Ground-based, Near-infrared Exospectroscopy. II. Tentative Detection of Emission From the Extremely Hot Jupiter WASP-12b

2.6 MB·English

by  Ian J. M. Crossfield

Accepted to ApJ: 2012 Jan 04
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
GROUND-BASED, NEAR-INFRARED EXOSPECTROSCOPY. II. TENTATIVE DETECTION OF EMISSION
FROM THE EXTREMELY HOT JUPITER WASP-12b
Ian J. M. Crossfield1, Brad M. S. Hansen1, Travis Barman2
Accepted to ApJ: 2012 Jan 04
ABSTRACT
We report the tentative detection of the near-infrared emission of the Hot Jupiter WASP-12b with
the low-resolution prism on IRTF/SpeX. We find a K −H contrast color of 0.137%±0.054%, cor-
responding to a blackbody of temperature 2400+1500 K and consistent with previous, photometric
−500
observations. We also revisit WASP-12b’s energy budget on the basis of secondary eclipse observa-
2
tions: thedaysideluminosityisarelativelypoorlyconstrained(2.0−4.3)×1030 ergs−1, butthisstill
1
allows us to predict a day/night effective temperature contrast of 200−1,000 K (assuming A =0).
0 B
Thus we conclude that WASP-12b probably does not have both a low albedo and low recirculation
2
efficiency. Our results show the promise and pitfalls of using single-slit spectrographs for characteri-
n zation of extrasolar planet atmospheres, and we suggest future observing techniques and instruments
a
which could lead to further progress. Limiting systematic effects include the use of a too-narrow slit
J
ononenight–whichobserverscouldavoidinthefuture–andchromaticslitlosses(resultingfromthe

4 variable size of the seeing disk) and variations in telluric transparency – which observers cannot con-
trol. Single-slit observations of the type we present remain the best option for obtaining λ > 1.7µm
]
spectra of transiting exoplanets in the brightest systems. Further and more precise spectroscopy is
P
needed to better understand the atmospheric chemistry, structure, and energetics of this, and other,
E
intensely irradiated planet.
.
h Subject headings: infrared: stars — planetary systems — stars: individual (WASP-12) — techniques:
p spectroscopic
-
o
r
t 1. INTRODUCTION (Swain et al. 2010) was obtained with a different ap-
s proach: medium-resolution spectroscopy of HD 189733b
a 1.1. Ground-based Characterization of Exoplanet
with the 3 m NASA Infrared Telescope Facility (IRTF)
[ Atmospheres
covering the K and L bands. However, these results are

1 Transiting extrasolar planets allow the exciting possi- indispute: theKbandmatchesHST/NICMOSobserva-
v bilityofstudyingtheintrinsicphysicalpropertiesofthese tions which have in turn been called into question (see
3 planets. The last several years have seen rapid strides Swain et al. 2008; Sing et al. 2009; Gibson et al. 2011;
2 in this direction, with measurements of precise masses Deroo et al. 2010), while the L band exhibits an ex-
0 and radii, detection of numerous secondary eclipses and tremely high flux peak attributed variously to non-LTE
1 phasecurves,andthestartofground-basedopticalspec- CH emission (Swain et al. 2010) and to contamination
1. troscopy (Redfield et al. 2008; Snellen et al. 2008; Bean by 4telluric water vapor (Mandell et al. 2011). In con-
0 et al. 2010). trast,thetentativespectroscopicdetectionofWASP-12b
2 Though ground-based, near-infrared (NIR) photome- we present in this paper reproduces previous, high S/N
1 try of exoplanets is becoming commonplace, until re- ground-based photometry (Croll et al. 2011) and we
: cently there were no successful detections via ground- demonstrate that our final result is not likely to be cor-
v
based NIR spectroscopy (Brown et al. 2002; Richard- ruptedbytelluricvariationsoutsideofwell-definedspec-
i
X son et al. 2003; Deming et al. 2005; Barnes et al. 2007; tral regions.
Knutson et al. 2007). Several groups have employed
r
a high-resolution spectrographs with some form of tem-
1.2. The WASP-12 System
platecross-correlation(Demingetal.2005;Snellenetal.
2010; Crossfield et al. 2011) with varying degrees of suc- The transiting Hot Jupiter WASP-12b has an orbital
cess. Though cross-correlation provides a method to period of 1.1 days around its 6300 K host star, and the
test for the detection of a particular model, it has the planet’s mass and radius give it a bulk density only 25%
significant drawback that it does not provide a model- of Jupiter (Hebb et al. 2009; Chan et al. 2011). The
independent measurement. Furthermore, such observa- planet is one of the largest known and is significantly
tions require high-resolution cryogenic spectrographs on overinflatedcomparedtostandardinteriormodels(Fort-
large-aperture telescopes. ney et al. 2007). The planet is significantly distorted
The only published, model-independent, ground- and may be undergoing Roche lobe overflow (Li et al.
based, NIR spectrum of an exoplanetary atmosphere 2010), but tidal effects are not expected to be a signifi-
cant energy source. Though the initial report suggested
WASP-12bhadanonzeroeccentricity,subsequentorbital
1Department of Physics & Astronomy, University of Califor-
characterizationviatimingofsecondaryeclipses(Campo
niaLosAngeles,LosAngeles,CA90095,[email protected]
2Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, et al. 2011) and further radial velocity measurements
AZ86001,USA (Husnoo et al. 2011) suggest an eccentricity consistent
2 Crossfield, Hansen, and Barman
with zero.
TABLE 1
WASP-12bisintenselyirradiatedbyitshoststar,mak-
Observations
ing the planet one of the hottest known and giving it a
favorable ((cid:38) 10−3) NIR planet/star flux contrast ratio; UTdate 2009Dec28 2010Dec30
it has quickly become one of the best-studied exoplan- InstrumentRotatorAngle 225◦ 225◦
SlitPositionAngle 90◦ 90◦
ets. The planet’s large size, low density, and high tem-
Slit 1.6”x15” 3.0”x15”
perature have motivated an ensemble of optical, (L´opez- Grating LowRes15 LowRes15
Morales et al. 2010), NIR (Croll et al. 2011), and mid- Guidingfilter J K
infrared (Campo et al. 2011) eclipse photometry which OSfilter open open
Dichroic open open
suggests this planet has an unusual carbon to oxygen
IntegrationTime(sec) 15 20
(C/O)ratiogreaterthanone(Madhusudhanetal.2011). Non-destructivereads 4 4
However, a wide range of fiducial atmospheric models Co-adds 2 2
Exposures 502 356a
fit WASP-12b’s photometric emission spectrum equally
Airmassrange 1.01-1.91 1.01-2.70a
well despite differing significantly in atmospheric abun-
Wavelengthcoverage(µm) <1-2.5µm <1-2.5µm
dances and in their temperature-pressure profiles (Mad- WASP-12bphasecoverage 0.42-0.61 0.41-0.61
husudhan et al. 2011). Many hot Jupiters appear to
havehigh-altitudetemperatureinversions(Knutsonetal. a We limit the 30 Dec observations to airmass less than
2010; Madhusudhan & Seager 2010), but even WASP- 2.326,whichreducesthenumberofusableframesfrom379
12b’s precise, well-sampled photometric spectrum does to356.
