A Significant Increase in Detection of High-Resolution Emission Spectra Using a Three-Dimensional Atmospheric Model of a Hot Jupiter
Hayley Beltz, Emily Rauscher, Matteo Brogi, Eliza M.-R. Kempton
DDraft version September 22, 2020
Typeset using L A TEX twocolumn style in AASTeX63
A Significant Increase in Detection of High-Resolution Emission Spectra Using a Three-DimensionalAtmospheric Model of a Hot Jupiter
Hayley Beltz, Emily Rauscher, Matteo Brogi,
2, 3, 4 and Eliza M.-R. Kempton Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA Department of Physics, University of Warwick, Coventry CV4 7AL, UK INAF - Osservatorio Astrofisico di Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK Department of Astronomy, University of Maryland, College Park, MD 20742, USA
ABSTRACTHigh resolution spectroscopy has opened the way for new, detailed study of exoplanet atmospheres.There is evidence that this technique can be sensitive to the complex, three-dimensional (3D) atmo-spheric structure of these planets. In this work, we perform cross correlation analysis on high resolution( R ∼ , σ ) of the planet’s signal thanany of the hundreds of one-dimensional models we tested (maximum of 5 . σ ). We recover the planet’sthermal emission, its orbital motion, and the presence of CO in its atmosphere at high significance.Additionally, we analyzed the relative influences of 3D temperature and chemical structures in thisimproved detection, including the contributions from CO and H O, as well as the role of atmosphericDoppler signatures from winds and rotation. This work shows that the Hot Jupiter’s 3D atmosphericstructure has a first-order influence on its emission spectra at high resolution and motivates the use ofmulti-dimensional atmospheric models in high-resolution spectral analysis. INTRODUCTIONHigh Resolution Spectroscopy (HRS) is a relatively re-cent, powerful method for exoplanet atmospheric char-acterization. It uses a spectral resolution high enough( R (cid:38) , Corresponding author: Hayley [email protected] spectrum that are constant with time, one is left withnoise and the planet spectrum, which can then be de-tected via cross-correlation. Birkby (2018) presents areview of the HRS method and recent results from itsuse.HRS was first applied to the well-known hot JupiterHD 209458b using the CRIRES instrument on the VLT(Snellen et al. 2010), definitively detecting CO in trans-mission spectra from the planet. Further analysis ofthe transmission spectra of this planet at high resolu-tion have resulted in detections of water vapor (S´anchez-L´opez, A. et al. 2019) and helium (Alonso-Floriano, F.J. et al. 2019). Emission spectra of this planet have alsobeen measured with HRS, providing evidence againstan atmospheric temperature inversion (Schwarz et al.2015), as well as determining both carbon monoxideand water abundances when combined with lower res-olution data (Brogi et al. 2017; Gandhi et al. 2019).In this paper we present a re-analysis of the previouslypublished CRIRES/VLT data for this planet (Schwarz a r X i v : . [ a s t r o - ph . E P ] S e p et al. 2015), but with template spectra generated froma three-dimensional atmospheric model.One of the unique strengths of HRS is that at thehighest resolutions ( R ∼ , atmospheric mo-tion of the planet. The original HRS result by Snellenet al. (2010) found hints of day-to-night winds on theplanet in a net blue-shift of the planet’s spectrum by2 ± − (during transit, day-to-night winds blowtoward the observer). Transmission spectra of the hotJupiter HD 189733b also show evidence for atmosphericmotion, including both net Doppler shifts from windsand Doppler broadening from a combination of rota-tion and eastward equatorial winds (Louden & Wheatley2015; Brogi et al. 2016; Flowers et al. 2019). MeasuredDoppler broadening in high-resolution emission spectraof directly imaged planets/companions have also beenused to constrain the rotation rates of these objects(Snellen et al. 2014; Schwarz et al. 2016; Bryan et al.2020).The two sources of atmospheric motion—winds androtation—are not physically independent.For a recentreview of hot Jupiter dynamics, see Showman et al.(2020). One of the governing forces in determiningatmospheric circulation is the Coriolis force, meaningthat the rotation rate of a planet strongly influences thewind structure and speeds. Hot Jupiters are commonlyassumed to be tidally locked into rotation rates syn-chronous with their orbits (e.g., Rasio et al. 1996), butdeviations from this expected rotation state would haveconsequences for the speed and structure of atmosphericwinds (Showman et al. 2009), which then influences theexpected Doppler shifts and broadening in HRS data(Rauscher & Kempton 2014). It is an ongoing debatewithin the community as to how tidal forces interactwith the complex structure of hot Jupiters and whetherwe should assume them to be synchronized or not (Gu &Ogilvie 2009; Arras & Socrates 2010; Auclair-Desrotour& Leconte 2018; Lee 2020; Yu 2020).Given the exquisite spectral detail measurable byHRS, including constraints on atmospheric motions,we may wonder how sensitive it is to the full three-dimensional nature of the planet; and what degree ofbias will a one dimensional model introduce. Anotherway to state this is whether or not one-dimensional at-mospheric models are sufficient to accurately interpretHRS data. Especially for hot Jupiters, where we ex-pect hundreds of Kelvin temperature contrasts acrossthe globe (Rauscher & Menou 2012; Dobbs-Dixon &Agol 2013; Kataria et al. 2016; Parmentier et al. 2018;Deitrick et al. 2020; Drummond et al. 2020) , differ-ences in the local atmospheric structure can result in limb- or disk-integrated transmission or emission spec-tra (respectively) that are significantly different from aspectrum calculated using a 1-D model. Several studieshave considered how the 3-D nature of a planet can influ-ence lower resolution spectra (e.g., Fortney et al. 2006,2010; Burrows et al. 2010) and, in particular, ways thatthe use of 1-D models could bias our interpretation ofspectral data (e.g., Feng et al. 2016; Blecic et al. 2017;Caldas et al. 2019; Pluriel et al. 2020). For HRS data,several studies have simulated high-resolution spectrafrom different 3-D models, both in transmission (Miller-Ricci Kempton & Rauscher 2012; Showman et al. 2013;Kempton et al. 2014; Rauscher & Kempton 2014) andemission (Zhang et al. 2017; Harada et al. 2019), demon-strating that the complex atmospheric structures of hotJupiters can influence HRS data.Flowers et al. (2019) presented a first-of-its-kind anal-ysis of HRS data, using simulated transmission spec-tra from 3-D models as template spectra in the cross-correlation analysis of observations of the hot JupiterHD 189733b. Not only was the planet’s signal detectedat high significance (supporting the validity of the 3-D models), but this work also consistently detected theDoppler signature of day-to-night winds on this planet.When the Doppler effects from the winds were arti-ficially excluded from the calculation of the templatespectra, the planet’s signal was detected with an anoma-lous blue-shift; when the effects of the winds were in-cluded, the detection was at the expected planet veloc-ity. That is, ignoring the Doppler effects on simulatedtransmission spectra resulted in incorrect inferred plan-etary motion, confirming their measurable influence inthe observed spectra.Here we present an analogous study to Flowers et al.