Warm Spitzer Photometry of the Transiting Exoplanets CoRoT-1 and CoRoT-2 at Secondary Eclipse
ABSTRACT We measure secondary eclipses of the hot giant exoplanets CoRoT-1 at 3.6 and 4.5 μm, and CoRoT-2 at 3.6 μm, both using Warm Spitzer. We find that the Warm Spitzer mission is working very well for exoplanet science. For consistency of our analysis we also re-analyze archival cryogenic Spitzer data for secondary eclipses of CoRoT-2 at 4.5 and 8 μm. We compare the total data for both planets, including optical eclipse measurements by the CoRoT mission, and ground-based eclipse measurements at 2 μm, to existing models. Both planets exhibit stronger eclipses at 4.5 than at 3.6 μm, which is often indicative of an atmospheric temperature inversion. The spectrum of CoRoT-1 is best reproduced by a 2460 K blackbody, due either to a high altitude layer that strongly absorbs stellar irradiance, or an isothermal region in the planetary atmosphere. The spectrum of CoRoT-2 is unusual because the 8 μm contrast is anomalously low. Non-inverted atmospheres could potentially produce the CoRoT-2 spectrum if the planet exhibits line emission from CO at 4.5 μm, caused by tidal-induced mass loss. However, the viability of that hypothesis is questionable because the emitting region cannot be more than about 30% larger than the planet's transit radius, based on the ingress and egress times at eclipse. An alternative possibility to account for the spectrum of CoRoT-2 is an additional opacity source that acts strongly at wavelengths less than 5 μm, heating the upper atmosphere while allowing the deeper atmosphere seen at 8 μm to remain cooler. We obtain a similar result as Gillon et al. for the phase of the secondary eclipse of CoRoT-2, implying an eccentric orbit with e cos(ω) = –0.0030 ± 0.0004.
arXiv:1011.1019v1 [astro-ph.EP] 3 Nov 2010
Accepted for the Astrophysical Journal
Preprint typeset using LATEX style emulateapj v. 11/12/01
WARM SPITZER PHOTOMETRY OF THE TRANSITING EXOPLANETS COROT-1 AND
COROT-2 AT SECONDARY ECLIPSE
Drake Deming1, Heather Knutson2,3, Eric Agol4, Jean-Michel Desert5, Adam Burrows6,
Jonathan J. Fortney7, David Charbonneau5, Nicolas B. Cowan4,8, Gregory Laughlin7,
Jonathan Langton9, Adam P. Showman10, and Nikole K. Lewis10
Accepted for the Astrophysical Journal
We measure secondary eclipses of the hot giant exoplanets CoRoT-1 at 3.6 and 4.5µm, and CoRoT-2
at 3.6µm, both using Warm Spitzer. We find that the Warm Spitzer mission is working very well for
exoplanet science. For consistency of our analysis we also re-analyze archival cryogenic Spitzer data for
secondary eclipses of CoRoT-2 at 4.5 and 8µm. We compare the total data for both planets, including
optical eclipse measurements by the CoRoT mission, and ground-based eclipse measurements at 2µm,
to existing models. Both planets exhibit stronger eclipses at 4.5 than at 3.6µm, which is often indicative
of an atmospheric temperature inversion. The spectrum of CoRoT-1 is best reproduced by a 2460K
blackbody, due either to a high altitude layer that strongly absorbs stellar irradiance, or an isothermal
region in the planetary atmosphere. The spectrum of CoRoT-2 is unusual because the 8µm contrast
is anomalously low. Non-inverted atmospheres could potentially produce the CoRoT-2 spectrum if the
planet exhibits line emission from CO at 4.5µm, caused by tidal-induced mass loss. However, the
viability of that hypothesis is questionable because the emitting region cannot be more than about 30%
larger than the planet’s transit radius, based on the ingress and egress times at eclipse. An alternative
possibility to account for the spectrum of CoRoT-2 is an additional opacity source that acts strongly at
wavelengths less than 5µm, heating the upper atmosphere while allowing the deeper atmosphere seen at
8µm to remain cooler. We obtain a similar result as Gillon et al. (2010) for the phase of the secondary
eclipse of CoRoT-2, implying an eccentric orbit with ecos(ω) = −0.0030± 0.0004.
Subject headings: stars: planetary systems - eclipses - techniques: photometric
An especially interesting class of giant extrasolar plan-
ets, the ‘very hot Jupiters’ (hereafter, VHJs), orbit ex-
tremely close to solar-type stars, within 0.03 AU in sev-
eral cases. The temperature structure in the atmosphere
of such a planet is likely to be significantly perturbed
by the strong stellar irradiation.
radiation is one possible energy source that may drive
atmospheric temperature inversions. Temperature inver-
sions with height appear to be common in hot Jupiter
atmospheres; they occur over a wide range of stellar ir-
radiation level (Knutson et al. 2008; Machalek et al. 2008;
Christiansen et al. 2010; Todorov et al. 2010), but are not
well understood. The emergent spectra of VHJs are an
important key to this problem. The emergent spectrum
of a transiting planet can often be measured by observing
the decrease in total light as the planet passes behind the
star during secondary eclipse (Charbonneau et al. 2005;
Deming et al. 2005). Eclipses of the VHJs offer the oppor-
tunity to determine their emergent spectra at wavelengths
Absorption of stellar
as short as visible light (Alonso et al. 2009a; Snellen et al.
2009). Fortunately, VHJs have high transit probabilities,
and are represented by transiting planets such as WASP-12
(Hebb et al. 2009), WASP-19 (Hebb et al. 2010), CoRoT-
1 (Barge et al. 2008), and CoRoT-2 (Alonso et al. 2008).
The CoRoT planets are particularly important in the
study of VHJ temperature structure. Their emergent flux
has been measured at secondary eclipse using infrared (IR)
wavelengths, and also in the visible by the CoRoT mission.
The currently available secondary eclipse measurements
for the CoRoT planets are summarized in Table 1, includ-
ing the results from this paper. While eclipses of CoRoT-2
have been measured at 4.5µm and 8.0µm using the Spitzer
Space Telescope (Gillon et al. 2010), no Spitzer measure-
ments have been reported for CoRoT-1. In this paper,
we report measurements of CoRoT-1 using Warm Spitzer
(Deming et al. 2007) at 3.6- and 4.5µm, and we complete
Spitzer’s measurement of CoRoT-2 by adding the 3.6µm
observation. These additional data allow us to address
the existence and nature of the inversion phenomenon in
1Planetary Systems Laboratory, NASA’s Goddard Space Flight Center, Greenbelt MD 20771
2Department of Astronomy, University of California at Berkeley, Berkeley CA 94720
3Miller Research Fellow
4Department of Atronomy, University of Washington, Box 351580, Seattle, WA 98195
5Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138
6Department of Astrophysical Sciences, Princeton University, Princeton, NJ 05844
7Department of Astronomy and Astrophysics, University of California at Santa Cruz,
Santa Cruz, CA 95064
8Currently: CIERA Fellow, Department of Physics & Astronomy, Northwestern University, 2131 Tech Drive, Evanston, IL 60208
9Department of Physics, Principia College, Elsah, IL 62028
10Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721
2Deming et al.
peak of the VHJ’s spectral energy distribution, we can
speak to whether the visible wavelength eclipse measure-
ments are sensing primarily thermal radiation, as opposed
to reflected light.
