---
title: 'TOI-1516b: Hot Jupiter with TTV and Orbital Decay'
url: https://www.emergentmind.com/topics/toi-1516b
type: topic
---

# TOI-1516b: Hot Jupiter with TTV and Orbital Decay

Searching arXiv for the specified TOI-1516b papers to ground the article in published sources.
TOI-1516b is a hot Jupiter on a short-period orbit around the F-type main-sequence star TOI-1516 (TIC 376637093). It was presented as one of three new hot Jupiters discovered by the *TESS* space mission and confirmed through joint transit and radial-velocity analysis, with subsequent work extending the system’s characterization through a combined *TESS* and ground-based study of transit timing variations (TTVs) [2205.01860; 2509.21551]. The planet is characterized by an orbital period near $2.056$ days, a mass of $3.16 \pm 0.12\,M_{\mathrm{J}}$, a radius of $1.36 \pm 0.03\,R_{\mathrm{J}}$, and a highly irradiated orbit at $a = 0.0330 \pm 0.0010$ AU [2205.01860]. Later timing analysis found that, although an orbital-decay ephemeris minimizes the Bayesian Information Criterion (BIC), the O$-$C residuals contain a periodic component with false-alarm probability $0.00014$, which the authors state “suggests a likely dynamical origin that warrants further investigation” [2509.21551].

## 1. Discovery, confirmation, and observational setting

TOI-1516b was confirmed by combining *TESS* photometry with extensive radial-velocity monitoring from a coordinated network of mid-aperture telescopes at Ondřejov (OES), Tautenburg (TCES), and McDonald Observatory (Tull) [2205.01860]. In the discovery and characterization study, the system was observed by *TESS* in Sectors 17, 18, 24, and 25 using 30-minute full-frame images, and the team extracted SAP light curves and modeled them with the Transit and Light Curve Modeller (TLCM) [2205.01860]. Because only full-frame images were available, TLCM used subexposure numerical integration with five subexposures per cadence to mitigate the long-integration effects [2205.01860].

Ground-based confirmation was obtained through a follow-up transit observed at CRCAO (0.6 m) in Rc band on 2020 August 10, with $205 \times 90$ s exposures, and the combined *TESS*+ground dataset was modeled jointly [2205.01860]. High-resolution imaging with Gemini-North ‘Alopeke speckle imaging at 562 and 832 nm found no companions, achieving $\Delta \mathrm{mag} \approx 4$ at $0.2$ arcsec and thereby ruling out contaminating blends [2205.01860]. The planetary interpretation was further supported by the large, coherent radial-velocity semi-amplitude, the consistency of the RV phase with the transit ephemeris, and the multi-instrument agreement after fitting instrument-specific velocity offsets [2205.01860].

The confirmation paper emphasized that the main instruments used for the radial-velocity follow-up of TOI-1181b, TOI-1516b, and TOI-2046b were located at Ondřejov, Tautenburg and McDonald Observatory, all on 2–3 meter aperture telescopes, illustrating the role of mid-aperture telescope networks in follow-up of gas giants discovered by *TESS* and, prospectively, by *PLATO* [2205.01860]. This places TOI-1516b within an observational program that was not limited to discovery, but extended to coordinated photometric, imaging, and spectroscopic validation.

## 2. Stellar host and system parameters

The host star TOI-1516 is classified as an F8 V star from template fitting of iodine-free Tull spectra degraded to $R \approx 5500$ using the Indo-US library [2205.01860]. Its adopted atmospheric parameters in the discovery modeling are $T_{\mathrm{eff}} = 6520 \pm 90$ K, $[\mathrm{Fe}/\mathrm{H}] = -0.05 \pm 0.10$, and $\log g = 4.25 \pm 0.15$, with projected rotation $v \sin i = 11.8 \pm 1.5$ km s$^{-1}$ [2205.01860]. The derived stellar mass and radius are $M_* = 1.14 \pm 0.06\,M_\odot$ and $R_* = 1.14 \pm 0.02\,R_\odot$, consistent with ARIADNE SED-fit results of $M_* = 1.085^{+0.061}_{-0.066}\,M_\odot$ and $R_* = 1.245^{+0.031}_{-0.032}\,R_\odot$ [2205.01860].

The star has stellar density $\rho_* = 1090 \pm 31$ kg m$^{-3}$ and an age of $4.82^{+2.44}_{-1.29}$ Gyr from ARIADNE isochrones using Gaia EDR3 parallax [2205.01860]. The Gaia parallax is $4.0540 \pm 0.0098$ mas, corresponding to a distance of approximately $247 \pm 1$ pc; the catalog photometry includes $\mathrm{TESSmag} = 10.377 \pm 0.006$ and $V = 10.858 \pm 0.008$ [2205.01860]. A periodogram shows a dominant peak at $0.470$ c/d, corresponding to approximately $2.13$ d, together with low-frequency peaks, but the detection of the rotational frequency expected from $v \sin i$ and $R_*$ was reported as inconclusive in subsets [2205.01860].

