Mantle Convection and Nightside Volcanism on Lava World K2-141 b

The Setting: A Planet Split in Two

Imagine a planet called K2-141 b. It's a "Super-Earth" (bigger and heavier than us) that orbits its star so closely it completes a lap in just 6.7 hours. Because it's so close, it's tidally locked, meaning it always shows the same face to its star, just like our Moon always shows the same face to Earth.

This creates a planet with two very different personalities:

The Dayside: A scorching, permanent noon. It's so hot (over 2,000°C) that the rock is melted into a global magma ocean. Think of it as a giant, churning pot of lava.
The Nightside: A permanent midnight. It's so cold (near absolute zero) that the rock is frozen solid.

The scientists wanted to know: What happens underground on a planet like this? Does the heat from the magma ocean drive the planet's internal engine? Does the cold side freeze the engine? And does this planet have volcanoes?

The Engine: The Planet's "Stomach"

Deep inside the planet, the rock isn't just sitting there; it's moving. This is called mantle convection.

The Analogy: Imagine a pot of thick soup on a stove. The heat from the bottom makes the soup rise, cool at the top, and sink back down.
On K2-141 b: The "stove" is the planet's hot core, but the "lid" of the pot is weird. One side is a boiling lava lake (the dayside), and the other is a frozen rock slab (the nightside).

The researchers used powerful computer simulations to watch how the planet's interior "stirred" over billions of years.

The Big Discovery: The "Terminator" Recycling

The most surprising finding is how the planet moves its rock around.

On Earth, we have plate tectonics: giant plates of rock slide past each other, crash, and sink (subduction). But K2-141 b doesn't have plates. It has a single, solid lid on the nightside and a liquid ocean on the dayside.

So, how does the planet recycle its crust?

The Analogy: Imagine a conveyor belt. On the dayside, the "soup" (magma) rises up. It flows toward the edges where the hot day meets the cold night (called the terminators).
The Result: At these twilight boundaries, the hot, rising rock hits the cold, solid nightside crust. The cold crust gets heavy and brittle. Instead of sliding smoothly, it gets pushed down into the hot soup, creating a downward whirlpool.
The "Single-Lid" Tectonics: The entire nightside crust acts like one giant raft. It slowly drifts toward the twilight zone, gets pushed down into the mantle, and is recycled. It's like a slow-motion garbage disposal that only works at the edge of the day and night.

The Volcanoes: The "Night Shift" Workers

You might think volcanoes only happen on the hot side. But the study found something counter-intuitive: The volcanoes are on the cold side.

How it works: As the cold nightside crust gets pushed down into the hot mantle (at the twilight zones), the pressure and heat cause the rock to melt. This new melt rises back up and erupts onto the frozen nightside surface.
The Result: The nightside is constantly being repaved with fresh, volcanic rock (basalt), even though it's freezing cold. It's like a factory that only runs its assembly line at night.

The Atmosphere: A "Ghost" of a Chance

The researchers tracked gases like Carbon Dioxide (CO2) and Water (H2O) trapped in the rock.

The Outgassing: As the volcanoes erupt on the nightside, they release these gases. Over billions of years, the simulations suggest the planet could have pumped out enough gas to create an atmosphere with a pressure of 10 to 200 bars (Earth is 1 bar; Venus is 92 bars).
The Catch: The star is so intense that it likely blows this atmosphere away (like a leaf blower in a hurricane). Also, the gases might freeze out on the cold nightside. So, while the planet could have a thick atmosphere, it might be very thin or non-existent.

Can We See It? (The Telescope Problem)

The scientists asked: "If we point the James Webb Space Telescope (JWST) at this planet, will we see the volcanoes?"

The Answer: Probably not.
The Analogy: Imagine trying to see a single candle flame on the dark side of a planet that is being lit up by a giant spotlight (the star). The volcanic heat is there, but it's tiny compared to the star's glare.
The Signal: The heat from the volcanoes is so faint that it would only change the planet's brightness by a tiny fraction (less than 1 part per million). Current telescopes aren't sensitive enough to spot this "ghostly" glow.

