A search for He I airglow emission from the hot Jupiter tau Boo b
Yapeng Zhang, I.A.G. Snellen, P. Mollière, F. J. Alonso-Floriano, R. K. Webb, M. Brogi, A. Wyttenbach
AAstronomy & Astrophysics manuscript no. helium c (cid:13)
ESO 2020September 15, 2020
A search for He i airglow emission from the hot Jupiter τ Boo b
Yapeng Zhang , I.A.G. Snellen , P. Mollière , , F. J. Alonso-Floriano , R. K. Webb , M. Brogi , , , A. Wyttenbach ,
1: Leiden Observatory, Leiden University, Postbus 9513, 2300 RA, Leiden, The Netherlands2: Max-Planck-Institut für Astronomie , Königstuhl 17, 69117 Heidelberg, Germany3: Department of Physics, University of Warwick, Coventry CV4 7AL, UK4: INAF - Osservatorio Astrofisico di Torino, Via Osservatorio 20, I-10025 Pino Torinese, Italy5: Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill, Coventry, CV4 7AL, UK6: Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, FranceReceived 13 May 2020; accepted 24 July 2020
ABSTRACT
Context.
The helium absorption line at 10830 Å originating from the metastable triplet state 2 S, has been suggested as an excellentprobe for the extended atmospheres of hot Jupiters and their hydrodynamic escape processes, and has recently been detected in thetransmission spectra of a handful of planets. The isotropic re-emission will lead to helium airglow that may be observable at otherorbital phases.
Aims.
The goal of this paper is to investigate the detectability of He i emission at 10830 Å in the atmospheres of exoplanets usinghigh-resolution spectroscopy, providing insights into the properties of the upper atmospheres of close-in gas giants. Methods.
We estimate the expected strength of He i emission in hot Jupiters based on their transmission signal. We search for theHe i τ Boo b in three nights of high-resolution spectra taken by CARMENES at the 3.5m Calar Altotelescope. The spectra in each night were corrected for telluric absorption, sky emission lines and stellar features, and shifted to theplanetary rest frame to search for the emission.
Results.
The He i emission is not detected in τ Boo b, reaching a 5 σ contrast limit of 4 × − for emission line widths of >
20 km s − .This is roughly a factor ∼ i transit absorption of 1% for hot Jupiters).This suggests that targeting the He i emission with well-designed observations using upcoming instruments such as VLT / CRIRES + and E-ELT / HIRES is possible.
Key words. planets and satellites: atmospheres – planets and satellites: individual ( τ Boo b) – techniques: spectroscopic – Infrared:planetary systems
1. Introduction
The atmospheres of close-in exoplanets are strongly a ff ected bythe high-energy irradiation from their host stars, making theirupper atmospheres weakly bound and susceptible to hydrody-namic escape (Owen 2019). For gas-giant planets, Lyman- α ab-sorption in transit measurements has been the primary probe fortheir extended atmospheres, e.g., HD 209458b (Vidal-Madjaret al. 2003), GJ 436b (Kulow et al. 2014; Ehrenreich et al. 2015)and GJ 3470b (Bourrier et al. 2018). Such observations tracethe exospheres with neutral hydrogen extending far beyond theRoche lobe radius, and cast light on the hydrodynamic escapeand mass loss, which drives the evolution of the atmospheric andbulk composition of close-in exoplanets (Ehrenreich et al. 2015).In addition to Ly α , helium at 10830 Å was also identifiedto be a powerful tracer of the extended atmospheres (Seager &Sasselov 2000), which was recently reassessed by Oklopˇci´c &Hirata (2018). This helium line has several advantages over Ly α because it su ff ers less from the interstellar absorption and can beobserved from the ground with high-resolution spectrographs,opening a new window into the characterization of exospheres.The theoretical work by Oklopˇci´c & Hirata (2018) has re-sulted in a breakthrough in helium measurements. Excess ab-sorption was first detected by the Hubble Space Telescope / WideField Camera 3 in WASP-107b (Spake et al. 2018) and inde-pendently confirmed by ground-based observations (Allart et al. 2019; Kirk et al. 2020) showing an absorption level of 5.54 ± ± ± ± ± ± i absorption were derived for Kelt-9b and GJ 436b at 0.33% and0.41% (Nortmann et al. 2018), for WASP-12b at 59 ±
143 ppmover a 70Å band (Kreidberg & Oklopˇci´c 2018), for GJ 1214b at3.8% ± S, which ismainly populated via recombination of ionized helium. The ion-ization of He i requires photons with wavelengths smaller than504 Å, i.e. X-ray and extreme-ultraviolet (EUV). Therefore, thehelium absorption is expected to be enhanced for planets irra-diated with higher X-ray and EUV flux (Nortmann et al. 2018).However, the level of EUV irradiation may not be the only de-termining factor. The mid-ultraviolet radiation near 2600 Å can Article number, page 1 of 9 a r X i v : . [ a s t r o - ph . E P ] S e p & A proofs: manuscript no. helium de-populate the triplet state 2 S via ionization. Therefore, thestrength of the helium absorption has been proposed to dependon the ratio between EUV and mid-UV stellar fluxes, and K-type stars may provide the most favorable stellar environment(Oklopˇci´c 2019). Hitherto, the exoplanets with detected heliumabsorption generally support this trend with four out of six orbit-ing K-type stars. More detections will help to better understandthe factors that a ff ect the He i absorption level.As helium atoms at the triplet state 2 S absorb photons toreach 2 P state, the opposite transition will happen concurrently,with 10830 Å photons re-emitted in random directions. Basedon the absorption level, we estimate the amount of emissionexpected from the planetary atmospheres. The study of He i airglow emission allows for better understanding of the radia-tion fields and level populations under non-local thermodynamicequilibrium in the upper atmospheres. In addition, it providesa way of probing the extended atmospheres of non-transitingclose-in gas giants, which have not been investigated before.In this paper, we address the detectability of He i emissionin the atmospheres of close-in exoplanets. We first calculate theexpected emission level (Section 2), then perform a case studyon τ Boo b (Section 3) searching for helium airglow emissionin high-resolution spectroscopic data from CARMENES (CalarAlto high-Resolution search for M dwarfs with Exoearths withNear-infrared and optical Echelle Spectrographs) in Section 4and 5. We discuss our results and future prospects in Section 6.
