HATP26b: A LowDensity NeptuneMass
Planet Transiting a K Star^{1}
Abstract
We report the discovery of HATP26b, a transiting extrasolar planet
orbiting the moderately bright
V=11.744 K1 dwarf star GSC 032001027, with a
period d, transit epoch
(BJD
Subject headings:
planetary systems — stars: individual (HATP26, GSC 032001027) techniques: spectroscopic, photometric1. Introduction
Transiting exoplanets (TEPs) are tremendously useful objects for
studying the properties of planets outside of the solar system because
their photometric transits, combined with precise measurements of the
radial velocity variations of their host stars, enable determinations
of their masses and radii. Of the confirmed TEPs discovered
to date
While the gas giant planets exhibit a wide range of radii at fixed
mass (and hence a great diversity in their physical structure at fixed
mass), the low mass TEPs, together with the six Solar System planets
smaller than Saturn, appear to follow a nearly monotonic relation
between mass and radius. The two SuperNeptunes with precise radius
measurements (GJ 436b and HATP11b) have radii that are similar to
one another (to within 15%) as well as to Uranus ( ,
In this paper we present the discovery of HATP26b, a TEP orbiting the relatively bright star GSC 032001027 with a mass similar to that of Neptune, but with a radius of or 65% larger than that of Neptune. This is the 26th TEP discovered by the Hungarianmade Automated Telescope Network (HATNet; Bakos et al., 2004) survey. In operation since 2003, HATNet has now covered approximately 14% of the sky, searching for TEPs around bright stars (). HATNet operates six widefield instruments: four at the Fred Lawrence Whipple Observatory (FLWO) in Arizona, and two on the roof of the hangar servicing the Smithsonian Astrophysical Observatory’s Submillimeter Array, in Hawaii.
The layout of the paper is as follows. In Section 2 we report the detection of the photometric signal and the followup spectroscopic and photometric observations of HATP26. In Section 3 we describe the analysis of the data, beginning with the determination of the stellar parameters, continuing with a discussion of the methods used to rule out nonplanetary, false positive scenarios which could mimic the photometric and spectroscopic observations, and finishing with a description of our global modeling of the photometry and radial velocities. Our findings are discussed in Section 4.
2. Observations
2.1. Photometric detection
The transits of HATP26b were detected with the HAT5 and HAT6 telescopes in Arizona, and with the HAT8 and HAT9 telescopes in Hawaii. Two regions around GSC 032001027, corresponding to fields internally labeled as 376 and 377, were both observed on a nightly basis between 2009 Jan and 2009 Aug, whenever weather conditions permitted. For field 376 we gathered 11,500 exposures of 5 minutes at a 5.5 minute cadence. Approximately 1500 of these exposures were rejected by our photometric pipeline because they yielded poor photometry for a significant number of stars. Each image contained approximately 17,000 stars down to Sloan . For the brightest stars in the field, we achieved a perimage photometric precision of 4 mmag. For field 377 we gathered 5200 exposures with the same exposure time and cadence; we rejected aproximately 700 exposures. Each image contained approximately 19,000 stars down to Sloan . We achieved a similar photometric precision for the brightest stars in this field.
The calibration of the HATNet frames was carried out using standard photometric procedures. The calibrated images were then subjected to star detection and astrometry, as described in Pál & Bakos (2006). Aperture photometry was performed on each image at the stellar centroids derived from the Two Micron All Sky Survey (2MASS; Skrutskie et al., 2006) catalog and the individual astrometric solutions. The resulting light curves were decorrelated (cleaned of trends) using the External Parameter Decorrelation (EPD; see Bakos et al., 2010) technique in “constant” mode and the Trend Filtering Algorithm (TFA; see Kovács et al., 2005). The light curves were searched for periodic boxshaped signals using the Box LeastSquares (BLS; see Kovács et al., 2002) method. We detected a significant signal in the light curve of GSC 032001027 (also known as 2MASS 14123753+0403359; , ; J2000; V=11.744 Droege et al., 2006), with an apparent depth of mmag ( mmag when using TFA in signalreconstruction mode), and a period of days (see Figure 1). The drop in brightness had a firsttolastcontact duration, relative to the total period, of , corresponding to a total duration of hr.
We removed the transits from the combined 376/377 light curve and searched for additional transiting objects using the BLS method; no significant signals were found in the data. We also searched the transitcleaned light curve for periodic variations (e.g. due to stellar rotation) using the Discrete Fourier Transform (e.g. Kurtz, 1985), and found no coherent variation with an amplitude greater than mmag.
2.2. Reconnaissance Spectroscopy
As is routine in the HATNet project, all candidates are subjected to careful scrutiny before investing valuable time on large telescopes. This includes spectroscopic observations at relatively modest facilities to establish whether the transitlike feature in the light curve of a candidate might be due to astrophysical phenomena other than a planet transiting a star. Many of these false positives are associated with large radialvelocity variations in the star (tens of ) that are easily recognized.
To carry out this reconnaissance spectroscopy, we made use of the Tillinghast Reflector Echelle Spectrograph (TRES; Fűrész, 2008) on the 1.5 m Tillinghast Reflector at FLWO. This instrument provides highresolution spectra which, with even modest signaltonoise (S/N) ratios, are suitable for deriving RVs with moderate precision ( ) for slowly rotating stars. We also use these spectra to estimate effective temperatures, surface gravities, and projected rotational velocities of the target star. Using the medium fiber on TRES, we obtained two spectra of HATP26 on the nights of 2009 Dec 26 and 2009 Dec 27. The spectra have a resolution of and a wavelength coverage of 39008900 Å. The spectra were extracted and analyzed according to the procedure outlined by Buchhave et al. (2010) and Quinn et al. (2010). The individual velocity measurements of and were consistent with no detectable RV variation within the measurement precision. Both spectra were singlelined, i.e., there is no evidence for additional stars in the system. The atmospheric parameters we infer from these observations are the following: effective temperature , surface gravity (log cgs), and projected rotational velocity . The effective temperature corresponds to an early K dwarf. The mean heliocentric RV of HATP26 is .
2.3. High resolution, high S/N spectroscopy
Given the significant transit detection by HATNet, and the encouraging TRES results that rule out obvious false positives, we proceeded with the followup of this candidate by obtaining highresolution, highS/N spectra to characterize the RV variations, and to refine the determination of the stellar parameters. For this we used the HIRES instrument (Vogt et al., 1994) on the Keck I telescope located on Mauna Kea, Hawaii, between 2009 Dec and 2010 June. The width of the spectrometer slit was , resulting in a resolving power of , with a wavelength coverage of 3800–8000 Å.
We obtained 12 exposures through an iodine gas absorption cell, which was used to superimpose a dense forest of lines on the stellar spectrum and establish an accurate wavelength fiducial (see Marcy & Butler, 1992). An additional exposure was taken without the iodine cell, for use as a template in the reductions. Relative RVs in the solar system barycentric frame were derived as described by Butler et al. (1996), incorporating full modeling of the spatial and temporal variations of the instrumental profile. The RV measurements and their uncertainties are listed in Table 1. The periodfolded data, along with our best fit described below in Section 3, are displayed in Figure 2.
In the same figure we show also the index, which is a measure of the chromospheric activity of the star derived from the flux in the cores of the Ca ii H and K lines (Figure 3 shows representative Keck spectra including the H and K lines for HATP26). This index was computed and calibrated to the scale of Vaughan, Preston & Wilson (1978) following the procedure described by Isaacson & Fischer (2010). We find a median value of with a standard deviation of . Assuming based on the effective temperature measured in Section 3.1, this corresponds to (Noyes et al., 1984). From Isaacson & Fischer (2010) the lower tenth percentile value among California Planet Search (CPS) targets with is . The measured value is only slightly higher than this, implying that HATP26 is a chromospherically quiet star. We do not detect any significant variation of the index correlated with orbital phase; such a correlation might have indicated that the RV variations could be due to stellar activity, casting doubt on the planetary nature of the candidate.
BJD  RV 

