Extreme Irradiation in Hot Jupiters

• Most irradiated hot Jupiters are defined as gas giants in close orbits receiving incident stellar flux over 10^9 erg s⁻¹ cm⁻², resulting in equilibrium temperatures above 2000 K.
• High-precision spectroscopy, transit photometry, and parallax measurements are used to determine stellar parameters and orbital geometries, enabling accurate flux and temperature calculations.
• Extreme irradiation drives atmospheric inflation, thermal inversions, molecular dissociation, and substantial hydrodynamic mass loss, providing key insights into exoplanetary atmospheric physics.

A highly irradiated hot Jupiter is a gas-giant exoplanet on a close-in orbit (typically $a \lesssim 0.05$ AU) around a luminous main-sequence star, exposed to incident stellar fluxes $F_{\rm irr} \gtrsim 10^9$ erg s$^{-1}$ cm$^{-2}$ ($>2000$ K equilibrium temperature). The identification of the most irradiated objects enables investigation of extreme atmospheric physics, irradiation-driven inflation, and spectacular atmospheric escape. The current record-holder for the most irradiated hot Jupiter is KELT-9b, though a small group of hot Jupiters reside in the same extreme regime. This article surveys definitions, measurement methodologies, leading systems, and comparative context.

1. Quantitative Definition of Irradiation

The bolometric incident flux $F_{\rm irr}$ received by a planet is given by

$F_{\rm irr} = \frac{L_*}{4\pi a^2}$

where $L_*$ is stellar luminosity and $a$ the orbital semi-major axis. For equilibrium temperature (zero Bond albedo, global reradiation),

$$T_{\rm eq} = \left[\frac{L_*}{16 \pi \sigma a^2}\right]^{1/4}, \quad \sigma = 5.6704 \times 10^{-5}\ \mathrm{erg\,cm}^{-2}\,\mathrm{s}^{-1}\,\mathrm{K}^{-4}$$

Alternatively, in terms of fundamental stellar parameters,

$$F_{\rm irr} = \sigma T_{\rm eff,*}^4 \left( \frac{R_*}{a} \right)^2$$

where $T_{\rm eff,*}$ and $R_*$ are stellar effective temperature and radius. Uncertainties propagate from parallax (for $L_*$), photometry, and transit-derived $a$.

2. Leading Most-Irradiated Hot Jupiters

A decisive ranking is extracted from precise system parameters and consensus flux comparisons. The following table summarizes incident flux $F_{\rm irr}$ and equilibrium temperature $T_{\rm eq}$ for archetypes:

Planet	$F_{\rm irr}$ (erg s$^{-1}$ cm$^{-2}$)	$T_{\rm eq}$ (K)	Notes
KELT-9b	$\gtrsim 7 \times 10^9$	$\sim 4000$	Most irradiated known
WASP-33b	$\sim 5.0 \times 10^9$	$\sim 3000$	A5 host, robust inversion
WASP-12b	$\sim 2.5 \times 10^9$	$\sim 2500$	Max. prior to KELT-9b’s discovery
HD 202772A b	$4.7 \pm 0.3 \times 10^9$	$2132^{+37}_{-33}$	Top five; not record-holder
WASP-72b	$\sim 5.5 \times 10^9$		Among uppermost fluxes
TOI-1431b	$7.24^{+0.68}_{-0.64} \times 10^9$	$2370 \pm 70$	Dayside $>3000$ K, top three
KELT-16b	$8.22^{+0.77}_{-0.61} \times 10^9$	$2453^{+55}_{-47}$	Ultra-short period, extreme regime

These values are all as reported or directly calculated from published stellar and orbital parameters (Wang et al., 2018, Lothringer et al., 2018, Addison et al., 2021, West et al., 2013, Gillon et al., 2012, Haswell, 2017, Oberst et al., 2016, Haynes et al., 2015).

KELT-9b is the current record-holder, receiving by far the largest incident flux. WASP-33b, TOI-1431b, KELT-16b, WASP-82b, and WASP-72b are among the handful of planets surpassing $5 \times 10^9$ erg s$^{-1}$ cm$^{-2}$.

3. Methods of Determining Incident Flux and Temperature

Determination of $F_{\rm irr}$ and $T_{\rm eq}$ demands precise stellar parameters and orbital geometries, ideally derived via high-S/N spectroscopy, transit photometry, and parallax:

• $L_*$ from $L_* = 4\pi R_*^2 \sigma T_{\rm eff,*}^4$
• $a$ from transit fits and stellar density
• $T_{\rm eq}$ under Bond albedo $A_B = 0$ and full redistribution
• $F_{\rm irr}$ consistency checks via direct application of the above formulae
• Uncertainties stem from $L_*$, $a$, and $A_B$, with errors on $F_{\rm irr}$ typically $<10\%$

For dayside/nightside brightness temperatures, secondary-eclipse and phase-curve photometry (e.g., TESS, HST, Spitzer) are used to fit blackbody or radiative-transfer models, yielding $T_{\rm day}$ and $T_{\rm night}$ (Addison et al., 2021).

