You are an expert at summarizing long articles. Proceed to summarize the following text: 
kepler-22b  is a recently validated extrasolar planet detected by the _ kepler mission _ via the transit technique ( @xcite , b12 hereafter ) . orbiting a star with 75% of solar luminosity once every 290days , kepler-22b   receives an insolation just 10 - 15% greater than that received by the earth and thus was claimed to be the first transiting planet discovered to orbit within the so - called habitable - zone of its parent sun ( b12 ) . although habitable - zone exoplanets have been detected by radial velocity surveys @xcite , kepler-22b  is a fascinating object thanks to the plethora of follow - up opportunities afforded by transiting planets @xcite . this excitement is evident in the preceding astronomical literature with speculation about the planet s habitability @xcite , a presently undetected exomoon s habitability @xcite and considerable efforts to redefine the so - called habitable - zone ( e.g. @xcite ) .    despite the excitement generated by the pioneering discovery of kepler-22b  by b12 , the planet can not be considered `` earth - like '' given its radius of 2.4@xmath0 . observationally , the composition of the planet is essentially unconstrained since the upper limit on the planetary mass is quite broad at @xmath7@xmath2 ( 2@xmath8 ) ( b12 ) . the most well - characterized planet with a radius similar to kepler-22b  would seem to be gj1214b @xcite with a radius of 2.7@xmath0 , which has a low bulk density indicating that it can not have a rock - dominated composition @xcite . although kepler-22b  may not be a rocky habitable earth - like world , there is a distinct possibility for the system to yet maintain such a world if kepler-22bpossesses a large moon . recently , there has been considerable speculation about the potential habitability of such a moon @xcite since it is thought that exomoons should be detectable around transiting planets using kepler @xcite . despite this speculation , we note that , to our knowledge , no - one has ever conducted a search for an exomoon in this system . indeed , we note that there has never even been a search for an exomoon around a habitable - zone _ candidate _ planet , let alone a validated one , in the present literature . the `` hunt for exomoons with kepler '' ( hek ) project @xcite is presently the only systematic program we are aware of attempting to observationally identify extrasolar satellites . searching for such signals is computationally challenging due to the highly multimodal , complex and high - dimensional parameter space one is faced with @xcite , the need for calculating the bayesian evidence integral @xcite and the photodynamic forward modeling required to simulate exomoon signals @xcite . to provide some context , the light curve fits presented in this work required 49.7years of cpu time . to date , eight kepler objects of interest ( kois ) have been analyzed for evidence of extrasolar moons each with null detections leading to upper limits on the satellite - to - planet mass ratio of @xmath9-@xmath10% @xcite .    in this work , we present an analysis of the first habitable - zone planet by hek . this target was identified as a target - of - opportunity by the project because it i ) is in the habitable - zone ii ) is a validated planet iii ) has radial velocity measurements iv ) has a quiet , bright ( @xmath11 ) host star v ) has a host star with asteroseismology constraints ( b12 ) . in this work , we include several new modes to thoroughly explore the exomoon parameter space . these include retrograde (  [ sub : retro ] ) and eccentric moon solutions (  [ sub : eccentricity ] ) , informative and uninformative limb darkening priors (  [ sub : ldpriors ] ) , applying bayesian model averaging (  [ sub : bma ] ) , high - resolution fitting (  [ sub : hires ] ) , leveraging the radial velocities (  [ sub : rvs ] ) and asteroseismology constraints (  [ sub : astero ] ) and injecting and retrieving synthetic moon signals (  [ sec : injected ] ) . we also take this opportunity to provide updated constraints on the mass , radius , composition , habitability and orbit of kepler-22b  using new _ kepler _ data (  [ sec : planetonly ] ) . in the discovery paper of kepler-22b  ( b12 ) , three transits were detected by the _ kepler mission _ occurring in quarters 1 , 4 and 7 ( q1 , q4 and q7 ) . since this time , an additional three transits should have been observed by _ kepler _ : a @xmath12 transit in q11 , a @xmath13 transit in q14 , and a @xmath14 transit in q17 . the @xmath12 transit was successfully recorded but unfortunately the @xmath13 was not due to a data gap in the q14 time series . the @xmath14 transit is unlikely to have been recorded because it occurred during a safe mode event from may @xmath15 to may @xmath14 2013 . further , soon after this _ kepler _ lost functionality of a second reaction wheel on may @xmath16 , putting future science observations in doubt . therefore , it is quite possible that the four transits of kepler-22b   analyzed in this paper will be the only transits ever observed by _ kepler_. the first transit was observed in long - cadence ( lc ) mode only , whilst the latter three have short - cadence ( sc ) data . we downloaded the reduced data from the mikulski archive for space telescopes ( mast ) . in this work , we always make use of the `` raw '' ( labelled as `` sap_flux '' in the header ) data processed by the data analysis working group ( dawg ) pipeline ( see accompanying data release notes for details ) . the `` raw '' data has been processed using pa ( photometric analysis ) , which includes cleaning of cosmic ray hits , argabrightenings , removal of background flux , aperture photometry and computation of centroid positions . for the sake of brevity , we do not reproduce the details of the pa pipeline here , but direct those interested to @xcite and the data release