Impact of anisotropic photon emission from sources during the epoch of reionisation

This study demonstrates that anisotropic photon emissions from early cosmic sources significantly alter the geometry and power spectrum of the 21-cm signal during reionisation, causing a 10–40% suppression of power at observable scales without introducing measurable directional anisotropy in the signal itself.

The Gist

Imagine the early universe as a giant, pitch-black room filled with thick, cold fog. This fog is made of neutral hydrogen gas. Suddenly, the first stars and galaxies ignite like lightbulbs in the dark. Their job is to blast out ultraviolet light (photons) to burn away the fog, turning the cold, neutral gas into hot, ionized gas. This process is called the Epoch of Reionization.

For a long time, scientists have modeled this process with a simple assumption: they imagine these cosmic lightbulbs shine isotropically. That means they glow equally in every direction, like a perfect, round lightbulb filling a room with a spherical bubble of light.

But what if the lightbulbs are broken?

What if, instead of glowing in all directions, the light escapes only through specific cracks or holes in the galaxy? Maybe the light shoots out in a narrow, powerful beam, like a flashlight or a laser, leaving the rest of the room in the dark. This is anisotropic emission.

This paper asks: Does it matter if the light comes out in a sphere or a cone?

The Experiment: The "Flashlight" Universe

The researchers built a massive computer simulation of the early universe. They created two types of universes:

1. The "Sphere" Universe: The standard model where light spreads out evenly in all directions (like a glowing ball).
2. The "Cone" Universe: A new model where light is forced to escape only through narrow channels, like a flashlight beam. To make the experiment fair, they made sure the total amount of light was the same in both universes; they just changed the shape of the beam.

What They Found

1. The Shape of the Bubbles

In the "Sphere" universe, the ionized gas forms nice, round bubbles. In the "Cone" universe, the bubbles look like ice cream cones or narrow tunnels.

• Early on: When the universe is just starting to clear up (less than 30% ionized), the "Cone" universe has many small, scattered bubbles. The light gets stuck in narrow channels and can't spread out as fast as the round light. It's like trying to fill a room with water using a garden hose vs. a firehose; the hose (cone) creates small, isolated puddles first.
• Later on: As time goes on, these narrow bubbles grow and eventually crash into each other. By the middle of the process, the "Cone" bubbles grow big enough to look very similar to the "Sphere" bubbles. The universe ends up looking roughly the same, just with a slightly different history of how it got there.

2. The "Power Spectrum" (The Fingerprint)

Astronomers don't just look at pictures; they look at the "power spectrum," which is like a musical fingerprint of the universe. It tells us how much "clumpiness" exists at different sizes.

The researchers found a major difference here. The "Cone" universes produced a suppressed signal (about 10% to 40% weaker) at specific scales.

• The Analogy: Imagine listening to a choir. If everyone sings in a perfect circle (Sphere), the sound is uniform. If everyone sings through a megaphone pointed in random directions (Cone), the sound waves interfere with each other differently, creating a "quiet spot" in the middle frequencies.
• Why it matters: Current radio telescopes (like HERA and the future SKA) are looking for this exact signal. If we assume the light is spherical when it's actually beamed, we might misinterpret the data and get the wrong answer about how many stars existed or how fast the universe changed.

3. The "Direction" Surprise

You might think that if the light is beamed, the whole universe would look "lopsided" or directional.

• The Result: Surprisingly, it didn't. Even though individual galaxies were shooting beams, there were so many galaxies pointing in random directions that the "lopsidedness" canceled itself out. The overall universe still looked the same from every angle. It's like standing in a forest where every tree is leaning in a different direction; from a distance, the forest looks perfectly symmetrical.

The Big Takeaway

This paper is a warning to astronomers: Don't assume the lightbulbs are perfect spheres.

If the first galaxies were actually leaking light through narrow cracks (which high-resolution simulations suggest they might), our current models of the early universe are slightly off. This could change how we interpret the data from the world's most powerful radio telescopes.

In short: The universe might have been clearing up its fog not with a gentle, round glow, but with thousands of flashlights beaming in random directions. While the end result looks similar, the journey there leaves a unique fingerprint that we are just starting to learn how to read.

Technical Summary

1. Problem Statement

The Epoch of Reionisation (EoR) describes the transition of the Intergalactic Medium (IGM) from neutral to ionised, driven by the first stars, galaxies, and accreting black holes. A critical uncertainty in modelling this process is the escape fraction and directionality of ionising (UV) photons from these sources.

• Current Assumption: Most large-scale cosmological reionisation simulations (e.g., 21cmFAST, HMreio) and semi-numerical frameworks assume isotropic (spherically symmetric) photon emission.
• The Reality: High-resolution simulations of individual galaxies suggest that photon escape is often anisotropic, occurring through narrow "leakage channels" or cones due to scattering and absorption in the interstellar medium.
• The Gap: It is unknown whether neglecting this anisotropy in large-scale simulations significantly biases our understanding of reionisation geometry, bubble size distributions, and observable 21-cm signals.

2. Methodology

The authors performed a suite of cosmological reionisation simulations to isolate the effects of anisotropic emission while keeping the total photon budget constant.

