THE TRANSIT INGRESS AND THE TILTED ORBIT OF THE EXTRAORDINARILY ECCENTRIC EXOPLANET HD 80606b

The ingress was expected to begin between UT 23:00 June 4 and 06:00 June 5, and to last 4–5 hr. However, in June, HD 80606 is only observable from a given site for a few hours (at most) following evening twilight. To overcome this obstacle we organized a transcontinental¹⁸ campaign, with observers in Massachusetts, New Jersey, Florida, Indiana, Texas, Arizona, California, and Hawaii.

On the transit night, each observer obtained a series of images of HD 80606 and its neighbor HD 80607. In most cases, we used only a small subraster of the CCD encompassing both stars, and defocused the telescope, both of which allow an increase in the fraction of time spent collecting photons as opposed to reading out the CCD. Defocusing also has the salutary effects of averaging over pixel-to-pixel sensitivity variations, and reducing the impact of natural seeing variations on the shape of the stellar images.

Each observer also gathered images on at least one other night when the transit was not occurring to establish the baseline flux ratio between HD 80606 and HD 80607 with the same equipment, bandpass, and range of air mass as on the transit night. Details about each site are given below. (Observations were also attempted from Brookline, MA; Princeton, NJ; Lick Observatory, CA; and Winer Observatory, AZ; but no useful data were obtained at those sites due to poor weather.) In what follows, the dates are UT dates, i.e., "June 5" refers to the transit night of June 4–5 in U.S. time zones.

George R. Wallace Jr. Astrophysical Observatory, Westford, MA. Thick clouds on the transit night prevented any useful data from being obtained. However, out-of-transit data in the Cousins R band were obtained on June 3 using a 0.41 m telescope equipped with a POETS camera (Souza et al. 2006), and a 0.36 m telescope equipped with an SBIG STL-1001E CCD camera.

Rosemary Hill Observatory, Bronson, FL. We observed in the Sloan i band using the 0.76 m Tinsley telescope and SBIG ST−402ME CCD camera. Conditions were partly cloudy on the transit night, leading to several interruptions in the time series. Control data were also obtained on June 11.

De Kalb Observatory, Auburn, IN. We used a 0.41 m f/8.5 Ritchey–Chretien telescope with an SBIG ST10−XME CCD camera. Data were obtained in the Cousins R band on May 30 and on the transit night. Conditions were clear on both nights.

McDonald Observatory, Fort Davis, TX. Two telescopes were used: the McDonald 0.8 m telescope and its Loral 2048² prime focus CCD camera with an R_C filter, and the MONET-North¹⁹ 1.2 m telescope with an Alta Apogee E47 CCD camera and SDSS r filter, controlled remotely from Göttingen, Germany. Conditions were partly cloudy on the transit night, shortening the interval of observations and causing several interruptions. Control data were obtained with the McDonald 0.8 m telescope on June 11, and with the MONET-North 1.2 m telescope on May 31 and June 4.

Fred L. Whipple Observatory, Mt. Hopkins, AZ. We used the 48 in (1.2 m) telescope and Keplercam, a 4096² Fairchild CCD camera. Cloud cover prevented observations on the transit night, but out-of-transit data were obtained on June 6 in the Sloan riz bands. Out-of-transit data in the i band were also obtained on 2009 February 13 and 14.

Mount Laguna Observatory, San Diego, CA. We observed in the Sloan r band with the 1.0 m telescope and 2048² CCD camera. Conditions were humid and cloudy. The target star was observable through a thin strip of clear sky for several hours after evening twilight. Out-of-transit data were obtained on June 8.

Mauna Kea Observatory, HI. We used the University of Hawaii 2.2 m telescope and the Orthogonal Parallel Transfer Imaging Camera (OPTIC; Tonry et al. 1997). Instead of defocusing, we used the charge-shifting capability of the OPTIC to spread the starlight into squares 40 pixels (54) on a side (Howell et al. 2003). We observed with a custom "narrow z" filter defining a bandpass centered at 850 nm with a full width at half-maximum of 40 nm. Out-of-transit data were obtained on June 4.

