TrES-1 b: Insights into a Cool Hot Jupiter

• TrES-1 b is a Jupiter-sized exoplanet orbiting a cool star with a 3.03-day period and an almost isothermal dayside at approximately 1200 K.
• Spitzer thermal emission data reveal efficient heat redistribution and moderate molecular absorption, indicating a non-inverted, blackbody-like atmosphere.
• Combined transit, eclipse, and radial velocity analyses suggest orbital decay or apsidal precession, hinting at potential unseen companions affecting its dynamics.

TrES-1 b is a Jupiter-sized hot Jupiter orbiting a $0.878\,M_\odot$, $0.807\,R_\odot$ host star on a $\sim 3.03$ d orbit at $a=0.03924$ AU. It was the first planet discovered by any transit survey and one of the first exoplanets from which thermal emission was directly observed. In published analyses, it is characterized as one of the coolest hot Jupiters observed by Spitzer, with an equilibrium temperature reported as 1200 K in one analysis and as $T_{\rm eq}\approx1150\,\rm K$ under zero albedo and full redistribution in a later system summary (Cubillos et al., 2014, Hagey et al., 20 Aug 2025).

1. System architecture and classification

TrES-1 b has fixed parameters $M_p = 0.697\,M_{\rm J}$ and $R_p = 1.067\,R_{\rm J}$ in the consolidated secular-evolution analysis, with an orbital period $P = 3.03007008\,$d used in light-curve fits and a derived semi-major axis $a = 0.03924\,$AU (Hagey et al., 20 Aug 2025). The host-star effective temperature used in the Spitzer brightness-temperature analysis is $T_{\rm eff}=5230$ K, and the planet-to-star radius ratio adopted there is $0.807\,R_\odot$0 (Cubillos et al., 2014).

Within the hot-Jupiter population, TrES-1 b occupies the relatively cool end. One interpretation in the Spitzer analysis is that its atmosphere behaves more like a blackbody than the strongly inverted, hotter planets such as HD 209458 b (Cubillos et al., 2014). This places TrES-1 b in a regime where broad-band emission measurements are informative about day-night redistribution and molecular absorption, but less diagnostic of strong stratospheric heating.

2. Secondary eclipses, thermal emission, and atmospheric structure

A five-band Spitzer joint fit yielded the following eclipse depths and corresponding brightness temperatures (Cubillos et al., 2014):

Band	Eclipse depth (\%)	$0.807\,R_\odot$1 (K)
$0.807\,R_\odot$2	$0.807\,R_\odot$3	$0.807\,R_\odot$4
$0.807\,R_\odot$5	$0.807\,R_\odot$6	$0.807\,R_\odot$7
$0.807\,R_\odot$8	$0.807\,R_\odot$9	$\sim 3.03$0
$\sim 3.03$1	$\sim 3.03$2	$\sim 3.03$3
$\sim 3.03$4	$\sim 3.03$5	$\sim 3.03$6

These brightness temperatures were derived by inverting

$\sim 3.03$7

with numerical inversion of the Planck function using the actual bandpasses. The near-constant $\sim 3.03$8 K across five bands implies an almost isothermal dayside, consistent with equilibrium at zero albedo and substantial day-night energy redistribution, reported as up to $\sim 3.03$9 (Cubillos et al., 2014).

The atmospheric modeling employed line-by-line, plane-parallel radiative transfer under hydrostatic equilibrium and local thermodynamic equilibrium, with opacities from H$a=0.03924$0O, CO, CH$a=0.03924$1, CO$a=0.03924$2, and H$a=0.03924$3–H$a=0.03924$4 collision-induced absorption. A global-energy-balance constraint required the integrated emergent flux to match the incident stellar flux times $a=0.03924$5. Two representative pressure-temperature profiles, with and without a stratospheric inversion, both assumed solar-abundance chemistry and both reproduced the broad-band eclipse depths within the uncertainties (Cubillos et al., 2014).

The $a=0.03924$6 band is sensitive to CO and CO$a=0.03924$7 absorption, and the slightly lower brightness temperature at $a=0.03924$8 than at $a=0.03924$9 was interpreted as hinting at molecular absorption rather than emission, disfavoring a strong inversion. However, the quoted error bars were too large for a unique determination of abundances. Accordingly, the published conclusion was that there is no strong evidence for a thermal inversion, while molecular absorbers likely shape the spectrum (Cubillos et al., 2014).

