Atmospheric Characterization and Further Orbital Modeling of κ Andromeda b

2.1.1. Subaru/SCExAO+HiCIAO

2.1.2. Keck/NIRC2

Basic imaging processing—e.g., flat-fielding, dark subtraction, bad-pixel masking, distortion correction, and precise PSF registration—followed previous methods taken for SCExAO/HiCIAO data (Currie et al. 2017; Garcia et al. 2017). In the distortion correction, we used a master distortion map of SCExAO+HiCIAO, which was made by observing a globular cluster of M15 (Currie et al. 2017). Registered images were visually inspected to identify a few with poorer AO correction and/or data transfer errors from HiCIAO (e.g., sporadic NaN stripes in one or two channels).

For PSF subtraction of the HiCIAO data sets, we used a slightly modified version of the locally optimized combination of images (LOCI) pipeline (Lafrenière et al. 2007), inverting the covariance matrix in LOCI using a truncated singular value decomposition (SVD), as in A-LOCI (Currie et al. 2012a, 2019b). As κ And b is visible in the raw H-band data, we opted for conservative settings for both filters: a rotation gap of 0.75 λ/D, an optimization zone from which we constructed a weighted reference PSF of 300 PSF footprints, and a light SVD cutoff of 10⁻⁷.

For the Keck/NIRC2 coronagraphic data, basic image processing followed previous methods (e.g., Currie et al. 2012b). Briefly, after applying corrections for linearity, dark subtraction, and flat-fielding, we registered the images to a common center using the stellar PSF seen through the partially transmissive mask. For PSF subtraction, we used A-LOCI with local masking and an SVD cutoff of 10⁻⁶.

Our data reduction detected κ And b with S/Ns of ∼10 in the Y band and ∼130 in the H band (see Figure 1) for the 2016 SCExAO+HiCIAO data sets and S/N ∼ 14 in the Keck/NIRC2 data. We also detected κ And b with an S/N of >80 in the 2015 engineering data (see Figure 2). Compared to Carson et al. (2013), who measured an S/N ∼ 20–25 in the H band with the Subaru/HiCIAO+AO188, our H-band data yielded higher-S/N detections. Hinkley et al. (2013) used Project 1604/Palomar integral field spectroscopy to extract κ And b's spectrum in the YJH bands. Over the five channels encompassing the Y band, the mean ratio of their flux-to-flux uncertainty is ∼3, where uncertainties are drawn from the local properties of the noise. Assuming no contribution from systematic uncertainties and an S/N gain from median-combining channels scaling with the square root of the number of channels, their band-integrated S/N should be ∼6.5 or less. Thus, our Y-band data likely detect κ And b at a higher S/N. The H-band detections are comparable in significance to that achieved with high-quality SCExAO+CHARIS data from Currie et al. (2018) due to our data's greater depth and field rotation.

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We also calculated contrast limits for κ And data sets (see Figure 3). We convolved the final images, which were normalized with exposure times, and extracted noise profiles from them. Figure 3 shows the calculated 5σ contrast limits of SCExAO+HiCIAO observations. The H band achieved a better contrast level than the Y-band observation; the 5σ contrast limit is 1.5 × 10⁻⁴, 2.8 × 10⁻⁵, and 2.7 × 10⁻⁶ at 025, 05, and 1'', respectively. At ρ ∼ 03–075, the planet-to-star contrasts for the SCExAO/CHARIS broadband data in Currie et al. (2018) are about a factor of 2–5 better than those reported here for SCExAO/HiCIAO at the H band due to the CHARIS data's better PSF quality and utilization of ADI+SDI for PSF subtraction. Similarly, the SCExAO/HiCIAO H-band contrasts in Kühn et al. (2018), which were taken on a different date, 2016 November 12 UT, are typically a factor of 2 deeper, likely due to usage of the vector vortex coronagraph.