Our results, together with those of Hebrard et al.
(2010), are among the first to be reported for transit-
ing exoplanets using Warm Spitzer. The Warm phase of
Spitzer refers to operation of the observatory after the loss
of cryogen, with only the 3.6- and 4.5µm channels of the
IRAC instrument remaining operational. The InSb detec-
tors used at these wavelengths are now functioning at a
temperature of approximately 29 Kelvins, cooled by pas-
sive radiation. This very different operating temperature
regime may have significant implications for the observa-
tory performance as regards high precision photometry.
Therefore, we comment on the performance of the obser-
vatory, within the limits allowed by the fact that we have
observed relatively faint stars.
In Sec. 2 we describe the observations, aperture pho-
tometry, and linear regression procedures to derive eclipse
depths and central phases. Sec. 3 discusses the implica-
tions of our results for the orbital and atmospheric prop-
erties of these giant CoRoT planets, and in the Appendix
we discuss some details concerning the performance of the
Warm Spitzer observatory for this type of exoplanet sci-
Moreover, because we measure near the
2. observations and photometry
We observed CoRoT-1 at 4.5µm on 23 November 2009,
starting at 11:06 UT (orbital phase 0.380), for a dura-
tion of 465.7 minutes, yielding 888 30-second exposures.
Among transiting systems, CoRoT-1 is relatively faint,
having V=13.6 and K=12.1, and a short orbital period of
P=1.509 days (Barge et al. 2008). We observed this sys-
tem at 3.6µm on 26 November 2009, starting at 11:30 UT
(orbital phase 0.379) for the same duration, and the same
exposure time per frame. The CoRoT-1 observations at
both wavelengths used full frame (256 × 256-pixel) mode.
Following the eclipse observations, we acquired 9 minutes
of additional data (17 exposures) by offsetting the tele-
scope to view blank sky using the same detector pixels as
The detectors in the Warm mission are significantly af-
fected by an artifact called column pull-down11, wherein
the presence of a bright star reduces the signal level for
an entire detector column. This, as well as other artifacts,
are significantly mitigated in the cBCD files produced by
Spitzer’s pipeline processing. However, neither CoRoT-1
nor CoRoT-2 lie on columns affected by pull-down, and
in any case we would want to remove any such artifacts
as an integral part of our photometry, so that we could
fully judge their impact. We therefore extracted photom-
etry using the Basic Calibrated Data (BCD) files produced
by version S18.12.0 of the Spitzer pipeline, not the cBCD
files. We calculated orbital phase using the UTC-based
HJD values for the start of each observation from the FITS
headers of the BCD files, and we correct the values to the
time of mid-exposure.
As a first step, we stack the blank sky images and
median-filter each pixel in time to construct an average
blank sky frame. We subtract this sky frame from each
CoRoT-1 image immediately after reading each BCD file.
In principle, this subtraction of a sky-nod will remove
the background radiation, but we nevertheless fit and re-
move residual background anyway, as described below. Al-
though the true sky background should be constant to an
excellent approximation, we find that the background does
vary significantly from frame to frame. This is one signif-
icant difference from the cryogenic mission, as we discuss
in the Appendix.
We locate and correct energetic particle events by com-
paring the time history of each pixel to a 5-point median
filter of that pixel intensity vs. time, and we replace > 4σ
outliers with the median value.
we correct varies between 0.45% and 0.55%, depending
on which planet and wavelength are analyzed. We per-
form aperture photometry on the images, after first ap-
plying corrections for variations in pixel solid angle, and
for slightly different flat-field response for point sources
vs. extended sources12. Prior to subtracting the residual
background and performing aperture photometry, we con-
vert the pixel intensities to electrons, using the calibration
information given in the FITS headers. This facilitates the
evaluation of the photometric errors.
Our photometry code locates the centroid of the stellar
point spread function (PSF) by fitting a symmetric 2-D
Gaussian to the PSF-core (Agol et al. 2010). We calculate
the flux within a centered circular aperture, of variable ra-
dius, using radii of 2.0 to 4.5 pixels, in 0.5-pixel steps.
To determine the residual background intensity, we fit a
Gaussian to a histogram of pixel intensities for each frame.
The center histogram bin, defined to fractional precision
by the Gaussian fit, is adopted as the residual background
intensity. Subtracting the resultant background from the
raw aperture photometry, yields 6 photometric time series
for the star corresponding to aperture radii from 2.0 to 4.5
pixels. We tabulate the magnitude of the point-to-point
scatter in our photometry, and errors in our final results,
as a function of aperture radius. We find that both the
scatter and final parameter errors depend only weakly on
aperture radius, with best values near 2.5 to 3.0 pixels.
We adopt a radius of 3.0 pixels for all of our photometry.
The aperture photometry for CoRoT-1 at 3.6µm, un-
corrected for instrument systematic effects, is shown in
the top panel of Figure 1. The corresponding time series
at 4.5µm is shown in the top panel of Figure 2.
The fraction of pixels
CoRoT-2 (V=12.6, K=10.3) observations at 3.6µm be-
gan on 24 November 2009 at 18:22 UT (orbital phase 0.4),
for a duration of 467.6 minutes. CoRoT-2 being brighter
than CoRoT-1, these observations used subarray mode.
We collected 215 data cubes, each comprising 64 2-second
exposures of 32 × 32 pixels, followed by 3 data cubes of
We perform photometry on the CoRoT-2 data cubes in
a similar manner to the full-frame data for CoRoT-1. We
inspect the aperture photometry for the 64 frames within
12see Secs. 5.3, and 5.6.2 of the IRAC Data Handbook, V3.0
Warm Spitzer Photometry of CoRoT Planets3
each data cube, and zero-weight outliers exceeding the av-
erage by more than 4σ. The first frame in each data cube
is consistently found to be an outlier, and is always ig-
nored. We analyze the remaining 63-frame data cubes
so as to produce two distinct versions of the photometry,
and we perform the entire eclipse-fitting and error anal-
ysis for each version. In the first (default) version, we
average the background-subtracted aperture photometry
for all 63 frames in each data cube, to produce a single
photometric point. For the second version, we use each
of the 63 frames as a separate photometric point. Using
these individual frames potentially exploits the short-term
pointing jitter to better define the intra-pixel effect. How-
ever, in practice the frame-to-frame fluctuations within a
data cube are dominated by photon noise for these rela-
tively faint stars. The eclipse results and errors from these
two versions of the photometry are close to being identi-
cal (difference much less than 1σ). Note that the default
method is essentially just a binning of the data. We prefer
the default version because the eclipse plot (Figure 3) is
We also explored a third version of the photometry,
wherein we average the actual data frames in each data
cube, omitting the first frame and using a median filter to
reject outlying pixels. We then perform aperture photom-
etry on the averaged frame. This method gives essentially
the same result as our default method: the eclipse ampli-
tude (see below) differed by 0.4σ and the phase differed
2.3. Eclipse Amplitudes
CoRoT-1 and -2 have well defined transit parame-
ters (planetary and stellar radii, orbit inclination, etc.).
