92 (P) Adopted value: -4.690 ± HD 16141 G8 -5.050 individual? 5-5.110 70 obs in 23 month bins. Report σ = 1.44% 13 (O) Adopted value: -5.109 ± c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 6 – continued
Name Type log R ′ HK Observations Ref.HD 17051 G0 -4.650 individual 5-4.590 individual on 2001 Aug 04 92 (P) Adopted value: -4.620 ± HD 17156 G5 -5.040 25 Keck spectra from JD 2453746.75596 –2454138.76720 (392 days) 22 (O) Adopted value: -5.040 ± HD 19994 G0 -4.880 12 obs in 4 month bins. Report σ = 0.69% 13-4.770 individual? 18 (P) Adopted value: -4.872 ± HD 20367 G0 -4.500 2 obs in 1 month. Report σ = 0.53% 13 (P) Adopted value: -4.500 ± HD 20782 G3 -4.910 1 obs on 12/12/1992 26-4.850 individual on 2001 Aug 04 92 (P) Adopted value: -4.880 ± HD 22049 K2 -4.455 1967 – 1991. Shows moderate variation but nowell defined cycle. Estimate peak variation of log R ′ hk -4.52 – -4.36 from Fig. 1g of Baliunas et al. (1995) butvery well averaged 14-4.510 13 obs in 4 month bins 13-4.470 5 obs on 10 & 13/12/1992, and 30/06–02/07/1993 38-4.430 average of 2 obs on 2002 Jul 02 & 2004 Aug 23/24 92 (E) Adopted value: -4.457 ± HD 23079 F8/G0 -4.940 1 obs on UT 11/12/1992 38-5.040 average of the above + 2 more individuals 1-4.950 individual on 2001 Aug 04 92 (P) Adopted value: -5.018 ± HD 23127 G2 -5.000 1 obs on UT 04/08/2001 27-5.000 individual on 2001 Aug 04 92 (P) Adopted value: -5.000 ± HD 23596 F8 -5.060 individual 13 (P) Adopted value: -5.060 ± HD 27442 K1/2 -5.570 individual 1-5.350 individual on 2001 Aug 04 92 (P) Adopted value: -5.460 ± HD 27894 K2 -4.900 20 HARPS spectra over 437 days from Oct 2003– Jan 2005 10 (O) Adopted value: -4.900 ± HD 28185 G5/6 -4.828 individual in 1998 or 1999 88-4.820 individual 91-4.990 average of 2 individuals 1 (P) Adopted value: -4.907 ± HD 30177 G8 -5.120 average of 2 individuals 1-5.080 individual on 2001 Aug 04 92 (P) Adopted value: -5.107 ± HD 33283 G3 -5.600 25 Keck spectra from JD 2453014.852 –2453752.878 (738 days) 28 (G) Adopted value: -5.600 ± HD 33564 F7 -4.950 individual? 29 (P) Adopted value: -4.950 ± HD 33636 G1/2 -4.850 25 obs in 13 month bins. Report σ = 2.32% 13-4.810 21 Keck spectra from JD 2450838.7594 –2452188.1390 (1349 days) 52 (G) Adopted value: -4.832 ± HD 37124 G0 -4.900 38 obs in 17 month bins. Report σ = 2.48% 13-4.880 30 obs from JD 2450420.0466 –2452334.7856 (1915 days) c (E) Adopted value: -4.891 ± HD 38529 G8 -4.960 49 obs in 19 month bins. Report σ = 6.92% 13-4.890 individual? 5 c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 6 – continued
Name Type log R ′ HK Observations Ref. (O) Adopted value: -4.959 ± HD 39091 G1 -4.970 1 obs on UT 11/12/1992 38-4.900 average of above + extra individual 1 (P) Adopted value: -4.900 ± HD 40979 F8 -4.630 25 obs in 8 month bins. Report σ = 2.52% 13 (O) Adopted value: -4.630 ± HD 41004A K1 -4.660 1 obs on UT 14/12/1992 31 (P) Adopted value: -4.660 ± HD 45350 G5 -5.100 19 obs in 10 month bins. Report σ = 1.32% 13 (O) Adopted value: -5.100 ± HD 46375 K0 -4.960 69 obs in 14 month bins. Report σ = 1.97% 13 (O) Adopted value: -4.960 ± HD 49674 G0 -4.800 37 obs in 9 month bins. Report σ = 4.61% 13-4.800 24 obs from JD 2450883.0580 –2451334.8197 (452 days) c (G) Adopted value: -4.800 ± HD 50499 G0/2 -5.020 25 obs in 17 month bins. Report σ = 1.67% 13-5.060 1 obs on UT 12/12/1992 38 (O) Adopted value: -5.022 ± HD 50554 F8 -4.950 20 obs in 7 month bins. Report σ = 1.49% 13-4.940 average of 26 obs from JD 2460831.805 –2462294.897 (1463 days) 32 (G) Adopted value: -4.944 ± HD 52265 G0 -4.910 individual? 