--- title: Neptunian Ridge in Exoplanet Demographics url: https://www.emergentmind.com/topics/neptunian-ridge type: topic --- # Neptunian Ridge in Exoplanet Demographics Searching arXiv for recent papers on the Neptunian ridge and related exoplanet-demographics work. arXiv search query: "Neptunian ridge exoplanet desert savanna" The **Neptunian ridge** is an occurrence-rate feature in exoplanet demographics: a recently identified overdensity of short-period planets with sizes between Neptune and Saturn that lies between the **Neptunian desert** at shorter periods and the **Neptunian savanna** at longer periods. In the observational framework introduced by Castro-González et al., it is defined primarily in the planet-radius–orbital-period plane by planets with \(5.5\,R_\oplus < R_{\rm p} < 8.5\,R_\oplus\) concentrated at \(3.2 \lesssim P_{\rm orb} \lesssim 5.7\) days, often summarized more loosely as a \(3\)–\(6\) day structure [2409.10517]. In current usage, the term refers to this exoplanet population feature rather than to any structure in Neptune’s ring system; reviews of Neptune’s rings do not use the term “Neptunian Ridge” [2003.02325]. ## 1. Definition and discovery The ridge emerged from a reanalysis of **Kepler DR25** occurrence statistics in which the close-in exo-Neptunian population was corrected for geometric transit probability and survey detectability. In that analysis, the close-in landscape was recast as a three-part sequence—**desert \(\rightarrow\) ridge \(\rightarrow\) savanna**—rather than as a smooth recovery in occurrence beyond the Neptunian desert. The ridge was identified in the conservative Neptune-radius interval \(5.5\,R_\oplus < R_{\rm p} < 8.5\,R_\oplus\), where the weighted cumulative frequency is nearly flat for \(P_{\rm orb} \lessapprox 3.2\) d, rises sharply for \(3.2 \lessapprox P_{\rm orb} \lessapprox 5.7\) d, and increases more mildly beyond \(5.7\) d [2409.10517]. The statistical case is explicit. The ridge stands out at \(4.7\sigma\) above the desert and at \(3.5\sigma\) above the savanna; the corresponding occurrence ratios are \(f_{\rm ridge/desert}=8\pm3\), \(f_{\rm ridge/savanna}=2.7\pm0.5\), and \(f_{\rm savanna/desert}=3.0\pm0.9\) [2409.10517]. This establishes the ridge as a real excess in corrected occurrence, not merely a visual label applied to a few well-known planets. The same work provided ready-to-use approximations for the revised desert boundaries. In logarithmic variables, \[ \mathcal{L_R} = \log_{10}(R_{\rm p}/R_\oplus), \qquad \mathcal{L_P} = \log_{10}(P_{\rm orb}/{\rm d}), \] the upper and lower desert boundaries were written as \[ \mathcal{L_{R} = -0.43 \times \mathcal{L_{P} + 1.14, \qquad \text{if } \mathcal{L_{P} \in [0.12, 0.47] \] and \[ \mathcal{L_{R} = +0.55 \times \mathcal{L_{P} + 0.36, \qquad \text{if } \mathcal{L_{P} \in [-0.30, 0.47]. \] In the Neptunian domain, the desert edge becomes effectively vertical at \[ \mathcal{L_{P} = +0.47, \] corresponding to \(P_{\rm orb}\approx 3\) d, which is precisely where the ridge begins [2409.10517]. A central implication is that the ridge physically truncates the desert tip in the Neptune-to-sub-Saturn regime. ## 2. Demographic location in period, radius, and stellar-type space Operationally, the ridge is most often treated as a period-radius overdensity of **Neptune-to-sub-Jovian** planets. Several later papers adopt the Castro-González et al. boundaries directly and use the ridge as the contextual frame for interpreting individual systems and homogeneous samples. In this usage, the desert is the dearth of intermediate-size planets at the shortest periods, the ridge is the overdensity at roughly \(3.2\)–\(5.7\) d, and the savanna is the moderately populated region at longer periods [2504.16164]. The ridge is adjacent to, but not identical with, the desert. A homogeneous TESS+HARPS study emphasized that the updated bias-corrected desert boundaries “are not limited by an