handbooks . the _ kepler _ photometry contains several systematic effects which require detrending before a precise transit light curve analysis can be conducted . these effects can be instrumental ( such as focus drift , pointing tweaks , safe modes , etc ) or astrophysical ( such as flaring , rotational modulations , etc ) . in this work , we utilize the cofiam  ( cosine filtering with autocorrelation minimization ) algorithm described in @xcite for detrending these various effects . cofiam  can be thought of as a high - pass , low - cut periodic filter optimized to undisturb all periodicities at or below the so - called `` protected timescale '' , @xmath17 . the algorithm builds upon initial applications of cosine filtering by @xcite for corot photometry and @xcite for _ kepler _ photometry . cofiam  regresses the following sum of harmonic functions to the time series :    @xmath18 , \label{eqn : linearcosinefilter}\end{aligned}\ ] ]    where @xmath19 is the total baseline of the data under analysis , @xmath20 are the time stamps of the data , @xmath21 & @xmath22 are model variables and @xmath23 is the highest harmonic order . for any given @xmath17 , one may define the maximum number of distinct harmonic cosines functions ( @xmath24 ) to regress to the data without disturbing the timescale @xmath17 as :    @xmath25    however , choosing any @xmath26 will also protect the timescale @xmath17 . exploiting this fact , cofiam   explores every possible variation ( in total there are @xmath27 variations ) . the detrended light curve after each cofiam  regression is trimmed to within twice the `` window '' timescale ( @xmath28 ) of the predicted transit time and then a final linear slope is fitted through the data ( excluding the transit itself ) to serve as a final normalization . after every detrending , we compute the autocorrelation on a 30minute timescale using the durbin - watson metric :    @xmath29    where @xmath30 are the residuals and @xmath31 is the number of data points . the value of @xmath32 always lies between 0 and 4 , with 2 representing an absence of autocorrelation , @xmath33 implying otherwise . cofiam  therefore selects the value of @xmath23 which minimizes @xmath34 ( hence `` autocorrelation minimization '' ) . cofiam  is applied to each transit epoch individually and the inputted data is pre - screened for any sharp , discontinuous offsets ( due to say a pointing tweak ) as well as a general outlier rejection phase using median filtering . we never attempt to stitch two quarters together since there is no reason to expect the detrending function to be smooth between rolls of the spacecraft ( which occur every quarter ) .    in this work , we chose @xmath35 where @xmath36 is the first - to - fourth contact transit duration . @xcite showed that @xmath36 is the lowest periodicity in the fourier transform of a transit and so we multiply this by three to provide a small cushion . the `` window '' timescale is defined to be @xmath37 $ ] ( the 1.2 factor is again a cushioning factor ) where @xmath38 is the hill sphere timescale . for this we define @xmath39^{1/3 } [ p_{b*}/(2\pi)]$ ] where @xmath40 is the planet s orbital period , @xmath41 is the planet s mass and @xmath42 is the stellar mass . for all of these quantities we simply used the best - fit values quoted in b12 ( for @xmath41 we used the 3@xmath8 upper mass limit ) . we stress that the detrending function is regressed independently of the later transit fits . this is done because the form of the detrending function is varied and we typically try between @xmath43-@xmath44 different models per transit . to perform the detrending in conjunction with the transits would thus require around @xmath45 unique models i.e. @xmath46 $ ] for kepler-22b . given the very costly compuational demands of even a single photodynamical fit , this would be unrealistic with current computational capabilities . after detrending with cofiam , we find @xmath47 , @xmath48 , @xmath49 and @xmath50 and the detrending functions are plotted over the pa data in figure  [ fig : qaraw ] .     +   + we first fit and model the light curve as being due to a single planet transiting the host star , to serve as a benchmark for the subsequent planet - with - moon fits . the planet - only light curve is modeled as was done in @xcite , using the popular @xcite algorithm . we assume a quadratic limb darkening law for the host star , where the specific intensity is described by @xmath51 where @xmath52 , @xmath53 is the normalized radial coordinate on the stellar disk and @xmath54 & @xmath55 are the limb darkening coefficients . planet - with - moon models are generated using the photodynamic luna  algorithm @xcite , which inherently accounts for the various timing effects on the planet induced by a moon @xcite . we direct the reader to @xcite for details on how the photodynamical light curves are computed . model light curves are fitted to the data using the multimodal nested sampling algorithm multinest  @xcite . by using this code , we not only obtain parameter posteriors but also the bayesian evidence of each model attempted , thus allowing for later bayesian model selection and model averaged posteriors . bayesian model selection is a crucial tool in detecting exomoons due to the roughly doubling of free parameters combined with the complex parameter space @xcite .    in general , the methods described above are the same as those implemented in our previous hek surveys ( e.g. see @xcite ) . notably , the choice of priors follows that of @xcite and are shown in table  [ tab : priors ] . however , in studying kepler-22b , we introduced several new changes to our methodology to improve both the accuracy of our derived results and the speed of the computations . these modifications are discussed in what follows .      