6-5.020 26 obs in 12 month bins. Report σ = 1.87% 13-4.990 17 Keck spectra from JD 2450838.8806 –2451585.9235 (747 days) 90 (G) Adopted value: -5.006 ± HD 63454 K4 -4.530 57 HARPS and Coralie spectra between Feb 2004 –Jan 2005 10 (O) Adopted value: -4.530 ± HD 68988 G0 -5.040 24 obs in 11 month bins. Report σ = 2.46% 13-5.070 13 Keck spectra from JD 2450552.0229 –2451064.7680 (513 days) 52 (G) Adopted value: -5.051 ± HD 69830 K0 -4.950 individual 13-4.970 74 HARPS spectra from JD 2452939.87402 –2453765.66138 (826 days) 35 (G) Adopted value: -4.970 ± HD 70642 G8/K1 -4.900 individual 1-4.950 average of 2 obs on 2003 Apr 21 & 2004 Aug 23/24 92 (P) Adopted value: -4.933 ± HD 72659 G2 -5.020 17 obs in 10 month bins. Report σ = 2.05% 13-5.000 12 obs from JD 2450838.8934 –2452362.9627 (1524 days) c (G) Adopted value: -5.012 ± HD 73256 G8/K0 -4.490 1 obs on UT 12/12/1992 38 (P) Adopted value: -4.490 ± HD 73526 G6 -5.000 individual 1-5.050 individual on 2005 Jun 16 92 (P) Adopted value: -5.025 ± HD 74156 G1 -5.080 9 obs in 6 month bins. Report σ = 1.97% 13 (O) Adopted value: -5.080 ± HD 75289 G0 -5.000 individual 5 (P) Adopted value: -5.000 ± HD 75732 K0 -5.040 384 obs in 37 month bins. Fig. 2 of Henry et al.(2000) shows obs taken in 1984 and 1993 – 1999. Activitycycle has quite large amplitude, reasonably sampled.Report σ s = 6.4% 5 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 6 – continued
Name Type log R ′ HK Observations Ref.-4.949 21 obs in 8 month bins. Report σ = 3.11% 13 (E) Adopted value: -5.035 ± HD 76700 G6 -4.940 individual 1-5.140 average of 3 obs, 2 on 2003 Apr 21 and 1 on2005 Jun 16 which vary from log R ′ HK = -5.02 – -5.22 92 (P) Adopted value: -5.090 ± HD 80606 G5 -5.090 22 obs in 10 month bins. Report σ = 1.41% 13 (O) Adopted value: -5.090 ± HD 81040 G0 -4.480 4 obs from JD 2451291.36542 –2451545.63921 (254 days) 42 (O) Adopted value: -4.480 ± HD 82943 G2/3 -4.950 individual? 5-4.920 17 obs in 8 month bins. Report σ = 6.32% 13-4.820 individual? 18 (P) Adopted value: -4.916 ± HD 83443 K0/1 -4.840 37 obs in 8 month bins. Report σ = 2.62% 13-4.850 uncertain, individual? 18 (O) Adopted value: -4.840 ± HD 86081 G1 -5.030 26 Keck spectra from JD 2453694.156 –2453781.064 (87 days) 28 (P) Adopted value: -5.030 ± HD 88133 G5 -5.160 individual 1 (P) Adopted value: -5.160 ± HD 89307 G0 -4.950 2 obs in 2 month bins 13 (P) Adopted value: -4.950 ± HD 89744 F8 -4.940 12 obs in 3 month bins 13-5.120 1966 – 1991. Very flat / no cycle fromFig. 1b of Baliunas et al. (1995)Report σ = 1.20% 14 (E) Adopted value: -5.113 ± HD 92788 G6 -5.040 individual? 5-5.050 26 obs in 11 month bins. Report σ = 2.90% 13-4.730 individual? 18 (O) Adopted value: -5.038 ± HD 93083 K3 -5.020 16 obs from JD 2453017.84496 –2453400.79648 (383 days). Report error of ± .