(2019), but for emission spectra (as opposed to transmis-sion), in which we use simulated spectra from 3-D mod-els in the HRS cross-correlation analysis. In additionto studying a complimentary observational technique—emission instead of transmission—we also target a dif-ferent bright hot Jupiter than that analysis, namelyHD 209458b. HRS transmission spectra can be di-rectly influenced by atmospheric motion, but are onlysecondarily affected by the three-dimensional tempera-ture structure Flowers et al. (2019). We expect thatHRS emission spectra may be much more sensitive todifferences in atmospheric thermal structure around theplanet, given that any Doppler effects from atmosphericmotion will be most sensitive to the brightest regions ofthe planet (Zhang et al. 2017). In this paper we empiri-cally determine how sensitive HRS emission spectra areto the 3-D nature of a particular planet, as well as towhat degree various aspects of the atmospheric struc-ture contribute to the observed data. Specifically, westudy the sensitivity of the data to the planet’s rota-tion period by running a suite of 3-D models for a rangeof rotation rates, producing a set of consistent temper-ature and wind structures for each case. We also testthe sensitivity of the data to atmospheric chemistry bycomparing an assumption of well-mixed abundances orlocal chemical equilibrium values in the radiative trans-fer routine we use to post-process the 3-D models andcreate simulated spectra. We also analyze the relativecontributions of the two main opacity sources over thewavelengths of observation (2.285 to 2.348 µ m): carbonmonoxide and water. Finally, we test the sensitivity ofthe data to Doppler effects from atmospheric motions bycross-correlating with simulated spectra calculated withand without those effects.In Section 2, we explain the various numerical meth-ods used in this work: the three-dimensional atmo-spheric model and the radiative transfer routine usedto post-process the 3-D models and calculate simulatedemission spectra. Additionally, we briefly describe theresults of these standard hot Jupiter models. In Sec-tion 3 we describe the observational data, along with de-tails of our reduction and analysis methods. In Section4 we present the results of our cross-correlation analy-sis, comparing the strength of planetary signal detectedwhen using template spectra from 1-D or 3-D models,and comparing the aforementioned assumptions regard-ing chemistry, opacity sources, Doppler effects, and rota-tion rates. In Section 5 we summarize our main results. NUMERICAL MODELS: 3D GCMS ANDSIMULATED EMISSION SPECTRAIn order to create simulated high-resolution emissionspectra for HD 209458b, we first use a General Cir-culation Model to predict the three-dimensional atmo-spheric structure of the planet—that is, thermal andwind structure— and then post-process the results usinga detailed radiative transfer routine that accounts for thecorrect geometry and atmospheric Doppler shifts. Thesemodeling methods and results are not particularly novel,having formed the basis of previous papers (Miller-RicciKempton & Rauscher 2012; Rauscher & Menou 2012;Rauscher & Kempton 2014; Roman & Rauscher 2017;Zhang et al. 2017); however, our suite of models forthis particular planet have not been published previ-ously and so we briefly describe the results in order toset the stage for the comparison between the simulatedemission spectra and observed data.2.1.
General Circulation Model
General Circulation Models (GCMs) are three-dimensional computational atmospheric models that simulate the underlying physics and circulation patternsof planetary atmospheres. For this work, we utilized theGCM from Rauscher & Menou (2012) with the radia-tive transfer scheme upgraded as described in Roman &Rauscher (2017). This model solves the primitive equa-tions of meteorology: the standard set of fluid dynamicsequations with simplifying assumptions appropriate forthe atmospheric context, solved in the rotating frameof the planet (see an early review by Showman et al.2010). The radiative heating and cooling of the atmo-spheric uses a double-gray scheme. That is, radiationis treated with two different absorption coefficients un-der two regimes; an infrared coefficient to model thethermal interaction of the gas with radiation and anoptical coefficient to model the absorption of incomingstarlight. For a more detailed explanation of the GCM,see Rauscher & Menou (2012) and Roman & Rauscher(2017). We model the hot Jupiter HD 209458b usingthe parameters listed in Table 1, with system param-eters from Stassun et al. (2017), a high internal heatflux appropriate for this inflated hot Jupiter (Thorngrenet al. 2019), and absorption coefficients and gas proper-ties set to match our previous models of hot Jupiteratmospheres (e.g., Rauscher & Menou 2012). Typically,we assume that hot Jupiters have been tidally lockedinto synchronous orbits, meaning that the rotation pe-riod and orbital period are equal. In order to empiri-cally test this, we ran the GCM for a total of 12 dif-ferent rotation rates spanning values faster and slowerthan synchronous. The slowest rotation rate was cho-sen to ensure that at least one of the models fell intothe disrupted circulation regime for slow rotation previ-ously found in Rauscher & Kempton (2014). We thenextended our rotation rate sampling (at 0.25 km/s in ro-tation speed) to comparably cover faster rotation rates.We list the set of chosen rotation periods and their cor-responding equatorial rotational velocities in Table 2,along with some representative wind speeds from eachmodel.We ran each model at a horizontal spectral resolutionof T31, corresponding to a physical scale of ∼ f = 0 .
375 here). Each simulation was allowedto run for 3000 orbits; by this point the upper atmo-sphere (including the infrared photosphere) had reacheda steady state. Carone et al. (2019) recently demon-strated that the treatment of the deep atmosphere in
Table 1.
HD 209458b System ParametersParameter ValuePlanet radius, R p . × mGravitational acceleration, g − Orbital Period 3.525 daysOrbital revolution rate, ω orb . × − s − Synchronous rotation speed a − Substellar irradiation, F irr . × W m − Planet internal heat flux, F int − Optical absorption coefficient, κ vis × − cm g − Infrared absorption coefficient, κ IR × − cm g − Specific gas constant, R − K − Ratio of gas constant to heat capacity,
R/c p R ∗ . M (cid:12) Stellar effective temperature, T ∗ eff a In the case of synchronous rotation, this is the correspondingvelocity at the equator, calculated as 2 πR p /ω orb . hot Jupiter simulations—in particular the depth of thebottom boundary and the assumed strengths of convec-tive adjustment and frictional/magnetic damping—caninfluence the circulation results predicted for the upper,observable atmosphere. Nevertheless, their models ofHD 209458b show that this planet exhibits the stan-dard hot Jupiter circulation pattern, in agreement withour results here. 2.2. GCM Results
Most of our models display the quintessential featuresexpected for hot Jupiters: a strong eastward equato-rial jet which advects the hottest spot on the planetslightly eastward of the substellar point and reduces—but does not eliminate—a large day-to-night tempera-ture contrast of hundreds of Kelvin. We show this tem-perature structure for the synchronous model in Figure1. The equatorial jet characteristically extends through-out most of the atmosphere; Figure 2 shows the zonallyaveraged winds for the synchronous model. Higher inthe atmosphere an additional, significant component ofthe winds is a substellar-to-antistellar flow pattern; inFigure 2 this shows up as a decrease in the averagedeast-west wind speed.Figures 14 and 15 in the Appendix show maps of thetemperature and winds at the infrared photosphere forall of the 12 models with different rotation rates. Inline with results from previous investigations of non-synchronously rotating hot Jupiters (Showman et al.2009; Rauscher & Kempton 2014; Flowers et al. 2019),
Table 2.
