Five New Transits of the Super-Neptune HD 149026
Joshua N. Winn, Gregory W. Henry, Guillermo Torres, Matthew J. Holman
aa r X i v : . [ a s t r o - ph ] N ov Five New Transits of the Super-Neptune HD 149026b
Joshua N. Winn , Gregory W. Henry , Guillermo Torres , Matthew J. Holman ABSTRACT
We present new photometry of HD 149026 spanning five transits of its “super-Neptune” planet. In combination with previous data, we improve upon the determina-tion of the planet-to-star radius ratio: R p /R ⋆ = 0 . +0 . − . . We find the planetaryradius to be 0 . ± . R Jup , in accordance with previous theoretical models invokinga high metal abundance for the planet. The limiting error is the uncertainty in thestellar radius. Although we find agreement among four different ways of estimatingthe stellar radius, the uncertainty remains at 7%. We also present a refined tran-sit ephemeris and a constraint on the orbital eccentricity and argument of pericenter, e cos ω = − . ± . Subject headings: planetary systems — stars: individual (HD 149026)
1. Introduction
Many clues about the processes of planet formation and evolution have been discovered bystudying the ensemble properties of exoplanets, such as the “brown dwarf desert” (Halbwachs etal. 2000, Marcy & Butler 2000) and the tendency for metal-rich stars to have more detectableplanets (Santos et al. 2003, Fischer & Valenti 2005). However, there are also individual exoplanetswhose properties bear directly on theories of planet formation and evolution. One of the bestexamples is the transiting planet HD 149026b (Sato et al. 2005).Compared to Saturn, HD 149026b has a similar mass but its radius is 15% smaller, despite theintense irradiation from its parent star that should enlarge the radius. Sato et al. (2005) modeledHD 149026b as a dense heavy-element core surrounded by a fluid envelope of solar composition.They found a core mass of 70-80 M ⊕ , which is 65-75% of the total mass of the planet. This is largerthan the canonical core mass of 10-20 M ⊕ that is expected from the core-accretion theory of planetformation (Mizuno 1980, Pollack et al. 1996). The finding of a highly metal-enriched composition Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute ofTechnology, Cambridge, MA 02139, USA Center of Excellence in Information Systems, Tennessee State University, 3500 John A. Merritt Blvd., Box 9501,Nashville, TN 37209, USA Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA .
36; Sato et al. 2005).The observation of a large core in such a metal-rich system would seem to support the core-accretiontheory as opposed to coreless alternatives such as gravitational instability (Boss 1997). However,the larger-than-expected core mass raises some questions. Why did the growing protoplanet notaccrete gas efficiently? Or if it did, what happened to its envelope of light elements? Many scenarioshave been proposed: a collision of two massive protoplanets (Sato et al. 2005, Ikoma et al. 2006), in situ formation in a low-pressure nebula (Broeg & Wuchterl 2007), a viscous and evaporatinggas disk (Ikoma et al. 2006), and a separation of gas from planetesimals at the magnetospheric “Xpoint” (Sato et al. 2005).More recently, Harrington et al. (2007) found that the 8 µ m brightness temperature of HD 149026bexceeds its expected blackbody temperature, even if the planet is assumed to absorb all of the inci-dent stellar radiation. In this sense the planet is anomalously hot. The high temperature may resultfrom novel atmospheric or structural properties. Most recently, Torres et al. (2007) announced thediscovery of a transiting planet, HAT-P-3b, whose measured mass and radius indicate that it toois highly enriched in heavy elements.In short, HD 149026b seems to be the harbinger of an entirely new kind of planet that currentmodels of planet formation, evolution, and structure cannot accommodate without interesting andpossibly exotic modifications. Because of this situation, it is desirable to improve the reliabilityand the precision of estimates of the system parameters, and especially a key parameter that makesthis planet unusual: its small radius.One can measure the planetary radius by gathering photometry during transits, modelingthe light curve, and supplementing the model with external information about the stellar radius.Previously, Sato et al. (2005) analyzed 3 light curves, and Charbonneau et al. (2006) added 3 lightcurves. In this paper we present another 5 light curves of comparable or higher quality to thepreviously published data, and we simultaneously model all of the data to derive the most preciseplanetary, stellar, and orbital parameters that are currently available. We present our observationsand data reduction procedure in § §
3. We providethe results in §
4, along with an extended discussion about the limiting error: the uncertainty inthe stellar radius. The final section summarizes the results and speculates on future prospects forimprovement.