2. Helium emission from extended atmospheres
The concept of probing He i airglow emission is illustrated inFig. 1. We consider the extended atmosphere as an optically thincloud surrounding the exoplanet. The cloud absorbs a fraction ofirradiation from the host star due to the transition at 10830 Å, re-sulting in the helium atoms at state 2 S to be excited to the higherstate 2 P. The absorbed radiation is reemitted isotropically whenthe excited electrons jump back down to the metastable tripletstate. Assuming the extended atmosphere has a low density andis optically thin, the reemitted photons can freely escape andbe observed as an emission feature. We would like to point outthat during transit the feature is seen in absorption because onlya small fraction of the radiation is reemitted along the line-of-sight. Consequently, we can detect He i absorption lines duringtransit, while emission lines from other viewing angles.To estimate the strength of the He i emission, the cloud isassumed to absorb a fraction of the incident stellar energy at10830 Å, emitting it back isotropically. Assuming the upper en-ergy level not being (de-)populated in another way, we can esti-mate (see Seager 2010, Chap. 3)4 π R F S c = F S ∗ f abs (cid:18) R ∗ a (cid:19) π R (1)where R c is the radius of the cloud that absorbs radiation at thatwavelength, R ∗ is the stellar radius, a is the orbital distance of theplanet, f abs is the fraction of energy absorbed at 10830 Å, whichis linked to the column density of helium atoms at state 2 S inthe cloud, F S c and F S ∗ denote the 10830 Å flux at the surfaceof the planet and the star respectively. The corresponding fluxesthat we observe at Earth are F c = F S c (cid:18) R c D (cid:19) , F ∗ = F S ∗ (cid:18) R ∗ D (cid:19) (2) Fig. 1.
Illustration of He i emission from an exosphere of a close-inplanet. The gray disk represents the extended atmosphere around suchplanet. He i absorption is observed during transit, while airglow emis-sion can be probed at other orbital phases. where D is the distance of the system to Earth. Thus, the planetto star contrast at 10830 Å is F c F ∗ = f abs R a = R ∗ a T λ = − (cid:18) T λ (cid:19)(cid:18) a / R ∗ (cid:19) (3) T λ is the excess absorption at 10830 Å that can be measured bytransmission spectroscopy, with T λ = f abs R / R ∗ .Uncertainties regarding this estimate are further discussed inSection 6.1. A more detailed derivation involving radiative trans-fer is presented in Appendix A. Given Equation 3, we expectcontrast levels of ∼ − , which may be reached by combiningmultiple nights of observations.
3. The τ Boo system
The hot Jupiter τ Bootis b is among the first exoplanets dis-covered (Butler et al. 1997), orbiting a bright F7V type main-sequence star (V = ◦ by tracking CO absorption in its thermaldayside spectrum (Brogi et al. 2012), confirmed by measure-ments of H O (Lockwood et al. 2014). The properties of the τ Boo system are summarized in Table 1. Unfortunately, becausethe planet is not transiting, there is no direct measure of its ra-dius (meaning that its surface gravity is unknown), and the He i × erg s − (Huensch et al. 1998),and a reconstructed EUV luminosity of 2 . × erg s − (Sanz-Forcada et al. 2011), which are among the highest values foundin the planet-hosting stars. The intense X-ray and EUV radiationcan deposit substantial energy in the planetary atmosphere, facil-itating the expansion and evaporation of gas. Although τ Boo isnot a K-type star (which is possibly the most favorable spectraltype for probing the helium line), however, due to the high levelof stellar X-ray and EUV emission, τ Boo b could well havean extended atmosphere with a large population of helium at thetriplet state, and forms a promising target to search for the He i emission at 10830 Å. Article number, page 2 of 9apeng Zhang et al.: He i airglow emission from τ Boo b
Table 1.
Properties of the star τ Boo (upper part) and τ Boo b (lowerpart).
