sponchpop: Population synthesis to investigate volatile sulfur as a fingerprint of gas giant formation histories

This paper introduces SPONCHPOP, a novel planet population synthesis model that incorporates multi-phase sulfur chemistry to demonstrate how volatile sulfur serves as a powerful diagnostic tool for tracing gas giant formation histories and predicting the sulfur budgets of rocky planets.

The Gist

Imagine you are a detective trying to solve the mystery of how a planet was born. For years, astronomers have been looking at the "fingerprint" of a planet's atmosphere, specifically the ratio of Carbon to Oxygen, to guess where it was born and how it grew up.

This paper introduces a new, powerful clue: Sulfur.

Think of Sulfur not just as a boring element, but as a chameleon that changes its costume depending on where it is and how hot it gets. The authors built a new computer simulation called sponchpop (a playful nod to the elements Sulfur, Phosphorus, Oxygen, Nitrogen, Carbon, and Hydrogen) to track this chameleon from the cold, dusty birth of a star to the final, massive planet.

Here is the story of their discovery, broken down into simple concepts:

1. The Great Costume Change (The "Sulfur Desert")

In the cold, dark clouds of space where stars are born, Sulfur is mostly a gas. It's floating around freely. But as the cloud collapses to form a solar system, things get interesting.

• The Hot Zone (Near the star): It's too hot for ice, but just right for a chemical reaction. Here, the gaseous sulfur grabs onto iron dust and turns into a solid rock (like a mineral). The authors call this the "Sulfur Desert." In this zone, the gas is stripped of its sulfur because it's all locked up in rocks.
• The Cold Zone (Far from the star): It's freezing cold. Here, sulfur freezes into ice (like water freezing into snow).

The Analogy: Imagine a party where sulfur is a guest.

• In the Hot Zone, the guest is forced to wear a heavy, solid rock costume (FeS) and can't move around.
• In the Cold Zone, the guest puts on a fluffy ice coat (H2S ice).
• In the Middle, the guest is just floating around in a gas suit.

2. How Planets Eat (The "All-You-Can-Eat Buffet")

Planets grow by eating two things:

1. Gas: The invisible atmosphere of the disk.
2. Solids: Rocks, pebbles, and icy chunks (planetesimals).

The paper asks: What happens if a planet eats at different parts of the buffet?

• Scenario A: The Gas-Only Eater. If a planet forms in the "Sulfur Desert" (where sulfur is locked in rocks) and only eats gas, its atmosphere will be sulfur-poor. It's like eating a meal where the salt has been removed.
• Scenario B: The Rock Eater. If a planet forms far out in the cold, eats icy rocks rich in sulfur, and then crashes those rocks into its atmosphere, its atmosphere becomes sulfur-rich. It's like adding a massive amount of salt to the soup.

3. The Big Discovery: It's All About the "Late Night Snack"

The most exciting finding is about timing.

The authors found that to get a planet with a lot of sulfur in its atmosphere (like Jupiter or Saturn), it's not enough to just be born in the right place. The planet needs a "Late Night Snack."

• The "Snack" is Planetesimal Ablation: This is a fancy way of saying the planet crashes into and melts down a bunch of rocky/icy bodies after it has already started growing its giant gas envelope.
• The Result: If a planet eats these sulfur-rich rocks late in its life, its atmosphere gets a massive boost of sulfur. If it doesn't, the atmosphere stays relatively plain.

The Metaphor: Imagine a giant balloon (the planet's atmosphere).

• If you blow it up with just air (gas), it's light and plain.
• If you stuff it full of heavy, sulfur-rich rocks (planetesimals) while it's inflating, the balloon gets heavy and the air inside becomes thick with sulfur.

4. Why This Matters for Our Solar System

The authors tested their model against our own Solar System:

• Jupiter: It has more sulfur than the Sun. The model suggests Jupiter formed far out, ate some sulfur-rich rocks, and then migrated inward.
• Saturn, Uranus, Neptune: These planets have huge amounts of sulfur (up to 46 times more than the Sun!). The model shows that to get this much sulfur, these planets must have been bombarded by a massive amount of sulfur-rich rocks and ice late in their formation.