We adopt these parameters from Barge et al. (2008) and
Alonso et al. (2008), and we calculate eclipse curves nu-
merically, following Todorov et al. (2010). We maintain
the known durations of ingress and egress, but we vary
the central phase and eclipse depth when fitting to the
Both the 3.6- and 4.5µm channels show the well known
intra-pixel sensitivity variation (Morales-Calderon et al.
2006). We fit for the eclipse depth and the coefficients
of the intra-pixel correction using linear regression. The
details of the fitting procedure vary with wavelength, but
at all wavelengths we search for the best central phase by
repeating the linear regressions at many phase values in
a dense grid (spacing 0.0002 in phase), and we adopt the
central phase yielding the best χ2. We always perform
this grid-search in phase when fitting for eclipse ampli-
tude, for both planets at all wavelengths and also for our
Monte-Carlo trials to define errors (see below).
We apply the linear regressions using an iterative proce-
dure. We first decorrelate the photometry to remove the
intra-pixel effect, while ignoring the eclipse, and then we
fit for the eclipse depth using a second regression on the
decorrelated data. After removing the fitted eclipse depth
from the original photometry, we then re-fit and decorre-
late the intra-pixel variation, then re-fit the eclipse. This
procedure converges in two cycles. In principle, iteration
is unnecessary because the regressions are linear and an
identical result can be achieved by solving simultaneously
for both the intra-pixel coefficients and the eclipse depth.
(We verified this by actually doing the simultaneous fit
for a simple case.) Nevertheless, we use the iterative pro-
cedure because in actual practice it is more flexible and
it affords the opportunity to use variants of the fit that
would be awkward to implement in a simultaneous solu-
tion. This should become apparent from the description
At 3.6µm the intra-pixel signature in the photometry
(∼ 2% peak-to-peak) is larger than the eclipse (see top
panel of Figure 1). Our first step is to solve for a provi-
sional intra-pixel decorrelation. The provisional decorrela-
tion function is assumed to be linear in both δX and δY ,
which are defined as the change in X- and Y-pixel position
of the image centroid after removing a trend in X and Y
with time. The approximately 1-hour quasi-periodic jitter
in position has peak-to-peak amplitude in δX and δY of
about 0.03 and 0.08-pixels, respectively. The trends (slow
drifts) are smaller, about 0.005-pixels in X over the entire
dataset, and 0.06-pixels in Y. The provisional intra-pixel
decorrelation function is linear in both δX and δY , and
includes a term linear in time that accounts for both the
slow drift in position as well as possible change in detector
sensitivity. We solve for the coefficients using linear re-
gression (matrix inversion), and correct the original pho-
tometry using this decorrelation function.
Following the provisional intra-pixel decorrelation, we
solve for the eclipse depth, again using linear regression.
This regression formally allows a linear baseline in time,
but that term is effectively accounted for by the intra-pixel
decorrelation of the previous step. We remove the fitted
eclipse from the original photometry, and begin the second
cycle of the iteration. This implements a more sophisti-
cated version of the intra-pixel decorrelation, expressing
the decorrelation function as linear in both time and the
radial distance of the image from pixel center (called pixel
phase). Because there is slow drift of the image toward
pixel center by about 0.06 pixels over the duration of the
observations, intrinsic spatial variation in the intra-pixel
sensitivity (i.e., a change of spatial slope) may be man-
ifest as a change in the decorrelation coefficient of pixel
phase. In this particular case (CoRoT-1 at 3.6µm), vi-
sual inspection of the data indeed suggested a change in
the slope of the intrapixel effect. To allow for this change
in slope, we divide the decorrelation into two halves, the
first half before mid-eclipse and the second half after mid-
eclipse. In effect, this is a minimalist implementation of
using a quadratic term in the intrapixel fit. Although it
is unconventional, we judge it to be the best approach to
this particular case. The coefficients of both halves are
found via linear regression on the eclipse-removed data.
The separate decorrelation functions for the first and sec-
ond halves of the data can be discerned on the top panel
of Figure 1. Note that they are almost continuous at the
break near phase 0.5. None of the conclusions of this pa-
per would be different if we restricted the decorrelation
to more conventional methodology, but the quality of the
3.6µm eclipse fit for CoRoT-1 would be degraded.
After this decorrelation, we again remove the intra-pixel
effect from the original photometry, and re-solve for the fi-
nal eclipse depth and a possible linear baseline via regres-
sion. The eclipse fit uses all of the data, not breaking it
into halves. Decorrelated CoRoT-1 data and the best-fit
4Deming et al.
eclipse are shown in the middle panel of Figure 1, and are
binned (to 100 bins) in the bottom panel of Figure 1.
We use a nearly identical procedure to fit the 3.6µm
eclipse of CoRoT-2, shown in Figure 3, except that we
do not break the decorrelation at mid-eclipse. The first
∼ 30 minutes of these data (not illustrated in Figure 3)
exhibit a transient decrease in flux, similar to the ramp
effect seen at longer wavelength, but decreasing instead of
increasing, and not correlated with the image position on
the detector. Transient effects at this wavelength are not
well understood, so we simply omit the 19 data cubes prior
to orbital phase 0.41.
Another difference for CoRoT-2 is that a correction is
needed for diffracted light from an M-dwarf lying 4 arc-
sec distant (Gillon et al. 2010). Since we also re-analyze
archival data at 4.5 and 8µm for CoRoT-2 (see below),
we need to estimate the diffracted light contributed by
the M-dwarf in the CoRoT-2 aperture at 3.6, 4.5, and
8µm. We calculated the flux ratio (M-dwarf to CoRoT-
2) in the IRAC bands, using the the flux estimation tool
(STAR-PET) on the Spitzer website, and the 2MASS K-
magnitudes and J-K colors of the two stars. Knowing their
relative brightness, we also need to know the fraction of the
M-dwarf flux that is diffracted into the photometry aper-
ture for CoRoT-2. We estimated this by placing the aper-
ture at a symmetric location on the other side of CoRoT-2,
where the diffracted light is contributed almost exclusively
by CoRoT-2 itself. Using that diffracted fraction together
with the flux ratio of M-dwarf to CoRoT-2, we infer that
the diffracted light from the M-dwarf contributes 5.9%,
5.0%, and 8.3% to CoRoT-2 at 3.6, 4.5 and 8.0µm, re-
spectively. The eclipse photometry and derived parame-
ters for CoRoT-2 in our Figures and Tables have all been
corrected for this diffracted light. Gillon et al. (2010) in-
ferred 16.4% and 14.3% at 4.5 and 8µm, respectively, but
he used aperture radii of 4.0 and 3.5 pixels, respectively,
vs. 3.0 pixels in our case.
