A 0.8-2.4 Micron Transmission Spectrum of the Hot Jupiter CoRoT-1b
aa r X i v : . [ a s t r o - ph . E P ] J a n Draft version July 15, 2018
Preprint typeset using L A TEX style emulateapj v. 04/17/13
A 0.8-2.4 MICRON TRANSMISSION SPECTRUM OF THE HOT JUPITER COROT-1B
E. Schlawin , M. Zhao , J. K. Teske , T. Herter Draft version July 15, 2018
ABSTRACTHot Jupiters with brightness temperatures & K =12.2) with a measured planetary transmission spectrum. Subject headings: radiative transfer, planets and satellites: individual (CoRoT-1b), stars: individual(CoRoT-1), (stars:) planetary systems INTRODUCTION
Transiting hot Jupiters are among the most ob-servationally favorable sources for measuring atmo-spheric composition, global winds, temperature inver-sions and disequilibrium chemistry (e.g., Pont et al.2013; Snellen et al. 2010; Rogers et al. 2009; Moses et al.2011). Their large physical radii, frequent transits, hightemperatures and large radial velocity amplitudes per-mit both the measurement of physical parameters (mass,radius, orbital elements) and the ability to test atmo-spheric models. The primary transit, when the planetgoes in front of its host star, and the secondary eclipse,when the planet goes behind, are valuable opportuni-ties to spectroscopically characterize the atmosphere.These spectra can be compared with models to deter-mine mixing ratios of atmospheric gases, clouds, scat-terers and/or aerosols. Furthermore, high quality spec-tra can be used to constrain the formation of exoplan-ets (e.g., Spiegel & Burrows 2012), the extent of equilib-rium/disequilibrium chemistry (e.g., Moses et al. 2011),vertical mixing (e.g., Visscher & Moses 2011) and putthe Solar System in context.Transmission spectra and emission spectra of hotJupiter atmospheres have already been used to detectNa (Charbonneau et al. 2002), K (Sing et al. 2011), Ca Astronomy Department, Cornell University, Ithaca NY14853 Department of Astronomy, Pennsylvania State University,University Park PA 16802 Center for Exoplanets and Habitable Worlds, UniversityPark PA 16802 Astronomy Department, The University of Arizona, TucsonAZ 85721 (Astudillo-Defru & Rojo 2013), H (Vidal-Madjar et al.2003), H O (e.g., Deming et al. 2013; Birkby et al.2013), CO (e.g., Snellen et al. 2010) and possibly CH ,(Swain et al. 2008, though see Gibson et al. (2012a)).Furthermore, emission and transmission spectra havebeen used to constrain the mixing ratios of these atomsand molecules. Of considerable interest is the relativeabundances such as the C/O ratio (Teske et al. 2013;Madhusudhan 2012; Madhusudhan et al. 2011a), whichgives clues as to the formation of planets such as cir-cumstellar disk composition and location within the disk(e.g., ¨Oberg et al. 2011; Moses et al. 2013).Infrared observations of prominent molecular bands inhot Jupiters during secondary eclipse are used to infer anatmospheric temperature profile (e.g., Line et al. 2013b).The level of emission by gases of upper layers as com-pared to lower levels indicates their relative tempera-tures. For example, the brightness temperature of the4.5 µ m Spitzer band is expected to be higher than the3.6 µ m band for temperature-inverted planets becauseit encompasses several molecular bands that are high inopacity (and high in altitude), whereas the 3.6 µ m bandsees deeper in the atmosphere (Knutson et al. 2010).Broadly, hot Jupiter atmospheres have been classi-fied into (1) planets that have temperatures that de-crease with altitude for observable pressures and (2)planets that contain a temperature inversion or strato-sphere at observable pressures. We include an isother-mal (constant temperature with altitude) in the latercase. One possible explanation for the bifurcation intotheses profiles is that TiO and VO absorption of stel-lar flux creates temperature inversions in some plan- Schlawin, Zhao, Teske, Herterets and not others (Hubeny et al. 2003; Fortney et al.2008a). An alternative explanation is that the obser-vational techniques to infer temperature inversions (likethe 4.5 µ m to 3.6 µ m brightness ratio) are actually sens-ing the difference between clear atmospheres and dustyatmospheres, such as has been observed in HD 189733b(Pont et al. 2013; Evans et al. 2013). Recently, spectro-photometry of HAT-P-32b (Gibson et al. 2013b), HAT-P-12b (Line et al. 2013a), WASP-17b (Mandell et al.2013), GJ 1214b (Kreidberg et al. 2014), GJ 436b(Knutson et al. 2014) and phase curves of Kepler-7b(Demory et al. 2013) indicate that clouds and hazes maybe common in exoplanet atmospheres.The very short period hot Jupiters, such asWASP-12b (Hebb et al. 2009, P =1.09 days), WASP-19b (Hebb et al. 2010, P =0.79 days), HAT-P-32b(Hartman et al. 2011, P =2.2) and CoRoT-1b(Barge et al. 2008, P =1.51 days), are in the tem-perature regime where TiO and VO may be abundantatmospheric constituents (Fortney et al. 2010) – theirbrightness temperatures are respectively 3600 K(Crossfield et al. 2012), 2700 K (Abe et al. 2013),and 2500 K (Deming et al. 2011). TiO and VO aremolecules that are so sensitive to the C/O ratio thattheir abundances decreases by a factor of ∼
