Euclid preparation. The impact of redshift interlopers on the two-point correlation function analysis

Using 1,000 synthetic Euclid catalogues, this study demonstrates that a minimal modeling approach accounting for signal attenuation is sufficient to recover unbiased cosmological parameters from the two-point correlation function despite redshift interloper contamination, as the resulting systematic errors remain smaller than expected statistical uncertainties for the DR1 analysis.

The Gist

Imagine you are trying to build a 3D map of the universe using millions of galaxies as your building blocks. To do this, you need to know exactly how far away each galaxy is. In astronomy, we measure this distance using "redshift"—essentially, how much the light from a galaxy has been stretched as it travels through the expanding universe.

The Euclid space telescope is a massive project designed to take a picture of billions of galaxies and measure their redshifts to create the most detailed 3D map of the cosmos ever made. However, just like a photographer trying to take a picture in a crowded room with a slightly blurry lens, Euclid faces a tricky problem: mistaken identities.

The Problem: The "Imposter" Galaxies

In this paper, the scientists are worried about "redshift interlopers." Think of these as imposters in a crowd.

When Euclid looks at a galaxy, it tries to identify a specific fingerprint in its light (a bright line called H-alpha). Sometimes, the telescope gets confused:

1. The Wrong Fingerprint: It sees a different fingerprint (from a different type of gas) and mistakes it for the H-alpha one. It thinks the galaxy is at distance A, but it's actually at distance B.
2. The Static Noise: Sometimes, the telescope sees a random spike of static noise and thinks, "Ah, that's a galaxy!" It assigns a random distance to a speck of dust or a star that isn't even a galaxy.

These imposters get mixed into the final list of galaxies. If you try to build your 3D map with these fake distances, the map gets distorted. You might think a galaxy is right next to you when it's actually millions of light-years away, or vice versa.

The Experiment: A Cosmic Stress Test

The authors of this paper didn't just worry about this; they simulated it. They created 1,000 fake universes (called "EuclidLargeMocks") that look exactly like what Euclid will see, including the imposters.

They asked a simple question: "If we ignore these imposters and just analyze the data as if it were perfect, how much will our map and our physics calculations be wrong?"

They focused on two main things:

1. The Clumping Pattern (2PCF): Galaxies aren't scattered randomly; they clump together in a specific pattern, like foam on a beer. This pattern tells us about the history of the universe.
2. The Cosmological Parameters: They wanted to see if the imposters would mess up their calculations for:
   • How fast the universe is growing: (The growth rate of structure).
   • The shape of the universe: (Alcock-Paczynski parameters, which tell us if space is stretching differently in different directions).

The Findings: The "Minimalist" Approach Works

Here is the surprising result, explained with an analogy:

Imagine you are trying to hear a specific song in a noisy room.

• The Complex Approach: You try to identify every single person in the room, figure out exactly who is singing off-key, and mathematically subtract their voices from the recording. This is hard and requires knowing exactly who everyone is.
• The Minimalist Approach: You just realize, "Okay, the room is a bit noisy, so the song sounds a little quieter than it should." You just turn up the volume slightly to compensate for the noise and listen to the song.

The paper found that for the Euclid DR1 (Data Release 1) survey, the Minimalist Approach is enough.

• For the "Clumping" (Growth Rate): Even if they didn't perfectly model the imposters, just accounting for the fact that the signal is "diluted" (weaker) because of the noise was enough. The error in their calculations was only 1% to 3%. This is tiny compared to the natural statistical uncertainty (the "fuzziness" of the data) they expect to have at this stage. It's like trying to measure a mountain with a ruler that has a 10-meter error margin; a 1% error doesn't matter.
• For the "Shape" (BAO Parameters): The results were even better. The imposters didn't change the estimated shape of the universe at all. The "noise" in the room didn't change the melody of the song enough to confuse the listener. The measurements for the universe's geometry remained accurate and precise.

Why Does This Matter?

You might wonder, "If the imposters are there, why don't we need a complex model to fix them?"

The answer is that the imposters are randomly scattered in a way that mostly just makes the signal weaker, rather than creating a fake pattern that looks like real physics. It's like adding a little bit of water to a glass of juice; it makes the juice less strong, but it doesn't turn it into a different flavor.

