A SPITZER SEARCH FOR TRANSITS OF RADIAL VELOCITY DETECTED SUPER-EARTHS

HD 1461 b has a minimum mass of 8.1 M_⊕ and orbits a G-type star with a period of 5.77 days. Its eccentricity is estimated to be fairly low at 0.16. Two other planets with minimum masses of 28 and 87 M_⊕ may exist in the system at periods of 446 and 5017 days but have yet to be confirmed (Rivera et al. 2010a).

HD 7924 b has a minimum mass of 9.26 M_⊕ and orbits a K-type star with a period of 5.40 days. Eccentricity of the planet is close to zero and fixed at this value in the fits here. No additional planets have been reported in this system (Howard et al. 2009).

HD 97658 b has a minimum mass of 8.2 M_⊕ and orbits a K-type star with a period of 9.50 days. Its eccentricity is estimated at around 0.13. No other planets have been reported in this system (Howard et al. 2011b). Note that a transit detection and further constraints on planet properties have been recently made by Dragomir et al. (2013) using MOST; see Section 4 for details and discussion of this target.

HD 156668 b has a minimum mass of 4.15 M_⊕ and orbits a K-type star with a period of 4.64 days. Orbital solutions from fits to RV measurements were found for both eccentricities of 0 (fixed) and 0.22, and include the possible effects of one additional planet candidate in the system with a minimum mass of 45 M_⊕ and a period of 810 days (Howard et al. 2011a).

HIP 57274 b has a minimum mass of 11.6 M_⊕ and orbits a K-type star with a period of 8.14 days. Orbital solutions from fits to RV measurements were found for both eccentricities of 0 (fixed) and 0.20. HIP 57274 also has two additional detected planets in the system, one with a minimum mass of 0.4 M_Jup and a period of 32 days, and the other with a minimum mass of 0.53 M_Jup and a period of 432 days (Fischer et al. 2012).

GJ 876 d has a minimum mass of 5.85 M_⊕ and orbits an M-type star with a period of 1.94 days. This planet is estimated to have an eccentricity of about 0.21, and is the inner-most planet in a system with at least three others. These include a second planet with a minimum mass of 0.71 M_Jup and a period of 30 days, and a third planet with a minimum mass of 2.3 M_Jup and a period of 61 days (Rivera et al. 2005; Correia et al. 2010). A fourth planet was also recently detected with a minimum mass of 14.6 M_⊕ and a period of 124 days (Rivera et al. 2010b).

The required length of the observation window, and therefore the constraint that RV measurements placed on ephemerides, limited the initial selection of targets for transit investigation. We chose six targets for this Spitzer program that had relatively low uncertainties for their predicted transit times and for most cases required observation windows with durations less than 20 hr. We also excluded any super-Earths with existing Spitzer observations spanning predicted transit windows.

Details on the target system properties and the RV determined ephemerides are given in Table 1. We utilize updated ephemerides obtained by a fit to both published and unpublished data for these systems from the California Planet Search group (A. W. Howard et al., in preparation). Our fits for HD 1461 b appear to prefer an eccentric solution, and we therefore leave eccentricity as a free parameter. For HD 7924 b we assume a circular orbit for the planet, as there was no convincing evidence for a non-zero eccentricity. We used the preliminary transit detection from Henry et al. (2011) to define our transit window for HD 97658 b; see Section 4 for a complete discussion of this target. For HD 156668 b and HIP 57274 b there was marginal evidence for non-zero eccentricities, and we therefore selected modestly longer transit windows spanning both the circular and eccentric predictions for the transit time. The transit times of GJ 876 d are expected to deviate from a linear ephemeris due to perturbations from the other planets in the system, and we therefore calculated individual transit windows spanning the epoch of our observations using an N-body integration of the planet parameters given in Table 2 of Rivera et al. (2010b).

These observations were obtained using the Infrared Array Camera in the 4.5 μm channel operated in sub-array mode; additional details are shown in Table 2. There is a known instrumental effect during Spitzer observations that consists of a ramp up in pixel sensitivity with time, usually occurring up to an hour in duration at the start of an observation. We therefore padded our light curves with additional time before the predicted center of transit in case it was necessary to trim the initial data affected by the ramp, as is standard practice in Spitzer analyses. This results in a slightly off-center observation window for each of our targets with regards to their predicted centers of transit.

