The Warm Neptunes around HD 106315 Have Low Stellar Obliquities

We observed a partial spectroscopic transit of HD 106315c on 2018 March 01 with the Magellan Inamori Kyocera Echelle (MIKE; Bernstein et al. 2003) on the 6.5 m Magellan Clay telescope, located at Las Campanas Observatory, Chile. To achieve the highest spectroscopic resolution possible, the observations were performed with the 035 slit, yielding a resolution of $\lambda /{\rm{\Delta }}\lambda \equiv R=65000$ in the red arm of the spectrograph (4900–10000 Å) and R = 85000 in the blue arm (3200–5000 Å). A total of 81 observations were made over the time period of 03:03–09:08 UTC (covering orbital phases 0.997 to 1.009, with the transit being from phase 0.9953 to 1.0047), with the target staying below airmass 1.7, and seeing of ∼1'', throughout the observations. Each observation was a 200 s integration in the blue and red cameras. Wavelength calibration is provided via ThAr arc lamp exposures taken every ∼30 minutes. Flat field calibrations were obtained in the afternoon via a quartz lamp and a diffuser. The observations were reduced using the Carnegie CarPy package (Kelson et al. 2000; Kelson 2003).

To measure the planetary transit signal, we derive stellar line profiles for each observation via a least-squares deconvolution technique against a synthetic spectral template (Donati et al. 1997). A non-rotating infinite resolution template matching the spectral classification of HD 106315 is synthesized via the SPECTRUM code (Gray & Corbally 1994) using the ATLAS9 atmosphere models (Castelli & Kurucz 2004). The stellar line profile, derived using the deconvolution technique, is the kernel that convolves the synthetic template to the observation and contains contributions from the stellar rotational broadening, non-rotating broadening effects such as macroturbulence, and broadening due to the instrument profile. To derive a high signal-to-noise broadening profile for each spectrum, we perform deconvolutions over individual orders spanning 4900–6200 Å in wavelength, and then weighted-average the resulting line profile kernels based on the signal-to-noise of the derived line profiles from each order.

2.1.1. Correction of Instrument Profile Variations Via Telluric Features

Since MIKE is a slit-fed spectrograph, the instrumental line spread function is subject to variations induced by the target star's position on the slit. As the star "wobbles" on the slit due to variable seeing and guiding errors, the spectroscopic instrument profile changes in shape and velocity. In addition, thermal and pressure fluctuations can also induce changes in the instrument profile. These variations traditionally prohibit slit-based spectrographs from achieving radial velocity precision of better than ∼200 m s⁻¹ without additional corrections (Figure 2), and in our case completely wash out the spectroscopic signal of a 1 mmag planetary transit. Similar instrument profile variations were discussed in Albrecht et al. (2013) regarding the Doppler tomographic detection of Kepler-25c. To correct for these variations, we take inspiration from early precise radial velocity spectroscopists and make use of the telluric water features to correct for the instrument profile variations (Griffin 1973; Griffin & Griffin 1973).

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To correct for instrument profile variations during the transit, we search for a kernel that convolves the instrument profile of each observation to that of a template spectrum. The instrument profile of each observation is assumed to be the line profile of the telluric absorption features, derived from a least-squares deconvolution over the unsaturated telluric water features at 7900–8100 Å and 7000–7100 Å against an artificial R = 10⁶ template synthesized with the ESO SkyCalc Sky Model Calculator (Moehler et al. 2014). We then choose the broadest instrument profile during the night as the template, and fit for an asymmetric Gaussian kernel that would convolve the instrument profile of each observation to that of the template. The asymmetric Gaussian kernel is parameterized by two width terms (σ_left, σ_right), a height scaling factor, and a velocity offset. The kernel parameters are fitted for with a Markov chain Monte Carlo process, using the module emcee (Foreman-Mackey et al. 2013). At each iteration, the trialed kernel is convolved with the telluric profile, and the resulting "corrected" profile is compared against the template profile, with the goodness of fit used to maximize the likelihood. The best-fit asymmetric Gaussian kernel is then convolved with the stellar broadening kernel. This correction removes the large point-to-point "jumps" in the instrument line profile and associated velocities, but a smoothly varying trend remains, possibly due to intrinsic variations in the telluric lines over the night as a function of water content and observational airmass. Since we do not expect to observe any velocity variation during the transit within our detection limits, we shift each observed stellar line profile to rest by fitting for their velocity variations with a fourth-order polynomial. The telluric profiles and corrections are derived using spectra from red arm of MIKE, and the same corrections are applied to spectra from both the blue and red arms. The velocities derived from the stellar line profiles before and after the telluric and polynomial corrections are plotted in (Figure 2), and the line profile variations, as well as the telluric correction, are shown in Figure 3. We note that at times the telluric lines do not represent the instrument profile well, and as such, the velocity and line profile corrections we apply exhibit systematic offsets. These correction imperfections are labeled in Figure 2 and correspond with poorly corrected line profile residuals in Figure 3, near phase 0 and phase 0.008.

