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Article

Update on WASP-19

1
Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Box 43, 22100 Lund, Sweden
2
Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain
3
Instituto de Astrofísica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain
*
Author to whom correspondence should be addressed.
Universe 2024, 10(1), 12; https://doi.org/10.3390/universe10010012
Submission received: 11 December 2023 / Revised: 24 December 2023 / Accepted: 25 December 2023 / Published: 27 December 2023
(This article belongs to the Special Issue The Royal Road: Eclipsing Binaries and Transiting Exoplanets)

Abstract

:
Tidal interaction between a star and a close-in massive exoplanet causes the planetary orbit to shrink and eventually leads to tidal disruption. Understanding orbital decay in exoplanetary systems is crucial for advancing our knowledge of planetary formation and evolution. Moreover, it sheds light on the broader question of the long-term stability of planetary orbits and the intricate interplay of gravitational forces within stellar systems. Analyzing Transiting Exoplanet Survey Satellite (TESS) data for the ultra-short period gas giant WASP-19, we aim to measure orbital period variations and constrain the stellar tidal quality parameter. For this, we fitted the TESS observations together with two WASP-19 transits observed using the Las Cumbres Observatory Global Telescope (LCOGT) and searched for orbital decay in combination with previously published transit times. As a result, we find a deviation from the constant orbital period at the 7 σ level. The orbital period changes at a rate of P ˙ = 3.7 ± 0.5 ms year 1 , which translates into a tidal quality factor of Q = ( 7 ± 1 ) × 10 5 . We additionally modeled WASP-19 b’s phase curve using the new TESS photometry and obtained updated values for the planet’s eclipse depth, dayside temperature, and geometric albedo. We estimate an eclipse depth of 520 ± 60 ppm, which is slightly higher than previous estimates and corresponds to a dayside brightness temperature of 2400 ± 60 K and geometric albedo of 0.20 ± 0.04 .

1. Introduction

Ultra-short period (USP) gas giants, a class of exoplanets characterized by their mass ( M p > 0.5 M J ) and proximity to their host stars ( P < 1 day ), provide a unique opportunity to study the effect of tidal interactions on the evolution of stellar and planetary systems (e.g., [1]). The proximity to their hosts also means that their atmospheres can be studied using phase curves, even in the optical passbands (e.g., [2]). Unfortunately, only a few planets have been discovered in this regime, including TOI-2109 b [3], NGTS-10 b [4], and WASP-19 b [5], all exhibiting the shortest orbital periods ( P < 0.8 day ) detected so far. This paucity of USP hot Jupiters may be explained by tidal interactions that ultimately lead to tidal disruption of the planet [6,7].
Such close-in planets that are not in tidal equilibrium are expected to gradually spiral towards their host stars due to tidal dissipation (e.g., [8,9]). This phenomenon, known as tidal orbital decay, means that, due to tides raised by a close-in planet, the tidal bulge of the star exerts a torque on the planet. This torque transfers energy and angular momentum from the planet’s orbit to the stellar spin (e.g., [10,11]). Consequently, the stellar rotational period decreases, and the orbit of the planet shrinks [12].
Orbital decay can be detected through its effect on the timing of transits due to its change in orbital period (e.g., [13,14]). This approach found evidence for orbital decay in WASP-12 b [15,16,17,18,19,20] and Kepler-1658 b [21]. Among the USP gas giant planets, WASP-19 b, with an orbital period of 0.78 days, has emerged as a prime target for the search for orbital decay using transit timings [22,23,24,25]. Some studies predict a measurable effect on WASP-19 b’s transit times after 10 years. The magnitude of the transit shift, however, varies from 11 s [1] to 70 s [14] to 257 s [23].
The analysis of WASP-19 b’s transit timings and the exploration of potential orbital decay have been subjects of numerous studies, yielding conflicting outcomes [20,24,26,27,28,29,30,31]. While some studies report significant orbital period changes [24,28], others find no evidence for a shrinking orbit [20,26,27,29,30,31]. Stellar spot activity, as detected by several studies [26,31,32], may contribute to these inconsistencies, as highlighted by Patra et al. [24]. Given the divergent findings, continued monitoring of WASP-19 b’s transit times and further investigations into potential period changes are essential.
WASP-19 b’s short orbital period also makes it an excellent target for phase curve studies. The dayside of the planet can be expected to be hot enough for thermal emission to be detected in the optical TESS passband, and recent studies hint that the planet may have a higher albedo than what is generally expected for ultra-hot Jupiters, also leading to a strong reflected light signal [33,34].
Here, we present an analysis of the transit times of WASP-19 b using new ground-based and space-based observations to search for orbital decay and to set constraints on the tidal quality factor. Our analysis further improves upon the previous studies by using a logistic error distribution to model the observational errors instead of a normal distribution. This approach makes the estimation of the orbital decay posterior more robust against outliers arising from stellar activity and instrumental sources. We additionally present a phase curve analysis that is based on the new TESS photometry used in the orbital decay analysis. The previous TESS WASP-19 b phase curve analysis by Wong et al. [33] was based on the TESS Sector 9 light curve, while the analysis of Eftekhar and Adibi [34] used TESS Sectors 9 and 36. We improve upon these by modeling TESS Sectors 9, 36, 62, and 63 jointly without phase folding or pre-whitening of the photometry and by representing the stellar variability as a Gaussian Process (GP) with hyperparameters as free parameters in the posterior sampling.

