Analysis Of Transit Timing Variations Research Articles

Validating AU Microscopii d with Transit Timing Variations

AU Mic is a young (22 Myr), nearby exoplanetary system that exhibits excess transit timing variations (TTVs) that cannot be accounted for by the two known transiting planets nor stellar activity. We present the statistical “validation” of the tentative planet AU Mic d (even though there are examples of “confirmed” planets with ambiguous orbital periods). We add 18 new transits and nine midpoint times in an updated TTV analysis to prior work. We perform the joint modeling of transit light curves using EXOFASTv2 and extract the transit midpoint times. Next, we construct an O−C diagram and use Exo-Striker to model the TTVs. We generate TTV log-likelihood periodograms to explore possible solutions for d’s period, then follow those up with detailed TTV and radial velocity Markov Chain Monte Carlo modeling and stability tests. We find several candidate periods for AU Mic d, all of which are near resonances with AU Mic b and c of varying order. Based on our model comparisons, the most-favored orbital period of AU Mic d is 12.73596 ± 0.00793 days (T C,d = 2458340.55781 ± 0.11641 BJD), which puts the three planets near 4:6:9 mean-motion resonance. The mass for d is 1.053 ± 0.511 M ⊕, making this planet Earth-like in mass. If confirmed, AU Mic d would be the first known Earth-mass planet orbiting a young star and would provide a valuable opportunity in probing a young terrestrial planet’s atmosphere. Additional TTV observations of the AU Mic system are needed to further constrain the planetary masses, search for possible transits of AU Mic d, and detect possible additional planets beyond AU Mic c.

Revisiting the Transit Timing and Atmosphere Characterization of the Neptune-mass Planet HAT-P-26 b

We present a transit-timing variation (TTV) and planetary atmosphere analysis of the Neptune-mass planet HAT-P-26 b. We present a new set of 13 transit light curves from optical ground-based observations and combine them with light curves from the Wide Field Camera 3 on the Hubble Space Telescope, the Transiting Exoplanet Survey Satellite, and previously published ground-based data. We refine the planetary parameters of HAT-P-26 b and undertake a TTV analysis using 33 transits obtained over seven years. The TTV analysis shows an amplitude signal of 1.98 ± 0.05 minutes, which could result from the presence of an additional ∼0.02 M Jup planet at a 1:2 mean-motion resonance orbit. Using a combination of transit depths spanning optical to near-infrared wavelengths, we find that the atmosphere of HAT-P-26 b contains % H2O with a derived temperature of K.

Transit timing variation analysis of the low-mass brown dwarf KELT-1 b

ABSTRACT We investigate whether there is a variation in the orbital period of the short-period brown dwarf-mass KELT-1 b, which is one of the best candidates to observe orbital decay. We obtain 19 high-precision transit light curves of the target using six different telescopes. We add all precise and complete transit light curves from open databases and the literature, as well as the available Transiting Exoplanet Survey Satellite (TESS) observations from sectors 17 and 57, to form a transit timing variation (TTV) diagram spanning more than 10 yr of observations. The analysis of the TTV diagram, however, is inconclusive in terms of a secular or periodic variation, hinting that the system might have synchronized. We update the transit ephemeris and determine an informative lower limit for the reduced tidal quality parameter of its host star of Q$_{\star }^{\prime } \gt (8.5 \pm 3.9) \times 10^{6}$ assuming that the stellar rotation is not yet synchronized. Using our new photometric observations, published light curves, the TESS data, archival radial velocities, and broadband magnitudes, we also update the measured parameters of the system. Our results are in good agreement with those found in previous analyses.

Refining the Masses and Radii of the Star Kepler-33 and its Five Transiting Planets

Kepler-33 hosts five validated transiting planets ranging in period from 5 to 41 days. The planets are in nearly coplanar orbits and exhibit remarkably similar (appropriately scaled) transit durations indicative of similar impact parameters. The outer three planets have a radius of 3.5 ≲ R p/R ⊕ ≲ 4.7 and are closely packed dynamically, and thus transit timing variations can be observed. Photodynamical analysis of transit timing variations provide 2σ upper bounds on the eccentricity of the orbiting planets (ranging from <0.02 to <0.2) and the mean density of the host star (). We combine Gaia Early Data Release 3 parallax observations, the previously reported host-star effective temperature and metallicity, and our photodynamical model to refine properties of the host star and the transiting planets. Our analysis yields well-constrained masses for Kepler-33 e () and f () along with 2σ upper limits for planets c (<19 M ⊕) and d (<8.2 M ⊕). We confirm the reported low bulk densities of planet d (<0.4 g cm−3), e (0.8 ± 0.1 g cm−3), and f (0.7 ± 0.1 g cm−3). Based on comparisons with planetary evolution models, we find that Kepler-33 e and f exhibit relatively high envelope mass fractions of and f env = 10.3% ± 0.6%, respectively. Assuming a mass for planet d ∼4 M ⊕ suggests that it has f env ≳ 12%.

