THE GEMINI NICI PLANET-FINDING CAMPAIGN: THE ORBIT OF THE YOUNG EXOPLANET β PICTORIS b

β Pic is a young (∼12–21 Myr; Barrado y Navascués et al. 1999; Zuckerman et al. 2001; Binks & Jeffries 2014), nearby (19.44 pc; van Leeuwen 2007) A6 star that hosts one of the most prominent known debris disks (e.g., Smith & Terrile 1984; Wahhaj et al. 2003; Weinberger et al. 2003; Golimowski et al. 2006; Lagrange et al. 2012a). The disk midplane is warped, with a 4° offset between the inner warped disk and the outer main disk, suggesting a giant planet influencing the disk (Mouillet et al. 1997). This planet β Pic b was first detected in data from 2003, and the planet reappeared on the other side of the star in 2009 (Lagrange et al. 2009, 2010). β Pic b is one of the first planets to be directly imaged and has the smallest projected physical separation of any imaged planet to date. With a contrast of 9 mag at K_S band and a current projected separation of ∼04, the planet is challenging to detect even with state-of-the-art adaptive optics.

Orbital properties of directly imaged planets can encode clues to their formation. The eccentricities of these planets, for example, may trace migration or planet–planet interactions (e.g., Takeda & Rasio 2005; Jurić & Tremaine 2008; Wang & Ford 2011). β Pic b represents the longest-period exoplanet whose full orbital parameters can be determined with present observations. The estimated orbital period of ∼20 yr allows us the opportunity to determine the orbit of this planet, whereas most other directly imaged planets will require many more decades of observations for a robust orbit determination. The orbital parameters of β Pic b are of particular interest since they allow us to study the relationship between the planet and the debris disk.

The Gemini NICI Planet-Finding Campaign was a four-year survey to detect extrasolar planets conducted between 2008 and 2012 (Liu et al. 2010; Nielsen et al. 2013; Wahhaj et al. 2013b; Biller et al. 2013). In addition to detecting a number of brown dwarf companions (Biller et al. 2010; Wahhaj et al. 2011; Nielsen et al. 2012), we detected the planet β Pic b at multiple epochs over the course of the Campaign. We combine these observations with new data from Magellan MagAO and previous work to determine the orbit of the planet.

VLT/NACO: Chauvin et al. (2012) present nine epochs of β Pic b astrometry from VLT NACO, between 2003 and 2011. Bonnefoy et al. (2013) present an additional epoch from 2012 January, as well as an improved orbital fit. We use the 10 astrometric observations and errors as reported in these works.

Gemini-South/NICI: We observed β Pic b with NICI at Gemini-South at four epochs between 2009 and 2012 (Table 1). Reductions were performed with the Gemini NICI Planet-finding Campaign pipeline, described in depth in Wahhaj et al. (2013a). These data are discussed in detail in Males et al. (2014), which also includes a comparison to an independent analysis of some of the data by Boccaletti et al. (2013). We find that for overlapping epochs there is good agreement between the NICI and NACO astrometry, indicating that there is no significant astrometric offset between the two instruments. In addition, NICI measurements have smaller uncertainties compared to those from NACO: the median separation and P.A. uncertainties are 0005 and 06 for NICI and 0011 and 181 for NACO. This increased precision is due to the partially transparent focal plane mask of NICI, which allows for an accurate measurement of the location of the star relative to the planet. Bonnefoy et al. (2013) note the primary source of error in their astrometry is the uncertainty in the position of the star.

Magellan/MagAO: β Pic b was observed on UT 2012 December 4 in the Y_S (0.985 μm) filter of Magellan MagAO+VisAO, and on UT 2012 December 1, 2, 4, and 7 in the 3.1 μm, 3.3 μm, L', and M' filters of Magellan MagAO+Clio2. The astrometry and photometry from MagAO+VisAO is described in detail in Males et al. (2014) and from MagAO+Clio2 in K. M. Morzinkski et al. (2014, in preparation). Similar to NICI, the Magellan MagAO+VisAO instrument has a partially transmissive focal plane mask so the primary star is unsaturated in the data. MagAO+Clio2 data in 3.1 μm, 3.3 μm, and L' were taken with long and short exposures of saturated and unsaturated data, while M' data were entirely short unsaturated exposures.