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We used aperture photometry for measuring photometry and PSF fitting for estimating FWHM and astrometry in this section. For absolute photometric calibration, we primarily relied on unsaturated images of other stars obtained through well-calibrated neutral density filters. As a photometric reference of the Y-band image to calibrate both κ And A and κ And b, HIP 118133 (Y-band magnitude of 6.60 ± 0.06 mag; Pickles & Depagne 2010) was used. HIP 118133 was observed immediately after κ And and at a comparable airmass.²⁰ The implied Y-band photometry for κ And A (4.28 ± 0.09) is consistent with the primary having (near-)zero infrared colors, as expected for a B9V star (e.g., Currie et al. 2010; Pecaut & Mamajek 2013).

We also checked our H-band photometric results. Although unsaturated frames of κ And in the H band were taken at both epochs (2015 and 2016), those data used the ND0.1 filter, which was reported to have a high uncertainty in its transmission efficiency. Therefore, we used another set of unsaturated images of HIP 79977, which has an H-band magnitude of 7.854 ± 0.03 mag (2MASS; Cutri et al. 2003), for the H-band photometric reference. In the engineering run, the ND1 filter was used to take one unsaturated frame, and we used this image as the photometric reference.

To estimate the throughput correction for κ And b needed to compensate for signal loss due to PSF subtraction, as well as the astrometric biasing, we injected synthetic companions that are made from an unsaturated PSF of the central star observed through the neutral density filter in each bandpass or (for Keck) with an intensity distribution approximating the star as seen through the partially transmissive coronagraph mask. In the H and K_s bands, we calculated the throughput correction and astrometric biasing over a FWHM-wide area. In the Y band, we adopted a smaller aperture (4.4 pixels or 37 mas), corresponding to most of the PSF core and the apparent PSF size of the real κ And b. To confirm the reliability of our PSF model at the Y band, we verified that the FWHM of the partially annealed synthetic planet PSF matches that of the real κ And b. The signal throughput in each case is high—above 80% for all data sets and ∼90% for the Keck/NIRC2 data.

Table 3 shows our photometric results for the κ And system. Our H-band photometry agrees with that derived from SCExAO/CHARIS (H = 15.01 ± 0.07; Currie et al. 2018) and earlier AO188/HiCIAO photometry from Bonnefoy et al. (2014b; H = 14.95 ± 0.13). Because the photometric uncertainty with our data is higher than that with the SCExAO/CHARIS results, we use only our Y-band result to update the photometric parameters of κ And b for atmospheric analysis. Table 4 summarizes photometric results of κ And b. The H-band data are used for astrometric analysis. Table 5 summarizes the astrometric results of our data sets, as well as previous studies.²¹ As mentioned above, we calculated astrometric biases when we estimated throughputs by injecting fake sources, which is included in the errors. The major contributors for the astrometric errors are the intrinsic S/N of the detection and the uncertainty in the centroid position. In case of the Keck data set, we have 0003 errors in x- and y-position measurement of κ And b and half a pixel uncertainties of in the centroid measurement, which resulted in 0006 errors in Table 5. The centroid was measured by using the PSF seen underneath the partially transmissible coronagraph mask, which gave a better S/N for κ And b than estimating the centroid using the halo outside the mask. Orbital fitting using these results is described in Section 5.

We first investigated a color–magnitude diagram of κ And b by comparing it to other low-mass objects with precise parallaxes and various gravities reported in Liu et al. (2016). The Liu et al. (2016) sample includes 67 MLT dwarfs with new, precise parallaxes and another 35 with literature parallaxes and near-infrared photometry. Drawing from the Liu et al. (2016) polynomial fits for absolute magnitudes versus spectral for different gravity classes, we constructed linear fits to magnitudes and colors in Y/Y − K space.

Figure 4 shows how κ And b's color–magnitude diagram position fits within the context of other substellar objects. The companion appears redder than a typical field-gravity L object (red), in between these colors and those for a typical low-gravity L object (yellow) at its Y-band luminosity. Moreover, its location appears on the locus (gray dashed line) connecting the L2 field and low surface gravity objects. The uncertainty of the Y − K color of κ And b and the amplitude of the scatter of objects about the polynomial fits from Liu et al. (2016) preclude us from excluding a high- or low-gravity scenario at a significant level using only the Y- and K-band luminosities.