The Conclusion

The paper concludes that for the first batch of data (DR1) from Euclid, scientists don't need to panic about these imposters. They can use a simple, robust model that just accounts for a slight loss in signal strength.

• The Good News: The universe's map will be accurate, and our understanding of dark energy and dark matter won't be ruined by these measurement errors.
• The Future Caveat: As Euclid collects more data in the future (DR3), the data will become so precise that the "fuzziness" of the measurement will shrink. At that point, the 1% error from the imposters might become significant, and they will need to build that complex "identify every voice" model. But for now, the simple approach is perfectly safe.

In short: The Euclid telescope might get a few things wrong about where some galaxies are, but it won't be fooled enough to change our understanding of how the universe works. The map is safe!

Technical Summary

1. Problem Statement

The Euclid space mission aims to map the large-scale structure of the Universe using slitless spectroscopy to measure redshifts for tens of millions of emission-line galaxies (ELGs). However, the medium-low spectral resolution ($R < 1000$) and limited wavelength coverage of the NISP instrument create significant challenges:

• Redshift Ambiguity: The primary method for determining redshift relies on identifying the H$\alpha$ emission line. Due to resolution limits, H$\alpha$ is often blended with the [N II] doublet, and other strong lines (specifically [O III] $\lambda5008$ and [S III] $\lambda9531$) can be misidentified as H$\alpha$.
• Interloper Galaxies: This leads to "catastrophic" redshift errors where galaxies are assigned incorrect distances. These contaminants are categorized as:
  • Line Interlopers: Galaxies with genuine emission lines (e.g., [O III], [S III]) misidentified as H$\alpha$. Their redshift error is deterministic based on the wavelength ratio.
  • Noise Interlopers: Objects where random noise fluctuations mimic an emission line, leading to random, catastrophic redshift errors.
• Impact on Cosmology: These errors displace galaxies along the line of sight, distorting the observed spatial distribution. This affects the Two-Point Correlation Function (2PCF), potentially biasing the inference of key cosmological parameters: the growth rate of structure ($f\sigma_8$), the Alcock–Paczynski (AP) parameters ($\alpha_\parallel, \alpha_\perp$), and the clustering amplitude ($b\sigma_8$).

2. Methodology

The study utilizes a comprehensive simulation-based approach to forecast the impact of these interlopers on the Euclid Data Release 1 (DR1) analysis.

• Data Source: The analysis is based on 1,000 synthetic spectroscopic catalogues known as EuclidLargeMocks. These mocks mimic the Euclid Wide Survey (EWS) area and selection function, incorporating realistic end-to-end simulations of the NISP instrument to model the probability distribution of measured redshifts ($P(z_{meas}|z_{true})$).
• Interloper Classification: The mocks distinguish between "correct" galaxies, line interlopers ([O III], [S III]), and noise interlopers. The contamination fractions vary by redshift bin (e.g., noise interlopers dominate at $z \sim 1.0$, while line interlopers become significant at $z > 1.3$).
• Theoretical Framework:
  • The measured 2PCF ($\xi_m$) is decomposed into a sum of auto-correlation and cross-correlation terms of different populations (correct, line interlopers, noise interlopers), weighted by their fractions and geometric dilation factors ($\gamma_\parallel, \gamma_\perp$).
  • The authors test various phenomenological models of increasing complexity to fit the contaminated signal:
    1. Minimal Model: Assumes the sample is pure but attenuated by a global damping factor $(1-f_{tot})^2$.
    2. Intermediate Model: Includes auto-correlation of line interlopers.
    3. Complex Model: Includes auto-correlation of line interlopers and cross-correlation between correct galaxies and noise interlopers.
• Analysis Techniques:
  • Full-Shape Analysis: Uses Markov Chain Monte Carlo (MCMC) to constrain $f\sigma_8$, $b\sigma_8$, and pairwise velocity dispersion ($\sigma_p$) using the full shape of the 2PCF multipoles (monopole, quadrupole, hexadecapole).
  • BAO Analysis: Fits the Baryon Acoustic Oscillation (BAO) peak to constrain the AP parameters ($\alpha_\parallel, \alpha_\perp$) using a standard BAO template that does not explicitly model interlopers.