As a check, we repeated our diffracted light correc-
tion using apertures having the same size as Gillon et al.
(2010). Because the diffracted light is not uniform, the
values do not simply scale as the area of the aperture.
For the same apertures as Gillon et al. (2010), we obtain
corrections of 14.2% and 12.0% at 4.5 and 8.0µm, respec-
tively, in reasonably good agreement with the independent
determination of Gillon et al. (2010). Uncertainty in the
diffracted light correction is not included in our eclipse
amplitude error estimates.
with the diffracted light corrections of Gillon et al. (2010),
and given that we use smaller photometric apertures than
Gillon et al. (2010), we conclude that uncertainty in the
diffracted light correction does not contribute significantly
to the errors on our measured eclipse depths.
The best-fit eclipse depths and errors are listed in Ta-
ble 1, and the central phases and errors are listed in Ta-
Given our good agreement
2.4. Error Estimation
The ideal method to calculate errors would be to re-
peat all of the observations and analysis, and compare the
results from analyzing many independent sets of obser-
vations. This is obviously impractical, so we mimic some
key aspects of that ideal procedure. We generate fake pho-
tometric datasets having the same properties as the real
photometry, and we repeat the entire iterative fitting pro-
cess - including intra-pixel corrections and ramp fitting -
on each fake dataset. We calculate the standard devia-
tion of the collection of eclipse depths and central phases
resulting from the repetitions of the analysis on the fake
To generate each fake dataset, we subtract the best-fit
eclipse curve (plus baseline and intra-pixel decorrelation
function) from the original photometry to produce a set
of photometric residuals. We likewise produce a set of im-
age position residuals by subtracting a multi-point running
average of the X and Y-pixel positions from each individ-
ual (X,Y) position measurement. We permute all of the
residuals and add them back to the best-fit function (pho-
tometry) or running average coordinate (position) to make
an individual fake dataset. We permute the residuals using
two methods, to make two distinct collections of fake data.
The first permutation method scrambles the residuals ran-
domly, which is equivalent to the conventional bootstrap
Monte Carlo technique (Press et al. 1992). We generate
104bootstrap datasets (trials) using this method, and cal-
culate the standard deviation of eclipse depth and central
phase from the distributions of these parameters over the
104trials. These distributions are close to Gaussian.
A second method to permute the residuals preserves
their relative order but shifts their initial phase; this is
sometimes called the ‘prayer-bead’ method (Gillon et al.
2009b). In this case, the number of trials equals the num-
ber of original photometry points. This is 888 for CoRoT-
1, and 13,545 for version 2 of the CoRoT-2 subarray pho-
tometry. These are adequate to define the distributions of
eclipse depth and phase. The prayer-bead method is more
sensitive to the presence of red noise in the data. Neverthe-
less we find that the distribution of eclipse depth remains
consistent with a Gaussian, but for CoRoT-1 the distribu-
tion of eclipse phase shows about 7% of the central phases
lie below the 3σ point in the distribution. We attribute
this to the presence of some red noise before mid-eclipse,
visible in the bottom panel of Figure 1.
For CoRoT-2, the distributions of eclipse depth and
phase were close to Gaussian, so errors from the prayer-
bead method were quite close to the values from the boot-
strap method.This indicates relatively little red noise
in the CoRoT-2 data (after we omitted the first 19 data
points, as noted above). For both CoRoT-1 and -2, we
adopted the greater of the bootstrap and prayer-bead er-
rors for each parameter. CoRoT-1 errors are uniformly
larger than for CoRoT-2 because the star is fainter and the
red noise is slightly greater. Tables 1 & 2 list the errors on
eclipse depth and central phase for all three eclipses, plus
our results from re-analysis of CoRoT-2 at 4.5 and 8µm
2.5. CoRoT-2 at 4.5and 8µm
We check our methodology by analyzing archival Spitzer
data for CoRoT-2 at 4.5- and 8µm, for comparison to the
results of Gillon et al. (2010). Our analysis at 4.5µm pro-
ceeds as described above for CoRoT-1. At 8µm our eclipse
fitting procedure uses a ‘ramp’ baseline (Deming et al.
2006; Knutson et al. 2009) that is fit simultaneously with
the eclipse depth by linear regression. The ramp is com-
Warm Spitzer Photometry of CoRoT Planets5
prised of a term linear in time, a term linear in the log-
arithm of time, with a zero-point on the time axis as de-
scribed by Todorov et al. (2010). We also find that the
photometry exhibits a rather rapid decrease in flux during
the first 100 data points. Investigating this, we find an ap-
proximately 0.1-pixel change in the image Y-position dur-
ing those first 100 points. This transient positional drift is
not in sync with the well known telescope pointing oscil-
lation. Although the pointing oscillation has not (to our
knowledge) been shown to affect 8µm Spitzer photometry,
the 0.1-pixel transient drift apparently does. We therefore
include a Y-position term in the linear regression fit for
the eclipse depth. Without this term, the eclipse depth
would be 0.42%, versus our result of 0.446% (Table 1).
We also perform trial fits using the double-exponential
ramp of Agol et al. (2010). These fits, like the log ramp
discussed above, omit the first 100 points and include a Y-
position term. The ramp observed in the 8µm data (illus-
trated by Gillon et al. 2010) is very shallow, and the scat-
ter is relatively large compared to the ramp-related flux
change. For this reason, we use a single exponential ramp,
not a double exponential ramp. We experimented with
double-exponential fits, but our Levenberg-Marquardt fit-
ting procedure produced degeneracies when attempting to
fit two exponentials to such a shallow ramp. We believe
that only one exponential is warranted in this case. More-
oever, the best-fit exponential ramp is close to a straight
line, since the ramp curvature is minimal. As will become
apparent in Sec. 3.2, the 8µm eclipse depth of CoRoT-2
is crucial to the interpretation of our results, so we will
return to the implications of fitting the exponential ramp
during that discussion.
Our results for CoRoT-2 at 4.5 and 8µm are included in
Tables 1 and 2. The eclipse depth using the exponential
ramp at 8µm is included in Table 1, but the phase re-
sults for that ramp are the same as the log ramp, and are
not listed separately in Table 2. Overall, we find excellent
agreement with Gillon et al. (2010).
3. results and discussion
3.1. Orbital Phase
For CoRoT-1, we compute the weighted average of the
central eclipse phase using both 3.6- and 4.5µm eclipses,
adopting weights equal to the inverse of the variance
of each measurement.This yields a central phase of
0.4994 ± 0.0013, and |ecos(ω)| < 0.006 to 3σ. Our limit
indicates that the orbit is close to circular, but a small
non-zero eccentricity (such as we infer for CoRoT-2, see
below) is not excluded.
For CoRoT-2, Gillon et al. (2010) found ecos(ω) =
−0.00291±0.00063. Our result for the 3.6µm eclipse (cen-
tral phase at 0.4994± 0.0007) is displaced in the same di-
rection as Gillon et al. (2010) infer, but with insufficient
precision to confirm or reject the Gillon et al. (2010) claim.