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Second, we use a large sample of substellar objects with different spectral types and gravity classifications to provide a context for κ And b's near-infrared colors. We compiled a library of 2011 M-, L-, and T-dwarf spectra drawn from the SpeX Prism library²² (Burgasser 2014), IRTF Spectral Library²³ (Cushing et al. 2005), Montreal Spectral Library²⁴ (e.g., Gagné et al. 2015; Robert et al. 2016), and the sample of young ultracool dwarfs presented in Allers & Liu (2013). We do not incorporate the library of young, low-gravity objects presented in Bonnefoy et al. (2014a) and used by Currie et al. (2018) in their analysis of κ And b, as the SINFONI spectra do not extend into the Y band and thus cannot be compared to the new photometry presented in this work. The spectral types were obtained from a number of literature source and are given for a number of sources highlighted in the remainder of this section. We preferentially used the near-infrared spectral type if both an optical and a near-infrared classification were available. Gravity classifications for a subset of the objects were also obtained from the literature, using either of the schemes outlined by Kirkpatrick (2005), Kirkpatrick et al. (2006), Cruz et al. (2009; α, β, γ, δ in descending order of surface gravity), or Allers & Liu (2013; fld-g, int-g, vl-g, similarly). Both of these classification schemes share three categories: surface gravity indicators consistent with those observed in old field dwarfs (α, fld-g), intermediate surface gravity (β, int-g), and a very low surface gravity observed for substellar objects in nearby young moving groups (γ, vl-g). The fourth classification, δ, was defined by Kirkpatrick (2005) for objects that exhibit stronger gravity-sensitive features than seen for those classified as γ/vl-g.

We computed synthetic Y_HiCIAO, J_MKO, H_MKO, and K_s,MKO photometry for the library by convolving the spectra with the appropriate filter response curves given in Figure 14 and Tokunaga et al. (2002). Figure 5 compares κ And b's Y − J and J − K colors to library objects with different gravity classifications. The main locus of library colors extends from Y − J/J − K ∼ 0.6/0.8 to 1.3/1.5 for M5 to L3 dwarfs. Young objects with intermediate or (very) low gravity appear systematically redder in J − K, as expected from previous studies (Liu et al. 2016). The position of κ And b lies between typical L0 and L2 colors, above the positions for most field objects and overlapping with younger, lower-gravity objects.

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To assess the overall best-fitting objects among the libraries, we fit κ And b's Y-band photometry and CHARIS spectra. Library spectra were convolved and interpolated to CHARIS's wavelengths and spectral resolution, assuming a constant resolution of R = 20 across the full spectrum. We removed 20 library spectra that did not have wavelength coverage spanning the Y through K bands. A small subset of the library had H-band spectra that were truncated at ∼1.75 μm, shorter than the reddest H-band channel in the CHARIS spectrum at 1.8 μm. For these 135 spectra, we excluded this CHARIS channel from the fit and reduced the number of degrees of freedom by one when calculating ${\chi }_{\nu }^{2}$.

We computed the goodness of fit for each object by calculating ${\chi }_{\mathrm{spec}}^{2}$ from a comparison of the κ And b spectrum to the smoothed library spectra using the correlation matrix given in Currie et al. (2018) and ${\chi }_{\mathrm{phot}}^{2}$ from a comparison of the near-infrared photometry of κ And b to the synthetic photometry of the objects within the library. As we were primarily interested in comparing the spectral morphology of κ And b to the objects within the library, we computed the scaling factor to apply to the library spectrum and photometry that minimized ${\chi }^{2}={\chi }_{\mathrm{spec}}^{2}+{\chi }_{\mathrm{phot}}^{2}$. We did not incorporate the library spectra measurement uncertainty; these were typically negligible when convolved to CHARIS's resolution.

