Astronomy 241: Foundations of Astrophysics I

20. Other Planetary Systems xkcd: Exoplanets –38–

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The Evolution of L and T Dwarfs in Color-Magnitude Diagrams

Fig. 6.— Evolution of the luminosity of brown dwarfs This shows the same cloudless sequence as in Fig. 2 (solid lines), compared with the cloudless cooling sequences of Burrows et al. (1997) (dotted lines). NASA's Hubble Reveals Rogue Planetary Orbit For Fomalhaut B Exoplanet Plots xkcd: Exoplanet Names Hot Jupiters

Exoplanet Plots Solar System Planets (except Mercury)

Exoplanet Plots Hot Jupiters LETTER RESEARCH ab 20

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10 Earth-like Mercury-like Planet radius ( 1.5 Water Iron 5 Rock Hydrogen Iron 1.0

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Planet mass (M⊕)

Figure 2 | Masses and radii of well-characterized planets. Extrasolar planets idealized planets consisting of pure hydrogen, water, rock (Mg2SiO4), and iron are denoted by red circles and Solar System planets are represented by green are shown as blue lines. Green and brown lines denote Earth-like composition triangles. a spans the full range of sizes and masses on logarithmic axes. The (67% rock, 33% iron) and Mercury-like composition (40% rock, 60% iron). shaded grey rectangle denotes the range of parameters shown in b on linear Exoplanet masses, radii and their associated errors are from the Exoplanet mass and radius axes. Kepler-78b is depicted as a black filled circle in a and Orbit Database25 (http://exoplanets.org; downloaded on 1 September 2013). as a distribution of allowed masses and radii with a dotted red ellipse marking Planets with fractional mass uncertaintiesA rocky of composition over 50% for arean Earth-sized not shown. exoplanet the 68% confidence region in b. Model mass–radius relationships11,24 for

We explored some possibilities for the interior structure of Kepler- be relevant to understanding the interiors of cooler extrasolar planets 78b using a simplified two-component model11 consisting of an iron with atmospheres, establishing the range of core sizes in giant planet core surrounded by a silicate mantle (Mg2SiO4). This model correctly formation, and explaining Mercury’s unusually high iron abundance. reproduces the masses of Earth and Venus given their radii and assum- ing a composition of 67% silicate rock and 33% iron by mass. Applied METHODS SUMMARY to Kepler-78b, the model gives an iron fraction of 20% 6 33%, similar We fitted Keck-HIRES spectra of Kepler-78 with stellar atmosphere models using to that of Earth and Venus but smaller than that of Mercury (approxi- Spectroscopy Made Easy to measure the star’s temperature, gravity and iron abun- mately 60%; ref. 12). dance. These spectroscopic parameters were used to estimate the host star’s mass, With a star–planet separation of 0.01 astronomical units (1 AU is the radius and density—crucial parameters from which to determine the planet’s mass, Earth-to-Sun distance), the dayside of Kepler-78b is heated to a tem- radius and density—from empirical relationships calibrated by precisely charac- perature of 2,300–3,100 K. Any gaseous atmosphere around Kepler- terized binary star systems. Using this stellar density as a constraint, we reanalysed 78b would probably have been lost long ago to photoevaporation by the Kepler photometry to refine the planet radius measurement. We observed the intense starlight13. However, based on the measured surface gravity Kepler-78 with HIRES using standard procedures including sky spectrum subtrac- of 11 m s22, the liquid and solid portions of the planet should be stable tion and wavelength calibration with a reference iodine spectrum. We measured against mass loss of the sort14 that is apparently destroying the smaller high-precision relative radial velocities using a forward model where the de-convolved planet KIC 12557548b (ref. 15). stellar spectrum is Doppler-shifted, multiplied by the normalized high-resolution Kepler-78b is a member of an emerging class of planets with orbital iodine transmission spectrum, convolved with an instrumental profile, and matched 6,16,17 to the observed spectra using a Levenberg–Marquardt algorithm that minimizes periods of less than half a day . Another member is KOI 1843.03 the x2 statistic. The time-series radial velocities on eight nights were analysed with (refs 18 and 19), which has been shown to have a high density (more 23 several parametric models to account for the small-amplitude, periodic signal from than about 7 g cm ), although the deduction in that case was based on the orbiting planet and the larger-amplitude, quasi-periodic apparent Doppler shifts a theoretical requirement to avoid tidal destruction rather than direct that are due to rotating starspots. In our adopted harmonic spot model the star-spot measurement. That planet’s minimum density is similar to our estimated signal was modelled as a sum of sine functions whose amplitudes and phases were z2:0 23 density for Kepler-78b (which is 5:3{1:6 gcm ). These two planets free parameters. We sampled the multi-dimensional model parameter space with provide a stark contrast to Kepler-11f, which has a similar mass to an MCMC algorithm to estimate parameter confidence intervals and to account Kepler-78b, but a density that is ten times smaller20. for covariance between parameters. We found multiple families of models that With only a handful of low-mass planets with measured densities described the data well and they gave consistent measures of the Doppler ampli- known (Fig. 2b), we see solid planets primarily in highly irradiated, tude, which is proportional to the mass of Kepler-78b. close-in orbits and low-density planets swollen by thick atmospheres Online Content Any additional Methods, Extended Data display items and Source in somewhat cooler orbits. Measurements of additional planet masses Data are available in the online version of the paper; references unique to these and radii are needed to assess the significance of this pattern. Additional sections appear only in the online paper. ultrashort-period planets with detectable Doppler amplitudes (K P21/3) have been identified by the Kepler mission and are ready for mass/ mea- Received 25 September; accepted 11 October 2013. surements. With an ensemble of future measurements, the masses and Published online 30 October 2013. radii of ultrashort-period planets may reveal a commonality or diversity 1. Howard, A. W. et al. Planet occurrence within 0.25 AU of solar-type stars from of density and composition. This knowledge of hot solid planets may Kepler. Astrophys. J. 201 (Suppl.), 15 (2012).

