The First Near-infrared Transmission Spectrum of HIP 41378 f, A Low-mass Temperate Jovian World in a Multiplanet System

We observed a single primary transit of HIP 41378 f with HST/WFC3 using the G141 grism, which provides spectroscopy between 1.125 and 1.643 μm at a spectral resolving power of R ∼ 130 around λ = 1.4 μm. Taken as part of GO 16267 (PI: Dressing) on UT 2021 May 19–21, the observations were scheduled over three consecutive HST visits of six orbits each to accommodate the target's long transit duration (18.998 hr; Vanderburg et al. 2016). To ensure that the target remained centered in the instrument's field of view, we took an image of the target using the F126N filter with an exposure time of 7.317 s at the beginning of the first and third visits as well as at the beginning of the last orbit of the second visit. We then obtained time-series spectroscopy with the G141 grism and used round-trip spatial scanning for all visits with a scan rate of 0.419'' s⁻¹ to permit taking longer exposures without saturating the detector (McCullough & MacKenty 2012).

Due to South Atlantic Anomaly (SAA) passages during the transit, we varied the sampling sequence for affected orbits. The first three were impacted by SAA passages, making roughly half, a third, and a quarter of the respective orbits unusable. The 4th through 10th orbits were less affected, so we were able to use almost all exposures taken during these orbits. For the remaining orbits (orbits 11–18), we again faced interruptions due to the SAA. Ultimately, we used the SPARS10 sampling sequence with seven to nine nondestructive reads per exposure (NSAMP = 7–9). As a result of these NSAMP changes, the total integration times ranged from 37.010 to 51.703 s, and scans were taken across approximately 126–178 pixel rows in the cross-dispersion direction. With this instrument setup, we read out a 512 × 512 pixel subarray for each science exposure and obtained a total of 274 science exposures over the 18 orbits observed.

We reduced the observations for this program using the methods outlined in Alam et al. (2020), which we briefly summarize here. We started our analysis using the bias-corrected, flat-fielded ima images from the CALWF3 pipeline. The flux for each exposure was extracted by taking the difference between successive reads and then performing a background subtraction to suppress contamination from nearby stars. For the background subtraction, we subtracted the median flux from a box 32 pixels away from the spectrum. To correct for cosmic-ray events, we followed the procedure of Nikolov et al. (2014).

Next, we extracted stellar spectra by summing the flux within a rectangular aperture. To determine the size of the aperture (accounting for the different-sized spatial scans; see Section 2.1), we fit for the aperture width along the dispersion and cross-dispersion axes. We scanned each row of the raw ima images and fit a top-hat function to the data to determine the center of the point-spread function (i.e., the center of the 2D spectrum along the cross-dispersion axis). To determine the center of the spectrum along the dispersion direction, we scanned each column and fit a top-hat distribution to the data. We then used these fitted x and y center points as initial guesses for calculating the centroid positions on each image using the flux-weighted first moments in the x and y pixel position. To determine the wavelength solution, we cross-correlated each stellar spectrum to a grid of model spectra from the WFC3 Exposure Time Calculator (ETC) with temperatures ranging from 4060 to 9230 K. To determine shifts along the dispersion axis, we used the closest matching model of 6200 K. The final wavelengths assigned to each element of the spectrum are the wavelengths from the ETC model with the shift applied.

We compare our observed transmission spectrum to model spectra generated using a 1D radiative-convective-thermochemical-equilibrium model (Saumon & Marley 2008) assuming clear, solar-composition atmospheres with metallicities 1×, 30×, and 300× solar. Considering HIP 41378 f's low bulk density and featureless transmission spectrum, we also compare to models incorporating high-altitude hazes and circumplanetary rings. The hazy models were computed using the Community Aerosol and Radiation Model for Atmospheres (CARMA; Gao et al. 2018) by adding a downward flux of haze particles to the 1× solar model atmosphere and tracking particle coagulation, sedimentation, and mixing (as in, e.g., Adams et al. 2019). We assumed spherical haze particles with compositions of soots and tholins for haze column production fluxes of 10⁻¹⁰, 10⁻¹¹, 10⁻¹², 10⁻¹³, and 10⁻¹⁴ g cm⁻² s⁻¹ (Lavvas & Koskinen 2017; Kawashima & Ikoma 2019). We considered one soot model and one tholin model at each of the five haze production rates for a total of 10 hazy models.