in this work , we use two different priors for the limb darkening coefficients : i ) informative priors ii ) uninformative priors . the informative priors are computed using a monte carlo forward modeling of stellar atmosphere models . first , we draw a random normal variate from the effective temperature ( @xmath56 ) and stellar surface gravity ( @xmath57 ) and then compute the associated quadratic limb darkening coefficients using the @xcite stellar atmosphere model database convolved with the _ kepler _ bandpass ( see @xcite for more details ) . we repeat this process until @xmath58 fair realizations of @xmath54 and @xmath55 have been computed . for @xmath56 and @xmath57 , we used the quoted values from b12 of @xmath59k and @xmath60 but doubled the uncertainties for both .    the @xmath58 realizations of @xmath54-@xmath55 form a joint prior probability for the limb darkening coefficients . for computational expedience , it is desirable to characterize this joint prior probability with a simple analytic form , such as a bivariate gaussian , rather than calling a stellar atmosphere model at every realization in the light curve fits . however , a bivariate gaussian is not ideal since our @xmath54-@xmath55 joint prior probability displays a strong covariance ( correlation coefficient of -0.97 ) . despite this , a bivariate gaussian can be applied by re - parameterizing the limb darkening coefficients . to this end , we perform a principal components analysis ( pca ) on the joint prior probability of @xmath54-@xmath55 and re - parameterize the terms into the orthogonal components @xmath61 and @xmath62 following the suggestion of @xcite :    @xmath63    where we derived @xmath64 from the pca . using this transformation , we computed a joint prior probability for @xmath61-@xmath62 with negligible covariance . the lack of covariance , combined with the fact the resulting distributions are unimodal and approximately symmetric means that a bivariate gaussian is now a reasonable analytic approximation . regressing a gaussian to each cumulative density function ( cdf ) , we derive normal priors of @xmath65 and @xmath66 . in figure [ fig : u1u2prior ] , we compare the pdf in @xmath54 and @xmath55 predicted by these priors relative to the actual prior probability initially generated , where one can see the good agreement .        the second type of prior we try is an uninformative one . @xcite recently showed that uniform priors in @xmath54-@xmath55 can be drawn , without ever sampling unphysical limb darkening coefficients , by applying the `` triangular sampling '' technique . this is achieved by re - parameterizing the coefficients to @xmath67-@xmath68 and sampling uniformly between zero and unity in each , where    @xmath69    employing triangular sampling is approximately twice as efficient than the uninformative priors used previously in @xcite . this is because previously we used uniform priors in @xmath70 and @xmath71 , which spends exactly half of its time sampling from unphysical ( and thus rejected ) parameter ranges @xcite .      in principle , cofiam  should provide a light curve with an out - of - transit baseline flux equal to exactly unity . in practice , even with cofiam s final stage linear normalization , it is prudent to regress a baseline normalization factor for each transit epoch simultaneous to the transit parameters . one major benefit of doing so is that the uncertainty of the baseline normalization is propagated into the uncertainty of the other transit parameters . in the past , we have treated the normalization factor as a free parameter in multinest  like any other term . for planets with many transits epochs , this is problematic since the regression now includes a very large number of free parameters leading to laborious cpu times . the fact that a relatively minor nuisance parameter causes this dramatic slow - down makes the situation somewhat impractical .    in this work , we introduce a new refinement to the hek fitting strategy which simply treats the baseline parameters ( @xmath72 ) as a set of nuisance parameters . rather than marginalizing over these terms , every realization of the transit model simply optimizes the baseline parameters to the data . this is easily achieved using a weighted linear minimization which is both extremely quick and guaranteed to always find the global minimum . in principle , one should wish to marginalize over nuisance parameters rather than simply maximize the likelihood , but in practice we find this procedure has little effect on the other transit parameters and leads to a significant speed - up . unlike previous surveys , we decided to investigate the potential for eccentric orbits for both the planet and the moon due to the high - priority nature of kepler-22b . eccentric fits always require dramatically more time to explore due to i ) the introduction of two new free parameters ii ) the requirement to solve kepler s transcendental equation @xmath73trillions of times during the course of a single fit . eccentric orbits can also produce unphysical scenarios , unless limits are enforced on the allowed range in @xmath74 ( eccentricity of the planet - satellite barycentre around the host star ) and @xmath75 ( eccentricity of the satellite around the planet - satellite barycentre ) . first of all , parameter realizations reproducing collisions should be avoided . we therefore enforce that @xmath76 , i.e. the periastron separation between the planet and the satellite exceeds two planetary radii ( we use two planetary radii since the satellite s radius is @xmath77 ) . we use two planetary radii because the satellite s radius can be up to one planetary radius in our fits . similarly , for the planetary orbits , we enforce @xmath78 . additionally , @xcite showed that the maximum stable planet - satellite separation is attenuated for eccentric orbits . @xcite showed that all satellites must conform to :    @xmath79    where @xmath80 is equal to the semi - major axis of the satellite relative to the planet in units