not constrain the presence or absence of such an inver- the IRTF Cassegrain focus. Our observations during
sion. Thussignificantdegeneraciesremain;thisisacom- eclipses on 28 and 30 December 2009 (UT) comprise a
mon state of affairs in the field at present even for such total of 10.2 hours on target and 8.3 hours of integra-
relatively well-characterized systems (Madhusudhan & tion time. We list the details of our observations and
Seager2010). Thisisbecause(a)broadbandphotometry our instrumental setup in Table 1. One of our eclipses
averagesoverfeaturescausedbyseparateopacitysources overlapsoneofthoseobservedbyCrolletal.(2011)with
and (b) atmospheric models have many more free pa- broadband photometry from the Canada-France-Hawaii
rameters than there are observational constraints. Spec- Telescope(CFHT),alsoonMaunaKea,onUT27-29De-
troscopy,properlycalibrated,canbreaksomeofthesede- cember 2009. Our first night, 28 Dec, is the same night
generacies, test the interpretation of photometric obser- as their H band observation.
vations at higher resolution, and ultimately has the po- On both nights we observed the WASP-12 system
tential to more precisely refine estimates of atmospheric continuously for as long as conditions permitted using
abundances,constrainplanetarytemperaturestructures, SpeX’s low-resolution prism mode, which gives uninter-
and provide deeper insight into high-temperature exo- ruptedwavelengthcoveragefrom<1−2.5µm. Wechose
planetary atmospheres. prism mode because it offers roughly twice the through-
putoftoSpeX’sechellemodes(Rayneretal.2003, their
1.3. Outline
Fig. 7), though it has a necessarily reduced capability
This paper presents our observations and analysis of to spectrally resolve, separate, and mitigate telluric fea-
two eclipses of WASP-12b in an attempt to detect and tures. We nodded the telescope along the slit to remove
characterizetheplanet’sNIRemissionspectrum. Thisis the sky background; as we discuss below, this induced
part of our ongoing effort to develop the methods neces- substantial flux variations in our spectrophotometry at
saryforrobust,repeatableground-basedexoplanetspec- shorter wavelengths and we urge future exoplanet ob-
troscopy, and we use many of the same techniques intro- servers to eschew nodding at these wavelengths (the ex-
duced in our first paper (Crossfield et al. 2011, hereafter ception to this rule would be for instruments that suffer
Paper I). from time-varying scattered light, such as SpeX’s short-
We describe our spectroscopic observations and initial wavelength cross-dispersed mode). We deactivated the
data reduction in Sec. 2. The data exhibit substantial instrument’s field rotator to minimize instrumental flex-
correlatedvariability,andwedescribeourmeasurements ure, but this meant the slit did not track the parallac-
of various instrumental variations in Sec. 3. We fit a tic angle and atmospheric dispersion (coupled with vari-
simple model that includes astrophysical, instrumental, able seeing and telescope guiding errors) causes large-
and telluric effects to the data in Sec. 4. Chromatic slit scale, time-dependent, chromatic gradients throughout
losses(resultingfromwavelength-dependentatmospheric the night. As we describe in Sec. 5.2 and 5.3, this effect
dispersionandseeing)andtellurictransmittanceandra- is reduced (but not eliminated) by using a wider slit,
diance effects can confound ground-based NIR observa- andwestronglyadvisethatfutureobservationscovering
tions, so in Sec. 5 we investigate these systematic error alargewavelengthrange(a)useaslargeaslitaspossible
sources in detail. We present our main result – a ten- and (b) keep the slit aligned to the parallactic angle.
tative detection of WASP-12b’s emission – in Sec. 6 and On our first night, 28 Dec, we observed with the 1.6”
compare it to previous observations. Finally, we discuss slit to strike a balance between sky background and
the implications of our work for future ground-based, frame-to-frame variations in the amount of light enter-
NIR spectroscopy in Sec. 7 and conclude in Sec. 8. ing the slit. After this run an initial analysis suggested
we could further decrease spectrophotometric variabil-
2. OBSERVATIONSANDINITIALREDUCTION
itywithoutincurringsignificantpenaltiesfromskyback-
2.1. Summary of Observations
ground, and so we used the 3.0” slit on the second night
WeobservedtheWASP-12systemwiththeSpeXnear- (30 Dec).
infrared spectrograph (Rayner et al. 2003), mounted at WASP-12 is sufficiently bright (K=10.2) that we were
Ground-based NIR Spectroscopy of WASP-12b 3
able to guide on the faint ghost reflected from the trans- and
missive, CaF slit mask into the NIR slit-viewing guide
camera. Guiding kept the K band relatively stationary λ30(p)/µm=4.85652782×10−12p4−6.49601098×10−9p3+
but because SpeX covers such a wide wavelength range 4.97530220×10−7p2+4.78270230×10−3p+
the spectra suffer from differential atmospheric refrac-
0.371045967
tion; this results in substantially larger motions over the
course of the night at shorter wavelengths. We did not where p is the pixel number, an integer from 0 to 563,
record guide camera frames, but we recommend that fu- inclusive. Weapplythesewavelengthsolutionstoallour
ture observers save all such data to track guiding errors, spectra after shifting them to a common reference frame
measure the morphology of the two-dimensional point using the shift-and-fit technique described by Deming
spread function, and measure the amount of light falling et al. (2005) and implemented in Paper I.