4. Atmospheric Effects of Extreme Irradiation

Planets exposed to $F_{\rm irr} \gtrsim 2 \times 10^9$ erg s$^{-1}$ cm$^{-2}$ display distinctive physical regimes:

• Thermal inversions: Driven by strong absorption of short-wavelength stellar output. Causative opacities include TiO/VO (at $T_{\rm eq} \sim 2000-2500$ K) and in ultra-hot cases, atomic metals (Fe, Mg), SiO, and H$^-$, as shown for KELT-9b (Lothringer et al., 2018, Haynes et al., 2015).
• Atmospheric dissociation: At $T \gtrsim 2500$ K and $p \lesssim 10^{-2}$ bar, H$_2$O, TiO, and VO undergo strong thermal dissociation, with CO being a rare survivor. This biases molecular abundance retrievals in the IR (Lothringer et al., 2018).
• Influence on inflation: There is a robust correlation between extreme incident flux and planetary radius inflation, with the most irradiated planets appearing “bloated” by comparison to their less-irradiated counterparts (West et al., 2013).
• Dynamical consequences: Dayside-nightside contrasts can approach $\Delta T \sim 2000$ K for KELT-9b; for TOI-1431b, a much lower contrast ($\sim 420$ K) signals unusually efficient heat redistribution (Addison et al., 2021).
• Mass loss: Hydrodynamic escape, Roche-lobe overflow, and high upper-atmosphere temperatures can produce mass-loss rates up to $10^{13}$ g s$^{-1}$ (as inferred from WASP-12b’s exosphere and circumstellar shroud) (Haswell, 2017).

5. Extreme Systems: Observational Highlights

Several representative objects illustrate the diversity of ultra-irradiated properties:

• KELT-9b: Exposed to $F_{\rm irr} \sim 6 \times 10^7$ W m$^{-2}$, equilibrium $T_{\rm eq} \sim 4000$ K. PHOENIX modeling predicts deep H$^-$-dominated thermal inversions, nearly complete dissociation of most molecules, and a quasi-featureless IR continuum with CO emission (Lothringer et al., 2018).
• WASP-33b: Receives $F_{\rm irr} \sim 1.3 \times 10^7$ W m$^{-2}$, dayside brightness temperature $\sim 2950$ K exceeds $T_{\rm eq}$ ($\sim 2730$ K), robust inversion and TiO emission detected with HST/WFC3; uniquely orbits a $\delta$-Scuti A5 star (Haynes et al., 2015).
• TOI-1431b: $F_{\rm irr} = 7.24^{+0.68}_{-0.64} \times 10^9$ erg s$^{-1}$ cm$^{-2}$, $T_{\rm eq} = 2370 \pm 70$ K, direct TESS phase-curve yields $T_{\rm day} = 3004 \pm 64$ K, $T_{\rm night} = 2583 \pm 63$ K and exceptional redistribution efficiency ($\epsilon = 0.76 \pm 0.05$) (Addison et al., 2021).
• WASP-12b: Once the most extreme, now surpassed. $F_{\rm irr} \sim 9 \times 10^9$ erg s$^{-1}$ cm$^{-2}$, $T_{\rm eq} \sim 2500$ K, ongoing mass loss, circumstellar material detected in NUV transit (Haswell, 2017).

6. Uncertainties, Assumptions, and Limitations

• Albedo and reradiation: Calculations usually assume $A_B = 0$; realistic $A_B = 0.1$–$0.3$ can lower $T_{\rm eq}$ by up to $\sim 10\%$ (Wang et al., 2018).
• Redistribution: Equilibrium temperatures typically assume full day–night energy redistribution. If only the dayside reradiates, $T_{\rm eq}$ increases by $2^{1/4} \approx 1.19$.
• Stellar parameters: Parallax and bolometric correction systematics impact $L_*$, while $a$ is primarily transit-derived.
• High-energy irradiation: UV/X-ray flux, not fully incorporated in $F_{\rm irr}$, can enhance atmospheric escape but contributes only a few percent to total incident power for F–A stars (Wang et al., 2018).
• Observational constraints: Phase-curve and secondary-eclipse photometry is required for temperature mapping; systematics in detrending can impact brightness temperature estimates.

7. Comparative Context and Future Prospects

A handful of hot Jupiters (KELT-9b, WASP-33b, TOI-1431b, KELT-16b, WASP-82b, WASP-72b) are recognized as the most strongly irradiated known, with KELT-9b unambiguously the record-holder to date (Lothringer et al., 2018, Addison et al., 2021). Atmospheric characterization of these planets probes regimes where planetary and stellar atmospheres intersect, including thermal dissociation, wavelength-dependent opacity by atomic metals, and hydrodynamic mass loss. The characterization of heat redistribution, spectral signatures (e.g., CO emission, H$^-$ continuum), and atmospheric escape via high-precision time-resolved observations (HST, Spitzer, JWST) provides ongoing diagnostic leverage.

This systematic identification of extreme hot Jupiters enables comparative exoplanetology at the limits of irradiation-driven atmospheric physics and informs models of planet formation, orbital migration, and the fate of irradiated gas giants. Remaining uncertainties are concentrated in the measurement of true albedo, redistribution efficiency, and the role of high-energy flux, motivating further multiwavelength monitoring and spectroscopic campaigns.