Niebla: an open-source code for modeling the extragalactic background light

This paper introduces *Niebla*, the first open-source code to model the extragalactic background light (EBL) from optical to far-infrared wavelengths using a customizable phenomenological approach that evolves stellar populations and incorporates diverse dust reemission prescriptions, enabling precise constraints on EBL parameters and the distinction between competing dust models through gamma-ray attenuation studies.

The Gist

The Big Picture: The Cosmic "Fog"

Imagine the universe isn't just empty black space. It's actually filled with a very faint, invisible "fog" made of light. This fog is called the Extragalactic Background Light (EBL). It's the combined glow of every star and galaxy that has ever existed, stretching from the time of the Big Bang until today.

This fog is mostly made of two things:

1. Visible light (like the sun or a lightbulb).
2. Infrared light (heat radiation, like the warmth you feel from a fire).

The problem? We can't see this fog directly. It's like trying to see a faint mist while standing in a blindingly bright spotlight (our own solar system and galaxy). The "spotlight" is so bright that it drowns out the faint cosmic fog.

The Problem: Gamma Rays Getting Lost

When high-energy particles called gamma rays travel across the universe from distant explosions (like blazars), they have to pass through this cosmic fog.

• The Analogy: Imagine throwing a tennis ball (a gamma ray) through a dense forest (the EBL).
• The Interaction: If the ball hits a tree branch (a photon from the fog), it doesn't just bounce off; it disappears and turns into two new particles (an electron and a positron).
• The Result: By the time the gamma rays reach Earth, many of them have been "eaten" by the fog. The higher the energy of the gamma ray, the more likely it is to get eaten.

To understand what the distant explosion actually looked like, scientists need to know exactly how thick and dense the fog is. But because we can't measure the fog directly, we have to build a computer model to guess what it looks like.

The Solution: Introducing "Niebla"

The authors of this paper created a new, free computer program called Niebla (which means "fog" in Spanish). Think of Niebla as a virtual weather station for the universe.

Instead of just guessing, Niebla builds the fog from the ground up using a "recipe":

1. The Ingredients (Stars): It calculates how much light stars have produced over billions of years, accounting for how fast stars are born and how "metal-rich" they are (stars get heavier with age).
2. The Dust (The Filter): Stars emit light, but much of it gets swallowed by cosmic dust. This dust heats up and re-emits the light as infrared heat. Niebla has different "recipes" for how this dust behaves.
   • Recipe A: Uses real-life photos of dusty galaxies as a template.
   • Recipe B: Uses simple math (blackbody curves) to guess the heat.
3. The Extras: It can even add "secret ingredients" like light from stray stars floating between galaxies or hypothetical particles called axions.

What They Did: Testing the Recipes

The scientists used Niebla to create three different versions of the cosmic fog. They then compared these versions against real data we do have, such as:

• Counts of how many galaxies we can see.
• Measurements of how fast stars are being born.
• Measurements of the chemical makeup of the universe.

The Result: All three recipes fit the data reasonably well. However, the recipe that used real-life galaxy templates (the "Chary" model) seemed to fit the data the best.

The Use Case: The "Markarian 501" Test

To see if these different fog models actually matter, the authors ran a simulation. They imagined a powerful telescope (LHAASO) looking at a famous distant galaxy called Markarian 501 during a massive flare (a burst of energy).

• The Experiment: They asked, "If we see this galaxy through our three different fog models, will the telescope see different things?"
• The Finding:
  • If the galaxy's light is very simple (a straight line on a graph), the telescope can tell the difference between the fog models. Specifically, it could tell the difference between the "template" model and the others.
  • However, if the galaxy's light is complex (curved or bumpy), the fog models look almost identical to the telescope. The complexity of the galaxy's light "hides" the differences in the fog.

The Takeaway

The paper concludes that Niebla is a powerful, flexible tool for the scientific community. It allows researchers to:

1. Build their own custom models of the cosmic fog.
2. Test how different assumptions about cosmic dust change our view of the universe.
3. Prepare for future telescopes that might finally be able to distinguish between these different "fog" recipes, helping us understand the history of star formation and the nature of dust in the cosmos.

In short, Niebla is a new, open-source toolkit that helps astronomers stop guessing about the universe's background light and start calculating it with precision.

Technical Summary

1. Problem Statement

The Extragalactic Background Light (EBL), comprising the Cosmic Optical Background (COB) and Cosmic Infrared Background (CIB), is a diffuse photon field permeating the universe. It plays a critical role in high-energy astrophysics because extragalactic gamma rays interact with EBL photons via electron-positron pair production ($e^-e^+$), leading to energy-dependent attenuation.

• Measurement Challenges: Direct measurement of the EBL is hindered by strong foreground contamination (e.g., Zodiacal light, Galactic dust, atmospheric emission). Current direct measurements are often treated as upper limits, while galaxy count extrapolations provide only lower limits.
• Modeling Limitations: Existing EBL models vary in spectral shape and rely on different methodologies (forward-evolution vs. empirical). Many gamma-ray analyses use fixed EBL models with simple renormalization, preventing the community from constraining the underlying physical parameters (e.g., dust reemission properties, star formation history) or distinguishing between different dust models.
• Need for Flexibility: There is a lack of open-source tools that allow users to customize inputs (e.g., Star Formation Rate Density, metallicity evolution, dust templates) to test specific cosmological scenarios against Very High Energy (VHE) observations.

2. Methodology

The authors present Niebla (Spanish for "fog"), a phenomenological Python code designed to compute the EBL from optical to far-infrared wavelengths. The code calculates EBL intensity by integrating the emissivity of source populations over cosmic time.