Suite of General Circulation ModelsRotation Rotational Max. wind speed Max. wind speedperiod speed at IR photosphere at 0.1 mbar(days) (km/s) (km/s) (km/s)9.08 0.79 2.50 6.286.91 1.04 2.64 4.445.57 1.29 5.65 6.874.67 1.54 5.64 6.764.02 1.79 5.61 6.64
Note —The bolded values are for the model in a tidally-locked,synchronous rotation state. The rotational speeds are calculatedas 2 πR p /ω rot . Continuum emission comes from the IR photo-sphere (at ∼
65 mbar), while the absorption line cores come frompressure regions nearer to 0.1 mbar. Wind speeds are measuredin the rotating frame of the planet.
Figure 1.
The temperature structure near the infrared pho-tosphere ( ∼
65 mbar), for our synchronously rotating modelof HD 209458b, centered on the substellar point (at 0,0).Streamlines have been overplotted, with thicker lines showingstronger winds. In the eastward direction, the winds reacha speed of 5.6 km/s. The hottest gas has been advected tothe east of the substellar point by a strong equatorial jet, inthe typical hot Jupiter circulation pattern. we find that as the rotation rate increases, the strongerCoriolis force causes the equatorial jet to become morenarrow and eventually secondary, higher latitude jetsform. The wind speeds tend to decrease with increasing
75 50 25 0 25 50 75Latitude [degrees]10 P r e ss u r e [ b a r s ] -1.00.01.02.03.04.05.0 E - W W i n d Sp ee d [ k m / s ] Figure 2.
Longitudinally averaged east-west wind speedsthroughout the atmosphere, for the synchronous rotationcase. The eastward equatorial jet (dark blue) extends deepinto the atmosphere. The black contour shows the boundarybetween eastward (positive) and westward (negative) winds. rotation rate (see Table 2), conspiring to create gener-ally similar temperature patterns at the infrared photo-spheres of each model (Figure 14).The exceptions to these trends are the two most slowlyrotating models, whose circulations have been disruptedfrom the standard hot Jupiter pattern. This disruptionfor very slow rotators was first identified by Rauscher &Kempton (2014), and the dynamics have been studiedby Penn & Vallis (2017). For the purpose of this pa-per, these most slowly rotating models help to provide alower limit to the possible rotation rate of HD 209458b,as the westward flow and corresponding advection ofthe hottest region of the atmosphere would result in anorbital phase curve of thermal emission significantly dif-ferent from what has been previously observed for thisplanet. In Figure 3 we show phase curves of the totalthermal emission from each model, calculated through-out one orbit. While most of the models do show similarcurves, which peak near the measured phase of max-imum flux at 4.5 micron (0 . ± . Due to the double-gray radiative transfer in our GCM, the ther-mal emission is effectively bolometric, making it challenging tocompare directly to the 4.5 micron flux from Zellem et al. (2014).The phase of peak flux, however, is more directly comparable asit is indicative of the photospheric temperature structure.
Orbital Phase F l u x [ W m ] P=9.079 daysP=6.909 daysP=5.568 daysP=4.669 daysP=4.015 daysP=3.525 daysP=3.140 daysP=2.831 daysP=2.578 daysP=2.366 daysP=2.186 daysP=2.033 days
Figure 3.
Calculated orbital phase curves of total ther-mal emission from our suite of models with different rotationrates. Only the models with the slowest two rotation rates—with circulation patterns disrupted from the standard hotJupiter eastward flow—have phase curves that peak aftersecondary eclipse (which would occur at a phase of 0.5, notshown here). Since phase curves measured at 4.5 microns ofHD 209458b show a peak before the secondary eclipse (at0 . ± .
017 Zellem et al. 2014, shown by the black dashedline and grey shaded area), we find that all models exceptthe two slowest rotators are consistent with observations. in order to investigate how they are constrained by HRSdata.Finally, since the CRIRES/VLT emission spectra ofHD 209458b are the focus of our paper, we also show thetemperature structure and line-of-sight velocities (fromboth winds and rotation) in the upper atmosphere ofthe synchronous model in Figure 4, shown in an ori-entation corresponding to the first night of observation.This is the region of the atmosphere from which the fluxin the CO line cores emerges, meaning that the detailedstructure of those line shapes comes from the brightness-weighted local Doppler shifts, integrated across the vis-ible hemisphere. Since the winds are dominantly east-ward, they contribute to the Doppler shifts in the samedirection as the rotation field. However, the line-of-sight velocity contours are slightly bent away from beingstrictly aligned with the rotation axis by the specific at-mospheric flow pattern.The full set of orthographic projections for our suite of12 models is shown in Figure 16 in the Appendix. Asidefrom the two most slowly rotating models, we see sim-ilar temperature and line of sight velocity fields across
Figure 4.
The temperature structure of the upper atmo-sphere ( ∼ . ±
2, 4, and 6 km/s. Theblack dotted contour shows the boundary of 0 km/s. Notethat whereas at the infrared photosphere the hottest regionis east of the substellar point, here it is west of the substel-lar point due to convergence in the atmospheric flow at thatlocation. the rest of the models. While higher blue-shifted line-of-sight velocities occur on the visible hemisphere, thered-shifted flow extends across a larger fraction of theplanet disk. In contrast, the two slowest rotators haveweak contributions to the velocity field from their ro-tation, and the winds generally work in an opposite di-rection to the rotation, leading to very little Dopplershifting compared to the other models. In addition, thetemperature structure is fairly uniform across the visiblehemisphere.A hot feature exists on the western side of the planet(from our perspective, to the left of the subobserverpoint), where we also see strongly blue-shifted veloci-ties from the combination of rotation and winds blow-ing around from the night side. Chevron features likethis, regions of flow convergence and associated heating,are commonly seen in hot Jupiter GCMs (e.g., Show-man et al. 2009; Rauscher & Menou 2010; Komaceket al. 2019) and are related to the transport of momen-tum from higher latitudes to the equator (Showman &Polvani 2011). Depending on the particular model—and the pressure level within the atmosphere—chevron fea-tures may appear to the east or west of the substellarpoint. Here we see multiple chevron features, both nearthe infrared photosphere and in the upper atmosphere.New state-of-the-art GCMs in Deitrick et al. (2020) alsoshow these features, at multiple resolutions and robustagainst assumptions regarding vertical hydrostatic equi-librium (see their Figures 19 and 22).While we have already determined that the phasecurve data for HD 209458b excludes the two slowest ro-tation states for this planet (Figure 3), we are still in-terested to compare the simulated high-resolution emis-sion spectra from these models to the rest of the suite.For most of the models, based on Figures 4 and 16we expect that the integrated emission spectra shouldshow both red- and blue-shifting of the CO lines, butthe detailed line shapes will be controlled by the com-plex three-dimensionality of the atmospheric tempera-ture and line-of-sight velocity structures. Due to theslowing of the winds with increasing rotation rate (seeTable 2 and Figure 16) we may expect similar Doppler-induced line profiles for these models. In contrast, forthe two most slowly rotating models there may be veryminimal Doppler effects shaping the line shapes in theirsimulated emission spectra.2.3.