BS 

Phase  

(2,454,000)  ()  ()  ()  ()  
Note. – For the iodinefree template exposures there is no RV measurement, but the BS and index can still be determined.
2.4. Photometric followup observations
In order to permit a more accurate modeling of the light curve, we conducted additional photometric observations with the KeplerCam CCD camera on the FLWO 1.2 m telescope. We observed five transit events of HATP26 on the nights of 2010 Jan 05, Mar 31, Apr 04, May 08 and May 25 (Figure 4). These observations are summarized in Table 2.
Facility  Date  Number of Images  Median Cadence (s)  Filter 

KeplerCam/FLWO 1.2 m  2010 Jan 05  191  40  Sloan band 
KeplerCam/FLWO 1.2 m  2010 Mar 31  161  59  Sloan band 
KeplerCam/FLWO 1.2 m  2010 Apr 04  291  64  Sloan band 
KeplerCam/FLWO 1.2 m  2010 May 08  596  44  Sloan band 
KeplerCam/FLWO 1.2 m  2010 May 25  298  59  Sloan band 
The reduction of these images, including basic calibration, astrometry, and aperture photometry, was performed as described by Bakos et al. (2010). We performed EPD and TFA to remove trends simultaneously with the light curve modeling (for more details, see Section 3, and Bakos et al. 2010). The final time series are shown in the top portion of Figure 4, along with our bestfit transit light curve model described below; the individual measurements are reported in Table 3. The combined phasefolded followup light curve is displayed in Figure 5.
BJD  Mag 
Mag(orig) 
Filter  

