With the recent advancements in the Lyman-alpha observations, it becomes more and more important to have theoretical models to help us decode the intricate Lyman-alpha spectral line. Scientists at MPA developed a theoretical approach to describe the escape of Lyman-alpha from scenarios where there is an empty hole to emulate the porous gas around galaxies.
Hydrogen is the most abundant element in the Universe, so it is no surprise that its first transition from an excited state to the ground state is crucial for studying the cosmos. This transition, known as the Lyman-alpha spectral line, lies in the ultraviolet region of the electromagnetic spectrum with a resting wavelength of 1215.67 angstroms. Over 50 years ago, Partridge and Peebles first highlighted the importance of Lyman-alpha for studying the high-redshift Universe, recognizing its brightness as particularly effective for detecting the most distant galaxies and learning about their formation.
Since then, scientists have made significant efforts to observe it through instruments like MUSE on the Very Large Telescope (VLT). The most recent step in this development came through the launch of the James Webb Space Telescope (JWST), which has revolutionized the observation of Lyman-alpha and opened new doors for exploring the high-redshift Universe. Alongside the observational data, there is a growing need for theoretical models to describe and interpret this spectral line fully.
Just like galaxies, the gas around them is highly anisotropic. It is subject to phenomena such as galactic outflows induced by supernova explosions. These outflows often clear out gas, creating low-density channels or holes and making the gas porous, facilitating the escape of radiation from the host galaxy. The study of Lyman alpha emission in this environment is particularly interesting as it provides information about the distribution and state of hydrogen in the Universe. Furthermore, in the Epoch of reionization, these holes and their signature in the Lyman-alpha profile could explain how ionizing photons escaped to reionize the Universe.
With all this in mind, a group of scientists at MPA led by PhD student Silvia Almada Monter performed a theoretical study of the behavior of Lyman-alpha photons in a slab filled with neutral gas in the presence of a simple empty hole. While this setup does not fully represent the complex gas geometry in real galaxies, boiling this problem down to the essentials helped to formulate a theory and understand how Lyman-alpha photons escape even in more complicated setups. This theoretical study was backed by Monte-Carlo radiative transfer simulations, which are known to yield highly accurate numerical results by tracking individual photon "packages" in space (and frequency). Despite the seemingly straightforward setup, these simulations revealed an unexpected and puzzling result.
Hydrogen is the most abundant element in the Universe, so it is no surprise that its first transition from an excited state to the ground state is crucial for studying the cosmos. This transition, known as the Lyman-alpha spectral line, lies in the ultraviolet region of the electromagnetic spectrum with a resting wavelength of 1215.67 angstroms. Over 50 years ago, Partridge and Peebles first highlighted the importance of Lyman-alpha for studying the high-redshift Universe, recognizing its brightness as particularly effective for detecting the most distant galaxies and learning about their formation.
Since then, scientists have made significant efforts to observe it through instruments like MUSE on the Very Large Telescope (VLT). The most recent step in this development came through the launch of the James Webb Space Telescope (JWST), which has revolutionized the observation of Lyman-alpha and opened new doors for exploring the high-redshift Universe. Alongside the observational data, there is a growing need for theoretical models to describe and interpret this spectral line fully.
Just like galaxies, the gas around them is highly anisotropic. It is subject to phenomena such as galactic outflows induced by supernova explosions. These outflows often clear out gas, creating low-density channels or holes and making the gas porous, facilitating the escape of radiation from the host galaxy. The study of Lyman alpha emission in this environment is particularly interesting as it provides information about the distribution and state of hydrogen in the Universe. Furthermore, in the Epoch of reionization, these holes and their signature in the Lyman-alpha profile could explain how ionizing photons escaped to reionize the Universe.
With all this in mind, a group of scientists at MPA led by PhD student Silvia Almada Monter performed a theoretical study of the behavior of Lyman-alpha photons in a slab filled with neutral gas in the presence of a simple empty hole. While this setup does not fully represent the complex gas geometry in real galaxies, boiling this problem down to the essentials helped to formulate a theory and understand how Lyman-alpha photons escape even in more complicated setups. This theoretical study was backed by Monte-Carlo radiative transfer simulations, which are known to yield highly accurate numerical results by tracking individual photon "packages" in space (and frequency). Despite the seemingly straightforward setup, these simulations revealed an unexpected and puzzling result.
Figure 1 Lyman-alpha unexpected triple-peaks emerge from a setup of a slab with a hole. Different colors indicate different hole sizes and the gas is more dense in the panels from left to right.
The puzzle: Walls or windows?
In a high-density medium, Lyman alpha photons diffuse in frequency due to Doppler shifts caused by the thermal motion of hydrogen atoms, resulting in a double-peak line. Conversely, in low-density environments, Lyman alpha behaves as a single-peaked line (like in the video). However, the probability of photons escaping through very dense gas is much smaller than the probability of them finding the hole and escaping through it with no resistance, as the hole is empty. This reasoning naively leads to the thought that the emerging Lyman-alpha from the slab with a pinched hole would be a centered single-peaked line because most of the light we see should have escaped through the hole.