100 goingfrom C/O=0.54 (solar) to C/O=1 (Madhusudhan et al.2011b). Their presence should be accompanied by agreater radius for the optical wavelengths ( ∼
450 to ∼ & V =13.6 star (Barge et al. 2008), isbetter matched with models that include a temper-ature inversion (Rogers et al. 2009; Gillon et al. 2009;Zhao et al. 2012) or an isothermal profile (Deming et al.2011). It is thus is a potential candidate for strong ob-servable signatures of TiO/VO. This makes CoRoT-1ba useful comparison planet to WASP-19b and WASP-12b because it has a similarly high brightness tem- perature ( > R p = 1.49 R Jup
Barge et al. 2008), hightemperature ( T blackbody = 2450 K Deming et al. 2011)and moderate mass M p = 1.03 M Jup , which combine togive it a large scale height H = kT /µmg ≈ . R Jup where k is Boltzmann’s constant, T is the kinetic tem-perature, µ is the mean molecular weight =2.3 for asolar mixture, m is one atomic mass unit and g is thelocal gravitational acceleration. Furthermore, there isa nearby reference star close in brightness and color(within 0.7 magnitudes in the J , H and K bands)that permits characterization with the multi-object spec-troscopy (MOS) method (Bean et al. 2010; Sing et al.2012; Gibson et al. 2013a; Bean et al. 2013).The MOS method is to divide a target star spectrumby one (or an average of several) reference stars to cor-rect for variability in telluric (Earth’s) transmission andthe response of the instrument. Close proximity of areference star to the target provides an advantage forcalibration, as their atmospheric turbulence and telluricfluctuations are highly correlated. The reference stars’spectra are obtained simultaneously either with multipleslits or, as in our observations, a long slit that includesboth the planet hosting star and the reference star.One observational challenge with the CoRoT-1 systemis its faintness at K =12.2. This makes it difficult to ob-tain sufficient signal to noise for high resolution measure-ments but we demonstrate that the Infrared TelescopeFacility (IRTF) with SpeX and MORIS instruments ina low resolution prism mode (with no diffraction grat-ing) can achieve high precision characterization down tothis faint magnitude. We present a 0.8 µ m to 2.4 µ mtransmission spectrum to constrain the presence of in-frared absorbing molecules and measure the optical/nearIR radius slope as compared to TiO/VO absorption. OBSERVATIONS
We observed CoRoT-1b with the SpeX instrument(Rayner et al. 2003) on the Infrared Space Telescope Fa-cility in a low resolution prism mode. When the large3” x 60” slit is placed on CoRoT-1, the actual resolu-tion for the target star is set by the point spread func-tion at R ≈
80. A reference star – 2MASS 06482020-0306339 – was placed simultaneously on the slit to cor-rect for telluric transmission variations as well as corre-lated (common mode) instrumental variations. The 3”x 60” slit was selected to minimize slit losses but it stillserves to reduce the background levels as compared to acompletely slit-less instrument. The reference star with J =11.72, H =11.54, K =11.50 is slightly brighter thanCoRoT-1 J =12.46, H =12.22, K =12.15 as determinedfrom 2MASS (Skrutskie et al. 2006) so that the photonnoise of the planet host star dominates the photon noiseof the measurement. We kept the exposure times shortto keep the counts of the two objects well within the lin-ear regime of the detector. At the same time, their fluxesare close enough so that flux-dependent non-linearity isnegligible.oRoT-1b Transmission Spectrum 3 N o r m a li z ed F l u x CoRoT−1Reference StarBackground O r b i t a l P ha s e R e l a t i v e F l u x Fig. 1.—
Top
Normalized spectra for the planet hosting star,the reference star and background for Jan 04, 2012 indicate theregions where there are strong telluric absorption features, strongbackground emission and detector effects (spurious absorption fea-tures at 2.41 µ m and 1.58 µ m). Bottom : Dynamic spectrum for thenight of Jan 04, 2012. Each row in the image is a single spectrumof CoRoT-1 divided by the reference star and re-normalized witha linear baseline. The transit (encompassed by horizontal yellowdashed lines at ingress/egress) is clearly detected in all wavelengthchannels save the ends of the spectrograph.