(2,400,000)  
Note. – This table is available in a machinereadable form in the online journal. A portion is shown here for guidance regarding its form and content.
3. Analysis
3.1. Properties of the parent star
Fundamental parameters of the host star HATP26 such as the mass () and radius (), which are needed to infer the planetary properties, depend strongly on other stellar quantities that can be derived spectroscopically. For this we have relied on our template spectrum obtained with the Keck/HIRES instrument, and the analysis package known as Spectroscopy Made Easy (SME; Valenti & Piskunov, 1996), along with the atomic line database of Valenti & Fischer (2005). SME yielded the following values and uncertainties: effective temperature K, stellar surface gravity (cgs), metallicity dex, and projected rotational velocity , in which the uncertainties for and have been increased by a factor of two over their formal values to include our estimates of the systematic uncertainties.
In principle the effective temperature and metallicity, along with the surface gravity taken as a luminosity indicator, could be used as constraints to infer the stellar mass and radius by comparison with stellar evolution models. However, the effect of on the spectral line shapes is quite subtle, and as a result it is typically difficult to determine accurately, so that it is a rather poor luminosity indicator in practice. For planetary transits a stronger constraint is often provided by the mean stellar density, which is closely related to the normalized semimajor axis. The quantity can be derived directly from the combination of the transit light curves (Seager & MallénOrnelas, 2003; Sozzetti et al., 2007) and the RV data (required for eccentric cases, see Section 3.3). This, in turn, allows us to improve on the determination of the spectroscopic parameters by supplying an indirect constraint on the weakly determined spectroscopic value of that removes degeneracies. We take this approach here, as described below. The validity of our assumption, namely that the adequate physical model describing our data is a planetary transit (as opposed to a blend), is shown later in Section 3.2.
Our values of , , and were used to determine auxiliary quantities needed in the global modeling of the followup photometry and radial velocities (specifically, the limbdarkening coefficients). This modeling, the details of which are described in Section 3.3, uses a Monte Carlo approach to deliver the numerical probability distribution of and other fitted variables. For further details we refer the reader to Pál (2009b). When combining (a luminosity proxy) with assumed Gaussian distributions for and based on the SME determinations, a comparison with stellar evolution models allows the probability distributions of other stellar properties to be inferred, including . Here we use the stellar evolution calculations from the YonseiYale (YY) series by Yi et al. (2001).
For the case of HATP26b, the eccentricity is poorly constrained
by the RV data due to the low semiamplitude of the signal. This in
turn leads to a significant uncertainty on . However, not all
combinations of , and are realized by
physical stellar models. In particular, if we conservatively adopt a
maximum stellar age of Gyr, corresponding approximately to the
age of the universe (Komatsu et al., 2010, find Gyr), and a minimum age of Myr,
corresponding roughly to the zeroage mainsequence
Adopting the parameters which result from allowing the eccentricity to vary while requiring the star to have an age between 0.1 Gyr and 13.8 Gyr yields a stellar surface gravity of , which is very close to the value from our SME analysis. The values for the atmospheric parameters of the star are collected in Table 4, together with the adopted values for the macroturbulent and microturbulent velocities.
The stellar evolution modeling provides color indices that may be compared against the measured values as a sanity check. The best available measurements are the nearinfrared magnitudes from the 2MASS Catalogue (Skrutskie et al., 2006), , and ; which we have converted to the photometric system of the models (ESO) using the transformations by Carpenter (2001). The resulting measured color index is . This is within 1 of the predicted value from the isochrones of . The distance to the object may be computed from the absolute magnitude from the models () and the 2MASS magnitude, which has the advantage of being less affected by extinction than optical magnitudes. The result is pc, where the uncertainty excludes possible systematics in the model isochrones that are difficult to quantify.
An additional check on our stellar model can be performed by comparing the isochronebased age estimate to activitybased age estimates. Using the activityrotation and activityage relations from Mamajek & Hillenbrand (2008, equations 5 and 3) we convert the value of determined in Section 2.3 into a Rossby number (, where is the rotation period and is the convective turnover timescale) and an age. We find , and or Gyr, where we adopt the estimated uncertainties on and from Mamajek & Hillenbrand (2008). The value may be converted to a rotation period using the relation for given by Noyes et al. (1984). We find d. The rotation period and color may also be used to obtain a separate age estimate from the gyrochronology relation given by Mamajek & Hillenbrand (2008, equation 12). This gives Gyr, where the scatter on this relation is less than the scatter on the ageactivity relation because it includes a correction for stellar color. The age inferred from is consistent with the isochronebased age of Gyr. The equatorial rotation period inferred from the spectroscopic determination of assuming is d, which is shorter than the expected value based on , though the upper limit is poorly constrained.
As discussed below in Section 3.3 we measure a RV jitter of for HATP26. From Isaacson & Fischer (2010) the lower tenth percentile jitter among HIRES/Keck observations for CPS stars with and is , implying that HATP26 has an exceptionally low jitter value–only a handful of stars in this color range have measured jitter values less than that of HATP26. We note that the jitter may be higher ( ) if the orbit is circular, though this value is still quite low.
Parameter  Value  Source 

Spectroscopic properties  
(K)  SME 

SME  
()  SME  
()  SME  
()  SME  
()  TRES  
Photometric properties  
(mag)  11.744  TASS 
(mag)  TASS  
(mag)  2MASS  
(mag)  2MASS  
(mag)  2MASS  
Derived properties  
()  YY++SME 

()  YY++SME  
(cgs)  YY++SME  
()  YY++SME  
(mag)  YY++SME  
(mag,ESO)  YY++SME  
Age (Gyr)  YY++SME  
Distance (pc)  YY++SME 
3.2. Excluding blend scenarios
Our initial spectroscopic analyses discussed in Section 2.2 and Section 2.3 rule out the most obvious astrophysical false positive scenarios. However, more subtle phenomena such as blends (contamination by an unresolved eclipsing binary, whether in the background or associated with the target) can still mimic both the photometric and spectroscopic signatures we see. In the following sections we consider and rule out the possibility that such scenarios may have caused the observed photometric and spectroscopic features.
Spectral linebisector analysis
Following Queloz et al. (2001); Torres et al. (2007), we explored the possibility that the measured radial velocities are not real, but are instead caused by distortions in the spectral line profiles due to contamination from a nearby unresolved eclipsing binary. A bisector analysis based on the Keck spectra was done as described in §5 of Bakos et al. (2007). While the bisector spans show no evidence for variation in phase with the orbital period, the scatter on these values ( RMS) is large relative to the RV semiamplitude ( ), and thus the lack of variation does not provide a strong constraint on possible blend scenarios. We note that some of the scatter in the bisector spans may be due to contamination from the sky background (predominately moonlight)–correcting the bisector spans for sky contamination as discussed by Hartman et al. (2010) reduces the RMS to , however the precision is still insufficient to rule out blend scenarios.
Contamination from a background eclipsing binary
Following our earlier work (Bakos et al., 2010; Hartman et al., 2009) we make use of the high proper motion of HATP26 to rule out the possibility that the observed transits and RV variation may be due to a background eclipsing binary that is aligned, by chance, with the foreground K1 dwarf HATP26. To reproduce the observed deep transit, the background object cannot be more than 5.6 mag fainter than HATP26 (objects fainter than this would contribute less than 0.6% of the total combined light and so could not cause the transit even if they were to be completely eclipsed by an object that emits no light). Because HATP26 has a high proper motion ( ; Roeser et al., 2010) it is possible to use the Palomar Observatory Sky Survey plates from 1950 (POSSI, red and blue plates) to view the sky at the current position of HATP26. Between 1950 and the followup observations in 2010, HATP26 has moved . Figure 7 shows an image stamp from the POSSI plate compared with a recent observation from the FLWO 1.2 m. We can rule out a background object down to mag within of the current position of HATP26. Any background object must be mag fainter than HATP26 and thus could not be responsible for the observed transit.
Detailed blend modeling of a hierarchical triple
Following Bakos et al. (2010), Hartman et al. (2009), and Torres et al. (2005) we attempt to model the observations as a hierarchical triple system. We consider 4 possibilities:

One star orbited by a planet,

Three stars, 2 fainter stars are eclipsing,

Two stars, 1 planet, planet orbits the fainter star,

Two stars, 1 planet, planet orbits the brighter star.
Here case 1 is the fiducial model to which we compare the various blend models. We model the observed followup and HATNet light curves (including only points that are within one transit duration of the primary transit or secondary eclipse assuming zero eccentricity) together with the 2MASS and TASS photometry. In each case we fix the mass of the brightest star to ; this ensures that we reproduce the effective temperature, metallicity, and surface gravity determined from the SME analysis when using the Padova isochrones (see below). We have also attempted to perform the fits described below allowing the mass of the brightest star to vary. We find that in this case the mass of the brightest star is still constrained to be close to by the broadband photometry, even if the spectroscopic parameters are not included. We therefore conclude that fixing the mass of the brightest star is justified. In all cases we vary the distance to the system and two parameters allowing for dilution in the two HATNet light curves, and we include simultaneous EPD and TFA in fitting the light curves (see Section 3.3). In each case we draw the stellar radii and magnitudes from the 13.0 Gyr Padova isochrone (Girardi et al., 2000), extended below 0.15 with the Baraffe et al. (1998) isochrones. We use these rather than the YY isochrones for this analysis because of the need to allow for stars with , which is the lower limit available for the YY models. We use the JKTEBOP program (Southworth et al., 2004a, b) which is based on the Eclipsing Binary Orbit Program (EBOP; Popper & Etzel, 1981; Etzel, 1981; Nelson & Davis, 1972) to generate the model light curves. We optimize the free parameters using the Downhill Simplex Algorithm together with classical linear least squares for the EPD and TFA parameters. We rescale the errors for each light curve such that per degree of freedom is 1.0 for the out of transit portion of the light curve. Note that this is done prior to applying the EPD/TFA corrections, as a result per degree of freedom is less than 1.0 for each of the bestfit models discussed below. If the rescaling is not performed, the difference in between the bestfit models is even more significant than what is given below, and the blendmodels may be rejected with higher confidence.
Case 1: 1 star, 1 planet: In addition to the parameters mentioned above, in this case we vary the radius of the planet and the impact parameter of the transit. The bestfit model has for 3567 degrees of freedom. The parameters that we obtain for the planet are comparable to those obtained from the global modelling described in Section 3.3.
Case 2: 3 stars: For case 2 we vary the masses of the eclipsing components, and the impact parameter of the eclipse. We find no model of three stars which reproduces the observations. The transit depth and duration cannot be fit when the three stars are constrained to fall on the same isochrone, and the brightest star has . The bestfit case 2 model consists of equal masses for the brightest two stars, and (the lowest stellar mass in the Baraffe et al. 1998 isochrones) for the transiting star. Such a model is inconsistent with our spectroscopic observations (it would have been easily identified as a doublelined binary at one of the quadrature phases), and as we will show, can be rejected from the light curves alone. The bestfit case 2 model yields for 3566 degrees of freedom and produces model transits that are too deep compared to the observed transit. The case 1 model achieves a lower with fewer parameters than the case 2 model, so the case 1 model is preferred over the case 2 model. Assuming that the errors are uncorrelated and follow a Gaussian distribution, the case 2 model can be rejected in favor of the case 1 model at the confidence level. Alternatively, one might suppose that any apparent correlations in the residuals of the bestfit case 2 model are not due to errors in the model but instead are due to uncorrected systematic errors in the measurements; large systematic errors in the measurements would increase the probability that case 1 might give a better fit to the data, by chance, than case 2. To establish the statistical signficance with which we may reject case 2 while allowing for possible systematic errors in the measurements, we conduct 1000 Monte Carlo simulations in which we assume the bestfit case 2 model scenario is correct, shuffle the residuals from this fit in a manner that preserves the correlations (this is done by taking the Fourier Transform of the residuals, randomly changing phases of the Transform while preserving the amplitudes, and transforming back to the time domain), and fit both the case 2 and case 1 models to the simulated data. The median value of is with a standard deviation of . None of the 1000 trials have , the measured value. Based on this analysis we reject case 2, i.e. the hierarchical triple star system scenario, at the level.
Case 3: 2 stars, planet orbits the fainter star: In this scenario HATP26b is a transiting planet, but it would have a radius that is larger than what we infer (it may be a Saturn or Jupitersize planet rather than a Neptunesize planet). For this case we vary the mass of the faint planethosting star, the radius of the planet, and the impact parameter of the transit. We assume the mass of the planet is negligible relative to the mass of its faint host star. Figure 8 shows as a function of the mass of the planethosting star for this scenario. The bestfit case 3 solution has for 3566 degrees of freedom, and corresponds to a system where the two stars are of equal mass and the planet has a radius of . As the mass of the planet host is decreased the value of increases. Repeating the procedure outlined above to establish the statistical significance at which we may reject case 3 we find that the limit on is , which results in a lowerlimit of on the mass of the planet hosting star. We may thereby place a lower limit of on the band luminosity ratio of the two stars. A second set of lines with a luminosity ratio of would have easily been detectable in both the Keck and TRES spectra unless the stars had very similar velocities (the spectral lines are quite narrow with ). The poor fit for this blend model relative to the fiducial model together with the tight constraints on the relative velocities and luminosity ratios of the stars in the blend models that may yet fit the data leads us to reject this blend scenario in favor of the simpler model of a single star hosting a transiting planet.