2. Observations and Data Reduction
We used three of the 0.8 m automated photometric telescopes (APTs) at Fairborn Observatoryto measure the transits of HD 149026b that occurred on UT 2006 April 26, 2006 May 20, 2007 May 3, 3 –2007 June 18, and 2007 June 21. We observed the first three transits with the T11 APT andobserved the last two transits simultaneously with the T8, T10, and T11 APTs. All three telescopesare equipped with two temperature-stabilized EMI 9124QB photomultiplier tubes for measuringphoton count rates simultaneously through Str¨omgren b and y filters.On a given night, each telescope automatically acquired brightness measurements of HD 149026( V = 8 . B − V = 0 .
61) and the comparison star HD 149504 ( V = 6 . B − V = 0 . ′′ for all the integrations. The integration time was 20 secondson the comparison star and 30 seconds on the (fainter) target star. We computed the magnitudedifference for each pair of target-comparison observations. To increase the signal-to-noise ratio ofeach measurement, the differential magnitudes from the b and y pass bands were averaged, resultingin a differential magnitude for a synthetic ( b + y ) /
3. Determination of System Parameters
We fitted all of our new photometric data jointly with the three ( b + y ) / g and r light curves presented by Charbonneau et al. (2006). We useda parameterized model based on a two-body circular orbit. The orbit is specified by the massesof the star and planet ( M ⋆ and M p ), the inclination with respect to the sky plane ( i ), the orbitalperiod ( P ) and a particular midtransit time ( T c ). The star and planet are taken to be spheres We did not include the V -band light curve of Charbonneau et al. (2006) because of its comparatively large errorsand sparse time sampling. b + y ) / b + y ) / R ⋆ and R p respectively, and when their sky-projected centers are within R ⋆ + R p ofone another we use the Mandel & Agol (2002) formulas to compute the flux decrement due to thepartial blockage of the limb-darkened stellar surface. This is the same code that has been developedfor the Transit Light Curve project (Holman et al. 2006, Winn et al. 2007). For HD 149026, weassumed the limb darkening law to be linear, with a coefficient given by Claret (2000) for a star ofthe appropriate temperature and surface gravity. For the ( b + y ) / b and y coefficients.Not all of the parameters listed above can be determined from transit photometry alone. Oneset of parameters that can be determined from an individual light curve is T c , R p /R ⋆ , a/R ⋆ , and i ,where a is the semimajor axis. Our approach was to fix M ⋆ , M p , and P at previously determinedvalues (thereby fixing a through Kepler’s third law), and then fit for R p , R ⋆ , i , and T c . The resultsfor R ⋆ and R p are specific to the choice of M ⋆ , but they scale as M / ⋆ because a ∝ M / ⋆ when theuncertainty in P is negligible, as it is here. We assumed M ⋆ = 1 . M ⊙ , following Sato et al. (2005),a choice that was subsequently corroborated by our analysis of the observable stellar propertiesand the results for a/R ⋆ (see § χ = N f X j =1 (cid:20) f j (obs) − f j (calc) σ j (cid:21) , (1)where N f is the number of flux measurements, f j (obs) is the flux observed at time j , σ j controlsthe weights of the data points, and f j (calc) is the calculated flux. Experience has shown that thedata weights σ j should account not only for the single-measurement precision but also the time-correlated (“red”) noise that afflicts most time-series photometry (see, e.g., Gillon et al. 2006).The most important timescale in a transit light curve is the ∼
10 min duration of the ingress andegress, since the resolution of ingress and egress is what permits the determination of a/R ⋆ and i in addition to R p /R ⋆ . To assess the noise on this timescale, we first calculated the standarddeviation of the unbinned out-of-transit data ( σ ) for each light curve. Then we averaged the out-of-transit data into 10 min bins consisting of N data points, where N depended on the observingcadence, and recalculated the standard deviation ( σ N ). In the absence of red noise, one wouldexpect σ N = σ / √ N , but in practice σ N was larger than σ / √ N by some factor β . Therefore, weset the data weights equal to β σ . The results for β ranged from 1.05 to 1.27.We used a Markov Chain Monte Carlo algorithm to determine the best-fitting parameter valuesand confidence intervals. This algorithm delivers an estimate of the a posteriori joint probabilitydistribution for all of the parameters (see Holman et al. 2006 or Winn et al. 2007 for more details).For each parameter, we took the mode of the distribution after marginalizing over all other pa-rameters to be the “best value.” We defined the 68% confidence limits p lo and p hi as the valuesbetween which the integrated probability is 68%, and for which the two integrals from p min → p lo and p hi → p max were equal.At first, the preceding computations were performed using free parameters for both the orbital 6 –period and a single midtransit time. Thus the transits were required to be spaced by integralmultiples of a fixed period. However, we also wanted to measure the individual transit times, inorder to search for variations that might be indicative of additional bodies in the planetary system(Agol et al. 2005, Holman & Murray 2005). To do this, we fixed R p , R ⋆ , and i at the best valuesdetermined in the first step, and then performed a three-parameter fit of each individual light curve.The parameters were T c along with the zero point and slope of the linear function that was used tocorrect the out-of-transit data. (Fixing the values of R p , R ⋆ , and i is justified because the errorsin those parameters are not correlated with the error in the transit time.) We did this not only forthe 5 new light curves, but also for the 5 previously published light curves, to provide consistencyin the treatment of errors. We then used these transit-time measurements to refine the estimatesof P and T c (see § R p /R ⋆ , a/R ⋆ , and i , we reran the MCMC algorithm on the entire data set, using fixed values of P and T c from ourrefined ephemeris.