Theoretical Framework

The EBL intensity $I_\nu$ is calculated by integrating the source emissivity $\epsilon_\nu$ over redshift $z$:
$$\nu I_\nu(\lambda, z) = \frac{c}{4\pi\lambda} \int_z^{z_{max}} \epsilon_\nu \left( \lambda \frac{1+z}{1+z'}, z' \right) \left| \frac{dt}{dz'} \right| dz'$$
The total emissivity is the sum of the COB (direct starlight) and CIB (dust reemission):
$$\epsilon_\nu(\lambda, z) = f_{esc,dust}\epsilon_\nu^{COB} + \epsilon_\nu^{CIB}$$

Key Components of the Model

1. Stellar Contribution (COB):

   • Modeled using Single Stellar Populations (SSPs) evolving with redshift.
   • Inputs include the Star Formation Rate Density (SFRD), mean metallicity evolution, and Initial Mass Function (IMF).
   • Supports standard parametrizations (e.g., Madau & Dickinson for SFRD, Tanikawa et al. for metallicity) and allows custom inputs.
   • Includes optional contributions from stripped stars, intra-halo light (IHL), and Active Galactic Nuclei (AGN).

2. Exotic Contributions:

   • Includes a module for the decay of Axion-Like Particles (ALPs) into photons, contributing a narrow spectral feature to the EBL.

3. Dust Reemission (CIB):
   The code offers three distinct prescriptions to model how absorbed starlight is reemitted in the infrared:

   • Spectral Templates (Chary & Elbaz): Uses synthetic spectra of Ultra-Luminous Infrared Galaxies (ULIRGs) rescaled by a factor $f_{TIR}$ and a wavelength cutoff.
   • Spectral Templates (BOSA): Uses a computational tool generating templates based on specific metallicities, normalized to a reference SSP.
   • Blackbody (BB) Sum: Models dust emission as a sum of blackbodies at different temperatures (e.g., one for Mid-IR, one for Far-IR).

4. Fitting Procedure:

   • The code fits model parameters to observational data using a combined $\chi^2$ minimization.
   • Data Sets: Galaxy number counts (lower limits), emissivity data, SFRD measurements, and mean metallicity evolution.
   • Systematics: The authors introduce a fractional systematic uncertainty (found to be optimal at 14%) to account for discrepancies between different surveys.

3. Key Contributions

• Open-Source Software: Release of niebla (available on GitHub), the first open-source code allowing fully customizable inputs for EBL modeling.
• Modular Architecture: Users can swap SFRD parametrizations, metallicity evolutions, and dust reemission models, or inject custom emissivities (e.g., for specific dark matter decay scenarios).
• Three Validated Models: The authors present three specific EBL models fitted to data using different dust prescriptions:
  1. Chary: Based on ULIRG templates.
  2. BOSA: Based on metallicity-dependent templates.
  3. 2BB: Based on a two-component blackbody model.
• Use Case Demonstration: A simulation of a VHE observation of the blazar Markarian 501 (Mkn 501) using the Large High Altitude Air Shower Observatory (LHAASO) to test the code's ability to distinguish between dust models.

4. Results

• Model Fitting:
  • All three dust prescriptions yield acceptable fits to observational data.
  • The Chary template model achieved the lowest reduced $\chi^2$ (0.97 with systematics), followed closely by the 2BB model (1.07) and BOSA (1.00).
  • The optical regime emissivity data drives the fits, while infrared data remains sparse.
  • The Chary and 2BB models produce similar results in the Mid-IR, consistent with previous work by Finke et al.
• Parameter Constraints:
  • Dust reemission parameters (e.g., $f_{TIR}$, dust temperatures) are found to be weakly correlated with SFRD and metallicity parameters, allowing them to be constrained independently.
  • Fitted dust temperatures and stellar mass fractions are consistent with observations of local galaxies.
• VHE Simulation (Mkn 501):
  • The authors simulated a flare similar to the 1997 HEGRA observation, assuming a future observation by LHAASO.
  • Discrimination Capability:
    • If the intrinsic spectrum is a simple Power Law (PL), the BOSA model can be statistically distinguished from the Chary (true) model at 95% confidence.
    • The Chary and 2BB models are difficult to distinguish even with high-statistics data.
    • If the intrinsic spectrum includes curvature (e.g., Broken Power Law, Log Parabola), the spectral parameters can compensate for differences in EBL optical depth, rendering the dust models indistinguishable via likelihood ratios.

5. Significance

• Advancing Cosmology: Niebla shifts the paradigm from using EBL as a fixed "nuisance" parameter to a tool for constraining cosmological and physical parameters (dust properties, star formation history) directly.
• Future Observatories: The code is specifically designed to leverage data from upcoming facilities like the Cherenkov Telescope Array (CTAO) and LHAASO. It enables the community to move beyond simple renormalization of EBL models to testing specific physical scenarios.
• Dark Matter Constraints: By allowing custom inputs, the code facilitates the search for exotic physics, such as constraints on Axion-Like Particles (ALPs) through their decay signatures in the EBL.
• Community Resource: As an open-source tool with extensive documentation and Jupyter notebooks, it lowers the barrier to entry for researchers to perform sophisticated EBL modeling and fitting.

In conclusion, Niebla provides a robust, flexible framework for modeling the EBL, successfully fitting current data with multiple dust prescriptions and demonstrating the potential for future VHE observations to discriminate between specific dust reemission models, provided the intrinsic source spectra are sufficiently simple.