Case 4: 2 stars, planet orbits the brighter star: As in the previous case, in this scenario HATP26b is a transiting planet, but the dilution from the blending star means that the true radius is larger than what we infer in Case 1. In this case we vary the radius of the planet, the mass of the faint star, and the impact parameter of the transit. Again we assume the mass of the planet is negligible relative to the mass of its bright host star. Figure 8 shows as a function of the mass of the faint star. The smallest value of is achieved when the faint star contributes negligible light to the system, which is effectively equivalent to the fiducial scenario represented by Case 1. Two effects cause to increase with stellar mass. First, the shape of the transit is subtly changed in a manner that gives a poorer fit to the observations. Second, when the mass of the faint star is less than that of the transit host the model broadband photometry for the blended system is redder than for the single star scenario, and is inconsistent with the observed photometry. This gives rise to the peak in at . The case 4 model where the faint star has can be rejected as in Case 3. For lower masses, we place a upper limit of 0.55 on the mass of the faint star, yielding a upper limit on the luminosity ratio of . We conclude that at most the planet radius may be 8% larger than what we find in Section 3.3 if there is an undetected faint secondary star in the system.
3.3. Global modeling of the data
Here we summarize the procedure that we followed to model the HATNet photometry, the followup photometry, and the radial velocities simultaneously. This procedure is described in greater detail in Bakos et al. (2010). The followup light curves were modeled using analytic formulae based on Mandel & Agol (2002), with quadratic limb darkening coefficients for the Sloan band interpolated from the tables by Claret (2004) for the spectroscopic parameters of the star as determined from the SME analysis (Section 3.1). We modeled the HATNet data using an approximation to the Mandel & Agol (2002) formulae as described in Bakos et al. (2010). The RVs were fitted with an eccentric Keplerian model.
Our physical model consisted of 8 main parameters, including: the time of the first transit center observed with HATNet (taken to be event ), , and that of the last transit center observed with the FLWO 1.2 m telescope, , the normalized planetary radius , the square of the impact parameter , the reciprocal of the half duration of the transit as given in Bakos et al. (2010), the RV semiamplitude , and the Lagrangian elements and , where is the longitude of periastron. Five additional parameters were included that have to do with the instrumental configuration. These are the HATNet blend factors , and , which account for possible dilution of the transit in the HATNet light curves from background stars due to the broad PSF ( FWHM), the outoftransit magnitudes for each HATNet field, and , and the relative zeropoint of the Keck RVs. The physical model was extended with an instrumental model for the followup light curves that describes brightness variations caused by systematic errors in the measurements. We adopted a “local” EPD and “global” TFAmodel (Bakos et al., 2010), using 20 template stars for the TFA procedure and six EPD parameters for each followup light curve. In summary, the total number of fitted parameters was 13 (physical model with 5 configurationrelated parameters) + 30 (local EPD) + 20 (global TFA) = 63, i.e., much smaller than the number of data points (1450, counting only RV measurements and followup photometry measurements).
As described in Bakos et al. (2010), we use a combination of the downhill simplex method (AMOEBA; see Press et al., 1992), the classical linear least squares algorithm, and the Markov Chain MonteCarlo method (MCMC, see Ford, 2006) to obtain a bestfit model together with a posteriori distributions for the fitted parameters. These distributions were then used to obtain a posteriori distributions for other quantities of interest, such as . As described in Section 3.1, was used together with stellar evolution models to obtain a posteriori distributions for stellar parameters, such as and , which are needed to determine and .
The resulting parameters pertaining to the light curves and velocity curves, together with derived physical parameters of the planet, are listed under the “Adopted Value” column heading of Table 5. Included in this table is the RV “jitter”. This is a component of assumed astrophysical noise intrinsic to the star, possibly with a contribution from instrumental errors as well, that we added in quadrature to the internal errors for the RVs in order to achieve from the RV data for the global fit. Auxiliary parameters not listed in the table are: (BJD), (BJD), the blending factors , and for the HATNet field 376 and 377 light curves, respectively, and . The latter quantity represents an arbitrary offset for the Keck RVs, but does not correspond to the true centerofmass velocity of the system, which was listed earlier as in Table 4.
We find a mass for the planet of and a radius of , leading to a mean density . We also find that the eccentricity of the orbit may be different from zero: , . However, as we show in Section 4.3, this is at best significant at only the 88% confidence level.
We also carried out the analysis described above with the eccentricity fixed to zero. The resulting parameters are given in Table 5 under the column heading “”. The results are discussed further in Section 4.3.
Finally, we conducted an independent model of the system based on Kipping & Bakos (2010b). The primary differences between this model and the adopted model are differences in the choice of parameters to vary in the fit: we use as defined in Kipping & Bakos (2010b) rather than , rather than , and rather than . We also allowed for a linear drift in the radial velocities , and a time shift in the radial velocities due to possible additional bodies in the system on Trojan orbits with HATP26b. We chose to include both and rather than fixing them to zero as the value of the Bayseian Information Criterion (BIC; e.g. Kipping et al., 2010) was lower for the bestfit model including these parameters, than for models where one or both of these parameters were fixed to zero. The resulting parameters are given in Table 5 under the column heading “.” The parameter values from this model are consistent with those from the adopted model, which gives confidence that our results are robust to changes in the choice of fitting parameters.
Parameter  Adopted Value  Value  Value 