Figure 6 displays the ${\chi }_{\nu }^{2}$ distribution for M0–T0 objects in the library. Early L-type objects show a clear minimum, consistent with analyses presented in Bonnefoy et al. (2014b) and Currie et al. (2018). The exact location of the minimum differs for field and low-gravity objects; at L1 for γ/vl-g objects and L2–L3 for α/fld objects, a consequence of the redder near-infrared colors of low-gravity objects is compared to field objects of the same spectral type (e.g., Liu et al. 2016, Figure 15). This effect is also seen when comparing κ And b to the L-type standards proposed by Cruz et al. (2018), shown in Figure 7, where the best-fit low-gravity standard is L1 (${\chi }_{\nu }^{2}=1.8$) and later spectral types (L3–L4) fit far worse, while the best-fit field-gravity standards are L2–L3 and earlier spectral types (e.g., L0) fit far more poorly. This trend is consistent with that seen for synthetic spectral templates (composites of individual spectral standards for a given spectral type/gravity class; Cruz et al. 2018) in Currie et al. (2018): they found that the best-fit low-gravity template (L0_γ; ${\chi }_{\nu }^{2}\sim 1.26$) is three subtypes earlier than the best-fit field-gravity template (L3; ${\chi }_{\nu }^{2}\sim 1.51$).

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Of the objects within the complete library, the best fit was 2MASS J11480096–2836488 (${\chi }_{\nu }^{2}=1.2$), previously classified as an L1 intermediate-gravity member of the 10 Myr (Bell et al. 2015) TWA moving group (Gagné et al. 2015, 2018) and an isochronal mass of ∼8 M_Jup (Gagné et al. 2015). While the S/N of the spectrum for this object is lower than the typical library spectrum, the uncertainties are comparable to those of the spectrum of κ And b when degraded to the same resolution. Good fits were also found to 2MASS J01174748–3403258 (${\chi }_{\nu }^{2}=1.3;$ previously classified as L1 γ) and to 2MASS J02055138–0759253 and ULAS J230538.10+052407.2 (${\chi }_{\nu }^{2}\,=1.2$ and 1.3), which previously were unclassified or classified as being field-gravity L2 dwarfs. In total, 36 objects have a ${\chi }_{\nu }^{2}\lt 1.7$ (95% confidence level) with the following previous classifications: one L0 (vl-g), five L1 (two int-g, three vl-g), 22 L2 (11 without classification, eight fld-g, two int-g, one vl-g), four L3 (three without classification, one fld-g), and four L4 (two without classification, one fld-g, and one int-g). For reference, the complete library contains 656 objects between L0 and L4: 381 without classification, 112 fld-g, 80 int-g, and 81 vl-g.

To further investigate the nature of the four best-fit objects, we separately estimated spectral types using the derived gravity classifications following the spectral index–based methods in Allers & Liu (2013): i.e., the H₂0, H₂0-1, H₂0-2, and H₂0-D indices for spectral typing and Fe_z, VO, KI_J, and H_cont for gravity scoring. We nominally box-car smooth the spectrum using a window size of three spectral channels and explore the results obtained with different windows. Our analysis recovers the previous classification for 2MASS J01174748–3403258 (L1 γ). However, it favors reclassifying 2MASS J02055138–0759253 and ULAS J230538.10+052407.2 as L2 β objects (gravity scores 1111 and 1120), respectively; Banyan-Σ suggests that 2MASS J02055138–0759253's kinematics may be consistent with membership in the 40 Myr old Columba association, depending on its parallax. Given the noisiness of 2MASS J01174748–3403258's spectrum, we cannot derive a gravity score from Fe_z, VO, and KI_J. However, its H_cont index (1.05 ± 0.05) suggests a low gravity and possible reclassification to L1 γ. It is likely that the other well-fitting objects previously given a field classification or no classification at all are in fact low-gravity objects.

To investigate the constraining power of our new Y-band photometry, we compared the χ² for each object with and without this measurement. For objects between L0 and L1, we typically find a larger Δχ² for field-gravity objects (median Δχ² of 4.1 compared to 1.2), indicating that the Y-band photometry is more consistent with that of a low-gravity object over this range of spectral types. For later spectral types, this is reversed, with Δχ² typically being larger for low-gravity objects between L2 and L5 (median Δχ² of 6.9 compared to 0.7). This is a consequence of the red color of low-gravity objects; an object with a given Y-band flux (or Y − J color) either has lower gravity and an earlier spectral type or higher gravity and a later spectral type.