outside the slit. Typical frames had maximum count
rates of (cid:46)2,000 ADU pix−1 coadd−1, safely within the
3. CHARACTERIZATIONOFSYSTEMATICEFFECTS
10242 Aladdin 3 InSb detector’s linear response range.
3.1. Instrumental Sources
The initially extracted spectra shown in Fig. 1 ex-
2.2. Initial Data Reduction
hibit temporal variations due to a combination of tel-
We reduce the raw echelleograms using the SpeXTool luric, instrumental, and astrophysical sources, with the
reduction package (Cushing et al. 2004), supplemented last of these the weakest of the three effects. We wish
byourownsetofPythonanalysistools. SpeXTooldark- to quantify and remove the instrumental and telluric ef-
subtracts, flat-fields, and corrects the recorded data for fects to the extent that we can convincingly detect any
detectornonlinearities,andwefindittobeanaltogether astrophysical signature – i.e., a secondary eclipse. The
excellentreductionpackagethatfutureinstrumentteams strongest variations in Fig. 1 are largely common-mode
woulddowelltoemulate. WeusedSpeXToolinoptimal (i.e.,theyappearinallwavelengthchannels)andaredue
“A−B” point source extraction mode with extraction tovariationsinlightcoupledintothespectrographdueto
and aperture radii of 2.5”, inner and outer background changesinseeing,pointing,and/ortellurictransparency.
apertureradiiof2.8”and3.5”, respectively, andalinear Longer-termtelluricvariationsaredistinguishablebythe
polynomial to fit and remove the residual background in manner in which they increase in severity in regions of
each column. known telluric absorption.
The extracted spectra have H and K band fluxes of We approximate the amount of light coupled into
∼5500 and ∼2000 e− pix−1 s−1, respectively. After the spectrograph slit by measuring the flux in regions
removing observations rendered unusable for telescope clear of strong telluric absorption, as determined using
or instrumental reasons (e.g., loss of guiding or server our high-resolution telluric absorption spectrum (Hin-
crashes),weareleftwith502and356usableframesfrom kle et al. 2003) convolved to our approximate reso-
ourtwonights. TheextractedspectraareshowninFig.1 lution. The flux in these channels should only de-
andsubstantialvariationsareapparent; wediscussthese pend on the frame-to-frame changes in starlight enter-
in Sec. 3. ing the spectrograph slit, which in turn depends on the
SpeX typically uses a set of arc lamps for wavelength (temperature-andpressure-dependent)atmosphericdis-
calibration,butSpeXToolfailstoprocessarcstakenwith persion, the (wavelength-dependent) size and shape of
the 3” slit in prism mode. Instead, we calculate wave- the instrumental response, telescope guiding errors, and
length solutions by matching observed telluric absorp- achromaticchangesintellurictransparency. Intheinter-
tion features with an empirical high-resolution telluric ests of simplicity we initially treat this as a wavelength-
absorption spectrum (Hinkle et al. 2003) convolved to independent quantity; we return to address the validity
the approximate spectral resolution of our observations. and limitations of this assumption in Sec. 5.2.
We estimate a precision of 1.7 nm for the individual line Ateachtimestepwesumthefluxinthesetelluric-free
positions and use this uncertainty to calculate the χ2 parts of each spectrum, creating a time series represen-
and Bayesian Information Criterion3 (BIC) for fits us- tativeoftheachromaticslitlossessufferedbytheinstru-
ing successively higher degrees of polynomials: for both ment. Although we refer to this quantity as the slit loss,
nights a fourth-order polynomial gives the lowest BIC, it is actually a combination of instrumental slit losses
indicating this to be the preferred model. The RMS of (spillover) and changing atmospheric transmission. The
the residuals to these fits are 1.3 and 1.6 nm for 28 Dec achromatic slit loss time series is plotted for each night
and 30 Dec, respectively, while maximum residuals for in Figs. 2 and 3, along with other candidate systematic
each night are 3.1 nm (at 2.35µm) and 2.9 nm (at 1.3, sources described below. We ultimately compute this
1.85, and 2.32µm), respectively. quantity by summing the flux between 1.63 − 1.73µm
Ourwavelengthsolutionsfor28and30Decarerespec- and 2.10−2.21µm, spectral regions we show in Sec. 5.1
tively to be mostly free of telluric contamination.
SpeX is a large instrument and is mounted at the
λ28(p)/µm=6.77626638×10−12p4−9.82847002×10−9p3+ IRTF’s Cassegrain focus, where its spectra can exhibit
2.52383166×10−6p2+4.26945216×10−3p+ several pixels of flexure due to changing gravity vector;
similarly, atmospheric dispersion (Filippenko 1982) in-
0.414989079
troduces many pixels of motion at shorter wavelengths
(because we keep the star in the slit by guiding at
3 BayesianInformationCriterion(BIC)=χ2+klnN,wherek K band). Apparent spectrophotometric variations can
isthenumberoffreeparametersandN thenumberofdatapoints. be induced by such instrumental changes (e.g., Knutson
4 Crossfield, Hansen, and Barman
1.05
0T.14 5
e
as 0.5 1.03
h
P
al
bit
Or
0.55
T4
ux 1.01
Fl
0.6 d
e
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 z
ali
m
r
o
0T.14 5 N 0.99
e
s
a
h
P 0.5
al
bit 0.97
Or
0.55
T4
0.95
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Wavelength [um]
Fig. 1.—Spectrophotometricdataforthenightsof28Dec2009(top)and30Dec2009(bottom);eachcolumnhasbeennormalizedbyits
medianvalue. Thevariations(duetoacombinationofairmasseffectsandinstrumentalslitloss)arelargelycommonmode;variationsare
lesson30Dec,probablybecauseofthewiderslitusedthen. Thefirst(T1)andfourth(T4)pointsofcontactoftheeclipseareindicated,
ascalculatedfromtheephemerisofHebbetal.(2009).
etal.2007,PaperI).Wemeasurethemotionofthespec- dependsonacombinationofatmosphericconditions, in-
tral profiles in the raw frames perpendicular to (x) and strumentalfocus,andpointingjitterduringanexposure,
parallel to (y) the long axis of the spectrograph slit as but we hereafter refer to it merely as seeing.
follows. We compute the x motion of the star on the slit Previous studies (Deming et al. 2005, Paper I) report
while aligning the spectra to a common reference frame that an empirical measure of atmospheric absorption is
asdescribedinSec.2.2above. Fory wefitGaussianpro- preferabletothecalculatedairmassvaluewhenaccount-
files to the raw spectral traces, then fita low-order poly- ing for telluric extinction. We measured the flux in a
nomial to the measured positions in each frame. The x number of telluric absorption lines for the species CO ,
2
and y motions aretypically 2-4pixels inK bandand are CH , and H O in a manner similar to that in Paper I.