Light curve parameters  
(days)  
()


(days)


(days)


(deg)  
Limbdarkening coefficients 

(linear term)  
(quadratic term)  
RV parameters  
()  




(deg)  
(m s d)  
(d) 

RV jitter ()  
RV fit RMS ()  
Secondary eclipse parameters  
(BJD)  
Planetary parameters  
()  
()  


()  
(cgs)  
(AU)  
(K)  


() 

() 

()

4. Discussion
We have presented the discovery of HATP26b, a transiting Neptunemass planet. Below we discuss the physical properties of this planet, and compare them to the properties of similar planets; we comment on the possibility that the planet has undergone significant evaporation, on the significance of its orbital eccentricity, and on the possible presence of additional bodies in the system; and we discuss the prospects for detailed followup studies.
4.1. Physical Properties of HATP26b
Figure 9 compares HATP26b to the other known TEPs on a massradius diagram. With a density of , HATP26b is significantly less dense than the four other Neptunesize planets with well measured masses and radii (Uranus, Neptune, GJ 436b, HATP11b). For Kepler4b, Kipping & Bakos (2010a) find a large uncertainty on the radius which results from significant uncertainties on the eccentricity and the transit impact parameter. Kepler4b may be comparable in size to GJ 436b and HATP11b, or it could be even less dense than HATP26b.
From the theoretical models of Fortney et al. (2007), HATP26b has a radius that is well above the maximum radius of for a planet lacking a hydrogenhelium envelope (i.e. a planet with a 100% waterice composition). The bestfit mass and radius for HATP26b falls just below the 4 Gyr model with a 10 rocky core and 8 gas envelope, implying that a 4 Gyr model with a slightly higher core mass would provide a better match to the mass and radius. We note that the isochronebased age ( Gyr) and the activitybased age ( Gyr) for the HATP26 system are somewhat older than 4 Gyr, so the inferred coremass would therefore be somewhat smaller.
We also compare HATP26b to the theoretical models of Baraffe et al. (2008) which predict more significant inflation due to irradiation for low mass planets than do the Fortney et al. (2007) models. In this case the radius of HATP26b is intermediate between the and heavyelement enrichment models.
4.2. Evaporation
Observations of the transiting hot Jupiters HD 209458b and HD 189733b in the H i Lyman line have indicated that both planets are evaporating at a rate of up to g s (e.g, VidalMadjar et al., 2003; Lecavelier des Etangs et al., 2010). Prompted by the observations for HD 209458b, several theoretical studies have indicated that atmospheric evaporation is likely to be important for closein planets, particularly those with low surface gravities, such as hot Neptunes (see for example Lammer et al., 2003 and the review by Yelle et al., 2008). It has even been suggested that some closein Neptunemass and smaller planets may be the evaporated cores of planets which initially had masses comparable to Saturn or Jupiter (e.g. Baraffe, 2005). In the case of energylimited escape, the evaporative massloss is given by (see Erkaev et al., 2007, and Yelle et al., 2008; see also Valencia et al., 2010 and Jackson et al., 2010 for applications to CoRoT7b):
(1) 
where is the incident flux of extreme ultraviolet (XUV) stellar radiation, is the heating efficiency and is estimated to be for the case of HD 209458b (Yelle et al., 2008), and is a factor that accounts for an enhancement of the evaporation rate in the presence of tides, and is given by:
(2) 
where is the ratio of the Roche radius to the planet radius. Ribas et al. (2005) find that for solar type stars the XUV flux at 1 AU integrated over the wavelength range Å to Å is given by:
(3) 
where is the age in Gyr. To our knowledge, a similar study has not been completed for K dwarfs, however long term Xray observations of the 56 Gyr Cen AB system reveal that on average the K1 dwarf star Cen B has an Xray luminosity in the 660 Å band that is approximately twice that of the Sun, while the G2 dwarf Cen A has a luminosity that is approximately half that of the Sun (Ayers, 2009). For simplicity we therefore assume that the total XUV luminosity of HATP26 is comparable to that of the Sun (4.64 ergs s cm at 1 AU; Ribas et al., 2005), which is likely correct to within an order of magnitude. Assuming , we estimate that the expected presentday massloss rate for HATP26b is . To determine the total mass lost by HATP26b over its lifetime, we integrate equation 1 assuming an age of Gyr, for Gyr and for Gyr, neglecting tidal evolution of the orbit, and assuming that the radius is constant. We find that HATP26b may have lost a significant fraction its mass ( 30%); the exact value depends strongly on several poorly constrained parameters including and its dependence on age for a K1 dwarf, , and the age of the system.
4.3. Eccentricity
Using the relation given by Adams & Laughlin (2006), the expected tidal circularization timescale for HATP26b is Gyr which is much less than the age of the system. This timescale is estimated assuming a large tidal quality factor of , and that there are no additional bodies in the system exciting the eccentricity. However, because at least two of the three hot Neptunes have significant eccentricities (GJ 436b has , Demory et al., 2007; and HATP11b has , Bakos et al., 2010; the eccentricity for Kepler4b is poorly constrained, Kipping & Bakos, 2010a), we cannot conclude that the eccentricity must be zero on physical grounds, and therefore do not adopt a zeroeccentricity model for the parameter determination.
As discussed in Section 3.1 the eccentricity of HATP26b is poorly constrained by the RV observations, and is instead constrained by requiring that the star be younger than the age of the universe (without the age constraint we get , whereas including the age constraint gives ). To establish the significance of the eccentricity measurement, we also fit a model with the eccentricity fixed to zero. An Ftest (e.g. Lupton, 1993) allows us to reject the null hypothesis of zero eccentricity with only 79% confidence. Alternatively, the Lucy & Sweeney (1971) test for the significance of an eccentricity measurement gives a false alarm probability of % for detecting with an error of , or 88% confidence that the orbit is eccentric. If the eccentricity is fixed to zero, the required jitter to achieve is 2.4 , which is closer to the typical Keck/HIRES jitter of other chromospherically quiet early K dwarfs than the jitter of that is obtained with an eccentric orbit fit. We therefore are not able to claim a significant eccentricity for HATP26b, and instead may only place a confidence upper limit of . For the model discussed at the end of Section 3.3, the confidence upper limit is . Further RV observations, or a photometric detection of the occultation of the planet by its host star, are needed to determine if the eccentricity is nonzero.