The Takeaway

This paper tells us that K2-141 b is a unique laboratory for geology.

It has a new type of tectonics: Instead of moving plates, it has a "single-lid" system where the crust gets recycled only at the twilight zones.
It has night volcanoes: The cold side is actually the most active volcanic zone because that's where the crust gets recycled.
It's a hard puzzle: Even though the planet is churning with volcanic activity, it's incredibly difficult for us to see or smell the atmosphere it creates because the star is just too bright and the planet is too small.

In short, K2-141 b is a planet of extremes: a boiling day, a frozen night, and a hidden, churning engine underneath that recycles its own skin in the twilight.

1. Problem Statement

Ultra-short period (USP) rocky exoplanets, often termed "lava worlds," are subjected to extreme stellar irradiation, leading to permanent tidal locking. This creates a stark hemispheric temperature contrast: a dayside covered by a magma ocean and a cold, solid nightside. While recent studies have focused on the equilibrium between magma oceans and atmospheres, the role of solid-state mantle dynamics in these extreme environments remains poorly understood.

Specifically, the paper addresses three critical gaps:

How does the extreme day-night temperature gradient influence mantle convection patterns and tectonic regimes on a tidally locked planet?
Can volcanic activity and volatile outgassing occur on the cold, solid nightside of such a planet?
What are the implications for the planet's thermal evolution, surface composition, and the potential detectability of volcanic signatures or atmospheric buildup?

The study focuses on K2-141 b, a well-characterized USP super-Earth ($1.54 R_\oplus $,$ 5.31 M_\oplus$) with a dayside brightness temperature of ~2050 K and a nightside consistent with 0 K, suggesting a lack of a thick heat-redistributing atmosphere.

2. Methodology

The authors employed two-dimensional (2D) spherical annulus mantle convection simulations using the code StagYY (Tackley 2008).

Physical Setup:
- Geometry: 2D spherical annulus representing the mantle from the Core-Mantle Boundary (CMB) to the surface.
- Boundary Conditions:
  - Dayside: Radiative boundary condition with a fixed temperature of 3000 K (representing the magma ocean).
  - Nightside: Radiative boundary condition with a fixed temperature of 50 K (solid surface).
  - CMB: Fixed temperature (6500 K) or cooling over time (simulating core heat loss).
- Rheology: Diffusion creep viscosity law with Arrhenius dependence on pressure and temperature. Models tested included:
  - Strong Lithosphere: No plastic yielding ( $\sigma_y = \infty$ ).
  - Weak Lithosphere: Plastic yielding included ( $\sigma_y = 100$ MPa).
- Heating Scenarios:
  - Basal Heating: Heat flux only from the core.
  - Mixed Heating: Basal heating + uniform internal radiogenic heating (Earth-like).
- Melt & Volatiles:
  - Tracer Particles: Lagrangian tracers tracked composition (pyrolite: 20% basalt, 80% harzburgite), melt fraction, and volatile concentrations (Carbon and Water).
  - Outgassing: Volatiles partitioned between solid and melt phases using batch melting models ( $D_{H2O} = 0.01$ , $D_{CO2} = 5.5 \times 10^{-4}$ ). Melt erupts if generated at depths <135 km and the surface is solid.
  - Intrusion: One model included a scenario where 70% of melt is intruded into the crust rather than erupted.
Simulation Duration: Models were run for up to 6.5 Gyr to reach statistical steady states.

3. Key Contributions

Discovery of a New Tectonic Regime: The paper identifies a unique "terminator-recycling" regime. Unlike Earth's plate tectonics or a stagnant lid, this regime features a single, continuous lid where crustal recycling occurs specifically at the day-night terminators due to flow convergence, despite the absence of plastic yielding.
Nightside Volcanism Quantification: The study provides the first quantitative estimates of volcanic heat flux and volatile outgassing rates on the cold nightside of a lava world, demonstrating that continuous volcanism can persist for billions of years.
Observability Constraints: The authors rigorously calculate the detectability of nightside volcanic thermal emission, concluding that even large eruptions produce signals below current detection thresholds (JWST), but localized outgassing near terminators may offer transmission spectroscopy signatures.
Atmospheric Evolution Limits: The study estimates the maximum potential atmospheric pressure buildup from volcanic outgassing, providing upper limits for secondary atmospheres on USP planets.