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One full transit of HD 106315c was obtained with the Tillinghast Reflector Echelle Spectrograph (TRES; Furesz 2008), on the 1.5 m telescope at the Fred Lawrence Whipple Observatory, Arizona, USA. TRES is a fiber-fed echelle spectrograph with a wavelength coverage of 3900–9100 Å, spanning 51 echelle orders at a resolution of R = 44000. A total of 36 observations were obtained on 2017 April 20. Each observation consists of three consecutive exposures, totalling 450 s integration time, combined to reduce the impact of cosmic rays. Wavelength solutions are provided by ThAr lamp exposures that bracket each observation. The observations are reduced as per Buchhave et al. (2010).

The line profile analysis of the TRES transit largely follows the process described in Zhou et al. (2016a). Line profiles are derived from order-by-order least-squares deconvolutions over 34 orders spanning the spectral range 3900–6250 Å. The spectral template used in the convolution is the same as that used for the MIKE analyses, generated with the ATLAS9 non-rotating synthetic templates. TRES is a fiber-fed echelle spectrograph typically capable of measuring radial velocities at the 10 m s⁻¹ level (Quinn et al. 2014), and as such, no telluric corrections were necessary in the processing of the TRES observations. The resulting line profile variations measured by TRES are shown in Figure 4.

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In addition to the full transit observed on 2017 April 20, 30 other TRES observations were obtained of HD 106315. These included series of observations taken near transit on 2017-03-09 that were obtained in poor conditions, and not used in the Doppler tomographic analyses, as well as a set of spectra taken out of transit presented in Rodriguez et al. (2017). These observations are used in the line broadening profile analyses described in Section 2.3.1.

Transits of HD 106315c were observed with the High Accuracy Radial Velocity Planet Searcher (HARPS; Mayor et al. 2003) on the ESO 3.6 m telescope at La Silla Observatory, Chile. HARPS is a fiber-fed echelle spectrograph with a spectral resolution of R = 115000, and a wavelength coverage of 3780–6910 Å. Two transits were observed with HARPS: one on 2017 March 9 consisting of 75 exposures with 350 s integration times, and one on 2017 March 30, consisting of 47 exposures with 500 s integration times. On both nights, the observations covered the entire transit events. The reduced two-dimensional (2D) echelle spectra were obtained from the public ESO archive.

Line broadening kernels from the HARPS observations were derived via a least-squares deconvolution, similar to that performed on the MIKE observations. The spectra were deconvolved against a set of ATLAS9 non-rotating spectral templates over the spectral range of 3980–5490 Å, yielding a series of line broadening kernels. Because HARPS is a highly stablized fiber-fed spectrograph, the line profiles were free of systematic variations. The line profile variations measured by the combined HARPS observations are shown in Figure 5.

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2.3.1. Measuring Line Broadening Velocities

Though both the in situ and in-disk migration scenarios predict well aligned planetary systems with low mutual inclinations, it is possible to excite the mutual inclinations of compact systems via exterior Jovian planets (e.g., Becker & Adams 2017; Huang et al. 2017; Mustill et al. 2017). Our Doppler tomographic observations constrain the spin–orbit angle of HD 106315c, the largest planet in the system. The inner planet, HD 106315b, is too small for spectroscopic transit follow-up by the current generation of instruments. Despite this, we can still constrain the obliquity and mutual inclination of the system via dynamical arguments.

