# Variable and super-sonic winds in the atmosphere of an ultra-hot giant
planet

Anusha Pai Asnodkar The Ohio State University, McPherson Laboratory, 140 W 18th Ave., Columbus, OH 43210, USA  Ji Wang (王吉) The Ohio State University, McPherson Laboratory, 140 W 18th Ave., Columbus, OH 43210, USA  Jason D. Eastman Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, Cambridge, MA 02138, USA  P. Wilson Cauley Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO 80303  B. Scott Gaudi  The Ohio State University, McPherson Laboratory, 140 W 18th Ave., Columbus, OH 43210, USA  Ilya Ilyin  Leibniz-Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, D–14482 Potsdam, Germany  Klaus Strassmeier Leibniz-Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, D–14482 Potsdam, Germany Anusha Pai Asnodkar<EMAIL_ADDRESS>
###### Abstract

Hot Jupiters receive intense irradiation from their stellar hosts. The
resulting extreme environments in their atmospheres allow us to study the
conditions that drive planetary atmospheric dynamics, e.g., global-scale
winds. General circulation models predict day-to-nightside winds and
equatorial jets with speeds on the order of a few km $\mathrm{s^{-1}}$. To
test these models, we apply high-resolution transmission spectroscopy using
the PEPSI spectrograph on the Large Binocular Telescope to study the
atmosphere of KELT-9 b, an ultra-hot Jupiter and currently the hottest known
planet. We measure $\sim$10 km $\mathrm{s^{-1}}$ day-to-nightside winds traced
by Fe II features in the planet’s atmosphere. This is at odds with previous
literature (including data taken with PEPSI), which report no significant day-
to-nightside winds on KELT-9 b. We identify the cause of this discrepancy as
due to an inaccurate ephemeris for KELT-9 b in previous literature. We update
the ephemeris, which shifts the mid-transit time by up to 10 minutes for
previous datasets, resulting in consistent detections of blueshifts in all the
datasets analyzed here. Furthermore, a comparison with archival HARPS-N
datasets suggests temporal wind variability $\sim$5-8 km $\mathrm{s^{-1}}$
over timescales between weeks to years. Temporal variability of atmospheric
dynamics on hot Jupiters is a phenomenon anticipated by certain general
circulation models that has not been observed over these timescales until now.
However, such large variability as we measure on KELT-9 b challenges general
circulation models, which predict much lower amplitudes of wind variability
over timescales between days to weeks.

exoplanets, exoplanetary atmospheres

††journal: AAS Journals††facilities: LBT (PEPSI), TNG (HARPS-N), Fred L.
Whipple Observatory (TRES)††software: scipy (Virtanen et al., 2020),
petitRADTRANS (Mollière et al., 2019), SME (Valenti & Piskunov, 1996, 2012),
Time Utilities (Eastman, 2012), emcee (Foreman-Mackey et al., 2013), george
(Ambikasaran et al., 2014), EXOFASTv2 (Eastman et al., 2019)

##  1 Introduction

Among transiting exoplanets, hot Jupiters (HJs) are the most accessible and
exotic class of planets for atmospheric characterization. Their large size and
proximity to their host stars establishes them both as ideal targets for
transit techniques and unique laboratories for exploring the interplay between
radiative, chemical, and dynamical processes in gas giant atmospheres.
Transmission and emission spectroscopy studies suggest that more highly
irradiated HJ atmospheres display a diversity of thermal structures.

Table 1: Datasets used to study the atmospheric dynamics of KELT-9 b and KELT-20 b: columns provide the name of the instrument, the date of the starting observation, the start and end times of observing, and the number of observations. Target | Instrument | Night |  $t_{\mathrm{start}}$ (UTC) |  $t_{\mathrm{end}}$ (UTC) | $N_{\mathrm{obs}}$
---|---|---|---|---|---
KELT-9 b | HARPS-N | 2017-07-31 | 20:59:04.0 | 05:19:10.0 | 49
| PEPSI | 2018-07-03 | 04:07:34.4 | 11:16:41.3 | 82
| HARPS-N | 2018-07-20 | 21:20:24.0 | 05:09:58.0 | 46
| PEPSI | 2019-06-22 | 05:19:33.7 | 11:29:06.5 | 65
KELT-20 b | HARPS-N | 2017-08-16 | 22:26:04.7 | 04:00:39.4 | 90
| HARPS-N | 2018-07-12 | 21:27:47.4 | 05:14:51.9 | 116
| HARPS-N | 2018-07-19 | 21:26:28.1 | 04:24:36.4 | 78
| PEPSI | 2019-05-04 | 07:23:06.0 | 11:57:55.7 | 22