We know this phenomenon when we see the light through a window: if the window is clean, the light gets through without any resistance, while a wall blocks the light completely. Similarly, in galaxies, abundant neutral hydrogen should act like a wall, completely stopping light from escaping, while empty channels should behave like clean windows, allowing light to escape effortlessly. In other words, one would expect all Lyman-alpha photons to escape through the low-density channel (window) and not through the wall (high-density gas). Surprisingly, the theoretical and simulation results are out of common sense. They found triple-peaked spectra: the expected two peaks emerge from the high-density gas, while a central peak exits from the empty channel. Lyman alpha photons escape not only from the path of least resistance (the window) but also somehow manage to get through the thick wall! How is this possible?
We know this phenomenon when we see the light through a window: if the window is clean, the light gets through without any resistance, while a wall blocks the light completely. Similarly, in galaxies, abundant neutral hydrogen should act like a wall, completely stopping light from escaping, while empty channels should behave like clean windows, allowing light to escape effortlessly. In other words, one would expect all Lyman-alpha photons to escape through the low-density channel (window) and not through the wall (high-density gas). Surprisingly, the theoretical and simulation results are out of common sense. They found triple-peaked spectra: the expected two peaks emerge from the high-density gas, while a central peak exits from the empty channel. Lyman alpha photons escape not only from the path of least resistance (the window) but also somehow manage to get through the thick wall! How is this possible?
Figure 2 The transmission fraction of the simulations (data points) aligns better with the new theoretical approach (solid line) than with the previously expected theoretical one (dashed lines). As the optical depth grows, the data points start approaching the oldt theoretical approach.
The solution: The Gambler's Ruin and the Fall of a Goat.
After examining the interaction of Lyman alpha photons with the gas, specifically their transmission and reflection, the MPA scientists solved the riddle. Due to the high column densities (the wall), most Lyman alpha photons are reflected upon encountering the gas. However, instead of simply bouncing out like ping-pong balls, they penetrate the gas, scatter, and then are reflected. How many times do they scatter? To answer this question, imagine a goat standing one step to the right of a cliff. The goat can either move right and fall or go left and survive. It makes this decision consecutively, performing a random walk until it reaches a safe place or falls to the cliff. The scenario of the goat falling off the cliff after having a random walk is an analogy for a photon scattering in the gas before being reflected. This problem is also known in statistics as 'The Gambler's Ruin Problem,' where, instead of photons (or goats), a gambler bets one euro on each turn, with the possibility of either winning or losing one euro. In this scenario, the probability of losing all the money (or the goat falling off the cliff/the photon being reflected) is 100%. Thus, eventually, all gamblers and goats face an unfortunate destiny. However, the expected time to reach this destiny is infinite! The gambler has no time limit to bet, the goat has no time limit to walk, and the photon has no time limit to scatter. Hence, it scatters many, many times.
This mathematical result directly affects the escaping Lyman-alpha photons and is the key to explaining the puzzling results. A large number of scattering events increases the chances of the photon shifting in frequency and mean free path enough to 'jump' the wall instead of crashing against it. Many more photons manage to pass through the high-density gas. After solving the appropriate diffusion equations, the MPA scientists found that the number of scattering events per reflection closely follows a Lévy distribution and is much greater than expected. This result implies that the transmission probability is orders of magnitude greater than anticipated. In the context of the slab with the hole, the probability of photons finding the hole is not as different than the probability of being transmitted through the gas as expected. As a result, the spectrum's double arise simultaneously with the central peak.
According to the literature, the presence of low-density channels in galaxies implies that the Lyman-alpha emission traces only the gas within them. However, these recent results indicate that due to the increased transmission probability, Lyman-alpha photons could trace the gas simultaneously in both high-density regions and low-density channels. In other words, Lyman-alpha can trace more average quantities of gas. Furthermore, it was previously believed that obtaining triple-peaked spectra was only possible with a tiny channel, an assumption that could be relaxed thanks to these findings. Additionally, these results affect the use of Lyman-alpha as a tracer for Lyman Continuum, as ionized channels are a likely escape route.
This mathematical result directly affects the escaping Lyman-alpha photons and is the key to explaining the puzzling results. A large number of scattering events increases the chances of the photon shifting in frequency and mean free path enough to 'jump' the wall instead of crashing against it. Many more photons manage to pass through the high-density gas. After solving the appropriate diffusion equations, the MPA scientists found that the number of scattering events per reflection closely follows a Lévy distribution and is much greater than expected. This result implies that the transmission probability is orders of magnitude greater than anticipated. In the context of the slab with the hole, the probability of photons finding the hole is not as different than the probability of being transmitted through the gas as expected. As a result, the spectrum's double arise simultaneously with the central peak.
According to the literature, the presence of low-density channels in galaxies implies that the Lyman-alpha emission traces only the gas within them. However, these recent results indicate that due to the increased transmission probability, Lyman-alpha photons could trace the gas simultaneously in both high-density regions and low-density channels. In other words, Lyman-alpha can trace more average quantities of gas. Furthermore, it was previously believed that obtaining triple-peaked spectra was only possible with a tiny channel, an assumption that could be relaxed thanks to these findings. Additionally, these results affect the use of Lyman-alpha as a tracer for Lyman Continuum, as ionized channels are a likely escape route.
Author:
Silvia Elizabeth Almada Monter
PhD student
2011
almada@mpa-garching.mpg.de
Original Publication:
Silvia Almada Monter, Max Gronke
Crossing walls and windows: the curious escape of Lyman-𝛼 photons through ionised channels
https://arxiv.org/pdf/2404.07169
Source