In all data sets, we extract flux information from the Basic Calibrated Data files provided by the Spitzer pipeline. We calculate the flux using techniques described in several previous studies (Knutson et al. 2012; Lewis et al. 2013; Todorov et al. 2013). First, we find the center of the stellar point spread function using a flux-weighted centroiding routine, then we perform aperture photometry, testing both fixed and time variable aperture sizes. The fixed aperture radii we tested ranged from 2.0 to 3.0 pixel widths, in steps of 0.1; the time variable apertures were scaled based on the noise pixel parameter (Mighell 2005). The noise pixel parameter is proportional to the square of the full width half max of the stellar point spread function, and described by Equation (1) below:

$$\begin{equation} \beta =\frac{\left(\sum \limits _{n}I_{n}\right)^{2}}{\sum \limits _{n}I_{n}^{2}}, \end{equation} \tag{ 1 }$$

where I_n is the measured intensity of the nth pixel.

We then empirically re-scale the noise pixel aperture radii either as $r = a\sqrt{\beta }$, where a is a scaling factor between 0.8 and 1.7 pixel widths, in steps of 0.1; or alternatively as $r = \sqrt{\beta }+C$, where C is a constant between −0.2 and 1.0 pixel widths, also in steps of 0.1.

We account for variations in intrapixel sensitivity by adopting a nearest neighbor weighting algorithm, such that the flux at each time step is normalized by a weighted sum of its 50 nearest neighbors in X and Y space on the pixel array, as described in Knutson et al. (2012) and Lewis et al. (2013).

We then evaluate each of the aperture radius models to find the lowest resulting scatter in the residuals of the fitted light curve. Although the best fit aperture radius varied depending on target, in each case an adjustment based on noise pixel yielded improvements over fixed aperture photometry; however, both methods resulted in null transit detections. The median best fit aperture radius for each light curve is shown in Table 2. Figure 1 shows the raw flux photometry for each observation. Figure 2 shows the corresponding normalized flux photometry after utilizing the nearest neighbor algorithm.

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We fix the orbital parameters for each planet to the values obtained from the RV measurements, and only the time of transit center, the planet radius, and the impact parameter are varied in the fits. The forward model for a transit (Mandel & Agol 2002) takes as input these three transit parameters, as well as the orbital period and planet semi-major axis from RV measurements, and limb darkening coefficients based on each target's stellar parameters (Sing 2010).

Characterization of transit parameter posterior likelihoods is carried out using a pseudo-grid search method: given a fixed impact parameter and transit center time, a best fit planet radius is found by Levenberg–Marquardt chi-squared minimization. Planet radius is effectively allowed to be negative in these fits by calculating a transit light curve using the absolute value of the planet radius, then inverting the curve for negative radius values. This is done in order not to bias the fits and to better characterize the noise level of the observations. Figure 3 shows histograms of planetary radii for a fixed impact parameter of zero (an equatorial transit), and fixed transit center times that are stepped across the window of observation in increments of approximately 30 s. This effectively finds the best fit planet radius at each location in the light curve. As no significant transits are detected in any of the light curves, these histograms characterize the magnitude of the combined Gaussian (white) and time correlated (red) noise, and therefore provide empirical thresholds for detection of possible transits. 2σ limits are calculated that encompass 95% of the histogram (i.e., 47.5% of the distribution lies above the median and below the upper limit, 47.5% below the median and above the lower limit). The 2σ limits corresponding to positive planetary radii are then taken as thresholds for transit detection, as negative radii are non-physical solutions. These 2σ thresholds are shown in Table 3, along with values of planet radii corresponding to models with 100% Fe, 100% MgSiO₃, and 100% H₂O bulk composition (Zeng & Sasselov 2013), derived using the planet minimum masses found from RV measurements. Although we expect that a pure iron planet would be very unlikely based on current planet formation models, this limiting case allows us to place a strict lower limit on the range of possible radii for our target planets. Our estimated radii also assume that the planets have negligible atmospheres, and the presence of a thick atmosphere would only serve to increase the transit depth for a given interior composition.

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In addition to determining transit detection limits, we confirm the validity of these limits by inserting artificial transits with depths above the detection threshold into the data and verifying that we can reliably retrieve them in our fits. Analysis of these artificially inserted transits yielded consistent results for detection thresholds of planetary radii.

In Figure 4 we evaluate the sensitivity of our detection limits to changes in the assumed impact parameter b. We find that our limits on planetary radius are fairly insensitive to changes in impact parameter, though this sensitivity varies depending on the target. The limits for HD 97658 and HD 156668 remain nearly constant out to impact parameters of 0.9, while the thresholds for the other targets tend to vary more noticeably but still mostly remain below a planet radius of 1 R_⊕. The unusual behavior of HD 7924 in this case is likely due to a correlated noise feature in the observed light curve of similar duration and depth as a model transit with an impact parameter of around 0.5 and a planet radius of about 1.1 R_⊕. The relatively short duration of the HD 7924 light curve influences the sensitivity of this impact parameter test to the noise in the data, but note that even in this case, a planet radius of 1.1 R_⊕ remains an unphysical solution.

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