Parameter Symbol Value
Distance (pc) a d . ± . ff ective temperature (K) b T e ff ± L (cid:12) ) b L ∗ . ± . M (cid:12) ) b M ∗ . ± . R (cid:12) ) b R ∗ . ± . c log g . + . − . Systemic velocity (km s − ) d γ − . ± . − ) b v sin( i ) 14 . ± . − ) e K ∗ . ± . b [M / H] 0 . ± . b . ± . e P . ± . · − Semi-major axis (AU) b a . ± . d i . ± . b e . ± . M J ) b M p . ± . e T . ± . − ) d K P . ± . References. ( a ) Gaia Collaboration et al. (2018); ( b ) Borsa et al. (2015);( c ) Takeda et al. (2007); ( d ) Brogi et al. (2012); ( e ) Justesen & Albrecht(2019)
4. Observations and Data analysis
We observed and analyzed the τ Boo system for five nightswith the CARMENES spectrograph mounted on the 3.5m Calar-Alto Telescope (Quirrenbach et al. 2016), on 26 March 2018, 11May 2018, 12 March 2019, 15 March 2019 and 11 April 2019.CARMENES has two channels, VIS and NIR, covering the opti-cal wavelength range (520-960 nm) and the near-infrared wave-length range (960-1710 nm) respectively. The resolving poweris 94,600 in the VIS channel and 80,400 in the NIR channel.Each channel is fed with two fibers: fiber A targeting the starand fiber B obtaining a sky spectrum simultaneously. The He i line at 10830 Å falls on echelle order 56 (10801-11001 Å) in theNIR channel, on which we focused our analysis.The details of the observations are shown in Table 2 andFig. 2. The observations probed thermal emission from τ Boob, covering a wide range in planet orbital phases each night(see Fig. 2). The exposure times were adjusted according to theweather conditions, maintaining a S / N ≥ (cid:48)(cid:48) and 1.4 (cid:48)(cid:48) respectively, delivering lower S / Nper spectrum than during the other nights with longer exposuresand better weather conditions. The drop-o ff in S / N during theend of night 2 was due to the increasingly high airmass. The rel-ative humidity during night 1, 2 and 5 continuously exceeded85%, in contrast to the lower value ( ∼ / N in these nights. For night3, although the relative humidity was not as high as the firsttwo nights, it underwent strong variation overnight, possibly ac-counting for the drastic change in S / N.The standard data reduction, such as bias removal, flat field-ing, cosmic ray corrections, and wavelength calibration, wasperformed with the CARMENES pipeline
CARACAL v2.10 (Ca-ballero et al. 2016). The output of the pipeline was provided inthe observer’s frame with a vacuum wavelength solution. We A i r m a ss Night 1Night 2Night 3Night 4Night 5 H u m i d i t y [ % ] S / N L i n e v a r i a t i o n [ % ] Fig. 2.
Variation in airmass (upper panel), relative humidity (mid panel),S / N (lower panel) and variation around the mean of the stellar He i line (bottom panel) during observations in the di ff erent nights. The S / Nof each spectrum is defined as the average signal-to-noise ratio of thecontinuum near the He i converted the vacuum wavelength solution into air wavelengthsand used it throughout our analysis. First, we manually corrected for additional hot pixels and cosmicrays present in the pipeline-reduced spectra by substituting thosevalues with the linear interpolation of adjacent pixels or adja-cent time series. Subsequently, each spectrum was normalized tounity using the continuum both at the blue and red side of the he-lium line over the ranges 10804.0-10805.2 Å, 10818.5-10819.0Å and 10839.0-10840.3 Å. After normalization, the spectral se-ries of each night were handled as a two-dimensional matrix asshown in Fig. 3(a). Each row in the matrix represents one spec-trum, with the frame number on the y-axis, corresponding to or-bital phase or time.Before correcting for the telluric lines, we first removedthe stellar Si line and He i triplet at 10827.1 Å and 10829.09,10830.25 and 10830.34 Å. In order to achieve this, we built anempirical stellar model for each night by combining all spectrawith S / N >
100 in the stellar rest frame, where we set all valuesoutside of the two stellar features to unity. This model was thenshifted to the observer’s rest frame, scaled and removed fromeach spectrum. Subsequently, the spectra were free of stellarlines in the wavelength region near the planetary helium line (seeFig. 3(b)).The residual matrix in Fig. 3(b) shows the telluric lines nearthe planetary helium signal that required removal, including theH O absorption features at 10832.1 Å and 10834.0 Å, and theOH emission lines at 10824.7 Å, 10829.8 Å and 10831.3 Å.The strengths of telluric lines vary overnight, which mainly re-sults from the change in airmass and / or water column. To cor-rect for telluric absorption lines, we measured the temporal vari-ation of the flux at the centers of several deep H O absorptionfeatures and combined them to serve as a representation forthe atmospheric change overnight. Such temporal variation was
Article number, page 3 of 9 & A proofs: manuscript no. helium
Table 2.
Observations Summary
Night Date Proposal No. Program PI No. of spectra Exposure time (s) On-target time (h) S / N (a) (b) Å ]050100150 (c) Fig. 3.
Illustration of our data reduction steps applied to the spectralseries taken on Night 4. Each row in the matrix represents one spectrum,with the y-axis corresponding to time. As detailed in Section 4.1, thesteps include: (a) normalization of the continuum; (b) correction forstellar lines in each spectrum using an empirical model; (c) removal oftelluric contamination by correcting the temporal variation of the flux intelluric lines using a column-by-column linear regression. The trail ofan artificially injected planetary helium line (with a magnitude of 0.3%and a width of 11 km s − ) can be seen as a slanted white band near10830 Å, shifting in time due to the change in the radial component ofthe orbital velocity of the planet. then removed using a column-by-column linear regression whileavoiding the columns that contain the assumed planetary He i emission. We removed the sky emission lines in a similar way,using their mean-variation overnight. After telluric correction,each column of the matrix was subsequently normalized as fol-lows. The spectra were combined via weighted average, with theweights defined as the squared S / N of each exposure, to builda master spectrum. Each individual spectrum was subsequentlydivided by this master spectrum to obtain the residual spectralseries as shown in Fig. 3(c).We note that during the telluric removal and final normali-sation, we masked the region in each spectrum where the plan-etary He line is expected to appear, so that we could avoid self-subtraction of the signal, if present. This is particularly important
Night 5Night 4Night 3Night 210827 10828 10829 10830 10831 10832Wavelength [ Å ]Night 1 Fig. 4.