intersection at \(\sim 10\)–15 days, but instead are limited by an over-density of planets in the \(\sim 3.2\)–5.7 days orbital period range,” and treated that overdensity as the transition between the desert and the ridge-facing population [2504.16164]. In the same framework, the lower edge of the ridge appears near \(P_{\rm orb}\sim3.5\) d in that sample because the period break is mapped through planet-by-planet equilibrium temperatures rather than redefined physically. The ridge is not purely an FGK-star construct. An M-dwarf comparison based on a sample of **146 planets around 105 M dwarfs** and **2637 planets around 1994 FGK hosts** found that the opening/ridge location in period-radius space shifts only slightly inward from \(3.3\pm1.4\) d for FGK hosts to \(2.2\pm1.0\) d for M-dwarf hosts, a difference described as not statistically significant and within \(\sim1\sigma\) [2603.12345]. In instellation-radius space, however, the opening differs much more strongly, from \(830.7\pm0.1\,S_\oplus\) for FGK hosts to \(57.8\pm0.2\,S_\oplus\) for M-dwarf hosts [2603.12345]. This suggests that the ridge has a robust demographic identity across stellar types, while the mapping between period and irradiation depends strongly on host star properties. A plausible implication is that the ridge is best regarded as an occurrence-defined feature in the period-radius plane, with additional structure revealed only after composition, density, obliquity, and host-star dependence are added. ## 3. Physical interpretations The earliest physical interpretation linked the ridge to the **hot-Jupiter three-day pile-up**. The period range of the ridge, \(3.2 \lessapprox P_{\rm orb} \lessapprox 5.7\) d, closely matches the \(3.2 \lessapprox P_{\rm orb} \lessapprox 5.8\) d hot-Jupiter pile-up, suggesting that related migration and tidal processes may act on both populations [2409.10517]. The difference is that Jupiter-size planets do not drop abruptly into a desert on the short-period side, whereas Neptunes do, which immediately brings atmospheric erosion into the picture. One interpretation therefore combines **high-eccentricity tidal migration (HEM)** with **photoevaporation**. In this view, early-arriving Neptunes that reach very short periods are eroded and help create the desert, whereas a fraction of Neptunes delivered inward later in their lives by HEM survive near the desert edge and accumulate in the ridge [2409.10517]. This interpretation is consistent with independent discussions that planets along the upper edge of the desert are massive enough that photoevaporation alone is insufficient there, and that mechanisms such as high-eccentricity migration and tidal stripping or disruption near pericenter are required for larger short-period Neptunes and sub-Saturns [2509.11565]. More recent theory makes that connection quantitative. One HEM-based formulation writes the tidal survival scale as \[ r_{\mathrm{tide} = \eta \, R_{\mathrm{p} \left(\frac{M_\star}{M_{\mathrm{p}\right)^{1/3}, \] with post-circularization semimajor axis \[ a_{\mathrm{F} \simeq 2\, r_{\mathrm{p}, \] so that the minimum final period obeys \[ P_{\rm tide}\propto \rho_{\rm p}^{-1/2}. \] Using empirical mass-radius quantiles, the sharp disruption limit becomes a finite tidal survival band, \[ P_{\rm tide}(q=0.8413) < P \leq P_{\rm tide}(q=0.1587), \] which was argued to coincide with the ridge at \(3\lesssim P_{\rm orb}\lesssim6\) d [2604.16300]. In this formulation the ridge is the locus of shortest-period HEM survivors, while the desert boundary marks where planets are disrupted. A complementary dynamical-tide theory attributes both the ridge and the desert to tidally excited planetary \(f\)-modes during HEM. In that framework, close passages excite \(f\)-modes; shocks that cool diffusively circularize orbits and bunch them near the hot-Jupiter pile-up and the Neptune ridge, whereas shocks that drive outflows unbind envelopes