Combining our 3.6µm result with the eclipses analyzed by
Gillon et al. (2010) could increase the significance of the
total result. For maximum consistency, we re-analyzed the
4.5- and 8µm eclipse data, as described above. We verified
that our adopted transit ephemeris (see Table 2) should
not be a significant source of error when propagated to
the eclipse times. Weighting each eclipse phase (3.6, 4.5
and 8, see Table 2) by the inverse of its variance yields
an average central phase of 0.49809 ± 0.00028. Including
the 28 seconds for light to cross the planetary orbit, we
expect to find the eclipse at phase 0.500019 if the orbit is
circular. Hence, we derive ecos(ω) = −0.0030 ± 0.0004.
The excellent agreement with Gillon et al. (2010) is in part
because we are analyzing much of the same data. How-
ever, the result is heavily weighted by the single eclipse at
4.5µm, which is a reason to be cautious concerning a claim
of non-zero eccentricity. Nevertheless, at face value we are
able to reproduce the result of Gillon et al. (2010) using an
independent analysis, and improve the precision slightly.
Gillon et al. (2010) point out that a non-zero eccentricity
does not require an additional planet in the system, since
incomplete two-body tidal circularization is a plausible al-
ternative for this system.
3.2. Atmospheric Temperature Structure
Our results for both planets are summarized in Figure 4,
which shows all available eclipse data in comparison to var-
ious models. The caption of Figure 4 gives reduced χ2val-
ues for the comparison between each model and the eclipse
data. Since Figure 4 is a comparison of the data to model
predictions, not a fit involving adjustable parameters, we
take the degrees of freedom to equal the number of data
points when calculating the reduced χ2.
The model comparison for CoRoT-1 (top panels of
Figure 4) suggest an inverted atmospheric temperature
structure.The best overall account of the data is ac-
tually produced using a T = 2460K blackbody spec-
trum (Rogers et al. 2009, green line, see reduced χ2val-
ues in Figure 4 caption).
cates the presence of a high altitude absorbing layer, and
such layers are implicated in driving the inversion phe-
nomenon (Burrows et al. 2007; Knutson et al. 2008). The
nature of the absorber is the subject of current debate
(Fortney et al. 2008; Spiegel et al. 2009).
tional model (black line, Burrows et al. 2008) shows signif-
icant absorption due to the CO bandhead that occurs near
4.7µm, and the Spitzer data show no sign of being affected
by this feature. An inverted model using TiO absorption
(blue line) shows much better agreement with the data
than the non-inverted model, but does not account par-
ticularly well for the ground-based (2µm) measurements.
An atmosphere with a nearly isothermal region over ex-
tended heights will produce a blackbody-like spectrum,
and can be regarded as a special case of an inverted tem-
perature structure. The inverted and blackbody model
for CoRoT-1 both give good agreement with the Spitzer
data, as well as the CoRoT optical eclipse measurements
(Snellen et al. 2009; Alonso et al. 2009b). This indicates
that the optical emission is predominately thermal in ori-
gin. The models that account for our Spitzer data, when
compared to the optical eclipses (Figure 4), leave little
room for a reflected light component. Based on the models
of Seager, Whitney, & Sasselov (2000), a geometric albedo
near unity would produce a reflected light eclipse depth of
approximately 520 ppm, whereas the difference between
the CoRoT-1 observations (Snellen et al. 2009) and the in-
verted model (blue curve on Figure 4) is 84 and 21 ppm at
0.6 and 0.71µm, respectively. Also, Cowan & Agol (2010)
inferred a Bond albedo of < 10% for CoRoT-1. Our results
therefore support the conclusion of Snellen et al. (2009)
However, this likely indi-
6Deming et al.
and Cowan & Agol (2010) that CoRoT-1 is a dark planet.
CoRoT-2 (bottom panels of Figure 4) is more com-
plex than CoRoT-1. A conventional model (black line,
Burrows et al. 2008) produces excellent agreement with all
of the data except for the 4.5µm point, where the disagree-
ment is substantial. Since the 4.5- to 3.6µm contrast ratio
is even greater than for CoRoT-1, a temperature inversion
is suggested. But inverted models do not reproduce the
8µm contrast and, based on the reduced χ2values (Fig-
ure 4 caption), no model gives a reasonable account of the
total data. Both the 4.5 and 8µm observed values are
in good agreement between our analysis and Gillon et al.
(2010), so the problem does not seem to lie with the ob-
servations. We first mention some caveats, and then we
suggest two hypotheses to account for the contrast values
of this unusual planet.
One caveat that applies to CoRoT-2 is the fact that
the star is active (Alonso et al. 2008). However, because
the planet passes behind the star during eclipse, there is
no time-variable blocking of active regions on the stellar
disk. The primary consequence of stellar activity is the
photometric variation of the star itself. This variation can
manifest itself in two ways. First, stellar variations can
appear directly in the eclipse curve. The dominant stellar
variation will be due to rotational modulation of active
regions, with a 4.5-day period (Lanza et al. 2009). This
time scale is more than an order of magnitude longer than
the 2.2-hour eclipse duration. Although rotation of active
regions can still affect eclipse data (e.g., by perturbing the
photometric baseline) we do not discern any indications
of it, so we interpret our data at face value. The second
way in which stellar variations can affect eclipse depth is
through the normalization. When the star is fainter, the
disappearance of the planet during eclipse translates to
a larger fraction of the stellar flux. This effect can alter
eclipse depths on long time scales. However, the 4.5 and
8µm observations made by Gillon et al. (2010) were simul-
taneous, so long-term stellar variability cannot be a factor
in the puzzling spectrum of CoRoT-2.
A final caveat concerns the ramp effect for CoRoT-2
at 8µm. We find that fitting the exponential model of
Agol et al. (2010) increases the eclipse depth to 0.51% (Ta-
ble 1). However, this does not alter the situation concern-
ing the interpretation of the CoRoT-2 results, so we now
discuss two hypotheses to account for the totality of the
CoRoT-2 data as summarized in Tables 1 & 2.
3.3. Possible Mass Loss for CoRoT-2
Our first hypothesis for CoRoT-2 is that the plane-
tary atmosphere is well described by a conventional (non-
inverted) model, but the 4.5µm eclipse appears anoma-
lously deep because it contains carbon monoxide emission
lines due to mass loss. We find that a conventional model
lacking CO absorption (see Figure 4) does not increase the
contrast sufficiently in the 4.5µm band to account for the
data - the reduced χ2is 13.5 (Figure 4). Actual emission
from mass loss would be required. Mass loss for close-in
giant exoplanets can occur via tidal stripping (Li et al.
2010), and also via energy deposition from stellar UV
flux. The latter process is particularly important for plan-
ets orbiting young, UV-bright stars (Baraffe et al. 2004;
Hubbard et al. 2007). CoRoT-2 orbits very close-in, where
the tidal force is strong (0.026 AU, Barge et al. 2008).
Moreover, the star is young and active (Bouchy et al.
2008), possibly as young as 30 Ma (Guillot & Havel 2010).
