Survival of ultraheavy nuclei in astrophysical sources: applications to protomagnetar outflows

This paper develops new analytic fitting formulae for photodisintegration cross sections to demonstrate that the survival of ultraheavy nuclei in protomagnetar outflows is highly sensitive to the outflow geometry and engine properties, with spherical winds allowing survival only in the early phase and jetted outflows permitting survival primarily in low-spin-down energy scenarios before jet breakout.

The Gist

Imagine the universe as a giant, chaotic kitchen where the most extreme chefs—protomagnetars (newly born, super-fast-spinning, super-magnetic neutron stars)—are trying to bake the heaviest, most complex ingredients possible: ultraheavy atomic nuclei (like gold, platinum, and even heavier stuff).

These chefs are working in a very dangerous environment. They are surrounded by a storm of high-energy light particles called photons. Think of these photons not as gentle sunlight, but as a barrage of tiny, super-fast hammers.

The big question this paper asks is: Can these heavy "cookies" (nuclei) survive the journey out of the kitchen without getting smashed into crumbs?

Here is the breakdown of the research using simple analogies:

1. The Problem: The "Hammer Storm"

When these heavy nuclei try to escape the star, they have to pass through a dense cloud of light. If the light is too energetic, it hits the nuclei like a sledgehammer, shattering them back into smaller pieces (a process called photodisintegration).

If the nuclei get smashed, they can't become the "Ultra-High-Energy Cosmic Rays" (UHECRs) that scientists detect on Earth. So, for these heavy elements to reach us, they need a safe exit strategy.

2. The New Recipe: Better Math for "Smashing"

The authors first realized that the old math used to predict how easily these nuclei get smashed was based on data for lighter elements (like iron). It was like trying to predict how a bowling ball breaks by looking at how a tennis ball breaks.

They used a powerful computer simulation (called TALYS) to test heavy nuclei all the way up to gold. They created a new, more accurate formula (a "recipe") to calculate exactly how likely a heavy nucleus is to get smashed by a photon.

• The Analogy: They realized that as nuclei get heavier, they don't just get slightly harder to break; the way they interact with light changes in a specific, predictable curve. Their new formula captures this perfectly.

3. The Escape Routes: Two Types of "Tunnels"

The paper looks at two different ways these nuclei might try to escape the star:

• Route A: The Spherical Wind (The Open Door)
  Imagine the star blowing a giant, spherical bubble of wind in all directions.

  • The Result: For the first 100 seconds, the "light storm" is mostly soft and warm (thermal). The nuclei can survive this. But then, the wind speeds up, and the light turns into a high-energy "laser storm" (nonthermal).
  • The Catch: If the star is spinning very fast and has a super-strong magnetic field, the wind gets so fast that the "laser storm" hits the nuclei before they can escape. They get smashed. Only if the star is a bit "sluggish" (slower spin, weaker magnet) do the nuclei survive.

• Route B: The Jet (The Narrow Tunnel)
  Imagine the star shooting a focused beam of energy like a firehose or a laser pointer. This is a Jet.

  • The Result: This depends entirely on how thick the "walls" of the star are (the stellar envelope).
  • The "Wolf-Rayet" Star (Thin Walls): The jet punches through quickly. The nuclei escape before the "laser storm" gets dangerous. They survive!
  • The "Red Supergiant" Star (Thick Walls): The jet has to chew through a massive, thick cloud of gas. This takes a long time. By the time the jet finally breaks through the wall, the "laser storm" has already turned into a high-energy nightmare. The nuclei get smashed to bits.

4. The Verdict: Who Survives?

The paper concludes that survival isn't just about the nuclei; it's about timing and speed.

• The "Goldilocks" Zone: Heavy nuclei can only survive if they escape the star before the light around them turns into high-energy hammers.
• Fast Engines vs. Thick Walls: If you have a super-powerful engine (fast spin, strong magnet) but a thick wall (Red Supergiant), the nuclei die. They get stuck in the "kitchen" too long and get smashed.
• Slow Engines vs. Thin Walls: If the engine is weaker or the wall is thin, the nuclei escape quickly and make it to the universe intact.