3. Transit ephemerides, eccentricity, and transit-timing analyses

A joint fit to secondary-eclipse midtimes, 33 radial-velocity datapoints, and 84 transit midtimes produced

$T_{\rm eq}\approx1150\,\rm K$0

$T_{\rm eq}\approx1150\,\rm K$1

$T_{\rm eq}\approx1150\,\rm K$2

$T_{\rm eq}\approx1150\,\rm K$3

with an eclipse-timing offset of approximately $T_{\rm eq}\approx1150\,\rm K$4 minutes, consistent with zero to within $T_{\rm eq}\approx1150\,\rm K$5, and therefore with a circular orbit (Cubillos et al., 2014).

A later transit-only ephemeris analysis used 46 high-quality MicroObservatory transits from 2010–2020 together with 47 archival ETD transits from 2004–2020 and obtained

$T_{\rm eq}\approx1150\,\rm K$6

The combined $T_{\rm eq}\approx1150\,\rm K$7 diagram spans $T_{\rm eq}\approx1150\,\rm K$8 to $T_{\rm eq}\approx1150\,\rm K$9 and has overall reduced $M_p = 0.697\,M_{\rm J}$0 about $M_p = 0.697\,M_{\rm J}$1, which was interpreted as consistency with a strictly linear ephemeris at the $M_p = 0.697\,M_{\rm J}$2–$M_p = 0.697\,M_{\rm J}$3 level (Yeung et al., 2022).

The same study searched for periodicity in the $M_p = 0.697\,M_{\rm J}$4 residuals using the Astropy implementation of the Lomb–Scargle periodogram over $M_p = 0.697\,M_{\rm J}$5 to $M_p = 0.697\,M_{\rm J}$6 cycles d$M_p = 0.697\,M_{\rm J}$7, corresponding to periods of $M_p = 0.697\,M_{\rm J}$8–$M_p = 0.697\,M_{\rm J}$9 d. MicroObservatory transits alone showed a highest-power peak with $R_p = 1.067\,R_{\rm J}$0, indicating no significant periodicity. In the combined MOBS + ETD set, three peaks with $R_p = 1.067\,R_{\rm J}$1 were found at $R_p = 1.067\,R_{\rm J}$2 c d$R_p = 1.067\,R_{\rm J}$3 ($R_p = 1.067\,R_{\rm J}$4 d), $R_p = 1.067\,R_{\rm J}$5 c d$R_p = 1.067\,R_{\rm J}$6 ($R_p = 1.067\,R_{\rm J}$7 d), and $R_p = 1.067\,R_{\rm J}$8 c d$R_p = 1.067\,R_{\rm J}$9 ($P = 3.03007008\,$0 d), with semi-amplitudes of order $P = 3.03007008\,$1–$P = 3.03007008\,$2 min in $P = 3.03007008\,$3; the published caution was that further high-cadence follow-up would be required to confirm their astrophysical origin (Yeung et al., 2022).

4. Inference pipelines and data-analysis methodology

The Spitzer eclipse and transit analysis was performed with the Photometry for Orbits, Eclipses, and Transits (POET) pipeline. POET flags bad pixels, computes BJD$P = 3.03007008\,$4, tests four centroiding methods—Gaussian-fit, center-of-light, PSF-fit, and least asymmetry—and extracts light curves with both classical aperture photometry and optimal photometry (Cubillos et al., 2014).

The optimal-photometry estimator used in that analysis is

$P = 3.03007008\,$5

where $P = 3.03007008\,$6 is the PSF model and $P = 3.03007008\,$7 the variance of pixel $P = 3.03007008\,$8. Instrumental systematics were handled with BLISS intrapixel mapping, analytic ramp functions of the form $P = 3.03007008\,$9, and per-AOR flux scalings (Cubillos et al., 2014).

Posterior sampling in POET used differential-evolution MCMC,

$a = 0.03924\,$0

with $a = 0.03924\,$1. The reported benefits were elimination of manual tuning of proposal covariances, automatic adaptation to correlated posteriors, better exploration of phase space, and $a = 0.03924\,$2 times faster convergence than a Metropolis random-walk MCMC (Cubillos et al., 2014).

The later transit-timing analysis used the EXOplanet Transit Interpretation Code (EXOTIC). Its workflow comprised dark subtraction, target and comparison-star identification, aperture photometry with local sky subtraction, optimization of aperture and comparison choices by minimizing the RMS of the residuals to a transit model, linear detrending against airmass and/or time, analytic transit modeling via the Mandel & Agol (2002) formalism with fixed quadratic limb-darkening coefficients, and Markov-chain Monte Carlo estimation of the free parameters, including mid-transit time, depth, duration, baseline level, and detrending coefficients (Yeung et al., 2022). In the secular-evolution study, light curves were refit where possible using pylightcurve, with a uniform detrending and common limb-darkening priors (Hagey et al., 20 Aug 2025).