2. Observation and Data Reduction

2.1. TESS  Photometry

The Transiting Exoplanet Survey Satellite (TESS; [35]) observed 115 transits of WASP-19 b with a two-minute cadence during TESS Sectors 9, 39, 62, and 63. The TESS Presearch Data Conditioning (PDC) photometry [36,37,38], generated by the Science Processing Operations Center (SPOC) pipeline [39], was utilized. The photometry exhibits an average point-to-point (ptp) scatter of 3000 ppm.

2.2. LCOGT  Photometry

We observed four full transits of WASP-19 b with the Sinistro cameras installed in the Las Cumbres Observatory Global Telescope ([40]; LCOGT) network 1.0 m telescopes. The first transit was observed from the South African Astronomical Observatory (SAAO) on 27 December 2022, the second from the Cerro Tololo Inter-American Observatory (CTIO) on 29 December 2022, the third from CTIO on 4 December 2023, and the fourth from SAAO on 13 December 2023. The observations were scheduled through TESS Transit Finder, a customized version of the Tapir software package [41], spanning three hours centered around the expected transit center. Sloan i passband was used with 20 s exposure times, resulting in average ptp scatters of 2400, 1400, 2000, and 2400 ppm. The difference in the scatter can be attributed to observing conditions. The raw frames were reduced with the standard LCOGT BANZAI pipeline [42], and the relative photometry was computed using our own LCOGT photometry pipeline based on the MuSCAT2 photometry pipeline [43].

3. Theory and Numerical Methods

3.1. Estimation of Transit Center Times

The direct detection of orbital decay is possible through its effect on the transit times, as suggested by Ragozzine and Wolf [13] and Birkby et al. [14]. Orbital decay will cause a shift in the transit center times following Ragozzine and Wolf [13]:
T mid T 0 + N P + 1 2 N 2 P P ˙ ,
where T mid is the transit center time, T 0 is the zero epoch, N is the transit number, P is the orbital period, and  P ˙ = d P / d t is the change in the orbital period over time.
We searched for long-term transit variations resulting from orbital decay in WASP-19 b’s transit times. For this, we simultaneously fitted TESS photometry with the two LCOGT transits using the Python Tool for Transit Variation (PyTTV) to estimate transit center times, following the approach described in Korth et al. [44]. The transits from TESS and LCOGT are modeled with the quadratic transit model by Mandel and Agol [45], incorporating the Taylor-series expansion from Parviainen and Korth [46] as implemented in PyTransit  [47]. The fit uses orbital period, P, zero epoch T 0 , planet radius relative to stellar radius R p / R k , transit center times T c , and impact parameter b = a / R cos i , where a is the semi-major axis, R is the radius of the star, and i is the orbital inclination, as free parameters. Shared parameters during the fit included quadratic limb darkening parameters q 1 , q 2 , as introduced in Kipping [48], and the stellar density ρ . The LCOGT observations were carried out in the Sloan i band that is similar enough to the TESS band that we do not need to care about the differences in limb darkening between the two datasets. Thus, we used one set of limb darkening coefficients shared by the TESS and LCOGT data. To address known stellar activity in the WASP-19 b light curve data, the baseline was modeled as a Gaussian Process (GP) with a Matérn 3/2 kernel, as implemented in celerite  [49]. We set wide normal priors on P, T 0 , and k, where the prior means correspond to the values reported in Hebb et al. [5]. Uniform priors were used for other parameters, and parameter posteriors were estimated through Markov chain Monte Carlo (MCMC) sampling as implemented in emcee  [50].
We combined the newly estimated transit center times with those reported in Kokori et al. [28] as part of the ExoClock project [51,52] and in Petrucci et al. [27] to extend our baseline. Kokori et al. [28] already provided transit center estimates for TESS Sectors 9 and 36. However, as we simultaneously fit these sectors with the new Sectors 62 and 63, not covered by their dataset, along with LCOGT observations, we consequently excluded their TESS center times and utilized our calculated values instead. Additionally, we incorporated center times observed and published by Mancini et al. [26] and Patra et al. [24], which were not part of the ExoClock collection. A list of the transit times is reported in Table A1.

