Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation

This study uses 1D simulations to demonstrate that while MHD-driven discs experience less photoevaporative erosion due to limited radial spreading, their overall lifetimes are comparable to viscous discs, with the survival of dust crucial for planet formation ultimately determined by the interplay between radial spreading, inward drift, and external FUV erosion strength.

The Gist

Imagine a protoplanetary disc as a giant, swirling pizza dough spinning around a central chef (the star). This dough is made of gas and tiny specks of dust. Eventually, some of that dust clumps together to form planets. But before that can happen, the dough has to survive long enough.

This paper asks a big question: What kills the pizza dough faster, and how can we save it?

The dough faces two main enemies:

1. Internal Mechanics: How the dough moves and spreads out on its own. Is it being pushed by a sticky, viscous sauce (viscosity) or pulled by invisible magnetic strings (MHD winds)?
2. External Enemies: A giant, scorching heat lamp from a neighboring star (external FUV radiation) that tries to blow the dough away.

Here is the breakdown of what the scientists found, using some everyday analogies.

1. The Two Ways the Dough Moves

Scientists have been arguing about how the dough spreads:

• The "Viscous" Way (The Sticky Sauce): Imagine the dough is thick and gooey. If you push the middle, the whole thing slowly spreads outwards like a slow-motion ripple. This is the "Viscous" model.
• The "Magnetic Wind" Way (The Invisible Strings): Imagine invisible strings pulling the dough upwards and outwards. This is the "MHD Wind" model. In this scenario, the dough doesn't spread out sideways as much; it just gets thinner and gets pulled away.

2. The Big Misconception

For a long time, scientists thought: "If the dough doesn't spread out (like in the Magnetic Wind model), it stays compact. If it stays compact, the heat lamp from the neighbor star can't blow as much of it away. So, Magnetic Wind discs should last longer!"

The paper says: Nope. That's wrong.

3. The Real Villain: The "Vacuum Cleaner" Effect

The authors ran computer simulations (like a video game for stars) to see what actually happens. They found that the Magnetic Wind discs actually die faster than the Viscous ones, especially when the heat lamp is on full blast.

Here is why, using a new analogy:

• The Viscous Disc (The Spreading Crowd): Imagine a crowd of people (dust) in a room. If the room is sticky (viscous), the people spread out to the edges. When the "vacuum cleaner" (the heat lamp) turns on at the door, it sucks up the people at the edge. Because the crowd is spread out, the vacuum has a lot of people to grab. However, the sticky floor also pulls new people from the center to the edge, constantly refilling the spot where the vacuum is working.
• The Magnetic Wind Disc (The Compact Crowd): Now imagine the crowd is packed tight in the center because the magnetic strings are pulling them up, not letting them spread. The vacuum cleaner at the door can't reach them as easily. BUT, because they are packed so tight and not spreading out, they are all sliding rapidly toward the center of the room (the star) like water down a drain.

The Result: In the Magnetic Wind scenario, the dust doesn't get blown away by the neighbor star as much, but it gets sucked into the star much faster because it's sliding inward so quickly. It's like a runner who avoids the wind but trips and falls into a pit before they can finish the race.

4. The "Protoplanetary" Problem

The goal is to make planets. Planets need dust to hang around for millions of years.

• The study found that in very bright, harsh environments (like a neighborhood with many massive, hot stars), the type of internal movement (sticky vs. magnetic) doesn't matter much. The dust gets destroyed or swallowed too fast.
• The Only Hope: The only thing that might save the dust is if the dough has bumps and ridges (substructures). Think of these like little walls or speed bumps in the pizza dough. If the dust gets stuck in a "trap" behind a bump, it can't slide into the star, and it can't be blown away by the wind.

5. The Takeaway for Planet Hunters

If we look at young star systems in harsh environments and see that they still have lots of dust (and are old enough to have formed planets), we should look for those "bumps" or substructures.