Recent efforts in exoplanet characterization seek empirical constraints on HJ
atmospheric circulation (Snellen et al., 2010; Ehrenreich et al., 2020; Cauley
et al., 2021). Atmospheric dynamics are a critical form of energy transport
and significantly contribute to the full energy budget of highly irradiated
exoplanet atmospheres. The strong temperature contrast between the day and
nightsides of hot Jupiters drives global day-to-nightside winds and
superrotating equatorial jets. General circulation models (GCMs) of classic
HJs like HD 209458 b or HD 189733 b predict strong ($\sim$1-3 km
$\mathrm{s^{-1}}$) day-to-nightside winds (Showman et al., 2013). Equatorial
jets ($\sim$3-4 km $\mathrm{s^{-1}}$) are predicted to offset the dayside
hotspot eastward of the sub-stellar point (Showman et al., 2008; Showman &
Polvani, 2011). Notably, few GCMs that explore low pressure dynamics exist,
especially in the millibar to $\mu$bar range relevant to high-resolution
transmission spectroscopy observations (Hoeijmakers et al., 2019).

GCM predictions for HJs have been validated by phase curve observations
(Knutson et al., 2007; Kataria et al., 2016; Wong et al., 2020) and high-
resolution Doppler spectroscopy (Snellen et al., 2010; Louden & Wheatley,
2015). Global day-to-nightside winds can be probed with transmission
spectroscopy between the 2nd and 3rd contact of a transit to measure the
terminator-averaged spectrum of the planet’s atmosphere. During transit, day-
to-nightside winds manifest as lines that are blueshifted relative to the
planet’s orbital velocity. Empirical measurements of these winds on HJs thus
far corroborate the $\sim$few km $\mathrm{s^{-1}}$ prediction from GCMs. The
first such measurement was traced by CO absorption in the near-infrared,
revealing $2\pm 1$ km $\mathrm{s^{-1}}$ day-to-nightside winds on HD 209458 b
(Snellen et al., 2010). A study of CO and $\rm{H_{2}O}$ absorption features
retrieved day-to-nightside wind speeds of $1.7^{+1.1}_{-1.2}$ km
$\mathrm{s^{-1}}$ on HD 189733 b (Brogi et al., 2016). Wind velocity and
hotspot offset measurements provide direct evidence for the extremity and
relevance of atmospheric dynamics in shaping the thermal structure of highly
irradiated giant planets. Atmospheric dynamics in HJs can also have first-
order effects on the template spectra that should be used in the analysis and
interpretation of high-resolution spectroscopy observations (Beltz et al.,
2021a; Flowers et al., 2019).

In this work, we report on the atmospheric dynamics of KELT-9 b (Gaudi et al.,
2017) and KELT-20 b (Lund et al., 2017; Talens et al., 2018), both of which
fall in a categorically distinct class of objects known as ultra-hot Jupiters
(UHJs). The unique atmospheric thermal structures and chemical composition of
giant planets with $T_{\mathrm{eq}}\gtrsim 2500$ K motivate this separate
class of HJs. Most notably, thermal inversions (regions of the atmosphere
analogous to Earth’s stratosphere where temperature increases with decreasing
pressure, i.e. increasing altitude) only occur in the hottest HJs. The
majority of ultra-hot Jupiters display nearly isothermal pressure-temperature
(P-T) profiles around milibar pressures and lower (Lothringer & Barman, 2019)
while some decrease outward in temperature (Madhusudhan, 2019). A small subset
of UHJs exhibit evidence of thermal inversions, including the classic examples
WASP-18 b (Sheppard et al., 2017), WASP-121 b (Evans et al., 2017), WASP-33 b
(Haynes et al., 2015), and our target of focus, KELT-9 b (Pino et al., 2020).