Hence both mass loss mechanisms are potentially impor-
tant for this planet.
Li et al. (2010) have predicted significant CO emission
in the ∆V = 2 overtone bands near 2.29µm, due to tidally-
stripped mass loss from WASP-12. This mass should also
emit in the CO ∆V = 1 bands, which are intrinsically
stronger than the overtone bands, and arise from upper
levels that are easier to excite. Emission from the ∆V = 1
bands will fall within the 4.5µm bandpass, increasing the
eclipse depth. Tidal-induced mass loss is at least qualita-
tively consistent with the apparent non-zero eccentricity
of the orbit. However, recent results show that the orbit
of WASP-12b is likely to be more circular than Li et al.
(2010) suppose (Campo et al. 2010; Husnoo et al. 2010).
The evidence for non-circularity is better in the CoRoT-2
case than for WASP-12, so we explore whether a mass loss
and CO emission scenario might be profitably applied to
We calculate what mass loss rate is required to in-
crease the 4.5µm contrast sufficiently over the conven-
tional model to account for the observed eclipse depth. We
compare the requisite mass loss rate with model calcula-
tions for both tidal-stripping, and evaporation by stellar
UV flux. If the required mass loss rate is (for example) so
large that the planet would disappear within an unaccept-
ably small time scale, then we could discard the mass loss
Prior to calculating the mass loss required to account
for the 4.5µm eclipse, we mention a potentially serious
problem with this hypothesis. This problem derives from
the eclipse curve itself. In a variant of our bootstrap
error analysis, we allowed the ingress and egress times
of the eclipse to vary.We implemented variations in
ingress/egress time by applying linear transformations to
the time axis prior to second contact, and subsequent to
third contact. We find that the 1σ precision of the ob-
served ingress/egress time is about 10%.
that the radius of any CO-emitting volume cannot be more
than about 30% larger (3σ limit) than the radius of the
planet. Given the requisite mass loss rate (see below), we
calculated a synthetic spectrum for the resultant CO col-
umn density of 1019cm−2, adopting excitation tempera-
tures from 3000K to 15,000K. Many individual lines in this
spectrum are optically thick, and attain intensities closely
equal to the Planck function at the excitation temperature.
However, the line density in the 4.5µm Spitzer bandpass
is insufficient to produce the required eclipse flux unless
the excitation temperature exceeds 15,000K. Since CO is
primarily dissociated at such temperatures, we cannot eas-
ily match the required eclipse flux using such a compact
source of CO emission. Nevertheless, the details of mass
loss in the Roche lobe and through the inner Lagrangian
point are not completely understood, so we present our
calculation of the mass loss required to account for the
4.5µm eclipse depth.
Let the continuum flux from the star, integrated over the
4.5µm band be denoted Fs, in ergs cm−2sec−1. Let the
flux from the hypothetical CO cloud be denoted FCO in
the same units. Then the excess over the standard model
Warm Spitzer Photometry of CoRoT Planets7
atmosphere for the planet (Figure 4) requires:
A Phoenixmodel atmosphereforthestar
(Hauschildt et al. 1999), integrated over the 4.5µm band-
pass, gives the same flux as blackbody having T = 5237K,
so Fs= ∆νΩsBν, where Bν = 5.17 × 10−6is the Planck
function (in cgs units) at 5237K, Ωs is the solid angle of
the star as seen from Spitzer, and ∆ν is the bandwidth of
the 4.5µm band in Hz. We also have FCO = L/(4πd2),
where L is the luminosity of the CO-emitting cloud within
the 4.5µm band (ergs sec−1), and d is the distance to the
system. The solid angle Ωs = πR2/d2, where R is the
radius of the star. We substitute for d2in the expression
for FCO, and then (1) becomes:
L ≈ 0.2∆νBνR2≈ 6.2 × 1028ergs sec−1
The number of CO molecules required to produce this
luminosity depends on their excitation state and on the
Einstein-A values for the emission. We first adopt a ther-
mal distribution at T = 3000K for the CO vibrational
levels, and we use the rotationless Einstein A-values Aji
for ∆V = 1 from Okada et al. (2002). Summing over the
vibrational levels, we find that the effective emitting rate
is 28 sec−1per CO molecule. Since hν ≈ 4.42 × 10−13,
L ≈ 1.4×1041photons sec−1. This requires 4.9×1039CO
molecules in the emitting volume. Adopting a solar carbon
abundance (10−3.5), and stipulating that all of the carbon
appears in CO, the total mass in the emitting volume is
approximately 1.5 × 10−11Jupiters.
To determine a mass loss rate from the total mass in
the emitting volume, we must estimate the transit time of
CO molecules. This has been discussed by Li et al. (2010),
who conclude that mass flows through the Roche lobe at
the sound speed, and forms a disk around the star. Most
of that disk emission will not be modulated by the sec-
ondary eclipse, so our observations refer only to the mass
flowing out of the Roche lobe itself. The relevant time
is therefore the Roche lobe radius a(Mp/3Ms)1/3divided
by the sound speed (γP/ρ)1/2.
lobe radius for CoRoT-2 of 4.3 × 105km, and a sound
speed of 4.5 km sec−1. These values yield a mass loss
rate of ∼ 5 × 10−9MJ per year. This value is in close ac-
cord with a minimum value for WASP-12, calculated by
Lai, Helling & van den Heuvel (2010). It is also a reason-
able value for a giant planet close-in to a young active star
(Hubbard et al. 2007).
The greatest uncertainty in the above calculation is the
excitation state of the CO molecules. Because the pop-
ulation of the vibrational levels varies exponentially with
vibrational temperature, the effective emitting rate could
vary by orders of magnitude and still be consistent with
our ignorance. If CO lost from the planet is vibrationally
cold (T=300K, for example), as will tend to happen in the
absence of collisional excitation, then the effective emission
rate drops by over 4 orders of magnitude, and the required
mass loss rate increases by that factor, and becomes unac-
ceptably large. Indeed, in the arguably applicable limit of
no collisional excitation, each CO molecule would emit ap-
proximately one photon as it expanded from the planetary
atmosphere through the Roche lobe. That limit would re-
We calculate a Roche
quire a mass loss rate as high as 10−2MJ per year, which
is unacceptably high.
Although the requisite mass loss rate is within the range
for tidal-stripping and UV-energy deposition models, we
conclude that this CO-emission hypothesis is an unlikely
interpretation of the Spitzer data, due to the difficulty
with the ingress/egress time and the necessity of main-
taining collisional excitation. However, it cannot be ab-
solutely ruled out without more detailed models as well
as observed high resolution spectroscopy of the system. If
this hypothesis could be confirmed, the consequent lack
of an atmospheric temperature inversion for this planet
- orbiting an active star - would be consistent with the
emerging anti-correlation between the presence of inver-
sions and stellar activity levels (Knutson et al. 2010).