of the hill radius . under the assumption that @xmath81 , @xcite showed that @xmath82 , where @xmath83 is the period of the satellite around the planet - satellite barycentre . this allows us to enforce the @xcite condition as :    @xmath84    these constraints are optimistic in the sense that the orbits are assumed to be coplanar and the moon is simply a test particle . more realistic solutions can be found by exploring the three - body solution with non - zero masses and three - dimensional geometry ( e.g. see @xcite ) , but we reserve these more detailed dynamical investigations for the final posterior analyses . we also enforce the same limits on the planet and satellite densities used in @xcite . these various limits are all imposed by simply rejecting any trials reproducing such behavior . due to the computationally much higher cost of exploring eccentric solutions , we only explored eccentric - planet or eccentric - moon solutions but not both simultaneously , as such fits were found to be prohibitively cpu expensive . since the hill stability of a putative moon decreases strongly with increasing eccentricity for both terms , we do not envisage it likely that this significantly hinders our detection ability . in @xcite we did not explore retrograde orbits for the exomoon , which luna  defines as being when @xmath85 , following the definition used for a planet transiting a star . ] . in this work , we present a method to explore such orbits whilst still maintaing an isotropic prior in @xmath86 . one difficultly in doing this is that an isotropic prior is uniform in @xmath87 but this trigonometric function is not uniquely defined over the interval @xmath88 . for example , @xmath89 may refer to @xmath90 or @xmath91 . our resolution to this is to introduce an auxiliary cosine term which we dub @xmath92 and is defined over the interval @xmath93 . the inverse of this function is given by :    @xmath94   & \text{if } -1 < \cos'i_{sb } \leq + 1 , \\ \cos^{-1}[\cos'i_{sb}-2]+\pi & \text{if } + 1 < \cos'i_{sb } \leq + 3 . \end{cases } \label{eqn : inclination}\ ] ]    by enforcing a uniform prior in @xmath93 and inverting the above , we reproduce an isotropic prior in inclination and still explore the full range of inclinations ( i.e. both prograde and retrograde orbits ) . unlike the previous kois analyzed in survey i @xcite , kepler-22  has asteroseismology constraints available . consequently , there exists a strong empirical prior on @xmath95 , the mean stellar density of @xmath96g@xmath97 ( b12 ) . in all fits , we treat @xmath95 as a normal prior following this measurement . usually , the light curve fitted eccentricity and stellar density are highly degenerate but the presence of a strong prior on the latter breaks this degeneracy . this trick was first noted in @xcite and was dubbed `` single - body asterodensity profiling '' by the authors , or sap . we are therefore able to provide sap - derived eccentricity constraints in the light curve fits provided in this work . we also note that b12 are able to combine their precise @xmath95 measurement with stellar evolution isochrone models to provide precise estimates of the stellar radius and mass ( @xmath98 and @xmath42 ) . although these are not model parameters in any our fits , we can use them later to derive physical parameters .      as part of the campaign to validate the planetary nature of kepler-22b , b12 obtained sixteen high resolution spectra of the target star between 17 august 2010 and 25 august 2011 using the hires spectrometer on the keck i 10 m telescope , which we utilize in this work . the spectra yield @xmath99ms@xmath100 precision radial velocities and show no clear detection of kepler-22b . the null - detection is consistent with a low - mass planet , as expected for the radius of kepler-22b . by leveraging these radial velocities , we can constrain various parts of the parameter space explored by multinest , such as excluding massive planets or moderate - mass planets on highly eccentric orbits .    including the rvs requires only two extra free parameters to our model , @xmath101 and @xmath102 ( the radial velocity jitter ) , since all of the other orbital parameters are included in our fits anyway . the jitter term behaves like an additional error which is simply added in quadrature to the reported rv uncertainties . unlike b12 , we do not choose a fixed @xmath102 value of @xmath103ms@xmath100 but rather we fit the parameter using a modified jeffrey s prior , as advocated by @xcite . following @xcite , we choose the inflection point of the modified jeffrey s prior to be equal to the median rv uncertainty and set the maximum to be equal to twice the range of the reported rvs . the same prior is also used for @xmath101 . the radial velocities can be used to derive the planetary mass , @xmath41 , given a known stellar mass , @xmath42 . to determine @xmath41 , we solve the cubic equation of the well - known mass - function using equation 3.18 of @xcite . whilst some authors , such as b12 , have advocated exploring negative @xmath101 solutions to avoid positive - biases in fitting joint rv + transit data , this is actually unnecessary for multinest  as the nested sampling technique does not suffer boundary condition biases , unlike markov chains . a new feature we implement in this work for the hek project is the exploration of negative @xmath104 solutions i.e. negative radii moons . negative radii moons are of course not physically plausible and our implementation simply involves flipping the transit signal component caused by the moon in such cases . we exploit this trick as a vetting test such that solutions favoring a negative radius moon can be easily dismissed . this replaces the previous test of @xcite of fitting for zero - radius moons and comparing the bayesian evidence . we find that negative - radius moon exploration is more efficient computationally since we do not require