Residual spectral series from night 1 to 5. The y-axis representsthe time or orbital phase. The residuals are binned to 0.006 in phasefor clarity. The slanted dashed lines in red trace the expected planetaryhelium line. The dotted lines in blue denote the positions of the stellarHe i triplet. The shaded region in night 2 contains the telluric H O ab-sorption and OH emission line, overlapping with the expected planetaryhelium line. if the planetary He i line is broad. In the case that the line width islarger than the change of the planetary radial velocity overnight,the planetary signal would be (partially) subtracted out, makingit less likely to be detected. After correcting for the stellar and telluric e ff ects, we shifted theresidual spectral series of all five nights into the stellar rest frameby correcting for the systemic velocity, barycentric velocity, andstellar reflex motion of τ Boo, as shown in Fig. 4. The spectrawere binned to 0.006 in phase (y-axis) for a better identificationof the noise structure. We noticed that the observations in nights2 and 3 su ff er from broad noise structures, which may originatefrom the variability of stellar lines or the residuals of telluriccorrections.As we noted in section 3, the star τ Boo shows a high level ofchromospheric activity. The stellar He i line as a chromosphericdiagnostic may undergo temporal variation due to flaring. Thestrength of the stellar He i line can also show periodic modula-tion by rotation if the line is not homogeneous on the stellar disk(Andretta et al. 2017). Moreover, the fast spin of τ Boo mayresult in residual noise features shifting in wavelength up to itsrotation velocity ( ∼
15 km s − ). To quantify the e ff ect of stellarvariability, we measured the strength of the stellar He i line at10830 Å during each night by fitting a Gaussian profile to thedata and measuring the amplitude of the best-fit Gaussian pro-file. We define the line variation as the relative depth with respectto the average stellar spectrum of each night, and then bin theresults to 0.006 in phase (see Fig. 2 bottom panel). During a sin-gle night, the variation is generally ≤ ff ectour analysis. However, it is possible that the variation can buildup as we combine di ff erent frames during the night, leading to Article number, page 4 of 9apeng Zhang et al.: He i airglow emission from τ Boo b N o r m a li z e d f l u x Night 1Night 2Night 3Night 4Night 5 Å ]-2.00%0.00%2.00% V a r i a t i o n Fig. 5.
Upper panel: the average profile of the stellar helium line ineach night. Lower panel: the di ff erence of each profile with respect tothe mean. The deep absorption line at 10832.2 Å in night 2 (blue curve)is a telluric H O line. The small peaks on top of the helium line in night1 and 5 are caused by sky OH emission. systematic noise in the combined residual spectrum. For exam-ple, the variability of He i line may be responsible for the varia-tion in the residual flux at 10830.3 Å in night 2 (see Fig. 4). Wealso compared the average line profile of di ff erent nights (Fig. 5).On a night-to-night basis, we note that the helium line profile innight 2 is distinct from other nights, perhaps due to the influenceof the nearby strong telluric line or the higher level of stellaractivity.In addition, we note that the spectral S / N in the middle ofnight 3 abruptly dropped by a factor of two as shown in Fig. 2,probably due to the changing weather condition. This may leadto the inconsistency of the data in the region from 10829.4 to10830.2 Å. Unfortunately, the trail of the planetary signal innight 3 resides exactly in this problematic wavelength range,overwhelmed by artifacts (see Fig 4). As for the night 2 observa-tions, telluric lines show a high level of strength and variabilitydue to the high relative humidity and the variation of the pre-cipitable water vapor, which could not completely be removed.The residuals of the deep telluric H O line at 10832.1 Å and OHsky emission at 10831.3 Å coincide with the trail of the plane-tary signal (see Fig 4), making it di ffi cult to preserve it whileremoving the telluric contamination. In such condition, addingthe night 2 data does not enhance the S / N because more noisewas introduced along with the diminished signal. Consequently,we excluded the observations of night 2 and 3 from further anal-ysis.Based on the ephemeris listed in Table 1, we shifted theresidual spectra to the planetary rest frame. The residual spec-tral series from di ff erent nights were then combined with eachresidual spectrum weighted by its variance over the radial veloc-ity ranges from -150 to -50 km s − and from 50 to 150 km s − .
5. Result
Fig. 6 shows the time-averaged spectrum around the helium linein the planet rest-frame, with the amplitude scaled to make thestandard deviation equal to unity around the targeted He i W=3.7km/s S / N W=14.9km/s
Data_convolvedInjectionDifference
150 100 50 0 50 100 150
Radial velocity [km s ] W=29.8km/s
Fig. 6.
Combined (3 nights) residual spectra in the planetary rest framecentered at the 10830 Å He i line. In the three panels, the solid blackline indicates the residual spectra, boxcar-smoothed by 3.7 km s − (top),14.9 km s − (middle), and 29.8 km s − (bottom). The dotted curves showan artificially injected signal at a S / N of 5, with the solid red curve thedi ff erence between the injected and original data. The values are scaledby the standard deviation of the observed residuals so that the y-axisrepresents the S / N. Å line. We find no statistically significant signal from the plane-tary He i As we have no information on the profile of the potential He i line originating from τ Boo b, we assumed a box profile cen-tered at 10830.3 Å, which has a clear definition of the line widthcompared to a Gaussian profile. We performed signal injectionsconsidering various widths ( W ) of the planetary emission, rang-ing from 3.7 km s − (equal to the instrument resolution) to 37 kms − (which is limited by the self-subtraction of broad signals).The combined residuals of both the observations and injectionsare shown in Fig. 6 for three di ff erent line widths as examples.We regarded the original residuals (without signal injection) asthe noise, and convolved it with the corresponding signal profileto take the width of the signal into account. The noise level isdefined as the standard deviation (from -150 to +
150 km s − )of the convolved residuals. These were then scaled by this noiselevel, so that the y-axis represents the signal-to-noise ratio (S / N).The strength of the signal in each injection case was determinedby measuring the amplitude of the recovered signal, which isthe di ff erence between the injected and the original residuals, asshown by the red curves in Fig. 6. The 5 σ detection limits were Article number, page 5 of 9 & A proofs: manuscript no. helium W [km/s]0.30.40.50.60.70.80.9 c o n t r a s t li m i t [ × ] y W E W [ m Å ] Fig. 7.