3.2. Estimation of Orbital Period Change

We estimate the change of WASP-19 b’s orbital period over time, P ˙ , using a basic Bayesian parameter estimation approach where we infer the posterior densities for Equation (1) parameters given our transit center data set. The unnormalized log posterior probability density is defined as:
log P ( θ | t , σ ) = log P ( θ ) + log P ( t , σ | θ ) ,
where θ is a vector containing the model parameters T 0 , P, and  P ˙ ; t is a vector containing the transit center times; σ is a vector containing the center time uncertainties; log P is the log prior density; and log L is the log likelihood. We assume the transit center uncertainties are independent and follow a logistic distribution, which leads to a log likelihood:
log P ( t , σ | θ ) = i log e ( t i m i ) / s i s i 1 + e ( t i m i ) / s i ,
where s i = σ i 3 / π , and  m i are the transit mid-center time model values (Equation (1)). We use a logistic error distribution instead of a normal one because its heavier tails make it more robust to individual outliers and because its scale parameter, s, is directly related to the distribution’s variance.
We set weakly informative normal priors on the zero epoch, period, and period change. For zero epoch, we use N ( μ = 2457518.131796 , σ = 0.01 ) , where the value corresponds to the measured transit center time nearest the center of the time span covered by the observations. For period, we use N ( μ = 0.7888399 , σ = 0.001 ) based on Hebb et al. [5]. Finally, for  P ˙ , we use a wide zero-centered prior, N ( μ = 0 , σ = 10 8 ) . The role of the priors is mainly to help the optimizer and the MCMC sampler, and we checked that the priors did not significantly constrain the posteriors after the MCMC sampling phase.
We inferred the posterior densities for Equation (1) parameters by first finding the global posterior mode using a differential evolution global optimizer implemented in PyTransit. Next, we obtained a sample from the posterior using the emcee MCMC sampler started with a parameter vector population created by the differential evolution optimizer. We used a parameter vector population size of 50, ran the emcee sampler over 50,000 iterations, and created the final posterior from the last 10,000 iterations using a thinning factor of 50. This led to a final sample size of 10,000. Considering the simplicity of the model, the optimization and MCMC sampling take less than a minute of computing time on a normal laptop computer.

3.3. Estimation of Tidal Quality Factor

Orbital decay translates into a constant change in the orbital period under the assumption of zero stellar obliquity, negligible tidal dissipation, circularized orbits, and synchronized stellar spin within the simplified constant phase lag model [16,53], as:
P ˙ = 27 π 2 Q M p M R a 5 ,
where Q is the tidal quality factor defined as Q = 3 Q / 2 k 2 , in [54], with the dissipation factor Q = 1 / Δ t assuming a contact time lag model and a stellar Love number k 2 , , M p is the planet mass, M is the stellar mass, and R / a is the stellar radius relative to the semi-major axis. Solving for Q , we obtain:
Q = 27 π 2 M p M R a 5 1 P ˙ ,
where the planet–star mass ratio, M p / M , is obtained from RV mass measurements, the scaled semi-major axis, a / R , from transit light curve modeling, and the change of orbital period in time, P ˙ , from the transit center time modeling described earlier in Section 3.1.

3.4. Phase Curve Analysis

The phase curve analysis closely follows the analyses detailed in [2,55]. We change the modeling approach slightly by assuming that the dayside brightness temperature equals its equilibrium temperature: [56]
T Eq = T a s 1 / 2 f ( 1 A B ) 1 / 4 ,
where T is the stellar effective temperature, a s is the scaled semi-major axis ( a s = a / R ), f is the heat redistribution factor, and A B is the Bond albedo. We fix the effective stellar temperature to 5500 K [5] and set a normal prior on the heat redistribution factor, N ( 0.66 , 0.02 ) , to focus on the solutions with low heat redistribution, since previous studies suggest that WASP-19 b’s nightside is cool [33,34].

