A Habitable-zone Earth-sized Planet Rescued from False Positive Status

The Kepler space telescope observed Kepler-1649 (KIC 6444896/KOI 3138) for a total of 756 days between 2010 and 2013 during its primary mission. Kepler-1649 was observed during Quarters 6–9 (as part of guest investigator proposal GO20031, PI: Di Stefano) and Quarters 12–17 (after KOI 3138.01/Kepler-1649 b was designated a PC).

A signal with period P ≈ 8.689 days was first detected, designated as KOI 3138.01, and dispositioned as a PC in the Burke et al. (2014) catalog, which used data from Quarter 1 to Quarter 8, or only nine months of data for this target (Quarters 6, 7, and 8). It was also dispositioned as a PC in each subsequent catalog that re-examined it (the last two of which were based on the Robovetter; Coughlin 2017; Thompson et al. 2018). This signal eventually became known as Kepler-1649 b after statistical validation by Angelo et al. (2017).

A second signal with P ≈ 19.535 days was only detected in the final Kepler pipeline run (TCE 6444896-02; Twicken et al. 2016). The Thompson et al. (2018) Robovetter dispositioned the TCE as a not-transit-like FP (i.e., a false alarm) with a comment of "MOD_NONUNIQ_ALT," which indicates it failed the Model-Shift Uniqueness test (see Section A.3.4 of Thompson et al. 2018). This outcome indicates that the Robovetter judged the signal's significance to be too low compared to the systematic noise level to be a PC. The Robovetter assigned the 19.5 days TCE a "disposition score" (see Section 3.2 of Thompson et al. 2018) of 0.374, which indicates only weak confidence in the FP disposition (scores near 0.0 indicate high-confidence FPs, while scores near 1.0 indicate high-confidence PCs). All TCEs with disposition scores >0.1 were assigned KOI numbers by Thompson et al. (2018), and thus KOI 3838.02 was created. For convenience, we hereafter refer to this new PC (KOI 3138.02) as Kepler-1649 c.

Our team inspected the transit signal of Kepler-1649 c as part of our systematic review of Kepler's FP objects of interest. Though our assessments of the FPs were usually in good agreement with the Robovetter, we were not confident in the Robovetter's FP classification. Unlike most of the false alarms that the Robovetter fails with the Model-Shift Uniqueness test, Kepler-1649 c has a relatively short orbital period and dozens of observed transits, which were consistent in shape and depth over time. We found no compelling evidence that Kepler-1649 c was an FP, and instead identified it as a possible PC.

We hypothesized that Kepler-1649 c failed the Robovetter's Model-Shift Uniqueness test because of the atypical noise properties of the light curve produced by the Kepler pipeline. The Kepler pipeline light curve shows strong quarterly variations in its photometric scatter; for example, the photometric scatter in Quarter 7 ($\approx 3500$ ppm) is almost four times greater than the photometric scatter in Quarter 6 ($\approx 900$ ppm). We traced this effect to the choice of photometric apertures by the Kepler pipeline. Kepler-1649 has a high proper motion of 168.2 mas per year, but its motion was not taken into account when the Kepler pipeline selected optimal pixels for aperture photometry (Bryson et al. 2010). Instead, the pixel selection algorithm assumed Kepler-1649's J2000 position, about 2'' (or half of a Kepler pixel) from its true position during Kepler's observations. Because Kepler-1649 is faint, its optimal photometric apertures were small enough that this half-pixel error caused Kepler-1649 to fall at the edge or outside of the aperture in some quarters, while remaining within the photometric aperture in other quarters. The variation of the pixel position of Kepler-1649 relative to the pixels selected for photometry significantly weakened the transit signal in the original pipeline photometry.

We therefore chose to produce our own light curves from the Kepler target pixel files (DR25). Following Vanderburg et al. (2016), we extracted light curves from a set of 20 different photometric apertures. Half of these apertures were circular, defined by identifying all pixels within 10 different radii of Kepler-1649's position. The other half were shaped like the Kepler Pixel Response Function (PRF), defined by fitting the PRF to a representative Kepler image for each quarter and selecting all pixels where the model PRF exceeded 10 different fractions of the peak model flux. We selected the aperture that produced the light curve with the highest photometric precision¹² in each quarter after accounting for diluting flux from nearby fainter stars. The resulting light curve had much more consistent photometric scatter across quarters, improving significantly upon the Kepler pipeline light curve in the quarters where its aperture selection was suboptimal. We use this new light curve in our analysis throughout the rest of the Letter and show the phase-folded transit signals of Kepler-1649 b and c in Figure 1. We also experimented with fitting the Kepler images with a model based on the telescope's measured PRF to produce light curves (as done by Angelo et al. 2017), but never achieved higher photometric precision than our well-optimized aperture photometry.