and place gas-giant cores in the Neptune desert [2606.20789]. That paper explicitly identifies the ridge with clustering of sub-Saturns at \(\sim3\)–\(5\)-\(6\) d and the desert with the sharp deficit interior to 3 d. These models do not eliminate atmospheric escape; rather, they imply that the ridge is where migration physics and atmospheric survival intersect most sharply. This suggests that the ridge is neither a purely evaporative boundary nor a purely dynamical pile-up, but an interface shaped by both. ## 4. Composition, density, and internal-structure context A major development after the ridge’s identification was the discovery that it has a **compositional counterpart**. In a homogeneous TESS+HARPS sample, inferred envelope mass fractions (EMFs) show a sharp split at \(T_{\rm eq}\approx1300\) K, corresponding in that sample to \(P_{\rm orb}\sim3.5\) d. Below this period, EMFs are “compatible with zero”; above it, in and around the ridge, they are typically about \(20\%\)–\(40\%\) and scale linearly with planetary mass, with a Pearson coefficient \(r=0.87\) and \(p=5.2\times10^{-5}\) for the cooler planets [2504.16164]. The EMF was defined as \[ \mathrm{EMF}=1-\mathrm{CMF}, \] with interiors modeled primarily by GASTLI [2504.16164]. This compositional split implies that the ridge is not only an occurrence excess but also the period regime where close-in Neptune-like planets begin to retain substantial H/He envelopes. The same study argued that inside the desert-facing regime, especially for \(P_{\rm orb}\lesssim3.5\) d and \(T_{\rm eq}\gtrsim1300\) K, atmospheric escape has stripped away primordial envelopes, whereas in the ridge the substantial envelopes and EMF–mass scaling resemble the core-accretion trend known in gas giants [2504.16164]. Density statistics sharpen that contrast. A study centered on TOI-5005 b, a super-Neptune in the savanna near the ridge, found statistical evidence that planets in the savanna tend to have lower densities than planets in the ridge, with an empirical dividing line around \(1\,{\rm g\,cm^{-3}}\). In the same analysis, ridge and desert planets tend to have densities larger than \(1\,{\rm g\,cm^{-3}}\), with median \(1.3\,{\rm g\,cm^{-3}}\), while savanna planets are typically below \(1\,{\rm g\,cm^{-3}}\), with median \(0.6\,{\rm g\,cm^{-3}}\); the uncertainty-aware Kolmogorov-Smirnov test gave \(D=0.39\pm0.04\) and \(p\)-value \(=0.0092^{+0.018}_{-0.0066}\) [2409.18129]. Another boundary-case study described savanna planets as being “about \(\rm 0.5\,g\,cm^{-3}\), very rarely surpassing \(\rm 1\,g\,cm^{-3}\),” whereas ridge planets “frequently show densities as high as \(\rm 1.5-2.0\,g\,cm^{-3}\)” [2501.02272]. The period-density plane may encode more than a simple threshold. One HEM study reported a persistent concentration of ridge planets near \(\rho_{\rm p}\sim1.7\,\mathrm{g\,cm^{-3}}\), alongside a broader peak near \(\rho_{\rm p}\sim0.6\)–\(0.8\,\mathrm{g\,cm^{-3}}\) [2604.16300]. The paper did not claim proven bimodality, but interpreted the \(\sim1.7\,\mathrm{g\,cm^{-3}}\) feature as a persistent local density concentration associated especially with ridge planets. Taken together, these results suggest that the ridge marks the onset of envelope retention outside the most hostile inner region, but also that ridge planets are not simply low-density savanna planets shifted inward. In density and inferred structure, they are systematically different. ## 5. Spin-orbit architecture as a dynamical diagnostic Because the ridge may reflect a dynamically excited migration channel, stellar obliquity has become one of its main diagnostics. The projected obliquity \(\lambda\) is typically measured from the Rossiter-McLaughlin effect, while the true 3D spin-orbit angle is inferred from \[ \cos\psi = \sin i_\star\sin i_\mathrm{orb} \cos\lambda + \cos i_\star \cos i_\mathrm{orb}, \] once the stellar inclination \(i_\star\) is constrained [2509.11565]. TOI-2374 b is a central case. It lies squarely inside the ridge with \(P = 4.3136193 \pm 0.0000015\) d and \(R_p = 0.668 \pm 0.018\,R_{\rm J}\), about \(7.5\,R_\oplus\). Spectroscopic transits with the Keck Planet Finder detected an RM anomaly of amplitude \(3.2\,{\rm m\,s^{-1}}\). The canonical RM fit yielded \(\lambda = 81^{+23}_{-22}\) deg, \(i_\star = 19.5^{+5.1}_{-4.7}\) deg, and \(v\sin i_\star = 0.46 \pm 0.11\,{\rm km\,s^{-1}}\); a reloaded RM analysis yielded \(\lambda = 65^{+21}_{-24}\) deg and \(v\sin i_\star = 0.42^{+0.12}_{-0.09}\,{\rm km\,s^{-1}}\). Combined with a Tierras rotation period of \(P_{\rm rot}=26.38^{+0.90}_{-0.80}\) d, the adopted 3D obliquity is \(\psi = 85.9^{+4.3}_{-5.2}\) deg, כלומר a nearly polar orbit [2509.11565]. Population arguments based on short-period ridge+desert samples were initially suggestive. Restricting to \(P_{\rm orb}<5.7\) d and \(5.54.0\,R_\oplus\), the contrast became \(6/13\) short-period polar versus \(1/15\) longer-period, with a probability of about \(10^{-4}\) under the same base-rate assumption [2509.11565]. That apparent excess, however, became less secure when WASP-156 b was reobserved. New ESPRESSO and MAROON-X transit spectroscopy, together with NGTS photometry, revised the system to an aligned architecture with \(\lambda=-8\pm16^\circ\) from the preferred ESPRESSO reloaded-RM analysis and \(v\sin i_\star = 0.40\pm0.11\,{\rm km\,s^{-1}}\), in contrast to the earlier polar claim [2605.27291]. The new paper concluded that WASP-156 b’s aligned and circular orbit, together with the lack of Jupiter-mass companions within 5 au, is consistent with in situ formation or early disc-driven migration [2605.27291]. The immediate consequence is methodological as much as astrophysical. The ridge may well contain a higher incidence of misaligned or polar planets than comparable longer-period systems, but the evidence remains sample-limited and sensitive to low-amplitude RM systematics, heterogeneous data quality, and prior choices on \(v\sin i_\star\). This is why recent programs such as **ATREIDES**, which proposes a systematic RM census of 60 close-in Neptunes, treat the ridge as a key laboratory for measuring the distribution of 3D obliquities across the desert-ridge-savanna landscape [2509.15746]. ## 6. Representative systems and boundary cases The ridge is now populated by a set of systems that illustrate both its demographic coherence and its internal diversity. **TOI-2374 b** is a ridge planet by both radius and period and currently one of the clearest nearly polar cases [2509.11565]. **TOI-672 b**, orbiting an M0 dwarf, has \(P = 3.633581 \pm 0.000001\) d, \(R_p = 5.31^{+0.24}_{-0.26}\,R_\oplus\), \(M_p = 50.9^{+4.5}_{-4.4}\,M_\oplus\), and \(\rho_p = 1.86^{+0.34}_{-0.26}\,{\rm g\,cm^{-3}}\), placing it within the ridge and just outside the desert in both period-radius and instellation-radius space [2603.12345]. Its substantial H/He envelope, roughly \(20\)–\(30\%\) by mass depending on core composition, makes it a useful counterexample to models in which planets near the ridge are all on the brink of complete evaporation [2603.12345]. Some systems lie just beyond the nominal ridge period range but retain ridge-like structural properties. **TOI-6038 A b** has \(P = 5.8267311^{+0.0000074}_{-0.0000068}\) d, \(R_P = 6.41^{+0.20}_{-0.16}\,R_\oplus\), \(M_P = 78.5^{+9.5}_{-9.9}\,M_\oplus\), and \(\rho_P = 1.62^{+0.23}_{-0.24}\,\rm g\,cm^{-3}\). Its period places it just beyond the nominal \(\simeq3.2\)–\(\simeq5.7\) d ridge interval, but its density lies squarely inside the dense-ridge range \(\rho_{\rm P}\simeq1.5\)–2.0 \(\rm g\,cm^{-3}\), making it a transition object between ridge and savanna [2501.02272]. Internal-structure modeling yielded \(M_{\rm core}=58.0\pm7.8\,M_\oplus\) and \(f_{\rm env}=0.261\pm0.036\), reinforcing the view that ridge-like density can reflect a massive heavy-element core plus only a modest H/He