5. Secular evolution: evidence and competing dynamical interpretations

A comprehensive joint analysis of 123 mid-transit times spanning 2004–2022, five Spitzer/IRAC eclipses corrected for the light-travel time across the orbit ($a = 0.03924\,$3s), and 37 radial velocities from 2004–2016 reported clear downward curvature in the transit and eclipse $a = 0.03924\,$4 residuals relative to a circular, constant-period model (Hagey et al., 20 Aug 2025). Apparent variations from systemic motion and light-travel-time effects were evaluated and found to be too small: the Shklovskii effect gives $a = 0.03924\,$5, apparent apsidal precession from space motion is $a = 0.03924\,$6, and the long-term RV trend needed for the quoted $a = 0.03924\,$7 estimate is not observed (Hagey et al., 20 Aug 2025).

The statistical evidence for evolution was quantified with nested-sampling evidence. The Bayes factor comparing the best-fit apsidal-precession model to a circular constant-period orbit was

$a = 0.03924\,$8

which was characterized, following Kass & Raftery (1995), as “very strong” evidence for evolution (Hagey et al., 20 Aug 2025).

Under the apsidal-precession model, the dominant quadrupole term in the planet is

$a = 0.03924\,$9

with best-fit parameters

$T_{\rm eff}=5230$0

$T_{\rm eff}=5230$1

corresponding to a precession period of approximately $T_{\rm eff}=5230$2 yr. Standard contributions from GR plus rotational and tidal bulges in the star and planet sum to only $T_{\rm eff}=5230$3/yr, so a pure precession explanation at the fitted rate would require an unseen close-in companion with $T_{\rm eff}=5230$4 and $T_{\rm eff}=5230$5d (Hagey et al., 20 Aug 2025).

An alternative fit uses orbital decay, with

$T_{\rm eff}=5230$6

For planetary obliquity tides at $T_{\rm eff}=5230$7,

$T_{\rm eff}=5230$8

and matching $T_{\rm eff}=5230$9ms/yr requires $0.807\,R_\odot$00 for $0.807\,R_\odot$01. Pure eccentricity tides with $0.807\,R_\odot$02 would require $0.807\,R_\odot$03, while the measured eccentricity in that analysis is reported as $0.807\,R_\odot$04, making that route implausible (Hagey et al., 20 Aug 2025).

6. Companion candidates, observational implications, and unresolved issues

The same secular-evolution study identified a second RV signal, designated “TrES-1 c,” after subtraction of the best-fit TrES-1 b orbit. The joint fits gave

$0.807\,R_\odot$05

corresponding to $0.807\,R_\odot$06AU (Hagey et al., 20 Aug 2025). However, its long period is much greater than the 18 yr transit baseline, and the reported consequences for timing are small: any light-travel or LTT TTV semi-amplitude is only $0.807\,R_\odot$07 s, gravitational TTVs are $0.807\,R_\odot$08 s, and its precession forcing on TrES-1 b is negligible (Hagey et al., 20 Aug 2025).

This separates two distinct timing questions. The 2022 study found no unambiguous periodic TTV signal in MicroObservatory data alone and only candidate few-minute periodicities in the combined ground-based sample (Yeung et al., 2022). The later joint transit-eclipse-RV analysis instead favored secular evolution over a constant-period orbit (Hagey et al., 20 Aug 2025). This suggests that short-timescale periodic TTV claims and long-timescale secular trends should not be conflated.

The observational program recommended in the secular analysis is correspondingly multi-technique: continued high-precision transit timing from the ground and from TESS, additional secondary-eclipse timings to constrain $0.807\,R_\odot$09 and break degeneracies with decay, and extended RV monitoring both to test the long-period companion candidate and to search for any very short-period perturber required by a pure precession scenario (Hagey et al., 20 Aug 2025). The earlier ephemeris work likewise emphasized that regular small-telescope follow-up can maintain precise transit predictions and support TTV searches relevant to scheduling JWST time-series spectroscopy, CHEOPS photometry, and large ground-based observations (Yeung et al., 2022).

TrES-1 b therefore occupies a distinctive position in exoplanet studies. Its Spitzer eclipses indicate a nearly isothermal dayside at approximately $0.807\,R_\odot$10 K, efficient heat transport, moderate molecular absorption, and no compelling inversion (Cubillos et al., 2014). Its transits were long consistent with strict periodicity at the few-minute level in ground-based timing work (Yeung et al., 2022), yet a longer-baseline synthesis of transit, eclipse, and RV data now points to either apsidal precession requiring an undetected close-in companion or orbital decay plausibly driven by planetary obliquity tides (Hagey et al., 20 Aug 2025).