POLAR-II: modeling star formation history of galaxies on the 21-cm signal from Epoch of Reionization

This study utilizes the Jiutian-300 simulation and L-Galaxies 2020 model to demonstrate that incorporating realistic, time-varying star formation histories—specifically those dependent on stellar age and redshift—significantly alters the topology, timing, and thermal state of the Intergalactic Medium during the Epoch of Reionization, thereby producing distinct 21-cm global signals and power spectra compared to models assuming constant star formation rates.

The Gist

Imagine the early universe as a giant, dark, cold room filled with thick fog (neutral hydrogen gas). For a long time, this room was pitch black. Then, the first stars and galaxies were born, acting like millions of tiny lightbulbs and heaters. Their light began to burn away the fog, turning the universe into a clear, hot, and ionized space. This era is called the Epoch of Reionization (EoR).

Scientists are trying to take a "photo" of this process using a special kind of radio signal called the 21-cm signal. It's like trying to see the fog clearing by listening to the static on a radio.

This paper, titled POLAR-II, is about how we build the computer models to understand exactly how that fog cleared. The authors realized that previous models were a bit too simple. They treated galaxies like lightbulbs that just turned on and stayed on at a steady brightness. But in reality, galaxies are more like complex machines that have "starbursts" (periods of intense activity) and "quenching" (periods where they slow down or stop making stars).

Here is a simple breakdown of what they did and what they found:

1. The Problem: The "Steady Light" vs. The "Flickering Bulb"

Imagine you are trying to figure out how fast a room heats up.

• Old Model: You assume a heater runs at a constant 1000 watts forever.
• Real Life: The heater might blast at 2000 watts for a while, then drop to 500 watts, then spike again. Even if the total energy used over a year is the same, the timing of that energy changes how the room feels.

The authors asked: Does the "flickering" history of a galaxy (its Star Formation History) change how the universe heats up and clears of fog, even if the total amount of light is the same?

2. The Tools: A Cosmic Movie Set

To answer this, they used a "movie set" approach:

• The Stage (Jiutian-300): A massive computer simulation of dark matter (the invisible skeleton of the universe) where galaxies form.
• The Script (L-Galaxies 2020): A set of rules that tells the galaxies how to grow, merge, and change their star-making rates over time. This script is much more realistic than just saying "galaxies make stars at a steady rate."
• The Camera (Grizzly): A tool that takes the galaxy data and calculates how their light and heat travel through the fog, creating a 3D map of the clearing universe.

3. The Key Discovery: Age Matters

The researchers found that the age of the stars inside a galaxy is a crucial detail. They used a metric called $\tau_{age}$ (tau-age), which is basically the "average age" of the stars in a galaxy.

• Young Galaxies (Low $\tau_{age}$): These are like energetic teenagers. They have been making stars very recently. They produce a lot of high-energy X-rays.
  • Result: They heat the surrounding fog very effectively and create larger bubbles of clear space.
• Old Galaxies (High $\tau_{age}$): These are like retired grandparents. Most of their stars were born a long time ago. They produce less X-ray heat.
  • Result: They create smaller bubbles of clear space because the gas cools down and recombines (turns back into fog) faster.

4. The Big Reveal: It's Not Just About Total Light

The most important finding is that timing matters.
Even if two galaxies produce the exact same total amount of light over their entire lives, the one that made its stars recently (young) will clear the fog faster and heat the gas more than the one that made its stars long ago (old).

When they compared their new, realistic model (where galaxies have complex histories) against the old, simple model (constant star formation):

• The Realistic Model: The universe cleared up slightly faster, and the gas was slightly warmer.
• The "Bubbles": The holes in the fog were slightly bigger and shaped differently.

Why Does This Matter?

Think of the 21-cm signal as a "soundtrack" of the universe's history. If you use the wrong model (the simple, steady lightbulb), you might misinterpret the soundtrack. You might think the universe cleared up at a different time or that the galaxies were different than they actually were.

By adding the "flickering" history of galaxies into their model, the authors are helping future radio telescopes (like the SKA, a massive telescope array being built in Australia and South Africa) interpret the data correctly. They are essentially giving the scientists a better "decoder ring" to understand the story of how the dark, cold universe became the bright, hot place we live in today.

In a nutshell: The universe didn't just turn on a switch. It was a complex dance of galaxies growing, merging, and changing their star-making habits. To understand the history of the cosmos, we have to listen to the rhythm of that dance, not just the total volume of the music.

Technical Summary

Here is a detailed technical summary of the paper "POLAR-II: modeling star formation history of galaxies on the 21-cm signal from Epoch of Reionization".

1. Problem Statement

The Epoch of Reionization (EoR) is a critical phase in cosmic history where the neutral Intergalactic Medium (IGM) transitioned to an ionized state. While the 21-cm hyperfine line of neutral hydrogen offers a powerful probe of this era, accurately modeling the process remains challenging.

• The Gap: Current semi-numerical simulations of the EoR often rely on simplified assumptions regarding the Star Formation History (SFH) of galaxies, typically assuming a constant Star Formation Rate (SFR) or ignoring the stochastic nature of star formation (starbursts and quenching) driven by mergers and feedback.
• The Consequence: Although galaxies with the same total stellar mass may emit a similar total number of ionizing photons over their lifetime, their temporal distribution of star formation (SFH) affects the recombination rates of ionized gas and the heating efficiency of the IGM. Neglecting these variations leads to inaccuracies in predicting the topology of ionized bubbles and the resulting 21-cm signal.