It is difficult for a system of Neptunes with a large mutual inclination to maintain a constant transit node. We setup a series of N-body models of the HD 106315 system with the REBOUND tool (Rein & Liu 2012) to investigate the impact of mutual inclination on the transit configuration. We initiate 5000 models of the system, starting with configurations where both planets transit, and measure the fraction of times the systems remain in this alignment given an initial mutual inclination. The models are initiated with the two planets having a uniform distribution of mutual inclinations. The semimajor axes and masses for the model systems are drawn from Gaussian distributions about their published values from Barros et al. (2017). Given the lack of a strict constraint on the eccentricity of the two planets, we draw eccentricities from uniform distributions based on the 1σ upper limits given in Barros et al. (2017), with ${ \mathcal U }(0,0.2)$ for planet b, and ${ \mathcal U }(0,0.37)$ for planet c, with the argument of periapsis ω drawn from a uniform distribution of ${ \mathcal U }(0,2\pi )$.

We allow the N-body models to run for 10⁵ years and calculate the fraction of times both planets remain in the transit configuration from our line of sight. Figure 7 shows the timescale of this dual-transit configuration as a function of the initial mutual inclination of the system. Only those systems with initial mutual inclinations <5° remain in the dual-transit configuration for more than 10% of the time. Systems with larger initial mutual inclinations tend to precess out of the dual-transit geometry within ∼100 years. Given the rapid fall off of the dual-transit timescale at higher mutual inclinations, and the low a-priori geometric likelihood of observing dual transits in a high mutual inclination system, we conclude that the orbit normals of both planets in HD 106315 are well aligned with the spin axis of the host star. However, if the system does have a significant mutual inclination, we expect to detect precession of the orbits via transit duration variations, and eventually, the disappearance of transits, within the decades timescale.

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We note that our N-body model assumes a three-body system. The possibility of a third outer planet was noted in Crossfield et al. (2017), though Barros et al. (2017) saw no evidence for additional planets in the HARPS radial velocities. For an external companion to influence the mutual inclination of planets b and c, it needs to be close-in enough to break the coupling between the inner planets. The coupling of planets b and c under the influence of an external companion can be estimated as per Lai & Pu (2017, Equation (12)). We estimate that planet b and c can be considered coupled (₁₂ ≪ 1) for external planets as massive as 15 M_Earth at semimajor axes beyond 0.4 au (92 day period). Saturn massed companions will need to be beyond 0.75 au for the inner planets to remain coupled.

HD 106315 is an F-star hosting a system of two planets, a super-Earth in a 9.55 day orbit, and a Neptune in a 21.06 day orbit. We presented a series of Doppler tomographic observations for the transits of the warm Neptune HD 106315c, finding its projected spin–orbit axis to be well aligned with the spin axis of the host star. From these observations, and dynamical arguments presented in Section 4.1, we find the planets in the HD 106315 system likely inhabit low obliquity, low mutual inclination orbits.

HD 106315 is only the ninth multi-planet transiting system to have the obliquity of at least one planet measured. Figure 8 shows these nine system in the context of all multi-planet transiting systems. Spectroscopic transits and analyses of spot crossing events have been performed on a number of Jovian-sized planets in the multi-planet systems, including KOI-94 (Hirano et al. 2012; Albrecht et al. 2013), Kepler-30 (Sanchis-Ojeda et al. 2012), WASP-47 (Sanchis-Ojeda et al. 2015), and Kepler-9 (Wang et al. 2018), finding these to be well aligned systems. The warm Neptune systems Kepler-25 (Albrecht et al. 2013; Benomar et al. 2014; Campante et al. 2016), Kepler-50, Kepler-60 (Chaplin et al. 2013), and HD 106315 all inhabit low obliquity orbits too. The Kepler-56 system, with two warm Jupiters, is the only system found to be misaligned via asteroseismology (Huber et al. 2013).

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In the hot-Jupiter obliquity distribution, planets orbiting stars cooler than the Kraft break (Kraft 1967, 1970) tend to be found in low obliquity orbits, while those orbiting hotter stars exhibit a wide distribution of angles (e.g., Winn et al. 2010a; Albrecht et al. 2012). Numerous mechanisms have been posed to explain this trend. Tidal interactions between the convective envelope of cool stars and the strong gravitational pull of close-in massive planets can re-align the spin axis of the outer envelope of the host star (e.g., Lai 2012; Rogers & Lin 2013; Xue et al. 2014). Torquing of the inner disk by massive exterior inclined companions may also occur (e.g., Batygin 2012; Lai 2014), and realignment of the disk of cooler disks around cooler stars may happen more quickly than those around hotter stars, leading to the observed distribution (Zanazzi & Lai 2017).