02 on log R ′ hk (O) Adopted value: -5.020 ± HD 95128 G0 -5.041 obs in 1985, 1991, 1993 – 1999 (see Fig. 2of Henry et al. 2000). Flat. Report σ s = 2.80% 5-5.020 29 obs in 1 month bin. Report σ = 1.18% 13 (E) Adopted value: -5.039 ± HD 99109 G8/K0 -5.060 31 obs in 14 month bins. Report σ = 6.27% 13 (O) Adopted value: -5.060 ± HD 99492 K2/4 -4.940 2 individuals + 28 obs in 20 month bins 1 (O) Adopted value: -4.940 ± HD 100777 G8 -5.030 29 HARPS spectra from JD 2453063.7383 –2453920.5110 (857 days) 47 (G) Adopted value: -5.030 ± HD 101930 K1 -4.990 16 obs from JD 2453038.78552 –2453400.81929 (362 days). Report error of ± .
02 on log R ′ hk (O) Adopted value: -4.990 ± HD 102117 G6 -5.030 13 obs from JD 2453017.85639 –2453400.83082 (383 days). Report error of ± .
02 on log R ′ hk (O) Adopted value: -5.030 ± HD 102195 K0 -4.560 19 HARPS spectra from JD 2453501.574413 – c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 6 – continued
Name Type log R ′ HK Observations Ref.2453936.476701 (435 days) 49-4.450 1 FOCES spectrum, 2006 Jan 14 48-4.300 individual in 1998 or 1999 88 (G) Adopted value: -4.542 ± HD 104985 K0 -5.580 1 obs in 1 month bin 1 (P) Adopted value: -5.950 ± HD 106252 G0 -4.970 individual 13-4.970 15 obs from JD 2460831.984 –2462295.022 (1463 days) 32 (G) Adopted value: -4.970 ± HD 107148 G5 -5.030 24 obs in 12 month bins. Report σ = 2.61% 13 (O) Adopted value: -5.030 ± HD 108147 F8/G0 -4.780 individual 5-4.720 individual? 60 (P) Adopted value: -4.750 ± HD 108874 G5 -5.080 34 obs in 15 month bins. Report σ = 1.81% 13-5.070 20 obs from JD 2450340.8062 –2451446.8056 (1106 days) c (G) Adopted value: -5.076 ± HD 109749 G3 -5.040 individual? 52 (P) Adopted value: -5.040 ± HD 111232 G8 -4.980 individual on UT 30/06/1993 38 (P) Adopted value: -4.980 ± HD 114386 K3 -4.740 2 individuals + 37 obs over 3 years 1 (G) Adopted value: -4.740 ± HD 114729 G0 -5.050 44 obs in 21 month bins. Report σ = 1.55% 13-5.040 1 obs on UT 30/06/1993 38-5.020 38 obs from JD JD 2450463.1474 –2452487.7399 (2025 days) c (E) Adopted value: -5.036 ± HD 114783 K1 -4.960 37 obs from JD 2450983.7917 –2452127.7826 (1144 days) 52 (G) Adopted value: -4.960 ± HD 117176 G0 -5.115 obs in 1981, 1991 – 1999 (see Fig. 2of Henry et al. 2000). Well sampled & flat.Report σ = 4.60% 5-4.990 6 obs in 1 month bin 13 (E) Adopted value: -5.103 ± HD 117207 G8 -5.060 33 obs in 22 month bins. Report σ = 1.77% 13-5.000 1 obs on UT 30/06/1993 38 (G) Adopted value: -5.058 ± HD 120136 F5 -4.700 5 obs in 2 month bins 13-4.733 obs in 1981, 1991 – 1999. Well sampled,fairly flat. Report σ = 4.20% 87-4.775 1967 – 1991. Slight evidence of activity cycle.Estimate peak variation of log R ′ hk -4.696 – -4.855 fromFig. 