We observed CoRoT-1 for 3 nights on the UT dates ofDec 23, 2011 (full transit), Dec 29, 2011 (half transit) andJan 04, 2012 (full transit). The first half of Dec 29, 2011was lost due to high wind ( >
45 MPH) and closure of thetelescope. The remainder of the Dec 29, 2011 night wasaffected by large seeing fluctuations from 0.9” to 1.5”.For the full transits, the 2.5 hour transit duration wasstraddled by 30 to 120 minutes of out-of-transit observa-tions to establish a baseline flux level. Table 1 lists theexposure times and number of exposures obtained for thethree transits.We also used MORIS, a high-speed, high-efficiencyoptical camera (Gulbis et al. 2011) simultaneously withSpeX to obtain photometry at the Sloan z ′ band forCoRoT-1. We used a 0.9 µ m dichroic to split visible lightshort-ward of 0.9 µ m into the MORIS beam path. Thefield of view of MORIS is similar to the guide camera ofSpeX (1’ x 1’ arcmin), permitting us to include two refer-ence stars in addition to CoRot-1 on the MORIS detec-tor. We used short exposures of 5s and 10s to ensure thefluxes were well within the linear regime of the camera.The observing log of MORIS is also included in Table 1. Photometric data reduction was carried out following thepipeline and steps of Zhao et al. (2012). The total fluxof the two reference stars (2MASS 06482101-0306103 and2MASS 06482020-0306339) was used for flux calibration.We determined that an aperture size of 36 pixels (cor-responding to 4.1” for a pixel scale of 0.114”/pixel) anda 35-pixel wide background annulus provided the bestlight curve precision for all 3 nights, although aperturesizes with ± IRAFccdproc procedures with four to eight flat frames, darksubtraction from identical exposure time frames and oneto two wavelength calibration frames. Wavelength cali-brations were performed with a narrower (0.3”x60”) slitto better centralize the Argon emission lines. Addition-ally, we rectify all science images using the Argon lampspectrum as a guide to make sure all vertical columns inthe image correspond to individual wavelengths.Simultaneous H + K band exposures were made withthe infrared guider on SpeX to ensure good alignmentof the target and reference star. The stars are visible asreflections off the slit, permitting a simultaneous checkthat the stars are centered during spectrograph scienceexposures. In addition to the reflections from the slit,nearby additional reference stars off the slit were alsoevaluated for centroid motions. The centroid motionsshow that guiding using the H + K guider was accurateto within 0.3”, minimizing slit loss errors in the spec-trograph. No correlations are visible between telescopeshifts (measured from H + K images) and the individualtarget and reference stars’ fluxes or ratio spectrum be-tween the planet host and reference star.We extracted all of the spectra with the twodspec pro-cedures in IRAF (Tody 1993, 1986). We used a centeredaperture of 15 pixels (2.3”) with optimal extraction (spa-tial pixels weighted by S/N ratio) on the planet host starand reference star (FWHM ≈ J , H and K telluricwindows. Schlawin, Zhao, Teske, Herter UT Date t spec D spec N spec t phot N phot (s) (s)Dec 23, 2011 10.0 49% 813 5 2636Dec 29, 2011 15.0 51% 233 10 691Jan 04, 2012 15.0 51% 600 5 3319 TABLE 1
Summary of the 2.5 transits observed for CoRoT-1b including theexposure time for SpeX spectra t spec , number of spectralexposures N spec , spectral duty cycle D spec , MORIS photometricexposure time t phot and number of photometric frames N phot .The non redundant reads were increased at longer spectrographexposure times, thus maintaining almost the same duty cycle. Noise Measurements
The most critical part of measuring a planet’s spec-trum is achieving high signal to noise (S/N) ratios. Mea-surement errors are closely approximated by “minimumnoise” at the highest time resolution and spectral resolu-tion but are considerably larger when the data is binned.For this paper, “minimum noise” includes constant readnoise per pixel of the detector, shot noise of the sourceand shot noise of the background. Minimum noise de-creases as 1 / √ N for N independent measurements, butwe find that the measured noise falls off more slowly,as expected for high precision measurements dominatedby systematics. These additional error sources are alsoknown as time-correlated or wavelength-correlated rednoise (e.g., Pont et al. 2006; Carter & Winn 2009). Fig-ure 2 and 3 show the measured out-of-transit error as afunction of bin size and also shows the minimum noisefor comparison. O u t o f T r an s i t R M S ( % ) Std Dev Near 1.26 umStd Dev Near 1.43 umStd Dev Near 2.14 umMinimum Noise Near 2.14 umMinimum Noise Near 1.43 umMinimum Noise Near 1.26 um
Fig. 2.—