The 5 σ detection limit of the He i airglow emission as a functionof the line width of the potential signal using 3 nights of observationsof τ Boo b (solid black line), and corresponding equivalent widths ofthe detection limit (solid red curve). The dashed line represents a scaledrelation of W − / , expected for pure Gaussian white noise. thus determined as the minimum line emission leading to a re-covered S / N of 5 in our injection tests. The detection limit as afunction of the line width is shown in Fig. 7. We note that theS / N is determined at the peak of the emission signal (namelythe amplitude of the box profile). Therefore, detecting a broadersignal requires a lower level of the peak contrast, as shown inthe black line in Fig. 7. However, this does not mean that thedetectability increases when it comes to broad signals. As theflux is distributed into wider velocity space due to broadeningmechanisms, it actually requires larger amount of integrated flux(namely higher Equivalent Width) to detect broader signals. Thecorresponding Equivalent Width limit required for 5 σ detectionis plotted in the red curve in Fig. 7.The width of the signal is a ff ecting the S / N of a potentialdetection in the following ways. First, the level of white noisedecreases with the square root of the line width. Although theresidual noise in our case is not fully uncorrelated due to im-perfect stellar and telluric corrections, the S / N can still be en-hanced, if not as much as by a factor of √ W . Secondly, for alarger W a wider part of the planet emission line trail is maskedout, changing the residual noise pattern of the data, as shownin Fig. 6, where the observed residuals (solid black curves) fordi ff erent widths are not identical. Furthermore, the detection ofbroad planetary signals is hindered by the self-subtraction prob-lem as discussed in section 4.1. Hence, the detectability dropssignificantly for widths larger than 25 km s − , which is compa-rable to the radial velocity change of the planet during a night.Overall, the detection limit drops significantly towards larger W ,but reaches a plateau at W >
20 km s − , for which we reach a5 σ limit of 4 × − . Prior knowledge of the planetary orbit was used to mask the trailin the spectral series to avoid self-subtraction of the potentialsignal (see section 4.1). In order to assess the influence of thisprocedure on the final result, we repeated the whole analysisadopting a grid of planetary orbits with di ff erent semi-amplitude K P and phase o ff set ∆ φ when applying the mask. In Fig. 8, wemapped the S / N of the residuals at 10830.3 Å in the planetaryrest frame for each hypothetical orbit in the grid. As a compari-son, we produced a similar map when injecting an artificial plan-etary signal with a strength of 3 . × − and a width of 30 km K p [ k m / s ] Observation
Injection
Fig. 8.
The S / N map for a grid of planetary orbits with di ff erent semi-amplitude K P and phase o ff set ∆ φ . There is no salient signal in theobservations (left panel). An injected signal at K P =
110 km s − and ∆ φ = s − , which is recovered at K P =
110 km s − and ∆ φ =
6. Discussion
Using three nights of observations ( ∼ τ Boo b using CARMENES, we reached a contrast limit of4 × − for a planetary He i emission with a boxcar profile witha width >
20 km s − . However, following Equation 3, the esti-mated amplitude of the He i emission is typically ≤ − . At thisstage, no detection is expected with these observations.We note that we made several assumptions for simplicity.First, we assume the atmosphere extends significantly beyondthe planet radius and the He i cloud is considered to be opticallythin. The stellar radiation is absorbed uniformly in the cloud andreemitted isotropically. In addition, Equation 3 assumes that theenergy is conserved at the particular wavelength 10830 Å, mean-ing that we only take into account the transition between the he-lium 2 S and 2 P states.In practice, the flux ratio can deviate from this simplifiedmodel in the following ways. (a) The flux emission of the cloudcan be higher than our estimation if the extent of the exosphereis even larger than the stellar disk, in which case the measured f abs in the transmission spectrum is lower than the actual ab-sorption level of the entire cloud. (b) Analysis on the line ra-tio of He i triplet detected in transmission observations suggeststhat the planetary signal could also originate from an opticallythick part of the atmosphere, especially for Jupiter-mass plan-ets such as HD 189733b and HD 209458b, where the He i ab-sorption feature traces compact atmospheres with an extent ofonly a fraction of planetary radii (Salz et al. 2018; Lampón et al.2020). If the cloud is not optically thin or the He i atmosphereis not significantly larger with respect to the planet, the reradi-ation is not isotropically emitted from the cloud in 4 π but withpreferential directions, as an analogy to scattered light. In thiscase, the emission flux at the full phase (i.e. when the illumi-nated hemisphere is totally in view) is enhanced as compared tothe value in Equation 3, yet it also needs to be scaled with thephase function Φ α at di ff erent orbital phases (where we observedi ff erent portions of the illuminated hemisphere). (c) If the He i cloud is not optically thin, the planetary thermal emission pass-ing through the cloud can be absorbed along the line of sight,which cancels out a portion of the airglow emission. To evalu-ate this e ff ect, we compare the absorbed thermal emission to the Article number, page 6 of 9apeng Zhang et al.: He i airglow emission from τ Boo b airglow emission flux as follows. Assuming the planet emits as ablackbody with an equilibrium temperature of T p , we can calcu-late the planetary thermal emission flux in contrast to the stellarflux at 10830 Å. Taking τ Boo system as an example, the fluxcontrast is F th / F ∗ ∼ − ∼ . F c / F ∗ . To the optically thicklimit, where all thermal emission is absorbed by the He i cloud,it counterbalances ∼