4 2
plottedforbothnightsinFigs.2and3. Anindependent However,inourempiricalairmasstermswestillseesub-
method to measure the x and y motions would be to use stantial contamination from both slit losses and A/B
imagesrecordedbySpeX’sslit-viewingcamera: sincethe nodding, and so in our final analysis we use the airmass
slit is slightly reflective one would then be able to mea- valuesreportedbythetelescopecontrolsystemandplot-
suredirectlythestar’spositionontheslitattheguiding ted in Figs. 2 and 3.
wavelength. We recommend observers investigate this
approach in the future. 3.2. Slit Loss Effects
Wemeasurethefull-widthathalfmaximum(FWHM)
Absolute spectrophotometry is difficult with narrow
of the spectral profiles during the spectral fitting and
slitsbecauseguidingerrors,seeingvariations,and(when
tracing described above. Again, we fit a low-order poly-
the slit is not aligned to the parallactic angle) atmo-
nomial to the measured values to smoothly interpolate
sphericdispersion,allresultinatime-varyingamountof
the compute values. The value we measure (which does
starlight coupled into the spectrograph slit (e.g., Knut-
notscaleasλ−1/5aswouldbeexpectedfromatmospheric son et al. 2007, Paper I). After extracting the spectra,
Kolmogorov turbulence; Quirrenbach 2000) presumably our next step is to remove the large-scale flux variations
Ground-based NIR Spectroscopy of WASP-12b 5
mentation of the simplified formulation of Green (1985)
28 Dec 2009 does not reflect reality with sufficient fidelity, or because
Airmass221...406 vtoariinatsitornusmdenutealtoeffteeclltusr.icAsnouirncdeespoevnedrewnhtetlmestthcoouselddbuee
1.2 performedin futureefforts by recordingimages from the
1.04
Slit loss01..9060 selnitt-evriinewgitnhgecsalmit,ertaheanshdadpiereocftltyhemPeaSsFu,rianngdtihtes pligohsittinoont.
0.92
Instead, following Paper I we divide the flux in ev-
Seeing ["]111...402 elorsyswtaimveelesnegritehs.chTanhniselstbeyparwemavoevleesngththe-ianbdseopluentedeenctlipslsiet
depth (the mean depth over the slit loss wavelength
x [pix] 02 roafntghee)efmroimssioanllssppeeccttrruaml cshhaonunledlsr,ebmuatinthteheovsaermaell.sHhaowpe-
y_A [pix]222468 eacvrteesarh,seotsrhtreearpqwiudaalvlyietyaletnosgfhtthohrstisebreccowaraurvesecelteiaoninrg’tswhr.iellEfrdsapecgeticrvaiaedleliynrdwaepixtihdinlya-
y_B [pix] 222975 naiarrmroawsss(liats(oansd3u0riDnegco)u,rth2i8sDcaencocabusesrevaatgiorneast)eorrpartohpiogrh-
tion of the short-wavelength flux to fall outside the slit.
0.4
Nod 0.0 Nonetheless,weareunwillingtoventurebeyondremoval
0.4 of this simple achromatic trend, given our inability to
0.45 0.50 0.55 0.60 accurately model the chromatic slit loss component.
Fig. 2.—TheobservablequOarbnittailt Piehass(edescribedinSec.2.2)mea-
Dividing the data by this time series substantially re-
sured during the course of our observations on 28 Dec 2009. As
describedinthetext,weultimatelydetrendourobservationswith duces the variability in regions clear of telluric absorp-
a combination the airmass reported by the telescope control sys- tion, as shown in Figs. 4, 5, and 6. Note however that
temandthenodpositionvector. Asnotedinthetextwemeasure some correlated variability remains even after this cor-
theseeingFWHMandypositionasafunctionofwavelength,but
rection step, as seen for example near orbital phase 0.45
here we plot only the approximate K-band values of these quan-
tities. The dashed lines indicate the four points of contact of the on 28 Dec (Figs. 4 and 5). These residual variations
eclipseascalculatedfromtheephemerisofHebbetal.(2009). are wavelength-dependent, and support our conclusion
that chromatic slit losses are affecting our data. Wider
slitsshouldreducethiseffect,andindeedsuchchromatic
30 Dec 2009 residuals are reduced by a factor of ∼ 2 on 30 Dec (see
mass22..40 FiOg.u4r),siwmhpelne cwoerruescetdiotnhreewveiadlesraslrite.sidual sawtooth-like
Air11..62 pattern in the photometry in phase with the A/B nod-
Slit loss01..9060 d(<ing1.4aµndm)e,sapsesceiaelnlyinpFriogms.in4,en5t,aantds6h.oTrtheersawwavtoeoletnhghthass
beenpreviouslynotedwithSpeXinechellemode(Swain
Seeing ["]0111....9351 efltata-lfi.el2d01c0o)rraecntdiopnroefsutmheadbilffyerreesnutilatslsfernomsitiavnityimbpetewrfeeecnt
thetwonodpositionsonthedetector. Wefitthedataat
x [pix] 011 btoot0h.5paotsitthioenAssnimodusltaanndeo−u0sl.y5baytitnhceluBdinnogdasvinecotuorrseeqtuoafl
potential systematic-inducing observables (as described
y_A [pix]222468 iwnaSveecle.n4gbthelsowm)a.yTihnadtictahteestahwattooththeifisdsetrliotnygoefrathteshSoprteeXr
y_B [pix] 222975 ic(nCatsreeorlntlhaeletfleaacltl.ipfi2se0el1ds1si)gi,snaawnladivseblseetncraogunthsge-edrtehapetenlsodhneognretter.rSw-wianavcveeeleliennngagtnhthys
0.4
Nod 0.0 raetgmioonspsheexrpicerrieefnrcaectliaorngearnmdoltairognesrosnysttheemdaetticecbtoiarsedsuedutoe
0.4
0.45 0.50 0.55 0.60 to chromatic slit losses (described in Sec. 5.2), we ulti-
Fig. 3.—SameasFig.2,bOurtbiftoalr Pthhaseenightof30Dec2009. mately discard the shortest-wavelength data.
present in the data.
4. SEARCHINGFORTHEECLIPSESPECTRUM
As described in Sec. 5.2 we try to empirically cali-
4.1. Fitting to the Data
brate the amount of light entering the spectrograph slit.