Radiative Transfer Post-Processing
In order to generate high-resolution emission spectrafrom our three-dimensional models, we apply the codeand method outlined in Zhang et al. (2017). Briefly,we take the output from the GCM (temperature andwinds at 48 × ×
60 points in latitude × longitude × pressure; see Figure 5 for the synchronous case andFigure 17 for all of the GCM outputs) and solve theradiative transfer equation in a geometrically-consistentmanner to produce the thermal emission spectrum em-anating from the visible hemisphere of the planet.The radiative transfer equation is solved in the limitof pure thermal emission: I ( λ ) = B o e − τ + (cid:90) τ o e − τ B dτ, (1)where I is the intensity at each wavelength λ , B isthe Planck function (calculated from the local temper-atures) and τ is the slant optical depth along the lineof sight toward the observer, taking into account vary-ing opacities throughout the path. We strike 2,304(= 48 × /
2) individual line-of-sight intensity raysthrough the atmosphere and then integrate with respectto the solid angle subtended by each grid cell to producethe planet’s emission spectrum in flux units.To correctly account for the line-of-sight geometry wemust first interpolate the temperature and wind output
Figure 5.
Temperature-pressure profiles throughoutthe atmosphere for our synchronously rotating model ofHD 209458b. The rainbow lines show equatorial profiles,with the hue corresponding to the longitude east of the sub-stellar point. The gray profiles are from the entire planet. Weuse this 3-D atmospheric structure, together with the localwind velocities, to calculate simulated high-resolution emis-sion spectra for cross-correlation with the observed data.Theblack lines show examples of four temperature-pressure pro-files from a suite of 1D models (described in Section 4.1)also used to simulate spectra. These models cover the sametemperature range realized by our 3-D models, but use onlya single profile to represent the entire planet. Note thatthe best-fit model from this suite has an unrealistic super-adiabatic profile. from the GCM onto a fixed- altitude vertical grid. Thisinterpolation allows us to readily strike straight-throughrays along the observer’s sight line. This geometrically-consistent approach to the radiative transfer is some-what unique in calculations of emission spectra fromGCMs. A more common and computationally less chal-lenging technique is to calculate the radiative transferalong radial profiles and assume isotropic emission fromthe top of the atmosphere. Caldas et al. (2019) have re-cently shown that using correct ray-tracing geometry isimportant in calculating transmission spectra from 3-Dmodels; we are not aware of a similar study of geome-try’s importance in calculating emission spectra.As a consequence of having varying temperature con-ditions over the visible hemisphere of the planet, we may expect that our integrated spectra are influencedby spatial variations in the chemical abundances of ourmain opacity sources. Based on the temperature rangespanned by the GCM outputs and the wavelength rangemodeled (2.28 – 2.35 µ m), we expect that H O and COwill be the dominant opacity sources. One of the sim-plest assumptions we can make about the abundancesof H O and CO is that they are in chemical equilibriumfor the local conditions at each location in the atmo-sphere. However, this neglects the important influenceof mixing from atmospheric dynamics, which is likelyto bring these species out of chemical equilibrium. Thephysically and chemically sophisticated work by Drum-mond et al. (2020) demonstrated that 3-D mixing is ex-pected to alter the chemical structure of hot Jupiter at-mospheres, with the vertical and horizontal advectioncomponents both being significant (with similar resultsalso found by Mendon¸ca et al. 2018). In their model ofHD 209458b, however, they found minimal differencesin the abundances of CO and H O between their kinet-ics model and the assumption of chemical equilibrium.While they predicted minimal differences between thesecases in their simulated (lower resolution) emission spec-tra, here we further investigate the influence of chemicalabundances in high resolution emission spectra.The double-gray radiative transfer scheme within ourGCM simplifies the multi-wavelength opacities of theatmosphere, meaning that we do not prescribe a spe-cific chemistry, nor does the simulation predict chemicalmixing. In order to investigate the impact of chemistryon the emission spectra, we consider two extreme caseswithin our post-processing framework: abundances de-termined everywhere by local chemical equilibrium, orabundances that are fully homogenized throughout theatmosphere and set to some constant volume mixing ra-tio (VMR). The first assumption applies to the limitwhere dynamics do not create any significant chemicaldisequilibrium, while the second may be a proxy for fullyefficient mixing, with the caveat that we still need tochoose a value for the homogenized abundances. Wechoose to fix the values for water and CO to the best-fitvalues from a previous retrieval analysis of these samedata (VMR values of 1 × − . for CO and 1 × − forwater, Brogi et al. 2017).There is significant evidence in the literature suggest-ing a water abundance below the solar equilibrium value(which would be ∼ × − ; Madhusudhan 2012) forHD 209458b (although see Line et al. 2016). From previ-ous analysis of these HRS data, a marginal evidence forH O was claimed by Brogi & Line (2019), with a peakaround VMR ∼ × − . but with an unbounded lowerlimit. From HST transmission spectroscopy, Barstowet al. (2017) and Pinhas et al. (2019) both retrieve alow water abundance of 1 × − and 1 × − . , respec-tively. These results are particularly significant as theyare obtained with models accounting for the presenceof aerosols, and therefore include their known abilityto mimic a low water abundance by reducing the con-trast of the water band in the WFC3 pass-band. Lastly,a recent attempt at combining both low-resolution andhigh-resolution emission spectroscopy was presented byGandhi et al. (2019), resulting in a VMR of 1 × − . .The observational constraints presented above and theweak detection of water in these data inspired us to ex-plore an additional set of models without water vapor,along with our constant VMR models with water under-abundant compared to equilibrium calculations.In order to self-consistently account for Doppler shiftsresulting from winds and rotation in the high-resolutionspectra given that the resolution is comparable to thespeeds of atmospheric motion ( ∼ km/s), we calculate theline-of-sight velocity for a latitude-longitude ( θ , φ ) pairat an atmospheric height of z as: v LOS ( θ, φ ) = − u sin( θ ) − v cos( θ ) sin( φ )+ w cos( θ ) cos( φ ) − ( R p + z )Ω sin( θ ) cos( φ ) (2)where u, v, w are the wind speeds in the east-west, north-south, and radial directions, respectively, and Ω is theplanet’s bulk rotation rate. We calculate simulatedspectra both with and without these Doppler shifts, sothat we can quantitatively evaluate how much they con-tribute to the observed data. We calculate the simu-lated emission spectra at a higher spectral resolution( R ∼ , µ m). Duringthe data analysis, the simulated spectra are convolvedwith a Gaussian kernel to match the resolving power ofCRIRES ( R = 100 , .
6% on average. Thus, in our interpolation process, the re-sultant changes to the spectra were on order of a fewpercent at most.2.4.