4. Key Results

A. Mantle Convection and Tectonics

Degree-2 Convection: In models without plastic yielding, the mantle stabilizes into a degree-2 convection pattern.
- Upwellings: Form at the substellar (dayside) and antistellar (nightside) points.
- Downwellings: Form near the day-night terminators where the hot magma ocean meets the cold solid crust.
Terminator Recycling: The convergence of flow at the terminators forces the cold, stiff lithosphere to subduct. This creates a form of asymmetric, single-lid tectonics where crustal material is recycled into the mantle at the terminators, even without a weak lithosphere (plastic yielding).
Plastic Yielding Effects: Models with plastic yielding ( $\sigma_y = 100$ MPa) showed more efficient cooling, numerous small-scale downwellings on the nightside, and a lack of the distinct terminator recycling pattern.

B. Thermal Evolution and Magma Ocean

Magma Ocean Depth: The dayside magma ocean stabilizes at a depth of 200–300 km (approx. 2–3% of the planet's radius).
Cooling Rates: Models with internal heating (MixCC, MixIntr) maintained higher mean mantle temperatures (~~3470 K) compared to purely basally heated models (~~3300 K). Models with core cooling showed a gradual decline in temperature over time.

C. Volcanism and Outgassing

Nightside Volcanism: Continuous volcanic eruptions occur on the nightside, producing a basaltic crust.
Outgassing Rates: Over 6.5 Gyr, volcanic activity can outgas tens of bars of volatiles.
- MixIntr (Mixed heating + intrusion): ~242 bar.
- MPlastic (Plastic yielding): ~195 bar.
- MixCC (Mixed heating): ~93 bar.
- MBasal (Basal heating only): ~10 bar (lowest due to limited melting).
Volatile Depletion: The mantle loses significant volatile budgets (e.g., MPlastic lost ~77% of its carbon budget), though the rate is highest during the initial 500 Myr spin-up phase.

D. Observability

Thermal Emission: The thermal emission signal from nightside volcanism is extremely weak. Even for large eruptions, the planet-to-star flux contrast is < 1 ppm, well below the noise floor of JWST/MIRI (approx. 25 ppm).
Spatial Distribution: Outgassing is often concentrated near the day-night terminators. While thermal emission is undetectable, this spatial concentration suggests that transmission spectroscopy might detect localized atmospheric signatures (e.g., CO2, H2O) if the atmosphere does not collapse or escape immediately.

5. Significance and Implications

New Tectonic Paradigm: The study challenges the binary view of "stagnant lid" vs. "plate tectonics," proposing a "terminator-recycling" mode unique to tidally locked magma ocean worlds. This mechanism allows for crustal recycling and volatile transport without the need for a weak, plastic lithosphere.
Atmospheric Retention: While the models suggest significant outgassing (up to ~240 bar), the authors caution that these are upper limits. Strong stellar XUV radiation and hydrodynamic escape (potentially stripping the atmosphere) and the lack of a magnetic field (though a dynamo is plausible) mean the actual atmosphere might be thin or non-existent.
Observational Strategy: The results guide future observations of lava worlds. Direct thermal detection of nightside volcanism is unlikely with current technology. However, transmission spectroscopy targeting the terminator regions offers a more promising avenue for detecting volcanic outgassing signatures.
Future Work: The paper highlights the need for coupled 3D interior-atmosphere models that include redox chemistry, volatile solubility, and atmospheric escape to fully characterize the habitability and evolution of such extreme worlds.

In summary, this paper demonstrates that the extreme thermal forcing of K2-141 b drives a unique mantle convection regime that facilitates continuous nightside volcanism and crustal recycling, potentially sustaining a secondary atmosphere despite the harsh stellar environment, though detecting these signatures remains a significant observational challenge.