Table 2: KELT-9 system parameters (reproduced from Pai Asnodkar et al. 2022). Parameter | Units | Symbol | Value | Source
---|---|---|---|---
Stellar parameters: |  |  |  |
Stellar mass | $M_{\odot}$ | $M_{\star}$ | $2.52^{+0.25}_{-0.20}$ | Gaudi et al. 2017
Stellar radius | $R_{\odot}$ | $R_{\star}$ | $2.362^{+0.075}_{-0.063}$ | Gaudi et al. 2017
Stellar density | g $\mathrm{cm^{-3}}$ | $\rho_{\star}$ | $0.2702\pm 0.0029$ | Gaudi et al. 2017
Effective temperature | K | $T_{\mathrm{eff}}$ | $10170\pm 450$ | Gaudi et al. 2017
Projected rotational velocity | km s-1 | $v\sin{i}$ | $111.4\pm 1.3$ | Gaudi et al. 2017
Planetary parameters: |  |  |  |
Planet mass | $M_{J}$ | $m_{\mathrm{p}}$ | $2.88\pm 0.84$ | Gaudi et al. 2017
Planet radius | $R_{J}$ | $R_{\mathrm{p}}$ | $1.891^{+0.061}_{-0.053}$ | Gaudi et al. 2017
Semi-major axis | AU | $a$ | $0.03462^{+0.00110}_{-0.00093}$ | Gaudi et al. 2017
Eccentricity |  | $\varepsilon$ | $0$ | Gaudi et al. 2017
Spin-orbit alignment | degree | $\lambda$ | $-84.8\pm 1.4$ | Gaudi et al. 2017
Orbital inclination | degree | $i_{\mathrm{orbit}}$ | $86.79\pm 0.25$ | Gaudi et al. 2017
Ephemeris: |  |  |  |
Mid-transit time | $\mathrm{BJD_{TDB}}$ | $T_{0}$ | 2458566.436560 $\pm$ 0.000048 | This work
Time of secondary eclipse | $\mathrm{BJD_{TDB}}$ | $T_{\mathrm{S}}$ | 2458584.950546 $\pm$ 0.000048 | This work
Orbital period | days | $P$ | 1.48111890 $\pm$ 0.00000016 | This work
Ingress/egress transit duration | days | $\tau$ | $0.012808^{+0.000027}_{-0.000026}$ | This work
Total transit duration | days | $T_{14}$ | $0.15949\pm 0.00011$ | This work

UHJs are further distinguished by their composition and lack of molecular
features (e.g. water, molecular hydrogen) due to dissociation at extreme
temperatures. Extending giant planet GCMs to the extreme pressure-temperature
regime of UHJs requires introducing additional chemistry due to the
dissociation of molecular hydrogen and magnetic effects due to metal
ionization. For this reason, UHJs are challenging to model and are relatively
new territory in GCM literature. Accounting for the thermodynamic effect of
$\rm{H_{2}}$ dissociation has been shown to horizontally (i.e. across
longitudes) homogenize heat redistribution (Roth et al., 2021), resulting in
weaker day-to-nightside winds than expected without dissociation (Tan &
Komacek, 2019). Wind measurements may answer questions regarding the role of
second-order effects in UHJ atmospheres like molecular dissociation and
magnetic drag from thermally ionized winds (Perna et al., 2010; Rogers &
Komacek, 2014).

Previous studies of atmospheric dynamics on KELT-9 b report no significant
day-to-nightside winds (Yan & Henning, 2018; Yan et al., 2019; Cauley et al.,
2019; Hoeijmakers et al., 2019; Wyttenbach et al., 2020). In this work, we
present new day-to-nightside wind measurements of KELT-9 b that challenge
previous measurements and theoretical predictions. We employ two epochs of
observations from the Potsdam Echelle Polarimetric and Spectrographic
Instrument (PEPSI) (Strassmeier et al., 2015) on the Large Binocular Telescope
(LBT). We apply both a high resolution line-by-line analysis and the cross-
correlation technique to study the Doppler signature of Fe II in the
atmosphere of KELT-9 b. We compare the PEPSI findings with archival data from
the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere
(HARPS-N) originally presented in Hoeijmakers et al. 2019. We also validate
our methods against previous literature using KELT-20 b as a test case. We
discuss our wind measurements across techniques and datasets, compare with
previous literature, and discuss the consequences for GCMs of UHJs.