Simulated Emission Spectra
Simulated spectra from the full set of 12 rotation mod-els over a partial range of the total wavelength coveragefor a time near the beginning of the observation (phaseof ∼ P ∼ . − T ∼ − ∼ × − ,only slightly higher than the value we use for our con-stant VMR assumption.In contrast, the assumption of local chemical equilib-rium produces significantly different water abundancesthan the constant VMR value we use (the best-fitvalue from a previous 1-D analysis of these data; Brogiet al. 2017). For the temperature and pressure con-ditions probed by these emission spectra, local chem-ical equilibrium abundances for water have VMR ∼ − − − , with the hottest and lowest pressure re-gions dipping down to VMR ∼ − . These abundancesare mostly significantly higher than our constant VMRvalue (10 − ), leading to much more visually apparentspectral features in Figure 7. These differences will Wavelength [ m] F l u x d e n s i t y [ W / m / H z ] + o ff s e t
1e 9 P=2.033 daysP=2.186 daysP=2.366 daysP=2.578 days P=2.831 daysP=3.140 daysP=3.525 daysP=4.015 days P=4.669 daysP=5.568 daysP=6.909 daysP=9.079 days
Figure 6.
Simulated spectra from post-processing the atmospheric structures predicted by our GCM, color coded by therotation rate assumed for each model (with the synchronous model in black). In these spectra we only include opacity from CO(not water; see Figure 7 for comparison) and assume local chemical equilibrium abundances. The dashed lines show spectraproduced without the influence of Doppler effects while the solid lines account for shifts and broadening due to winds androtation. The main result of the atmospheric motion is to produce significant line broadening; for most of the models theamount of broadening is similar, due to a trade-off between the contributions from winds and rotation. The two most slowlyrotating models have very little broadening, due to the weak contribution from rotation, but also because of westward winds inthese models. strongly influence the significance of detection in ourdata analysis, as discussed in Section 4.One measure of the effect of Doppler shifting acrossthe entire spectrum can be assessed by cross correlatingeach simulated emission spectrum with the non-Dopplershifted spectrum calculated from the same model, asshown in Figure 8, where we have plotted these crosscorrelation functions for each of our 12 rotation mod-els. The dashed black line shows the spectrum from thesynchronous model without Doppler effects cross cor-related with itself, to characterize the intrinsic widthof the cross-correlation function. The two slowest rota-tors have the least amount of broadening and the secondslowest rotator actually has a cross-correlation functionsimilar to the unshifted reference. All of the other rota- tion rates produce roughly similar levels of broadening,with only minimal net red- or blue-shifts (and no trendin the shift with rotation rate), in agreement with ourprevious findings in Zhang et al. (2017).The similarity in Doppler broadening between all butthe two most slowly rotating models is to be expected,from the discussions of circulation patterns above andfrom visual inspection of their spectra in Figure 6. Asa more quantitative comparison, in Figure 9 we showthe width of the cross correlation function, calculated at80% of its maximum (shown in Figure 8) as a functionof the rotation period of the simulated planet, normal-ized to the synchronous model. This width serves asa proxy to understand the degree of broadening causedby the differing sources of Doppler effects. The filled0
Wavelength [ m] F l u x d e n s i t y [ W / m / H z ] + o ff s e t
1e 9 CO Const VMR CO + H O Const VMR CO Chem EQ CO + H O Chem EQ
Figure 7.
Simulated emission spectra, post-processed fromour 3D atmospheric model, comparing the different assump-tions used for the abundances of water and CO, the mainsources of opacity at these wavelengths. These spectra arefrom the synchronously rotating model, over a fraction ofthe wavelength coverage of the observations; the solid anddashed spectra are produced with and without the Dopplereffects of winds and rotation, respectively. The spectra pro-duced assuming abundances determined by local chemicalequilibrium and fixed to a constant value look very simi-lar for the CO features. The assumption of local chemi-cal equilibrium results in much more abundant water withmuch stronger spectral features in comparison to the con-stant value that best-matches previous observations. and unfilled circles correspond to spectra that have beenbroadened by both winds and rotation and only rota-tion, respectively. The scatter in the unfilled circles isa result of differences in temperature structure in thecorresponding GCM. Aside from the two slowest rotat-ing models—which exhibit westward flow, opposite ofthe direction of rotation—allowing the spectra to alsobe broadened by the winds cause the width to increase.We show the result of a single temperature structure ar-tificially broadened at the various rotation rates with theblack dashed line. The unfilled circles lie both above andbelow this line, meaning that the amount of broadeningin the lines themselves does not allow us to constrain therotation rate strongly. Because the total broadening ofthe line is sensitive to temperature and wind structuresin addition to rotation rate, we are unable to retrieve arotation rate from the broadening width of the spectraalone. 2.5.
1D Atmospheric Models
In addition to producing post-processed spectra fromthe 3-D GCM outputs, it is also instructive to compare C r o ss C o rr e l a t i o n UnshiftedP=9.079P=6.909P=5.568P=4.669 P=4.015P=3.525P=3.140P=2.831 P=2.578P=2.366P=2.186P=2.033
Figure 8.
For each of our 12 models with different rota-tion rates, we cross-correlate two simulated spectra from thesame model: one with Doppler effects included and one with-out. (The solid black line is the synchronous model.) Theresulting cross correlation functions, plotted here, allow usto assess the contribution of the planet’s winds and rotationto the overall Doppler shifting and broadening of the lines inthe emission spectra. The gray dashed line shows the syn-chronous model’s non-Doppler shifted spectrum, cross cor-related with itself, to show the intrinsic broadening in thespectra. The dotted vertical lines mark the velocity at thepeak of the cross correlation function for each model. All butthe two most slowly rotating models show significant—andsimilar—broadening, while none of the models exhibit largenet red- or blue-shifts. CRIRES allows us to fully resolvethe shapes of these line profiles since its instrumental profile(approx ∼ our results against spectra produced from 1-D models ofHD 209458b. We perform comparisons against a suite ofpreviously published 1-D models (described in Section4.1) and choose four representative T-P profiles to showin Figure 5. These four chosen representatives consist ofthe best fit 1-D model to the observations, two profilesthat bound the temperatures produced in our GCM,and a model that approximately reproduces the averageequatorial T-P profile produced by our GCM. OBSERVATIONAL DATA OF HD 209458BThe data we re-analyze in this paper were originallypublished in Schwarz et al. (2015), where the full de-tails of the observations can be found. In brief, thestar HD 209458 (K=6.31 mag) was observed for a to-tal of 17.5 hours with the CRIRES instrument on theVLT as part of the ESO program 186.C-0289 in Augustand September 2011. The system was observed on threeseparate nights, always shortly after secondary eclipse.Here we utilize only the first two nights of data, which1
Figure 9.