4. Results
The results of the light-curve analysis are given in Table 2 and discussed in § § § The a posteriori probability distributions for R p /R ⋆ , a/R ⋆ , and i are shown in Fig. 2. Themost well-constrained of these three basic light curve parameters is the radius ratio, R p /R ⋆ =0 . +0 . − . , with a precision of approximately 2.3%. The radius ratio is determined largely bythe observed transit depth, which is the smallest among all of the 20 transiting planets known todate. While there are smaller planets, such as the Neptune-sized GJ 436b (Gillon et al. 2007), theyall orbit smaller stars, making their radius ratios and transit depths larger than that of HD 149026.Less well-constrained are a/R ⋆ and i , the parameters that depend on the observed durationsof the ingress, egress, and total phases of the transit. Table 2 gives the results for those parametersas well as the impact parameter and the durations, which can be derived in terms of R p /R ⋆ , a/R ⋆ , 7 –Fig. 2.— Estimated a posteriori probability distributions from the joint fit to the transit lightcurves. The top panels show the single-variable distributions, in which the mode is marked witha solid line and the 68% confidence limits with dashed lines. The bottom panels show the two-dimensional distributions, in which the contours mark the 68% and 95% confidence limits. 8 –and i . The data are consistent with impact parameters ranging from − .
36 to 0 .
36. As withany eclipsing binary system, the data cannot distinguish between positive and negative impactparameters; the probability distributions are perfectly symmetric about b = 0 and i = 90 ◦ . In thiscase the peak probability occurs at the central values b = 0, i = 90 ◦ . The quantity a/R ⋆ has ahighly asymmetric error bar. The observed duration of the entire transit event enforces the upperlimit on a/R ⋆ , while the ratio of the ingress (or egress) duration to the total duration enforces thelower limit on a/R ⋆ .Our findings are consistent with the two previous light-curve analyses, by Sato et al. (2005)and Charbonneau et al. (2006), although our analysis method is different in several ways besidesthe use of an expanded dataset. First, we have attempted to account for time-correlated noise inthe photometry, which was neglected in the previous analyses. Second, unlike the previous authors,we have not incorporated any a priori constraints on the stellar properties into our fitting statistic.We made this choice in order to clarify what information is derived from the light curves themselves;for example, the previous works did not call attention to the results for R p /R ⋆ even though thatparameter is more precisely known than either R p or R ⋆ . In addition, our analysis method providesan estimate of a/R ⋆ that is independent of any assumptions about the parent star, except for thevery weak dependence on the chosen limb darkening parameter. This is useful because a/R ⋆ canbe used to determine the stellar mean density (Seager & Mallen-Ornelas 2003, Sozzetti et al. 2007,Holman et al. 2007): ρ ⋆ = 3 πGP (cid:18) aR ⋆ (cid:19) − ρ p (cid:18) R p R ⋆ (cid:19) . (2)The last term in this expression may be neglected in this case because ρ p ∼ ρ ⋆ and ( R p /R ⋆ ) ∼ − .Our independent estimate of ρ ⋆ is useful in characterizing the parent star, as described below. To determine the quantity of intrinsic interest, R p , we can multiply our result for R p /R ⋆ by avalue of R ⋆ obtained by other means. We have investigated four different methods for determining R ⋆ : Stefan-Boltzmann Law. —The bolometric luminosity, effective temperature, and photosphericradius of HD 149026 are related via L bol = 4 πR ⋆ σT . We use the Hipparcos parallax and apparentmagnitude ( π = 12 . ± .
