Variable and Supersonic Winds in the Atmosphere of an Ultrahot Giant Planet

Using the HARPS-N data sets, our results are blueshifted relative to the measurements in Hoeijmakers et al. (2019) by ∼4 km s⁻¹. They originally measured no significant atmospheric blueshift with these same data (statistically consistent with v_wind = 0 km s⁻¹) as traced by numerous metal species, including Fe ii, using cross correlation. We can account for this discrepancy due to our revised midtransit time ephemeris; see Table 2 (also given as Table 2 in Pai Asnodkar et al. 2022). The revised ephemeris results in a propagated midtransit time that is 4.2 minutes earlier for the HARPS-N 2017 epoch and 5.8 minutes earlier for the HARPS-N 2018 epoch than the original ephemeris presented in Gaudi et al. (2017), which Hoeijmakers et al. (2019) adopt. According to our measurement of the orbital motion of the planet, these revised midtransit times result in day-to-nightside winds that are correspondingly blueshifted by 3.0 km s⁻¹ and 4.1 km s⁻¹ relative to the measurement using the original midtransit time ephemeris.

Table 2. KELT-9 System Parameters (Reproduced from Pai Asnodkar et al. 2022)

Parameter	Units	Symbol	Value	Source
Stellar parameters:
Stellar mass	M⊙	M⋆	${2.52}_{-0.20}^{+0.25}$	Gaudi et al. (2017)
Stellar radius	R⊙	R⋆	${2.362}_{-0.063}^{+0.075}$	Gaudi et al. (2017)
Stellar density	g cm−3	ρ⋆	0.2702 ± 0.0029	Gaudi et al. (2017)
Effective temperature	K	Teff	10170 ± 450	Gaudi et al. (2017)
Projected rotational velocity	km s−1	$v\sin i$	111.4 ± 1.3	Gaudi et al. (2017)
Planetary parameters:
Planet mass	MJ	mp	2.88 ± 0.84	Gaudi et al. (2017)
Planet radius	RJ	Rp	${1.891}_{-0.053}^{+0.061}$	Gaudi et al. (2017)
Semimajor axis	AU	a	${0.03462}_{-0.00093}^{+0.00110}$	Gaudi et al. (2017)
Eccentricity		ε	0	Gaudi et al. (2017)
Spin–orbit alignment	degree	λ	−84.8 ± 1.4	Gaudi et al. (2017)
Orbital inclination	degree	iorbit	86.79 ± 0.25	Gaudi et al. (2017)
Ephemeris:
Midtransit time	BJDTDB	T0	2458566.436560 ± 0.000048	This work
Time of secondary eclipse	BJDTDB	TS	2458584.950546 ± 0.000048	This work
Orbital period	days	P	1.48111890 ± 0.00000016	This work
Ingress/egress transit duration	days	τ	${0.012808}_{-0.000026}^{+0.000027}$	This work
Total transit duration	days	T14	0.15949 ± 0.00011	This work

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For a visual understanding of how midtransit timing affects the measured day-to-nightside winds, refer to Figure 3. We define orbital phase as $\phi =\tfrac{t-{T}_{0}}{P}$ such that ϕ = 0 corresponds to midtransit. At this phase, the planet's atmospheric signature is only shifted by the day-to-nightside winds (given that the data has been corrected for the systemic velocity, the orbital radial velocity of the planet at midtransit is 0 km s⁻¹). Hoeijmakers et al. (2019) found no significant day-to-nightside winds, so the velocity of the atmospheric absorption signature they measure (represented by the red solid curve in Figure 3) at ϕ = 0 is 0 km s⁻¹. According to our definition of orbital phase, an earlier midtransit time effectively shifts the atmospheric absorption signature (and the whole flux map) up in phase. Based on the orientation of the atmospheric absorption signature during transit, shifting the absorption signature up in phase according to our revised ephemeris (represented by the blue solid line in Figure 3) results in a more blueshifted absorption signature during midtransit and thus yields a more blueshifted measurement of day-to-nightside winds.