Measured out of transit errors as a function of wave-length bin size for the night of Dec 23, 2011. The errors scale withminimum noise but in a non-linear way. We choose the maximumbin size possible while still resolving some broad molecular bandsand use 0.17 µ m bins for time series analysis. The minimum noisedrops quickly for the 0.3 µ m bin near 1.43 µ m because there is asharp increase in photons outside of the telluric absorption feature. For the data analysis, we used nine equally spacedwavelength bins which minimize the out-of-transit noisewhile still maintaining sufficient spectral resolution toresolve molecular bands. As expected for high precisionflux measurements, the measured noise has componentsthat do not scale as minimum noise decreases. We bin the O u t o f T r an s i t R M S ( % ) Std Dev 1.17um to 1.35umStd Dev 1.35um to 1.52umStd Dev 2.05um to 2.22umMinimum Noise 2.05um to 2.22umMinimum Noise 1.35um to 1.52umMinimum Noise 1.17um to 1.35um
Fig. 3.—
Measured out of transit errors as a function of time binsize for the night of Dec 23, 2011 using 0.17 µ m wide bins. As withthe wavelength binning, the measured noise falloff is not as sharpas with minimum noise. For 0.17 µ m wide wavelength bins thereis an approximate noise floor around 0.1% and a baseline functionmust be used to remove long term trends. The variations in RMSfor long time bins are due to small number statistics for the handfulof out-of-transit flux points. time data slightly to ∼ ∼
10 to ∼ LIGHT CURVE FITTING
As described in Section 2.1, all R =80 spectral datawere binned into nine equally spaced wavelength binsand they are analyzed independently. Figure 4 showsthe time series for each wavelength bin and it can beseen that the baseline is non-linear. Figures 5 and 6 alsoshow that the shape of the baseline changes from nightto night. It is possible to model the baseline as a slowlyvarying function like a polynomial (e.g., Bean et al. 2013)and we initially fit the light curve with a third orderLegendre polynomial. The Legendre polynomials wereused because their orthogonality reduces the covariancebetween fitted coefficients. The polynomial fits showeddiscrepancies between nights, so we use a non-parametricapproach detailed in Section 3.1 rather than impose aspecific shape on the baseline fit. Gaussian Process Model
We use a Gaussian process (Gibson et al. 2012b,2013a) to model red noise and the flux baseline. Theadvantage of the Gaussian process framework is that itdoes not assume that the baseline follows a pre-definedfunction like a polynomial where the coefficients are fit-ted parameters. Instead, the Gaussian process assumesthe baseline and mid-transit follow a correlated normaldistribution described by a covariance kernel. For re-peated experiments following a Gaussian process, the ac-tual shape of the baseline can vary from realization torealization while maintaining the same covariance ker-nel. The Gaussian Process method uses Bayesian modelselection so that it weights against complex models tooRoT-1b Transmission Spectrum 5 −0.05 0 0.05Orbital Phase0.750.80.850.90.951 F l u x R a t i o + O ff s e t z−prime0.91 um1.08 um1.26 um1.43 um1.61 um1.79 um1.96 um2.14 um2.31 um Fig. 4.—
Time series for the night of January 04, 2012 binnedinto 100 time points. The top curve (z-prime) is the MORISphotometry whereas the remaining nine are equally spaced SpeXbands. The transit light curves are fit with the Mandel & Agol(2002) light curve model and with a Gaussian process error ma-trix (Gibson et al. 2012b) that includes red noise but imposes nospecific baseline function for the time series. mitigate overfitting.We use the integer form of the Mat´ern covariance ker-nel (Rasmussen 2006), C nm = Θ exp − Θ s (cid:18) p + 12 (cid:19) | x n − x m | ! Γ( p + 1)Γ(2 p + 1) × Σ pi =0 ( p + i )! i !( p − i )! Θ | x n − x m | s (cid:18) p + 12 (cid:19)! p − i + δ nm σ n (1)where C nm is the covariance between data points ( x n , y n )and ( x m , y m ), Θ is a hyper-parameter describing thestrength of the correlation between data points, Θ is theinverse time scale hyper-parameter, p is the index of theMat´ern kernel, δ nm is the Kronecker delta function and σ n is the white-noise component of an individual point’serror. This is a generalized form of the p = 1 Mat´ernkernel used on WASP-29b transit data (Gibson et al.2013a). We let the p parameter be another hyper-parameter with the possible values of 0, 1, 2 or infinity(a squared exponential kernel C nm = Θ e − Θ ( x n − x m ) / )because higher values of p are essentially indistinguish-able from the infinity case (Rasmussen 2006). The fourdifferent kernels are parametrized by Θ with values of −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08Orbital Phase0.750.80.850.90.951 F l u x R a t i o + O ff s e t z−prime0.91 um1.08 um1.26 um1.43 um1.61 um1.79 um1.96 um2.14 um2.31 um Fig. 5.—
Same as Figure 4 for the night of Dec 23, 2011.
