OBSERVATIONAL CONSTRAINTS ON COMPANIONS INSIDE OF 10 AU IN THE HR 8799 PLANETARY SYSTEM

NRM (Baldwin et al. 1986; Readhead et al. 1988) achieves contrast ratios of ∼10²–10³ at very small inner working angles, usually within ∼$\frac{1}{3}\lambda /D \hbox{--} 4\lambda /D$ (∼20–300 mas for Keck L'-band imaging). Applications of this technique (e.g., Tuthill et al. 2000; Lloyd et al. 2006; Monnier et al. 2007; Woodruff et al. 2008; Bernat et al. 2010) use AO along with an opaque mask containing several holes, constructed such that the baseline between any two holes samples a unique spatial frequency in the pupil plane. A key feature of this technique is its ability to sample the "closure-phase" quantity between any three baselines (e.g., Baldwin et al. 1986; Haniff et al. 1987). While the effective transmission of the telescope is reduced by ∼90%–95% due to the mask, the effectiveness of NRM is limited primarily by the ability to calibrate the point-spread function. Hence, the importance of measuring closure phases using carefully chosen calibrator stars exceeds the need for gathering additional flux. Assuming the aperture holes are small relative to the characteristic size of any atmospheric turbulence, and in the regime where the AO system is providing overall phase stability, the closure-phase quantity is largely unaffected by atmospheric turbulence. Under good conditions, this technique can achieve L'-band contrasts of 10²–10³. This technique is particularly well suited for studies of stellar multiplicity and the brown dwarf desert (e.g., Kraus et al. 2008; Ireland & Kraus 2008), or detecting giant planets orbiting young stars (≲50–100 Myr).

We imaged the HR 8799 system using NRM operating at L' band (3.76 μm) on the nights of UT 2009 August 5 and 6 using AO and the NIRC2 infrared camera on the Keck II telescope at Mauna Kea. While no seeing measurements were made, non-NRM observations obtained each night verified that the AO system was able to return apparently diffraction-limited images at the K band. An observing sequence consisted of observing a star in both the upper left and lower right quadrants of the NIRC2 detector with the Keck nine-hole aperture mask (see Figure 1, left panel). At each detector position, we obtained 15 images with 20 s exposures. Nine and ten such 30-image sequences of HR 8799 were obtained on the first and second nights, respectively. Observations of a calibrator star were obtained using a similar 30-image sequence in between each of the HR 8799 target sequences, with the calibration star interferogram placed in the identical manner on the array. A different calibrator star was observed in between each HR 8799 sequence. The HR 8799 and calibrator star observations, plus observing overheads, required ∼4 hr on each night. We selected these calibrator stars from the compilation of stars with stable radial velocity measurements by Nidever et al. (2002), who found them to have root mean square (rms) variations of <0.1 km s⁻¹ over an interval of ∼10 years; this criterion was meant to select against binary systems that would not be suitable for calibration. All calibrators were selected to be near HR 8799 on the sky (ρ ≲ 15°) and to have similar optical V magnitudes (to obtain similar AO correction) and similar or brighter near-infrared K magnitudes (to match or exceed the signal to noise in the HR 8799 masking data). A summary of the observations is presented in Table 1.

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To find the contrast limits of our data, we first added a calibration error in quadrature to uncertainties estimated directly from the scatter in the data so that the chi-squared for a null model with no companion was equal to the number of measured closure phases. We then scaled the chi-squared value by the ratio of the total number of linearly independent closure phases to the total number of closure phases (28/84) for the purpose of standard least squares fitting, which assumes independent measured quantities. We have found this technique to be nearly equivalent, but much simpler than the detailed estimation of covariance matrices as detailed in Kraus et al. (2008). We then simulated 10⁴ data sets with closure-phase standard deviations that matched these modified uncertainties. For each simulation, we found the best contrast at each value of separation (searching over position angle) and assigned the 99% confidence limit to the contrast where 99% of the simulations had no best-fit companion above this limit. When fitting to the actual data using a grid search, we also found no tentative solutions above this limit, therefore, we are reporting a null result.

Figure 2 shows our L'-band detection limits achieved with the two nights of Keck NRM data. In Figure 2, we show the brightnesses and positions for the four planetary mass companions discussed in Marois et al. (2008, 2010). The HR 8799 "d" and "e" companions are within the angular range probed by our NRM observations. Both components are approximately ΔL' ∼ 9.3 mag fainter than the star, while our observations achieve ΔL' ∼ 7.78 and ΔL' ∼ 7.74 at these orbital separations and are unable to detect these companions. However, we are able to probe much closer in to the host star than these separations. We achieve our best contrast of 7.99 mag at the L'-band diffraction limit of the Keck telescopes, corresponding to a 3 AU projected orbital separation for HR 8799. This orbital separation is comparable to the 2–4 AU ice line boundary for a mid-A star (Kennedy & Kenyon 2008) in the 3–5 Myr time frame for the formation of gaseous giant planets.