4. Results

The results from the transit center time analysis are shown in Figure 1. We find a deviation from the constant period at a 7 σ level. The orbital period changes at a rate of P ˙ = 3.7 ± 0.5 ms year 1 , which translates into a tidal quality factor of Q = ( 7 ± 1 ) × 10 5 , assuming a planet–star mass ratio of 0.00116 ± 0.00005 taken from [26] and a scaled semi-major axis of 3.57 ± 0.03 from our transit light curve modeling (Table 1). The posterior distributions for both quantities are shown in Figure 2.
We show our final phase curve model in Figure 3. We obtain a TESS passband eclipse depth, D e , of 520 ± 60 ppm, corresponding to a geometric albedo, A g , of 0.20 ± 0.04 and equilibrium temperature of 2400 ± 60 K. We do not detect any offsets in the hotspot location and cannot claim that the TESS photometry would be able to constrain the planet’s nightside brightness temperature. We also obtain improved stellar, orbital, and planetary parameters from the analysis and list them in Table 1.

5. Discussion and Conclusions

We find a significant orbital decay of P ˙ = ( 1.2 ± 0.1 ) × 10 10 for WASP-19 b using the TESS, LCOGT, and archival transit times, which agrees within the uncertainties with the results from Patra et al. [24] of P ˙ = ( 2.06 ± 0.42 ) × 10 10 and Kokori et al. [28] of P ˙ = ( 0.87 ± 0.13 ) × 10 10 . In contrast, Rosário et al. [29] found no significant evidence for orbital decay, with a rate of P ˙ = ( 0.35 ± 0.22 ) × 10 10 . Petrucci et al. [27] also failed to detect a statistically significant estimate for P ˙ , but our estimate of P ˙ = 3.7 ± 0.5 ms year 1 agrees with their upper limit of P ˙ = 2.3 ms year 1 . Ivshina and Winn [30] found a variation near the 3 σ limit of P ˙ = 3.54 ± 1.18 ms year 1 that agrees well with our values for the orbital decay of WASP-19 b. Finally, Yeh et al. [20] observed variations in transit times but did not attribute them to orbital decay.
During the writing of this paper, another study was published that searched for long-term orbit period variations of hot Jupiters using the latest TESS Sectors 62 and 63, including WASP-19 b [58]. They found different values for P ˙ depending on the inclusion of two transit center times published by [27,32] and reported the detection as marginal. Our approach is less sensitive to individual outliers due to our use of a robust error distribution. Even then, testing how our P ˙ estimate changes by removing the same transit center time estimates as removed by Wang et al. [58] leads to qualitatively similar behavior as by Wang et al. [58]: our P ˙ value changes by 1 σ after the removal of the point at 2,457,796.59224 but agrees closely again with the original P ˙ estimate after the removal of the point at 2,457,448.71292. This sensitivity can be explained by the nature of the two estimates: the first is from transmission spectroscopy observations observed with the Hubble Space Telescope (HST) by Espinoza et al. [32], and the second is from similar observations carried out with the Very Large Telescope (VLT) by Sedaghati et al. [59]. Both transit center time estimates have six times smaller uncertainties (≈6 s) than the median uncertainty in the final dataset (≈40 s), so the two points can be expected to have an impact on the final P ˙ result.
As reported in previous studies [24,26,31,32], the differences in P ˙ might be attributed to stellar activity. One of our LCOGT observations shows a significant 6 ± 1 min deviation from the transit center time expected based on our best-fit linear ephemeris (see Figure 4, LCOGT observation 29.12.2022). The light curve shows slightly higher amplitude baseline variations than the other LCOGT-observed light curves, but the amplitude of the center time discrepancy is still curious. The Gaussian Process baseline variability should be reflected in the transit center time posteriors (that is, the transit center posterior should still agree with the linear ephemeris within uncertainties), and our analysis does not support the conclusion that the discrepancy would be due to photometric variability.
A parameter to quantify orbital decay is the tidal quality factor Q , as introduced by Goldreich and Soter [53]. This factor characterizes the efficiency of energy dissipation during tidal interactions. A higher Q value indicates that the star is less efficient at dissipating tidal energy, resulting in weaker tidal forces and slower changes in the system over time. Conversely, a lower Q value suggests more efficient dissipation, leading to stronger tidal forces and faster evolution of the system. The exact value for Q for a particular star is uncertain, and there is no way to measure it directly except via orbital decay (e.g., [14]). Theoretical modeling of Q is also challenging because the strength of tidal decay depends on various factors, encompassing stellar properties like age, mass, interior structure, and rotation rate, as well as planet properties like orbital period and mass. Additional influences involve the conversion of tidal energy to heat, as well as the mass of the stellar convective fluid envelope (e.g., [1,23,60]).
Considering our P ˙ value as a secure detection of orbital decay, we derived a tidal quality factor of Q = ( 7 ± 1 ) × 10 5 . This value agrees with the Q range of 10 5 < Q < 10 6 for gas giants in our solar system [53,61]. Several authors have calculated theoretical Q values of magnitude 10 6 for WASP-19 [62,63,64]. However, our Q value agrees more with the calculations from Essick and Weinberg [23], who derived a range of Q values from 10 5 to 10 6 . Additionally, Weinberg et al. [25] estimated Q < 10 6 for systems similar to WASP-19 b with M < 1.1 M and P < 1 day, in agreement with our Q .
A decreasing orbital period can also be caused by mechanisms other than orbital decay. One of them is the Rømer effect, which is a light–time effect (LTE) induced by a wide-orbit companion [65]. Whether the observed period change is caused by the Rømer effect instead of orbital decay can only be solved through radial velocity measurements over a long time span. Another mechanism that can cause long-term TTVs is produced through apsidal precession of eccentric orbits [13]. Whether WASP-19 b’s eccentricity is large enough to produce apsidal precession can be solved by future eclipse center time observations. While orbital decay leads to decreasing periods of the transit and eclipse times, apsidal precession leads to an anti-correlated period trend between transit and eclipse center times. In addition, Watson and Marsh [66] calculated that the Applegate effect can have a measurable influence on USP gas giants depending on the stellar activity cycle. Whether this is the case for WASP-19 b can be tested by extending the observing time span to several stellar activity cycles.
Our secondary eclipse depth of 520 ± 60 ppm agrees with the value of 494 48 + 59 ppm by Eftekhar and Adibi [34] and the value of 470 110 + 130 ppm by Wong et al. [33]. Our uncertainties are similar to those by Eftekhar and Adibi [34], even when their analysis was based on only two TESS Sectors, but this can be explained by our differences in baseline modeling and data pre-whitening. Eftekhar and Adibi [34] detrend the TESS photometry before the phase curve analysis, which can easily lead to underestimated uncertainties, since the uncertainties in the stellar variability and systematics are not included in the analysis robustly. Our approach using GPs to model the baseline flux should be more reliable and also lead to more reliable uncertainties.
We repeated the phase curve analysis using individual TESS Sectors to test for possible time variations in any of the model parameters. The analyses did not show any variability, and it appears that the parameters are stable from TESS Sector to Sector.