The paper concludes that we shouldn't worry too much about whether the disc is "sticky" or "magnetic" to save the dust. Instead, we need to look for traffic jams in the dust flow. Without those traffic jams (substructures), the dust will vanish too quickly for planets to form, no matter how the disc is moving internally.

In short:

• Old Idea: Magnetic winds protect discs by keeping them small.
• New Idea: Magnetic winds actually make discs die faster because the dust slides into the star too quickly.
• The Real Savior: "Speed bumps" (substructures) in the disc that trap the dust, giving it time to turn into planets.

Technical Summary

Here is a detailed technical summary of the paper "Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation" by Pichierri et al.

1. Problem Statement

Protoplanetary discs evolve under the influence of internal angular momentum transport mechanisms (viscous turbulence vs. magnetohydrodynamic [MHD] winds) and external environmental factors, particularly Far-UV (FUV) radiation from nearby massive stars.

• The Conflict: It is currently unclear whether discs are primarily driven by viscous stresses ($\alpha_{SS}$) or MHD disc winds ($\alpha_{DW}$). Furthermore, while external photoevaporation is known to truncate and disperse discs, its interplay with internal transport mechanisms and the survival of the solid (dust) component is poorly understood.
• The Gap: Previous studies have modeled gas evolution or dust in isolation, but no study has systematically compared the evolution of both gas and dust in viscous, MHD-wind, and hybrid discs under varying external FUV fluxes.
• Key Question: Under what conditions can the dust component survive long enough for planet formation to succeed in highly irradiated environments, and does the angular momentum transport mechanism (viscous vs. MHD) offer protection?

2. Methodology

The authors performed a suite of 1D numerical simulations using a modified version of the DiscEvolution code.

• Disc Model:

  • Gas: Modeled using a hybrid viscous and MHD-wind framework (Tabone et al. 2022a). The evolution is governed by the continuity equation including radial viscous diffusion, MHD wind mass loss, and external photoevaporation.
  • Dust: Modeled using a two-population approach (Birnstiel et al. 2012) distinguishing between small grains (fixed size) and large grains (limited by growth, fragmentation, and radial drift).
  • Physics: Includes radial drift, gas drag, diffusion, and dust entrainment in photoevaporative winds. Dust removal by MHD winds was initially neglected (verified as negligible in Appendix B).

• External Photoevaporation:

  • Utilized the updated FRIEDv2 grid (Haworth et al. 2023) to calculate mass-loss rates based on FUV flux ($G_0$).
  • Implemented a "truncation radius" ($R_t$) approach where mass loss is determined by the transition between optically thick and thin regimes, distributing mass loss inward-out from $R_t$.

• Parameter Space:

  • Stellar Mass: $1 M_\odot$.
  • Initial Disc Mass: $100 M_{Jup}$.
  • Angular Momentum Transport: Varied total $\alpha_{tot} = \alpha_{SS} + \alpha_{DW}$ ($10^{-4}$to$10^{-2}$) and the ratio$\psi_{DW} = \alpha_{DW}/\alpha_{SS}$(ranging from purely viscous$\psi_{DW}=0$to purely MHD$\psi_{DW} \gg 1$).
  • External FUV Flux: $0, 10, 100, 1000 G_0$.
  • Initial Disc Size ($R_c$): $10, 30, 100$ AU.

• Diagnostics:

  • $t_{dep,gas}$ and $t_{dep,dust}$: Time for gas/dust mass to drop to $1/1000$ of initial mass.
  • $t_{acc}$: Time for accretion rate to drop below $10^{-11} M_\odot$/yr.
  • $t_{IR.ex}$: Time until the disc becomes optically thin at 1 AU (no IR excess).
  • $f_{PE.wind}$: Fraction of dust mass removed by external winds.