Generalized Peas in a Pod: Extending Intra-system Mass Uniformity to Non-TTV Systems via the Gini Index

It has been demonstrated that planets belonging to the same close-in, compact multiple-planet system tend to exhibit a striking degree of uniformity in their sizes. A similar trend has also been found to hold for the masses of such planets, but considerations of such intra-system mass uniformity have generally been limited to statistical samples wherein a majority of systems have constituent planetary mass measurements obtained via analysis of transit timing variations (TTVs). Since systems with strong TTV signals typically lie in or near mean motion resonance, it remains to be seen whether intra-system mass uniformity is still readily emergent for nonresonant systems with non-TTV mass provenance. We thus present in this work a mass uniformity analysis of 17 non-TTV systems with masses measured via radial velocity measurements. Using the Gini index, a common statistic for economic inequality, as our primary metric for uniformity, we find that our sample of 17 non-TTV systems displays intra-system mass uniformity at a level of ∼2.5σ confidence. We provide additional discussion of possible statistical and astrophysical underpinnings for this result. We also demonstrate the existence of a correlation (r = 0.25) between characteristic solid surface density (Σ0) of the minimum-mass extrasolar nebula and system mass Gini index, suggesting that more-massive disks may generally form systems with more-unequal planetary masses.

The Transit Timing and Atmosphere of Hot Jupiter HAT-P-37b

Abstract We perform transit timing variation (TTV) and transmission spectroscopy analyses of the planet HAT-P-37b, which is a hot Jupiter orbiting a G-type star. Nine new transit light curves are obtained and analyzed together with 21 published light curves from the literature. The updated physical parameters of HAT-P-37b are presented. The TTV analyses show a possibility that the system has an additional planet that induced the TTVs amplitude signal of 1.74 ± 0.17 minutes. If the body is located near the 1:2 mean-motion resonance orbit, the sinusoidal TTV signal could be caused by the gravitational interaction of a sub-Earth-mass planet with mass of 0.06 M ⊕. From the analysis of an upper-mass limit for the second planet, a Saturn-mass planet with orbital period less than 6 days is excluded. The broadband transmission spectra of HAT-P-37b favors a cloudy atmospheric model with an outlier spectrum in the B filter.

A Pair of Warm Giant Planets near the 2:1 Mean Motion Resonance around the K-dwarf Star TOI-2202*

Abstract TOI-2202 b is a transiting warm Jovian-mass planet with an orbital period of P = 11.91 days identified from the Full Frame Images data of five different sectors of the TESS mission. Ten TESS transits of TOI-2202 b combined with three follow-up light curves obtained with the CHAT robotic telescope show strong transit timing variations (TTVs) with an amplitude of about 1.2 hr. Radial velocity follow-up with FEROS, HARPS, and PFS confirms the planetary nature of the transiting candidate (a b = 0.096 ± 0.001 au, m b = 0.98 ± 0.06 M Jup), and a dynamical analysis of RVs, transit data, and TTVs points to an outer Saturn-mass companion (a c = 0.155 ± 0.002 au, m c = 0.37 ± 0.10 M Jup) near the 2:1 mean motion resonance. Our stellar modeling indicates that TOI-2202 is an early K-type star with a mass of 0.82 M ⊙, a radius of 0.79 R ⊙, and solar-like metallicity. The TOI-2202 system is very interesting because of the two warm Jovian-mass planets near the 2:1 mean motion resonance, which is a rare configuration, and their formation and dynamical evolution are still not well understood.

Kepler-90: Giant Transit-timing Variations Reveal a Super-puff

Abstract Exoplanet transit-timing variations (TTVs) caused by gravitational forces between planets can be used to determine planetary masses and orbital parameters. Most of the observed TTVs are small and sinusoidal in time, leading to degeneracies between the masses and orbital parameters. Here we report a TTV analysis of Kepler-90g and Kepler-90h, which exhibit large TTVs up to 25 hr. With optimization, we find a unique solution that allows us to constrain all of the orbital parameters. The best-fit masses for Kepler-90g and 90h are M ⊕ (Earth mass) and , respectively, with Kepler-90g having an unusually low apparent density of 0.15 ± 0.05 g cm−3. The uniqueness of orbital parameter solution enables a long-term dynamical integration, which reveals that although their periods are close to 2:3 orbital resonance, they are not locked in resonance, and the configuration is stable over billions of years. The dynamical history of the system suggests that planet interactions are able to raise the eccentricities and break the resonant lock after the initial formation.