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Finally, we re-ran the Model-Shift Uniqueness test using our new light curve, and found that this time, the PC solidly passed. We therefore consider Kepler-1649 c to be a viable PC.

Although the star Kepler-1649 was already well characterized by Angelo et al. (2017), we were able to improve upon their stellar parameters thanks to the newly released trigonometric parallax from Gaia Data Release 2 (DR2; Gaia Collaboration et al. 2016, 2018). We derive Kepler-1649's radius and mass using empirical relations between these quantities and the star's absolute K-band magnitude from Mann et al. (2015) and Mann et al. (2019), respectively. These relations yield a mass of M_⋆ = 0.1977 ± 0.0051 ${M}_{\odot }$ and radius of R_⋆ = 0.2317 ± 0.0049 ${R}_{\odot }$, which are consistent with, but several times more precise than, the estimates from Angelo et al. (2017). We adopt the spectroscopic metallicity and temperature reported by Angelo et al. (2017) of [M/H] = −0.15 ± 0.11 and ${T}_{\mathrm{eff}}=3240\pm 61$ K. Using an average of three different bolometric corrections for the 2MASS JHK magnitudes from Mann et al. (2015), we find that Kepler-1649 is only about half a percent as luminous as the Sun (L_⋆ = 0.00516 ± 0.00020 L_⊙). This value is in good agreement with the luminosity calculated from our adopted effective temperature and stellar radius using the Stefan-Boltzmann law (L_⋆ = 0.00533 ± 0.00046 L_⊙), indicating that our stellar parameters are self-consistent. Our adopted stellar parameters are listed in Table 1.

Table 1.  System Parameters for Kepler-1649

Parameter	Value	Comment
Other Designations
KIC 6444896
KOI 3138
LSPM J1930 + 4149
Gaia DR2 2125699062780742016
Basic Information
R.A.	19:30:00.9006122986	A
decl.	+41:49:49.513849537	A
Proper Motion in R.A. ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	−135.842 ± 0.112	A
Proper Motion in decl. ($\mathrm{mas}\,{\mathrm{yr}}^{-1}$)	−99.232 ± 0.139	A
Distance to Star (pc)	92.5 ± 0.5	A
Gaia G-magnitude	16.2682 ± 0.001	A
K-magnitude	12.589 ± 0.026	B
Stellar Parameters
Mass, ${M}_{\star }$ $({M}_{\odot })$	0.1977 ± $0.0051$	A,B,C
Radius, ${R}_{\star }$ $({R}_{\odot })$	0.2317 ± $0.0049$	A,B,C
Surface Gravity, $\mathrm{log}{g}_{\star }$ (cgs)	5.004 ± 0.021	A,B,C
Metallicity [M/H]	−0.15 ± 0.11	E
Effective Temperature, ${T}_{\mathrm{eff}}$ (K)	3240 ± 61	E
Luminosity $({L}_{\odot })$	0.00516 ± 0.00020	C
Kepler-1649 b
Orbital Period, P (days)	8.689099 ± $0.000025$	D
Radius Ratio, RP/R⋆	0.0402 ± $0.0018$	D
Scaled Semimajor Axis, a/R⋆	44.77 $\pm \,0.93$	D
Orbital Inclination, i (deg)	89.15${}_{-0.079}^{+0.11}$	D
Transit Impact Parameter, b	0.65${}_{-0.12}^{+0.072}$	D
Transit Duration, t14 (hr)	1.184${}_{-0.066}^{+0.085}$	D
Time of Transit, tt (BJD)	2455374.6219 ± 0.0016	D
Planet Radius, RP (R⊕)	1.017 ± $0.051$	A,B,C,D
Incident Flux, S (S${}_{\oplus })$	2.208 ± 0.094	A,B,C,D,E
Equilibrium Temperature, Teq (K)	307 ± 26	A,B,C,D,E,F
Kepler-1649 c
Orbital Period, P (days)	19.53527 ± $0.00010$	D
Radius Ratio, RP/R⋆	0.042${}_{-0.0038}^{+0.0055}$	D
Scaled Semimajor Axis, a/R⋆	76.8 $\pm \,1.6$	D
Orbital Inclination, i (deg)	89.339 $\pm \,0.056$	D
Transit Impact Parameter, b	0.875 ± $0.074$	D
Transit Duration, t14 (hr)	1.07${}_{-0.21}^{+0.15}$	D
Time of Transit, tt (BJD)	2455410.9777 ± 0.0033	D
Planet Radius, RP (R⊕)	1.06${}_{-0.10}^{+0.15}$	A,B,C,D
Incident Flux, S (S${}_{\oplus })$	0.750 ± 0.032	A,B,C,D,E
Equilibrium Temperature, Teq (K)	234 ± 20	A,B,C,D,E,F
Other Fit Parameters
Linear Limb-darkening Parameter (u1)	0.330 ± 0.070	G
Quadratic Limb-darkening Parameter (u2)	0.392 ± 0.069	G
Transformed Limb-darkening Parameter 1 (q1)	0.52 ± 0.14	G
Transformed Limb-darkening Parameter 2 (q2)	0.229 ± 0.036	G
Constant Flux Offset Parameter $(\delta F$)	0.000030 ± 0.000029	D