4.4. Additional Bodies in the System
The model discussed in Section 3.3 with parameters given in Table 5 includes a linear drift in the radial velocities, , as a free parameter. We find m s d. Conducting an odds ratio test (see Kipping et al., 2010), we conclude that the drift is real with 96.6% confidence, making this a detection. While the detection is not significant enough for us to be highly confident that there is at least one additional body in the system, this suggestive result implies that HATP26 warrants longterm RV monitoring. We also searched for a linear timeshift in the RVs due to potential Trojans. We do not detect a significant shift, and may exclude d with 95% confidence. This translates to an upper limit of on the mass of a Trojan companion, which is greater than the mass of the planet. With the present data we are thus not able to place a meaningful limit on the presence of Trojan companions.
4.5. Suitability for Followup
HATP26 has a number of features that make it an attractive target for potential followup studies. At , it is bright enough that precision spectroscopic and photometric observations are feasible with moderate integration times. The equatorial declination of also means that HATP26 is accessible to both Northern and Southern groundbased facilities. The exceptionally low jitter will facilitate further RV observations, which might be used to confirm and refine the eccentricity determination, to measure the RossiterMcLaughlin effect (RM; discussed in more detail below) and to search for additional planets in the system.
A detection of the occultation of HATP26b by HATP26 with IRAC/Spitzer would provide a strong constraint on , while the duration of the occultation would provide a constraint on . We note that the median value of the a posteriori distribution for the time of occultation that results from our global fit when the eccentricity is allowed to vary (Section 3.3) is h after the expected time of occultation assuming a circular orbit. The expected depth of the occultation event is a challenging and at 3.6 µm and 4.5 µm respectively. Scaling from TrES4, a somewhat fainter star at these wavelengths, for which Knutson et al. (2009) measured occultations at 3.6 µm and 4.5 µm using IRAC/Spitzer with precisions of and respectively, one may hope to achieve a and detection for HATP26b for one event at each bandpass. One would need to observe 5 and 4 occultations respectively to achieve a detection.
Recent measurements of the RM effect for TEPs have revealed a substantial population of planets on orbits that are significantly misaligned with the spin axes of their host stars (e.g. Triaud et al., 2010). Winn et al. (2010a) note that misalignment appears to be more prevalent for planets orbiting stars with K, and suggest that most closein planets migrate by planetplanet or planetstar scattering mechanisms, or by the Kozai effect, rather than disk migration, and that tidal dissipation in the convective surfaces of cooler stars realigns the stellar spin axis to the orbital axis of the closein massive planet. Schlaufman (2010) also finds evidence that planets orbiting stars with are more likely to be misaligned than planets orbiting cooler stars using a method that is independent of the RM measurements. One prediction of the Winn et al. (2010a) hypothesis is that lower mass planets orbiting cool stars should show a greater degree of misalignment than higher mass planets due to their reduced tidal influence. The detection of misalignment for HATP11b (Winn et al., 2010b; Hirano et al., 2010) is consistent with this hypothesis. Measuring the RM effect for HATP26b would provide an additional test. Using equation (40) from Winn (2010), the expected maximum amplitude of the RM effect for HATP26b is , which given the low jitter of HATP26, should be detectable at .
By measuring the primary transit depth as a function of wavelength it is possible to obtain a transmission spectrum of an exoplanet’s atmosphere. Such observations have been made for a handful of planets (e.g. Charbonneau et al., 2002; see also the review by Seager & Deming, 2010). Following Brown (2001), the expected difference in transit depth between two wavelengths is given approximately by:
(4) 
where is the scale height of the atmosphere, is the planet surface gravity, is the mean molecular weight of the atmosphere, and where and are the opacities per gram of material at wavelengths in a strong atomic or molecular line and in the nearby continuum respectively. Assuming a pure H atmosphere, kg, we find for HATP26b km, and . If instead we assume that the atmosphere has the same composition as Neptune (e.g. de Pater & Lissauer, 2001), we have kg, km, and . For comparison, assuming a pure H atmosphere, the planet HD 209458b has , while GJ 436b has , HATP11b has and Kepler4b has . Due to its low surface gravity, HATP26b easily has the highest expected transmission spectrum signal among the known transiting Neptunemass planets. While it is relatively faint compared to the well studied planets HD 209458b and HD 189733b, we note that Sing et al. (2010) used the Gran Telescopio Canarias (GTC) to detect a absorption level at 7582 Å due to Potassium in the atmosphere of XO2b, which orbits a early K star. Scaling from this observation, it should be possible to detect components in the atmosphere of HATP26b with at the level using the GTC.
4.6. Summary