Reduction of the CCD images from each observatory involved standard procedures for bias subtraction, flat-field division, and aperture photometry. The flux of HD 80606 was divided by that of HD 80607, and the results were averaged into 10 minute bins. This degree of binning was acceptable because it sampled the ingress duration with ≈15 points. We estimated the uncertainty in each binned point as the standard deviation of the mean of all the individual data points contributing to the bin (ranging in number from 8 to 63 depending on the telescope). We further imposed a minimum uncertainty of 0.001 per 10 minute binned point to avoid overweighting any particular point and out of general caution about time-correlated noise that often afflicts photometric data (Pont et al. 2006). Figure 1 shows the time series of the flux ratio based on the data from the transit night of June 5, as well as the out-of-transit flux ratio derived with the same telescope.

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Determining the out-of-transit flux ratio and its uncertainty was an important task. Since it was not possible to gather out-of-transit data on June 5, we needed to compare data from the same telescope that were taken on different nights. Systematic errors are expected from night-to-night differences in atmospheric conditions and detector calibrations. We believe this uncertainty to be approximately 0.002 in the flux ratio, based on the following two tests.

First, in two instances the out-of-transit flux ratio was measured on more than one night, with differences in the results of 0.0004 and 0.0017 from the MONET-North and FLWO telescopes, respectively. In the latter case, the data were separated in time by 112 days, raising the possibility that longer term instabilities in the instrument or the intrinsic variability of the stars contribute to the difference, and that the night-to-night repeatability is even better than 0.0017.

A second comparison can be made by including data from different telescopes that employed the same nominal bandpass. This should give an upper bound (worst-case) estimate for the systematic error in the measurement from a single telescope on different nights. Using the data in Table 1, we asked for each bandpass: what value of σ_sys must be chosen in order for

$$\begin{equation} \chi ^2 = \sum _{i=1}^{N} \frac{(f_{{\rm oot},i} - \bar{f}_{{\rm oot},i})^2}{\sigma _i^2 + \sigma _{\rm sys}^2 } = N-4, \end{equation} \tag{ 1 }$$

where f_oot,i is the ith measurement of the out-of-transit flux ratio, σ_i is the statistical uncertainty in that measurement, and $\bar{f}_{{\rm oot},i}$ is the unweighted mean of all the out-of-transit flux ratio measurements made in the same nominal bandpass as f_i. There are N = 15 data points, and N − 4 is used in Equation (1) because there are four independent bandpasses for which means are calculated.²⁰ In this sense, we fitted a model to the out-of-transit flux-ratio data with four free parameters. The quantities $(f_{{\rm oot},i} - \bar{f}_{{\rm oot},i})$ are plotted in Figure 2. The result is σ_sys = 0.0018.

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In our subsequent analysis, we assumed the error in the out-of-transit flux ratio to follow a Gaussian distribution with a standard deviation given by the quadrature sum of 0.0020 and statistical error given in Table 1. Given the preceding results, we believe this to be a reasonable and even a conservative estimate of the systematic error. Though it may seem too small to those readers with experience in synoptic photometry, it must be remembered that this is an unusually favorable case: the universe was kind enough to provide two stars of nearly equal brightness and color separated by only 20''. It is also worth repeating that for our analysis we did not need to place data from different telescopes on the same flux scale; we needed only to align data from the same telescope obtained on different nights.

We pay attention to a few key aspects of the time series in Figure 1: (1) all the observers measured the flux ratio between HD 80606 and HD 80607 to be smaller on the transit night than it was on out-of-transit nights. We conclude that the transit was detected. (2) The data from Rosemary Hill and De Kalb show a decline in the relative brightness of HD 80606 over several hours. We interpret the decline as the transit ingress. (3) The data from McDonald, Mt. Laguna, and Mauna Kea show little variability over the interval of their observations, suggesting that the "bottom" (complete phase) of the transit had been reached.

We measured the relative RV of HD 80606 using the Keck I 10 m telescope on Mauna Kea, Hawaii. We used the High Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994) in the standard setup of the California Planet Search program (Howard et al. 2009), as summarized here. We employed the red cross-disperser and used the iodine gas absorption cell to calibrate the instrumental response and the wavelength scale. The slit width was 086 and the exposure time ranged from 240 s to 500 s, giving a resolution of 65, 000 and a typical signal-to-noise ratio of 210 pixel⁻¹. Radial velocities were measured with respect to an iodine-free spectrum, using the algorithm of Butler et al. (1996) as improved over the years.