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Likewise, Cauley et al. (2019) reports no significant day-to-nightside winds on KELT-9b by studying individual metal lines (including Fe ii lines) in the PEPSI 2018 data set. In contrast, we measure very extreme winds of the order of 8–10 km s⁻¹ with the same data. Like Hoeijmakers et al. (2019); Cauley et al. (2019) adopt the midtransit timing ephemeris reported in Gaudi et al. (2017), which differs by 5.7 minutes from our ephemeris when both are propagated to the PEPSI 2018 data set epoch. This yields a 4.1 km s⁻¹ blueshift in our measurement of day-to-nightside winds relative to Cauley et al. (2019)'s. Furthermore, Cauley et al. (2019) neglected to convert the observation timings from the JD_UTC timing system to BJD_TDB, which is the timing system in which the Gaudi et al. (2017) ephemeris is given. This results in an additional 4.4 minute difference, which corresponds to an additional 3.1 km s⁻¹ discrepancy in our measurements. The residual difference in our measurements is ∼1–3 km s⁻¹. This difference captures the discrepancy between our derived systemic RV (v_sys,PEPSI = −17.86 ± 0.044 km s⁻¹) and the value adopted by Cauley et al. (2019; v_sys = −20.567 ±0.1 km s⁻¹ from Gaudi et al. 2017) as well as observational errors. Our reanalysis of previously presented data sets emphasizes the importance of precision timing in constraining the atmospheric dynamics of close-orbit planets.

Our revised midtransit timing ephemeris is more reliable than the value presented in Gaudi et al. (2017). As described in Section 3.1.3 of Pai Asnodkar et al. (2022), we refit the KELT-9 system with EXOFASTv2 (Eastman et al. 2019) to include recent TESS observations (Ricker et al. 2015) in addition to the followup light curves and TRES RVs from the discovery paper. The revision is especially critical for this analysis as the observations span multiple years; the error propagation using the original ephemeris can be as large as 4.8 minutes for the PEPSI 2019 data set. Incorporating the TESS 2019 data light curves to span a broader temporal baseline improves the precision of the ephemeris and mitigates the issue of "stale" ephemerides.

Wong et al. (2020) reports no significant temporal variability in KELT-9 b's dayside hotspot from TESS light curves, which seems to at odds with our observed variability of KELT-9 b's atmospheric dynamics. However, we note that the two observations probe different pressure levels and may not be relevant in the context of variability. The phase-curve observations probe ∼1 bar level, whereas our Fe ii line observations probe pressure levels at ≲1 μbar.

One nuance to address is that our global fit does not account for the distinctly observable gravity-darkening signature in the TESS transit light curves. However, Ahlers et al. (2020) similarly achieve subminute precision on the midtransit timing. They show that the midtransit timing ephemeris obtained from transit models with and without gravity-darkening differ by ∼0.2 minutes. Upon personal correspondence with the first author, we confirmed that they did not place a prior on midtransit timing in their model fits (J. Ahlers, personal correspondence, 2021 August 2). Therefore, the midtransit timings of both models (with and without gravity-darkening) inherently agree well within 1σ, especially when propagated to the different epochs of our observations. The difference of 0.2 minutes is not significant enough to yield an appreciable change in the measured day-to-nightside wind velocity as implied by Figure 3. Thus, we conclude that our midtransit timing maintains fidelity despite neglecting the photometric effects of gravity-darkening in our global fit.

Other nuances that may affect the day-to-nightside wind measurement are potential eccentricity in KELT-9 b's orbit and nodal precession. Both of these effects yield a discrepancy between our modeled versus the true orbital motion of the planet. First, we will address eccentricity.

To extract day-to-nightside winds, we model the RV of the fully in-transit atmospheric absorption signature as a circular Keplerian orbit with an offset due to day-to-nightside winds (we remove the RV shift due to systemic velocity before performing this analysis). Over the small range of phases exposed during a transit, the RV signal is approximately linear over time. In principle, this offset may not be entirely due to day-to-nightside winds if KELT-9 b's true orbit were sufficiently eccentric with an argument of periapsis significantly offset from the midtransit point along our line of sight. From the primary and secondary eclipse timings given by the eccentric models (models 5 and 8) in Gaudi et al. (2017), we constrain $| e\cos \omega | =0.00170\pm 0.00181$ using Equation (3) of Charbonneau et al. (2005); note that this uncertainty may be underestimated as it does not account for the covariance between the primary and secondary eclipse timings. When including this constraint, we find that introducing eccentricity only changes the slope of the RV signal over the course of the transit and does not change the linearity or offset of the signal for reasonably small eccentricities (0.001 < e < 0.2). Since the slope of the signal (K_p) is a free parameter in our fit, we conclude that our model sufficiently captures the orbital motion of the planet and the offset exclusively represents the day-to-nightside winds on KELT-9 b.