The Twist: The model predicts that planets born in the "Sulfur Desert" (close to the star) might end up with rocky cores that are completely sulfur-free. This is a big deal because sulfur is essential for life as we know it. If a rocky planet (like Earth) forms in this desert, it might be "sulfur-poor," which could change its geology and its ability to support life.

Summary: The New Detective Tool

Before this paper, astronomers looked at Carbon and Oxygen to guess a planet's history. Now, they have a new tool: Sulfur.

By measuring how much sulfur is in a gas giant's atmosphere, we can now tell:

1. Where it was born: Did it start in the hot "Sulfur Desert" or the cold "Ice Zone"?
2. What it ate: Did it just drink gas, or did it also eat a lot of sulfur-rich rocks?
3. How it moved: Did it migrate from the cold outer edges to the warm inner edges?

In a nutshell: Sulfur is the "smoking gun" that tells us the true story of a planet's childhood, revealing whether it was a picky eater of gas or a glutton of sulfur-rich rocks, and where it spent its formative years.

Technical Summary

Here is a detailed technical summary of the paper "sponchpop: Population synthesis to investigate volatile sulfur as a fingerprint of gas giant formation histories."

1. Problem Statement

Current population synthesis models used to link exoplanets to their formation environments predominantly focus on the Carbon-to-Oxygen (C/O) ratio. However, these models often treat Sulfur (S) as entirely refractory (locked in solid condensates like FeS), assuming it serves only as a tracer for accreted rocky solids. This assumption contradicts observational evidence from protoplanetary disks (e.g., ALMA/NOEMA detections of CS, SO, H2S) and the Interstellar Medium (ISM), where sulfur exists significantly as a volatile gas.

The paper addresses the gap in understanding how the chemical conversion of volatile sulfur (gas/ice) into refractory sulfur (solids) during disk evolution affects the final sulfur budget of planetary cores and atmospheres. Specifically, it investigates whether atmospheric sulfur abundances can serve as a diagnostic tool to distinguish between different formation and migration histories (e.g., in-situ formation vs. migration from beyond the H2S snowline).

2. Methodology

The authors introduce sponchpop, a modular, fully analytical, Python-based population synthesis code. The study focuses on the formation of gas giants over a 3 Myr duration.

A. Disk Models & Initial Conditions

The code implements three distinct disk evolution models:

1. Pure Viscous: Standard viscous evolution.
2. Viscous Irradiated: Includes stellar irradiation heating the outer disk.
3. MHD Wind: Includes magnetohydrodynamic disk winds (mass loss).

• Parameters: Solar-mass host stars, initial disk masses (0.01–0.1 $M_\odot$), and varying alpha-viscosity ($\alpha$).
• Chemistry: A minimalistic chemical kinetics network is implemented to track the conversion of H$_2$S (gas) to FeS (refractory solid) via reaction with iron grains. This replaces the equilibrium condensation assumption with time-dependent kinetics based on laboratory data (Lauretta et al. 1996).
  • Reaction: $\text{H}_2\text{S} + \text{gFe} \rightarrow \text{gFeS} + \text{H}_2$.
  • The model accounts for thermal desorption of H$_2$S (sublimation at ~50 K) and the formation of FeS (efficient at higher temperatures).

B. Planet Formation Physics

• Core Accretion: Cores grow via simultaneous accretion of pebbles (drifting inward) and planetesimals (static distribution).
  • Pebble growth is modeled using a "pebble predictor" based on Stokes number evolution.
  • Pebble accretion halts at the pebble isolation mass, triggering gas accretion.
• Gas Accretion: Envelope contraction follows a Kelvin-Helmholtz timescale (Piso & Youdin 2014), followed by runaway gas accretion.
• Migration: Planets undergo Type I migration (torque-driven) and Type II migration (gap-opening, viscous-driven) based on Tanaka et al. (2002) and Scardoni et al. (2020).
• Planetesimal Ablation ($p_{ratio}$): A critical free parameter dictating how accreted planetesimals contribute to the planet's composition:
  • $p_{ratio} = 0$: Planetesimals only add mass to the core.
  • $p_{ratio} = 0.5$ (Fiducial): 50% of accreted planetesimal mass (and sulfur) goes to the core, 50% ablates into the envelope.
  • $p_{ratio} = 1$: 100% of accreted planetesimals ablate in the envelope (enriching the atmosphere).

