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two separate peaks in ε: if short-period giant planets
have uniformly low albedos, then there appear to be two
modes of heat recirculation eﬃciency. We revisit this
idea below.
Figure 6 shows that planets in this sample are consis-
tent with a low Bond albedo. Note that this constraint
is based entirely on near- and mid-infrared observations,
and is thus independent from the claims of low albedo
based on searches for reﬂected light (Rowe et al. 2008,
and references therein). Furthermore, this is a constraint
on the Bond albedo, rather than the albedo in any lim-
ited wavelength range.
In Figure 7 we plot the dimensionless day-side eﬀec-
tive temperature, Td/T0, against the maximum expected
day-side temperature, Tε=0. The cyan asterisks in Fig-
ure 7 show the four hot Jupiters without temperature
inversions, while most of the remaining planets have in-
versions (Knutson et al. 2010). The presence or absence
of an inversion does not appear to aﬀect the eﬃciency of
day–night heat recirculation.
Planets should lie below the solid red line in Figure 7,
which denotes Tε=0= (2/3)1/4T0. Of the 24 planets in
our sample, only one (Gl 436b) has a day-side eﬀective
temperature signiﬁcantly above the Tε=0limit6. This
planet is by far the coolest in our sample, it is on an ec-
centric orbit, and observations indicate that it may have
a non-equilibrium atmosphere (Stevenson et al. 2010).
There is no reason, on the other hand, that planets
shouldn’t lie below the red dotted line in Figure 7:
all it would take is non-zero Bond albedo. That said,
only 3 of the 24 planets we consider are in this region,
6This is driven by the abnormally high 3.6 micron brightness
temperature; including the 4.5 micron eclipse upper limit d oes not
signiﬁcantly change our estimate of this planet’s eﬀective temper-
ature.8 Cowan & Agol
Fig. 7.— The dimensionless day-side eﬀective temperature,
Td/T0, plotted against the maximum expected day-side temper-
ature,Tε=0. The red lines correspond to three ﬁducial limits of
recirculation, assuming AB= 0: no recirculation (solid), uniform
day-hemisphere (dashed), and uniform planet (dotted). The gray
points indicate the default values (using only observation s with
λ >0.8 micron) for the four planets whose optical eclipse depths
may be probing thermal emission rather than just reﬂected li ght
(from left to right: TrES-2b, CoRoT-2b, CoRoT-1b, HAT-P-7b ).
For these planets we have here elected to include optical mea sure-
ments in our estimate of the day-side bolometric ﬂux and eﬀec tive
temperature, shown in black. The cyan asterisks denote thos e hot
Jupiters known notto have a stratospheric inversion according
to (Knutson et al. 2010). They are, from left to right: TrES-1 b,
HD 189733b, TrES-3b, WASP-4b. The two red x’s denote the ec-
centric planets in our sample, which are also the two worst ou tliers.
with the greatest outlier being HD 80606b, a planet on
an extremely eccentric orbit with superior conjunction
nearly coinciding with periastron. As such, it is likely
that much of the energy absorbed by the planet at that
point in its orbit performs mechanical work (speeding up
winds, puﬃngupthe planet, etc. SeealsoCowan & Agol
2010) rather than merely warming the gas. Gl 436b and
HD 80606b are denoted by red x’s in Figure 7.
The gray points in Figure 7 indicate the default val-
ues (using only observationswith λ>0.8 micron) for the
four planets whose optical eclipse depths may be probing
thermal emission rather than just reﬂected light (from
left to right: TrES-2b, CoRoT-2b, CoRoT-1b, HAT-
P-7b). For these planets we have here elected to use
all available ﬂux ratios (including optical observations
potentially contaminated by reﬂected light) to estimate
the day-side bolometric ﬂux and eﬀective temperature,
shown as black points in Figure 7.
If one takes these day-side eﬀective temperature es-
timates at face value, it appears that the planets with
Tε=0<2400 K exhibit a wide-variety of redistribution
eﬃciencies and/or Bond albedos, but are consistent with
AB= 0. It is worth noting that many of the best char-
acterized planets in this region have Td/T0≈0.75, and
this accounts for the sharp peak in the dotted line of Fig-
ure 5 atε= 0.75. The hottest 6 planets, on the other
hand, have uniformly high Td/T0, indicating that they
have both low Bond albedo andlow redistribution eﬃ-
ciency. These planets must not have the high-altitude,
reﬂective silicate clouds hypothesized in Sudarsky et al.
(2000). But this conclusion is dependent on how one
interprets the Keplerobservations of HAT-P-7b: if the
large optical ﬂux ratio is due to reﬂected light, then this
planet is cooler than we think, and even the hottest tran-siting planets exhibit a variety of behaviors.
5.SUMMARY & CONCLUSIONS
We have described how to estimate a planet’s incident
power budget ( T0), where the uncertainties are driven by
the uncertainties in the host star’s eﬀective temperature
and size, as well as the planet’s orbit. We then described
a model-independent technique to estimate the eﬀective
temperature of a planet based on planet/star ﬂux ra-
tiosobtained at variouswavelengths. When the observed
day-side and night-side eﬀective temperatures are com-
pared, one can constrain a combination of the planet’s
Bond albedo, AB, and its recirculation eﬃciency, ε. We
applied this analysis on 24 known transiting planets with
measured infrared eclipse depths.
Our principal results are:
1. Essentially all of the planets are consistent with low

two separate peaks in ε: if short-period giant planets

have uniformly low albedos, then there appear to be two

modes of heat recirculation eﬃciency. We revisit this

idea below.