Within this stellar context, TOI-1516b orbits an F main-sequence host star rather than an evolved subgiant, distinguishing it from TOI-1181b in the same discovery paper [2205.01860]. The host-star characterization is important because the later TTV analysis uses priors from Kabath et al. (2022) and Fox & Wiegert (2022) in EXOFASTv2 global light-curve and RV fits, and because the tidal-quality-factor estimate derived in the timing work depends explicitly on stellar and orbital parameters [2509.21551].

## 3. Planetary orbit, transit geometry, and bulk properties

The discovery solution reported an orbital period of $P = 2.056014 \pm 0.000002$ days and a reference mid-transit epoch $T_0 = \mathrm{BJD}\ 2458765.3250 \pm 0.0001$ [2205.01860]. The transit geometry is described by impact parameter $b = 0.09^{+0.10}_{-0.07}$, inclination $i = 90.0^\circ \pm 0.4^\circ$, scaled semi-major axis $a/R_* = 6.22^{+0.041}_{-0.077}$, and radius ratio $R_p/R_* = 0.1224 \pm 0.0005$, implying a transit depth $\delta \simeq (R_p/R_*)^2 = 0.01498 \pm 0.00012$, or approximately $1.498 \pm 0.012\%$ [2205.01860]. The transit duration is $T_{14} = 2.826^{+0.015}_{-0.014}$ hours [2205.01860].

The planet has mass $M_p = 3.16 \pm 0.12\,M_{\mathrm{J}}$ and radius $R_p = 1.36 \pm 0.03\,R_{\mathrm{J}}$ [2205.01860]. The radial-velocity semi-amplitude is $K = 460.7 \pm 9.0$ m s$^{-1}$, and the orbit was tested with *pyaneti*, which corroborated TLCM and favored a circular orbit; eccentricity was fixed to zero in the final solution [2205.01860]. The semi-major axis is reported as $a = 0.0330 \pm 0.0010$ AU, consistent with the relation
$$
a = \left[\frac{G(M_*+M_p)P^2}{4\pi^2}\right]^{1/3}.
$$
The planet’s mean density is $\rho_p = 1.66 \pm 0.13$ g cm$^{-3}$ and its surface gravity is $g_p \approx 42.3 \pm 2.5$ m s$^{-2}$ [2205.01860].

Assuming Bond albedo $A = 0$ and full heat redistribution, the equilibrium temperature is
$$
T_{\mathrm{eq}} = T_* \sqrt{\frac{R_*}{2a}},
$$
which yields $T_{\mathrm{eq}} \approx 1850 \pm 70$ K using $T_* = 6520 \pm 90$ K, $R_* = 1.14 \pm 0.02\,R_\odot$, and $a = 0.0330$ AU [2205.01860]. The estimated insolation is $F/F_\oplus \approx 1900$, so TOI-1516b receives about two thousand times Earth’s insolation [2205.01860]. The discovery paper placed the planet among highly irradiated hot Jupiters and described it as modestly inflated relative to Jupiter, with density indicating only moderate inflation compared to more extremely inflated systems [2205.01860]. No detections of a secondary eclipse or phase curve were reported, and spin–orbit alignment was not measured for TOI-1516b [2205.01860].

## 4. Transit-timing dataset and timing-extraction methodology

A later study expanded the temporal baseline for TOI-1516b by combining ground-based and space-based transit measurements from 2020 to 2024 [2509.21551]. Ground-based observations comprised 16 transits obtained with the 0.6 m telescope ADYU60 between September 2020 and December 2024 [2509.21551]. Space-based timing information came from *TESS* short-cadence 2-minute observations in four sectors, 57, 58, 77, and 78; the study also used previously published mid-transit times from the Exoplanet Transit Database (ETD) and one NEOSSat mid-time from Fox & Wiegert (2022) [2509.21551]. The O$-$C dataset therefore contained 1 mid-time from NEOSSat, 48 from ETD, 42 from *TESS*, and 16 from the new work [2509.21551].

The photometric reduction and modeling pipeline was heterogeneous but explicitly specified. AstroImageJ (AIJ) was used for calibration with bias and flat frames, differential photometry through Multi-Aperture, and extraction of detrend parameters including airmass, time, sky background, FWHM, comparison-star counts, and $x$–$y$ centroid [2509.21551]. Detrending in the subsequent light-curve modeling used an additive scheme in EXOFASTv2 with the same set of detrend parameters per source [2509.21551]. For *TESS*, the 2-minute TIC cadence light curves were extracted from target pixel files using aperture/background separation, quality-flag filtering, and iterative sigma-clipping [2509.21551].