1b of Baliunas et al. (1995) but very well averaged ? (E) Adopted value: -4.762 ± HD 121504 G2 -4.730 individual 5-4.570 individual? 18 (P) Adopted value: -4.650 ± HD 125612 G3 -4.850 18 Keck spectra from JD 2453190.83262 –2454251.82778 (1061 days) 22 (G) Adopted value: -4.850 ± HD 128311 K3 -4.347 individual 14-4.390 30 obs from JD 2450983.8269 –2452488.7709 (1505 days) c (G) Adopted value: -4.389 ± HD 130322 K0 -4.390 individual? 5 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 6 – continued
Name Type log R ′ HK Observations Ref.-4.780 11 obs in 9 month bins. Report σ = 6.47% 13 (O) Adopted value: -4.748 ± HD 134987 G5 -5.010 individual? 5-5.090 53 obs in 20 month bins. Report σ = 1.89% 13-5.040 individual on 2002 Jul 20 92 (O) Adopted value: -5.088 ± HD 136118 F7 -4.970 individual 13-4.880 33 obs from JD 2460832.069 –2462157.646 (1326 days) 32 (G) Adopted value: -4.883 ± HD 141937 G2/3 -4.940 7 obs in 3 month bins. Report σ = 1.26% 13-4.650 16 obs, dates not known 53 (P) Adopted value: -4.738 ± HD 142022A G9 -4.970 6 HARPS spectra from approximately JD 2453220 –2453520 ( ∼
300 days, from their Fig. 4) 54-5.010 individual on 2005 Jun 16 92 (O) Adopted value: -4.976 ± HD 142415 G1 -4.550 individual? between Aug 1998 and Mar 2000 18-4.660 1 obs on UT 28/06/1993 38-4.625 average of 2 obs (log R ′ HK = -4.66 & -4.59)on 2002 Jul 20 & 2004 Aug 23/24 92 (P) Adopted value: -4.615 ± HD 143761 G0 -5.048 obs from 1965 – 2000 (see Fig. 2of Henry et al. 2000). Well sampled and fairly flat.Report σ = 1.40% 5-5.080 10 obs in 1 month bin. Report σ = 1.32% 13-5.039 1966 – 1991.5. Fairly flat with possiblelong downwards trend but not strong fromFig. 1b of Baliunas et al. (1995). Report σ s = 1.00% 14 (E) Adopted value: -5.045 ± HD 145675 K0 -5.060 46 obs in 27 month bins. Report σ = 4.63% 13-5.070 35 obs from JD 2450605.9115 –2452486.7329 (1881 days) c (E) Adopted value: -5.064 ± HD 147506 F8 -4.720 13 Keck spectra from JD 2453981.7775 –2454220.9934 (239 days). Report error of ± .
05 on log R ′ hk (O) Adopted value: -4.720 ± HD 147513 G3/5 -4.520 1 obs on UT 29/06/1993 38 (P) Adopted value: -4.520 ± HD 149143 G3 -4.970 individual? 51 (P) Adopted value: -4.970 ± HD 150706 G0 -4.570 5 obs in 3 month bins. Report σ = 3.61% 13 (P) Adopted value: -4.570 ± HD 154857 G5 -5.000 3 obs on UT 20/07/2002, 23/08/2004 and24/08/2004 27-5.140 1 obs on UT 27/06/1993 38-4.995 average of 2 obs (log R ′ HK = -5.05 & -4.94)on 2002 Jul 20 & 2004 Aug 23/24 92 (P) Adopted value: -5.022 ± HD 159868 G5 -4.960 1 obs on UT 20/07/2002 27-5.090 1 obs on UT 27/06/1993 38 (P) Adopted value: -5.025 ± HD 160691 G3 -5.034 275 HARPS spectra over 8 nights in June 2004.Report error of ± .