3.4. An Inverted Atmosphere Variant for CoRoT-2
A second hypothesis to account for CoRoT-2b is a vari-
ant of an inverted atmospheric structure. The 8µm radi-
ation may hypothetically emerge from deeper and cooler
atmospheric layers, whereas the shorter wavelengths are
formed in a high altitude layer that is heated by absorp-
tion. Absorption in a high altitude layer has been impli-
cated (Burrows et al. 2007) as driving atmospheric tem-
perature inversions, by absorbing stellar irradiance and
heating the planetary atmosphere at altitude. Radiative
equilibrium of a high altitude absorbing layer that is op-
tically thick in the optical and near-IR could potentially
shield lower levels of the atmosphere from radiative heat-
ing. A high altitude layer would re-emit both to space
and to lower levels of the atmosphere, but the net down-
ward flux would be reduced by upward emission to space.
If the opacity of the absorbing layer is high in the opti-
cal and near-IR (λ < 5µm), eclipse observations at those
wavelengths may sense only the absorbing layer, whereas
longer wavelengths (e.g., 8µm) may penetrate and sense
the cooler lower atmosphere.
Recently, Guillot & Havel (2010) have concluded that
the IR opacity of CoRoT-2’s atmosphere is greater than
normal. We are here hypothesizing exactly the opposite of
that conclusion, but based in part on the additional 3.6µm
eclipse result that was not available to Guillot & Havel
One immediate problem with this hypothesis is that
8µm radiation is not believed to be formed any deeper
than the shorter wavelength IRAC bands (Burrows et al.
2007). Hence some additional source of short wavelength
opacity is required. Scattering by micron-sized haze parti-
cles or aerosols is a potential source of the required opacity
if such particles can be lofted and maintained at high alti-
tudes. Haze due to smaller particles at high altitudes has
been inferred for other planets (Pont et al. 2008). How-
ever, several caveats should be cited with regard to this hy-
pothesis. First, most scattering opacities from small parti-
cles have a very broad dependence on wavelength, whereas
a sharper long-wavelength cutoff might be required. If the
extra opacity is from absorption (as opposed to scatter-
ing) then it might perturb the atmospheric temperature
gradient so that the cooler lower atmosphere we envision
might not exist.
This hypothesis of a heated high altitude layer and
a cooler lower atmosphere brings to mind the situation
8Deming et al.
with respect to the global energy budget of HD189733b.
Barman (2008) pointed out that the efficiency of zonal
heat redistribution can be highly depth dependent. Deeper
layers can redistribute heat more efficiently because their
radiative time constant (Iro & Deming 2010) is compara-
ble to or exceeds the time for advection of heat by zonal
winds. In that case the lower atmosphere responds primar-
ily to the day-night average irradiation, whereas the upper
atmosphere comes to radiative equilibrium with day-side
irradiation on a short time scale. If 8µm radiation from
CoRoT-2 arises from deeper layers, then this effect can in
principle act to reinforce the presence of a temperature
If this second hypothesis is correct, then high opacity
at optical and near-infrared wavelengths could produce
a blackbody spectrum at these wavelengths. An 1866K
blackbody (green line on Figure 4) produces a reason-
able agreement with the 3.6 and 4.5µm data, but is be-
low the optical CoRoT measurements (Alonso et al. 2009a;
Snellen et al. 2010). Cowan & Agol (2010) invoked a sim-
ple analytic model of the published photometric observa-
tions of close-in exoplanets, and inferred T = 1866K and a
Bond albedo of 16% ± 7% for CoRoT-2b. This is qual-
itatively consistent with our second hypothesis for this
planet. Ground-based JHK eclipse measurements of this
unusual planet would be very useful in defining the black-
body shape and temperature of the near-infrared spec-
This work is based on observations made with the
Spitzer Space Telescope, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology,
under a contract with NASA. Support for this work was
provided by NASA. Eric Agol acknowledges support un-
der NSF CAREER grant no. 0645416. Adam Burrows
was supported by NASA grant NNX07AG80G and under
JPL/Spitzer Agreements 1328092, 1348668, and 1312647.
He is also pleased to note that part of this work was
performed while in residence at the Kavli Institute for
Theoretical Physics, funded by the NSF through grant no.
PHY05-51164. We thank Dr. Rory Barnes for informative
conversations regarding the tidal evolution of CoRoT-2,
and an anonymous referee for a very thorough review that
improved this paper significantly.
Because our results are among the first for exoplanets using Warm Spitzer, we take this opportunity to comment on the
photometric quality of the Warm mission exoplanet data. The loss of cryogen has increased the operating temperature of
the InSb detectors from 15K (cryogenic) to 29K (warm), and that has altered some characteristics of the detectors. For
example, the ‘column pull down’ effect has become more prominent. Bright stars cause the signal levels to drop for all
pixels in the column they overlap.
None of our target stars happen to lie on columns that are noticeably affected by pull-down. Our photometry code
calculates the theoretical limiting signal-to-noise ratio based on the Poisson statistics of the total number of electrons
recorded from the star, and we include a read noise of 10 electrons for each pixel within the numerical aperture. After
fitting the photometric time series to remove the intra-pixel variations and the eclipse, we calculate the scatter of the
residuals and compare this to the theoretical limiting noise. For CoRoT-1 at 3.6 and 4.5µm we achieve 87% and 92% of
the theoretical signal-to-noise, respectively. However, this seemingly excellent performance may be mis-leading because
these are relatively faint stars, where the stellar photon noise is high and will tend to dominate instrumental noise. A
more sensitive test for possible instrumental red noise is to calculate the reduced χ2of the binned data, after removing
the best fit eclipse (bottom panels of Figs. 1-3). We base the predicted error of each bin (error bars on the figures) on
the observed scatter of the unbinned points, reduced by the square-root of the number of points in each bin (typically, 9).
On this basis, the reduced χ2values are 1.10 and 1.31 for CoRoT-1 at 3.6 and 4.5µm, respectively. This indicates that a
small amount of red noise occurs for time scales longer than about 5 minutes.
In the case of CoRoT-2, the only binning we used was the averaging over 64-frames in each data cube. Measuring the
observed scatter after removing the fit, we find a ratio of 83% when using all individual frames of each 63-frame data cube,
but this reduces to 75% of the theoretical signal-to-noise when we average the frames in each data cube before fitting the
eclipse. Like CoRoT-1, this indicates the presence of a small amount of red noise.
We are interested in whether the column pull-down effect causes enhanced noise for stars that lie on affected columns.
Unfortunately, there are no suitably bright stars that overlie pulled-down columns in our CoRoT data, nor did we find any
optimal test stars in several other Warm Spitzer data sets that we examined. The best test star we located was HD189314,
lying in the Kepler field (D. Charbonneau, PID 60028). This relatively bright star (K=9.3) is above the 1% nonlinearity
limit for the 12-sec exposures we examined. Because pointing jitter moves the star toward and away from pixel-center, it
modulates the nonlinearity effect simultaneously with the intrapixel effect. We were unable to effectively decorrelate these
mixed instrumental effects. However, we were able to evaluate the point-to-point scatter in the photometry, by removing
a smoothing function (high-pass filtering). We find that the point-to-point scatter in the photometry achieves 76% of the
theoretical signal-to-noise. We tentatively conclude that the column pull-down effect does not add short-term noise to
Warm Spitzer photometry, even for stars overlying affected columns. We are unable to evaluate whether it causes increased
red noise, but we anticipate that this will become clear as additional Warm Spitzer observations are accumulated.