Why Does This Matter?

Scientists have been trying to figure out where the heaviest elements in the universe (and the most energetic particles hitting Earth) come from. This paper tells us that protomagnetars are great candidates, but only under specific conditions.

It's like saying, "Yes, you can bake a perfect cake, but only if you take it out of the oven exactly when the timer goes off. If you leave it in too long, it burns."

In short: The universe is full of heavy elements, but they are fragile. They can only survive their escape from dying stars if the star's "engine" and the star's "size" are perfectly matched to let them slip out before the cosmic light storm destroys them.

Technical Summary

Here is a detailed technical summary of the paper "Survival of ultraheavy nuclei in astrophysical sources: applications to protomagnetar outflows" by Ekanger et al.

1. Problem Statement

Ultrahigh-energy cosmic rays (UHECRs) are observed to contain a significant fraction of intermediate-to-heavy nuclei, potentially including ultraheavy nuclei. While rapidly rotating protomagnetars formed in core-collapse supernovae are attractive candidates for synthesizing these heavy elements (via the r-process) and accelerating them to UHECR energies, a critical bottleneck remains: survival.

As these nuclei travel through the relativistic outflows of protomagnetars, they are exposed to intense radiation fields. The primary threat is photodisintegration, where high-energy photons strip nucleons from the nuclei, destroying them before they can escape the stellar envelope and reach interstellar space. Previous studies often relied on cross-section approximations valid only up to iron ($A=56$) or assumed simplified photon spectra. This paper addresses the gap in understanding whether ultraheavy nuclei ($A > 56$) can survive photodisintegration in the specific environments of protomagnetar-driven spherical winds and jetted outflows.

2. Methodology

A. New Photodisintegration Cross-Section Formulae

The authors first updated the theoretical framework for calculating photodisintegration cross-sections for heavy nuclei ($4 \le A \le 197$).

• Simulation: They utilized the TALYS nuclear simulation tool (v1.95) to calculate photonuclear cross-sections over the Giant Dipole Resonance (GDR) and quasi-deuteron (QD) energy ranges ($\sim 1-100$ MeV).
• Fitting: They derived new analytic fitting formulae for the GDR parameters (peak cross-section $\sigma_{GDR}$, peak energy $\epsilon_{GDR}$, and width $\Delta\epsilon_{GDR}$) based on TALYS data up to Gold ($A=197$).
  • Unlike previous models (e.g., KT93) that assumed a constant width or linear scaling, the new fits show:
    • $\sigma_{GDR} \propto A^{1.35}$ (better than linear for $A>56$).
    • $\epsilon_{GDR} \approx 42.65 A^{-0.21}$ MeV.
    • $\Delta\epsilon_{GDR} \approx 21.05 A^{-0.35}$ MeV (replacing the constant 8 MeV assumption).
• Result: The total integrated cross-section scales approximately linearly with mass number $A$, consistent with the Thomas-Reiche-Kuhn sum rule, but the specific energy dependence is refined for ultraheavy nuclei.

B. Astrophysical Models

The authors applied these formulae to two distinct protomagnetar outflow models:

1. Spherical Wind Model: Consisting of a neutrino-driven wind (Region A) and a shocked pulsar wind nebula (Region B).
2. Jetted Outflow Model: A collimated jet propagating through a stellar envelope, divided into a pre-collimated region (Region C) and a collimated jet region (Region D).
   • Progenitors: They considered Wolf-Rayet (WR), Blue Supergiant (BSG), and Red Supergiant (RSG) progenitors with varying envelope densities and radii.

C. Survival Criterion

The survival of nuclei is determined by calculating the effective photodisintegration optical depth ($f_{A\gamma}$):
$$f_{A\gamma} = \frac{t_{dyn}}{t_{A\gamma}}$$
where $t_{dyn}$ is the dynamical timescale of the outflow and $t_{A\gamma}$ is the photodisintegration timescale.