Preference for a low surface gravity for κ And b can also be inferred using the gravity-sensitive spectral indices defined by Allers & Liu (2013). While these indices cannot be computed directly given the low resolution of the spectrum, they can be computed for the objects within the library with the most similar spectra to κ And b. Two of these indices are plotted in Figure 8, showing that the best-fit objects are more consistent with the population of low-gravity objects and (some) intermediate-gravity objects than the median of the field-gravity sequence.

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Our atmospheric modeling favors 1700–1900 K, a surface gravity of log(g) ∼ 4.0–4.5, and a radius of 1.3–1.6 R_Jup with a cloudy atmosphere. The best-fit model (the Drift-Phoenix model) is consistent with ≤40 Myr and <20 M_Jup in the evolutionary model. The object κ And b is a good laboratory for understanding the formation and an early stage of evolution of gas giant/low-mass brown dwarfs.

We reconfirmed that κ And b is likely to have a larger eccentricity and semimajor axis than GJ 504 b (Bonnefoy et al. 2018) and HR 8799 b, c, d, e (Wang et al. 2018). It may have experienced a strong excitation of the eccentricity by gravitational interactions between neighboring planets, such as planet–planet scattering. Planetesimal accretion and accumulation of disk gas cannot pump up the eccentricity of a planet's orbit up to ∼0.8. In fact, a wide orbit of κ And b cannot be reconciled with an in situ core accretion scenario. Although the minimum core mass for gas giant formation requires only a few Earth masses at ∼100 au (Piso & Youdin 2014), the core growth at 100 au takes a much longer time than the estimated age of the κ And system. Bonnefoy et al. (2014b) proposed another possible formation scenario for κ And b (i.e., a hot-start model); it may have formed via gravitational instability at almost the same orbital separation as the current location.

It may also be possible that κ And b was scattered to its current location (e.g., Marzari & Weidenschilling 2002; Ford & Rasio 2008; Nagasawa et al. 2008). Since the age of κ And A was estimated to be ∼40–50 Myr, dynamical instability was likely to have occurred if three or more giant planets coexisted in an outer region. An outwardly scattered planet, namely κ And b, can remain on a highly eccentric orbit because of less efficient/no dynamical friction damping of the eccentricity (Muto et al. 2011). To investigate this scenario, we consider that a planet–planet scattering event occurred after disk dispersal. The planet–planet scattering requires close encounters of planets, which are easily induced in a system of three or more planets. The behaviors of planet–planet scatterings that are involved in more than three planets need to be numerically examined by N-body simulations. In this study, we discuss a simple case with three giant planets. We assume (i) three massive gas giants/brown dwarfs are on nearly coplanar, circular, and tightly packed orbits around κ And; (ii) one of them is ejected from the system; (iii) κ And b is the outer planet of two remaining objects; (iv) the ejected planet has a smaller mass than κ And b (as shown by N-body simulations of planet–planet scatterings; Marzari & Weidenschilling 2002); and (v) the three objects have similar radii. Under these assumptions, we infer the mass and orbital elements of an unseen (potential) planet in the κ And system.

After dynamical instability happened, the eccentricity of an outer remaining object (κ And b) was determined by

$$\begin{eqnarray}&&{e}_{\mathrm{out}}\simeq \displaystyle \frac{{m}_{\mathrm{in}}}{{m}_{\mathrm{out}}}\times \sqrt{\displaystyle \frac{{m}_{\mathrm{out}}+{m}_{\mathrm{eje}}}{{m}_{\mathrm{out}}+{m}_{\mathrm{in}}}},\end{eqnarray} \tag{ 1 }$$

where m corresponds to the mass of an object and the subscripts "in," "out," and "eje" correspond to the inner, outer (κ And b), and ejected objects, respectively (Ida et al. 2013). Using Equation (1) and the mass and eccentricity of κ And b, i.e., m_out = 13 M_Jup and e_out = 0.77 ± 0.08, we can estimate the mass of the inner object as a function of the mass of the ejected object (see Table 8). We note that the error bar shown in Table 8 comes from only the error of eccentricity ExoSOFT provided. Estimating κ And b's mass largely depends on the age and evolutionary models, and we do not include this error. With these assumptions, the potential inner companion (planet) has a mass of m_in ≳ 10 M_Jup. We note that Equation (1) is not applicable to the case where κ And initially had four or more giant planets in an outer region because the orbital evolution of such a system cannot be described analytically any longer.