Note. A: Parameters come from Gaia DR2. B: Parameters come from 2MASS (Skrutskie et al. 2006). C: Parameters come from empirical relations (Mann et al. 2015, 2019). D: Parameters come from our transit analysis described in Section 2.3. E: Parameters come from Angelo et al. (2017). F: Equilibrium temperatures T_eq calculated assuming circular orbits, albedo α uniformly distributed between 0 and 0.7, and perfect heat redistribution. ${T}_{{eq}}={T}_{\mathrm{eff}}{(1-\alpha )}^{1/4}\sqrt{\tfrac{{R}_{\star }}{2a}}$. G: Constrained by an informative prior on u₁ and u₂ based on model limb-darkening parameters (Claret & Bloemen 2011).

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We determined planetary parameters with a Markov Chain Monte Carlo (MCMC) analysis of the Kepler light curve. We modeled the transit profiles of both planets simultaneously using Mandel & Agol (2002) curves, oversampling by a factor of 30 and integrating to account for the 29.4 minute Kepler long-cadence exposure times. We fit for the host's stellar density, ${\rho }_{\star }$, imposing a Gaussian prior centered at 22.5 ${\rm{g}}\,{\mathrm{cm}}^{-3}$ with width 1.4 ${\rm{g}}\,{\mathrm{cm}}^{-3}$, and calculated the scaled semimajor axes (a/R_⋆) for both planets from the ${\rho }_{\star }$ value at each MCMC step using Kepler's third law. Because both Kepler-1649 b and c orbit too far from their host star to have undergone tidal circularization, we model eccentric orbits for both planets, fitting in $\sqrt{e}\sin \omega$ and $\sqrt{e}\cos \omega$, where e is the orbital eccentricity, and ω is the argument of periastron. Several groups have shown that planets in multi-transiting systems tend to have lower orbital eccentricity than planets in single-transiting systems, so we imposed a Gaussian prior on each planet's eccentricity centered at 0 with width 0.103, the 2σ upper limit from van Eylen et al. (2019). We assumed a quadratic limb-darkening law, fitting for coefficients using the q₁ and q₂ parameterization recommended by Kipping (2013). Because the transits of Kepler-1649 b and c are both short-duration and heavily distorted by the Kepler long-cadence integration time, we imposed Gaussian priors on Kepler-1649's u₁ and u₂ limb-darkening coefficients. The priors were centered on values (u₁ = 0.33, u₂ = 0.39) predicted by model atmospheres calculated by Claret & Bloemen (2011) and had widths of 0.07, the empirically measured scatter between these model predictions and measured values (Müller et al. 2013). Finally, we limited the planet radii by enforcing ${R}_{p}/{R}_{\star }\lt 1$. In other words, the planets cannot be larger than their host star.

