Neptunian Desert Exoplanets

• Neptunian desert is defined as a gap in exoplanet parameters where Neptune-like planets are rare at orbital periods below 3–4 days.
• Observational studies reveal statistically significant boundaries in period–mass and period–radius diagrams, including an overdense ridge beyond the desert.
• Physical processes like photoevaporation, high-eccentricity migration, and host star metallicity together shape the desert’s structure and evolution.

The Neptunian desert is a statistically significant feature in the exoplanet population: a region in orbital parameter space—specifically in period–mass and period–radius diagrams—where planets with masses and radii comparable to Neptune are exceptionally rare at short orbital periods (typically below 3–4 days, extending up to ≈5–10 days in some definitions). This paucity cannot be ascribed to observational biases; many Neptune-like planets have been detected at longer periods. The boundaries and properties of the desert, as well as its implications for planetary formation, migration, and atmospheric evolution, have been robustly quantified in multiple large-sample analyses.

1. Statistical Definition and Boundaries

The desert is defined in both the period–mass and period–radius spaces, with boundaries empirically derived via statistical techniques such as stripe analysis and maximum likelihood methods (Mazeh et al., 2016, Castro-González et al., 16 Sep 2024). In logarithmic variables:

• For period–mass: $\mathcal{M} = \log_{10}(M_p/M_{\rm Jup})$, $\mathcal{P} = \log_{10}(P_{\rm orb}/{\rm d})$
  • Upper boundary: $\mathcal{M} = -0.99\mathcal{P} + 0.18$
  • Lower boundary: $\mathcal{M} = +0.98\mathcal{P} - 1.85$
• For period–radius: $\mathcal{R} = \log_{10}(R_p/R_{\oplus})$
  • Upper: $\mathcal{R} = -0.33\mathcal{P} + 1.17$
  • Lower: $\mathcal{R} = +0.68\mathcal{P}$

Recent work has refined the boundaries using population statistics from the Kepler DR25 catalog, providing period–radius formulas such as:

• Upper: $\mathcal{L}_R = -0.43\mathcal{L}_P + 1.14$ (for $\mathcal{L}_P \in [0.12, 0.47]$)
• Lower: $\mathcal{L}_R = +0.55\mathcal{L}_P + 0.36$ (for $\mathcal{L}_P \in [-0.30, 0.47]$) and a constant-period limit: $\mathcal{L}_P = +0.47$ (for $\mathcal{L}_R \in [0.61,0.92]$) (Castro-González et al., 16 Sep 2024).

The desert spans mass ranges from about 0.03–0.3 $M_{\rm Jup}$, radii from roughly 2–10 $R_{\oplus}$, and is most apparent for $P_{\rm orb} \lesssim 3$–4 d. In the irradiation domain, boundaries are well-fit by power laws:

• $R_p/R_{\oplus} = \beta (F/F_{\oplus})^{\alpha}$; examples: $\alpha \sim -0.27$ (lower), $+0.11$ (upper) (Magliano et al., 25 Nov 2024).

2. Observational Evidence and Demographics

The desert manifests as a pronounced drop in occurrence rates—quantified at a 3$\sigma$ significance level—with an overdensity (“Neptunian ridge”) emerging between the desert and the “savanna” at slightly longer periods (typically 3.2 d $\lessapprox P_{\rm orb} \lessapprox$ 5.7 d) (Castro-González et al., 16 Sep 2024). This ridge stands at a 4.7$\sigma$ excess above the desert, matching the pileup period regime observed for hot Jupiters.

Table 1: Boundaries of the Neptunian Desert

Plane	Lower Bound	Upper Bound
Period–mass	$\mathcal{M} = +0.98\mathcal{P} - 1.85$	$\mathcal{M} = -0.99\mathcal{P} + 0.18$
Period–radius	$\mathcal{R} = +0.68\mathcal{P}$	$\mathcal{R} = -0.33\mathcal{P} + 1.17$
Irradiation	$\alpha = -0.27$	$\alpha = +0.11$

Multi-planet systems are more often found near the lower boundary. Host stars of these desert planets are demonstrably more metal-rich than controls and akin to hot Jupiter hosts (Vissapragada et al., 17 Dec 2024, Doyle et al., 22 Apr 2025), supporting models where high disk metallicity fosters both core formation and envelope accretion.

3. Physical Processes Shaping the Desert

Photoevaporation by stellar XUV and EUV flux is the dominant process implicated in the creation of the desert’s lower boundary (Ionov et al., 2018, Vissapragada et al., 2022, Fernández et al., 2023). The mass loss rate in the energy-limited regime is approximated by: $$\dot{M} = \frac{\epsilon \pi R_{\rm p}^3 F_{\rm XUV}}{G M_{\rm p}}$$ where $\epsilon$ is the outflow efficiency (measured at $\sim$0.4 (Vissapragada et al., 2022)), $F_{\rm XUV}$ the incident high-energy flux, $R_{\rm p}$, $M_{\rm p}$ planetary parameters. Detailed numerical modeling—incorporating suprathermal electrons and Roche-lobe geometry—shows that photoevaporation can strip the envelopes from low-mass Neptunes on short orbits, but not from heavy Neptunes ($\gtrsim6 M_{\rm Nep}$), making upper boundary sculpting by evaporation ineffective (Ionov et al., 2018).

For the upper boundary, dynamical migration mechanisms dominate. These include:

• High-eccentricity migration (HEM): Dynamical excitations (Kozai-Lidov cycles, planet–planet scattering) drive Neptunes onto eccentric orbits, circularizing close-in with angular momentum transfer and tidal heating (Demangeon et al., 2017, Jenkins et al., 15 May 2025).
• Disk-driven migration (DDM): Smooth inward migration during the disk phase, generally maintaining spin-orbit alignment and producing “fluffy” Neptunes that may experience rapid envelope erosion upon approach (Bourrier et al., 19 Sep 2025).