another additional moon fit purely for vetting purposes . we select a uniform prior on the radius ratio term of @xmath105 . ._planet - moon parameters used in light curve fits and their associated priors . @xmath106 is a uniform prior between @xmath107 and @xmath108 . @xmath109 is a gaussian prior with a mean of @xmath107 and standard deviation @xmath108 . @xmath110 is a modified jeffrey s prior with a maximum at @xmath108 and an inflection point at @xmath107 . @xmath111 represents uninformative limb darkening coefficient priors ; informative priors are discussed in [ sub : ldpriors ] . _ [ cols="^,^ " , ]     [ tab : fakeevidence ]          as was done previously for kepler-22b  itself , we should now investigate whether the posterior distribution allows us to infer the habitability of our injected moon . given the complex parameter degeneracies and low - to - moderate signal - to - noise of the injected moon signal , it is not immediately clear that we are able to definitively determine the moon s habitability , given the broad and multimodal nature of the moon parameter posteriors . this is further complicated by the fact that moons possess several extra sources and sinks of thermal energy compared to their host planets . if their orbit around the planet is elliptical , they can experience tidal heating , which can significantly affect surface temperatures even for small eccentricities @xcite . they also suffer frequent stellar eclipses by their host planet , which can act as an effective energy sink @xcite . both of these phenomena are extremely sensitive to the dynamical properties of the planet - moon pair . as recently demonstrated by @xcite using latitudinal equilibrium balance models ( lebms ) , even the orbital direction of the moon can have consequences for a telluric exomoon s climate . the habitable zone of an exomoon is therefore a non - trivial multi - parameter manifold , and it is not generally the case that if the host planet is partially or completely uninhabitable , the moon must be also . we therefore can not rely on the habitable zone calculations of @xcite ( as was done for kepler-22b ) to determine the habitability of the exomoon . however , this does not preclude the possibility of a robust statistical analysis . we employ the same lebms as described in @xcite to investigate how well the posteriors allow us to recover the moon s habitability . the lebm allows us to evolve the moon s surface temperature as a function of latitude assuming it is earth - like in composition . in the simulation , the moon is subject to insolation from the host star , tidal heating from the host planet , eclipses by the planet , and infrared atmospheric cooling . the circulation of heat in the atmosphere is modeled by a diffusion equation ( see also @xcite and @xcite ) .    by using each realization of the posteriors as a set of inputs for a lebm simulation , we can construct a distribution of exomoon climates , which can then be compared to the climate derived from the `` true '' injected parameters . each lebm simulation is classified in the following fashion @xcite :    1 .   _ * habitable moons * _ - these moons possess a habitable surface that covers at least 10% of the total area . this figure is time - averaged , and the standard deviation in habitable surface over this time is less than 10% of the mean . * hot moons * _ - these moons display a surface habitability fraction of less than 10% , and typically possess surface temperatures above 373k across all seasons , and are therefore conventionally uninhabitable . 3 .   _ * snowball moons * _ - these moons also display surface habitability of less than 10% , and have undergone a snowball transition to a state where the entire moon is frozen , and are therefore conventionally uninhabitable . * variable moons * _ - these moons are similar to the habitable moons class above , but the standard deviation in habitable surface over time is high , greater than 10% of the mean .    the simulation run using the injected signal yields a stable , habitable climate with a mean temperature of approximately 320k . the moon is on a close to circular orbit , and hence tidal heating does not play a significant role in the resulting climate . how does this compare to the data retrieved from the posteriors ? figure [ fig : habhist_lebm ] shows the resulting classification of all posteriors . around 75% of all simulations run using the posterior data results in a habitable moon . the next most populous classification is the cold moon case - this is somewhat unsurprising , as the so - called `` snowball '' transition ( generated by a rapid increase in albedo as surface water freezes ) acts as a positive feedback mechanism , making cool climates colder , typically with no restorative warming mechanism to combat it . there is no analogous positive feedback at the other temperature extreme - indeed , hot climates possess a strong negative feedback mechanism through infrared cooling , and as a result the hot classification is less populated . as a further consequence of these differing feedback mechanisms , there is a small collection of moons which are classified as variable , the majority of which tend towards being too hot rather than too cold . we can see this in more detail in figure [ fig : tallhist_lebm ] , which shows the minimum , maximum and mean temperatures exhibited by each simulation . the majority of simulations possess minima and maxima which fit inside the 100k temperature range where water is expected to be liquid on a telluric planet s surface . there is a small tail at @xmath112 k , but this is not as populous as the `` snowball '' population with mean temperatures around 200k . the rapid albedo transition at 273k ensures that few moons can maintain steady surface temperatures in this regime , giving rise to the gap centered on @xmath113k . the mode of the mean temperature distribution is close to the `` true '' mean temperature of 320k , with a long tail out to around 450k . k and @xmath114k respectively.