00 MONTH 2013 | VOL 000 | NATURE | 3 ©2013 Macmillan Publishers Limited. All rights reserved Exoplanet atmospheres LETTER RESEARCH

ab 20

2.5 ter Wa

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) 2.0

⊕ Rock R

10 Earth-like Mercury-like Planet radius ( 1.5 Water Iron 5 Rock Hydrogen Iron 1.0

0 0.1 1 10 100 1,000 1 2 3 4 5 6 7 8 9 10

Planet mass (M⊕)

Figure 2 | Masses and radii of well-characterized planets. Extrasolar planets idealized planets consisting of pure hydrogen, water, rock (Mg2SiO4), and iron are denoted by red circles and Solar System planets are represented by green are shown as blue lines. Green and brown lines denote Earth-like composition triangles. a spans the full range of sizes and masses on logarithmic axes. The (67% rock, 33% iron) and Mercury-like composition (40% rock, 60% iron). shaded grey rectangle denotes the range of parameters shown in b on linear Exoplanet masses, radii and their associated errors are from the Exoplanet mass and radius axes. Kepler-78b is depicted as a black filled circle in a and Orbit Database25 (http://exoplanets.org; downloaded on 1 September 2013). as a distribution of allowed masses and radii with a dotted red ellipse marking Planets with fractional mass uncertaintiesA rocky of composition over 50% for arean Earth-sized not shown. exoplanet the 68% confidence region in b. Model mass–radius relationships11,24 for