25% of the airglow emission. Consequently,even in the extreme optically thick case, the helium is expectedto be seen in emission. (d) The emission level of He i P state aswell as the rates of the stimulated and spontaneous decay of 2 Pstate. Studying this requires detailed accounts and comparisonsof other de-populating processes including photoionization from2 P state, electron / H-atom collisions, and radiative excitation to2 D state (D3 line). Previous models of helium atmospheres,such as Oklopˇci´c & Hirata (2018); Lampón et al. (2020), ne-glect transitions related to 2 P state because the metastable 2 Sstate population is not significantly a ff ected by these processesas an atom in 2 P state just decays back to 2 S state (Oklopˇci´c &Hirata 2018). This indicates that the 2 P to 2 S decay is the ma-jor way of de-populating the 2 P state. Therefore, we can arguefor the connection between the level of absorption and airglowemission at 10830 Å.In addition to the amplitude of the He i emission, the ve-locity profile is rather uncertain. Current detections suggest thatthe He i excess absorption spans a wide range of line widths.For instance, Saturn or Neptune mass planets such as WASP-69b and HAT-P-11b (Allart et al. 2018; Nortmann et al. 2018)are reported to have broad absorption feature (up to ∼
30 kms − ), while Jupiter-mass planets such as HD 209485b (Alonso-Floriano et al. 2019) show a more narrow signature of ∼
10 kms − , implying a lower rate of atmospheric escape and mass loss.The line profile depends on the physical and hydrodynamic prop-erties such as the kinematic temperature of the exosphere and theatmospheric escape, which are not well understood (Salz et al.2016). Considering the diverse nature of planetary atmospheres,it is therefore recommended to explore a variety of line widthsand line positions in data analysis. Based on our data analysis, we find several aspects that should betaken into account when designing future observations to searchfor He i airglow emission. Firstly, the observations should avoidblending the planetary helium signal with strong telluric absorp-tion lines (such as during our night 2 observations). In such situa-tion, a large portion of the emission signal is removed along withthe telluric correction. Even if the signal is preserved with othermethods, strong telluric features cannot be corrected perfectly,introducing artifacts around the helium signal. Furthermore, theS / N of observations at the core of strong telluric absorption linesis significantly lower than in the continuum. Hence, the potentialsignal falling in such region is more di ffi cult to detect. Therefore,taking into account the relative position between the planetaryand telluric lines, and selecting the proper time for observationsaccording to the barycentric Earth radial velocity (BERV) andthe planetary radial velocity are desirable.The stellar activity is yet another factor to consider in dataanalysis because the stellar He i line as a chromospheric diag-nostic may undergo temporal variation during observations. Foran active star like τ Boo , this is likely to happen and introduceextra noise. Cauley et al. (2018), Salz et al. (2018) and Guilluy et al. (2020) evaluated the impact of stellar activity on probingthe planetary helium atmosphere in transmission. However, un-like transit observations, additional noise related to stellar ac-tivity should not significantly a ff ect measurements of emissionsignals from a planet, because there is always a radial velocityo ff set between the star and planet when probing emission. Onlywhen the radial velocity di ff erence is small (that is, during transitand secondary eclipse), can stellar activity contribute to noise atthe planetary rest frame and result in pseudo-signals. In terms ofdetecting airglow emission, the likely consequence of the vari-ability of stellar He i line is to introduce systematic noise struc-ture nearby the planetary signal in the temporal-combined resid-ual spectrum, instead of a ff ecting the level of planetary signal.Consequently, for highly active stars, there needs to be su ffi cientdi ff erence between the planet and stellar radial velocity, whichdepends on the orbital phase, during observations.In terms of target selection, we performed the case study on τ Boo because the star is significantly brighter than other knownhot-Jupiter systems, enabling high S / N observations. In addition,its high level of stellar activity likely results in an extended plan-etary atmosphere with the He i S populated. As shown in Fig 9,accounting for both the stellar brightness and the airglow emis-sion signal estimated using Equation 3, τ Boo b falls closest toour detection limit (denoted by the dashed line) among other po-tential targets. In the emission signal calculation, as we have nomeasurements of the He i absorption by the non-transiting τ Boob, we assume an absorption level of 1%, which, however, bringsabout some uncertainty. τ Boo as an F-type star may also havehigh levels of mid-UV radiation that can de-populate the heliumtriplet states, leading to a weaker signal. It remains unclear towhat extent these various factors contribute to the He i signal asa whole. In addition, the planet mass is significantly higher thanthat of most hot Jupiters, increasing the surface gravity, possi-bly making atmospheric escape more di ffi cult (Salz et al. 2016).A more secure choice is to investigate those targets with He i absorption already measured via transmission spectroscopy (de-noted with red dots in Fig 9), so that we have an expectation ofthe emission amplitude beforehand. Another benefit of targetinga transit planet is that we could obtain the stellar spectrum with-out any contribution from the planet during secondary eclipse.Using that as a reference spectrum, we can avoid self-subtractingthe planetary signal in analysis, which is particularly importantfor broad signatures. Furthermore, as discussed in Section 6.1,the airglow emission signal is partially counterbalanced by ab-sorption of planet thermal emission through the He i cloud whenit is compact. Consequently, planets with pu ff y and optically thinHe i clouds are better targets for this purpose. CRIRES + is an upgrade of the cryogenic high-resolution in-frared echelle spectrograph (CRIRES) located at the focus ofUT1 of the Very Large Telescope (VLT), providing a spectralresolving power of 100,000 (Follert et al. 2014). If we sim-ply scale the expected S / N for observations with CRIRES + bythe larger telescope diameter of the 8.2m VLT compared to the3.5m Calar Alto Telescope, also considering that the through-put of CRIRES + may be a factor of 1.5 lower than that ofCARMENES, while the observing condition at VLT site is gen-erally better, we expect in the same observing time to go a factor ∼ × − for a broad He i emission given the same amount ofintegration ( ∼ τ Boo b as an example, follow-ing Equation 3, we estimate the amplitude of the emission to be
Article number, page 7 of 9 & A proofs: manuscript no. helium Airglow emission signal468101214 V m a g WASP-107 bWASP-69 bHAT-P-11 bGJ 3470 bGJ 436 b WASP-12 bGJ 1214 bK2-100 b Boo b KELT-9 bHD 209458 b HD 189733 b
Fig. 9.