##  2 Methods

Our methodology is presented in greater detail in our previous paper Pai
Asnodkar et al. 2022, but we will summarize the key points here. We compile
observations of the KELT-9 system from the high-resolution spectrograph PEPSI
(R=50,000) on the LBT (see Figure 1) and archival data from HARPS-N
(R=115,000) on Telescopio Nazionale Galileo (TNG). Our analysis of PEPSI data
exclusively employs observations from the blue arm with cross-disperser 3
($\sim$4750–5430 Å). For comparison, we select the same wavelength range in
our examination of the HARPS-N data. As a test, we also perform a homogeneous
analysis of KELT-20 b’s atmospheric dynamics traced by the same six Fe II
lines and wavelength range for cross-correlation we investigate in KELT-9 b’s
atmosphere. We analyze an original PEPSI dataset as well as archival HARPS-N
observations of the KELT-20 system. We refer to the KELT-9 b datasets by their
instrument and year of observation (HARPS-N 2017, PEPSI 2018, HARPS-N 2018,
PEPSI 2019, and HARPS-N 2018 in chronological order). To avoid confusion, we
refer to the KELT-20 datasets by their instrument and full date of observation
(HARPS-N 20170816, HARPS-N 20180712, HARPS-N 20180719, and PEPSI 20190504).
Further details about the observations are presented in Table 1 and §2 of Pai
Asnodkar et al. 2022.

We employ transmission spectroscopy to probe the atmospheric dynamics of
KELT-9 b and KELT-20 b. We apply least-squares deconvolution (§3.1 of Pai
Asnodkar et al. 2022) on out-of-transit observations to determine stellar
radial velocities and fit for a circular stellar orbital solution to quantify
the systemic velocities for both systems as individually measured by the PEPSI
and HARPS-N instruments ($v_{\mathrm{sys,PEPSI}}=-17.86\pm 0.044$ km s-1 and
$v_{\mathrm{sys,HARPS-N}}=-17.15\pm 0.11$ km s-1)). We divide out the stellar
component encapsulated by the out-of-transit observations to recover the
transmission spectra and isolate the planet’s atmospheric absorption signature
(§3.2 of Pai Asnodkar et al. 2022). We perform both a line-by-line analysis
and cross-correlation analysis of the fully in-transit observations to avoid
asymmetries and velocity offsets from equatorial jets and rotation during
ingress/egress (Cauley et al., 2021; Casasayas-Barris et al., 2020; Yan &
Henning, 2018). We generate a grid of models of the secondary effects from the
Rossiter-McLaughlin effect (RME) and center-to-limb variation (CLV). We
simultaneously fit the in-transit secondary effects and planetary atmospheric
absorption signatures from individual Fe II lines and cross-correlation. We
model the planet’s absorption as a Gaussian feature shifted according to a
circular orbital solution modified by a constant blueshift ($v_{\rm{wind}}$)
due to day-to-nightside winds. See Pai Asnodkar et al. 2022 for more details.

A critical aspect in our analysis of the KELT-9 system is our revised
ephemeris. We refit the KELT-9 system with EXOFASTv2 (Eastman et al., 2019) to
include Transiting Exoplanet Survey Satellite (TESS) (Ricker et al., 2015)
lightcurves from 2019 in addition to the follow up lightcurves and TRES RVs
from the discovery paper. The updated ephemeris is critical for this analysis
since the observations span multiple years and precision deteriorates as the
ephemeris is propagated over a longer temporal baseline. In our analysis of
KELT-20 b, we adopt the system ephemeris given in Lund et al. 2017 (the Talens
et al. 2018 ephemeris does not yield significantly different wind velocities).
We do not update the KELT-20 ephemeris because the analysis of its atmospheric
dynamics is less sensitive to mid-transit timing due to its slower orbital
velocity and larger orbital period.