Nodal precession also modifies the planet's orbit in such a way that it could lead to a misinterpretation of our observations. Nodal precession can occur to a planet around an oblate star, where a nonzero gravitational quadrupole field causes the planet's orbital plane to precess. Consequently, the chord across the stellar disk transited by the planet changes over the years, which changes the orbital phases over which the planet's atmosphere is illuminated. Thus, our modeled orbital motion of the planet may not accurately capture the true orbital motion without accounting for nodal precession. The observed parameters modified by nodal precession are the impact parameter (directly related to orbital inclination by the transit observable $\tfrac{a}{{R}_{\star }}$) and spin–orbit angle, both of which can be measured by Doppler tomography. We estimate the effects of nodal precession on the orbital motion of KELT-9 b using preliminary measurements of these parameters across all four data sets (Wang & Stephan 2022). We find the greatest difference in midtransit timing due to nodal precession is between the PEPSI 2019 and HARPS-N 2017 data sets with a difference of 0.073 minutes. This is not significant enough to yield a measurable difference in wind velocity according to our prior precision timing argument. Furthermore, the transit timing and duration do not change drastically enough to yield a measurably significant difference in the observable orbital RVs of the planet during the course of the four transits. Thus, we conclude that nodal precession does not change the orbital motion of KELT-9 b enough to change the observed orbital RVs of the planet over the course of the four transits studied in this work. Additionally, the timescale of nodal precession (∼thousands of years) is too long to induce variability in midtransit timing and likewise the (inaccurate) measurement of day-to-nightside winds.

To emphasize how variability of atmospheric dynamics is unique to KELT-9 b and not an artifact of our analysis from two different instruments, we apply the same procedure to PEPSI and HARPS-N observations of another UHJ, KELT-20 b. From the PEPSI line-by-line analysis, we obtain a representative global blueshifted wind speed of −${2.55}_{-0.76}^{+0.99}$ km s⁻¹, which is consistent with the previous literature value of −2.8 ± 0.8 km s⁻¹ (also traced by Fe ii) in Casasayas-Barris et al. (2020). Cross correlation of the PEPSI 20190504 data set as well as the HARPS-N 20170816, 20180712, and 20180719 data sets also yields consistent results as demonstrated in the right panel of Figure 2. The lack of supersonic winds or wind variability from our analysis of Fe ii absorption in KELT-20 b's atmosphere highlights the exceptional nature of atmospheric dynamics on KELT-9 b.

We note that day-to-nightside wind measurements of KELT-20 b are significantly less sensitive to midtransit timing than KELT-9 b. From our Fe ii line-by-line analysis of the PEPSI data set, we measure KELT-20 b's orbital velocity to be ${168.8}_{-12.4}^{+21.0}$ km s⁻¹; this is consistent with the measurement given in Casasayas-Barris et al. (2020), which reports K_p = 174.4 ± 14.0 as traced by Fe ii lines. Consequently, due to KELT-20 b's slower orbital velocity and larger orbital period, even an offset in the midtransit time by 10 minutes would only correspond to a 2.1 km s⁻¹ shift in the recovered day-to-nightside wind velocity. Furthermore, a revised midtransit timing would not induce variability in wind measurements across epochs (assuming the orbital period from literature is robust).

Figure 4 displays representative measurements of day-to-nightside winds for KELT-9 b and KELT-20 b over time. This figure further demonstrates the dramatic variability of KELT-9 b's winds in contrast to KELT-20 b's temporal stability.

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4.4.1. Supersonic Winds

For physical context, we estimate the sound speed in KELT-9 b's atmosphere by assuming a hydrogen-dominated atmosphere (ρ = m_H n) that acts as an ideal gas (P = nkT) and exhibits an ideal, isothermal flow ($P={c}_{{\rm{s}}}^{2}\rho$). This yields the following relation for the sound speed:

$$\begin{eqnarray}&&{c}_{{\rm{s}}}=\sqrt{\displaystyle \frac{{kT}}{{m}_{{\rm{H}}}}},\end{eqnarray} \tag{ 1 }$$

where c_s is the sound speed, k is the Boltzmann constant, m_H is the mass of a hydrogen atom, and T is the temperature of the region in the atmosphere of interest. We estimate that the sound speed ranges between 6.8 and 7.5 km s⁻¹ in the region of the atmosphere probed by Fe ii absorption features. In obtaining these limits, we adopt lower and upper bounds on the temperature in the region of KELT-9 b's atmosphere ranging between 1 millibar and 1 μ bar, the pressure range relevant to transmission spectroscopy (Kirk et al. 2019), based on the P–T profile of KELT-9 b's atmosphere presented in Lothringer et al. (2018; Figure 14). Thus we conclude the high altitude day-to-nightside winds we measure span all the way from subsonic through supersonic speeds across epochs. While supersonic winds may be able to generate shocks locally, it is unknown to what extent these shocks can dissipate wind structures. In canonical HJs, acoustic shocks are predicted to yield ∼1 km s⁻¹ variability of equatorial jets on short timescales comparable to those we observe (Fromang et al. 2016; Menou 2020); this is insufficient to fully disrupt these jets but also not comparable in magnitude to our observed day-to-nightside wind variability on KELT-9 b. The measured high-speed winds are indirectly supported by the study of KELT-9 b's heat transport in Mansfield et al. (2020), which found that ∼10 km s⁻¹ day-to-nightside winds are necessary to explain the temperature contrast observed from the phase curve of KELT-9 b (X. Tan, personal correspondence, 2021 June 15).