Are There Transit Timing Variations for the Exoplanet Qatar-1b?

Abstract Motivated by the unsettled conclusion on whether there are any transit timing variations (TTVs) for the exoplanet Qatar-1b, 10 new transit light curves are presented and a TTV analysis with a baseline of 1400 epochs is performed. Because the linear model provides a good fit with a reduced chi-square of and the false-alarm probabilities of the possible TTV frequencies are as large as 35%, our results are consistent with a null-TTV model. Nevertheless, a new ephemeris with a reference time of T 0 = 2455647.63360 ± 0.00008 (BJD) and a period of P = 1.4200236 ± 0.0000001 (day) is obtained. In addition, the updated orbital semimajor axis and planetary radius in units of stellar radius are provided, and the lower limit of the modified stellar tidal quality factor is also determined.

Exploiting periodic orbits as dynamical clues for Kepler and K2 systems

Aims. Many extrasolar systems possessing planets in mean-motion resonance or resonant chain have been discovered to date. The transit method coupled with transit timing variation analysis provides an insight into the physical and orbital parameters of the systems, but suffers from observational limitations. When a (near-)resonant planetary system resides in the dynamical neighbourhood of a stable periodic orbit, its long-term stability, and thus survival, can be guaranteed. We use the intrinsic property of the periodic orbits, namely their linear horizontal and vertical stability, to validate or further constrain the orbital elements of detected two-planet systems. Methods. We computed the families of periodic orbits in the general three-body problem for several two-planet Kepler and K2 systems. The dynamical neighbourhood of the systems is unveiled with maps of dynamical stability. Results. Additional validations or constraints on the orbital elements of K2-21, K2-24, Kepler-9, and (non-coplanar) Kepler-108 near-resonant systems were achieved. While a mean-motion resonance locking protects the long-term evolution of the systems K2-21 and K2-24, such a resonant evolution is not possible for the Kepler-9 system, whose stability is maintained through an apsidal anti-alignment. For the Kepler-108 system, we find that the stability of its mutually inclined planets could be justified either solely by a mean-motion resonance, or in tandem with an inclination-type resonance. Going forward, dynamical analyses based on periodic orbits could yield better constrained orbital elements of near-resonant extrasolar systems when performed in parallel to the fitting of the observational data.

Impact of tides on the transit-timing fits to the TRAPPIST-1 system

Transit timing variations (TTVs) can be a very efficient way of constraining masses and eccentricities of multi-planet systems. Recent measurements of the TTVs of TRAPPIST-1 have led to an estimate of the masses of the planets, enabling an estimate of their densities and their water content. A recent TTV analysis using data obtained in the past two years yields a 34 and 13% increase in mass for TRAPPIST-1b and c, respectively. In most studies to date, a Newtonian N-body model is used to fit the masses of the planets, while sometimes general relativity is accounted for. Using the Posidonius N-body code, in this paper we show that in the case of the TRAPPIST-1 system, non-Newtonian effects might also be relevant to correctly model the dynamics of the system and the resulting TTVs. In particular, using standard values of the tidal Love number k2 (accounting for the tidal deformation) and the fluid Love number k2f (accounting for the rotational flattening) leads to differences in the TTVs of TRAPPIST-1b and c that are similar to the differences caused by general relativity. We also show that relaxing the values of tidal Love number k2 and the fluid Love number k2f can lead to TTVs which differ by as much as a few 10 s on a 3−4-yr timescale, which is a potentially observable level. The high values of the Love numbers needed to reach observable levels for the TTVs could be achieved for planets with a liquid ocean, which if detected might then be interpreted as a sign that TRAPPIST-1b and TRAPPIST-1c could have a liquid magma ocean. For TRAPPIST-1 and similar systems the models to fit the TTVs should potentially account for general relativity, for the tidal deformation of the planets, for the rotational deformation of the planets, and to a lesser extent for the rotational deformation of the star, which would add up to 7 × 2 + 1 = 15 additional free parameters in the case of TRAPPIST-1.