__,width=8 ]    in short , we can say with moderate confidence that we can reliably identify whether we expect a detected moon to be habitable or otherwise , given the posterior distribution , i.e. modeling the surface temperature using the posterior data gives similar results to those produced by modeling the injected signal . this being said , we should be cognizant of the long tail of the resulting temperature distributions produced , and we should also note that one in six posterior runs identify the moon as uninhabitable . we first begin by discussing the fits attempted under the assumption that a putative exomoon follows a circular orbit around the planet kepler-22b  ( although the planet itself is permitted to have an eccentric orbit ) . in total , there are four fits we attempted which fall into this category : a circular orbit planet with and without informative limb darkening priors ( models @xmath115 and @xmath116 respectively ) and an eccentric orbit planet with and without informative limb darkening priors ( models @xmath117 and @xmath118 respectively ) . none of these four fits show particularly significant model preferences , being in the range 1 - 2@xmath8 favorable over a simple planet - only fit ( see table  [ tab : evidence ] ) . as with @xcite , we consider only models above @xmath10@xmath8 to be considered as candidate exomoons . therefore , we find no compelling evidence for a circular orbit exomoon around kepler-22b .    out of the four models , @xmath118 shows the highest significance at 2.3@xmath8 and we show the corresponding maximum a - posteriori light curve fit from this model in figure  [ fig : bestfits_ep ] , which has a @xmath119 better fit for @xmath120 data points . although the signal is not significant , we note that the solution corresponds to a moderately eccentric planet of @xmath121 and mass @xmath122@xmath2 ( derived purely from moon dynamical model , not from rvs ) , which is consistent with that derived from the rvs . the corresponding satellite would have a radius of @xmath123@xmath0 and mass of @xmath124@xmath2 with a broad density posterior spanning @xmath125g@xmath97 . we estimate that only 64.7% of trials yield a physically plausible density by using the internal structure models of @xcite .    as with our previous survey @xcite , despite finding a non - detection we derive upper limits on the mass - ratio for a putative exomoon . applying bayesian model averaging over the four planet - only models and the four circular - orbit moon models ( i.e. eight models in total ) allows us to compute a model - averaged posterior for the mass ratio of @xmath126 . the 95% upper quantile of this posterior gives @xmath127 i.e. 6.2% . for the radius - ratio posterior , @xmath104 , we note that 97.8% of trials were positive ( recall we explored negative radius solutions ) , corresponding to 2.0@xmath8 significance using the odds - ratio test given by equation  4 in @xcite . unlike previous planets studied , we have a reliable mass constraint for the host planet from the radial velocities meaning we can translate this mass ratio into a physical mass upper limit . further more , kepler-22b  is a validated small - radius planet and so must conform with physically plausible mass - radius constraints . we therefore generate a posterior for @xmath128 in absolute units and then eliminate any trials where either the joint posterior of @xmath41-@xmath129 or @xmath128-@xmath129 corresponds to a density exceeding the maximum mass stripping limit of an iron - rich planet derived by @xcite . we find that this eliminates  5% of the posterior trials . from this , we estimate that @xmath130@xmath2 to 95% confidence . we therefore conclude that kepler-22b  is highly unlikely to host an earth - like moon on a circular orbit . both of the eccentric moon models , @xmath131 and @xmath132 , are strongly favored over the planet - only models at @xmath133@xmath8 and thus are significant enough to be further considered as a candidate , with the latter model being slightly preferred . in a @xmath134 sense , the maximum a - posteriori realization from model @xmath132 is superior to planet - only fit @xmath135 at @xmath136 and the circular moon fit @xmath116 at @xmath137 . the light curve fits appear to be heavily influenced by a transit - like feature occurring prior to the transit of kepler-22b  in the long - cadence data of q1 ( see fig  [ fig : bestfits_es ] ) . unlike the circular orbit fits , the eccentric fits have the flexibility to both explain this feature and yet remain comptable with the rest of the time series . although our bayesian model selection approach penalizes models for using more free parameters , such as these eccentric fits , our likelihood function assumes pure gaussian noise and so we must remain cautious in interpreting what could simply be a time - correlated noise feature of unknown origin . this is particularly salient in light of the fact cofiam   identified q1 has having the greatest degree of autocorrelation out of the four transits used in this work ( see  [ sub : cofiam ] ) . one of the key tests described in @xcite for vetting such systems is to inspect the derived posteriors and see if they are physically plausible or not . the bayesian model averaged posteriors of all ten models attempted are dominated by the eccentric moon fits due to the large odds ratios and so we inspect these posteriors to vet these solutions . the dynamically derived planet density appears rather high at @xmath138g@xmath97 yielding @xmath139@xmath2 . this may be compared with the rv derived @xmath41 from the same posteriors of @xmath140@xmath2 and @xmath141 to 95% confidence , from which we conclude the result is slightly incompatible .    