4.4.2. Nightside Condensation of Fe ii

The magnitude and potential variability of day-to-nightside winds on KELT-9 b provide critical empirical context for general circulation models of UHJ atmospheres. Observational measurements of day-to-nightside winds provide constraints on the drag time constant of horizontal atmospheric circulation. Currently HJ GCMs predict winds between ∼1–4 km s⁻¹ and an amplitude of variability of the order of ∼2 km s⁻¹ at most (if at all) over weekly timescales (Komacek & Showman 2020; Showman et al. 2020). Our measurement may be significantly higher than theory in part because UHJs (especially KELT-9 b) can have a stronger day–night temperature contrast than standard HJs which drives faster winds; UHJ GCMs typically do not explicitly state wind speeds due to additional unknowns from second-order effects. Additionally, these models typically do not investigate the higher altitudes of the atmosphere probed by high-resolution transmission spectroscopy and wind speeds generally increase with altitude. Our empirical work motivates future theoretical work in this extreme regime.

Modeling the UHJ regime is a greater challenge than HJ GCMs for several reasons. First, the opacity of species at the extreme P–T conditions of UHJ atmospheres are difficult to quantify, both empirically and theoretically. Furthermore, chemistry plays a larger role in heat transport across UHJs as, on the dayside, they satisfy the conditions for molecular dissociation, most notably the dissociation of the dominant species, molecular hydrogen. The current picture of UHJ chemistry predicts cooling from hydrogen dissociation on the dayside and heating from hydrogen recombination on the nightside. As a result, models that include molecular dissociation yield a weaker temperature contrast and consequently weaker day-to-nightside winds than models without it (Tan & Komacek 2019; Roth et al. 2021). This additional mechanism is a computationally intensive feature exclusive to UHJ GCMs.

The greatest challenge to UHJ atmospheric circulation theory is incorporating magnetism in a self-consistent fashion. Purely hydrodynamic models parameterize magnetic effects as a drag term (because winds that cross magnetic field lines are dampened or potentially even fully disrupted), which may not produce accurate atmospheric circulation patterns (Rauscher & Menou 2013; Komacek & Showman 2016; Tan & Komacek 2019). On the other end of the spectrum, current magnetohydrodynamical circulation models (Rogers & Komacek 2014; Rogers & McElwaine 2017) do not include a radiative transfer scheme that would allow these models to be compared with observations. They also adopt the anelastic approximation, which assumes small vertical density and temperature variations and thus underpredicts wind velocities on HJs. Beltz et al. (2021b) strikes a balance between both methodologies and adopts a spatially varying magnetic drag prescription to account for the temperature dependence and directionality of magnetic drag. However, this scheme assumes a static magnetic field and thus does not account for its evolution due to circulation in a fully self-consistent manner the way a MHD simulation would.

No UHJ GCM to date fully captures all the physical mechanisms at play. The large day–night temperature contrast on UHJs is expected to drive winds stronger than those on HJs, but the addition of both molecular dissociation and magnetic drag in UHJs are anticipated to weaken wind velocities; this could be in tension with the rapid, transonic to supersonic wind speeds we have presented. However, magnetic drag may not affect day-to-nightside winds propagated across the poles of a UHJ as strongly as equatorial jets due to the directionality of Lorentz forces (Beltz et al. 2021b). Preliminary efforts modeling the hot upper atmospheres of UHJs, the extreme P–T regime we probe with high-resolution transmission spectroscopy, show that this holds even at the ∼0.1 mbar level even though the effects of magnetism grow stronger with temperature.

An added complication for KELT-9 b is that it is on a near-polar orbit around a rapidly rotating oblate star. Thus it experiences variable heating over the course of its orbit as it passes a more intense radiation environment at the poles of the star than at the equator. This could drive the observed variability in wind dynamics in addition to the standard gyres and vortices predicted by GCMs (Fromang et al. 2016; Tan & Komacek 2019). MHD simulations also predict variability of winds, especially of zonal winds in the hottest HJs, which can entirely reverse from eastward to westward (Rogers & Komacek 2014; Hindle et al. 2021). Our measured scale of variability motivates further exploration of these models and their predictions for the day-to-nightside winds typically observed with high-resolution transmission spectroscopy in addition to the zonal winds commonly studied by theorists.