Author Contributions

Conceptualization, J.K. and H.P.; methodology, J.K. and H.P.; software, J.K. and H.P.; validation, J.K. and H.P.; formal analysis, J.K. and H.P.; investigation, J.K. and H.P.; resources, J.K. and H.P.; data curation, J.K.; writing—original draft preparation, J.K.; writing—review and editing, J.K. and H.P.; visualization, H.P.; supervision, J.K.; project administration, J.K.; funding acquisition, J.K. and H.P. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Swedish National Space Agency (SNSA; DNR 2020-00104), the Swedish Research Council (VR: Etableringsbidrag 2017-04945), and by the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC2021-031798-I.

Data Availability Statement

The TESS data presented in this study are openly available at MAST. Our LCOGT observations can be found in the GitHub repository connected to this paper.

Acknowledgments

This paper includes data collected by the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the TESS mission is provided by NASA’s Science Mission Directorate. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5–26555. This work makes use of observations from the Las Cumbres Observatory global telescope network.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
CTIOCerro Tololo Inter-American Observatory
GPGaussian Process
LCOGTLas Cumbres Observatory Global Telescope
MCMCMarkov chain Monte Carlo
PDCPresearch Data Conditioning
ptppoint-to-point
PyTTVPython Tool for Transit Variation
SAAOSouth African Astronomical Observatory
SPOCScience Processing Operations Center
TESSTransiting Exoplanet Survey Satellite
USPultra-short period