Time stamps were converted from JD to BJD through AIJ and Eastman applets, and BJD TDB was reported in the O$-$C tables [2509.21551]. Mid-transit times for TOI-1516 from ADYU60 and *TESS* runs were derived with EXOFASTv2; EXOTIC was used for T100 data in general, but T100 was not used for this system [2509.21551]. Global light-curve plus radial-velocity fits employed EXOFASTv2 with NOMIST and TORRES options, priors from Kabath et al. (2022) and Fox & Wiegert (2022), and convergence criteria of Gelman–Rubin $< 1.01$ and chain length $T_z > 1000$ [2509.21551]. For TOI-1516, adopted or interpolated quadratic limb-darkening values included example results $u_1(R) = 0.20 \pm 0.02$ for the *TESS* fit and $0.21 \pm 0.03$ for the ADYU60 fit, with $u_2(R) = 0.22 \pm 0.04$ for *TESS* and $0.34 \pm 0.04$ for ADYU60 [2509.21551].

The timing precision reported for TOI-1516 reflects the differing photometric quality of the data sources. For the global ADYU60 fit, the binned residual RMS is $0.98$ mmag, whereas for the *TESS* fit it is $0.33$ mmag [2509.21551]. The study also notes typical per-transit RMS of 1.2–4.2 mmag across all systems for ADYU60 observations [2509.21551]. Sigma-clipping was applied to the O$-$C sequences, and points removed in this process were marked as red crosses in the TOI-1516 O$-$C figure [2509.21551].

## 5. Ephemerides and model comparison

The timing analysis considered linear, orbital-decay, and apsidal-precession timing models [2509.21551]. The linear ephemeris adopted the timing law
$$
t_{tra} = t_0 + P\,E,\quad t_{occ} = t_0 + \frac{P}{2} + P\,E.
$$
For TOI-1516b, the best-fit parameters from the ExoPdot constant-period model are $t_0 = 2458765.325144 \pm 0.000073$ BJD TDB and $P_0 = 2.056013695 \pm 0.000000117$ days, with $\chi^2 = 1473.4$, $\mathrm{BIC} = 1482.7$, and $\Delta \mathrm{BIC} = 15.2$; under the Kass and Raftery interpretation adopted in the paper, this model is “Very Strongly Rejected” relative to the best model [2509.21551]. The study notes that Kabath et al. (2022) gave $P = 2.056014 \pm 0.000002$ d, and that the updated linear fit finds $P_0$ smaller by approximately $3.05 \times 10^{-7}$ d, or about $26$ ms, consistent within uncertainties [2509.21551].

The quadratic orbital-decay model used
$$
t_{tra} = t_0 + P\,E + \frac{1}{2}\frac{dP}{dE}E^2,\quad
t_{occ} = t_0 + \frac{P}{2} + P\,E + \frac{1}{2}\frac{dP}{dE}E^2,
$$
with $dP/dE$ in units of days epoch$^{-1}$ and negative $dP/dE$ indicating decay [2509.21551]. The best-fit TOI-1516b parameters are $t_0 = 2458765.3244 \pm 0.0001$ BJD TDB, $P_0 = 2.056017150 \pm 0.000000549$ days, and $dP/dE = -6.47\times10^{-9} \pm 9.99\times10^{-10}$ days epoch$^{-1}$, with reported “Transit timing shift” $\mathrm{PdT} = -99.33 \pm 15.35$ s, $\chi^2 = 1453.5$, $\mathrm{BIC} = 1467.5$, and $\Delta \mathrm{BIC} = 0.0$ [2509.21551]. This is the statistically preferred model in the paper’s BIC comparison.

The apsidal-precession model followed Patra et al. (2017):
$$
t_{tra} = t_0 + P_s E - \frac{eP_a}{\pi}\cos\omega,\quad
t_{occ} = t_0 + \frac{P_s}{2} + P_s E + \frac{eP_a}{\pi}\cos\omega,
$$
$$
\omega(E) = \omega_0 + \frac{d\omega}{dE}E,\quad
P_s = P_a\left(1 - \frac{d\omega/dE}{2\pi} \right).
$$
For TOI-1516b, the fit returned $t_0 = 2458765.3172^{+0.0012}_{-0.0018}$ BJD TDB, $P_s = 2.056013691 \pm (1.17\text{--}1.18)\times10^{-7}$ days, $e = 0.0123^{+0.0027}_{-0.0018}$, $\omega_0 = 2.68 \pm 0.05$ rad, and $d\omega/dE = 0.000869^{+0.0000885}_{-0.0000793}$ rad epoch$^{-1}$, with $\chi^2 = 1453.5$, $\mathrm{BIC} = 1476.8$, and $\Delta \mathrm{BIC} = 9.3$, hence “Strongly Rejected” [2509.21551].