• Criterion: Nuclei are considered to survive if $f_{A\gamma} < 1$. If $f_{A\gamma} \gtrsim 1$, significant disintegration occurs.
• Photon Fields: The authors tracked the transition of the photon field from thermal (optically thick, $\tau_T > 1$) to nonthermal (optically thin, $\tau_T < 1$). They calculated the Thomson optical depth ($\tau_T$) to determine the transition time ($t_{Th}$).
• Timescales: Survival depends on the competition between the escape time (determined by jet breakout time $t_{bo}$ or pair-dominated transition $t_{GJ}$) and the photon transition time ($t_{Th}$).

3. Key Results

A. Spherical Wind Models

• Early Survival: For the first $\sim 100$ seconds post-core collapse, nuclei can survive in both the neutrino-driven wind and the shocked nebula because the photon field is thermal and the optical depth is high.
• Late Destruction: As the wind accelerates (Lorentz factor $\Gamma$ increases) and transitions to a nonthermal spectrum, the photodisintegration optical depth rises sharply.
• Outcome: Nuclei generally do not survive in high-energy outflows (high magnetic field $B_{dip}$, short spin period $P_i$) after $\sim 100$ seconds. Only in low-energy configurations ($B_{dip} \sim 10^{13}$ G, $P_i \sim 30$ ms) might nuclei survive longer, but even then, leakage from the high-energy region eventually destroys them.

B. Jetted Outflow Models

The survival depends critically on the progenitor envelope size and the engine spin-down energy:

• Wolf-Rayet (WR) Progenitors (Compact):
  • The jet breakout time ($t_{bo}$) is short ($< 200$ s).
  • In most cases, $t_{Th} > t_{bo}$, meaning the jet breaks out while the photon field is still thermal.
  • Result: Nuclei survive in WR progenitors for low-to-moderate spin-down energies. Only in extreme high-spin-down cases (low $P_i$, high $B_{dip}$) do nonthermal photons destroy nuclei before breakout.
• Blue/Red Supergiant (BSG/RSG) Progenitors (Extended):
  • The breakout time is significantly longer ($t_{bo, RSG} \sim 300-500+$ s).
  • For high spin-down energy engines, the photon field transitions to nonthermal ($t_{Th} < t_{bo}$) before the jet breaks out.
  • Result: Nuclei are efficiently photodisintegrated in high-energy engines surrounded by extended envelopes. The long exposure to nonthermal photons destroys the heavy nuclei.

C. Mass Dependence

• The photodisintegration efficiency ($f_{A\gamma}$) increases monotonically with mass number $A$.
• Ultraheavy nuclei (e.g., Platinum, $A=197$) are less likely to survive than iron ($A=56$) due to the mass dependence of the GDR cross-section and their higher bulk kinetic energy ($E_A = \Gamma m_A c^2$), which shifts them into more destructive photon interaction regimes.

4. Significance and Implications

• UHECR Source Constraints: The results suggest that protomagnetars can only serve as sources of ultraheavy UHECR nuclei if specific conditions are met:
  • Low spin-down energy (low $B_{dip}$, long $P_i$).
  • Compact progenitors (like WR stars) to ensure rapid jet breakout before nonthermal photons dominate.
• Multimessenger Astronomy:
  • Neutrinos: Efficient photodisintegration produces free neutrons. If nuclei survive, the neutron flux is lower; if they are destroyed, the outflow becomes neutron-rich, potentially enhancing GeV neutrino production via neutron-proton collisions.
  • Gamma Rays: Stringent survival requirements imply low ambient photon densities, which limits high-energy neutrino production via photomeson interactions but guarantees the escape of very high-energy gamma rays.
• Theoretical Advancement: The paper provides the first set of analytic fitting formulae for GDR cross-sections applicable to ultraheavy nuclei ($A$ up to 197), correcting previous approximations that were limited to iron-peak elements.

Conclusion

The study concludes that while protomagnetar outflows are capable of synthesizing heavy nuclei, their ability to deliver ultraheavy nuclei to the interstellar medium as UHECRs is highly constrained. Survival is generally only possible in low-power engines or those embedded in compact stellar envelopes. In high-power engines or extended envelopes, photodisintegration effectively strips nuclei of their mass, potentially limiting the UHECR composition to lighter elements or requiring alternative acceleration mechanisms.