0, 1, 2 and 3 for the respective values of p . All formsof the above kernel have correlations that decrease withseparation in time. In other words, points that are closetogether are highly correlated but far away are less cor-related. For the data series in this work, x n and x m areorbital phase and y n and y m are normalized flux. Thechoice of kernel does not affect the individual white noiseerrors which are assumed to be independent and Gaus-sian distributed with a standard deviation σ n .The need for a covariance kernel is justified by thefact that the time series are not well fit by a flat base-line. If we do fit the time series to a flat, white noisebaseline model – with fixed semi-major axis, impact pa-rameter and orbital period from literature values (Bean2009) and free planet-to-star radius ratio R p /R ∗ and freelinear limb darkening – the resulting residuals show cor-relations, as visible in the autocovariance estimator. Ifthe autocovariance has a spike at zero lag and then is flatfor all lags greater than zero, the noise is independent andidentically distributed - white noise. On the other hand,if there is structure to the autocovariance, then there arecorrelation between flux measurements. Figure 7 showsa few examples of the autocovariance estimator of theresiduals and the autocovariance estimator of the best-fitGaussian process model. The autocovariance estimatoris a biased estimator (Wei 2006) so it can be differentfrom the covariance kernel. Appendix A shows the ker-nel, individual realizations and the ensemble average ofthe autocovariance of the same best-fit hyperparametersused in Figure 7.The inclusion of correlated noise requires that the full Schlawin, Zhao, Teske, Herter F l u x R a t i o + O ff s e t z−prime0.91 um1.08 um1.26 um1.43 um1.61 um1.79 um1.96 um2.14 um2.31 um Fig. 6.—
Same as Figure 4 for the night of Dec 29, 2011. likelihood function must be used in evaluating a modelinstead of a plain χ statistic. The full likelihood functionis L = 1(2 π ) n/ | C | / exp (cid:18) − r T C − r (cid:19) (2)where L is the likelihood function when evaluating amodel for covariance matrix C and residual vectors r n = y n − f n for data value y n and model value f n and T isthe transpose (Gibson et al. 2012b). In the case of sta-tistically independent non-correlated data Θ = 0 and L ∝ exp − χ where χ = P n ( y n − f n ) /σ n , the standardchi-squared statistic. However, we find that Θ = 0 andthat correlated noise is present in the data. Extracted Parameters
We fit all time series with the transit function fromMandel & Agol (2002) and use a series of MCMC chainsto explore the parameter uncertainty distributions. Theout-of-transit flux, planet-to-star radius ratio R p /R ∗ , lin-ear limb darkening u and hyper-parameters Θ , Θ andΘ are fitted to the data while all other transit param-eters – impact parameter, semi-major axis and orbitalperiod – are fixed at the literature values from Bean(2009). For all parameters and hyper-parameters weuse flat priors. All parameters and hyper-parameters areconstrained by the likelihood function except in the casewhere the covariance strength hyper-parameter (Θ ) ismuch smaller than the white noise, σ n . In these cases thetime scale hyper-parameter (Θ ) is poorly constrainedbut does not strongly affect the R p /R ∗ result over many orders of magnitude. For the continuous parameters,we use Gaussian proposal distributions from the currentvalue and for the discreet kernel index hyper-parameter(Θ ), we use a uniform proposal distribution over theintegers from 0 to 3.Each time step in the MCMC chain requires a matrixinversion when evaluating the likelihood, which can makeevaluation computationally expensive. To decrease chainevaluation time, the time series are binned to 100 timepoints for the nights of Dec 23, 2011 and Jan 04, 2012with a resulting bin sizes of ∼ z ′ light curve of Jan 04, 2012 in Figure 8 shows howthe fitted planet radius R p /R ∗ can correlate to the otherfitted parameters . This particular light curve showedthe strongest dependence of R p /R ∗ on the flux offset A and hyper-parameters Θ , Θ and Θ . For the remainingcurves, the R p /R ∗ posterior is nearly orthogonal to theother hyper-parameters.The same IRAF data analysis pipeline and MCMC lightcurve fitting is applied to all three nights of observationand the fitted radius ratio and uncertainties are shown inFigure 9. The three nights are consistent within errors fora given wavelength. However, there is a slight decreasein radius fit for the night of Jan 04, 2012.The three sets of observations in Figure 9 are combinedwith a weighted average to produce a final transmissionspectrum of the planet to be used in comparison to mod-els. The weights are the inverse squared error in eachwavelength bin for each night. We make the assumptionthat weather-related variability on the hot Jupiter itselfhas a negligible effect on the transmission spectrum. Wealso assume that the errors in radius from night to nightare independent.It is worth noting that the Gaussian process methodachieved higher precision than a polynomial baseline onthe half-transit observation for Dec 29, 2011. Figure 10shows a comparison between the best-fit radius when us-ing a third order Legendre baseline fit as compared to theGaussian correlated process. Both the scatter and errorbars are larger when imposing a specific baseline shape.There was one particular light curve, the MORIS z ′ pho-tometry for Jan 04, 2012, that showed a very strong de-pendence on the type of treatment of systematic errors.As seen in the time series, Figure 4, the flux bends down-ward after egress. When the light curve is fit with a thirdorder Legendre polynomial, this drop in flux is extrapo-lated to a higher flux during transit and thus the planet-to-star radius ratio estimate R p /R ∗ is large. When thelight curve is fit with the Gaussian Process method, thedeviations from a flat baseline are best-fit with shortertime scale correlations and an essentially flat baseline.Our Gaussian process kernel (Equation 3.1) incorporatesoRoT-1b Transmission Spectrum 7 -5 -5 -5 -5 -5 A u t o c o v a r i an c e -6 -6 -6 -6 -6 A u t o c o v a r i an c e -5 -5 -5 -5 -5 A u t o c o v a r i an c e -7 -7 -6 -6 -6 -6 A u t o c o v a r i an c e z-prime Time Series -6 -6 -6 -6 A u t o c o v a r i an c e z-prime Time Series -6 -6 -6 -6 -6 -6 A u t o c o v a r i an c e Fig. 7.—