Both mechanisms interplay with irradiation-driven mass-loss, resulting in a bifurcation: low-density, easily eroded Neptunes preferentially occupy shorter periods (and vanish), while dense, massive Neptunes can survive farther in—often delivered via HEM with misaligned spins orbits (Bourrier et al., 19 Sep 2025).

4. Internal Composition and Mass–Radius Relations

Desert planets characterized to date include both remnants stripped to rocky/water-dominated cores and “exposed interiors” of former giant planets (Osborn et al., 2023, Naponiello et al., 2023, Doyle et al., 22 Apr 2025). The measured densities ($\rho \sim 9.6$–9.8 g/cm³ for TOI-332 b, TOI-1853 b) require minimal H/He envelopes, incompatible with expectations from core accretion and disc models—implying formation scenarios such as giant impacts, gap opening, or envelope erosion post-migration.

Empirical mass–radius relations describe the desert’s edge: $$R_{\rm p}/R_{\rm Jup} \simeq (1.2 \pm 0.3)\left(\frac{M_{\rm p}}{M_{\rm Jup}}\right)^{0.27 \pm 0.11}$$ $\quad$(Mazeh et al., 2016), with analogous relations found in irradiation coordinates (Magliano et al., 25 Nov 2024). Planetary densities and envelope mass fractions show a sharp bifurcation: above equilibrium temperatures $T_{\rm eq} \sim 1300$ K (or periods $\lesssim$3.5 d), planets have EMF $\rightarrow$ 0, while below, envelopes scale $\sim$20–40% with mass (Doyle et al., 22 Apr 2025).

5. Host Star Properties, Multiplicity, and Environmental Correlations

Desert planet hosts are systematically more metal-rich than those of longer-period Neptunes and smaller planets; their metallicity distribution matches those of hot Jupiter hosts (Vissapragada et al., 17 Dec 2024, Doyle et al., 22 Apr 2025). Host star multiplicity is elevated for both hot Jupiter and Neptunian desert populations: confirmed desert hosts show a multiplicity rate of $16.7\pm5.8\%$, TESS candidates $27.5\pm2.6\%$ (cf. field rates $16.6\pm0.9\%$) (Eeles-Nolle et al., 27 Jun 2025). This elevation supports a role for dynamical interactions—via companion-induced Kozai-Lidov cycles or disk modification—in producing the observed deficit.

However, higher multiplicity among TESS candidates may also reflect unresolved false positives from binary/triple systems. Quality filtering only marginally affects rates, suggesting that environmental factors are likely contributors to the in situ formation and subsequent migration of desert planets.

6. The Ridge, Savanna, and Unified Landscape

Recent population analyses reveal the Neptunian landscape as tripartite: the desert (dearth at very short orbital periods), a “ridge” of overdensity at 3–5.7 d, and a “savanna” at longer periods (Castro-González et al., 16 Sep 2024, Bourrier et al., 19 Sep 2025). The ridge corresponds to a region where high-eccentricity migration (often late) brings denser Neptunes inward and they survive partial envelope erosion, whereas fluffy Neptunes delivered by disk migration are efficiently eroded and removed from the short-period regime. Measurement of 3D spin–orbit angles (e.g., $\psi_b = 57^{\circ}$, $\psi_c = 45^{\circ}$ for TOI-421 system) confirms that a substantial fraction of ridge/desert Neptunes have dynamically excited or misaligned orbits (Bourrier et al., 19 Sep 2025).

Table 2: Neptunian Landscape Features

Region	Period Range (days)	Typical Mass/Radius	Occurrence
Desert	$<$ 3–4 (up to 10)	$0.03$–$0.3 M_{\rm Jup}$, $2$–$10 R_{\oplus}$	Depleted
Ridge	$3.2$–$5.7$	“Survivors”	Overdense
Savanna	$>$ 5.7	Neptune-like	Mild falloff

The landscape is thus interpreted as a record of formation channel, migration history, and envelope erosion—features established by the sensitive dependence on both dynamical and atmospheric processes.

7. Future Directions and Theoretical Challenges

Theory and observation converge on several priorities:

• Integrated models coupling migration (DDM, HEM), envelope loss (photoevaporation, tidal heating), and interior evolution to reproduce the desert’s sharp boundaries and population structure (Ionov et al., 2018, Bourrier et al., 19 Sep 2025).
• Statistical mapping of host star metallicity, binarity, and obliquity, leveraging Gaia and next-generation RV/transit data (Vissapragada et al., 17 Dec 2024, Eeles-Nolle et al., 27 Jun 2025).
• Direct atmospheric composition measurements (e.g., via transmission spectroscopy and He 1083 nm surveys) to distinguish between exposed cores, stripped giants, and envelope survivors (Guilluy et al., 2023, Vissapragada et al., 2022).

Persistent questions include the mechanism underlying high-density survivors (TOI-332 b and TOI-1853 b), the detailed evolution of envelope retention across the desert/ridge boundary, and the fraction of desert dwellers formed by direct migration versus catastrophic evolutionary pathways (impacts, orbital chaos).

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In summary, the Neptunian desert is a physically distinct, statistically significant region of exoplanet parameter space. It is defined by empirically calibrated boundaries in mass, radius, period, and irradiation, and is shaped by the synthesis of atmospheric escape, migration mechanisms, and host star properties. The region encompasses a diversity of compositions and architectures, revealing the complex interplay of formation and evolutionary processes that drive the observed exoplanet demographics.