The V magnitude of host stars plotted against the airglow emis-sion signal estimated using Equation 3 for exoplanets with He i absorp-tion detections (in red dots) or upper limits (in blue triangles). The blackstar represents the estimated signal of τ Boo b assuming a typical ab-sorption level of 1%. The black dashed line shows the detection limit ofour analysis. ∼ × − assuming a typical "transit" absorption level of 1%.This means that a 3 σ detection of He i airglow emission couldbe obtained in ∼ i emission is demanding using the current generation of tele-scopes, it is promising with the High Resolution Spectrograph(HIRES) at ESO’s forthcoming Extremely Large Telescope (E-ELT) (Marconi et al. 2016). Thanks to the significantly larger di-ameter of the 39m E-ELT, the 5 σ detection of He i airglow emis-sion could be achieved with ∼
7. Conclusions
This paper explores the possibility of probing He i emission at10830 Å in the extended atmospheres of hot Jupiters, the am-plitude of which is estimated based on the He i absorption levelas observed during transit. We search for this emission from τ Boo b using CARMENES spectra. We correct for the telluricand stellar features nearby the expected He i signal and combinemultiple nights of observations. Given our estimation of the con-trast of ≤ − , the 6.5-hour data combined is not su ffi cient to putmeaningful constrains on the He i emission from the planet. Thedetection limit that we derive from our analysis is 4 × − fora broad emission signal with a width of >
20 km s − . While wedo not reach the required contrast with the current CARMENESdata, the He i airglow emission from hot-Jupiters is still promis-ing to probe with future instruments. Acknowledgements.
We thank the referee and editor for comments which helpedimproving the quality of the paper. Y.Z., I.S., F.A., and P.M. acknowledge fund-ing from the European Research Council (ERC) under the European Union’sHorizon 2020 research and innovation program under grant agreement No694513. P.M. acknowledges support from the European Research Council un-der the European Union’s Horizon 2020 research and innovation program un-der grant agreement No. 832428. M.B. acknowledges support from the UK Sci-ence and Technology Facilities Council (STFC) research grant ST / S000631 / References
Allart, R., Bourrier, V., Lovis, C., et al. 2019, A&A, 623, A58Allart, R., Bourrier, V., Lovis, C., et al. 2018, Science, 362, 1384Alonso-Floriano, F. J., Snellen, I. A. G., Czesla, S., et al. 2019, A&A, 629, A110Andretta, V., Giampapa, M. S., Covino, E., Reiners, A., & Beeck, B. 2017, ApJ,839, 97Borsa, F., Scandariato, G., Rainer, M., et al. 2015, A&A, 578, A64Bourrier, V., Lecavelier des Etangs, A., Ehrenreich, D., et al. 2018, A&A, 620,A147Brogi, M., Snellen, I. A. G., de Kok, R. J., et al. 2012, Nature, 486, 502Butler, R. P., Marcy, G. W., Williams, E., Hauser, H., & Shirts, P. 1997, ApJ,474, L115Caballero, J. A., Guàrdia, J., López del Fresno, M., et al. 2016, in Societyof Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.9910, Proc. SPIE, 99100ECauley, P. W., Kuckein, C., Redfield, S., et al. 2018, AJ, 156, 189Crossfield, I. J. M., Barman, T., Hansen, B., & Frewen, S. 2019, Research Notesof the American Astronomical Society, 3, 24Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, Nature, 522, 459Follert, R., Dorn, R. J., Oliva, E., et al. 2014, in Society of Photo-Optical In-strumentation Engineers (SPIE) Conference Series, Vol. 9147, Proc. SPIE,914719Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A, 616, A1Gaidos, E., Hirano, T., Mann, A. W., et al. 2020, MNRAS, 495, 650Guilluy, G., Andretta, V., Borsa, F., et al. 2020, arXiv e-prints, arXiv:2005.05676Hirano, T., Krishnamurthy, V., Gaidos, E., et al. 2020, arXiv e-prints,arXiv:2006.13243Huensch, M., Schmitt, J. H. M. M., & Voges, W. 1998, A&AS, 132, 155Justesen, A. B. & Albrecht, S. 2019, A&A, 625, A59Kirk, J., Alam, M. K., López-Morales, M., & Zeng, L. 2020, AJ, 159, 115Kreidberg, L. & Oklopˇci´c, A. 2018, Research Notes of the American Astronom-ical Society, 2, 