All in all, we fit 16 parameters: the stellar density, two limb-darkening parameters (q₁ and q₂), a constant flux offset, and for each planet, orbital period, transit time, orbital inclination, $\mathrm{log}({R}_{p}/{R}_{\star })$, $\sqrt{e}\sin \omega$, and $\sqrt{e}\cos \omega$. We explored parameter space with an affine invariant MCMC sampler (Goodman & Weare 2010) evolving each of 100 walkers for 100,000 steps, removing the first 10,000 steps as burn-in. The results of our fit are given in Table 1 and our best-fit model is plotted in Figure 1.

Kepler-1649 c is an Earth-sized planet orbiting within its host star's habitable zone (as calculated by Kopparapu et al. 2013, under conservative assumptions). Figure 2 shows a schematic of the Kepler-1649 system along with the location of the circumstellar habitable zone. Though Earth-sized habitable-zone planets are believed to be intrinsically common, they remain difficult to detect, and we only know of a handful today. Based on the NASA Exoplanet Archive Confirmed Planets table,¹⁴ and using Gaia-based radii from Berger et al. (2018) for Kepler planets, only four transiting planets (TRAPPIST-1 e, f, and g, Gillon et al. 2017, and TOI 700 d, Gilbert et al. (2020; Rodriguez et al. 2020; Suissa et al. 2020) and three non-transiting (Proxima Centauri b, Anglada-Escudé et al. 2016, Teegarden's Star c, Zechmeister et al. 2019, and GJ 1061 d Dreizler et al. 2020) have radii smaller than 1.25 R_⊕, or mass less than 2.0 M_⊕, and orbit within their star's conservative habitable zone.¹⁵

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In terms of size and incident bolometric flux, Kepler-1649 c is a near analog of Earth. Its radius (1.06${}_{-0.10}^{+0.15}$R_⊕) is consistent with that of Earth, and the planet receives about 75% of Earth's incident stellar flux. It seems likely, but not guaranteed, that Kepler-1649 c has a rocky composition—hot Earth-sized planets do tend to be rocky (Rogers 2015), but it may be unwise to extrapolate these results to cooler planets like Kepler-1649 c. Indeed, though some of Kepler-1649 c's bulk parameters are similar to Earth, the planet may not be at all "Earth-like." Many of Kepler-1649 c's properties remain uncertain, and planets orbiting M-dwarfs experience a very different environment (an extended era of ultraviolet (UV) irradiation, tidal locking, etc.) from the planets in our own solar system (Shields et al. 2016).

Like many other Kepler systems (Fabrycky et al. 2014), and especially mid M-dwarfs (Muirhead et al. 2015), Kepler-1649 hosts multiple close-in transiting planets. Generally, multi-transiting systems are nearly coplanar, with only a small spread in mutual inclinations (Fabrycky et al. 2014, though not always; see Mills & Fabrycky 2017). The Kepler-1649 system appears to fit this trend, as the inclinations of the two planets are consistent (at the 1σ level) with being perfectly coplanar.

The period ratio between Kepler-1649 b and c is 2.248250 ± 0.000013, only 0.08% inside of a 9/4 period ratio. Often, near-integer period ratios between neighboring planets indicate that the planets were or are in an orbital resonance, but the 9:4 resonance is weak; usually planet pairs are found near stronger resonances like the 2:1 or 3:2 ratios. We therefore suspect that there may be a third planet orbiting between Kepler-1649 b and c, forming a chain of 3:2 resonances. If we assume that Kepler-1649 b and c are in a three-body Laplace resonance with this hypothetical third planet, its period should be close to 13.029593 days (with an uncertainty of a few minutes). We checked the Kepler light curve for a planet with this orbital period, but found no transits deeper than about 600 ppm. Therefore, if there is a third planet orbiting between Kepler-1649 b and c, it is either too small to detect (roughly Mars-sized or less, though transit timing variations could hide a somewhat larger planet), or it is misaligned enough to prevent it from transiting.

