Ultra high-energy cosmic rays from relativistic outflows in accretion induced collapse of white dwarfs

This paper proposes that accretion-induced collapses of rapidly-rotating, highly magnetized white dwarfs can generate magnetically-dominated relativistic outflows capable of accelerating heavy nuclei to ultra-high energies, potentially accounting for the observed flux of ultra-high-energy cosmic rays.

The Gist

Imagine the universe as a giant, chaotic construction site where the most powerful explosions imaginable are constantly happening. For decades, scientists have been trying to figure out where the absolute "heaviest hitters" of the cosmic world come from: Ultra-High-Energy Cosmic Rays (UHECRs). These are subatomic particles traveling so fast they carry more energy than a baseball thrown by a professional pitcher, but they are billions of times smaller.

For a long time, we didn't know who was throwing these cosmic baseballs. This paper proposes a new, exciting candidate: White Dwarfs that collapse into super-spinning, super-magnetic neutron stars.

Here is the story of how this works, broken down into simple concepts:

1. The Setup: A Star Eating Too Much

Imagine a White Dwarf as a dead, dense star (like a burnt-out ember) that is slowly eating material from a nearby companion star. It's like a cosmic Pac-Man, gobbling up gas and dust.

• The Limit: Eventually, it eats so much that it hits a "weight limit" (called the Chandrasekhar limit).
• The Collapse: Instead of exploding like a normal supernova, this heavy star suddenly collapses in on itself. It's like a building imploding instantly.
• The Result: This collapse creates a newborn, super-dense star called a protomagnetar. Think of this new star as a cosmic top that is spinning incredibly fast (thousands of times a second) and has a magnetic field stronger than anything else in the universe.

2. The Engine: A Cosmic Firehose

Because this new "protomagnetar" is spinning so fast and is so magnetic, it acts like a powerful engine. It shoots out two narrow beams of energy and matter, like a cosmic firehose or a laser beam, shooting out in opposite directions.

• The Speed: These beams shoot out at speeds close to the speed of light.
• The Ingredients: The paper suggests that the material inside these beams is "heavy" (like iron nuclei), not just light particles like protons. This is important because the heaviest cosmic rays we see on Earth are heavy.

3. The Accelerator: The Cosmic Slingshot

How do these heavy particles get to such insane speeds? The paper suggests two ways the "firehose" acts as a slingshot:

• Magnetic Reconnection: Imagine the magnetic field lines in the beam getting tangled like rubber bands. When they snap and reconnect, they release a massive burst of energy, flinging particles forward.
• Internal Shocks: Imagine the firehose isn't steady. It shoots a fast wave of water, then a slower wave. The fast wave catches up to the slow wave and crashes into it. This collision creates a shockwave that acts like a cosmic airbag, slamming particles and accelerating them to extreme speeds.

4. The Journey: Surviving the Trip

Once these heavy particles are launched, they have to travel across the universe to reach Earth.

• The Danger: The universe is filled with light (photons). If a heavy particle hits a photon, it can break apart (like a Lego tower hitting a wall).
• The Good News: The authors calculated that because these particles are launched from relatively "nearby" cosmic events (within about 100 million light-years), they can survive the trip. They don't break apart before they reach us.

5. The Big Picture: Are They the Source?

The authors did the math to see if these collapsing white dwarfs are powerful enough to explain all the UHECRs we see.

• The Verdict: Yes, they likely are. If even a small fraction of these collapsing stars shoot out these powerful beams, they could be responsible for the majority of the ultra-high-energy cosmic rays we detect on Earth.
• The Evidence: The paper plots these events on a graph (Figure 1) showing that they fit perfectly into the "zone" where cosmic ray sources are expected to be.

Why This Matters Now

This isn't just theory anymore. The paper mentions that we are currently seeing strange cosmic events (like specific Gamma-Ray Bursts) that look exactly like what these collapsing white dwarfs would produce. With new, powerful telescopes coming online (like the Rubin Observatory and the James Webb Space Telescope), we might soon be able to "see" these events directly and confirm that these collapsing stars are indeed the cosmic slingshots launching the universe's most energetic particles.

In short: When a heavy, dead star collapses, it can spin up into a magnetic monster that shoots out beams of heavy atoms. These beams act as giant slingshots, launching particles so fast they become the most energetic messengers in the universe, eventually crashing into our atmosphere as Ultra-High-Energy Cosmic Rays.

Technical Summary

Technical Summary: Ultra high-energy cosmic rays from relativistic outflows in accretion induced collapse of white dwarfs

Problem Statement
The origins of ultra-high-energy cosmic rays (UHECRs) remain a significant mystery in astrophysics. Observational data impose stringent constraints on potential sources, requiring a specific energy spectrum, a nuclear composition that becomes increasingly heavy at the highest energies, and energy-dependent anisotropy. While powerful transients like gamma-ray bursts (GRBs) are proposed candidates, the nature of their central engines is debated. Standard models invoke black hole–accretion disk systems, but rapidly rotating magnetars offer an alternative. Specifically, the accretion-induced collapse (AIC) of white dwarfs (WDs) has been proposed as a channel to produce such engines. However, the potential of AIC-driven relativistic outflows to serve as sources of UHECRs, particularly heavy nuclei, has not been systematically modeled. Previous work on CRs from AICs focused on protons accelerated near the magnetosphere; this paper addresses the gap regarding the acceleration of heavy nuclei in the relativistic outflows themselves.