Despite considerable effort, we are only able to qualita- As noted previously, without external calibration we
tively match the variability in our observations. This cannotaccuratelyrecovertheabsoluteeclipsedepthfrom
could be because the PSF morphology (and especially the telluric-contaminated spectrophotometry. Instead,
the wavelength-dependent flux ratio between the core we self-calibrate as described in Sec. 3.2 above by divid-
and wings) cannot be accurately modeled using a sim- ing out a common time series, thereby largely removing
ple Gaussian function (perhaps due to alignment errors systematic effects (such as variable slit loss); informa-
within SpeX and/or guiding errors), because our imple- tion about the absolute eclipse depth is lost, but the
6 Crossfield, Hansen, and Barman
1.05
0T.14 5
e
as 0.5 1.03
h
P
al
bit
Or
0.55
T4
ux 1.01
Fl
0.6 d
e
z
ali
m
r
o
0T.14 5 N 0.99
e
s
a
h
P 0.5
al
bit 0.97
Or
0.55
T4
0.95
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Wavelength [um]
Fig. 4.— Spectrophotometric data for the nights of 28 Dec (top) and 30 Dec (bottom) after dividing all wavelength channels by the
achromaticslitlosstimeseriesandnormalizedbythemedianfluxineachwavelengthchannel. Stillnoeclipseisvisiblebecausedividing
by the achromatic slit loss term has removed the mean eclipse signal from all wavelength channels, but variations have been strongly
suppressed. Thefirst(T1)andfourth(T4)pointsofcontactoftheeclipsearenoted,ascalculatedfromtheephemerisofHebbetal.(2009).
shape of the spectrum is largely unchanged (note how- determined parameters.
everthatsystematiceffectsremainthatwillinfluencethe We fit each spectral time series (i.e., the flux in each
extracted planetary spectrum; we quantify these effects wavelengthbin)withthefollowingrelation,representing
in Sec. 5 below). We are then better able to look for the an eclipse light curve affected by systematic and telluric
eclipse signature as a differential effect while relying on effects:
the precise NIR photometric eclipse depths (Croll et al.
 
2H0o1w1e)vteor,pelvaecneaoftuerrmreemaosuvrinemgtehnetscoomnmanona-mbsoodluetteimsceaslee-. Fiλ =f0λ(cid:16)ebλai(cid:17)(cid:0)1+dλ(cid:96)i(cid:1)1+(cid:88)J cλjvij (1)
ries the eclipse signal is still masked by the photometric j=1
sawtooth, airmass dependencies, and general photomet-
ric noise. The symbols are: Fλ, the slit loss-corrected flux mea-
i
We cannot use cross-correlation techniques (Deming sured at timestep i in wavelength bin λ; fλ, the total
0
et al. 2005; Snellen et al. 2010, Paper I) in this analy- (star plus planet day side) flux that would be measured
sis because of our low resolution. We investigated the above the Earth’s atmosphere; a , the airmass, which is
i
use of the Fourier-based self-coherence spectrum tech- modulated by the coefficient bλ, an airmass-like extinc-
nique (Swain et al. 2010) but did not find it to remove tion coefficient in which the airmass is proportional to
correlated variability or to otherwise improve the qual- the log of observed flux; (cid:96) , the flux in an eclipse light
i
ity of our data. Instead, we follow Paper I and search curve scaled to equal zero out of eclipse and -1 inside
for differential eclipse signatures in our data by fitting eclipse; dλ, a scale parameter equal to the relative depth
a model that includes telluric, systematic, and eclipse of eclipse; v , the J state vectors (e.g., nod position,
ij
effects to the slit loss-corrected time series in each wave- x or y ) expected to have a small, linearly perturbative
i i
length channel; this approach also has the advantage of effect on the instrumental sensitivity; and cλ, the coeffi-
allowing an estimate of the covariances of the various j
cients for each state vector. To account for and remove
Ground-based NIR Spectroscopy of WASP-12b 7
wecomparedtheorbitalephemeridesfromseveraldiffer-
ent sources (Hebb et al. 2009; Campo et al. 2011; Croll
28 Dec 2009
ux1.04 et al. 2011; Chan et al. 2011) and found them all to
alized Fl01..9060 slitloss bepeoccohn,saisnteunntcetortawiintthyinin1s-i2gnmifiicnaunttesgiavtenoutrheobnsoeirsveaitnioonuarl
m data and our sampling rates. We therefore use the pa-
Nor0.92 rameters from Hebb et al. (2009), which we compute
1.00 1.170-1.255 using our Python implementation4 of the uniform-disk
formulae of Mandel & Agol (2002).
0.95 1.280-1.313
nstant0.90 1.507-1.596 4.2. Choice of Model
o AsinPaperI,wefitthedatasetsusingmanydifferent
C
x - 0.85 1.596-1.686 combinationsofstatevectorsandslitlosstimeseriesand
u
d Fl0.80 1.686-1.775 usetheBICtochoosewhichofthesemanymodelsbestfit
malize0.75 2.100-2.208 oinuvrodlvaetsa.coCmaplcuutliantginχg2tfhoerBeaIcChftoirmeeascehriseest,owfhpiachraimnettuerrns
Nor requiresustoassignuncertaintiestoeachdatapoint. We
2.208-2.315
0.70 estimate the uncertainties as follows. We initially com-
2.315-2.458 pute unweighted fits of Eq. 1 to the data using a mul-
0.65 tivariate minimization provided in the SciPy5 software
0.40 0.45 0.50 0.55 0.60 distribution (the function optimize.leastsq). Decor-
Orbital Phase
Fig. 5.— Several representative spectrophotometric time series relating using only the A/B nod position and airmass
for28Dec. Thetoppanelshowstherelativefluxcoupledintothe calculated from the telescope’s zenith angle, we fit and
spectrograph slit, as measured in regions free of deep telluric ab- compute the residuals for each time series. We scale the
sorptionlines;telluriccontinuumabsorption,seeingvariations,and uncertaintiesineachtimeseriessuchthattheχ2 ineach
guiding errors combine to produce large variations, wholly mask-
ing the (cid:46) 0.3% eclipse signature. The bottom panel shows time wavelength channel equals unity. For each combination
series for several different wavelength ranges, after removal of the of state vectors we then compute another, weighted, fit
commonmodeslitlosstermandbinnedoverthewavelengthrange and its associated χ2 and BIC. Although this method of
listed(inµm). Theeclipseisstillnotvisiblebecausedividingout
estimating uncertainties likely underestimates absolute
the common-mode slit loss term removes the mean eclipse signal
fromallthedata. Dashedlinesareasinthepreviousfigures. parameter uncertainties (Andrae 2010, and see Sec. 4.3
below), we feel it still allows us to compute useful quali-
tative estimates of the relative merit of various models.