006 on log R ′ hk (P) Adopted value: -5.032 ± HD 162020 K2 -4.120 individual 1 (P) Adopted value: -4.120 ± c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 6 – continued
Name Type log R ′ HK Observations Ref.HD 164922 G9 -5.050 47 obs in 24 month bins. Report σ = 1.45% 13 (G) Adopted value: -5.050 ± HD 168443 G6 -5.080 30 obs from 1996 – 1998.5. Report 6% scatterin S-index with no trend or periodicity 5-5.120 102 obs in 31 month bins. Report σ = 1.67% 13-4.800 individual, values from this author seemsystematically high (see HD 141937) 53 (E) Adopted value: -5.109 ± HD 168746 G5 -5.050 13 obs in 9 month bins. Report σ = 1.16% 13 (O) Adopted value: -5.050 ± HD 169830 F8 -5.070 11 obs in 9 month bins. Report σ = 1.87% 13-4.820 individual? 18 (O) Adopted value: -5.049 ± HD 170469 G5 -5.090 22 obs in 10 month bins. Report σ = 1.93% 13-5.060 13 Keck spectra from JD 2451705.96808 –2454250.01196 (2544 days) 22 (G) Adopted value: -5.079 ± HD 175541 G6/8 -5.230 30 obs in 20 month bins. Report σ = 3.06% 13-5.280 29 obs from JD 2450283.92 – 2453968.920(10.1 years) 61 (E) Adopted value: -5.255 ± HD 177830 K0 -5.280 individual? 5 (P) Adopted value: -5.280 ± HD 178911B G5 -4.980 15 obs in 9 month bins. Report σ = 3.86% 13 (O) Adopted value: -4.980 ± HD 179949 F8 -4.790 14 obs in 9 month bins. Report σ = 1.66% 13-4.720 average of above with 23 obs over 2 years+ 1 individual 1-4.740 average of 2 obs (log R ′ HK = -4.76 & -4.72)on 2002 Jul 20 & 2004 Aug 23/24 92 (G) Adopted value: -4.720 ± HD 183263 G5 -5.110 20 obs in 11 month bins. Report σ = 1.87% 13 (O) Adopted value: -5.110 ± HD 185269 G0 -5.140 individual? 62 (P) Adopted value: -5.140 ± HD 186427 G3 -5.115 obs in 1982, 1983, 1991, late 1993 – 1999(see Fig. 2 of Henry et al. 2000). Well-sampled and flat.Report σ = 13.80% which seems discrepant with their Fig. 2 5-5.080 individual 13 (E) Adopted value: -5.115 ± HD 187085 G0 -4.930 1 obs on UT 28/06/1993 38 (P) Adopted value: -4.930 ± HD 187123 G5 -4.930 individual? 5-5.030 60 obs in 17 month bins. Report σ = 1.41% 13 (O) Adopted value: -5.028 ± HD 189733 K2 -4.337 individual 14-4.537 individual 64 (P) Adopted value: -4.437 ± HD 190228 G5 -5.180 8 obs in 5 month bins. Report σ = 1.46% 13 (P) Adopted value: -5.180 ± HD 190360 G7 -5.090 67 obs in 21 month bins. Report σ = 1.54% 13-5.050 232 obs from 27/6/1967 – 22/5/1983 (16 years) 66-5.106 1978 – 1980, 1981 – 1991. Flat / no cyclefrom Fig. 1e of Baliunas et al. (1995). Report σ s < (E) Adopted value: -5.076 ± HD 190647 G5 -5.090 21 HARPS from JD 2452852.6233 –2453979.6654 (1127 days) 47-5.070 1 obs on UT 02/07/1993 38 c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
Table 6 – continued
Name Type log R ′ HK Observations Ref. (G) Adopted value: -5.089 ± HD 192263 K1/2 -4.387 individual 14-4.350 individual? 68-4.558 113 obs on 37 nights between Oct 1999 andSep 2001. Suggest a large activity variation 67 (P) Adopted value: -4.548 ± HD 192699 G8 -5.290 34 obs from JD 2453155.988 –2454170.058 (1014 days) 61 (G) Adopted value: -5.290 ± HD 195019 G5 -4.850 individual? 5-5.090 37 obs in 18 month bins. Report σ = 1.87% 13 (O) Adopted value: -5.084 ± HD 196050 G3 -4.650 individual? 18-5.040 1 obs on UT 02/07/1993 38 (P) Adopted value: -4.845 ± HD 196885 F8 -5.010 2 obs in 2 month bins 13 (P) Adopted value: -5.010 ± HD 202206 G6 -4.720 individual 1 (P) Adopted value: -4.720 ± HD 208487 G1/3 -4.900 1 obs on UT 29/06/1993 38 (P) Adopted value: -4.900 ± HD 209458 F8 -4.930 individual? 5-5.000 56 obs in 14 month bins. Report σ = 1.40% 13-4.988 individual 64 (O) Adopted value: -4.999 ± HD 210277 G8/K0 -5.060 36 obs from 1996.5-1998.7 (see Marcy et al. 1999).Report <
4% scatter in S-index with no trend or periodicity 5 (G) Adopted value: -5.060 ± HD 210702 K0 -5.350 29 obs from JD 2453241.863 –2454197.033 (955 days) 61 (G) Adopted value: -5.350 ± HD 212301 F8 -4.840 23 HARPS spectra from JD 2452856.82311094 –2453579.76714084 (723 days). Report error of ± .