In summary, HATP26b is a lowdensity Neptunemass planet. Its lowdensity relative to the other known Neptunemass planets means that HATP26b likely has a more significant hydrogenhelium gas envelope than its counterparts. The existence of HATP26b provides empirical evidence that, like hot Jupiters, hot Neptunes also exhibit a wide range of densities. Comparing to the Fortney et al. (2007) models, we find that HATP26b is likely composed of a gas envelope and a heavyelement core that are approximately equal in mass, while the Baraffe et al. (2008) models prefer a higher heavyelement fraction. It is also likely that irradiationdriven massloss has played a significant role in the evolution of HATP26b –we find that the planet may have lost of its presentday mass over the course of its history, though this conclusion depends strongly on a number of very poorly constrained parameters, particularly the XUV flux of HATP26 and its evolution in time. We place a 95% confidence upper limit on the eccentricity of . If further observations detect a nonzero eccentricity, it would mean that at least three of the four known Neptunemass TEPs have nonzero eccentricities, which may imply that the tidal quality factor is higher than expected for these planets. Observations of the planetary occultation event for HATP26b with IRAC/Spitzer would greatly constrain the eccentricity, however the low expected depth is likely to make this a challenging observation. We find suggestive evidence for a linear drift in the RVs which is significant at the level. If confirmed, this would imply the existence of at least one additional body in the HATP26 system. With an expected RM amplitude of and a low stellar RV jitter, HATP26b is a good target to measure the RM effect and thereby test the hypothesis that lowmass planets are more likely to be misaligned than highmass planets. The low surface gravity also makes HATP26b a good target for transmission spectroscopy.
Footnotes
 affiliation: Based in part on observations obtained at the W. M. Keck Observatory, which is operated by the University of California and the California Institute of Technology. Keck time has been granted by NASA (N018Hr and N167Hr).
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: NSF Fellow
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: University College London, Dept. of Physics and Astronomy, Gower St., London, UK
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: Konkoly Observatory, Budapest, Hungary
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: Department of Astronomy, University of California, Berkeley, CA
 affiliation: Department of Astronomy, Yale University, New Haven, CT
 affiliation: Department of Astrophysics, California Institute of Technology, Pasadena, CA
 affiliation: Department of Astronomy, University of California, Berkeley, CA
 affiliation: Department of Astronomy, University of California, Berkeley, CA
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: Niels Bohr Institute, Copenhagen University, DK2100, Copenhagen, Denmark
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: HarvardSmithsonian Center for Astrophysics, Cambridge, MA; email: gbakos@cfa.harvard.edu
 affiliation: Department of Physics, University of South Dakota, Vermillion, SD
 affiliation: Hungarian Astronomical Association, Budapest, Hungary
 affiliation: Hungarian Astronomical Association, Budapest, Hungary
 affiliation: Hungarian Astronomical Association, Budapest, Hungary
 Barycentric Julian dates throughout the paper are calculated from Coordinated Universal Time (UTC)
 e.g. http://exoplanet.eu
 Solar system masses are taken from the IAU WG on NSFA report of current best estimates to the 2009 IAU General Assembly retrieved from http://maia.usno.navy.mil/NSFA/CBE.html; We adopt equatorial radii for the Solar System planets from Seidelmann et al. (2007).
 The zeropoint of these velocities is arbitrary. An overall offset fitted to these velocities in Section 3.3 has not been subtracted.
 Internal errors excluding the component of astrophysical/instrumental jitter considered in Section 3.3.
 chromospheric activity index, calibrated to the scale of Vaughan, Preston & Wilson (1978).
 The outoftransit level has been subtracted. These magnitudes have been subjected to the EPD and TFA procedures, carried out simultaneously with the transit fit.
 Raw magnitude values without application of the EPD and TFA procedures.
 The lack of evidence for stellar activity indicates that HATP26 is unlikely to be a premain sequence star.
 SME = “Spectroscopy Made Easy” package for the analysis of highresolution spectra (Valenti & Piskunov, 1996). These parameters rely primarily on SME, but have a small dependence also on the iterative analysis incorporating the isochrone search and global modeling of the data, as described in the text.
 YY++SME = Based on the YY isochrones (Yi et al., 2001), as a luminosity indicator, and the SME results.
 : Reference epoch of mid transit that minimizes the correlation with the orbital period. It corresponds to . BJD is calculated from UTC. : total transit duration, time between first to last contact; : ingress/egress time, time between first and second, or third and fourth contact.
 : Reference epoch of mid transit that minimizes the correlation with the orbital period. It corresponds to . BJD is calculated from UTC. : total transit duration, time between first to last contact; : ingress/egress time, time between first and second, or third and fourth contact.
 : Reference epoch of mid transit that minimizes the correlation with the orbital period. It corresponds to . BJD is calculated from UTC. : total transit duration, time between first to last contact; : ingress/egress time, time between first and second, or third and fourth contact.
 Values for a quadratic law, adopted from the tabulations by Claret (2004) according to the spectroscopic (SME) parameters listed in Table 4.
 Lagrangian orbital parameters derived from the global modeling, and primarily determined by the RV data.
 Lagrangian orbital parameters derived from the global modeling, and primarily determined by the RV data.
 Timeoffset in the radial velocities due to companion planets in Trojan orbits.
 Correlation coefficient between the planetary mass and radius .
 The Safronov number is given by (see Hansen & Barman, 2007).
 Incoming flux per unit surface area, averaged over the orbit.
 Incoming flux per unit surface area, averaged over the orbit.
 Incoming flux per unit surface area, averaged over the orbit.
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