Our modeling approach is most successful in spectral
30 Dec 2009 regions largely clear of telluric absorption, which sug-
Flux1.04 slitloss geststelluricabsorbersmaybeoneoftheprimaryfactors
ed 1.00 limiting our analysis (as confirmed in Sec. 5.1 and 5.3).
aliz0.96 When restricting our analysis to the BIC values com-
m
or puted in regions largely clear of strong telluric effects
N
1.00 (1.52 − 1.72µm and 2.08 − 2.34µm), the instrumental
models which give the lowest BIC for our data use a slit
0.95 1.170-1.255 losstermcomputedusingtelluric-freespectralregionsin
nt 1.280-1.313 theHband,theairmassvaluesreportedbythetelescope
nsta0.90 1.507-1.596 controlsystem,andtwostatevectors: theA/Bnodposi-
o
C tion and an airmass-corrected, mean-subtracted copy of
ux - 0.85 1.596-1.686 the slit loss term. The BIC values do not change signifi-
d Fl0.80 1.686-1.775 cantly when we use slightly different wavelength ranges.
e
aliz 2.100-2.208 Althoughincludingthesetwodecorrelationvectorsap-
m0.75 pears warranted on statistical grounds, our modeling ef-
or 2.208-2.315
N forts (discussed in Sec. 5.3) demonstrate that decorre-
0.70
2.315-2.458 lating against the slit loss time series in the light curve
fits systematically biases the extracted planetary spec-
0.65
trum. Because the slit loss effects removed by including
0.40 0.45 0.50 0.55 0.60
Orbital Phase this vector are chromatic, the coefficient associated with
Fig. 6.—SameasFig.5,butforthenightof30Dec. Notethat this vector increases at shorter wavelengths. Since our
these data are less noisy than those shown in the previous figure, achromatic slit loss vector is not wholly orthogonal to
probablybecauseofthedifferentslitsizesused.
themodeleclipselightcurve,astheslitlossvector’sam-
plitude increases the eclipse depth tries to compensate,
the effect of any slow drifts we also tried including low-
and the extracted spectrum is corrupted. Our modeling
order Chebychev polynomials in orbital phase in the set
of the 30 Dec observations (when the 3.0” slit was used)
of state vectors, but these did not improve our results.
indicates that for these data this bias would mainly af-
We thus obtain the set of coefficients (fλ,dλ,cλ) from
0 j
our full set of observations; the dλ represent our mea- 4 Available from the primary author’s website; currently http:
sured emission spectrum. //astro.ucla.edu/~ianc/python/transit.html
To fix the parameters of our model eclipse light curve 5 Availableathttp://www.scipy.org/.
8 Crossfield, Hansen, and Barman
fect λ < 1.4µm, but the bias is stronger for the 28 Dec
data (when the 1.6” slit was used) and significantly af- 28 Dec 2009
fects the H band as well. Thus we again emphasize that
similar observations in the future should use as large a x/s]7000
slitaspossible,andshouldguideattheparallacticangle, e/pi5000
in order to mitigate the biases introduced by chromatic [F∗3000
1000
slit loss. For these reasons we include only the A/B nod
vector in our list of decorrelation vectors 0.03
C
−
4.3. Estimating Coefficient Uncertainties F∗0.01
/
Fp
Weassessthestatisticaluncertaintiesonthecomputed 0.01
planetary spectra using several techniques. First, we fit
0.06
to the data in each of the 564 wavelength channels as
dvieastciroinbeodfatbheovmeeaannd(cSoDmOpMut)eothfethmeepaanraamndetsetrasndinarwdadvee-- cnod 0.02
length bins of specified width. The SDOM provides a 0.02
measureofthepurelystatisticalvariationspresentinthe
planetary spectra. on) 0.0
After summing the data into wavelength channels ncti
25 nm wide (to ease the computational burden) we run exti 0.2
both Markov Chain Monte Carlo (MCMC) and prayer (b 0.4
bead (or residual permutation; Gillon et al. 2007) analy- 1.0 1.5 2.0 2.5
Fig. 7.— Best-fit coefficieWnatvselfernogmth [fiumtt]ing Eq. 1 to the slit loss-
sesforeachwavelength-binnedtimeseries. SinceMCMC corrected28DecobservationsshowninFig.4. Fromtoptobottom:
requires an estimate of the measurement uncertainties, stellarflux,eclipsedepth,A/Bnodsensitivitycoefficient,andtel-
we follow our earlier approach of setting the uncertain- luricextinctioncoefficient. RefertoSec.4foradescriptionofthe
tiesineachwavelengthchannelsuchthattheresultantχ2 fittingprocess.
valueequalsunity. Theresidualpermutationmethodfits Increased levels of precipitable water vapor (PWV)
multiplesyntheticdatasetsconstructedfromthebest-fit lead to increased telluric emittance and decreased trans-
model and permutations of the residuals to that fit, and mittance. If unaccounted for, such variations can mimic
it is similar to bootstrapping but has the advantage of and/or contaminate the desired eclipse spectrum (Man-
preserving correlated noise. dell et al. 2011, but see also Waldmann et al. 2011).
Theposteriordistributionsofeclipsedepththatresult The claim of a strong ground-based L band detection of
fromtheMCMCanalysisareallmuchnarrowerthanthe HD189733bineclipse(Swainetal.2010)waschallenged
uncertainties estimated from both the SDOM and from partially by an appeal to changes in telluric water con-
the prayer bead analysis. This suggests that artificially tent(Mandelletal.2011), soweinvestigatetheseeffects
requiring that χ2 equal unity has led to underestimated in our observations.
parameter uncertainties (cf. Andrae 2010). The prayer AscanbeseeninFig.7,the28Dececlipsespectrumis
beadandSDOMuncertaintiesarecomparableinmagni- stronglybiasedtowardlargereclipsedepthsinregionsof
tude, and to be conservative we use the larger of these greatertelluricabsorption. Thisdoesnotseemtobethe
two uncertainties in each wavelength bin as our statisti- case for the 30 Dec results (cf. Fig. 8), in which we see
cal uncertainty. variability (but no net deflection of the spectrum) in re-
Because we expect systematic uncertainties to play a gions of high telluric absorption. This behavior suggests
large role in our data, in the following section we now thatourdataarecompromisedbytelluriceffectsinthese
pause to examine possible sources of bias and their im- wavelength ranges, and the regions of greatest spectral
pact on our planetary spectra. deflection suggest telluric water vapor is the prime cul-
prit.