envelope [2501.02272]. By contrast, **TOI-5005 b** sits on the savanna side of the boundary at \(P_{\rm orb}=6.3085044^{+0.0000092}_{-0.0000088}\) d, with \(R_{\rm p}=6.25\pm0.24\,R_\oplus\), \(M_{\rm p}=32.7\pm5.9\,M_\oplus\), and \(\rho_{\rm p}=0.74\pm0.16\,{\rm g\,cm^{-3}}\) [2409.18129]. It is therefore important not because it is a ridge planet, but because it helps define what the ridge is not: in the immediate post-ridge savanna, low-density volatile-rich super-Neptunes appear common. These systems collectively show that the ridge is not reducible to a single planetary archetype. Some ridge planets are nearly polar, some aligned; some are dense and core-dominated, others retain substantial envelopes; some lie cleanly inside the occurrence peak, while others occupy structurally ridge-like transition territory just beyond \(5.7\) d. This suggests that “ridge membership” is demographic first and mechanistic second. ## 7. Debates, misconceptions, and current outlook Several misconceptions recur in the literature. The first is that the ridge is merely a convenient label for a handful of \(3\)–\(5\) d planets. The occurrence studies explicitly reject that view: the ridge was introduced as a statistically significant overdensity in completeness-corrected Kepler occurrence space [2409.10517]. The second is that the ridge is simply the outer edge of the desert. Later work instead treats the ridge as a distinct demographic and compositional regime separating the desert from the savanna [2504.16164]. The most active debate concerns causation. One camp emphasizes **photoevaporation**, especially because the EMF split aligns with \(T_{\rm eq}\approx1300\) K and \(P_{\rm orb}\sim3.5\) d [2504.16164]. Another emphasizes **HEM**, tidal survival, and dynamical-tide circularization, because the ridge geometry, density dependence, and similarity to the hot-Jupiter pile-up follow naturally from near-threshold tidal migration [2604.16300; 2606.20789]. A third, more synthetic view treats the ridge as a hotspot where early disk-driven migration, late HEM, and atmospheric erosion all contribute, with low-density planets mainly eroded and denser planets more likely to survive into the ridge and desert [2509.15746]. The available evidence does not uniquely select one mechanism. A second debate concerns obliquity demographics. The high frequency of misaligned or polar orbits among ridge and desert planets initially seemed reminiscent of the hot-Jupiter population and supportive of a shared dynamical origin [2509.11565]. The reclassification of WASP-156 b from a tentative polar case to an aligned one materially weakened that specific argument [2605.27291]. The remaining sample is still very small, heterogeneous in precision and technique, and potentially affected by host-star diversity, multiplicity differences, and selection effects. The present consensus is therefore provisional but technically coherent. The Neptunian ridge is a real population feature at \(3.2\)–\(5.7\) d among roughly \(5.5\)–\(8.5\,R_\oplus\) planets; it marks the transition from a short-period region where many Neptune-like planets are stripped or absent to a longer-period region where envelopes are more commonly retained. Its strongest empirical signatures are a corrected occurrence excess, a compositional break near \(1300\) K or \(3.5\) d, and a density contrast relative to the savanna, with many ridge planets lying near or above \(1\,{\rm g\,cm^{-3}}\) and some analyses finding a persistent concentration near \(\rho_{\rm p}\sim1.7\,{\rm g\,cm^{-3}}\) [2409.10517; 2504.16164; 2604.16300]. This suggests that the ridge is best understood as a structured transition regime rather than a single-process boundary. It records where close-in Neptunes and sub-Saturns survive, circularize, retain or lose envelopes, and preserve—or fail to preserve—their dynamical histories. Source: https://www.emergentmind.com/topics/neptunian-ridge