LensMC: A Novel Method for Precise Weak Lensing Cosmic Shear Measurement Using Forward Modelling and MCMC Sampling

Core Concepts

LensMC is a new, highly accurate method for measuring weak lensing cosmic shear, designed to meet the demanding accuracy requirements of Euclid and future Stage-IV surveys by addressing challenges like PSF convolution and galaxy density.

Abstract

LensMC: A New Method for Precise Weak Lensing Measurement

This research paper introduces LensMC, a novel method for measuring weak lensing cosmic shear, specifically developed for the Euclid telescope and future Stage-IV surveys. The paper emphasizes the increasing importance of accurate weak lensing measurements as upcoming surveys will observe significantly larger numbers of galaxies with improved resolution.

Addressing the Challenges of Precise Measurement

The core of the paper focuses on the challenges of achieving high accuracy in cosmic shear measurements. It discusses various sources of bias, including:

• Source clustering
• Faint objects
• Neighboring galaxies
• PSF leakage
• Astrometry
• Image artifacts
• Cosmic rays

Key Features of LensMC

The paper highlights LensMC's innovative approach to overcome these challenges:

• Forward Modelling: Effectively handles Euclid image undersampling and convolution by a PSF comparable in size to many galaxies.
• Joint Measurement: Accurately addresses bias due to neighboring galaxies by jointly measuring object groups.
• Masking: Improves accuracy by masking out objects from different groups.
• MCMC Sampling: Employs Markov chain Monte Carlo sampling to:
  • Sample the posterior in a multi-dimensional parameter space.
  • Calculate weights.
  • Correctly marginalize ellipticity over nuisance parameters and other objects in the same group.

Focus on Realism and Accuracy

The authors emphasize the realism of their simulations used to test LensMC, incorporating:

• Clustering of galaxies
• Presence of stars
• Object detection
• Handling of high galaxy number density
• Realistic undersampled chromatic PSF images with spatial variation

Preliminary Results and Future Directions

While acknowledging that further real-data effects need to be addressed, the paper presents promising initial results:

• When model bias, chromaticity, and selection biases are suppressed, LensMC achieves biases close to Euclid requirements.
• The measurement bias is mainly attributed to undetected faint galaxies.
• The bias demonstrates stability and insensitivity to various simulated effects.

The paper concludes by highlighting the need to calibrate the residual bias and model bias through image simulations. The authors are optimistic about LensMC's potential to achieve the high accuracy required for Euclid and future surveys.

Stats

Euclid will observe approximately 1.5 billion galaxies.
Euclid's target area covers 14,000 deg2.
Euclid has a depth of 24.5 (IE+YEJEHE filters).
Euclid's FWHM resolution is 0.′′2.
The required multiplicative bias for Euclid is σm < 2 × 10−3.
The required additive bias for Euclid is σc < 3 × 10−4.
The simulations used a mean surface number density of 250 arcmin−2 (IE < 29.5) for galaxies.
The simulations used a mean surface number density of 6 arcmin−2 (IE < 26) for stars.
The simulated PSF had a FWHM of 0.′′2.
LensMC measured objects with a density of 90 arcmin−2 (IE < 26.5) in 4500 deg2.
The measured multiplicative biases were m1 = (−3.6 ± 0.2) × 10−3 and m2 = (−4.3 ± 0.2) × 10−3.
The measured additive biases were c1 = (−1.78 ± 0.03) × 10−4 and c2 = (0.09 ± 0.03) × 10−4.
The measured PSF leakage values were α1 = (−9 ± 3) × 10−4 and α2 = (2 ± 3) × 10−4.

Quotes

"With the dramatic improvement in precision that will be achieved in the coming years, experiments are now focussing on understanding the accuracy of their analyses."
"In order to achieve an order of one-percent precision on the dark energy equation of state, a billion galaxies or more with median redshift around one need to be observed."
"The combined effect of improved survey area and angular resolution will be an enhanced ability to probe both the large and small scales via weak lensing and galaxy clustering, allowing us to constrain cosmological models and dark energy to percent-level precision."

Key Insights Distilled From

Euclid preparation. LIII. LensMC, weak lensing cosmic shear measurement with forward modelling and Markov Chain Monte Carlo sampling

by Euclid Colla... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2405.00669.pdf

Deeper Inquiries

How will LensMC be integrated with other data analysis pipelines for Euclid and future surveys to ensure a comprehensive and robust approach to weak lensing cosmology?