C. Simulation Scale

The study generated 45,000 individual planets across three disk models and three $p_{ratio}$ scenarios to statistically analyze sulfur abundance distributions.

3. Key Contributions

1. First Multi-Phase Sulfur Treatment: This is the first population synthesis model to explicitly couple volatile (gas/ice) and refractory (solid) sulfur reservoirs using chemical kinetics rather than static equilibrium assumptions.
2. Discovery of the "Sulfur Desert": The models predict a region in the protoplanetary disk (roughly 0.4–3.5 AU in fiducial cases) where efficient FeS formation depletes gas-phase sulfur, but temperatures are too high for H$_2$S ice to condense. This creates a zone of sulfur-poor solids and gas.
3. Diagnostic Framework: The study establishes that atmospheric sulfur abundance is not just a function of metallicity but a specific tracer of:
   • Formation location relative to the H$_2$S snowline.
   • The timing of gas accretion relative to planetesimal depletion.
   • The efficiency of late-stage planetesimal ablation.

4. Key Results

A. Atmospheric Sulfur Diversity

The final sulfur abundance in gas giant envelopes varies by six orders of magnitude depending on the formation scenario:

• No Planetesimal Ablation ($p_{ratio}=0$): Gas giants show a narrow sulfur range (0.7–1.4 $\times$ Solar). They cannot reproduce the high sulfur enrichments seen in Solar System giants (Jupiter, Saturn, Uranus, Neptune).
• Partial/Total Ablation ($p_{ratio} \ge 0.5$): The population splits into two distinct groups:
  1. "Normal" Population: Formed in the "sulfur desert" or exhausted local planetesimals; sulfur abundance remains near Solar values.
  2. "Enhanced" Population: Formed beyond the H$_2$S snowline and accreted sulfur-rich planetesimals during runaway gas accretion. These can reach up to 9.5 $\times$ Solar sulfur abundance.

B. Core vs. Envelope Trends

• Core Depletion: Planets born in the inner disk (1–3 AU) exhibit significant sulfur depletion in their cores. This is counter-intuitive but explained by the fact that this region is the "sulfur desert" where FeS formation is efficient, yet planetesimals there are sulfur-poor.
• Envelope Enrichment: High atmospheric sulfur requires the accretion of volatile-rich planetesimals from the outer disk after the onset of runaway gas accretion.

C. Solar System Comparison

• Jupiter: The model can reproduce Jupiter's sulfur abundance ($\sim$4.5 $\times$ Solar) only if $p_{ratio} \ge 0.5$ and the planet accreted planetesimals beyond the H$_2$S iceline.
• Ice Giants (Uranus/Neptune): The models fail to reproduce the extreme sulfur enrichments of Uranus (31 $\times$ Solar) and Neptune (46 $\times$ Solar), capping at $\sim$9.5 $\times$ Solar. The authors suggest this requires additional mechanisms not included in the 3 Myr timeframe, such as late-stage cometary bombardment or deep core-envelope mixing.

5. Significance

• New Formation Tracer: Sulfur abundance provides a complementary diagnostic to C/O ratios. While C/O traces the location of ice lines, Sulfur specifically traces the thermal history (FeS formation zones) and accretion timing (late-stage infall of planetesimals).
• Implications for Habitability: The models predict that rocky planets forming in the inner "sulfur desert" may be born sulfur-poor, which has profound implications for their geochemistry and potential habitability.
• Observational Relevance: With JWST and future missions (Ariel) detecting sulfur species (H$_2$S, SO$_2$) in exoplanet atmospheres, this framework provides the necessary theoretical tools to interpret these observations and reconstruct the formation histories of exoplanets.

In conclusion, sponchpop demonstrates that treating sulfur as a dynamic, multi-phase element fundamentally alters predictions of planetary composition, offering a powerful new method to decode the formation and migration histories of gas giants.