The VisAO astrometry calibration is tied to the wider field of view Clio2 camera, and the two cameras are mounted simultaneously on the same rotator so they will have some common systematics, but the observations of the planet by these two cameras are otherwise independent measurements. To calibrate the Clio2 astrometry, we observed the Trapezium Cluster in the Orion Nebula as a reference. Over the nights of 2012 December 3, 4, 6, and 8 UT, we locked the AO loop on either θ¹ Ori B or C. Stars θ¹ Ori A and E were also in the fields, as were many fainter Trapezium stars (see K. M. Morzinkski et al. 2014, in preparation for details). We compared the positions of the stars to their positions in Close et al. (2012) to derive the platescale, instrument angle, and distortion solution. We applied these solutions to our β Pic data to calibrate them. The position of the planet was then measured in the Clio2 images by a grid search over (x, y) positions.

3.1. Methods

3.2. Results

We present medians and confidence intervals for each parameter in the fixed-mass case in Table 2. The inclination angle, argument of periastron, position angle of nodes, and epoch of periastron passage have a GR statistic less than 1.01, and the other two parameters have a GR statistic less than 1.1, indicating that our posterior distributions for all parameters are reliable.

Table 2. Orbital Parameters of β Pic b

Parameter	Lowest χ2	Median	68% CI	95% CI	GR Stat.
Fixed-Mass
Semi-major axis (AU)	9.6	9.1	8.6–14.4	8.2–48.0	1.0827
Eccentricity	0.08	0.08	0.02–0.40	0.00–0.82	1.0580
Inclination angle (°)	88.8	88.9	88.2–89.6	87.4–90.4	1.0006
Argument of periastron (°)	6.5	−8	−102–85	−167–166	1.0022
Position angle of nodes (°)	211.9	211.8	211.5–212.1	211.2–212.4	1.0011
Epoch of periastron passage	2012.88	2012	2009–2019	2006–2023	1.0021
Period (yr)	22.60	21	19–41	18–251	⋅⋅⋅
Floating-Mass
Semi-major axis (AU)	83.6	24.3	9.1–75.2	8.4–96.7	1.2532
Eccentricity	0.90	0.65	0.11–0.89	0.01–0.91	1.2473
Inclination angle (°)	89.2	89.0	88.3–89.7	87.6–90.3	1.0047
Argument of periastron (°)	347.4	−16	−46–1	−133–116	1.0067
Position angle of nodes (°)	211.6	211.7	211.4–211.9	211.2–212.3	1.0115
Epoch of periastron passage	2011.52	2011	2010–2013	2006–2021	1.0012
Period (yr)	581.53	96	22–516	18–758	1.2282
Mass (M☉)	1.73	1.64	1.37–1.95	1.13–2.38	1.0012

Notes. Results from the MCMC fit to the orbit of β Pic b and orbital parameters for the lowest χ² within the 68% confidence interval from the chains (Figure 2). The final column gives the Gelman–Rubin statistic for each parameter: values closer to unity indicate a higher degree of convergence.

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Figure 1 displays the resulting marginalized posterior probability distributions for the orbital parameters and total system mass for both the fixed-mass and floating-mass cases. Figure 2 shows an example set of orbital parameters from the fixed-mass MCMC chains that has the lowest χ² within the 68% confidence region for all parameters ($\chi _\nu ^2$ = 1.38).