Table 8.  Mass Estimation of a Potential Inner Companion around κ And

Ejected Object [MJup]	Inner Object [MJup]
2	${13.2}_{-1.7}^{+1.9}$
4	${12.2}_{-1.6}^{+1.7}$
6	${11.3}_{-1.5}^{+1.6}$
8	10.6 ± 1.4
10	${10.0}_{-1.3}^{+1.4}$

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Since no point source other than κ And b is seen in Figure 1, we discuss the mass limit of a detectable planet around κ And. The latest SCExAO+CHARIS observation reached a better contrast limit in the wavelength-collapsed image (Currie et al. 2018): ∼15, ∼8–10, and ∼3–5 M_Jup at 12.5, 25, and 50 au, respectively, using a hot-start model (COND03; Baraffe et al. 2003). With the deepest contrast limits around κ And, SCExAO+CHARIS observations can suggest that an inner companion can be located at ≲25 au.

Combining RV methods with direct imaging enables us to give stringent constraints on the orbital parameters of a substellar-mass companion (e.g., Bonnefoy et al. 2018; Calissendorff & Janson 2018). The lack of absorption lines obscures precise RV measurements of massive stars such as κ And A (∼B9 star) due to high temperature and rapid rotation. In fact, archival RV observations reported large errors, >1 km s⁻¹ (Hinkley et al. 2013; Becker et al. 2015). Host-star astrometry is also useful, but estimating an accurate acceleration of such a bright star by a combination of Gaia and Hipparcos telescopes cannot avoid systematic errors between these telescopes (Brandt 2018). Accumulating Gaia data sets will possibly help to measure the dynamical mass of κ And b in the future.

Spectral features of substellar-mass objects within ∼1–5 μm depend on molecular absorption, such as FeH, H₂O, KI, CH₄, and CO. Effective temperature, surface gravity, or C/O ratio parameters affect the IR spectrum (e.g., Sorahana & Yamamura 2012, 2014). Our study uses only photometry and low-resolution spectroscopy, which can induce degeneracy between T_eff and log g and the best-fit objects for the field-gravity objects in Figure 7. Although a precise determination of the gravity of κ And b will require higher spectral resolution observations, our measurements demonstrate that the object likely has a low surface gravity when considering the age of the system, consistent with the planetary mass predicted from a comparison with evolutionary models (e.g., Currie et al. 2018). For future work, as introduced in Currie et al. (2018), higher-resolution spectroscopy helps to investigate κ And b's atmosphere in detail. Subaru/CHARIS has another spectroscopic mode with high resolution (R ∼ 65–75) in the J, H, and K bands.²⁵ Keck/OSIRIS could extract HR 8799 b's spectrum with higher resolution (R = 4000; Barman et al. 2015; Petit dit de la Roche et al. 2018). A mid-spectral-resolution integral field unit combined with AO has the capability to extract the detailed spectrum and investigate the atmospheric/evolutionary mechanisms of κ And b, as mentioned in Section 3.1. Furthermore, mid-IR (MIR) wavelength photometry/spectroscopy will also provide useful information. The James Webb Space Telescope (JWST)/MIRI is expected to obtain untouched atmospheric parameters of exoplanets at MIR, such as NH₃, CH₄, H₂O, CO₂, and PH₃ (Danielski et al. 2018). Combining these follow-up observations will provide improved models for κ And b.

We also investigate the possibility of detecting a potential inner planet. The RV and host-star astrometry are more sensitive to close-in planets than direct imaging. However, as mentioned in Section 6.1, it is difficult for these methods to search for inner planets around κ And. As we could not constrain an inclination of the potential inner planet, transit observation is almost a blind search. Future high-contrast imaging instruments with a better contrast level and inner working angle, e.g., the Thirty Meter Telescope (TMT), will help to search for inner planets and promote orbital evolution mechanisms of κ And b. Continuing direct imaging with current ground-based telescopes also helps to add further plots of κ And b for better orbital fitting.