before commenting on the putative exomoon s composition , we note that the orbit appears excited with @xmath142 and inclined @xmath143 ( highly multimodal posterior ) from the planet s orbital plane . for the composition , we find an unusually low density of @xmath144g@xmath97 , which favors a bulk density below that of water / ice . using the minimum atmospheric height method of @xcite and using the derived moon radius of @xmath145@xmath0 , we find that 93.3% of trials yield a radius exceeding a pure water / ice composition moon . the only way to explain this situation is an extended atmosphere but given that @xmath146@xmath2 , the moon would rapidly lose an atmosphere , given the equilibrium temperature of @xmath147k . given that kepler-22  is not a young star ( b12 ) and so presumably the exomoon has had plenty of time for an atmosphere to have escaped already , we must invoke a continuously replenishing atmosphere to explain these values . the orbit of the inclined , eccentric moon can also be shown to be unstable . the hill stability of inclined low - mass binaries in the three body problem was explored extensively in @xcite . @xcite presented expressions for the maximum stable eccentricity of an inclined binary in the case where the combined planet - moon mass is much less than that of the host star , as is applicable for the kepler-22b  system . using equation  25 of this work , which has a complex dependency with @xmath128 , @xmath41 , @xmath42 , @xmath86 , @xmath148 and @xmath149 , we estimate that 99.97% of the joint posterior realizations exhibit hill instability ( see figure  [ fig : eshisto ] ) . driving this determination is the wide - separation of the putative moon s orbit of @xmath150@xmath129 combined with the inclined , eccentric nature of the orbit . we therefore consider that the solution is a false - positive , likely induced by residual autocorrelation in the long - cadence data of q1 . this false transit signal can only be fitted by driving to high eccentricities . one effect of high exomoon eccentricity is to increase the r.m.s . ttv and tdv amplitudes induced by the moon on the planet @xcite . since no ttvs or tdvs occur in the kepler-22b  data ( figure  [ fig : ttvs ] ) , the algorithm is forced to set the moon to be a very low - mass object in order to explain the full data set . it has been shown that the @xmath133@xmath8 eccentric exomoon signal is a false positive i.e. spurious detection . spurious detections can not be used to derive upper limits for reasons discussed in @xcite and so we do not use these results to derive our excluded moon mass limits presented here . this is equivalent to assigning a negligible prior model probability to models @xmath132 and @xmath131 . performing bayesian model averaging over the remaining eight models provides reliable upper limits on the presence of an exomoon . we find that @xmath151% to 95% confidence which can be converted into a physical mass estimate by leveraging the @xmath152 constraint from the radial velocities and @xmath42 from asteroseismology to give @xmath153@xmath2 to 95% confidence . due to the large number of results in this paper , we summarize the most important findings below :    * we have conducted the first search for an exomoon around a habitable - zone exoplanet and find no compelling evidence for a companion to kepler-22b . furthermore , we constrain @xmath153@xmath2 to 95% confidence . * we have demonstrated that an earth - like moon would be detectable around kepler-22b  with the current data to 8.3@xmath8 by signal injection and recovery . * we have further shown that such an injected moon would very likely have conditions suitable for liquid water on the surface through latitudinal energy balance modelling ( lebm ) of the posteriors samplings . * we have introduced several new improvements to the hek methodology , including exploring negative - radius , retrograde and eccentric moon solutions , free limb darkening sampled from a dirichlet prior and bayesian model averaging . * for the first time , the radial velocities of kepler-22b  have been fitted with a model accounting for free eccentricity and free stellar jitter . combined with an updated ephemeris from a new transit in q11 , we derive a tighter mass constraint on kepler-22b  of @xmath154@xmath2 to 95% confidence . * utilizing single - body asterodensity profiling ( sap ) and the radial velocities , we provide the first constraints on the orbital eccentricity of kepler-22b  with @xmath155 and @xmath156 to 95% confidence . * from our refined transit model , we estimate that kepler-22b  has a @xmath5% probability of lying within the empirical habitable - zone but a @xmath6% probability of lying within the conservative habitable - zone ( as defined by @xcite ) . we derive an insolation of @xmath157@xmath158 . the above results were derived through photodynamical modeling and multimodal nested sampling regression requiring 49.7years of cpu time@xmath159 . compared to other systems analyzed during the hek project @xcite , this load is higher than average due to the high - resolution fitting mode employed here ( see  [ sub : hires ] ) . nevertheless , this highlights the unique computational challenges of seeking exomoons . we find no evidence for an earth - like exomoon around kepler-22b  and yet have shown that the present data can easily detect such an object via signal injection . current observations therefore dictate that kepler-22b  does not possess an earth - like habitable moon . our results then , combined with the very robust measurement of the planet s radius , mean that kepler-22  does not possess an earth analog . this does not mean that the system possesses no options for an inhabited world , with notable possiblities being a smaller , presently undetectable moon ( e.g. @xmath160@xmath2 ) or a possible ocean on kepler-22b . however , it is now clear that this is not the location to find a second earth .    