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Our results for the fixed-mass case show an orbit with semi-major axis of about 9 AU is favored, with inclination angle and position angle of nodes (the two angles that describe the orientation of the orbit on the sky) very tightly constrained and eccentricity mainly <0.2. Figure 3 shows covariances between some orbital parameters for the fixed-mass fit. There is a strong correlation between eccentricity and semi-major axis, with larger values of semi-major axis corresponding to more eccentric orbits. Given the presence of the disk, it is unlikely that the orbit of the planet is significantly noncircular (e ≳ 0.2), and we expect future observations to be most consistent with the shorter-period circular orbits from our MCMC chain. With a uniform prior on eccentricity, we find e < 0.15 at 68% confidence and e < 0.72 at 95% confidence. If we were to impose a prior that the eccentricity must be smaller than 0.2, we would obtain a = 8.9$^{+0.8}_{-0.3}$ AU and P = 20.1$^{+2.5}_{-1.2}$ yr, with the distributions for the other parameters about the same as in the uniform prior case. Our MCMC results find a median of the time of maximum elongation (when the projected star–planet separation reaches a maximum) of 2012.63 and 68% (95%) confidence interval between 2012.55 (2012.48) and 2012.70 (2012.79). Our Magellan epochs are after turnaround time in 99% of all orbits. So while the Magellan data represent the largest separation between star and planet in our astrometric record, our orbit fitting results indicate that maximum elongation was reached prior to these data being taken.

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Finally, we consider the floating-mass MCMC fit. Though generally less constrained than the fixed-mass fit, the posterior mass distribution (lower right panel of Figure 1) shows that the previous estimated mass of 1.75 M_☉ is well within the 68% confidence interval. While additional astrometry is required to place a more precise limit on the mass of the star β Pic, this total mass distribution of 1.6 ± 0.3 M_☉ indicates that our orbital fit and existing astrometric measurements are reasonable. Semi-major axis and period are highly correlated in our floating-mass fit, and while the chains have not converged for the semi-major axis and period individually (GR statistics of 1.2), the GR statistic for mass is 1.0012, indicating a reliable measurement of the mass. If we were to impose the prior that e < 0.2 in the floating-mass case, our mass constraints for β Pic would slightly tighten to 1.7 ± 0.2 M_☉. Similarly, the semi-major axis range would shrink from 24$^{+51}_{-15}$ AU to 9.0$^{+0.9}_{-0.4}$ AU. The minimum χ² reached in the floating-mass chain (41.64) is similar to that for the fixed-mass chain (41.67).

Crifo et al. (1997) estimate the mass of β Pic by comparing the position of the star on the HR diagram to theoretical evolutionary tracks, finding a good fit for masses between 1.7 and 1.8 M_☉. Blondel & Djie (2006) derive a similar mass, between 1.65 and 1.87 M_☉, again from evolutionary models and the HR diagram. Our dynamical mass is independent of any evolutionary model and so provides independent confirmation of the mass of the star, and indicates these previous estimates were accurate.

3.3. Comparison to Previous Fits

In order to compare the position angle of the orbit to the disk, we perform a custom reduction of our 2011 NICI data to recover the disk. We begin by removing the azimuthally averaged profile of the point spread function from the individual images, as described in Wahhaj et al. (2013a) except that the running azimuthal average used here is taken over 90 pixels instead of 30 pixels. This process removes large-scale (>90 pixels or 162) azimuthal structure from both the stellar halo and the disk. Since the β Pic disk is known to be edge-on, this procedure does not alter the disk profile significantly. After this step the disk reduction then proceeds with our standard ADI pipeline.

The signal-to-noise maps of the reduced images for the CH₄L and K_cont filters are shown in Figure 4. The north/east (NE) and the south/west (SW) extensions of the disk were considered separately. As a function of radius we fit two Gaussians to the azimuthal disk profile, taking a 20 AU width at each sampling and stepping by 1 AU. We compute the median position angles for the two sides of the outer disk (between 60 and 120 AU) of 20921 ± 005 and 2879 ± 006. The inner disk is only visible within 90 AU, and we find median values of the position angle between 60 and 90 AU of 21299 ± 007 and 3228 ± 007. These are errors in the fit only and do not include uncertainty in the direction of true north of 02, as we are concerned only with the relative offset between the orbital plane of the planet and the position angle of the disk. We present these values along with relative and absolute errors in Table 3.