Appendix A

Table A1. Transit center times and their uncertainties with epochs calculated from reference time 2,457,518.131796 days and an orbital period of 0.78884 days.
Table A1. Transit center times and their uncertainties with epochs calculated from reference time 2,457,518.131796 days and an orbital period of 0.78884 days.
Epoch T mid [ BJD TBD ] σ T mid [ BJD TBD ]Reference
−34772,454,775.338000.00020[28]
−34242,454,817.146370.00021[28]
−29782,455,168.969000.00060[28]
−28732,455,251.797070.00014[28]
−28722,455,252.585900.00010[28]
−28682,455,255.741240.00012[28]
−28632,455,259.684590.00036[27]
−28452,455,273.882530.00072[27]
−27682,455,334.625400.00021[28]
−27632,455,338.569260.00023[28]
−27442,455,353.556590.00024[28]
−27252,455,368.542850.00212[28]
−25082,455,539.723300.00030[28]
−24702,455,569.698300.00036[28]
−24562,455,580.741550.00057[27]
−24512,455,584.686840.00019[27]
−24512,455,584.686890.00024[27]
−24392,455,594.151880.00168[28]
−24302,455,601.251640.00071[28]
−24282,455,602.831410.00046[28]
−24252,455,605.194140.00180[26]
−24232,455,606.774670.00022[28]
−24222,455,607.562440.00033[28]
−24032,455,622.550590.00026[28]
−24012,455,624.127870.00142[28]
−23902,455,632.806140.00025[28]
−23612,455,655.682220.00045[28]
−23422,455,670.669760.00064[28]
−23332,455,677.770380.00195[28]
−23192,455,688.812010.00333[26]
−23182,455,689.602800.00030[28]
−23142,455,692.756740.00255[26]
−23132,455,693.546390.00013[28]
−23002,455,703.799330.00411[26]
−22992,455,704.590780.00034[28]
−22942,455,708.534950.00015[28]
−20682,455,886.812340.00208[26]
−20562,455,896.276110.00210[26]
−20322,455,915.209800.00065[28]
−20272,455,919.154850.00103[28]
−20232,455,922.309660.00555[26]
−19252,455,999.616340.00029[27]
−19252,455,999.616490.00020[27]
−19252,455,999.616360.00016[27]
−19252,455,999.616060.00019[27]
−19252,455,999.616140.00030[27]
−19252,455,999.616340.00020[27]
−19252,455,999.616370.00013[27]
−19252,455,999.616510.00022[27]
−19252,455,999.616750.00033[27]
−18972,456,021.703580.00016[27]
−18972,456,021.703340.00017[27]
−18972,456,021.703630.00011[27]
−18972,456,021.704080.00012[27]
−18972,456,021.703800.00013[27]
−18972,456,021.703230.00017[27]
−18972,456,021.703930.00012[27]
−18972,456,021.703710.00014[27]
−18972,456,021.704290.00048[27]
−18872,456,029.592500.00035[28]
−18822,456,033.537130.00074[27]
−18822,456,033.538000.00040[27]
−18822,456,033.538370.00029[27]
−18442,456,063.511700.00030[28]
−15132,456,324.620530.00061[27]
−15002,456,334.872070.00052[27]
−14292,456,390.880330.00053[27]
−13712,456,436.632880.00065[27]
−10122,456,719.826230.00055[27]
−9872,456,739.547360.00030[27]
−9872,456,739.547960.00005[28]
−9452,456,772.677890.00052[24]
−9402,456,776.623290.00007[28]
−6852,456,977.776470.00010[27]
−4332,457,176.564740.00009[28]
−1262,457,418.736820.00023[27]
−882,457,448.712920.00008[27]
02,457,518.131800.00040[27]
362,457,546.530200.00038[24]
362,457,546.529750.00028[27]
412,457,550.472700.00040[27]
742,457,576.504700.00070[27]
2622,457,724.807830.0008[27]
2812,457,739.794150.00050[27]
3292,457,777.657430.00100[27]
3382,457,784.758920.00020[27]
3482,457,792.647530.00080[27]
3532,457,796.592240.00006[28]
4192,457,848.655590.00007[28]
4292,457,856.543840.00011[28]
7122,458,079.785670.00020[27]
7502,458,109.763840.00200[27]
8822,458,213.887470.00024[27]
12802,458,527.845760.00050[27]
13012,458,544.411590.00049This work
13022,458,545.198780.00046This work
13032,458,545.988990.00042This work
13042,458,546.777300.00044This work
13052,458,547.566850.00044This work
13062,458,548.355040.00042This work
13072,458,549.144730.00047This work
13072,458,549.145100.00050[28]
13082,458,549.931620.00050This work
13092,458,550.721340.00053This work
13102,458,551.510010.00046This work
13112,458,552.299080.00048This work
13122,458,553.088020.00050This work
13132,458,553.876650.00045This work
13142,458,554.665540.00049This work
13152,458,555.454000.00046This work
13182,458,557.821440.00048This work
13192,458,558.647530.04132This work
13202,458,559.399480.00048This work
13212,458,560.186810.00044This work
13222,458,560.977470.00047This work
13232,458,561.765520.00046This work
13242,458,562.554100.00047This work
13252,458,563.343030.00047This work
13262,458,564.131850.00044This work
13272,458,564.921000.00044This work
13282,458,565.709450.00049This work
13292,458,566.498930.00045This work