79 mas, V = 8 . ± .
02; Perryman et al. 1997) to compute the absolute V magnitude, apply a bolometric correction of − . ± .
014 (Flower et al. 1996), and use thespectroscopically determined T eff = 6147 ± K (Sato et al. 2005). The result is R ⋆ = 1 . ± . R ⊙ .This is essentially identical to the value quoted by Sato et al. (2005) who used the same method. Spectral Energy Distribution Fit. —Masana et al. (2006) presented an alternative means ofestimating the effective temperature and bolometric correction, using
V J HK photometry. Theyalso provided radius estimates for many nearby stars based on this technique. Using the
Hipparcos V magnitude along with 2MASS near-infrared photometry, their result for HD 149026is R ⋆ = 1 . ± . R ⊙ . Yonsei-Yale Isochrone Fit. —Stellar evolutionary models may be used to estimate the mass,radius, and age of a star with a given effective temperature, luminosity (or gravity), and metallicity.We used the Yonsei-Yale models (Yi et al. 2001, Demarque et al. 2004) because they are convenientlyprovided with tools for interpolating isochrones in both age and metallicity. For the effectivetemperature, we used T eff = 6160 ±
50 K, a weighted mean of the results of Sato et al. (2005) andMasana et al. (2006). We used the photometric result for a/R ⋆ as our our proxy for surface gravity,and we explored the range of metallicities [Fe/H] = 0 . ± .
08. For each metallicity we considereda range of ages from 0.1 to 14 Gyr, in steps of 0.1 Gyr. We interpolated the isochrones using a finemass grid and compared the points with the measured values of T eff and a/R ⋆ . We computed χ at each point based on the modeled and observed values of T eff , a/R ⋆ , and metallicity. Then weweighted the points by exp( − χ /
2) and applied an additional weighting to take into account thedensity of stars on each isochrone, assuming a Salpeter initial mass function. The “best-fitting”stellar properties were taken to be the weighted mean of the properties of all the points. For moredetails and other applications of this analysis, see Torres, Winn, & Holman (in preparation). ForHD 149026, the results are M ⋆ = 1 . +0 . − . M ⊙ , L ⋆ = 2 . +0 . − . L ⊙ , and R ⋆ = 1 . +0 . − . R ⊙ .Similar results were obtained when the spectroscopically determined value of log g was used insteadof a/R ⋆ . The theoretical isochrones and the observational constraints are shown in Fig. 3. Kepler’sLaw with Stellar Mass Prior. —As mentioned earlier, the quantity a/R ⋆ that is determined fromthe transit photometry can be used to find ρ ⋆ (Eq. 2). With an a priori estimate of M ⋆ , one mayuse ρ ⋆ to determine R ⋆ . Taking M ⋆ = 1 . ± . M ⊙ based on the isochrone fit described above,we find R ⋆ = 1 . +0 . − . R ⊙ .All of the results for the stellar radius are summarized in Table 4. They are all consistent withone another at the 1 σ level, with a weighted mean of 1 . R ⊙ . However, it must be emphasizedthat while the methods are different, they are not wholly independent. The first two methods bothrely on the Hipparcos parallax, which is the largest source of error in both cases. The latter twomethods both rely on the Yonsei-Yale stellar evolutionary models. For this reason we cannot sayconfidently that the uncertainty in R ⋆ is any smaller than the uncertainty in each of the individualmeasurements, although the mutual agreement is certainly reassuring. In what follows we adoptthe consensus value R ⋆ = 1 . ± . R ⊙ , the same value used in the previous light curve analyses.Assuming a Gaussian error distribution for R ⋆ , and the error distribution for R p /R ⋆ obtainedfrom our light curve analysis, we find the planetary radius to be R p = 0 . ± . R Jup . Thiscan be compared to the previously published results of 0 . ± . R Jup (Sato et al. 2005) and0 . ± . R Jup (Charbonneau et al. 2006), keeping in mind our different method of analysis Sato et al. (2005) reported a metallicity of [Fe/H] = +0 .
36 with an internal uncertainty of 0 .
05. To be con-servative, we adopted a somewhat larger uncertainty of 0 .
08, recognizing that different methods for determining themetallicity often produce systematic differences of this size.