Kepler-1649 c is the first habitable-zone Earth-sized planet to be found among the mid M-dwarf stars observed by Kepler. Only about 450 such stars were observed during Kepler's primary mission (Hardegree-Ullman et al. 2019), so it is somewhat surprising that Kepler detected a transiting Earth analog in this small sample. We quantified the likelihood that Kepler would find at least one Earth analog around a mid M-dwarf with a Monte Carlo simulation. We generated many ($\approx {10}^{4}$) synthetic planet populations around 461 mid M-dwarfs (with spectral types M3-M5.5) observed by Kepler identified by Hardegree-Ullman et al. (2019), assuming planet occurrence statistics from Dressing & Charbonneau (2015). The planets had radii randomly drawn from a uniform distribution between 0.75 and 1.25 R_⊕, orbital periods drawn from a log-uniform distribution inside the habitable zone, and inclinations drawn from a uniform distribution in $\cos (i)$. We calculated the expected transit signal-to-noise for each favorably inclined planet, and used the Kepler detection efficiency curve from Christiansen (2017) to determine which simulated planets were detectable by Kepler. We found only a 3.7% chance that Kepler would detect an Earth-sized planet in the conservative habitable zone around a mid M-dwarf.

Given the long, but not insurmountable odds against its detection, it is possible that Kepler-1649 c's discovery was just lucky chance, but it is also possible that the intrinsic occurrence rate of such objects we used is incorrect. Our previous calculation assumed an occurrence rate calculated by Dressing & Charbonneau (2015) for planets between 1.0 and 1.5 R_⊕ orbiting a sample of mostly early M-dwarf stars. It is plausible that mid M-dwarf stars might form more Earth analogs than their more massive counterparts, thus boosting the chances we would detect such a planet in the Kepler sample. To test this, we calculated the occurrence rates of planets around mid M-dwarf stars observed by Kepler, while including the newly rescued Kepler-1649 c in our calculation. We modeled the population of planets orbiting mid M-dwarf stars (in particular, the sample defined by Hardegree-Ullman et al. 2019) with a joint (un-broken) power-law distribution in planet radius and orbital period (Burke et al. 2015; Bryson et al. 2020) and determined power-law parameters by exploring a Poisson likelihood function with MCMC. Other than the inclusion of Kepler-1649 c, the details of our calculation are identical to that of Bryson (2020).

We note that by including Kepler-1649 c in our calculations, we make an implicit assumption that the pipeline error leading to Kepler-1649 c's incorrect FP classification was rare and therefore not well represented in the Kepler DR25 vetting completeness experiments. This assumption seems reasonable—the root cause of Kepler-1649 c's incorrect FP disposition, the large quarter-to-quarter variations in the light curve's photometric scatter, is unusual in Kepler data, only affecting faint stars with high proper motions unknown to the Kepler pipeline. The quarterly variations in Kepler-1649's light curve are among the worst (95th percentile) of even the faint, high-proper-motion stars in the Kepler mid M-dwarf sample. A visual inspection of the TCEs and the DR25 injection/recovery results for other stars with high quarter-to-quarter variations in photometric scatter showed that no other PCs (real or simulated) were rejected on similar grounds to Kepler-1649 c. We therefore include Kepler-1649 c in our calculations with the caveat that if our assumption is incorrect, our occurrence rate may be biased slightly high.

We integrated the resulting power-law planet occurrence rates over the habitable zones for each star in our sample and calculated an average number of planets per star. Our result is shown in Figure 3, compared to the Dressing & Charbonneau (2015) occurrence rate for such planets around early M-dwarfs. We measure an occurrence rate higher than that of early M-dwarfs, though the statistical significance of this difference is not high. However, when taken together with previous suggestions of increased planet occurrence around mid M-dwarfs (Muirhead et al. 2012; Hardegree-Ullman et al. 2019) and the discovery of three Earth-sized planets in the conservative habitable zone of TRAPPIST-1 (Gillon et al. 2017), the detection of Kepler-1649 c provides further evidence that Earth analogs may be more common around mid M-dwarfs than higher-mass stars.

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Moving forward, automatic vetting of PCs can only become more important as data volume increases and classification techniques improve. There are likely hundreds of undiscovered planets left in K2 data (Dotson et al. 2019), and NASA's Transiting Exoplanet Survey Satellite (TESS) satellite produces more light curves and TCEs every month than the entire 10 yr Kepler mission (Guerrero et al. 2019). Expecting humans to keep up with such vast quantities of data is unsustainable, and automatic vetting techniques have already taken the bulk of the triage/vetting workload (Yu et al. 2019; Guerrero et al. 2019). However, as our rescue of Kepler-1649 c reinforces, careful human inspection will remain valuable going forward. Even if inspecting each FP TCE is unfeasible, examining a small but strategically chosen sample¹⁶ of targets could help improve automatic methods and enable new discoveries.