13302,458,567.287760.00046This work
13312,458,568.076480.00047This work
13472,458,580.697240.00040[24]
13522,458,584.641670.00030[27]
17022,458,860.736400.00050[28]
17162,458,871.779200.00070[28]
17212,458,875.723300.00040[28]
17262,458,879.668000.00040[28]
17312,458,883.611500.00060[28]
17402,458,890.712600.00040[28]
17492,458,897.809800.00060[28]
17502,458,898.599800.00060[28]
17542,458,901.756200.00040[28]
17592,458,905.699400.00030[28]
18022,458,939.620400.00040[28]
18452,458,973.540000.00040[28]
18502,458,977.484400.00040[28]
21332,459,200.725400.00030[28]
21422,459,207.826500.00040[28]
21712,459,230.701400.00030[28]
21802,459,237.801000.00040[28]
21992,459,252.788300.00040[28]
22042,459,256.732400.00050[28]
22322,459,278.820600.00050[28]
22372,459,282.763960.00041This work
22382,459,283.553580.00051This work
22392,459,284.342420.00056This work
22402,459,285.130520.00050This work
22412,459,285.919930.00047This work
22422,459,286.708880.00048This work
22432,459,287.496880.00050This work
22442,459,288.286080.00045This work
22452,459,289.075040.00043This work
22462,459,289.863650.00048This work
22472,459,290.652070.00048This work
22482,459,291.441180.00051This work
22492,459,292.229790.00048This work
22532,459,295.385240.00052This work
22542,459,296.175330.00049This work
22552,459,296.962800.00048This work
22562,459,297.750920.00051This work
22572,459,298.540220.00050This work
22582,459,299.329070.00047This work
22592,459,300.118610.00054This work
22602,459,300.907690.00045This work
22612,459,301.696470.00048This work
22622,459,302.484670.00049This work
22632,459,303.274110.00049This work
22642,459,304.063900.00049This work
22652,459,304.852150.00045This work
22662,459,305.640410.00049This work
22712,459,309.584300.00040[28]
22762,459,313.529500.00040[28]
22942,459,327.727700.00090[28]
25352,459,517.840200.00040[28]
30722,459,941.445520.00030This work (LCOGT)
30752,459,943.816050.00035This work (LCOGT)
31332,459,989.559850.10613This work
31342,459,990.353390.00049This work
31352,459,991.141690.00044This work
31362,459,991.930210.00053This work
31372,459,992.718700.00047This work
31382,459,993.507500.00043This work
31392,459,994.296610.00053This work
31402,459,995.086150.00090This work
31412,459,995.874440.00049This work
31422,459,996.663700.00045This work
31432,459,997.452440.00051This work
31442,459,998.241350.00046This work
31452,459,999.030330.00050This work
31462,459,999.817910.00041This work
31472,460,000.607730.00045This work
31502,460,002.975040.00046This work
31512,460,003.763060.00047This work
31522,460,004.551500.00047This work
31532,460,005.340000.00049This work
31542,460,006.129100.00046This work
31552,460,006.919090.00048This work
31562,460,007.664040.03918This work
31572,460,008.496370.00051This work
31582,460,009.284860.00049This work
31592,460,010.073790.00047This work
31602,460,010.862130.00044This work
31612,460,011.651410.00046This work
31622,460,012.441330.00049This work
31632,460,013.229120.00046This work
31642,460,014.017200.00043This work
31652,460,014.807060.00045This work
31662,460,015.595840.00049This work
31672,460,016.384770.00049This work
31682,460,017.172700.00043This work
31692,460,017.961710.00049This work
31702,460,018.751170.00051This work
31712,460,019.539590.00050This work
31722,460,020.328460.00047This work
31732,460,021.117280.00054This work
31742,460,021.905570.00050This work
31752,460,022.694650.00046This work
31762,460,023.484260.00046This work
31772,460,024.272670.00049This work
31782,460,025.062500.00051This work
31792,460,025.850620.00049This work
31802,460,026.639060.00048This work
31812,460,027.499010.03815This work
31822,460,028.217240.00045This work
31832,460,029.004640.00044This work
31842,460,029.794920.00046This work
31852,460,030.583640.00045This work
31862,460,031.371990.00048This work
31872,460,032.161430.00047This work
31882,460,032.949540.00048This work
31892,460,033.739130.00046This work
31902,460,034.527580.00050This work
31912,460,035.316150.00052This work
31922,460,036.105650.00050This work
31932,460,036.893070.00051This work
31942,460,037.682930.00045This work
31952,460,038.471640.00046This work
31962,460,039.259660.00049This work
31972,460,040.049130.00049This work
31982,460,040.839060.00056This work
35062,460,283.800470.00032This work (LCOGT)
35172,460,292.478020.00035This work (LCOGT)