The 73 measurements span 8 yr from 2001 to the present. Table 2 gives all of the RV data. There are 39 data points obtained prior to the upgrade of the HIRES CCDs in 2004 August, and 34 data points obtained after the upgrade. Results from the pre-upgrade data, and some of the post-upgrade data, were published by Butler et al. (2006). For our analysis, we re-reduced the post-upgrade spectra using later versions of the analysis code and spectral template. Due to known difficulties in comparing data with the different detectors, we allowed for a constant velocity offset between the pre-upgrade and post-upgrade data sets in our subsequent analysis.

The post-upgrade data include nightly data from the week of the June 5 transit, which in turn include a series of eight observations taken at 30 minute intervals on the transit night. Figure 3 shows the RV data as a function of time, and Figure 4 shows the RV data as a function of orbital phase. Figure 5 is a close-up around the transit phase. Shown in all of these figures is the best-fitting model, described in Section 3.

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Figure 7 shows the probability distributions for the parameters describing the RM effect, vsin i_⋆, and λ. A well-aligned system, λ = 0, can be excluded with high confidence. With 68.3% confidence, λ lies between 32° and 87°, and with 99.73% confidence, it lies between 14° and 142°. The distribution is non-Gaussian because of the correlation between λ and vsin i_⋆ shown in the right panel of Figure 7. No other parameter shows a significant correlation with λ.

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The strong exclusion of good alignment (λ = 0) follows from the observation that the RV data gathered on June 5 were blueshifted relative to the Keplerian velocity (see Figure 5), over a time range that proved to include the midtransit time. Were the spin and orbit aligned, the anomalous RV would vanish at midtransit because the planet would then be in front of the stellar rotation axis where there is no radial component to the stellar rotation velocity. The observed blueshift at midtransit implies that the midpoint of the transit chord is on the redshifted (receding) side of the star. This can only happen if the stellar rotation axis is tilted with respect to the orbital axis.

For the projected stellar rotation rate, we find vsin i_⋆ = 1.12^+0.44_−0.22 km s⁻¹. In their previous analyses using the SOPHIE data, Pont et al. (2009) imposed prior constraints on vsin i_⋆ based on the observed broadening in the stellar absorption lines. This was necessary to break a degeneracy between the transit duration, vsin i_⋆, and λ. Here we have determined vsin i_⋆ by fitting the data exhibiting the RM effect. This is preferable whenever possible, because of systematic effects in both methods of determining vsin i_⋆. The method based on the RM effect is subject to systematic errors in the "RM calibration" procedure (see Section 3 and Triaud et al. 2009). The method based on line broadening is subject to the systematic error because of the degeneracy between rotational broadening and other broadening mechanisms such as macroturbulence, which are of comparable or greater magnitude for slowly rotating stars such as HD 80606. These systematic effects may cause a mismatch in the results for vsin i_⋆ obtained by the two methods, which could lead to biased results for λ if the result from the line-broadening method were applied as a constraint on the RM model.

For comparison, we review the spectroscopic determinations of vsin i_⋆. Naef et al. (2001) found 0.9 ± 0.6 km s⁻¹, based on the width of the cross-correlation function measured with the ELODIE spectrograph, after subtracting the larger "intrinsic width" due to macroturbulence and other broadening mechanisms that was estimated using the empirical calibration of Queloz et al. (1998). This result might be considered tentative, given that Queloz et al. (1998) only claim their calibration to be accurate down to 1.5–2 km s⁻¹. Valenti & Fischer (2005) found vsin i_⋆ = 1.8 ± 0.5 km s⁻¹ based on synthetic spectral fitting to the pre-upgrade Keck spectra, and a particular assumed relationship between effective temperature and macroturbulence (see their paper for details). We used the same spectral model and macroturbulence relationship to analyze one of the post-upgrade Keck spectra, finding vsin i_⋆ = 2.0 ± 0.5 km s⁻¹, in good agreement with Valenti & Fischer (2005) but not Naef et al. (2001).