5. SYSTEMATICERRORSINHIGH-PRECISION Telluric water content is measured on Mauna Kea by
SINGLE-SLITSPECTROSCOPY
the 350µm tipping photometer at the Caltech Submil-
Our analysis is hampered by systematic biases aris- limeter Observatory6. We convert its 350µm opacity
ing from several sources. We discuss telluric contamina- measurements to PWV using the relation from Smith
tionarisingfromvariabletransmittanceand/orradiance et al. (2001):
(whichaffectsonlycertainwavelengthranges)inSec.5.1.
PWV =20(τ /23−0.016) mm (2)
In Sec. 5.2 we discuss chromatic slit losses, which result 350
from wavelength-dependent seeing and atmospheric dis- The PWV values for the two nights we observed are
persion; this introduces a smoothly varying bias across plotted in Fig. 9. Although the PWV along the tele-
theentirespectrum,increasinginseveritytowardshorter scope’s line of sight will scale with airmass, because our
wavelengths. Then we combine these effects in Sec. 5.3 fitting approach removes airmass-correlated trends we
and use all available information to simulate our obser- consider only the water burden at zenith. On 28 Dec
vations. Applying our standard reduction to these simu- the mean PWV values in and out of eclipse were 0.64
lationsdemonstratesthatwecanhopetosuccessfullyre- and 0.60 mm, respectively; on 30 Dec these values were
coveraplanetarysignalwithincertainwell-definedspec- 0.68 and 0.70 mm, respectively.
tral regions.
6 Data taken from http://ulu.submm.caltech.edu/csotau/
5.1. Telluric Contamination 2tau.pl
Ground-based NIR Spectroscopy of WASP-12b 9
30 Dec 2009
0.06
x/s]7000 00..0045 28 Dec 2009
[e/piF∗35000000 FC−∗00..0032
1000 F/P 0.01
0.00
0.03
0.01
C
− 0.02
F∗0.01
F/p 0.05 30 Dec 2009
0.01 0.04
C 0.03
0.06 −
F∗0.02
cnod 0.02 F/P 00..0001
0.01
0.02
0.02
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
on) 0.0 Fig. 10.— The effect of cWhaavnegleensgtihn [utmel]luric water absorption
cti during our observations. The thin black line shows the measured
n
xti 0.2 residual eclipse spectrum, while the thick gray line represents the
(eb 0.4 aupnpcoarrreenctteedclciphsaengsiegsnianlt(e∆lluTrriacnP)WthVatswhoowulndinbeFiing.fe9r.reTdhfero2m8Dthece
1.0 1.5 2.0 2.5 spectrum appears strongly correlated with the ∆Tran signal, but
Fig. 8.—SameasFig.7,Wbauvtelfeonrgtthh [eumn]ightof30Dec. the30Decspectrumdoesnot. Neither∆Transpectrumissignifi-
cantfarfromtelluricwaterabsorptionlines.
1.0 aperture. We validated our models against the study of
0.9 2009 Dec 28 Mandell et al. (2011) and match their results to within
m]0.8 15%,whichwedeemanacceptablematchgiventhelarge
m0.7 numberofuser-specifiedparametersinsuchsimulations.
WV [0.6 While we thus confirm that the 3−3.5µm L band spec-
P0.5 In Eclipse: Mean PWV=0.64 mm trum reported by Swain et al. (2010) for HD 189733b
0.4 Out of Eclipse: Mean PWV=0.60 mm appears similar to the spectrum that would result from
0.03.35 0.40 0.45 0.50 0.55 0.60 0.65 uncorrected variations in telluric water vapor emission,
1.0 Orbital Phase watervaporradianceeffectsdonotmatchtheirspectrum
2009 Dec 30
0.9 from 3.5−4µm, where eclipse depths of 0.5% would be
m]0.8 seen; nor do radiance effects match their K band spec-
m0.7 trum. A complete explanation of the Swain et al. (2010)
WV [0.6 results must involve more than merely telluric effects.
P0.5 In Eclipse: Mean PWV=0.68 mm Over our wavelength range we find that telluric ther-
0.4 Out of Eclipse: Mean PWV=0.70 mm mal radiation is low enough that |∆Rad| < |∆Tran| al-
0.3
0.35 0.40 0.45 0.50 0.55 0.60 0.65 ways, so we neglect radiance effects. We plot the ∆Tran
Fig. 9.—TelluricwatercontOerbnittald Puhrasinegourobservations,asmea- signals with the observed eclipse spectra in Fig. 10,
sured by the 350µm tipping photometer at the Caltech Submil- and the comparison is intriguing. The 28 Dec eclipse
limeter Observatory. The dashed lines represent the mean PWV
spectrum bears a striking resemblance to our calculated
values in and out of eclipse on each of the two nights, and also
indicatethestartandendofeachnights’observations. ∆Tran spectrum, suggesting these observations are af-
fected by variations in telluric water vapor transmission
We used two independent telluric modeling codes,
at some wavelengths. However, the 30 Dec observations
ATRAN (Lord 1992) and LBLRTM7 (Version 12.0;
show only a weak correlation with the ∆Tran signal (in
Clough et al. 2005), to generate NIR telluric spectra
the wings of strong water bands), suggesting that the
for the in- and out-of-eclipse PWV values; all spectra
CSO data allow for only a crude estimate of the effects
were computed using an airmass of unity. ATRAN sim-
of atmospheric water on the extracted planetary spec-
ulates atmospheric transmission only, while LBLRTM
trum.
simulates both transmission and emission. The appar-
For both nights, the ∆Tran spectra do not capture
ent eclipse signal induced by transmission changes is
the large spectral variations in the eclipse spectra from
∆Tran = (t − t )/t , where t and t are the
out in out in out 2−2.07µm where there are strong telluric CO absorp-
in-andout-of-eclipsetransmissionspectra;theradiance- 2
tion bands. We generate several ATRAN atmospheric
induced signal is ∆Rad = Ω(s − s )/(s + Ωs ),
out in ∗ out profileswithvaryingconcentrationsofCO butfindthat
where s and s are the sky radiance spectra in and 2
in out the in- and out-of-eclipse CO concentrations must dif-
out of eclipse, s is the incident stellar flux, and Ω is the 2
∗ fer by > 5 ppm to reproduce the features seen at these
solid angle on the sky of the effective spectral extraction
wavelengths. Such a change would be greater than any
hour-to-hour change recorded at Mauna Loa by the Na-
7 Run using MATLAB scripts made publicly
tional Oceanic and Atmospheric Administration Earth
available by D. Feldman and available at http:
//www.mathworks.com/matlabcentral/fileexchange/ System Research Laboratory (NOAA ESRL) during all
6461-lblrtm-wrapper-version-0-2 of 2009 (Thoning et al. 2010). Thus the telluric resid-
10 Crossfield, Hansen, and Barman
uals in this wavelength range, though clearly correlated persion direction. We see 10% variations in the seeing
withthetelluricCO bands,aremorelikelyattributable fromoneframetothenext(asmeasuredbythestandard
2
tothenon-logarithmicrelationshipbetweenfluxandair- deviationoftheframe-to-framechangeinseeingFWHM)
mass in near-saturating lines and not to time-variable – whether this represents our fundamental measurement
concentration. precision or the level of fluctuations in the instrument
As noted, ∆Rad is negligible across most of our pass- response, this level of variation prevents accurate and
band,reaching<2×10−4by2.4µmforourPWVvalues. precise modeling of the chromatic slit loss.