10 –Fig. 3.— Model isochrones from the Yonsei-Yale series by Yi et al. (2001) and Demarque etal. (2004), corresponding to ages of 1–14 Gyr (left to right), for the measured composition of[Fe/H] = +0 .
36, along with the observational constraints.
Top:
The vertical axis is log g , and theshaded box shows the 1 σ range based on the spectroscopically determined value of log g . Bottom:
The vertical axis is a/R ⋆ , which is proportional to the cube root of the stellar mean density (seeEq. 2). The shaded box shows the 1 σ range based on the photometrically determined value of a/R ⋆ . 11 –and treatment of observational errors. The results are all in agreement. Indeed the differences aresmaller than one would expect from Gaussian statistics, given the quoted error bars, though wenote that 5 of the 10 light curves we fitted were taken from those previous works. The precision in R p is not improved because the limiting error is the uncertainty in R ⋆ , which is unchanged. For planning future observations of this system it is important to be able to predict transittimes as precisely as possible. We used all of the transit times given in Table 3 to calculate aphotometric ephemeris for this system, T c ( E ) = T c (0) + EP, (3)where T c is the transit midpoint, E is the integral transit epoch, and P is the orbital period. Thelinear fit had χ /N dof = 0 .
63 and N dof = 9, suggesting that the errors quoted in Table 3 have beensomewhat overestimated. The results are: T c (0) = 2454272 . ± . P = 2 . ± . . (5)Our value for the orbital period is in agreement with the previously published values and is about25 times more precise. Figure 4 is the O − C (observed minus calculated) diagram for the transittimes.For a circular orbit, successive transits and secondary eclipses should be spaced by exactly halfan orbital period. Recently, Harrington et al. (2007) observed a secondary eclipse of HD 149026with the
Spitzer Space Telescope , allowing the assumption of a circular orbit to be checked. In thepresence of a small but nonzero orbital eccentricity, the time difference between the midpoint ofsecondary eclipse, T sec , and the time of transit, T tra , is T sec − T tra ≈ P (cid:18) π e cos ω (cid:19) , (6)where ω is the argument of pericenter (Kallrath & Milone 1999, p. 62). Harrington et al. (2007)measured the midpoint of a secondary eclipse to be HJD 2453606 . ± . − . ± . e cos ω = − . ± .
5. Discussion and Summary
We have presented 5 new transit light curves of the exoplanet HD 149026b and analyzed themalong with 5 previously published light curves. The joint analysis has resulted in much more precise 12 –Fig. 4.— Transit timing residuals for HD 149026b. The calculated times, using the ephemerisderived in § R p itself, and here we can offer no significant improvement. The limitingerror is the 7% uncertainty in the stellar radius. This error was not reduced by acquiring morelight curves, although we did find agreement between the results of 4 different (and intertwined)methods for estimating the stellar radius using all of the available data. Thus, we leave unchangedthe interpretation of this planet as a being unexpectedly small for its mass, and likely to be highlyenriched in heavy elements (Sato et al. 2005, Fortney et al. 2006, Ikoma et al. 2006, Burrows etal. 2006).Further improvement will depend upon progress in measuring the stellar radius. Baines etal. (2007) recently used optical interferometry to measure the angular diameter of the planet-hostingstar HD 189733, and combined it with the Hipparcos parallax to measure the stellar radius. ForHD 149026, similar observations are not likely to result in a more precise value of the stellar radius,at least not in the near future. This is not only because of the 6% uncertainty in the parallax, butalso because the expected angular diameter is only ≈ µ as, which is only 7–8 times larger thanthe measurement error that was achieved for HD 189733.Supposing the parallax were known with 10 µ as precision (as one might hope from a space-based interferometric mission), the error in the Stefan-Boltzmann method for determining R ⋆ wouldbe reduced to 2.7%. The limiting errors in that case would arise from the effective temperature andbolometric correction. In the nearer term, a possible path forward is the continued acquistion ofhigh-quality transit photometry, in