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To ensure that our reduction process has not biased these measurements we simulate the disk as a series of rings given the fit to the data, and then create a simulated data set with the same set of rotation angles in our ADI data set (a total range of 42°) to model self-subtraction. The offset between the initial model and the measurements of the self-subtracted simulation was much smaller than 01, and so this effect is not the dominant source of error. Rather it is residuals from the stellar point spread function that dominate the measurement of the disk position angle.

Our P.A. measurements are consistent with the cADI two-component fit reported by Lagrange et al. (2012a), who find 2907$^{+0.20}_{-0.19}$ and 20900$^{+0.16}_{-0.15}$ for the outer disk. Our measurements of offsets between the outer and inner disk of 3.78 ± 012 (SW) and 3.49 ± 013 (NE) are also close to the Lagrange et al. (2012a) cADI value of 3.9$^{+0.\!\!^\circ 6 }_{-0.1}$. Unlike Lagrange et al. (2012a), where the position of the center of the star is uncertain, the partially transmissive focal plane mask of NICI allows us to precisely measure the star position in images of the disk.

Using our position angle for the SW disk of 20921 ± 005, our measurement of the position angle of nodes of the orbit of 2118 ± 03 is 7.4σ discrepant with the position angle of the outer disk. The inner warped disk has a position angle of 2129 ± 007, which is discrepant at the 3.2σ level. Thus, we find the planet's orbital plane is not aligned with either disk.

Currie et al. (2011) presented a preliminary orbit based on four astrometric points (the bare minimum needed for an orbit fit) and a non-MCMC method and found the position angle of nodes to be between the two disks. When we apply our MCMC method to their data we find generally larger uncertainties in orbital parameters than Currie et al. (2011) report. Using an MCMC fit to their data, we find the position angle of nodes to be 210.9 ± 09, 1.8σ greater than the outer disk P.A. and 2.2σ less than the inner disk P.A. Chauvin et al. (2012) and Bonnefoy et al. (2013) fit more data with a similar MCMC method to ours and find the orbital plane of the planet to be consistent with the inner disk (Ω = 212.6 ± 15 and Ω = 212.0 ± 11, respectively, both within 1σ of the P.A. of the inner disk). By including our higher precision astrometric data and longer time baseline, we find the position angle of nodes to be between the two disks, though closer to the inner disk.

We now consider the implications of a misalignment between β Pic b and the two disks. Our observations recall a dynamical picture of the β Pic disk recently painted by Dawson et al. (2011). If a planet on an inclined orbit (inclination i_p) is introduced into a disk of noninteracting particles with zero initial inclination, the secular theory of Laplace–Lagrange (e.g., Murray & Dermott 1999) shows us that the inclinations of the particles will oscillate about i_p, creating a cuspy disk structure with apparent inclination 2i_p in its inner regions. Our measurement that the planet's inclination is intermediate between the two observed disk planes seems to support this picture. In contrast, earlier simulations by Mouillet et al. (1997) and Augereau et al. (2001) yielded a disk coplanar with the planet.

One important assumption built into the Dawson et al. (2011) model and supported by our observations is that the planetesimals are not yet collisionally relaxed (collisional relaxation in debris disks is the gradual process by which planetesimals lose energy and exchange momentum via collisions so that the distribution of their orbits approaches a steady state), as models of structure in other debris disks have assumed (e.g., Quillen 2006; Rodigas et al. 2014). Another important assumption built into the Dawson et al. (2011) model is that the planet is introduced instantaneously, fully formed, at time zero. We infer that the β Pic disk is probably not collisionally relaxed; this inference should yield some interesting constraints on models of the collisional evolution of planetesimals in debris disks (e.g., Nesvold et al. 2013). Moreover, if the Dawson et al. (2011) model is indeed correct, it appears that the β Pic planet was introduced to its current orbit suddenly compared to the secular timescale, perhaps scattered there by another planet.

This notion begs us to ponder the role of multiple planets in sculpting the disk. In the context of their model, Dawson et al. (2011) placed severe limits on the presence of a second planet in the system disturbing the disk. In addition, Absil et al. (2013) exclude a second planet more massive than ∼5 M_Jup outside of 02 based on L' high contrast images of β Pic. But what caused the inclination of β Pic b if not an interaction with another massive planet? And how did the planetesimals respond to this interaction? These questions remain unanswered.