Width of the cross correlation function, calcu-lated at at a height of 80% of its maximum (shown in Fig-ure 8) as a function of the rotation period of the simulatedplanet, normalized to the synchronous model. The filled cir-cles correspond to spectra that have been broadened fromboth wind and rotation and the open circles represent spec-tra that have been broadened only by rotation. To producethe black dotted line, we took the temperature structure ofthe synchronous model and calculated the resulting broad-ening for each rotation rate. For the two slowest rotatingmodels, we find that the westward rotating winds cause thefully broadened spectra to have a smaller width than thespectra only broadened by rotation. For all of the othermodels, we see the addition of winds cause the resulting cor-relation width to increase. Because the total broadening ofthe line is sensitive to temperature and wind structures inaddition to rotation rate, we are unable to retrieve a rotationrate from the broadening width of the spectra alone. were observed in nodding mode. We discard the thirdnight, because this was observed in staring mode fortesting purposes and shows a higher noise budget. Asexplained in Schwarz et al. (2015), the spectra were opti-mally extracted via the standard ESO pipeline and thenre-calibrated in wavelength using the known position oftelluric lines as a reference. Due to previously reportedissues with the fourth detector of CRIRES, we choseto include only the first three detectors in our analy-sis. Extracting the planetary signal from the calibratedspectra poses a unique challenge due to the highly un-equal flux ratio of the Hot Jupiter and the star. Further-more, for ground based observations, spectral absorp-tion lines formed in the Earth’s atmosphere (telluric fea-tures) must be accounted for and are often so strong thatparts of the data must be masked completely as they ex-hibit near-zero flux. In order to decouple the planet’sspectrum from the stellar and telluric lines, we utilizestandard analysis algorithms (see (Brogi & Line 2019, Section 3.2) for a detailed description for HRS. Theseare based on the principle that over the relatively shortperiod of observations, the planetary lines are Dopplershifted by a varying amount due to the changing or-bital motion of the exoplanet, while telluric and stellarlines are essentially stationary . Thus, by removing theparts of our signal that do not shift with time, we areleft with the planetary spectrum. We apply the latestiteration of the HRS analysis described in Brogi & Line(2019), to which we point the reader for a step-by-stepdescription. In short, the algorithm determines a modelfor the time-dependent stellar and telluric spectrum em-pirically from the observations, and normalizes the databy dividing out such model. The resulting data productonly contains the planet spectrum, deeply embedded inthe stellar photon noise at this stage.Similarly to previous studies of atmospheric circula-tion from transmission spectra (Brogi et al. 2016; Flow-ers et al. 2019) we run two parallel versions of the anal-ysis: one with the data as is (hereafter the real data),and one containing each model spectrum injected at asmall level (hereafter the injected data), chosen to be0.1 × the nominal value. Here the nominal value is theplanet’s emission spectrum in units of stellar flux, i.e.scaled by a blackbody at the stellar effective tempera-ture and multiplied by the planet-to-star surface ratio(see system parameters in Table 1). The exact valueof the scaling factor is not important for the outcome ofthe analysis, as long as it is significantly smaller than thenominal value. A small scaling factor is needed to realis-tically simulate the effects of the analysis on each modelspectrum without sensibly changing the signal contentof the data. In order to detect the planet’s emissionspectrum, buried in the stellar noise at this stage, weuse the standard technique in high-resolution spectra,where we cross-correlate a template spectrum—or set oftemplates—for the planet with the data. If the templateis a good representation of the planet’s spectrum, therewill be a maximum cross-correlation value at velocitiescorresponding to the planet’s orbital radial velocity dur-ing the time of observation.The significance of each tested model is determined asin previous work: we compute the difference between theCCF of the injected data and the CCF of the real data.This will remove the cross correlation noise and the cor-relation with the real planet signal, and provide us withthe model cross correlation. Note that this is different Stellar lines do shift by ∼
100 m s − per hour of observations dueto the barycentric velocity of the observer and the stellar motionaround the center of mass of the system, but these are negligiblecompared to the change in planet’s radial velocity. n - σ confidenceintervals are determined by the region in the parame-ter space where the detection significance drops by n σ .For the full explanation of how the chi-square statisticis utilized, we refer the reader to Brogi et al. (2016) andFlowers et al. (2019). DATA ANALYSIS RESULTSWe apply the cross correlation and significance testexplained in Section 3 to the spectra produced fromour three-dimensional model, as well as to a suite ofone-dimensional models for comparison. These one-dimensional models are taken from previous work andfurther information about them is provided in Section4.1.We find significant detection of the planet’s signal overthe range of template spectra tested, but our strongestdetection came from the spectra produced by post-processing our three-dimensional model, as reported inTable 3. In particular, we found the highest significanceof detection (at 6.8 sigma) for the model that was post-processed assuming uniform volume mixing ratios forCO and water, and that included the Doppler effectsfrom winds and rotation. Figure 10 shows the signifi-cance of cross-correlation detection for this model, overthe range of orbital and rest frame velocities includedin the analysis. Note that these observations have a rel-atively small phase range and they are taken close tosuperior conjunction, where the planet’s radial velocitycurve can be approximated with a linear function of timeat small signal to noise. This means that higher orbitalvelocities can be somewhat compensated for by allowingthe planet to have a positive rest frame velocity (i.e.,anomalous motion away from the observer), resultingin some inherent degeneracy between those parameters.Our detection agrees with a zero rest frame velocity forthe planet and the orbital velocity reported in Stassunet al. (2017).One of the main results from our analysis is this: thattemplate spectra from our 3-D model—calculated with-out any fine-tuning—outperform a large suite of tem-plate spectra from one-dimensional models (a 6.8 sigmadetection significance compared to 5.1; Table 3). Thisis evidence that the three-dimensional structure of thishot Jupiter’s atmosphere leaves detectable signatures in
20 10 0 10 20
Planet Rest Frame Velocity [ kms ] O r b i t a l V e l o c i t y , K p [ k m s ] f r o m p e a k > 3321 Figure 10.
The significance of our detection of the plan-etary signal, showing 1-, 2-, and 3- σ confidence intervalsfrom the peak detection (at 6.78 σ , for our spectra calcu-lated using water and CO with constant abundances), overthe velocity parameter space explored by the cross correla-tion fitting. The literature orbital velocity of the planet isshown as a white star, as is its expected rest frame velocity.Our analysis confidently detects the planet, at its expectedvelocity. the disk-integrated high-resolution emission spectrum ofthe planet. In the following sections we explore the var-ious physical properties that could contribute to thisenhanced detection and evaluate their influence.4.1. Comparison to 1D Models
To compare our results with the modeling presentedin past work, we estimated the significance of the crosscorrelation with two grids of models obtained withone-dimensional, plane-parallel radiative-transfer calcu-lations. The first grid of models is described in Schwarzet al. (2015) and consists of 704 models describing aparametric T − p profile with a region at constant lapserate ( dT /d log( p )) sandwiched between two isothermalregions. Pressure and temperature at the upper andlower boundaries can be changed, thus exploring a widerange of lapse rates up to d log( T ) /d log( p ) = 0 .
31, whichincludes non-physical super-adiabatic lapse rates. Rela-tive abundances of CO and H O are also varied in therange log(CO/H O) = 0-1.5. After excluding modelswith a thermal inversion layer (ruled out in Schwarzet al. (2015) we were left with 546 models to test. Sincethese models were not designed to explore high abun-dance ratios between CO and H O, we also tested asubset of the models described in Brogi et al. (2017)and sampled from the low-resolution posterior retrievedby Line et al. (2016). From that initial sample of3
Table 3.