2. Methodology

The authors developed an updated version of the semi-numerical code POLAR to incorporate realistic, evolving SFHs into reionization modeling. The workflow involves three main stages:

A. Galaxy Formation and Evolution

• Simulation: They utilized the Jiutian-300 N-body dark matter simulation (300 $h^{-1}$ cMpc box, $6144^3$ particles) combined with the semi-analytic model L-Galaxies 2020 (LG20).
• Output: LG20 provides a galaxy catalog containing stellar mass ($M_*$), metallicity, and detailed SFHs (star formation rates in time bins) for halos down to $2 \times 10^8 h^{-1} M_\odot$.
• Key Parameter: The stellar mass-weighted stellar age, $\tau_{age}$, is used as a proxy to characterize the SFH.

B. Source Modeling (UV and X-ray)

The authors calculated the Spectral Energy Distributions (SEDs) for three source types based on the LG20 output:

1. Stellar Sources: Integrated SEDs (iSED) derived using the BPASS binary population synthesis model.
2. X-ray Binaries (XRBs): Modeled using scaling relations from Madau & Fragos (2017), distinguishing between High-Mass (HMXB) and Low-Mass (LMXB) XRBs based on metallicity, SFR, and stellar age.
3. Shock-heated Hot-ISM: Soft X-ray emission from supernova shocks, modeled as linearly proportional to the SFR.

• Result: These components were integrated over the galaxy's history to create time-dependent source spectra.

C. Radiative Transfer and 21-cm Signal

• Code: The Grizzly 1D radiative transfer code was used to post-process the Jiutian-300 density field.
• Innovation: Unlike previous versions of Grizzly that assumed a constant SFR ($SFR = M_*/\tau_{age}$), this study replaced the constant SFR with the actual evolving SFH from LG20.
• Setup: Six simulations were run to isolate variables:
  • Fiducial: Using the full LG20 SFH.
  • Constant Age Models: Simulations with fixed $\tau_{age}$ (0.02, 0.1, 0.2 Gyr) but using LG20 SFHs.
  • Constant SFR Models: Simulations where the SFR was forced to be constant over the galaxy's history (for comparison).

3. Key Contributions

• POLAR-II Update: The first implementation of a semi-numerical framework that consistently couples semi-analytic galaxy formation (including complex SFHs) with radiative transfer for the EoR.
• Decoupling Mass and Age: The study explicitly separates the effects of stellar mass and stellar age ($\tau_{age}$) on the ionization and heating of the IGM.
• Source Population Integration: A comprehensive treatment of UV (stars) and X-ray (XRBs, hot-ISM) sources, showing how their relative contributions vary with SFH.

4. Key Results

A. Star Formation History (SFH) Characteristics

• $\tau_{age}$ Sensitivity: The SFH is highly dependent on $\tau_{age}$. Galaxies with smaller $\tau_{age}$ (younger stellar populations) exhibit higher SFRs at recent times ($t_b \approx 0$), while larger $\tau_{age}$ implies earlier star formation.
• Mass Dependence: For a fixed redshift, mean $\tau_{age}$ increases with stellar mass for $M_* < 10^6 M_\odot$ but decreases for $M_* > 10^6 M_\odot$ due to feedback quenching in smaller halos.

B. Impact on Ionization and Heating

• Ionized Bubble Size:
  • Effect of $\tau_{age}$: For a fixed stellar mass, galaxies with larger $\tau_{age}$ produce smaller ionized bubbles. This is because older stellar populations have higher recombination rates (more time for recombination to occur before the current epoch), reducing the effective ionizing photon budget available at a specific snapshot.
  • Effect of SFH Model: Galaxies with the realistic LG20 SFH produce slightly larger ionized bubbles (up to ~10% larger for young ages) compared to those with a constant SFR, due to the temporal clustering of star formation events.
• Gas Temperature ($T_k$):
  • Galaxies with larger $\tau_{age}$ produce less X-ray heating (fewer recent massive stars/XRBs), resulting in cooler IGM.
  • The LG20 SFH models result in higher gas temperatures compared to constant SFR models, as the bursty nature of star formation in LG20 enhances X-ray production efficiency.

C. The 21-cm Signal

• Global Signal ($\bar{T}_{21}$):
  • Simulations with smaller $\tau_{age}$ (stronger recent heating) show higher emission temperatures.
  • LG20 vs. Constant SFR: The LG20 models show higher $T_{21}$ at $z > 10$ due to enhanced heating, leading to an earlier end to the EoR (by $\Delta z \approx 0.5$ in extreme cases).
• Power Spectrum ($\Delta^2_{21}$):
  • High Redshift ($z > 9$): The power spectrum is dominated by X-ray heating fluctuations. Models with weaker heating (larger $\tau_{age}$) show higher power because the gas remains cooler, increasing the contrast in brightness temperature.
  • Low Redshift ($z < 8$): The power spectrum is dominated by ionization topology. Models with LG20 SFHs show peaks at slightly higher redshifts than constant SFR models, reflecting the earlier completion of reionization.

5. Significance

• Interpretation of Future Data: As next-generation telescopes like SKA, HERA, and LOFAR begin to constrain the 21-cm power spectrum, this work demonstrates that the inferred reionization history is sensitive to the assumed SFH. Ignoring the evolution of SFH (i.e., assuming constant SFR) can lead to biases in estimating the timing of reionization and the thermal state of the IGM.
• JWST Synergy: With JWST providing detailed constraints on high-redshift galaxy properties (UV luminosity functions, stellar masses), this model provides a necessary bridge to interpret how these specific galaxy populations drive the global reionization process.
• Physical Consistency: The study highlights that the "total ionizing photon budget" is not the only factor; the timing of photon emission (SFH) critically alters the recombination and cooling physics of the IGM, thereby changing the observable 21-cm signature.