Masses of the Kepler-419 planets from transit timing variations analysis

We perform dynamical fits to the Transit Timing Variations (TTVs) of Kepler-419b. The TTVs from 17 Kepler quarters are obtained from Holczer et al (2016, ApJS 225,9). The dynamical fits are performed using the MultiNest Bayesian inference tool, coupled to an efficient symplectic N-body integrator. We find that the existing TTV data alone are able to uniquely constrain the planetary masses of Kepler-419b and c. Our estimates are in a good agreement with previous mass determinations that combined different techniques and observations, such as TTVs, radial velocity measurements, and the photoeccentric effect. As expected, however, our mass estimates have larger uncertainty. We study the global stability of the system within the parameters uncertainties to discard possible unstable solutions. We conclude that our method applied to the Holczer et al. data can provide reliable determinations of the planetary parameters. In the fore-coming work, we will use Holczer et al. (2016b) data to determine planetary parameters for a large set of Kepler systems.

Transiting Exoplanet Monitoring Project (TEMP). IV. Refined System Parameters, Transit Timing Variations, and Orbital Stability of the Transiting Planetary System HAT-P-25

We present eight new light curves of the transiting extra-solar planet HAT-P-25b obtained from 2013 to 2016 with three telescopes at two observatories. We use the new light curves, along with recent literature material, to estimate the physical and orbital parameters of the transiting planet. Specifically, we determine the mid-transit times (TC) and update the linear ephemeris, TC[0] = 2456418.80996 ± 0.00025 [BJDTDB] and P = 3.65281572 ± 0.00000095 days. We carry out a search for transit timing variations (TTVs), and find no significant TTV signal at the ΔT = 80 s-level, placing a limit on the possible strength of planet–planet interactions (TTVG). In the course of our analysis, we calculate the upper mass-limits of the potential nearby perturbers. Near the 1:2, 2:1, and 3:1 resonances with HAT-P-25b, perturbers with masses greater than 0.5, 0.3, and 0.5 M⊕ respectively, can be excluded. Furthermore, based on the analysis of TTVs caused by light travel time effect (LTTE) we also eliminate the possibility that a long-period perturber exists with Mp > 3000 MJ within a = 11.2 au of the parent star.

Transit timing variation and transmission spectroscopy analyses of the hot Neptune GJ3470b

GJ3470b is a hot Neptune exoplanet orbiting an M dwarf and the first sub-Jovian planet to exhibit Rayleigh scattering. We present transit timing variation (TTV) and transmission spectroscopy analyses of multi-wavelength optical photometry from 2.4-m and 0.5-m telescopes at the Thai National Observatory, and the 0.6-m PROMPT-8 telescope in Chile. Our TTV analysis allows us to place an upper mass limit for a second planet in the system. The presence of a hot Jupiter with a period of less than 10 days or a planet with an orbital period between 2.5 and 4.0 days are excluded. Combined optical and near-infrared transmission spectroscopy favour an H/He dominated haze (mean molecular weight 1.08$\pm$0.20) with high particle abundance at high altitude. We also argue that previous near-infrared data favour the presence of methane in the atmosphere of GJ3470b.

DOPPLER MONITORING OF THE WASP-47 MULTIPLANET SYSTEM

We present precise Doppler observations of WASP-47, a transiting planetary system featuring a hot Jupiter with both inner and outer planetary companions. This system has an unusual architecture and also provides a rare opportunity to measure planet masses in two different ways: the Doppler method, and the analysis of transit-timing variations (TTV). Based on the new Doppler data, obtained with the Planet Finder Spectrograph on the Magellan/Clay 6.5m telescope, the mass of the hot Jupiter is $370 \pm 29~M_{\oplus}$. This is consistent with the previous Doppler determination as well as the TTV determination. For the inner planet WASP-47e, the Doppler data lead to a mass of $12.2\pm 3.7~ M_{\oplus}$, in agreement with the TTV-based upper limit of $<$22~$M_{\oplus}$ ($95\%$ confidence). For the outer planet WASP-47d, the Doppler mass constraint of $10.4\pm 8.4~M_{\oplus}$ is consistent with the TTV-based measurement of $15.2^{+6.7}_{-7.6}~ M_{\oplus}$.

One of the closest exoplanet pairs to the 3:2 mean motion resonance: K2-19b and c

The K2 mission has recently begun to discover new and diverse planetary systems. In December 2014 Campaign 1 data from the mission was released, providing high-precision photometry for ~22000 objects over an 80 day timespan. We searched these data with the aim of detecting further important new objects. Our search through two separate pipelines led to the independent discovery of K2-19b \& c, a two-planet system of Neptune sized objects (4.2 and 7.2 $R_\oplus$), orbiting a K dwarf extremely close to the 3:2 mean motion resonance. The two planets each show transits, sometimes simultaneously due to their proximity to resonance and alignment of conjunctions. We obtain further ground based photometry of the larger planet with the NITES telescope, demonstrating the presence of large transit timing variations (TTVs), and use the observed TTVs to place mass constraints on the transiting objects under the hypothesis that the objects are near but not in resonance. We then statistically validate the planets through the \texttt{PASTIS} tool, independently of the TTV analysis.