Left : Autocovariance estimator of the residuals fit with a white noise model and a flat baseline (black line) compared with theautocovariance estimator of a best-fit Gaussian Process model (orange line). These example light curves were for the SpeX 1.79 µ m binand SpeX 1.43 µ m bin, which have stronger baseline trends, and the z ′ filter for Jan 04, 2012 data, which was flatter. Appendix A showssimulated individual realizations of the same Gaussian Processes and how they compare to the covariance kernel. Right : The same lightcurves are fit with the Gaussian-Process model and the autocovariance of the final residuals (black line) show no correlation between data,just the white noise peak at zero lag. different shapes through the Mat´ern index, but does notincrease the upper limit to the same value as the poly-nomial baseline. We adopt the Gaussian Process modelfits, but given the dependence of R p /R ∗ on the method,we also evaluate our science results with the polynomialmodel fits.The average spectrum, listed in Table 2, has R p /R ∗ uncertainties ranging from 0.7% to 2% of the meanvalue ( R p , mean /R ∗ = 0.144) across the near-infraredcoverage. This uncertainty is comparable to the scaleheight of the atmosphere ( ∼ σ ) molecular features. COMPARISON WITH MODELS
The error-weighted average transmission spectrum forthe three nights is compared against a representativemodel for hot Jupiter atmospheres from Fortney et al.(2008b, 2010). We select this model as a starting pointbecause it has a published infrared spectrum, solar abun-dances and equilibrium chemistry. The blackbody tem-peratures fit to infrared data of ≈ T bb =2380K, T bb =2460K Zhao et al. 2012; Deming et al. 2011), andshort orbital period P = 1.509 days (Barge et al. 2008)indicate that it is comparable to the T kinetic =2500 K Schlawin, Zhao, Teske, Herter Fig. 8.—
Posterior density distribution for the fitted parameters for the night of Jan 04, 2012 for the MORIS z ′ time series from theMCMC chain. The star to planet radius ratio R p /R ∗ parameter correlates with the flux offset A , the hyper-parameters of the Gaussianprocess model Θ (strength of correlations) and Θ (inverse timescale of hyper-parameters) and Θ (the Mat´ern type) but not u (thelinear limb darkening parameter) because R p /R ∗ and u have nearly orthogonal distributions. The Θ parameter is a parametrization ofthe Mat´ern index p and is discrete – see Section 3.1 – so there is an apparent discontinuity in phase space. 95% and 68% confidence regionsfor each projected distribution are shown in red. The correlation between parameters is smaller for the rest of the other SpeX and MORISlight curves. Wavelength R p /R ∗ ( µ m)z’ (0.86) 0.1389 ± a ± ± ± ± ± ± ± ± ± TABLE 2
Weighted average planet-to-star radius ratio R p /R ∗ for the threenights of observations shown in Figure 9. Quoted error bars arecalculated by propagating the individual MCMC uncertainties inquadrature. The central wavelength for each 0.1755 µ m bin isgiven in the first column except for the photometry filter wherethe first moment is given in parentheses. a the MORIS z ′ timeseries showed particularly large sensitivity to the treatment ofsystematic errors. A polynomial baseline fit gives a weightedaverage R p /R ∗ = 0 . ± . isothermal model from Fortney et al. (2010).The equilibrium model from Fortney et al. (2008b,2010) shows substantial opacity in the optical as com-pared to the infrared due to mainly TiO and VO absorp- tion, so we compare the CoRoT derived radius (Bean2009) to our transmission spectrum, as seen in Figure 11.The Bean (2009) radius is larger than the original dis-covery (Barge et al. 2008), but we adopt the Bean (2009)value because it was found with a newer data process-ing pipeline. The combined CoRoT data and IRTF datashow no evidence for an optical to infrared slope. Fittinga flat spectrum to the data gives a reduced chi-squared( ¯ χ ) of 2.9 for 10 degrees of freedom whereas the modelwith TiO/VO gives ¯ χ of 4.6 for 10 degrees of freedom.The same model with TiO and VO artificially removed,gives ¯ χ of 2.4 for 10 degrees of freedom. As mentionedin Section 3.2, the MORIS results were particularly sen-sitive to the choice of model to fit the time series. Ifwe use a polynomial baseline fit to the time series, theTiO/VO rich model is again disfavored with a ¯ χ of 2.9as compared to the TiO-removed model with ¯ χ of 1.6and a flat line of ¯ χ of 1.3.The hot Jupiter WASP-19b also shows no evidence forTiO/VO absorption (Huitson et al. 2013; Mancini et al.2013). For this planet, TiO/VO depletion is expectedsince WASP-19b has no observed temperature inversion(stratosphere) (Anderson et al. 2013). WASP-12b sim-ilarly has no stratosphere, but does have a larger opti-cal to infrared transit depth ratio. Models for WASP-oRoT-1b Transmission Spectrum 9 µ m)0.110.120.130.140.150.16 R p / R * Jan 04Dec 29Dec 23Jan 04Dec 29Dec 23
Fig. 9.—
Fitted radius ratio parameter as a function of wavelength for the three independent nights of observations with horizontalerror bars as the bandwidths for spectral wavelength bins and vertical error bars with 68% uncertainty. Points with bold lines are thesimultaneous z ′ photometry with the MORIS camera with a filter transmission curve (normalized to unity and scaled to 1/10 the plotsize) shown in green. At a given wavelength, all points are within 2.1 σ of the weighted average, though there is a slight systematic shiftdownward for the night of Jan 04 (purple). The horizontal red line shows the CoRoT spacecraft radius (Bean 2009) and the dashed redlines indicate three scale heights above and below this value.