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Figure 1. Posterior TTV model with blue points, crosses, and dots showing the individual transit center time values for archival data, fitted TESS observations, and fitted LCOGT observations, respectively. Black dots with error bars show the transit center times binned to two years, the solid black line shows the median posterior TTV model, and the orange shading shows the 68% central posterior limits.
Figure 1. Posterior TTV model with blue points, crosses, and dots showing the individual transit center time values for archival data, fitted TESS observations, and fitted LCOGT observations, respectively. Black dots with error bars show the transit center times binned to two years, the solid black line shows the median posterior TTV model, and the orange shading shows the 68% central posterior limits.
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Figure 2. Posterior densities for P ˙ and Q . The derivation of these posteriors is detailed in Section 3.2 and Section 3.3.
Figure 2. Posterior densities for P ˙ and Q . The derivation of these posteriors is detailed in Section 3.2 and Section 3.3.
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Figure 3. Phase curve of WASP-19 b. The upper panel shows the full phase curve, including the transit, and the lower plot shows a zoomed view centered around the secondary eclipse. We have removed the median Gaussian Process baseline model from the photometry and phase-folded and binned it for visualization.
Figure 3. Phase curve of WASP-19 b. The upper panel shows the full phase curve, including the transit, and the lower plot shows a zoomed view centered around the secondary eclipse. We have removed the median Gaussian Process baseline model from the photometry and phase-folded and binned it for visualization.
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Figure 4. The newly-fitted WASP-19 b transits observed with TESS and the LCOGT 1 m telescopes. We center the TESS transits for each Sector around their fitted transit center times and bin the centered photometry over five minutes for visualization, but show the LCOGT transits individually without binning. The blue dots show the TESS photometry with the GP baseline removed, and black points show the binned TESS photometry and the LCOGT photometry with the GP baseline removed; the black line shows the transit model; the dashed gray vertical line shows the expected transit center based on best-fit linear ephemeris; and the solid black vertical line marks T T c = 0 .
Figure 4. The newly-fitted WASP-19 b transits observed with TESS and the LCOGT 1 m telescopes. We center the TESS transits for each Sector around their fitted transit center times and bin the centered photometry over five minutes for visualization, but show the LCOGT transits individually without binning. The blue dots show the TESS photometry with the GP baseline removed, and black points show the binned TESS photometry and the LCOGT photometry with the GP baseline removed; the black line shows the transit model; the dashed gray vertical line shows the expected transit center based on best-fit linear ephemeris; and the solid black vertical line marks T T c = 0 .
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Table 1. Stellar and planetary parameters for WASP-19 system from the literature and our analyses.
Table 1. Stellar and planetary parameters for WASP-19 system from the literature and our analyses.
Literature stellar and planetary parameters
M [M ] R [R ] T eff [K] log g [Fe/H]
0.935 ± 0.042 a 1.018 ± 0.015 a 5500 ± 100 b 4.3932 ± 0.0067 a 0.02 ± 0.09 b
P rot [days]Age [Gyr]e M p [M Jup ]
11.76 ± 0.09 c 11.5 2.7 + 2.8 c < 0.02 d 1.139 ± 0.036 a
Fitted parameters
P [days] T 0 [days] R p / R a / R b
0.78883894 ± 6 × 10 8 2 , 455 , 168.9690 ± 0.0003 0.146 ± 0.001 3.57 ± 0.03 0.65 ± 0.01
ρ [ g cm 3 ] A g D e [ppm] P ˙ [ ms year 1 ] Q
1.39 ± 0.03 0.20 ± 0.04 520 ± 60 3.7 ± 0.5 ( 7 ± 1 ) × 10 5
a Mancini et al. [26], bHebb et al. [5], cTregloan-Reed et al. [31], d Hellier et al. [57].
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Korth, J.; Parviainen, H. Update on WASP-19. Universe 2024, 10, 12. https://doi.org/10.3390/universe10010012

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Korth J, Parviainen H. Update on WASP-19. Universe. 2024; 10(1):12. https://doi.org/10.3390/universe10010012

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Korth, Judith, and Hannu Parviainen. 2024. "Update on WASP-19" Universe 10, no. 1: 12. https://doi.org/10.3390/universe10010012

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Korth, J., & Parviainen, H. (2024). Update on WASP-19. Universe, 10(1), 12. https://doi.org/10.3390/universe10010012

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