Illustration of the exoplanet WASP-12 b
Credit:NASA/JPL-Caltech
Credit:NASA/JPL-Caltech
Authors: Elisabeth R. Adams et al.
First Author’s Institution: Planetary Science Institute
Status: Accepted to PSJ
Ultra-hot Jupiters: Fleeting Beauties?
Ultra-hot Jupiters
are gas giants orbiting close to their stars, with orbital periods less
than roughly three days. Because these planets are large and close to
their stars, they produce large signals, making them promising targets
for detection and characterization. But, you know what they say: all
good things must come to an end. These planets are expected to
experience large tidal effects from their stars, resulting in a loss of
angular momentum, orbital decay, and, eventually, the star engulfing the
planet.
Several lines of evidence support the picture that ultra-hot Jupiters are subject to orbital decay over long timescales. For instance, stars hosting hot Jupiters tend to be younger than the average exoplanet host star, and ultra-hot Jupiters are rarer around older host stars. A recent research article even reports a direct detection of a planetary engulfment event from the sudden, short-lived increase in brightness of a faint star. While this evidence paints a compelling picture, it is difficult to estimate how quickly we expect ultra-hot Jupiters to experience orbital decay given theoretical uncertainty in stellar tidal effects.
Several lines of evidence support the picture that ultra-hot Jupiters are subject to orbital decay over long timescales. For instance, stars hosting hot Jupiters tend to be younger than the average exoplanet host star, and ultra-hot Jupiters are rarer around older host stars. A recent research article even reports a direct detection of a planetary engulfment event from the sudden, short-lived increase in brightness of a faint star. While this evidence paints a compelling picture, it is difficult to estimate how quickly we expect ultra-hot Jupiters to experience orbital decay given theoretical uncertainty in stellar tidal effects.
Keeping Time: Working Hard or Hardly Working?
Because we expect orbital decay to occur and we know of thousands of
transiting exoplanets, some of which have been observed for decades,
several teams have searched for orbital decay and found two promising
detections: WASP-12 b and Kepler-1658 b.
Searching for orbital decay relies on the detection of transit-timing
variations. This is when a planet passes in front of its star along our
line of sight earlier or later than expected. There are many sources of
transit-timing variations in addition to orbital decay, including precession, perturbations from companion planets or stars, or acceleration of the host star toward Earth.
Let’s say we observe the transit of a planet at time t = 0 and know its period, P. We expect to observe transits at time P, 2P, 3P, etc. In the case of orbital decay, the period of the planet is getting shorter as time goes on, meaning we need to factor in an additional quadratic term encoding the rate at which the period shrinks. Then, to detect a statistically significant signal of orbital decay, we need to show that the quadratic model fits the data better than the constant-period linear model. The authors of today’s article attempt to do exactly this but with an impressive level of care and attention to detail.
This science depends upon accurate and precise measurements of transit times for each planet in the authors’ sample, most of which have been observed by several teams with various instruments and methodologies over years or decades. Moreover, each transit time must be reported in one unified timing system (click here for more info on one of the most common timing systems). Not every transit observation properly identifies its timing system or accurately converts between timing systems, meaning any historical inaccuracies complicate such studies.
Let’s say we observe the transit of a planet at time t = 0 and know its period, P. We expect to observe transits at time P, 2P, 3P, etc. In the case of orbital decay, the period of the planet is getting shorter as time goes on, meaning we need to factor in an additional quadratic term encoding the rate at which the period shrinks. Then, to detect a statistically significant signal of orbital decay, we need to show that the quadratic model fits the data better than the constant-period linear model. The authors of today’s article attempt to do exactly this but with an impressive level of care and attention to detail.
This science depends upon accurate and precise measurements of transit times for each planet in the authors’ sample, most of which have been observed by several teams with various instruments and methodologies over years or decades. Moreover, each transit time must be reported in one unified timing system (click here for more info on one of the most common timing systems). Not every transit observation properly identifies its timing system or accurately converts between timing systems, meaning any historical inaccuracies complicate such studies.