12b that included either TiO/VO or TiH were consis-tent with initial data (Swain et al. 2013; Stevenson et al.2013) but adding optical data and including models withaerosols together suggest that WASP-12b has low levelsof TiO/VO (Sing et al. 2013).CoRoT-1b, by contrast, is better matched by mod-els with a stratosphere or isothermal temperature pro-file. Rogers et al. (2009) compare a suite of equilib-rium abundance models with multi-color photometricsecondary eclipses on CoRoT-1b. The molecular fea-tures in these models appear in absorption or emissiondepending on the temperature structure of a planet’satmosphere and Rogers et al. (2009)’s models with notemperature inversion fail to produce the Ks and nar-rowband 2.1 µ m brightness temperatures for the planet.The only models that come close to matching the obser-vations include an extra optical absorber at the 0.01 to0.1 bar level. Deming et al. (2011) also find that the sec-ondary eclipse fluxes are better fit with models that in-clude a temperature inversion than models without. Still, Deming et al. (2011) find consistency with a blackbodyspectrum, which could be due to an isothermal profile ora thick layer of high altitude dust.Plausible absorbers that could create a stratosphere inCoRoT-1b are TiO and VO (Fortney et al. 2008a), whichshould also increase the optical radius as compared tothe infrared. However, since our IRTF-CoRoT combinedspectrum is disfavored by models with TiO/VO absorp-tion, we expect another species is responsible for thetemperature inversion, such as sulfur-containing com-pounds (Zahnle et al. 2009). Alternatively, a high al-titude haze or dust (e.g., Pont et al. 2013) could ex-plain the blackbody-like emission from CoRoT-1b andalso flatten out molecular features in the transmissionspectrum.Many other atmospheric optical scattering and absorb-ing processes may occur in hot Jupiter atmospheres in-cluding (a list from Sing et al. (2013)): Raleigh scatter-ing off molecules, Mie and Raleigh scattering off dust,tholin hazes and gray absorbing clouds. The major-0 Schlawin, Zhao, Teske, Herter µ m)0.1250.1300.1350.1400.1450.1500.155 R p / R * µ m)0.080.100.120.140.160.180.200.22 R p / R * µ m)0.1300.1350.1400.1450.1500.155 R p / R * Fig. 10.—
Comparison between a polynomial baseline Levenberg-Marquardt fit and a Gaussian process method for the baseline and fluxvariations. Photometry points ( z ′ band) are shown with bold lines, and the corresponding z ′ bandpass is shown in green. The results arelargely consistent for the SpeX data on the full transits of Dec 23, 2011 and Jan 04, 2012, but differ on the half transit of Dec 29, 2011 andthe MORIS photometry for Jan 04, 2012. The MORIS photometry light curve for Jan 04, 2012 shows particularly large sensitivity to thefitting method because the flux bends down after egress – see Figure 4. For the half transits of Dec 29, 2011, the third order polynomial(due to the shorter time baseline) produces much larger scatter for the half transit than the Guassian process method because it is fittinga specific shape to the light curve in the presence of red noise. ity of these processes increase planetary radii at shortwavelengths as compared to long wavelengths. Our ob-servations, by contrast, show that the optical radius isnot significantly larger than the infrared radius basedon the CoRoT photometry. Gray absorbing cloudsare the one item on the above list that could equal-ize the optical and infrared transit depths. Recent ob-servations of HAT-P-32b (Gibson et al. 2013b), HAT-P-12b (Line et al. 2013a), and Kepler-7b (Demory et al.2013) indicate that high altitude clouds may be per-vasive in exoplanet atmospheres. In HAT-P-32b, gray-absorbing clouds may obscure TiO/VO features (or theTiO and VO may be present at very low abundances)(Gibson et al. 2013b). Analysis of the above a processesis limited with only CoRoT photometry, but additionaloptical spectroscopy would be useful in constraining thestrength of these scattering and absorbing phenomena.We observe a 2 σ peak at 1.4 µ m in the spectrum, closeto a 1.4 µ m water feature seen in all temperature classesof Fortney et al. (2010)’s equilibrium models. This samefeature was used to detect water vapor in WASP-19bwith HST (Huitson et al. 2013). However, if water vaporin CoRoT-1b caused the 2 σ feature at 1.4 µ m, the 1.8 µ m radius should also be elevated, which is not seen in ourspectrum. One possible explanation is that the 1.4 µ mpeak is due to H C or HCN, which are both predictedto be abundant in hot Jupiter atmospheres (Moses et al.2013). Unfortunately, the significance level of this peak istoo low to distinguish between these molecules or rule outthe possibility of a statistical deviation or un-removedtelluric absorption signature. CONCLUSION