Finally, we draw attention to another important difference between the cryogenic and Warm missions. With cryogenic
data, we sometimes evaluated the background for subarray photometry by considering a median over all pixels in a data
cube (fitting to a distribution), and using this single best-fit background value for each of the 64-frames in the data cube.
This had the advantage that the larger number of pixels over the entire data cube resulted in a more precisely determined
Warm Spitzer Photometry of CoRoT Planets9
value, but it was premised on the background being constant within each data cube. We find that this premise is no
longer accurate for the Warm mission: the background value varies significantly from frame to frame within a subarray
data cube. (The background is probably not due to impinging IR radiation, but is more likely to be electronic in nature.)
The statistical penalty of having fewer pixels available when measuring the background in individual frames is offset by
the necessity of following these frame-to-frame variations.
The background variations are illustrated in Figure 5, where we show the 3.6µm background per frame as a function
of the frame number within a data cube, and compare the cryogenic mission (represented by HD189733) to the Warm
mission (represented by CoRoT-2). Note that the 58th frame continues to exhibit a higher background value in the
Warm mission, as it did in the cryogenic mission (Harrington et al. 2007; Agol et al. 2010). We find, in agreement with
Agol et al. (2010), that the photometry from the 58th frame is well-behaved if the higher background is accounted for.
Because the Warm mission will inevitably observe fainter exoplanet host stars than during the cryogenic mission, accurate
background subtraction becomes a high priority. Our 3.6µm photometry for CoRoT-2 used the ‘per-frame’ method that
we now find to be necessary, and achieved the 83% of theoretical signal-to-noise as described above.
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10Deming et al.
Fig. 1.— Upper Panel: Photometry of CoRoT-1, vs. orbital phase, at 3.6µm (points), with the decorrelation function overplotted (red
line). Middle Panel: Photometry after correction with the decorrelation function, with the best-fit eclipse curve overlaid (blue line). Bottom
Panel: Decorrelated photometry binned to a resolution of approximately 0.002 in orbital phase (100 bins), with the best fit eclipse curve
overlaid (blue line). The error bars are based on the scatter of individual points within each bin. The best-fit central phase is 0.5012±0.0024.
Warm Spitzer Photometry of CoRoT Planets 11
Fig. 2.— Upper Panel: Photometry of CoRoT-1, vs. orbital phase, at 4.5µm (points), with the decorrelation function overplotted (red
line). Bottom Panel: Photometry with the decorrelation function removed, and binned to a resolution of approximately 0.002 in orbital phase
(100 bins), with the best fit eclipse curve overlaid (blue line). The error bars are based on the scatter of individual points within each bin.
The best-fit central phase is 0.4992 ± 0.0014.
12Deming et al.
Fig. 3.— Upper Panel: Photometry of CoRoT-2, vs. orbital phase, at 3.6µm (points), with the decorrelation function overplotted (red line).
Each point is the average of 63 temporal frames in a data cube of 32×32 pixels times 64 temporal frames (dropping the first). Bottom Panel:
Photometry with the decorrelation function removed, with the best fit eclipse curve overlaid (blue line). The error bars are the theoretical
limit based on the photon and read noise. The best-fit central phase is 0.4994 ± 0.0007.
Warm Spitzer Photometry of CoRoT Planets 13
Fig. 4.— Planet to star contrast ratios for CoRoT-1 and CoRoT-2 versus wavelength, from Table 1. The short wavelength data
are on left panels (contrast on log scale) and longer wavelength data on the right (contrast on linear scale). Data from CoRoT,
ground-based at 2µm, and Spitzer are all plotted with red points. Error bars on the abscissa give the half-intensity wavelength
limits of the bandpasses. For CoRoT-2 we plot our re-analysis of the Gillon et al. (2010) data at 4.5 and 8µm, but the original
Gillon et al. (2010) values are similar. The square point at 8.0µm is the eclipse depth using the exponential ramp (see table 1).
The black curves are non-inverted Burrows models having 30% redistribution of stellar irradiance to the night side, with no extra
absorbing layers at high altitude. For CoRoT-2, the black dotted portion near 4.5µm is the same Burrows model, only lacking
CO absorption. The blue lines are inverted models from Fortney and collaborators (Fortney et al. 2005, 2006, 2008) having TiO
absorption, and no re-distribution of stellar irradiance. The green lines are blackbodies having T = 2460K (CoRoT-1, Rogers et al.
2009) and T = 1866K (CoRoT-2, Cowan & Agol 2010). The reduced χ2values for the CoRoT-1 data as compared to the different
models are: conventional model (black line) = 12.6, inverted model (blue line) = 2.4, blackbody (green line) = 1.9. For CoRoT-2,
the reduced χ2values for those models are 61.4, 30.4, and 12.5, respectively. (These values use the log ramp point at 8µm, not
the exponential ramp.) The reduced χ2value for CoRoT-2 compared to the non-inverted model without CO absorption (dotted
portion) is 13.5.
14Deming et al.
Fig. 5.— Number of electrons per pixel in the background of CoRoT-2 at 3.6µm (points with line connecting), shown as a function of
the frame number in each 64-frame subarray data cube observed using Warm Spitzer. These results are averaged over all 215 data cubes
that were acquired, and the exposure time per frame was 2 seconds. The line without points shows the background for subarray photometry
of HD189733, using observations acquired during the cryogenic mission (Charbonneau et al. 2008). Since background contains both real
infrared radiation as well as electronic effects, it is not proportional to exposure time. The short-exposure (0.1-sec) HD189733 observations
were scaled upward by an arbitrary factor for this plot.
Warm Spitzer Photometry of CoRoT Planets15
Summary of Secondary Eclipse Measurements for CoRoT-1 and CoRoT-2
0.016% ± 0.006%
0.336% ± 0.042%
0.415% ± 0.042%
0.482% ± 0.042%
0.006% ± 0.002%
0.16% ± 0.09%
0.355% ± 0.020%
0.510% ± 0.042%
0.500% ± 0.020%
0.41% ± 0.11%
0.446% ± 0.10%
0.510% ± 0.059%
Alonso et al.(2009b)
Snellen et al.(2009)
Gillon et al.(2009)
Rogers et al.(2010)
Alonso et al.(2009a)
Snellen et al.(2010)
Alonso et al.(2010)
Gillon et al.(2010)
Gillon et al.(2010)
This paper - log ramp
This paper - exponential ramp
Eclipse Central Times and Phase for CoRoT-1 and CoRoT-2.
Note: Orbital phase for CoRoT-1 used T0= 2454524.62324 and P = 1.5089686 days (Gillon et al. 2009a). For CoRoT-2
we used T0= 2454237.53562 (Alonso et al. 2008) and P = 1.7429935 days (Gillon et al. 2010).