to date , nine systems have been surveyed for exomoons by the hek project @xcite and no detections have been made with most cases yielding detection sensitivities of @xmath161 . we caution that the number of systems analyzed remains too small to draw any meaningful conclusions about the occurrence of large moons , @xmath162 , but this is the ultimate goal of our project . in coming work , two future surveys will focus on i ) m - dwarf host star planetary candidates and ii ) planets exhibiting repeated visual anomalies . slowly then , the landscape of the frequency of exomoons will be revealed . this work made use of the michael dodds computing facility . we thank the anonymous reviewer for their thoughtful comments which improved the quality of our manuscript . dmk is funded by the nasa carl sagan fellowships . df gratefully acknowledges support from stfc grant st / j001422/1 . jh and gb acknowledge partial support from nsf grant ast-1108686 and nasa grant nnx12ah91h . dn acknowledges support from nsf ast-1008890 . 99 anglada - escud , g. et al . , 2012 , apj , 751 , l16 anglada - escud , g. , rojas - ayala , b. , boss , a. p. , weinberger , a. j. & lloyd , j. p. , 2013 , a&a , 551 , 48 balan , s. t. & lahav , o. , 2009 , mnras , 394 , 1936 borucki , w. j. et al . , 2012 , apj , 745 , 120 ( b12 ) charbonneau , d. et al . , 2009 , nature , 462 , 891 domingos , r. c. , winter , o. c. & yokoyama , t. , 2006 , mnras , 373 , 1227 donnison , j. r. , 2010 , p&ss , 58 , 1169 feroz , f. , hobson , m. p. & bridges , m. , 2009a , mnras , 398 , 1601 feroz , f. , gair , j. r. , hobson , m. p. & porter , e. k. , 2009b , cqg , 26 , 215003 forgan , d. & kipping , d. m. , 2013 , mnras , accepted ( astro - ph:1304.4377 ) gilliland . , r. et al . , 2010 , apj , 713 , 160 vladilo , g. , murante , g. , silva , l. , provenzale , a. , ferri , g. & ragazzini , g. , 2013 , apj , 767 , 65 heller , r. , 2012 , a&a , 545 , l8 heller , r. & barnes , r. , 2012 , arxiv:1210.5172 heller , r. & barnes , r. , 2013 , asbio , 13 , 18 kipping , d. m. , 2009 , mnras , 392 , 181 kipping , d. m. , 2009 , mnras , 396 , 1797 kipping , d. m. , fossey , s. j. & campanella , g. , 2009 , mnras , 400 , 398 kipping , d. m. , 2010 , mnras , 408 , 1758 kipping , d. m. et al . , 2010 , apj , 725 , 2017 kipping , d. m. & bakos , g. a. , 2011 , apj , 730 , 50 kipping , d. m. & bakos , g. a. , 2011 , apj , 733 , 36 kipping , d. m. , 2011 , mnras , 416 , 689 kipping , d. m. , 2011 , phd thesis , university college london ( astro - ph:1105.3189 ) kipping , d. m. , dunn , w. , jasinksi , j. m. & manthri , v. p. , 2012 , mnras , 421 , 1166 kipping , d. m. , bakos , g.  . , buchhave , l. , nesvorn , d. & schmitt , a. 2012 , apj , 750 , 115 kipping , d. m. , hartman , j. , buchhave , l. , schmitt , a. , bakos , g.  . & nesvorn , d. , 2013 , apj , 770 , 101 kipping , d. m. , spiegel , d. s. , sasselov , d. , 2013 , mnras , 434 , 1883 kipping , d. m. , 2013 , mnras , accepted ( astro - ph:1308.0009 ) kopparapu , r. k. et al . , 2013 , apj , 765 , 131 kurucz r. , 2006 , stellar model and associated spectra ( http://kurucz.harvard.edu/grids.html ) mandel , k. & agol , e. , 2002 , apj , 580 , 171 marcus , r. a. , sasselov , d. , hernquist , l. & stewart , s. t. 2010 , apj , 712 , 73 mazeh , t. & faigler , s. , 2010 , a&a , 521 , 59 neubauer , d. , vrtala , a. , leitner , j. j. , gertrude f. m. , hitzenberger , r. , 2012 , p&ss , 73 , 397 nesvorn , d. kipping , d. m. , buchhave , l. a. , bakos , g. a. , hartman , j. & schmitt , a. , 2012 , science , 336 , 1133 parkinson , d. & liddle , a. 2013 , sam , 6 , 3 pal , a. , 2008 , mnras , 390 , 281 reynolds , r. t. , mckay , c. p. & kasting , j. f. , 1987 , adspr , 7 , 125 scharf , c. a. , 2006 , apj , 648 , 1196 spiegel , d. s. , menou , k. & scharf , c. a. , 2008 , apj , 681 , 1609 southworth , j. , wheatley , p. j. & sams , g. , 2007 , mnras , 379 , 11 vogt , s. s. , butler , r. p. , rivera , e. j. , haghighipour , n. , henry , g. w. , williamson , m. h. 2010 , apj , 723 , 954 waldmann , i. p. , tinetti , g. , drossart , p. , swain , m. r. , deroo , p. & griffith , c. a. , 2012 , apj , 744 , 35 williams , d. m. & kasting , j. f. , 1997 , icarus , 129 , 254 winn , j. n. 2010 , arxiv:1001.2010 zeng , l. & sasselov , d. , 2013 , pasp , submitted ( astro - ph:1301.0818 ) zsom , a. , seager , s. & de wit , j. , 2013 , apj , submitted ( astro - ph:1304.3714 )
kepler-22b  is the first transiting planet to have been detected in the habitable - zone of its host star . at 2.4@xmath0 , 
 kepler-22b  is too large to be considered an earth - analog , but should the planet host a moon large enough to maintain an atmosphere , then the kepler-22  system may yet possess a telluric world . aside from being within the habitable - zone , the target is attractive due to the availability of previously measured precise radial velocities and low intrinsic photometric noise , which has also enabled asteroseismology studies of the star . for these reasons , kepler-22b  was selected as a target - of - opportunity by the `` hunt for exomoons with kepler '' ( hek ) project . in this work , we conduct a photodynamical search for an exomoon around kepler-22b  leveraging the transits , radial velocities and asteroseismology plus several new tools developed by the hek project to improve exomoon searches . 
 we find no evidence for an exomoon around the planet and exclude moons of mass @xmath1@xmath2 to 95% confidence . by signal injection and blind retrieval 
 , we demonstrate that an earth - like moon is easily detected for this planet even when the time - correlated noise of the data set is taken into account . 
 we provide updated parameters for the planet kepler-22b   including a revised mass of @xmath3@xmath2 to 95% confidence and an eccentricity of @xmath4 by exploiting single - body asterodensity profiling ( sap ) . 
 finally , we show that kepler-22b  has a @xmath5% probability of being within the empirical habitable - zone but a @xmath6% probability of being within the conservative habitable - zone .