We present a 0.8 µ m to 2.4 µ m transmission spectrumfor the hot Jupiter CoRoT-1b, the faintest ( K =12.2) hoststar for which the planet has been spectroscopically char-acterized to date. With the MOS method and a singlenearby simultaneous reference star, we achieve 0.03% to0.09% precision of the transit depth R /R ∗ when com-bining all three nights of data, comparable to one atmo-spheric scale height for this hot Jupiter’s temperature.We conclude the following items from our analysis: • The IRTF spectrum, when combined with the op-tical planet-to-star radius ratio derived from ob-servations by the CoRoT spacecraft (Bean 2009),disfavors a model that includes TiO/VO as com-oRoT-1b Transmission Spectrum 11 µ m)0.1360.1380.1400.1420.1440.1460.1480.150 R p / R * Equilbrium ChemistryTiO−Removed
Binned Model ValueThis WorkBean 2009Binned Model ValueThis WorkBean 2009
Fig. 11.—
Measured planet-to-star radius ratio spectrum compared to a 2500 K isothermal model (blue) from (Fortney et al. 2010) withno clouds or hazes but significant TiO/VO absorption. Black data points are the weighted average IRTF data for three transits withspectral data in thin lines and photometry data in thick lines. The red point is the CoRoT value from 36 transits (Bean 2009). Y error barsrepresent 1 σ uncertainties whereas X error bars span spectral windows, except in the cases of photometric data. Photometric filter curvesthat are normalized to unity and scaled to 1/10 of the figure are shown in with black lines for the CoRoT planet finder response (dashedline) and the MORIS z ′ filter (solid line). The IRTF data (black) combined with the CoRoT point (red) disfavor the TiO/VO-drivenoptical to infrared absorption slope and give a χ per degree of freedom of 4.6 as compared to a χ of 2.4 per degree of freedom for thesame model with TiO removed (green). pared to a model that is spectrally flat or hasTiO removed. This goes against the predic-tion that CoRoT-1b’s thermal inversion is dueto TiO/VO absorption. Other recently charac-terized hot Jupiters with similarly high tempera-tures, WASP-19b and WASP-12b, also lack strongTiO/VO (Anderson et al. 2013; Sing et al. 2013)features, but TiO/VO is expected to be depleted inthese planets because they have no observed tem-perature inversions. • No statistically significant molecular features areseen in the 0.8 µ m to 2.4 µ m transmission spec-trum, although there is a small 2 σ peak at 1.4 µ m, possibly due to H C or HCN. Our precision is nothigh enough to constrain the detailed compositionof H O, CO, and other gases due to the systematicsand faintness of the host star. • The Gaussian process method for determining sys-tematics and the baseline achieves better precisionin extracted parameters and more robustness whenapplied to the half-transit on Dec 29, 2011 as com-pared to a deterministic polynomial baseline. Fordata sets with strong out-of-transit curvature, theGaussian Process model can give significantly dif-ferent results from a polynomial baseline.
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This research was funded in part by the NewYork/NASA Space Grant Fellowship. Based on obser-vations made from the Infrared Telescope Facility, whichis operated by the University of Hawaii under Cooper-ative Agreement no. NNX-08AE38A with the NationalAeronautics and Space Administration, Science MissionDirectorate, Planetary Astronomy Program. M.Z. issupported by the Center for Exoplanets and HabitableWorlds at the Pennsylvania State University. Thanksto Eva-Maria Mueller and Joyce Byun for useful MCMCsuggestions. The authors wish to recognize and acknowl-edge the very significant cultural role and reverence thatthe summit of Mauna Kea has always had within the in-digenous Hawaiian community. We are most fortunateto have the opportunity to conduct observations fromthis mountain. We also thank the anonymous referee foruseful comments and corrections.4 Schlawin, Zhao, Teske, Herter APPENDIX A: SIMULATED SERIES
In order to compare an autocovariance of residuals toan input kernel, it is illustrative to show the autocovari-ance of some simulated time series. Figure 12 shows sim- ulations for the best-fit hyper-parameters from the 1.79 µ m, 1.43 µ m and z ′ light curves on the night of January04, 2012. The two autocovariance plots of the residualsare shown in Figure 7oRoT-1b Transmission Spectrum 15 σ = 0.0026, θ = 0.0036, θ = 22., θ = 2.0 −6 −6 −5 −5 A u t o c o v a r i an c e Individual ACInput KernelEnsemble Avg ACIndividual ACInput KernelEnsemble Avg ACIndividual ACInput KernelEnsemble Avg AC σ = 0.0015, θ = 0.010, θ = 6.4, θ = 2.0 −5 −5 −4 −4 A u t o c o v a r i an c e Individual ACInput KernelEnsemble Avg ACIndividual ACInput KernelEnsemble Avg ACIndividual ACInput KernelEnsemble Avg AC σ = 0.0020, θ = 0.0010, θ = 78., θ = 2.0 −6 −6 −6 −6 A u t o c o v a r i an c e Individual ACInput KernelEnsemble Avg ACIndividual ACInput KernelEnsemble Avg ACIndividual ACInput KernelEnsemble Avg AC