Statistical Methods: Comparing Models
The authors of today’s article compile transit times for 43 ultra-hot
Jupiters and take new transit data for six of those planets to extend
the temporal baseline of observations. To assess whether the linear
(constant period) or quadratic (changing period) model fits the data
better, the authors use the Bayesian information criterion (BIC), a
model selection criterion that awards a good fit but penalizes
additional parameters to avoid overfitting. The authors calculate the
difference in the BIC (ΔBIC) between the linear and quadratic models,
with a larger ΔBIC suggesting the quadratic model is preferred.
The authors additionally perform a variety of steps to ensure the quality of the data. They perform omit-one tests, where individual transit times are removed from the analysis and flagged if they alter the ΔBIC result by more than 25%. This step is essential since one transit time recorded inaccurately or in the wrong system could result in a spurious detection of orbital decay. The authors additionally perform a “rescaling test,” where the error bars are scaled up to account for unrealistically small error bars in reported transit times.
The authors additionally perform a variety of steps to ensure the quality of the data. They perform omit-one tests, where individual transit times are removed from the analysis and flagged if they alter the ΔBIC result by more than 25%. This step is essential since one transit time recorded inaccurately or in the wrong system could result in a spurious detection of orbital decay. The authors additionally perform a “rescaling test,” where the error bars are scaled up to account for unrealistically small error bars in reported transit times.
Results
As shown in Figure 1, four planets out of the sample of 43 had a ΔBIC
above the detection threshold, including WASP-12 b, which had been
found previously to show orbital decay. The authors measure WASP-12 b’s
period to be shrinking by 30 milliseconds per year, matching previously
reported values. The planets WASP-121 b and WASP-46 b show tentative
period increases, but these results are highly dependent on one or a few
data points, warranting further observations. The planet TrES-1 b has
prior tentative claims of its period decreasing, and the authors find a
tentative period decrease of 18 milliseconds per year. However, this
rate of period shrinkage suggests stellar tidal effects that would
differ greatly from theoretical predictions, perhaps suggesting a cause
of period decrease other than orbital decay.
Figure 1: The value of each planet’s ΔBIC shown relative to a threshold of ΔBIC = 30 (top), zoomed in results (middle), and rescaled results (bottom) with scaled up uncertainties, indicating only WASP-12 b definitively shows signs of orbital decay. Credit: Adams et al. 2024
Only one planet, WASP-12 b, was found to have a clear period decrease after rescaling error bars, as shown in the bottom panel of Figure 1. The authors predict that if the orbits of the other planets in the sample were decaying as rapidly as the orbit of WASP-12 b, they could have found significant detections of period decrease in roughly half the sample. There is thus no evidence that orbital decay is common among ultra-hot Jupiters, which is possibly confounding considering the other lines of evidence that suggest ultra-hot Jupiters are subject to decay. Though patience is required, as time goes on, it will be possible to search for orbital decay around more planets at higher precision, helping us ascertain the ultimate fate of close-in planets.
Only one planet, WASP-12 b, was found to have a clear period decrease after rescaling error bars, as shown in the bottom panel of Figure 1. The authors predict that if the orbits of the other planets in the sample were decaying as rapidly as the orbit of WASP-12 b, they could have found significant detections of period decrease in roughly half the sample. There is thus no evidence that orbital decay is common among ultra-hot Jupiters, which is possibly confounding considering the other lines of evidence that suggest ultra-hot Jupiters are subject to decay. Though patience is required, as time goes on, it will be possible to search for orbital decay around more planets at higher precision, helping us ascertain the ultimate fate of close-in planets.
Original astrobite edited by Ivey Davis.
About the author, Kylee Carden:
I am a first-year PhD student at The Ohio State University, where I am an observer of planets outside the solar system. I’m involved with the transiting exoplanet survey of the upcoming Roman Space Telescope and working with high-resolution spectroscopic observations of exoplanet atmospheres. I am a huge fan of my cat Piccadilly, cycling, and visiting underappreciated tourist sites.
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