Highest significance detections for the model spectra tested in this work. The highest increase in detection significancecame from using a 3D atmospheric model, compared to the 697 1D models tested. Note that the best fitting 1D model exhibitsa non-physical, super-adiabatic lapse rate. For detections broken down by rotation rate, see Table 4 in the appendix.Dimensions Abundances Molecules Included Doppler Effects On Doppler Effects Off3D Chemical equilibrium CO 6.49 6.40Chemical equilibrium CO and H O 4.22 3.39Constant volume mixing ratio CO 6.02 5.72Constant volume mixing ratio CO and H O 6.87 6.371D Constant volume mixing ratio CO and H O - 5.06 O) < . Omodels are already included in the grid from Schwarzet al. 2015), resulting in 151 additional models, span-ning abundance ratios up to log(CO/H O) = 3.0. Allthese models have a sub-adiabatic lapse rate in the range0 . < d log T /d log p < .
08. The only broadening thathas been applied to the 1-D model spectra arises fromthe pressure and thermal broadening components of theVoigt profile used to generate the spectral lines.Of the 697 one-dimensional models tested, the high-est measured significance is 5.06 σ , with only 14 modelsreaching a significance value greater than 4 σ . These aremodels with a steep lapse rate (0 . < d log T /d log p < .
31) and an abundance ratio of 10-30 between CO andH O. Thus, the vast majority of the 1-D models return asignificance below the threshold of detection (usually setat 4 σ for these HRS observations), and consistent withthe tentative detection reported in Schwarz et al. (2015).We note that the temperature-pressure profiles exploredin the set of 1-D models encompasses the range realizedin our 3-D model (Figure 5). This implies that the defi-ciency in the 1-D models is not that they didn’t includethe appropriate physical conditions of the planet, butrather that those conditions are inherently, and observ-ably, three-dimensional. In Figure 11, we show a subsetof the spectra produced from the 1D models and spectrafrom our best fitting 3D model. All the spectra shownseem to show the same absorption lines, yet still resultin a range of detection strengths. The subtleties in spec-tral line shapes and relative depths are not adequatelycaptured by the 1D models.4.2. Influence of Temperature Structure
As Table 3 hints at, and as we will discuss in subse-quent sections, the improvement in detection from usingthe 3-D models over the 1-D models is not primarily dueto the chemical or velocity structure of the atmosphere,as those influences on the spectrum only give marginalimprovements in the significance of detection. Instead,
Figure 11.
A comparison of the spectra produced from a 1Datmosphere with our best fitting 3D model (in black). Thesolid black spectrum has been broadened by Doppler effectsarising from winds and rotation. These sources of broaden-ing are not included in the dotted black spectrum or any ofthe 1D spectra. All of the models appear to show the sameabsorption lines but the relative depths of absorption, influ-enced by the underlying temperature structure and chemicalabundances, changes with each model. These variances inrelative depth and line shape result in a range of significanceof detection when cross correlated with the data. we find that the contribution from multiple regions ofthe planet, with different thermal structures, is a muchbetter match to the observed data than a representationof the planet with a single thermal profile. Whether theinfluence of spatial inhomogeneity is intrinsically within all
HRS emission observations requires further study,but for this particular planet we find it to be the case.Recent complementary work by Taylor et al. (2020) pre-dicts that James Webb Space Telescope observationsmay similarly contain inherent signatures of multiplethermal regions, although whether this inhomogeneitywill be measurable or not depends on wavelength cover-age and signal-to-noise.4.3.
Influence of Chemical Structure thermal inhomogeneity of the atmo-sphere, we can more accurately find the correct chemicalabundances (Taylor et al. 2020).In contrast to our results for CO, Table 3 shows astrong decrease in the significance of planet detectionwhen using chemical equilibrium values for water. Thedata prefer depleted abundances for water; Section 2.4and the discussion surrounding Figure 7 demonstratethat water at equilibrium values would result in largespectral features that are not apparent in the data, ac-cording to our analysis. It is noteworthy that the dataare not suggesting a complete lack of water; the very lowwater abundance used in calculating the spectra withconstant VMR does improve the planet detection overthe comparable CO-only model.A full gridded analysis of varying chemical abundancesis outside the scope of this work. Even without consid-ering a full grid,these results show that the 3-D chemicalstructure of the atmosphere contributes to our enhanceddetection, compared to 1-D models, insofar as it seemsto slightly more robustly predict the abundance of COin the atmosphere. Notably, we find that the data prefera water abundance that is orders of magnitude depletedbelow chemical equilibrium values.4.4.
Influence of Atmospheric Doppler Effects
In addition to predicting the 3-D temperature struc-ture of the planet’s atmosphere, our GCM also predictsthe wind vectors throughout, all of which are influencedby the rotation rate assumed for the planet. Here weexamine how the Doppler shifts and broadening due towinds and rotation in our simulated spectra may con-tribute to our enhanced detection of the planet’s signalover the 1-D models that do not include this additionalphysics, and whether the data can help to empiricallyconstrain the planet’s wind speeds and rotation rate(generally assumed to be synchronous with its orbit).In Table 3 we report that including the spectral lineshifting and broadening from winds and rotation doesenhance our detection of the planet, but with only aminor increase in significance over the spectra without Doppler effects. As discussed and shown above in Figure8, the main influence of the Doppler effects (for mostof the models) is to broaden the spectral lines, sinceboth winds and rotation contribute similar symmetricvelocity patterns. Thus we expect the main contributionto the increased detection is that the planet’s actualspectrum does contain some significant broadening fromwinds and rotation.Even with a symmetric velocity field, an unevenbrightness pattern across the planet can result in thered- or blue-shifted side of the planet contributing moreemission to the disk-integrated spectrum, resulting in anet Doppler shift (Zhang et al. 2017). Figure 8 has smallnet Doppler shifts for the models. Depending on theprecision of the data, this could result a small anoma-lous radial velocity of the planet if not included in theanalysis. In order to test whether a net Doppler shiftcontributes in any significant way to our detection, inFigure 12 we plot the models’ significance of detectionin velocity space, comparing the spectra with and with-out the Doppler effects included. While we see an over-all increase in detection significance with the Dopplereffects included, there is no very noticeable shift in ve-locity space between the models with and without them.This agrees with our discussion above, that the main im-provement in significance comes from the broadening ofthe lines, rather than any net Doppler shift.4.4.1.
Constraints on rotation and winds?