Figure 1: 2D maps of transmission spectra, focusing on the six Fe II
absorption lines in the PEPSI 2018 dataset chosen for fitting $K_{\mathrm{p}}$
and $v_{\rm{wind}}$. The blue track is the planet’s atmospheric absorption
while the red track is the Doppler shadow from the Rossiter-McLaughlin effect;
both tracks only form during a transit. Top panel displays fully in-transit
observations. Middle panel shows the best-fit model from MCMC sampling. The
bottom panel presents the residuals (data - model).

##  3 Results

(a)

(b)

Figure 2: Day-to-nightside winds measurements from Fe II line-by-line and
cross-correlation analyses with MCMC sampling errors for (a) KELT-9 b and (b)
KELT-20 b. We note that the Fe II $\lambda$5363.9 Å line is very weak with S/N
= 1.6; for comparison, the Fe II $\lambda$5169 Å line has S/N = 9.0 (see
Figure 1 for the observed relative line strength of KELT-9 b as an example).
Thus, this line is less reliable for measuring day-to-nightside winds.

The left panel of Figure 2 summarizes the global day-to-nightside winds
observed in KELT-9 b’s PEPSI 2018 and PEPSI 2019 datasets. Across the six
different Fe II lines we inspected, the measurements are generally consistent
within a given dataset. However, there is a systematic offset between the 2018
and 2019 measurements. The error-weighted median value with 1$\sigma$ errors
of the 2018 and 2019 measurements across all six lines are
$-8.79^{+0.56}_{-0.88}$ km $\mathrm{s^{-1}}$ and $-11.59^{+1.56}_{-1.13}$ km
$\mathrm{s^{-1}}$ respectively.

We also measure day-to-nightside winds from the two PEPSI datasets as traced
by Fe II absorption using cross-correlation. This analysis yields
$-9.55^{+0.56}_{-0.55}$ km $\mathrm{s^{-1}}$ and $-10.41^{+0.64}_{-0.57}$ km
$\mathrm{s^{-1}}$ for the PEPSI 2018 and PEPSI 2019 datasets respectively.
Thus the cross-correlation measurements are consistent with the line-by-line
analysis of their corresponding datasets.

In contrast, the HARPS-N measurements taken from cross-correlation differ by a
significant $\sim$5-8 km $\mathrm{s^{-1}}$ offset. In particular, the PEPSI
2018 and HARPS-N 2018 datasets were both taken in July and differ by
5.7$\sigma$ (5.3 km $\mathrm{s^{-1}}$). This discrepancy is not attributable
to an RV offset between the two instruments since the systemic velocities we
obtain for both instruments from our analysis of stellar RVs are consistent
within 1 km $\mathrm{s^{-1}}$. As there is no evidence to-date of a companion
in the system to cause significant transit-timing variations and upon
confirming that our conversion to the $\rm{BJD_{TDB}}$ timing system for all
datasets was applied correctly (see Section 2 of Pai Asnodkar et al. 2022), we
conclude that this discrepancy in our velocity measurements is most plausibly
astrophysical. The discrepancy suggests multi-epoch temporal variability of
global day-to-nightside winds on KELT-9 b.

##  4 Discussion

###  4.1 Comparison with previous literature

Figure 3: The sloped solid lines represent the center of the planet’s
absorption signature over the course of the transit, corrected by the systemic
velocity (see Figure 2 of Pai Asnodkar et al. 2022). The slope captures the
orbital motion of the planet while the velocity at mid-transit ($\phi=0$)
corresponds to the day-to-nightside wind velocity. 2 and 3 contact occur at
orbital phases beyond the range of this plot. Our revised ephemeris for the
KELT-9 system (1) shifts the atmospheric signature up in phase, resulting in
(2) a more blueshifted measurement of day-to-nightside winds.