Transit timing variation analysis in southern stars: the case of WASP-28

We present 4 new transit observations of the exoplanet WASP-28b observed between August 2011 and October 2013. Employing another 11 transits available in the literature we compute new ephemeris and redetermine the physical parameters of the star and the exoplanet. Considering 3 yrs of observations, we find no periodic TTVs or long-term variations of the inclination of the orbit, i, or the depth of the transit, k, that could be attributable to the presence of another planetary mass-body in the system. We also study the relations between i and k with different factors that characterize the light-curves. The fits suggest a possible weak correlation between k with the red noise factor, \beta, and the photometric noise rate, PNR, and a weak anticorrelation between i and PNR, although more points are needed to confirm these trends. Finally, the kinematic study suggests that WASP-28 is a thin disk star.

PlanetPack software tool for exoplanets detection: coming new features

AbstractWe briefly overview the new features of PlanetPack2, the forthcoming update of PlanetPack, which is a software tool for exoplanets detection and characterization from Doppler radial velocity data. Among other things, this major update brings parallelized computing, new advanced models of the Doppler noise, handling of the so-called Keplerian periodogram, and routines for transits fitting and transit timing variation analysis.

CHARACTERIZATION OF THE KOI-94 SYSTEM WITH TRANSIT TIMING VARIATION ANALYSIS: IMPLICATION FOR THE PLANET-PLANET ECLIPSE

The KOI-94 system is a closely-packed, multi-transiting planetary system discovered by the Kepler space telescope. It is known as the first system that exhibited a rare event called a "planet-planet eclipse (PPE)," in which two planets partially overlap with each other in their double-transit phase. In this paper, we constrain the parameters of the KOI-94 system with an analysis of the transit timing variations (TTVs). Such constraints are independent of the radial velocity (RV) analysis recently performed by Weiss and coworkers, and valuable in examining the reliability of the parameter estimate using TTVs. We numerically fit the observed TTVs of KOI-94c, KOI-94d, and KOI-94e for their masses, eccentricities, and longitudes of periastrons, and obtain the best-fit parameters including $m_{\rm c} = 9.4_{-2.1}^{+2.4} M_{\oplus}$, $m_{\rm d} = 52.1_{-7.1}^{+6.9} M_{\oplus}$, $m_{\rm e} = 13.0_{-2.1}^{+2.5} M_{\oplus}$, and $e \lesssim 0.1$ for all the three planets. While these values are mostly in agreement with the RV result, the mass of KOI-94d estimated from the TTV is significantly smaller than the RV value $m_{\rm d} = 106 \pm 11 M_{\oplus}$. In addition, we find that the TTV of the outermost planet KOI-94e is not well reproduced in the current modeling. We also present analytic modeling of the PPE and derive a simple formula to reconstruct the mutual inclination of the two planets from the observed height, central time, and duration of the brightening caused by the PPE. Based on this model, the implication of the results of TTV analysis for the time of the next PPE is discussed.

TRANSIT TIMING OBSERVATIONS FROM KEPLER . I. STATISTICAL ANALYSIS OF THE FIRST FOUR MONTHS

The architectures of multiple planet systems can provide valuable constraints on models of planet formation, including orbital migration, and excitation of orbital eccentricities and inclinations. NASA's Kepler mission has identified 1235 transiting planet candidates (Borcuki et al 2011). The method of transit timing variations (TTVs) has already confirmed 7 planets in two planetary systems (Holman et al. 2010; Lissauer et al. 2011a). We perform a transit timing analysis of the Kepler planet candidates. We find that at least ~12% of planet candidates currently suitable for TTV analysis show evidence suggestive of TTVs, representing at least ~65 TTV candidates. In all cases, the time span of observations must increase for TTVs to provide strong constraints on planet masses and/or orbits, as expected based on n-body integrations of multiple transiting planet candidate systems (assuming circular and coplanar orbits). We find that the fraction of planet candidates showing TTVs in this data set does not vary significantly with the number of transiting planet candidates per star, suggesting significant mutual inclinations and that many stars with a single transiting planet should host additional non-transiting planets. We anticipate that Kepler could confirm (or reject) at least ~12 systems with multiple transiting planet candidates via TTVs. Thus, TTVs will provide a powerful tool for confirming transiting planets and characterizing the orbital dynamics of low-mass planets. If Kepler observations were extended to at least six years, then TTVs would provide much more precise constraints on the dynamics of systems with multiple transiting planets and would become sensitive to planets with orbital periods extending into the habitable zone of solar-type stars.