We also computed transmission spectra with circumplanetary rings following the postprocessing method described in a companion paper (Ohno & Fortney 2022). In short, the method computes the spectrum by summing the transmittance of the ring-free planetary disk and the circumplanetary ring outside of the planetary disk. Using Equation (3) of Schlichting & Chang (2011), we estimate a minimum ring particle size of ∼10 cm and a system age of 3.1 ± 0.6 Gyr (Santerne et al. 2019). Because the particle size is much larger than the relevant wavelength, we first assume a gray ring opacity. The gray ring model grid comprises 80 models assuming a solar-composition atmosphere and an opaque ring with a morphology consistent with Akinsanmi et al. (2020). We varied the ring inclination between 21° and 28° from the sky plane (in increments of 1°) and varied the inner ring radius between 1.02 and 1.11 R₀ (the ring-free transit radius of 0.35R_J from the clear 1× solar model, derived based on the measured mass from Santerne et al. 2019 and the inferred bulk density estimate from Akinsanmi et al. 2020) in steps of 0.01. The outer ring radius was fixed to 2.55R₀, the Roche radius beyond which ring particles would coagulate into a satellite.

We also tested model grids for ring opacities computed using Mie theory and assuming a power-law size distribution for ring particles. The refractive indices are taken for astronomical silicates (Draine 2003). We assumed a ring mass surface density of 100 g cm⁻² with the largest particle size of 10 m, similar to Saturnian rings. Because tiny particles might survive in optically thick rings (Schlichting & Chang 2011), we set the smallest particle size to be 0.1 μm. We also tested the smallest sizes of 0.01 and 1 μm, but the results were almost unchanged. For all of the ringed models, the intrinsic atmospheric features are much smaller than those in the ring-free scenario because the surface gravity is about six times higher than the ring-free scenario, significantly reducing the true atmospheric scale height and thus the spectral features.

We fit all of the models described above to the observed WFC3 transmission spectrum (excluding the K2 point) by computing the mean model prediction of each spectroscopic channel and performing a least-squares fit of the band-averaged model to the spectrum. In our fits, we preserved the shape of the model by allowing the vertical offset in R_p/R_⋆ between the spectrum and model to vary while holding all other parameters fixed. The number of degrees of freedom for each model is n − m, where n is the number of data points and m is the number of fitted parameters. Because n = 30 for the HST spectrum and m = 1, the number of degrees of freedom is the same for each model.

From the fits, we quantified our model selection by computing the ${\chi }_{r}^{2}$ statistic. Figure 2 shows the clear atmosphere models, the best-fitting hazy and ringed models, and a flat model. We rule out clear, low-metallicity atmospheres (${\chi }_{r}^{2}$ = 5.80 and 8.44 for the 1× and 30× solar cases, respectively). We cannot, however, distinguish between the high-metallicity (300× solar; ${\chi }_{r}^{2}$ = 1.84), hazy (soots, prod = 10⁻¹³ g cm⁻² s⁻¹; ${\chi }_{r}^{2}$ = 0.97), gray opacity ringed model (R_in = 1.08R₀, i_ring = 28°; ${\chi }_{r}^{2}$ = 1.04), and nongray ringed case (R_in = 1.07R₀, i_ring = 28°, a_max = 10 μm; ${\chi }_{r}^{2}$ = 1.04) with the current observations. A flat spectrum (gray atmosphere) also matches the data well (${\chi }_{r}^{2}$ = 1.05).

HIP 41378 f (R_p = 9.2 ± 0.1 R_⊕) is approximately the same size as Saturn (R_p = 9.449 R_⊕) but has a much lower mass (12 ± 3 M_⊕ versus 95.16 M_⊕) and density (0.09 ± 0.02 g cm⁻³ versus 0.687 g cm⁻³). Although HIP 41378 f is also less dense than other exoplanets with similar radii or masses, it is not the only known low-density Saturn-sized planet. There are currently five planets with radii of 7R_⊕ < R_p < 10R_⊕ and densities lower than 0.15 g cm⁻³: Kepler-177 c (Vissapragada et al. 2020), Kepler-51 b, c, d (Masuda 2014; Libby-Roberts et al. 2020), and Kepler-79 d (Jontof-Hutter et al. 2014; Chachan et al. 2020). Kepler-51 b, Kepler-51 d, and Kepler-79 d have previously been observed in transmission using WFC3 and displayed (within the precision of those observations) flat, featureless transmission spectra consistent with high-altitude aerosols (Chachan et al. 2020; Libby-Roberts et al. 2020). HIP 41378 f displays a similarly flat spectrum (see Figure 2), suggesting that flat spectra may be a hallmark of temperate, ultra-low-density planets.