Using the HARPS-N datasets, our results are blueshifted relative to the
measurements in Hoeijmakers et al. 2019 by $\sim$4 km $\mathrm{s^{-1}}$. They
originally measured no significant atmospheric blueshift with these same data
(statistically consistent with $v_{\rm{wind}}=0$ km $\mathrm{s^{-1}}$) as
traced by numerous metal species, including Fe II, using cross-correlation. We
can account for this discrepancy due to our revised mid-transit time
ephemeris; see Table 2 (also given as Table 2 in Pai Asnodkar et al. 2022).
The revised ephemeris results in a propagated mid-transit 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 mid-transit times result in day-
to-nightside winds that are correspondingly blueshifted by 3.0 km
$\mathrm{s^{-1}}$ and 4.1 km $\mathrm{s^{-1}}$ relative to the measurement
using the original mid-transit time ephemeris.

For a visual understanding of how mid-transit timing affects the measured day-
to-nightside winds, refer to Figure 3. We define orbital phase as
$\phi=\frac{t-T_{0}}{P}$ such that $\phi=0$ corresponds to mid-transit. 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 mid-transit is 0 km
$\mathrm{s^{-1}}$). 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 $\phi=0$ is 0 km
$\mathrm{s^{-1}}$. According to our definition of orbital phase, an earlier
mid-transit 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 mid-
transit and thus yields a more blueshifted measurement of day-to-nightside
winds.

Likewise, Cauley et al. 2019 reports no significant day-to-nightside winds on
KELT-9b by studying individual metal lines (includeing Fe II lines) in the
PEPSI 2018 dataset. In contrast, we measure very extreme winds on the order of
8-10 km $\mathrm{s^{-1}}$ with the same data. Like Hoeijmakers et al. 2019,
Cauley et al. 2019 adopt the mid-transit 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 dataset epoch. This yields a 4.1 km
$\mathrm{s^{-1}}$ 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 $\rm{JD_{UTC}}$ timing system to
$\rm{BJD_{TDB}}$, 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 $\mathrm{s^{-1}}$ discrepancy in our
measurements. The residual difference in our measurements is $\sim$1-3 km
$\mathrm{s^{-1}}$. This difference captures the discrepancy between our
derived systemic RV ($v_{\mathrm{sys,PEPSI}}=-17.86\pm 0.044$ km
$\mathrm{s^{-1}}$ and the value adopted by Cauley et al. 2019
($v_{\mathrm{sys}}=-20.567\pm 0.1$ km $\mathrm{s^{-1}}$ from Gaudi et al.
2017) as well as observational errors. Our reanalysis of previously presented
datasets emphasizes the importance of precision timing in constraining the
atmospheric dynamics of close-orbit planets.

Our revised mid-transit 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
follow-up lightcurves and TRES RVs from the discovery paper. The revision is
especially critical for this analysis since the observations span multiple
years; the error propagation using the original ephemeris can be as large as
4.8 minutes for the PEPSI 2019 dataset. Incorporating the TESS 2019 data
lightcurves 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 lightcurves, 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 $\sim$1 bar
level whereas our Fe II line observations probe pressure levels at $\lesssim$1
$\mathrm{\mu}$bar.

###  4.2 Impact of Transit Fitting and Orbital Dynamics on Mid-Transit Timing

Figure 4: Day-to-nightside winds of KELT-9 b and KELT-20 b ordered
chronologically along the x-axis.

One nuance to address is that our global fit does not account for the
distinctly observable gravity-darkening signature in the TESS transit
lightcurves. However, Ahlers et al. 2020 similarly achieve sub-minute
precision on the mid-transit timing. They show that the mid-transit timing
ephemeris obtained from transit models with and without gravity-darkening
differ by $\sim$0.2 minutes. Upon personal correspondence with the first
author, we confirmed that they did not place a prior on mid-transit timing in
their model fits (J. Ahlers, personal correspondence, August 22, 2021).
Therefore, the mid-transit timings of both models (with and without gravity-
darkening) inherently agree well within 1$\sigma$, 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
mid-transit 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 modelled vs. 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 mid-transit 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 ($K_{\mathrm{p}}$) 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 non-zero 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 modelled 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 impact parameter (directly related
to orbital inclination by the transit observable $\frac{a}{R_{\star}}$) 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 datasets
(Wang & Stephan, in prep.). We find the greatest difference in mid-transit
timing due to nodal precession is between the PEPSI 2019 and HARPS-N 2017
datasets 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 4 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 4 transits studied in this work. Additionally, the timescale of
nodal precession ($\sim$thousands of years) is too long to induce variability
in mid-transit timing and likewise the (inaccurate) measurement of day-to-
nightside winds.