We explored some possibilities for the interior structure of Kepler- be relevant to understanding the interiors of cooler extrasolar planets 78b using a simplified two-component model11 consisting of an iron with atmospheres, establishing the range of core sizes in giant planet core surrounded by a silicate mantle (Mg2SiO4). This model correctly formation, and explaining Mercury’s unusually high iron abundance. reproduces the masses of Earth and Venus given their radii and assum- ing a composition of 67% silicate rock and 33% iron by mass. Applied METHODS SUMMARY to Kepler-78b, the model gives an iron fraction of 20% 6 33%, similar We fitted Keck-HIRES spectra of Kepler-78 with stellar atmosphere models using to that of Earth and Venus but smaller than that of Mercury (approxi- Spectroscopy Made Easy to measure the star’s temperature, gravity and iron abun- mately 60%; ref. 12). dance. These spectroscopic parameters were used to estimate the host star’s mass, With a star–planet separation of 0.01 astronomical units (1 AU is the radius and density—crucial parameters from which to determine the planet’s mass, Earth-to-Sun distance), the dayside of Kepler-78b is heated to a tem- radius and density—from empirical relationships calibrated by precisely charac- perature of 2,300–3,100 K. Any gaseous atmosphere around Kepler- terized binary star systems. Using this stellar density as a constraint, we reanalysed 78b would probably have been lost long ago to photoevaporation by the Kepler photometry to refine the planet radius measurement. We observed the intense starlight13. However, based on the measured surface gravity Kepler-78 with HIRES using standard procedures including sky spectrum subtrac- of 11 m s22, the liquid and solid portions of the planet should be stable tion and wavelength calibration with a reference iodine spectrum. We measured against mass loss of the sort14 that is apparently destroying the smaller high-precision relative radial velocities using a forward model where the de-convolved planet KIC 12557548b (ref. 15). stellar spectrum is Doppler-shifted, multiplied by the normalized high-resolution Kepler-78b is a member of an emerging class of planets with orbital iodine transmission spectrum, convolved with an instrumental profile, and matched 6,16,17 to the observed spectra using a Levenberg–Marquardt algorithm that minimizes periods of less than half a day . Another member is KOI 1843.03 the x2 statistic. The time-series radial velocities on eight nights were analysed with (refs 18 and 19), which has been shown to have a high density (more 23 several parametric models to account for the small-amplitude, periodic signal from than about 7 g cm ), although the deduction in that case was based on the orbiting planet and the larger-amplitude, quasi-periodic apparent Doppler shifts a theoretical requirement to avoid tidal destruction rather than direct that are due to rotating starspots. In our adopted harmonic spot model the star-spot measurement. That planet’s minimum density is similar to our estimated signal was modelled as a sum of sine functions whose amplitudes and phases were z2:0 23 density for Kepler-78b (which is 5:3{1:6 gcm ). These two planets free parameters. We sampled the multi-dimensional model parameter space with provide a stark contrast to Kepler-11f, which has a similar mass to an MCMC algorithm to estimate parameter confidence intervals and to account Kepler-78b, but a density that is ten times smaller20. for covariance between parameters. We found multiple families of models that With only a handful of low-mass planets with measured densities described the data well and they gave consistent measures of the Doppler ampli- known (Fig. 2b), we see solid planets primarily in highly irradiated, tude, which is proportional to the mass of Kepler-78b. close-in orbits and low-density planets swollen by thick atmospheres Online Content Any additional Methods, Extended Data display items and Source in somewhat cooler orbits. Measurements of additional planet masses Data are available in the online version of the paper; references unique to these and radii are needed to assess the significance of this pattern. Additional sections appear only in the online paper. ultrashort-period planets with detectable Doppler amplitudes (K P21/3) have been identified by the Kepler mission and are ready for mass/ mea- Received 25 September; accepted 11 October 2013. surements. With an ensemble of future measurements, the masses and Published online 30 October 2013. radii of ultrashort-period planets may reveal a commonality or diversity 1. Howard, A. W. et al. Planet occurrence within 0.25 AU of solar-type stars from of density and composition. This knowledge of hot solid planets may Kepler. Astrophys. J. 201 (Suppl.), 15 (2012).

00 MONTH 2013 | VOL 000 | NATURE | 3 ©2013 Macmillan Publishers Limited. All rights reserved 1000

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-1000 KIC-7877978 KIC-8183288 KIC-8611257 P 56.57 P 66.65 P 99.25 -1500 Rp 1.87 Rp 1.43 Rp 1.65 Fp 2.95 Fp 1.95 Fp 1.98 1000 Text 500

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-1000 KIC-9447166 KIC-11415243 KIC-11462341 P 62.87 P 168.81 P 42.34 -1500 Rp 1.48 Rp 1.74 Rp 1.04 Fp 2.93 Fp 0.80 Fp 2.28

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flux(ppm) -1000 KIC-12121570 P 91.50 -1500 Rp 1.95 Fp 2.16 -2000 −0.6−0.4−0.2 0.0 0.2 0.4 0.6 t - t0 [days] Prevalence of Earth-size planets orbiting Sun-like stars — Supporting Information

Figure S15: Phase folded photometry for ten Earth-size HZ candidates. Black point shows show TERRA- calibrated photometry folded on the best fit ephemeris listed in Table S2. The green symbols show the median flux value in 30-minute bins. The red dashed lines shows the best-fit Mandel-Agol model. We have annotated each plot with the KIC identifier, period, planet size (Earth-radii), incident flux level (relative to Earth). All measurements of planet size and incident flux are based on spectra taken with the Keck 10 m telescope. Spectra for KIC-6225454, KIC-7877978, KIC-9447166, and KIC-11462341 were obtained during peer-review and were added in proofS28 (see Table S3). Astronomers Conclude Habitable Planets Are Common HD 10180 Gliese 876 xkcd: Exoplanets