3. Key Contributions

• First Systematic Comparison: This is the first study to simultaneously track the evolution of gas and dust in viscous, MHD-wind, and hybrid discs under external FUV irradiation.
• Decoupling of Mechanisms: It quantifies how the distinction between viscous and MHD-driven discs is "obfuscated" by high external FUV fluxes, particularly regarding gas evolution.
• Dust Survival Analysis: It provides a rigorous assessment of whether MHD winds (which do not spread discs outward) offer a survival advantage for dust against external erosion compared to viscous discs.

4. Key Results

A. Gas Evolution

• Viscous Discs (VE): Expand outward due to viscous spreading. They reach a self-adjusted state where the accretion rate matches the photoevaporative rate, eventually losing memory of their initial size.
• MHD-Wind Discs (DW): Do not expand outward. They lack a restoring mechanism to equilibrate inner and outer regions.
• High FUV Effect: At high fluxes ($\gtrsim 100 G_0$), the distinction between VE and DW gas evolution diminishes. High external erosion dominates, making the internal transport mechanism less relevant for gas lifetime.
• Observational Signature: The correlation between accretion rate ($\dot{M}_{acc}$) and wind mass loss ($\dot{M}_{wind}$) is strong for VE discs but weak for DW discs. However, this distinction vanishes in hybrid models or high-flux environments.

B. Dust Evolution and Lifetimes

• Counter-Intuitive Finding: Contrary to the naive expectation that non-spreading MHD discs would be "safer" from external erosion, MHD-driven discs often have shorter dust lifetimes than viscous discs in moderate-to-high FUV environments.
• Mechanism:
  • In Viscous Discs, outward diffusion replenishes the outer regions, making them susceptible to photoevaporation. However, this spreading also keeps dust further from the star, slowing down inward radial drift.
  • In MHD Discs, the lack of outward diffusion means dust remains concentrated in the inner regions. Without the "buffer" of outward spreading, radial drift becomes the dominant removal mechanism, causing dust to accrete onto the star much faster.
• Role of FUV: High FUV fluxes ($\gtrsim 100 G_0$) reduce the sensitivity of dust lifetimes to the transport mechanism ($\psi_{DW}$) and total $\alpha$. The lifetime is primarily dictated by the competition between radial drift and photoevaporation.

C. Dust Mass Removal ($f_{PE.wind}$)

• Viscous discs lose a higher fraction of dust to external winds because they spread outward, exposing more surface area to the FUV field.
• MHD discs lose less dust to the wind (as they don't spread) but lose more dust to the star via drift.
• The fraction of dust lost to winds depends heavily on initial disc size and $\alpha_{SS}$, but is largely insensitive to $\alpha_{DW}$.

5. Significance and Implications

• Planet Formation in Harsh Environments: The results suggest that in highly irradiated regions (e.g., near massive stars), the internal angular momentum transport mechanism (viscous vs. MHD) is not the primary factor determining whether planet formation can occur.
• The Role of Substructures: Since smooth discs (both viscous and MHD) struggle to retain dust in high FUV environments due to rapid drift or erosion, the authors conclude that disc substructures (rings, gaps, traps) are likely essential. These structures can halt inward radial drift, allowing solids to survive long enough to form planetary cores, regardless of the underlying transport mechanism.
• Observational Bias: Current surveys often target low-mass star-forming regions with low FUV fluxes, potentially biasing our understanding of typical disc evolution. The paper argues that typical protoplanetary discs in the galaxy likely experience higher FUV fluxes, where standard smooth-disc models fail to explain long-lived dust reservoirs without invoking substructures.
• Future Directions: The authors highlight the need to include chemical evolution (C/O ratios) and internal photoevaporation in future models to fully understand the composition of forming planets in these environments.

In summary, the paper demonstrates that external photoevaporation and radial drift are the dominant drivers of disc dispersal in irradiated environments, often overriding the differences between viscous and MHD transport mechanisms. Consequently, the survival of dust for planet formation likely relies on the presence of substructures rather than the specific nature of the internal angular momentum transport.