###  4.3 Comparison with KELT-20 b

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 $-2.55^{+0.99}_{-0.76}$ km $\mathrm{s^{-1}}$, which
is consistent with the previous literature value of $-2.8\pm 0.8$ km
$\mathrm{s^{-1}}$ (also traced by Fe II) in Casasayas-Barris et al. 2020.
Cross-correlation of the PEPSI 20190504 dataset as well as the HARPS-N
20170816, 20180712, and 20180719 datasets also yield 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 mid-transit timing than KELT-9 b. From our Fe II line-by-
line analysis of the PEPSI dataset, we measure KELT-20 b’s orbital velocity to
be $168.8^{+21.0}_{-12.4}$ km $\mathrm{s^{-1}}$; this is consistent with the
measurement given in Casasayas-Barris et al. 2020, which reports
$K_{\mathrm{p}}=174.4\pm 14.0$ as traced by Fe II lines. Consequently, due to
KELT-20 b’s slower orbital velocity and larger orbital period, even an offset
in mid-transit time by 10 minutes would only correspond to a 2.1 km
$\mathrm{s^{-1}}$ shift in the recovered day-to-nightside wind velocity.
Furthermore, a revised mid-transit 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.

###  4.4 Implications

####  4.4.1 Super-sonic winds

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

$c_{\rm{s}}=\sqrt{\frac{kT}{m_{\rm{H}}}}$ (1)

where $c_{\rm{s}}$ is the sound speed, $k$ is the Boltzmann constant,
$m_{\rm{H}}$ is the mass of a hydrogen atom, and $T$ is the temperature of the
region in the atmosphere of interest. We estimate the sound speed ranges
between 6.8 to 7.5 km $\mathrm{s^{-1}}$ 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 to 1 µbar, 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 sub-
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 $\sim$1 km $\mathrm{s^{-1}}$ 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 $\sim$10 km
$\mathrm{s^{-1}}$ day-to-nightside winds are necessary to explain the
temperature contrast observed from the phase curve of KELT-9 b (X. Tan,
personal correspondence, June 15, 2021).

####  4.4.2 Nightside condensation of Fe II

The atmospheric absorption tracks display visibly discernible in-transit
variability; see Figure 1. To quantify this variability, we stack the
transmission spectra from the first and second half of the transit separately
in the planet’s rest-frame. We do not include observations in which the
Doppler shadow overlaps with the absorption feature. Then we fit the
absorption feature from each half of the transit with a Gaussian and adopt the
amplitude of the Gaussian as the absorption strength. For comparison, we take
the difference of the absorption strengths from the first and second half of
the transit. Based on the highest SNR lines (Fe II $\lambda$4923.9, 5018.4,
5169), the second half of the transit displays stronger absorption in the
PEPSI 2018 data by a mean of 1466 ppm. This is consistent with the original
findings presented in Cauley et al. 2019.