3. Key Contributions

• Quantitative Decomposition: The paper provides the first detailed breakdown of the contribution of each interloper type (line vs. noise, auto vs. cross-correlation) to the total 2PCF signal in the context of Euclid DR1.
• Model Efficiency Assessment: It systematically evaluates whether complex models (accounting for specific interloper types and cross-correlations) are necessary or if a minimal attenuation model suffices for current statistical precision.
• Redshift-Dependent Impact: It highlights that the nature of the dominant interloper changes with redshift (noise-dominated at low $z$, line-dominated at high $z$), affecting the required modeling strategy.

4. Key Results

A. Impact on the 2PCF Signal

• Dilution and Distortion: Interlopers dilute the clustering amplitude and distort the shape of the 2PCF. Line interlopers shift the BAO peak (towards smaller scales for [O III] and larger for [S III]), while noise interlopers smooth the signal.
• Dominant Terms: The correct galaxy auto-correlation is the dominant term. The next most significant contributions are the line interloper auto-correlation and the correct-noise cross-correlation. Other terms (e.g., noise-noise auto-correlation) are negligible.
• Systematic Errors: Neglecting interlopers entirely introduces systematic errors in the 2PCF residuals. However, these errors generally decrease with separation scale ($r$) and fall below 10% of the statistical uncertainty at scales $r > 100 \, h^{-1}\text{Mpc}$.

B. Impact on Cosmological Parameters ($f\sigma_8$ and $b\sigma_8$)

• Minimal Model Sufficiency: A simple model that only accounts for the attenuation of the clustering signal (via a global damping factor) is sufficient to recover unbiased values of $f\sigma_8$ and $\alpha_\parallel, \alpha_\perp$ for the DR1 dataset.
• Systematic Bias: Using a minimal model induces a systematic error on $f\sigma_8$ of 1%–3% depending on the redshift. Crucially, this bias is smaller than the expected statistical uncertainty for the Euclid DR1 survey.
• Contamination Fraction: The results are robust even if the contamination fraction ($f_{tot}$) is treated as a free parameter with a $\pm 10\%$ prior. However, if $f_{tot}$ is completely unconstrained (0 to 1), the uncertainty on $f\sigma_8$ degrades significantly, though the distortion parameter $\beta = f/b$ remains robust.

C. Impact on BAO Parameters ($\alpha_\parallel, \alpha_\perp$)

• Robustness: The BAO analysis is extremely robust to interloper contamination.
• No Bias: Ignoring interlopers in the BAO template introduces no significant systematic bias in the estimated AP parameters.
• Uncertainty Degradation: The presence of interlopers (specifically line interlopers) increases the uncertainty on $\alpha_\parallel$ and $\alpha_\perp$ by roughly 14–21% in high-redshift bins due to the broadening of the BAO peak. However, this degradation is still well within the statistical error budget for DR1 and even DR3.

5. Significance and Conclusions

• DR1 Readiness: The study concludes that for the Euclid DR1 analysis, complex modeling of interloper cross-correlations is not strictly necessary. A minimal model accounting for signal attenuation is sufficient to meet the mission's accuracy requirements.
• Future Outlook (DR3): As the survey progresses to DR3, statistical errors will decrease by a factor of $\sqrt{6}$. At that level of precision, the systematic errors from simplified interloper modeling (currently 1–3%) may become significant, necessitating more sophisticated models that include specific interloper contributions and cross-correlations.
• Validation: The findings are consistent with companion work in Fourier space (power spectrum analysis), reinforcing the reliability of these forecasts.
• Caveats: The authors note that if the actual contamination fraction in the early data release exceeds the simulated 20% threshold (as suggested by early Quick Data Release analyses), the impact of interlopers would need to be reassessed. Additionally, the ability to characterize interlopers relies on deep fields (EDS) which will only be fully available by DR3.

In summary, this paper provides a critical validation that Euclid's early cosmological analyses can proceed with robust, simplified models regarding redshift interlopers, ensuring that the first major cosmological results will not be compromised by these systematic effects.