• Simulation Setup:

  • Code: Used the $N$-body code CUBEP3M for structure formation and the radiative transfer code C2Ray for photon propagation.
  • Volume: $244 , h^{-1}\text{Mpc}$per side with$4000^3$ particles.
  • Sources: Ionising sources were associated with dark matter haloes ($M > 10^9 M_\odot$). To maintain computational efficiency, all haloes within a grid cell ($\sim 1 \, h^{-1}\text{Mpc}$) were treated as a single source.
  • Photon Budget: To ensure a fair comparison, the total number of photons escaping into the IGM was kept identical across all models. Anisotropic models used a boost factor ($B$) to compensate for the restricted solid angle, ensuring the global escape fraction remained consistent with the isotropic case.

• Models Tested:

  1. Sphere (Fiducial): Isotropic emission ($4\pi$ solid angle).
  2. Cone-1: Static conical emission with a narrow opening angle ($\Theta_c = 0.09\pi$, $\theta_c \approx 0.3$ rad).
  3. Cone-2: Static conical emission with a wider opening angle ($\Theta_c = 0.35\pi$, $\theta_c \approx 0.6$ rad).
  4. Cone-3: Conical emission with the same narrow angle as Cone-1, but the cone direction randomly re-oriented every 11.5 Myrs (simulating time-evolving channels).

• Analysis Tools:

  • Mean-Free-Path (MFP) Bubble Size Distribution: Measures the distance from an ionised cell to the first neutral cell.
  • Friends-of-Friends (FOF) Bubble Size Distribution: Measures the volume of topologically connected ionised regions to study percolation.
  • 21-cm Power Spectrum ($\Delta^2_{21}$): Spherically averaged power spectrum of the differential brightness temperature.
  • Anisotropy Ratio ($r_\mu$): A metric to detect directional dependence in the 21-cm signal relative to the line of sight.

3. Key Contributions

• First Large-Scale Exploration: This is the first study to systematically investigate the impact of anisotropic photon leakage on large-scale ($\gtrsim 100$ Mpc) reionisation morphology and observables.
• Modified Radiative Transfer: Successfully implemented a cone-based photon emission algorithm in C2Ray, allowing for the simulation of directional leakage without resolving individual galaxy sub-structures.
• Decoupling Effects: By boosting the photon flux in anisotropic models, the authors isolated the geometric effects of anisotropy from the effects of simply having fewer photons.

4. Key Results

A. Reionisation History and Morphology

• Delay in Reionisation: Anisotropic models (especially Cone-1) exhibit a delayed reionisation history compared to the isotropic Sphere model, even with the same total photon output. This is attributed to resolution effects where narrow cones miss high-density regions initially.
• Bubble Sizes (Early EoR): During early reionisation ($\bar{x}_{HI} < 0.3$), anisotropic models produce smaller ionised bubbles on average. The narrow cones create isolated, conical ionised regions rather than expanding spheres.
• Bubble Sizes (Late EoR): By the middle stages ($\bar{x}_{HI} \approx 0.5$), the bubble sizes converge. The differences in size distribution diminish as bubbles begin to overlap and merge.
• Percolation: Anisotropic models show a faster formation of the largest connected ionised cluster (percolation) compared to the isotropic case. The narrow cones allow photons to travel further along filaments of the cosmic web, creating long, winding ionised structures that merge earlier.

B. 21-cm Power Spectrum

• Power Suppression: The most significant finding is a suppression of the 21-cm power spectrum in the "intermediate" scale range ($k \approx 0.1 - 1 \, h\text{Mpc}^{-1}$).
  • For the narrowest cone (Cone-1), power is suppressed by 10–40% compared to the isotropic case.
  • This suppression is most pronounced at $k \approx 0.4 \, h\text{Mpc}^{-1}$ (a factor of 2 reduction in power for Cone-1 at $\bar{x}_{HI}=0.3$).
• Scale Dependence:
  • Small Scales ($k > 0.8$): Anisotropic models show higher power due to the grainy, small-scale structure of isolated cones.
  • Large Scales ($k < 0.1$): Differences are minimal, though slight amplitude variations exist due to the faster growth of large ionised clusters in anisotropic models.
• Observability: The suppression occurs precisely in the $k$-range targeted by current and future radio interferometers (LOFAR, HERA, SKA-Low), suggesting that assuming isotropy could lead to significant errors in inferring astrophysical parameters from observational data.

C. Signal Anisotropy

• No Measurable Anisotropy: Despite the sources emitting directionally, the 21-cm signal itself does not show measurable anisotropy ($r_\mu \approx 0$).
• Reasoning: The cumulative effect of millions of sources with random orientations, combined with the rapid overlapping of ionised bubbles, averages out the directional signature. The anisotropy of individual sources is "washed out" on cosmological scales.

5. Significance and Conclusions

• Impact on Interpretation: Neglecting photon anisotropy introduces a systematic uncertainty in reionisation modelling. Specifically, it can lead to a misinterpretation of the 21-cm power spectrum amplitude, potentially biasing estimates of the ionising efficiency and escape fraction.
• Modeling Uncertainty: The authors estimate that the difference between isotropic and anisotropic models provides a "rough upper estimate" of the modelling uncertainty. The suppression of power by up to 40% is a non-negligible effect that must be accounted for in future data analysis.
• Future Work: The current implementation uses simplified, static (or randomly changing) cones. Future work aims to link emission direction to physical halo properties (e.g., angular momentum vectors) and better resolve the resolution effects inherent in the grid-based cone model.

In summary, while anisotropic emission does not alter the global reionisation timeline drastically (once photon budgets are matched) nor introduce directional bias in the 21-cm signal, it fundamentally alters the geometry of ionised bubbles and significantly suppresses the 21-cm power spectrum at scales critical for current radio astronomy experiments.