As part of this investigation, we wanted to see whatconstraint, if any, could be placed on the rotation rate orwind speeds for HD 209458b. In Figure 13 we show howthe significance of detection depends on which rotationrate we use in our 3-D model of the planet (plotted hereas the planet’s equatorial velocity). The significance ofdetection is largely insensitive to the planet’s rotationrate, aside from the two most slowly rotating models be-ing slightly disfavored (and those are also inconsistentwith thermal phase curve data; see Figure 3 and discus-sion). Our small improvement in detection from includ-ing Doppler effects, combined with the strong similarityin Doppler broadening for all but the slowest models(Figure 8), makes this result unsurprising.However, it is a valuable result to determine that theamount of Doppler broadening for models across a widerange of rotation rates is so similar (quantified in Figure9). It indicates that we cannot constrain rotation ratesas well as we might think from rotational broadeningalone; the winds are faster in the more slowly rotat-ing models and their predominantly eastward directionlets them compensate for the weaker rotational broaden-ing. Although our particular analysis is only for observa-5
10 0 10
Rest Frame Velocity [ kms ] O r b i t a l V e l o c i t y , K p [ k m s ] No Doppler Effects
10 0 10
Rest Frame Velocity [ kms ]Doppler Effects D e t e c t i o n S i g n i f i c a n c e ()
10 0 10
Rest Frame Velocity [ kms ] O r b i t a l V e l o c i t y , K p [ k m s ] Preference for Doppler Effects
Figure 12.
A comparison between our significance of planet detection with and without Doppler effects included in our best-fitsimulated spectra ( left and middle plots), shown as a function the planet’s assumed orbital velocity and its rest frame velocity(which should be zero unless there is anomalous motion). The right plot shows the difference in significance caused by includingthe Doppler effects in our analysis. While there is a slight increase in detection significance, this does not correspond to any netshift in velocity space, indicating that it is largely due to the line broadening rather than any shifting. tions around one particular orbital phase, the eastwardwind pattern extends around the whole globe and sowe expect the same behavior regardless of orbital phase.This is the same general behavior previously reportedfor high-resolution transmission spectra in Flowers et al.(2019); we have now shown that emission spectra aresubject to this inherent physical uncertainty as well. CONCLUSIONS AND SUMMARYIn this project, we combined state of the art observa-tional and modeling techniques to obtain a higher sig-nificance detection than could be achieved with eitherof these techniques alone. We ran a 3D atmosphericmodel for the hot Jupiter, HD 209458b, for a rangeof rotation rates. We post-processed the resulting at-mospheric structures in a geometrically correct way togenerate template spectra. We then cross correlated thesynthetic spectra with previously published data for thisplanet from CRIRES/VLT and detected the planet at agreater significance than a whole suite of 1D models. Weexplored why the 3D models were a strong improvementover the 1D models by looking at properties such as tem-perature and chemical structure and Doppler shifts fromwinds and rotation. Our main findings are summarizedas follows: • High resolution emission spectra are sensitive tothe 3D structure of the atmosphere, at least forthese data of this particular hot Jupiter. • One dimensional models, despite covering thesame range in temperature and pressure, returneddetections that were at best ∼ . σ lower than ourbest fit from 3D models. • In terms of detection significance, the primary im-provement is from the use of a 3D temperature structure, with secondary improvements related tothe chemistry and Doppler effects. • Doppler shifts are present in the high resolutionspectra, but are unable to offer strong constraintsfor wind speed or rotation rate. We have shownthat the widths of the spectral lines cannot be di-rectly related to the planet’s rotation rate alone. • Our analysis detects water in these high resolutionspectra of HD 209458b, but at a significantly de-pleted value compared to the solar chemical equi-librium abundance .High resolution spectroscopy enables detailed char-acterization of exoplanets. It is becoming increasinglyclear that the three-dimensional nature of planets andtheir atmospheric dynamics influence high resolutionspectra. Looking toward the upcoming era of high res-olution spectrographs on Extremely Large Telescopes,we eagerly await what detailed atmospheric characteri-zations will be possible.ACKNOWLEDGMENTSThis research was supported in part by NASA Astro-physics Theory Program grant NNX17AG25G and theHeising-Simons Foundation. MB acknowledges supportfrom the UK Science and Technology Facilities Council(STFC) research grant ST/S000631/1. We thank thereferee for their constructive feedback which helped toimprove the clarity of this paper.6 O r b i t a l V e l o c i t y , K p [ k m s ] Equatorial Velocity [ kms ] R e s t F r a m e V e l o c i t y [ k m s ] f r o m p e a k > 3321 Figure 13.
Confidence intervals from cross-correlation be-tween the data and our 3D models with constant volumemixing ratios of CO and water, and Doppler effects included.Similar to Figure 10, the white star marks literature valuesand equatorial velocity for synchronous rotation. Here, thetwo plots show the 1-, 2-, and 3- σ confidence intervalsformodels with different rotation rates as a function of orbitalvelocity ( top ) and rest frame velocity ( bottom ). The datahave a slight aversion to the two most slowly rotating models(low values of equatorial velocity), but otherwise the temper-ature structures and wind patterns of all other models areroughly equally well allowed by the data. REFERENCES
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A., et al. 2014,The Astrophysical Journal, 790, 53,doi: 10.1088/0004-637x/790/1/53Zhang, J., Kempton, E. M. R., & Rauscher, E. 2017, ApJ,851, 84, doi: 10.3847/1538-4357/aa9891 igure 14.
Temperature and wind structure at the infrared photosphere (P=65 mbar) for all 12 GCMs. In each case theorientation of the map is such that the substellar point is in the center of the plot. While most models show a temperaturestructure influenced by the standard hot Jupiter eastward equatorial jet, the two most slowly rotating models have disruptedcirculation patterns and instead have their hottest regions shifted slightly westward of the substellar point.6.
APPENDIXHere we present the GCM results for our 12 models of HD 209458b with different rotation rates, showing thetemperature and wind structures of the model atmospheres.0
Figure 15.
Maps of the winds in the east-west direction (with eastward defined as positive values) at the infrared photosphere(P=65 mbar) of the planet, for our full suite of General Circulation Models. Each map is oriented to be centered on thesubstellar point. Most models show the standard eastward equatorial jet, but the two most slowly rotating models have nocoherent equatorial jet and instead have westward flow near the substellar point and across most of the planet. Figure 16.
Orthographic projections of the temperature structure for 12 different rotation rates shown at the atmosphericlevel responsible for the the strongest absorption lines in the post-processed spectra, orientated such that the subobserver pointis centered. Red and blue contours show constant line of sight velocities at 2, 4, and 6 km/s. The black dotted contourshows 0 km/s line of sight and the white star shows the substellar point. Aside from the models experiencing a disrupted flowpattern—corresponding to the slowest two rotation rates—the temperature structure and circulation pattern are fairly similarover different rotation rates. Even though the rotation rate of the planet is increasing, the winds are decreasing in strength insuch as way that results in similar line of sight velocity patterns across the models. We also see that these line of sight velocitypatterns are not symmetric and are influenced by the underlying wind structure. Figure 17.
Temperature pressure profiles for the suite of models examined. Similar to Figure 5, the grey profiles are from theentire planet. The rainbow lines show equatorial profiles. Since these rotation rates are not equal to the period, the subobserverand substellar longitudes are not constant. We report the subobserver longitudes, starting with the slowest rotator as: [210, 140,320, 330, 170, 350, 100, 70, 170, 240, 260, 310] degrees. The numerical noise, seen most prominently in the upper atmospheresof the two slowest rotators, has little effect on the resulting spectra. Table 4.