We investigated the effect of imposing an a priori constraint on vsin i_⋆ by adding the following term to Equation (2):

$$\begin{equation} \chi ^2_{{\rm rot}} = \left[ \frac{v\sin i_\star - 1.9 {\mathrm{\;km \;s}^{-1}}}{0.5 {\mathrm{\;km \;s}}^{-1}} \right]^2. \end{equation} \tag{ 7 }$$

After refitting, the results for the spin–orbit parameters were vsin i_⋆ = 1.37^+0.41_−0.33 km s⁻¹ and λ = 39⁺²⁸₋₁₃ deg. The best-fitting model is shown with a dashed line in Figure 5. The constraints on λ are tightened; the new credible interval is 25% smaller than the credible interval without the constraint. However, the improved precision does not necessarily imply improved accuracy, given the uncertainties mentioned previously regarding the RM calibration and other broadening mechanisms besides rotation. For this reason, we have emphasized the results with no external constraint on vsin i_⋆, and provide only those results in Table 3.

The preceding results did not make use of the SOPHIE data that Moutou et al. (2009) obtained during the 2009 February transit. By leaving out the SOPHIE data, we have provided as independent a determination of λ as possible. Figure 5 shows that the SOPHIE data seem to agree with the Keck data, and with the best-fitting model constrained by the Keck data. When the SOPHIE data are fitted simultaneously with the Keck data (with no prior constraint on vsin i_⋆), the results for λ are sharpened to 59⁺²¹₋₁₆ deg at 68.3% confidence, and 59⁺⁶³₋₃₅ deg at 99.73% confidence.

Our orbital parameters are generally in agreement with those derived previously. One exception is the argument of pericenter, for which our result (300.83 ± 0.15 deg) is 2σ away from the result of Laughlin et al. (2009) (300.4977 ± 0.0045 deg), although the uncertainty in the latter quantity seems likely to be underestimated. Another exception is that our orbital period differs from that of Laughlin et al. (2009) by 3σ, although our period agrees with the period found by Pont et al. (2009).

The transit parameters, including the transit duration, are related directly to the stellar mean density ρ_⋆ (Seager & Mallén-Ornelas 2003). In their previous studies, due to the poorly known transit duration, Pont et al. (2009) used theoretical expectations for ρ_⋆ to impose constraints on their light-curve solutions. Since we have measured the transit duration, we can determine ρ_⋆ directly from the data, finding ρ_⋆ = 1.63 ± 0.15 g cm⁻³.²³ This is 10%–30% larger than the Sun's mean density of 1.41 g cm⁻³, as expected for a metal-rich star with the observed G5 spectral type (Naef et al. 2001).

We used this new empirical determination of ρ_⋆ in conjunction with stellar-evolutionary models to refine the estimates of the stellar mass M_⋆ and radius R_⋆, which in turn lead to refined planetary parameters (see, e.g., Sozzetti et al. 2007; Holman et al. 2007). The models were based on the Yonsei–Yale series (Yi et al. 2001; Demarque et al. 2004), and were applied as described by Torres et al. (2008; with minor amendments by Carter et al. 2009). Figure 8 shows the theoretical isochrones, along with some of the observational constraints. The constraints were ρ_⋆ = 1.63 ± 0.15 g cm⁻³, along with T_eff = 5572 ± 100 K and [Fe/H] =+0.34 ± 0.10. The temperature and metallicity estimates are based on the spectroscopic analysis of Valenti & Fischer (2005), but with enlarged error bars, as per Torres et al. (2008). The results are given in Table 3.

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We did not apply any constraint to the models based on the spectroscopically determined surface gravity (log g_⋆), out of concern over systematic errors in that parameter (Winn et al. 2008b). Instead we performed the reverse operation: given our results for M_⋆ and R_⋆ we computed the implied value of log g_⋆, finding log g_⋆ = 4.487 ± 0.021. Reassuringly this in agreement with, and is more precise than, the spectroscopically determined values of 4.50 ± 0.20 (Naef et al. 2001) and 4.44 ± 0.08 (Valenti & Fischer 2005).

The RVs given in Table 2 were measured with respect to an arbitrary template spectrum, and therefore they do not represent the true heliocentric RV of HD 80606, which is known much less precisely. For reference, we measured the heliocentric RV to be γ = +3.95 ± 0.27 km s⁻¹, using the telluric "A" and "B" absorption bands of molecular oxygen to place the Keck/HIRES spectra on the RV scale of Nidever et al. (2002). This result is in agreement with the previously reported value of γ = +3.767 km s⁻¹ (Naef et al. 2001).