01 on log R ′ hk (G) Adopted value: -4.840 ± HD 213240 G0/1 -4.800 5 points over 1 year. Report σ s = 9.66% 91-5.000 1 obs on UT 13/12/1993 38 (P) Adopted value: -4.833 ± HD 216435 G0 -4.980 average of 3 individuals 1-5.000 1 obs on 30/06/1993 38-4.985 average of 2 obs (log R ′ HK = -5.01 & -4.96)on 2002 Jul 20 & 2004 Aug 23/24 92 (P) Adopted value: -4.985 ± HD 216437 G2/3 -5.010 individual? 18-5.030 1 obs on 2001 Aug 04 92 (P) Adopted value: -5.020 ± HD 216770 K0 -4.920 individual 13-4.840 individual? 38 (P) Adopted value: -4.880 ± HD 217014 G3 -5.068 obs from 1966 – 1999 (see Fig. 1of Henry et al. 2000). Well sampled, slight.downward trend. Report σ s = 3.90% 5-5.080 17 obs in 3 month bins 13-4.970 1 obs on UT 02/07/1993 38-5.076 1977 – 1991. Variable activity levelsestimate peak variation of log R ′ hk -5.00 – -5.15 fromfrom Fig. 1e of Baliunas et al. (1995) ? (E) Adopted value: -5.069 ± HD 219828 G0 -5.040 22 HARPS spectra from JD 2453509.928056 – c (cid:13) , 000–000 stimating the masses of extra-solar planets Table 6 – continued
Name Type log R ′ HK Observations Ref.2453975.734459 (466 days) 49 (O) Adopted value: -5.040 ± HD 221287 F7 -4.590 26 HARPS spectra from JD 2452851.8534 –2453980.7273 (1129 days) 47 (G) Adopted value: -4.590 ± HD 222404 K1 -5.320 average of several obs, including obsfrom 1998 – 2002 and individual obs taken in 1979 1 (G) Adopted value: -5.320 ± HD 222582 G5 -5.000 individual? 5 (P) Adopted value: -5.000 ± HD 224693 G2 -5.150 24 Keck spectra from JD 2453191.097 –2453752.761 (562 days) 28 (O) Adopted value: -5.150 ± HD 231701 G0 -5.000 17 Keck spectra from JD 2453190.98047 –2454286.00169 (1095 days) 22 (G) Adopted value: -5.000 ± HD 330075 G5 -5.030 individual HARPS 72 (P) Adopted value: -5.030 ± TrES-1 K0 -4.770 individual 74-4.785 individual 64 (P) Adopted value: -4.778 ± TrES-2 G0 -5.160 12 obs during summer 2006. Report error of ± .
15 on log R ′ hk (P) Adopted value: -5.160 ± HAT-P-1 F8 -5.030 9 spectra 78 (P) Adopted value: -5.030 ± OGLE-TR-10 G2 -4.804 individual 64 (P) Adopted value: -4.804 ± OGLE-TR-56 F8 -5.358 individual 64 (P) Adopted value: -5.358 ± OGLE-TR-111 K2 -4.812 individual 64 (P) Adopted value: -4.812 ± OGLE-TR-113 K4 -4.685 individual 64 (P) Adopted value: -4.685 ± c (cid:13) , 000–000 C. A. Watson, S. P. Littlefair, A. Collier Cameron, V. S. Dhillon and E. K. Simpson
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