In this context, the warm Neptune systems Kepler-25, Kepler-50, Kepler-65, and HD 106315 all orbit F stars close to the Kraft break, and are all found to be in well-aligned orbits. Their obliquities are shown as a function of orbital period in Figure 9. For comparison, in the hot-Jupiter sample, 17 planets orbit stars with 6000 < T_eff < 6300 K, of which four (24%) are found in misaligned geometries. The Neptunes in the multi-planet systems are all too distant, and too low-mass, to have influenced the spins of their host stars tidally. In the in situ formation scenario, we should expect all of these Neptune systems to be found in well aligned orbits barring the torquing of the protoplanetary disk. As such, these warm Neptunes systems around F stars are perfect laboratories to test the validity of this disk torquing mechanism. It is also interesting to note that the only other transiting Neptunes to have obliquities directly measured, the hot-Neptunes HAT-P-11b (Winn et al. 2010b; Hirano et al. 2011; Sanchis-Ojeda & Winn 2011), WASP-107b (Dai & Winn 2017), and GJ 436b (Bourrier et al. 2018), were all found in highly misaligned orbits around cooler stars (Figure 9). In all three cases, the low mass of the planets means the tidal realignment timescale is long despite their shorter orbital periods. If this trend holds, we may be seeing a dramatically different early history for hot and warm Neptunes.

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We note that a dichotomy of properties exists between single-planet systems and multi-planet systems in eccentricity (Xie et al. 2016) and obliquity (Morton & Winn 2014). The warm and hot-Jupiter populations also differ in multiplicity rates (Steffen et al. 2012; Huang et al. 2016): warm Jupiters are more likely to be found with exterior and interior companions than hot Jupiters. The pathways that led to these dichotomies are not yet clear. Hot Jupiters that have dynamically migrated inward are likely to exhibit a variety of obliquities and may also have disrupted any inner planetary systems (Mustill et al. 2015). These hot Jupiters may also have formed in situ, and then underwent dynamical evolution that torqued the inner hot Jupiter's obliquity to be misaligned to that of the outer planets (Batygin et al. 2016; Spalding & Batygin 2017). Differentiating between these scenarios will require additional radial velocity follow-up of existing single-planet hot-Jupiter and Neptune systems (e.g., Yee et al. 2018) or to search for non-transiting inner gas giants to compact multi-planet systems.

The intrinsically small radius ratios of Neptune systems make spectroscopic determination of obliquites difficult, HD 106315c is among the smallest planets to have its obliquity directly measured. Systems of Neptunes around bright, relatively rapidly rotating stars like HD 106315 are optimal for such observations. Luckily, we can expect to rapidly build on the obliquities of the four warm Neptune systems and two hot Neptunes in the near future.

With the recent successful launch of the Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2016), we will soon see thousands of new planets to be found around bright, hot stars. We expect TESS to find 35 multiple transiting planetary systems orbiting stars brighter than T_mag < 10 and hotter than T_eff > 6500 K, totalling 77 planets in multi-planet systems during its first year of operations (Huang et al. in-prep). Of these, 39 planets in these transiting multi-planets will be of Neptune size (2 < Rp < 6 R_Earth) and suitable for further follow-up. In addition, we expect 217 Neptunes in single-planet systems around similarly bright stars from the first year of TESS observations. A comparative sample of these populations will help us map the formation pathways of close-in Neptune-sized planets.

As we have shown, stable instrument profiles are essential in easily tracing the spectroscopic transits of smaller planets. Luckily, a new generation of stable, highly precise spectrographs on large telescopes are coming online. Figure 10 shows the expected Doppler tomographic signal of planets in the HD 106315 system as measured by ESPRESSO utilising one unit of the 8 m Very Large Telescopes (Pepe et al. 2014), and G-CLEF on the 24 m Giant Magellan Telescope (Szentgyorgyi et al. 2012). We expect the Doppler tomographic signal of Neptune-sized planets around stars brighter than V_mag = 10 to be detectable with a single transit from ESPRESSO at the 5σ significance, while ∼2 R_Earth super Earths like HD 106315b will require spectrographs on the upcoming generation of giant segmented mirror telescopes for clear detections from single transits. The detectability of the spectroscopic transits increases linearly with rotation of the host star. For a system around an equivalent host star rotating at $v\sin {i}_{\mathrm{rot}}=25\,\mathrm{km}\,{{\rm{s}}}^{-1}$, we expect a 4.7σ detection of planet b from three ESPRESSO transits.

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