The BIC itself was defined as
$$
\mathrm{BIC} = \chi^2 + k\ln(n),
$$
with $k$ the number of free parameters and $n$ the number of mid-times [2509.21551]. The interpretation adopted in the study classified $\Delta \mathrm{BIC} < 2$ as weak, $2$–$6$ as positive, $6$–$10$ as strong, and $\ge 10$ as very strong evidence against the higher-BIC model [2509.21551]. For TOI-1516b, this framework favors orbital decay over both constant period and apsidal precession [2509.21551].

| Model | Key parameters | Statistical result |
|---|---|---|
| Constant period | $t_0 = 2458765.325144 \pm 0.000073$, $P_0 = 2.056013695 \pm 0.000000117$ d | $\chi^2 = 1473.4$, BIC = 1482.7, $\Delta$BIC = 15.2 |
| Orbital decay | $t_0 = 2458765.3244 \pm 0.0001$, $P_0 = 2.056017150 \pm 0.000000549$ d, $dP/dE = -6.47\times10^{-9} \pm 9.99\times10^{-10}$ d epoch$^{-1}$ | $\chi^2 = 1453.5$, BIC = 1467.5, $\Delta$BIC = 0.0 |
| Apsidal precession | $e = 0.0123^{+0.0027}_{-0.0018}$, $\omega_0 = 2.68 \pm 0.05$ rad, $d\omega/dE = 0.000869^{+0.0000885}_{-0.0000793}$ rad epoch$^{-1}$ | $\chi^2 = 1453.5$, BIC = 1476.8, $\Delta$BIC = 9.3 |

## 6. TTV signal, physical interpretation, and outstanding issues

Although the orbital-decay ephemeris minimizes the BIC, the residual timing structure is not exhausted by a secular quadratic trend [2509.21551]. A Generalized Lomb–Scargle periodogram with analytic false-alarm probability assessment found, for TOI-1516b, a maximum power of $0.220967$, frequency $0.00286 \pm 0.00008$ (reported in the text with unit “Hz”), and a period of $349.96 \pm 10.17$ days [2509.21551]. The fitted sine amplitude is $0.00158 \pm 0.00024$ days, corresponding to $2.28 \pm 0.35$ minutes, with false-alarm probability $\mathrm{FAP} = 0.00014$, rounded to $0.0001$ in the abstract and explicitly described as well below the $0.01$ threshold [2509.21551].

The timing study therefore presents a tension between the preferred secular fit and the recovered periodicity. On the one hand, the decay parameter $dP/dE = -6.47\times10^{-9} \pm 9.99\times10^{-10}$ days epoch$^{-1}$ implies a cumulative $\mathrm{PdT}$ timing shift of $-99.33 \pm 15.35$ s over the fitted baseline [2509.21551]. Using
$$
Q = -\frac{9}{2} \cdot k_2 \cdot \left( \frac{M_p}{M_*} \right) \cdot \left( \frac{R_*}{a} \right)^5 \cdot \frac{n}{\frac{1}{a} \cdot \frac{da}{dt}},
$$
with $k_2 = 0.014$ and $n = 2\pi/P$, the authors estimate a host-star tidal quality factor $Q \approx 93.0$ for TOI-1516b [2509.21551]. On the other hand, the same study emphasizes that the highly significant periodic signal in the O$-$C residuals “suggests a likely dynamical origin that warrants further investigation,” while providing no explicit constraints on the mass or period of a putative perturber [2509.21551].

This does not amount to a settled detection of orbital decay in an unqualified sense. The paper notes caveats including variable ground-based photometric precision, exclusion of partial transits by quality cuts, possible red noise or systematics, and model degeneracies between secular effects and dynamical TTVs [2509.21551]. A plausible implication is that the decay-like quadratic term may partly absorb structure generated by an additional body, but the study does not claim such a decomposition explicitly. The phase of the GLS sinusoid is not tabulated, and the apsidal-precession phase parameter $\omega_0 = 2.68 \pm 0.05$ rad belongs to a model that is statistically disfavored for this system [2509.21551].

The recommended path forward is continued high-precision photometric monitoring and RV follow-up to determine whether the periodic TTVs arise from an additional body or can be reconciled with secular processes, and to refine both the decay parameter and the associated tidal constraints [2509.21551]. In that sense, TOI-1516b occupies a dual role in the current literature: it is both a well-characterized, fairly massive hot Jupiter around an F8 main-sequence star [2205.01860] and a timing system in which the statistically preferred ephemeris and the most conspicuous residual periodicity point toward different physical interpretations [2509.21551].

Source: https://www.emergentmind.com/topics/toi-1516b