Several theories have been proposed to explain the extremely low-density planets discovered to date. The large radii of the more highly irradiated planets could be attributed to ohmic dissipation (Pu & Valencia 2017) or obliquity tides (Millholland 2019), but these mechanisms are not expected to be significant heating sources for wide-orbit, cooler planets like HIP 41378 f. A large (>10%) gas mass fraction can naturally lead to an inflated radius, though acquiring and maintaining such an envelope may require formation near the water-ice line and inward migration (Lee & Chiang 2016) as well as a low rate of atmospheric loss. High-altitude aerosols can reduce the gas mass fraction needed to produce the observed radii and explain the flat transmission spectra (e.g., Gao & Zhang 2020; Ohno & Tanaka 2021). At the low equilibrium temperature of HIP 41378 f (T_eq = 294 K), methane is the dominant carbon carrier in a solar-metallicity atmosphere and therefore organic hazes are likely. Sulfur hazes produced from H₂S photochemistry are also possible (Zahnle et al. 2016; Gao et al. 2017).

Alternatively, the planets themselves could have higher densities but are surrounded by extended ring systems at an orientation that inflates their transit depths (Akinsanmi et al. 2020; Piro & Vissapragada 2020). All of the observed low-density exoplanets, including HIP 41378 f, are close enough to their host stars that any ring system would be warmer than the water-ice sublimation temperature (T_sub ≈ 170 K) and must therefore be composed of rocky particles rather than icy particles (Gaudi et al. 2003; Piro & Vissapragada 2020) with densities of 2–5 g cm⁻³, depending on the specific particle composition and porosity. The observed transit depths of Kepler-51 b, c, d and Kepler-79 d, for example, are so large that they can be explained by rocky rings only if the ring material is extremely porous—which might be possible if the ring material is particularly weak (Hedman 2015) or similar in composition to low-density asteroids (Carry 2012). It is thus more challenging to explain these planets with rocky rings.

An emerging trend in the haziness of cooler planets (see Crossfield & Kreidberg 2017; Libby-Roberts et al. 2020; Dymont et al. 2021; Yu et al. 2021) hints that planets with T_eq < 300 K may have clear atmospheres, as possibly shown by K2-18 b (T_eq = 282 K; Benneke et al. 2019; Tsiaras et al. 2019) and LHS 1140b (T_eq = 229 K; Edwards et al. 2021). Following Dymont et al. (2021), we compute the 1.4 μm H₂O feature amplitude (A_H) and add HIP 41378 f to the sample of cooler (T_eq < 1000 K) planets with measured WFC3 transmission spectra (Figure 3). We do not find a potentially linear (Crossfield & Kreidberg 2017; Libby-Roberts et al. 2020) or quadratic (Yu et al. 2021) trend in A_H with planetary equilibrium temperature, as previously suggested in the literature.

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This larger sample reiterates that cloudiness/haziness in exoplanet atmospheres is governed by complex chemical and physical processes that are controlled by multiple parameters. Despite their comparable irradiation levels, for example, the transmission spectrum of K2-18 b displays an atmospheric signature of H₂O whereas the spectrum of HIP 41378 f is essentially featureless. The different emergent spectra for these two planets with similar equilibrium temperatures may be due to their distinct bulk properties. Conversely, the observed atmospheric signal for K2-18 b may be caused by stellar surface inhomogeneities (Barclay et al. 2021).

We use the WFC3 white light curve to constrain the composition of putative ring particles for HIP 41378 f. We infer the ring properties following the framework of Akinsanmi et al. (2020), who found that the observed transit depth of HIP 41378 f could be explained by a ring system extending from 1.05 to 2.59R_p and inclined by ∼25°. In this scenario, the underlying planet would have a higher density (1.2 ± 0.4 g cm⁻³) and a smaller radius (${3.7}_{-0.2}^{+0.3}\,{R}_{\oplus }$), while the ring particles would possess a density of ρ_r = 1.08 ± 0.30 g cm⁻³—lower than expected for rocky materials but comparable to the densities of porous materials comprising some asteroids (Carry 2012).

Despite the lower signal-to-noise and time sampling of the WFC3 observations, we performed a joint fit to the HST white light curve and K2 (Campaigns 5 and 18) light curves, allowing for different underlying planetary radii in the different bandpasses. Our ringed model fit (constrained mostly by the K2 data) provides a ring density estimate of 1.07 ± 0.27 g cm⁻³, consistent with results in Akinsanmi et al. (2020). The ringed model fit ²³ suggests an underlying planetary radius of ${3.7}_{-0.2}^{+0.3}\,{R}_{\oplus }$ for the K2 data and ${3.9}_{-0.4}^{+1.2}\,{R}_{\oplus }$ for HST.