44Kulow, J. R., France, K., Linsky, J., & Loyd, R. O. P. 2014, ApJ, 786, 132Lampón, M., López-Puertas, M., Lara, L. M., et al. 2020, A&A, 636, A13Lockwood, A. C., Johnson, J. A., Bender, C. F., et al. 2014, ApJ, 783, L29Mansfield, M., Bean, J. L., Oklopˇci´c, A., et al. 2018, ApJ, 868, L34Marconi, A., Di Marcantonio, P., D’Odorico, V., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908,Proc. SPIE, 990823Ninan, J. P., Stefansson, G., Mahadevan, S., et al. 2020, ApJ, 894, 97Nortmann, L., Pallé, E., Salz, M., et al. 2018, Science, 362, 1388Oklopˇci´c, A. 2019, ApJ, 881, 133Oklopˇci´c, A. & Hirata, C. M. 2018, ApJ, 855, L11Owen, J. E. 2019, Annual Review of Earth and Planetary Sciences, 47, 67Palle, E., Nortmann, L., Casasayas-Barris, N., et al. 2020, A&A, 638, A61Quirrenbach, A., Amado, P. J., Caballero, J. A., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9908,Proc. SPIE, 990812Salz, M., Czesla, S., Schneider, P. C., et al. 2018, A&A, 620, A97Salz, M., Czesla, S., Schneider, P. C., & Schmitt, J. H. M. M. 2016, A&A, 586,A75Sanz-Forcada, J., Micela, G., Ribas, I., et al. 2011, A&A, 532, A6Seager, S. 2010, Exoplanet Atmospheres: Physical ProcessesSeager, S. & Sasselov, D. D. 2000, ApJ, 537, 916Spake, J. J., Sing, D. K., Evans, T. M., et al. 2018, Nature, 557, 68Takeda, G., Ford, E. B., Sills, A., et al. 2007, ApJS, 168, 297Vidal-Madjar, A., Lecavelier des Etangs, A., Désert, J. M., et al. 2003, Nature,422, 143Wright, J. T., Marcy, G. W., Butler, R. P., & Vogt, S. S. 2004, ApJS, 152, 261
Article number, page 8 of 9apeng Zhang et al.: He i airglow emission from τ Boo b
Appendix A: Derivation of helium emissionstrength with radiative transfer
During transit, the stellar flux F ∗ decreases by ∆ F ∗ due to theabsorption by helium atoms at 2 S state. The absorption depth T λ measured by transmission spectroscopy is T λ = ∆ F ∗ F ∗ = R c R ∗ f abs = R c R ∗ (1 − e − τ c ) , (A.1)where τ c is the optical depth of the He i cloud around the planet,and the structure of the cloud is neglected. Appendix A.1: Optically thick
For optically thick clouds, namely, τ c >>
1, Equation A.1 be-comes R c = R ∗ (cid:112) T λ . (A.2)The emission flux from the cloud can be approximated asisotropic scattering with an albedo of 1, resulting in a factor of2 / F S c = F S ∗ (cid:18) R ∗ a (cid:19) . (A.3)Substituting Equation 2 and A.2 into Equation A.3, we get F c F ∗ = ∆ F ∗ F ∗ (cid:18) R ∗ a (cid:19) = T λ (cid:18) R ∗ a (cid:19) . (A.4) Appendix A.2: Optically thin
For optically thin cases, we consider the simplified 1D plane-parallel equation of radiative transfer dId τ = I ( τ ) − S ( τ ) , (A.5)where I ν is the spectral radiance, S is the source function, and τ is the extinction optical depth which increases towards interiorof the cloud (i.e. the optical depth at the interior is τ c and that atthe surface is 0).The source function is approximated as S ( τ ) = J ∗ ( τ ) = π (cid:90) I ∗ ( τ ) d Ω = π (cid:18) R ∗ a (cid:19) F S ∗ e − τ . (A.6)Hence, the solution for the equation of radiative transfer can becomposed as I ( τ ) = ce τ + π (cid:18) R ∗ a (cid:19) F S ∗ e − τ . (A.7)Using the boundary condition I ( τ c ) =
0, the integral constant c is determined, making the solution simplified as I ( τ ) = π (cid:18) R ∗ a (cid:19) F S ∗ ( e − τ − e τ − τ c ) . (A.8)Then the emergent radiance from the cloud I c is I c = I (0) = π (cid:18) R ∗ a (cid:19) F S ∗ (1 − e − τ c ) . (A.9)The observed flux of the cloud is F c = (cid:90) I c ( n c · n detector ) d Ω = π (cid:18) R ∗ a (cid:19) F S ∗ (1 − e − τ c ) π R c D , (A.10) where n c and n detector represent the unit vectors along the inten-sity of the cloud and the normal direction of the detector surfacerespectively. Since the targets are far away, we can safely assume n c · n detector = F ∗ = F S ∗ R ∗ / D and Equation A.1 into Equa-tion A.10, we have F c = ∆ F ∗ (cid:18) R ∗ a (cid:19) − e − τ c − e − τ c . (A.11)At the optically thin limit ( τ c << F c F ∗ = ∆ F ∗ F ∗ (cid:18) R ∗ a (cid:19) = T λ (cid:18) R ∗ a (cid:19) , (A.12)which agrees with Equation 3.(A.12)which agrees with Equation 3.