Methodology
The authors model the acceleration of heavy iron (Fe)-like nuclei in relativistic outflows launched during the AIC of a rapidly rotating, highly magnetized white dwarf. The study proceeds through the following steps:

1. Outflow Modeling: The authors model the proto-neutron star (protomagnetar) formed post-AIC as a source of magnetically dominated relativistic outflows. They calculate the evolution of the outflow's magnetization ($\sigma_0$) and bulk Lorentz factor ($\Gamma_j$) based on the spin-down of the protomagnetar. Key parameters include an initial spin period of 2 ms, a magnetic field of $5 \times 10^{15}$ G, and a mass of $1.42 M_\odot$. The mass loss rate is driven by neutrino heating, which declines over time, causing the outflow to become increasingly magnetized and relativistic.
2. Acceleration Mechanisms: Two distinct acceleration sites within the jet are considered, analogous to GRB prompt emission mechanisms:
   • Magnetic Reconnection: Acceleration occurs at a saturation radius ($R_{mr}$) where the flow reaches terminal velocity. The acceleration timescale is balanced against cooling timescales (synchrotron and dynamical).
   • Internal Shocks: Acceleration occurs where faster shells of the outflow collide with slower ones ($R_{is}$). The shock radius is constrained to be outside the photosphere to avoid radiation-mediated shocks.
3. Energy Losses and Survival: The maximum energy achievable is determined by balancing acceleration timescales with cooling timescales (dominated by synchrotron cooling) and photodisintegration losses. The authors specifically evaluate the survival of Iron nuclei against photodisintegration by GRB photons at the source and by the extragalactic infrared background (EIB) during propagation. They adopt a survival criterion of $\tau_{\gamma-N} < 10$ interactions at the source.
4. Emissivity Calculation: The authors calculate the UHECR emissivity ($\varepsilon^2 Q$) by integrating the source spectrum over the assumed rate of AICs ($\dot{\rho}_{AIC}$). They assume a power-law spectrum with an exponential cutoff and a conversion efficiency ($\eta_{CR}$) of 10% of the jet energy into UHECRs.
5. Source Characterization: The effective number density and effective luminosity of AICs are plotted against other known astrophysical sources to assess their viability in explaining the observed UHECR flux.

Key Contributions and Results

• Acceleration Limits: The model demonstrates that both magnetic reconnection and internal shocks can accelerate Iron nuclei to energies exceeding $10^{19}$ eV. Specifically, magnetic reconnection yields a maximum comoving energy $\varepsilon'_{max} \sim 8.0 \times 10^{19}$ eV, while internal shocks reach $\sim 1.2 \times 10^{20}$ eV.
• Composition Survival: The study finds that Iron nuclei can survive photodisintegration at the source (with $\tau_{\gamma-N} < 10$) and during propagation to Earth over typical distances of $\sim 100$ Mpc. This supports the hypothesis that AICs can contribute to the observed heavy composition of UHECRs.
• Energy Generation Rate: Accounting for uncertainties in acceleration mechanisms and AIC rates, the authors estimate that AICs can contribute an energy generation rate density of $\sim$ a few $\times 10^{43} - 10^{45}$ erg Mpc$^{-3}$ yr$^{-1}$ (assuming Iron-like nuclei).
• Viability as Sources: When plotted on the source luminosity versus number density plane (Fig. 1), AICs occupy a region capable of explaining the observed UHECR flux, provided a significant fraction of AICs host relativistic outflows. The authors note that while uncertainties in the AIC rate and the fraction of AICs producing jets are large, the population has sufficient capability to power the observed UHECRs.

Significance and Claims
The paper claims to be the first to propose AICs of white dwarfs as potential sources of UHECRs, specifically leveraging the connection between AICs and relativistic outflows capable of powering GRBs. The authors argue that this scenario is timely given recent observational evidence linking AICs to kilonovae (e.g., GRB 21211A and GRB 230307A) and predictions that AICs will be observable by future facilities like the Vera C. Rubin Observatory (LSST), the James Webb Space Telescope (JWST), and MeV gamma-ray observatories (COSI, AMEGO-X).

The authors modestly conclude that despite large uncertainties in the acceleration physics and the true rate of AICs, a population of these events can indeed serve as potential UHECR sources at current observational levels. They emphasize that their work highlights the potential importance of AICs as UHECR sources and opens the door for future studies to test this scenario with more detailed calculations involving microphysics, propagation effects, and specific population analyses. They explicitly defer detailed propagation calculations and the interpretation of the observed UHECR cutoff (whether source or propagation limited) to future work.