The featureless near-infrared transmission spectrum of HIP 41378 f (Figure 2) might suggest the presence of circumplanetary rings—although high-altitude hazes, a combination of rings and hazes, or a high mean molecular weight atmosphere could also explain the lack of spectral features. Rings composed of large (>10 μm) particles would result in a fairly flat spectrum with weak spectral features in the limit where it dominates over any signal from the planet's atmosphere (Ohno & Tanaka 2021; Ohno & Fortney 2022). In contrast, hazes can flatten spectra fairly easily, as has been observed for other planets (e.g., Kreidberg et al. 2014; Libby-Roberts et al. 2020).

An enticing prospect for breaking the degeneracy between rings, metallicity, and aerosols is to obtain transmission spectra at near- and mid-infrared wavelengths. As shown by Ohno & Tanaka (2021), a super-puff with a hazy atmosphere would be expected to have a strongly sloped transmission spectrum in which the transit depth is much larger at bluer wavelengths than at redder wavelengths. This effect occurs because of the anticipated small size (<1 μm) of lofted dust particles. Conversely, planetary rings are likely composed of significantly larger particles, leading to less variation in transit depth with wavelength.

Using PandExo (Batalha et al. 2017), we simulated JWST observations ²⁴ of a single transit with MIRI LRS (∼5–12 μm), NIRSpec Prism (∼0.5–5.5 μm), NIRISS SOSS order 1 (∼0.6–3 μm), and NIRCam f322 (∼2.4–4 μm). At a resolution R = 100, we find that we can measure the transit depth for the high-metallicity clear, hazy, and nongray rings scenarios to precisions of 85–100 ppm with MIRI, 325–420 ppm with NIRSpec Prism, 230–310 ppm with NIRISS, and 220–280 ppm for NIRCam f322. Observations with MIRI, NIRSpec Prism, NIRISS SOSS, and NIRCam f322 would be able to distinguish between the hazy and clear high-metallicity cases at 3.6σ, 5.1σ, 4.8σ, and 3.4σ, between hazy and ringed cases at 5.4σ, 6.6σ, 6.0σ, and 5.1σ, or between ringed and clear high-metallicity cases at 1.6σ, 1.5σ, 1.2σ, and 1.7σ, respectively. As shown in Figure 2, the models differ in both transit depth and slope across the near- and mid-infrared. Given the intrinsic challenge of measuring absolute transit depths, the broader wavelength coverage of MIRI and NIRISS SOSS is advantageous because of the increased ability to measure trends in transit depth with wavelength. The ability of JWST to observe continuously for the full transit also provides the opportunity to reveal subtle ring-induced deviations near ingress and egress (Akinsanmi et al. 2020).

To update the prediction of future transits, we reproduced the transit timing variation (TTV) analysis described in Bryant et al. (2021), ²⁵ based on the Lithwick et al. (2012) formalism on the four epochs observed so far (two K2 epochs, one NGTS, and the HST transit presented in this manuscript). We assumed the timing variations of HIP 41378 f are dominated by the 2:3 resonance with HIP 41378 e. As in the aforementioned study, the interaction with the very-low-mass HIP 41378 d is expected to be negligible. We used emcee to explore the posterior distribution with 40 walkers of 200,000 steps after a burn-in of 100,000 iterations. Priors were defined following the results of Santerne et al. (2019). We predict that the next transits of HIP 41378 f should occur on T_C = BJD 2459897.046 ± 0.008 (midtransit on 2022 November 13 at 13:06:28.30 UT) and T_C = BJD 2460438.95 ± 0.02 (midtransit on 2024 May 8 at 10:47:02.33 UT).

As displayed in Figure 4, the measured transit time is 21 minutes later than the value predicted by Bryant et al. (2021) but is fully compatible with that prediction within 68.3%. We did not detect a transit of HIP 41378 e in our HST data, which is unsurprising given the short duration of our observations compared to the length of the transit window for the planet. Given the long period of HIP 41378 f, there are only a few opportunities to observe its transit during JWST's lifetime. No JWST observations are currently planned for future transits of this target, although these rare events present a unique opportunity to characterize the atmospheric properties of a cool, low-mass giant planet.

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