Figure 6 shows that planets in this sample are consis-

tent with a low Bond albedo. Note that this constraint

is based entirely on near- and mid-infrared observations,

and is thus independent from the claims of low albedo

based on searches for reﬂected light (Rowe et al. 2008,

and references therein). Furthermore, this is a constraint

on the Bond albedo, rather than the albedo in any lim-

ited wavelength range.

In Figure 7 we plot the dimensionless day-side eﬀec-

tive temperature, Td/T0, against the maximum expected

day-side temperature, Tε=0. The cyan asterisks in Fig-

ure 7 show the four hot Jupiters without temperature

inversions, while most of the remaining planets have in-

versions (Knutson et al. 2010). The presence or absence

of an inversion does not appear to aﬀect the eﬃciency of

day–night heat recirculation.

Planets should lie below the solid red line in Figure 7,

which denotes Tε=0= (2/3)1/4T0. Of the 24 planets in

our sample, only one (Gl 436b) has a day-side eﬀective

temperature signiﬁcantly above the Tε=0limit6. This

planet is by far the coolest in our sample, it is on an ec-

centric orbit, and observations indicate that it may have

a non-equilibrium atmosphere (Stevenson et al. 2010).

There is no reason, on the other hand, that planets

shouldn’t lie below the red dotted line in Figure 7:

all it would take is non-zero Bond albedo. That said,

only 3 of the 24 planets we consider are in this region,

6This is driven by the abnormally high 3.6 micron brightness

temperature; including the 4.5 micron eclipse upper limit d oes not

signiﬁcantly change our estimate of this planet’s eﬀective temper-

ature.8 Cowan & Agol

Fig. 7.— The dimensionless day-side eﬀective temperature,

Td/T0, plotted against the maximum expected day-side temper-

ature,Tε=0. The red lines correspond to three ﬁducial limits of

recirculation, assuming AB= 0: no recirculation (solid), uniform

day-hemisphere (dashed), and uniform planet (dotted). The gray

points indicate the default values (using only observation s with

λ >0.8 micron) for the four planets whose optical eclipse depths

may be probing thermal emission rather than just reﬂected li ght

(from left to right: TrES-2b, CoRoT-2b, CoRoT-1b, HAT-P-7b ).

For these planets we have here elected to include optical mea sure-

ments in our estimate of the day-side bolometric ﬂux and eﬀec tive

temperature, shown in black. The cyan asterisks denote thos e hot

Jupiters known notto have a stratospheric inversion according

to (Knutson et al. 2010). They are, from left to right: TrES-1 b,

HD 189733b, TrES-3b, WASP-4b. The two red x’s denote the ec-

centric planets in our sample, which are also the two worst ou tliers.

with the greatest outlier being HD 80606b, a planet on

an extremely eccentric orbit with superior conjunction

nearly coinciding with periastron. As such, it is likely

that much of the energy absorbed by the planet at that

point in its orbit performs mechanical work (speeding up

winds, puﬃngupthe planet, etc. SeealsoCowan & Agol

2010) rather than merely warming the gas. Gl 436b and

HD 80606b are denoted by red x’s in Figure 7.

The gray points in Figure 7 indicate the default val-

ues (using only observationswith λ>0.8 micron) for the

four planets whose optical eclipse depths may be probing

thermal emission rather than just reﬂected light (from

left to right: TrES-2b, CoRoT-2b, CoRoT-1b, HAT-

P-7b). For these planets we have here elected to use

all available ﬂux ratios (including optical observations

potentially contaminated by reﬂected light) to estimate

the day-side bolometric ﬂux and eﬀective temperature,

shown as black points in Figure 7.

If one takes these day-side eﬀective temperature es-

timates at face value, it appears that the planets with

Tε=0<2400 K exhibit a wide-variety of redistribution

eﬃciencies and/or Bond albedos, but are consistent with

AB= 0. It is worth noting that many of the best char-

acterized planets in this region have Td/T0≈0.75, and

this accounts for the sharp peak in the dotted line of Fig-

ure 5 atε= 0.75. The hottest 6 planets, on the other

hand, have uniformly high Td/T0, indicating that they

have both low Bond albedo andlow redistribution eﬃ-

ciency. These planets must not have the high-altitude,

reﬂective silicate clouds hypothesized in Sudarsky et al.

(2000). But this conclusion is dependent on how one

interprets the Keplerobservations of HAT-P-7b: if the

large optical ﬂux ratio is due to reﬂected light, then this

planet is cooler than we think, and even the hottest tran-siting planets exhibit a variety of behaviors.

5.SUMMARY & CONCLUSIONS

We have described how to estimate a planet’s incident

power budget ( T0), where the uncertainties are driven by

the uncertainties in the host star’s eﬀective temperature

and size, as well as the planet’s orbit. We then described

a model-independent technique to estimate the eﬀective

temperature of a planet based on planet/star ﬂux ra-

tiosobtained at variouswavelengths. When the observed

day-side and night-side eﬀective temperatures are com-

pared, one can constrain a combination of the planet’s

Bond albedo, AB, and its recirculation eﬃciency, ε. We

applied this analysis on 24 known transiting planets with

measured infrared eclipse depths.

Our principal results are:

1. Essentially all of the planets are consistent with low