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To convert the contrast limits to constraints on companion masses, we used the models of Baraffe et al. (2003) along with the Hipparcos distance of 39.4 pc (van Leeuwen 2007). These models were chosen to maintain consistency with Marois et al. (2008, 2010) as well as to provide ease of comparison with other studies. We assume an age of 30 Myr, which is consistent with the 20–150 Myr age assigned to this system by Moór et al. (2006) as well as the two age regimes (30⁺²⁰₋₁₀ and 60⁺¹⁰⁰₋₃₀ Myr) discussed in Marois et al. (2010). Moór et al. (2006) assigned an age of 20–150 Myr to the HR 8799 system. In addition, there is evidence that the system may be a member of the Columba moving group, and hence has an age of 30 Myr (Torres et al. 2008; R. Doyon 2010, private communication; Zuckerman et al. 2011). Moya et al. (2010), however, suggest the system may be as old as 1 Gyr. For consistency with Marois et al. (2008, 2010), we adopt an age of 30 Myr.

Table 2 summarizes the sensitivity limits to companion masses for an assumed age of 30 Myr. At a separation of 3 AU, we place an upper limit of 11 M_Jup to any companion, with a comparable sensitivity outward to 24 AU. Interior to 3 AU, we can place upper limits to additional companions of 13 M_Jup and 60 M_Jup at 2 AU and 1 AU, respectively. Our measurements are also able to probe to sub-AU levels in the system placing an upper limit mass of ∼80 M_Jup at 0.8 AU. For an age of 100 Myr, the masses of the currently known exoplanets would be estimated at 9–14 M_Jup, and our sensitivity at 1, 2, and 3 AU shifts to 80, 30, and 22 M_Jup, respectively.

Achieving very small inner working angles (10–250 mas) corresponding to projected orbital separations of a few AU will be crucial for the future ground- and space-based characterization of the circumstellar regions around young stars. Reaching appreciable contrast at such small inner working angles will allow significant sensitivity to objects orbiting much closer to the host star. Perhaps more importantly, the small inner working angles will allow observers to probe solar system scales of more distant targets, thereby increasing the number of available target stars, including those young stars in the nearest star-forming regions (Kraus et al. 2008). Though traditional high-contrast techniques such as dual imaging polarimetry (e.g., Oppenheimer et al. 2008) can achieve significant contrasts of ∼8–10 mag within 500 mas (e.g., Hinkley et al. 2009), the success of these techniques largely depends on a high polarization signal exhibited by the planets. However, NRM will have superior sensitivity at small inner working angles (20–300 mas) and will play a major role for ground-based high-contrast imaging of exoplanets and imaging close binaries (e.g., Lloyd et al. 2006; Hinkley et al. 2011a). Recent results suggest that ∼7.5 mag of K-band contrast at Keck has been achieved for a K = 8 star in three hours of observation (A. Kraus 2010, private communication).

The science return from NRM will be enhanced when the imaging science camera has multi-wavelength capabilities such as an integral field spectrograph (IFS). This has already been achieved with the Project 1640 IFS and coronagraph at Palomar Observatory (Hinkley et al. 2008, 2011b; N. Zimmerman et al. 2011, in preparation), and will be integrated with the Gemini Planet Imager coronagraph (Macintosh et al. 2008; Soummer et al. 2009). Furthermore, aperture masking will continue to be an efficient tool for characterizing stellar multiplicity. As several authors have suggested, more massive stellar systems may be more efficient at producing faint stellar companions (Dodson-Robinson et al. 2009; Kratter et al. 2010). Aperture masking will play a crucial role to supplement ongoing surveys of A star multiplicity (e.g., Hinkley et al. 2010; Zimmerman et al. 2010).

In the more distant future, NRM will play a prominent role for the planet-finding efforts of JWST (Beichman et al. 2010), significantly improving on the sensitivity presented in our study. The Tunable Filter Instrument camera which is integrated with the Fine Guidance System on JWST (e.g., Sivaramakrishnan et al. 2010; Doyon et al. 2010) will incorporate non-redundant aperture masking capabilities. Recent simulations indicate a limiting delta magnitude of ∼9.5 for integration times of a few hundred seconds in the JWST filters corresponding to the L' and M bands. These limits will provide sensitivity to objects of a few Jupiter masses for systems at ages of 10–100 Myr (Sivaramakrishnan et al. 2010).