order to improve upon our measurement of a/R ⋆ and therebyestablish the stellar mean density with greater precision. At fixed mean density, R ⋆ varies as M / ⋆ ,and our application of the Yonsei-Yale models to HD 149026 suggests that the stellar mass hasalready been pinned down to within 4.6%. If a/R ⋆ were known exactly, the fractional error inthe stellar radius would be approximately 1.5% (i.e., one-third as large as the fractional error inthe stellar mass). In effect, transit photometry measures M ⋆ /R ⋆ , and the stellar models generallyconstrain a different combination of M ⋆ and R ⋆ (see, e.g., Cody & Sasselov 2002). We encourageobservers to be persistent in gathering additional seasons of ground-based photometry and lookforward to the results of space-based photometry for this system.We are grateful to the anonymous referee for a thorough and helpful review of the manuscript.G.W.H. acknowledges support from NSF grant HRD-9706268 and NASA grant NNX06AC14G. GTacknowledges partial support for this work from NASA grant NNG04LG89G. 14 – REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
16 –Table 1. Photometry of HD 149026Heliocentric Julian Date Relative flux Uncertainty2453852.75015 1.0031 0.00272453852.75115 1.0061 0.00272453852.75215 1.0023 0.0027Note. — The data were obtained with the automaticphotometric telescopes (APTs) at Fairborn Observatory.Differential magnitudes were measured in the Str¨omgren b and y passbands, and the b and y results were averaged.The time stamps represent the Heliocentric Julian Date atthe time of mid-exposure. The uncertainties include the“red noise” correction described in §
3. We intend for thisTable to appear in entirety in the electronic version of thejournal. An excerpt is shown here to illustrate its format. 17 –Table 2. HD 149026: Transit Light Curve ParametersParameter Value 68% Upper Limit 68% Lower Limit R p /R ⋆ . . − . a/R ⋆ .
11 +0 . − . i [deg] 90 . . − . b ≡ a cos i/R ⋆ .
00 +0 . − . a .
254 +0 . − . b .
153 +0 . − . a Defined as the time between first and fourth contacts (i.e., between themoments when the projected planetary and stellar disks are externally tangent). b Defined as the time between first and second contacts (i.e., the durationover which the projected planetary disk crosses the stellar limb, from externaltangency to internal tangency). In our model, the ingress and egress durationsare equal.Note. — Results of fitting ten light curves: three light curves [( b + y ) /
2] fromSato et al. (2005); two light curves ( g and r ) from Charbonneau et al. (2006);and five light curves [( b + y ) /
2] from this work. Not all of the parameters areindependent. One may regard R p /R ⋆ , a/R ⋆ , and i as the basic parametersfrom which the other results in this table may be derived. 18 –Table 3. HD 149026: Midtransit timesTelescope Epoch Mid-transit time Uncertainty E [HJD] [days]T11 0.8m APT −
267 2453504 . . −
259 2453527 . . −
259 2453527 . . −
258 2453530 . . −
250 2453553 . . −
250 2453553 . . −
146 2453852 . . −
138 2453875 . . −
17 2454223 . . − . . . . T c ( E ) = T c (0) + EP with T c (0) = 2454272 . P =2 . σ uncertainty in the final two digits.Table 4. HD 149026: Stellar RadiusRadius Method Reference1 . ± .
10 Stefan-Boltzmann Law 1,31 . ± .
096 Spectral Energy Distribution Fit 21 . +0 . − . Yonsei-Yale Isochrone Fit 31 . +0 . − . Kepler’s Law with Stellar Mass Prior a a Using M ⋆ = 1 . ± .
06, based on the Yonsei-Yale isochrone fit to a/R ⋆ and T eff .Note. — References: (1) Sato et al. 2005; (2) Masana et al. 2006;(3) This work. 19 –Table 5. HD 149026: Planetary ParametersParameter Value Method M p [ M Jup ] 0 . ± .
03 Spectroscopic orbit a R p [ R Jup ] 0 . ± . R p /R ⋆ from light curves and R ⋆ = 1 . ± . g p [cgs] 3 . +0 . − . Light curve and spectroscopic orbit b ρ p [g cm − ] 1 . ± . M p , R p given aboveSemimajor axis, a [AU] 0 . ± . c e cos ω − . ± . da Using K = 43 . ± . − , from Sato et al. (2005); P from Table 2; and M ⋆ = 1 . ± . a/R ⋆ and T eff . b Using K = 43 . ± . − , from Sato et al. (2005); P from Table 2; and i , a/R p fromthe light curve analysis. This method is described in detail by Southworth et al. (2007) andSozzetti et al. (2007). c Using P from Table 2; and M ⋆ = 1 . ± .
06, based on the Yonsei-Yale isochrone fit to a/R ⋆ and T eff . d Using the secondary eclipse time HJD = 2453606 . ± ..