The magnitude of ∆Tran shown in Fig. 10 is <2×10−4 Whatever the cause of the disagreement, our model
forourobservationsinthewavelengthranges1−1.1µm, appears qualitatively similar to the spectrophotometric
1.22−1.30µm, 1.52−1.72µm, and 2.03−2.34µm. We variations apparent in our observations. We therefore
further exclude the spectral regions affected by CO proceed to extract a planetary spectrum after remov-
2
(2.00−2.08µm). So long as we restrict our analysis to ing an achromatic slit loss term as described in Sec. 3.2.
these regions we consider it unlikely that telluric water Although we input no planetary signal the spectrum ex-
or CO significantly affect our results on either night. tracted is nonzero because, in general, the projection of
2
Methane is another species whose abundance we are the achromatic slit loss vector onto the model eclipse
interested in measuring but whose telluric concentration light curve is nonzero. As the chromatic slit losses be-
can vary on short timescales. The NOAA ESRL also come more severe at shorter wavelengths, so too is the
measures atmospheric CH content (Dlugokencky et al. extracted planetary signal progressively more biased in
4
2011),soweexaminedthehourlylogs. Thelargesthour- thosesameregions. Wethenperformapseudo-bootstrap
to-hour change during our observations was ∼ 0.5%, analysis of the chromatic slit loss: we re-order the mod-
withtypicalhourlychangessmallerbyafactorofseveral. eled slit transmission series – i.e., we move the first
We again use ATRAN (Lord 1992) to simulate two at- frame’s modeled slit transmission to the end of the data
mospheric transmission spectra with methane amounts set and re-fit, then move the second frame’s transmis-
varying by 0.5% (PWV was set to 1 mm and we sim- sion to the end, and repeat – and each time extract a
ulated observations at zenith), and we then calculate planetary spectrum.
∆Tran as before. At our spectral resolution we find that The variations in the extracted spectrum represent a
∆Tranreachesamaximumofabout0.04%near2.36µm systematicbiasintroducedbyourwavelength-dependent
and is <10−4 outside of 2.23−2.4µm. We include this slit losses. As expected observations taken with a wider
∆Tran spectrum as a wavelength-dependent systematic slit fare better: for the 30 Dec observations the appar-
uncertainty in our final measurements. entvariationsinplanetaryemission(asmeasuredbythe
standard deviation in each wavelength channel) are low
5.2. Chromatic Slit Losses intheHandKbands,reaching(cid:38)0.1%(theapproximate
We quantify the impact of chromatic slit loss on magnitude of the expected signal) in J band and rising
our data by modeling this effect and then trying to shortward. However, our model of the 28 Dec observa-
extract spectroscopic information from the simulation. tionsindicatesasubstantiallyhigherlevelofsystematics:
For this modeling we use an implementation based on still low in the K band (where atmospheric dispersion is
lightloss.pro in the SpeXTool (Cushing et al. 2004) lessened; this is also our guiding wavelength, so varia-
distribution; this in turn is based on the discussion of tions are low here) but rising steeply with decreasing
atmospheric dispersion in Green (1985; their Eq. 4.31). wavelength, reaching ∼ 0.5% by the H band. We apply
A crucial factor in these simulations is the refractive in- these noise spectra to our final measurement uncertain-
dexofair,whichwemodelfollowingBoensch&Potulski ties to account for the possibility of systematic bias.
(1998) assuming air temperature, pressure, and compo- We also find that the induced spectral variations tend
sition that are constant but otherwise consistent with todependmoreonchangesinseeingthanonatmospheric
values typical for Mauna Kea. We also used our empir- dispersion when using a 3.0” slit. This result suggests
ical measurements of the wavelength-dependent seeing that our 30 Dec observations were not significantly com-
FWHM and the positions of the spectra along the slit. promised by our decision to lock down the instrument
We cannot measure atmospheric dispersion perpendicu- rotator.
lartotheslit’slongaxis,sowecalculatethiswavelength-
5.3. Result of Simulated Observations
dependent quantity and then shift it by the spectral off-
sets measured in Sec. 2.2. For completeness, we also combine our two dominant
The result is a model of our chromatic slit loss which sources of systematic uncertainties – telluric absorption
is based almost wholly on empirical data. We see some andchromaticslitlosseffects–inacomprehensivemodel
agreementbetweenthismodelandourspectrophotomet- of our observations, using all empirical data available to
ric throughput – e.g., less flux and chromatic tilt of the us. Weuseastellartemplateforthestar(Castelli&Ku-
spectrum during brief periods of poor seeing. Though rucz2004)andinjectamodelplanetaryspectrum(Mad-
our modeling can qualitatively reproduce the types of husudhan et al. 2011, the purple curve in their Fig. 1,
variations seen, in detail the data are highly resistant to in which temperature decreases monotonically with de-
accurate modeling and we suspect additional dispersion creasing pressure and with the largest predicted 2.36µm
and/or optical misalignments in SpeX may be to blame. CH bandhead) and modulated by an analytical eclipse
4
We suspect that our modeling is also limited by an light curve (Hebb et al. 2009). For each frame we sim-
imperfect knowledge of the (variable) instrument point ulate the telluric transmission for each observation with
spread function: the slit loss is most dependent on the LBLRTM (Clough et al. 2005), using the appropriate
distributionofenergyalongthedispersiondirection,but zenithangleandatmosphericwatercontent(determined
wecanonlymeasurethisshapeperpendiculartothedis- by interpolating the CSO observations in Sec. 5.1 to the