The in-transit variability of the atmospheric absorption signature seen in the
PEPSI 2018 data is consistent with a picture of nightside condensation of Fe
II on KELT-9 b as seen with Fe I on WASP-76 b (Ehrenreich et al., 2020;
Kesseli & Snellen, 2021). Over the course of a tidally-locked planet’s
transit, more of the dayside is visible on the leading limb during the first
half and on the trailing limb during the second half (see Figure 3 in
Ehrenreich et al. 2020). Assuming the same physical picture as presented in
Ehrenreich et al. 2020: 1) Fe II condenses out on the nightside and 2) more Fe
II is present in the gaseous phase at the evening side than the morning side
due to a longitudinal offset of the hotspot towards the evening terminator.
Invoking this picture of a chemical gradient across the planet implies
stronger absorption during the second half of the transit (as empirically
observed) when more dayside near the evening terminator of the planet is
exposed to the observer. Alternatively Savel et al. 2021 has shown that rather
than iron rainout, the asymmetric Fe absorption in WASP-76 b is better
explained by $\mathrm{Al_{2}O_{3}}$, Fe, or $\mathrm{Mg_{2}SiO_{4}}$ clouds on
the cooler leading limb, which could also explain the stronger Fe II
absorption we observe in the second half of KELT-9 b’s transit. Wardenier et
al. 2021 also reproduces the feature with a temperature asymmetry between the
leading and trailing limbs of the planet without invoking iron condensation.
Stronger absorption during the second half of the transit is not
quantitatively evident in the PEPSI 2019 data.

###  4.5 Expectations from GCMs

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 hydrodynamic HJ GCMs predict winds between $\sim$1-4 km
$\mathrm{s^{-1}}$ and an amplitude of variability on the order of $\sim$2 km
$\mathrm{s^{-1}}$ at most (if at all) over weekly timescales (Showman et al.,
2020; Komacek & Showman, 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.

Modelling the UHJ regime is a greater challenge than HJ GCMs for several
reasons. Firstly, the opacity of species at the extreme pressure-temperature
conditions of UHJ atmospheres are difficult to quantify, both empirically and
theoretically. Furthermore, chemistry plays a larger role in heat transport
across UHJs since 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 hot Jupiters.
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, trans- 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 pressure-temperature
regime we probe with high-resolution transmission spectroscopy, show that this
holds even at the $\sim$0.1 mbar level even though the effects of magnetism
are 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, vortices, and
other hydrodynamic instabilities predicted by hydrodynamic 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.

##  5 Conclusion

We revisit the atmospheric dynamics of KELT-9 b with a revised ephemeris and a
new high-resolution transmission spectroscopy dataset from the PEPSI
spectrograph on the LBT. Contrary to previous literature (Yan & Henning, 2018;
Yan et al., 2019; Cauley et al., 2019; Hoeijmakers et al., 2019), we detect
significant $\sim$4-10 km $\mathrm{s^{-1}}$ day-to-nightside winds as traced
by line-by-line analysis as well as cross-correlation of Fe II lines (§3). We
show that the velocity shift due to the planet’s orbital motion depending on
the choice of mid-transit timing accounts for the disagreement with previous
studies of the datasets explored in this work (§4). Our work motivates future
multi-epoch observations and analysis of UHJ atmospheric dynamics. The
magnitude and variability of winds we observe pose new challenges for GCMs of
UHJs, which require further theoretical exploration of second-order mechanisms
such as magnetic drag and $\rm{H_{2}}$ dissociation at the extreme pressure-
temperature regime probed in this work.

A.P.A would like to thank the David G. Price Fellowship in Astronomical
Instrumentation for funding her work this year. Work by B.S.G. and J.W. was
partially supported by the Thomas Jefferson Chair for Space Exploration
endowment from the Ohio State University. This work is based on observations
made with the Large Binocular Telescope. The LBT is an international
collaboration among institutions in the United States, Italy and Germany. LBT
Corporation partners are: The University of Arizona on behalf of the Arizona
Board of Regents; Istituto Nazionale di Astrofisica, Italy; LBT
Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The
Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The
Ohio State University, representing OSU, University of Notre Dame, University
of Minnesota and University of Virginia. This paper includes data collected by
the TESS mission. Funding for the TESS mission is provided by the NASA’s
Science Mission Directorate. We thank Dr. Marshall Johnson, Dr. Francesco
Borsa, Dr. Jens Hoeijmakers, Dr. Xavier Dumusque, Dr. Xianyu Tan, and Dr.
Johnathon Ahlers for contributing their valuable expertise regarding high-
resolution spectroscopy, the HARPS-N pipeline, and the KELT-9 system.
Additionally, we thank Prof. Emily Rauscher and Dr. Xianyu Tan for providing
critical feedback on the manuscript and sharing their indispensable
perspectives as theorists.

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