Finally, we consider the transit event noted by Lecavelier Des Etangs et al. (1995) in 1981 November and find very loose constraints on a transit of the planet given the available data. We search for such a transit by finding the smallest projected distance between star and planet between 2015 and 2019 and then subtract one or two orbital periods from the returned epoch for each step in our MCMC chains, choosing the epochs that are closest to 1981. We find the most recent closest approach to be at epoch 2007.44$^{+0.14}_{-0.17}$ (crossing behind the star), with the next closest approach (possible transit) to take place in 2017.59$^{+0.60}_{-0.18}$, adopting the orientation of the orbit from the RV measurements of Lagrange et al. (2012b) and Snellen et al. (2014).¹⁰ The median value for the epoch of closest approach one or two orbital periods earlier than 2017 is 1977.52, with a 68% confidence interval between 1971.07 and 1982.14 (95% confidence between 1768 and 1993, given the long tail of the posterior for the orbital period). The smallest projected distance from star to planet is less than 31 times the radius of β Pic (1.8 ± 0.2 R_☉; Di Folco et al. 2004) at 68% confidence (<51 times the radius at 95% confidence). Thus we cannot rule out a transit with the current orbital fit. Lecavelier Des Etangs et al. (1995) and Chauvin et al. (2012) speculate that the transit event may not be caused by the planet itself but rather by solid material entrained by the planet and carried in its Hill sphere. We cannot rule out this possibility either, and more data are required. We predict that the next transit will take place between 2017.41 and 2018.18 at 68% confidence (2017.27–2019.19 at 95% confidence), with a median epoch of 2017.59. Additional astrometric observations in the next few years will provide a more precise transit window and transit probability.

We have examined the orbit of β Pic b given five new epochs of data taken with Gemini/NICI and Magellan/MagAO, finding a semi-major axis of 9.1$^{+5}_{-0.5}$ AU and a period of 21$^{+21}_{-2}$ yr. The astrometric record of β Pic b is now long enough to be able to remove the assumption of the total system mass, which was needed by all previous fits to this orbit. When we solve for the mass of β Pic itself we find a value of 1.76$^{+0.18}_{-0.17}$ M_☉, consistent with the expected value of 1.75 M_☉. The position angle of nodes for our fixed-mass orbit is offset from the observed position angles of the inner warped disk (at 3.2σ significance) and from the outer disk (at 7.4σ significance), suggesting that the disk is not collisionally relaxed.

Numerous degenerate orbital solutions exist for astrometric data that show minimal acceleration during the timeframe of the observations, in particular between the semi-major axis, period, and eccentricity. Observing significant acceleration, and in particular the reversal of direction at maximum elongation, greatly reduces these degeneracies. Our orbital fit indicates that the planet has reached maximum elongation and is currently moving back toward the star, crossing to the other side of the star by ≈2018. β Pic b has been observed extensively since its reappearance in 2009 and the current window for studying the planet will remain open for just a few more years before the planet is undetectable behind the star again. Advanced planet-finding instruments such as GPI and SPHERE will likely allow for orbital monitoring of the planet closer to the star, so the time of lost contact is likely to be significantly shorter than it was between 2003 and 2009. The window for the next transit is between 2017.41 and 2018.18 at 68% confidence, and future astrometric monitoring will provide a more precise prediction to guide photometric monitoring.

We thank Jessica Lu and Adam Kraus for helpful discussions. B.A.B. was supported in part by Hubble Fellowship grant HST-HF-01204.01-A awarded by the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS 5-26555. This work was supported in part by NSF grants AST-0713881 and AST-0709484 awarded to M. Liu. The MagAO portion of this work is supported, in part, by the NASA Origins of Solar Systems (PI: L. Close). The Gemini Observatory is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil), and CONICET (Argentina). This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

Facilities: Gemini:South (NICI) - Gemini South Telescope, Magellan:Clay (MagAO+Clio2, MagAO+VisAO) - Magellan II Landon Clay Telescope