LensMC, as a shear measurement method, represents just one component within the broader data analysis pipeline for weak lensing cosmology in Euclid and future surveys. Here's how it fits into the bigger picture:
1. Data Acquisition and Pre-processing: Raw data from Euclid's VIS instrument will undergo several pre-processing steps, including bias and dark current correction, flat-fielding, and astrometric calibration. These steps are crucial for removing instrumental signatures and ensuring accurate measurements.
2. Object Detection and Cataloguing: Before LensMC can be applied, objects (galaxies and stars) need to be identified and catalogued. This involves sophisticated algorithms to distinguish astronomical sources from noise and each other. The output is a catalogue with object positions, magnitudes, and other basic properties.
3. Shear Measurement with LensMC: This is where LensMC comes in. Using the pre-processed images and object catalogues, LensMC will be employed to estimate the shapes (and thus shears) of the lensed galaxies. The outputs will be catalogues of galaxy ellipticities, along with associated uncertainties.
4. Photometric Redshift Estimation: Accurate redshift measurements are crucial for tomographic weak lensing analyses. Euclid's multi-band photometry will be used to estimate photometric redshifts (photo-z) for the lensed galaxies.
5. Shear-Ratio Tests and Systematics Mitigation: Before cosmological interpretation, rigorous systematics tests will be performed. This includes shear-ratio tests, which check for spurious lensing signals that might indicate residual systematics in the data or analysis.
6. Cosmological Inference: Finally, the measured shears, photo-zs, and their uncertainties will be fed into a cosmological inference pipeline. This pipeline will use statistical methods, such as Bayesian inference, to constrain cosmological parameters, including those related to dark matter and dark energy.
Integration and Robustness:

Modular Design: Modern astronomical pipelines, including Euclid's, are designed modularly. This allows for independent development and testing of individual components like LensMC while ensuring seamless integration.
End-to-End Simulations: Robustness is ensured through extensive end-to-end simulations. These simulations start from a cosmological model, generate mock Euclid observations (including realistic instrumental effects), and process the data through the entire pipeline. This allows for validation of the pipeline and quantification of systematic uncertainties.
Cross-Validation and Comparison: Multiple shear measurement methods, including LensMC, will be employed and their results cross-validated. This helps to identify potential biases or limitations associated with any single method.
By integrating LensMC within this comprehensive and carefully validated pipeline, Euclid and future surveys aim to extract robust and precise cosmological information from weak lensing observations.

Could the reliance on simulations for calibration in LensMC introduce biases or limitations if the simulations do not perfectly capture the complexities of real astronomical data?

Yes, the reliance on simulations for calibration in LensMC, while necessary, does introduce potential biases and limitations if the simulations do not fully capture the complexities of real astronomical data. This is a significant challenge in weak lensing analyses and a key focus of ongoing research. Here's a breakdown of the potential issues:
1. Simulation Fidelity:

Galaxy Morphologies: Simulations need to accurately model the diverse range of galaxy morphologies, including realistic bulge-to-disk ratios, Sérsic indices, and intrinsic alignments. If the simulated galaxies are not representative of the real population, the calibration will be biased.
Point Spread Function (PSF): The PSF, which describes the blurring of light from astronomical sources by the telescope optics, needs to be accurately modelled and incorporated into the simulations. Mismatches between the simulated and real PSF can lead to significant biases in shear measurements.
Observational Effects: Simulations need to account for a wide range of observational effects, including noise properties, pixelation, charge diffusion, and other detector effects. Neglecting or inaccurately modelling these effects can lead to biases in the calibration.
2. Unmodelled Physics and Systematics:

Baryonic Feedback: The impact of baryonic processes, such as star formation and supernova explosions, on galaxy formation and evolution is complex and not fully understood. Simulations that do not adequately capture these processes may lead to biased calibrations.
Unknown Systematics: There is always the risk of unknown or unanticipated systematic effects in both the data and the analysis. Simulations, by their nature, cannot account for effects that are not explicitly included in their design.
Mitigation Strategies:

Improved Simulations: Continuously improving the fidelity of simulations is crucial. This includes incorporating the latest astrophysical understanding, using more sophisticated modelling techniques, and increasing the realism of instrumental effects.
Data-Driven Calibration: While simulations are essential, incorporating data-driven calibration techniques is crucial. This includes using real data to validate and refine the simulations, as well as developing methods that are less reliant on simulations, such as metacalibration.
Blind Analyses: Employing blind analysis techniques, where the cosmological analysis is performed without prior knowledge of the expected results, helps to mitigate confirmation bias and ensure the robustness of the results.
Implications:
The reliance on simulations for calibration introduces a significant source of systematic uncertainty in weak lensing cosmology. While these uncertainties can be mitigated through the strategies outlined above, it is crucial to acknowledge and carefully quantify their potential impact on cosmological constraints. Failure to do so could lead to biased or inaccurate conclusions about the nature of dark matter, dark energy, and the fundamental laws of physics.

What are the potential implications of highly accurate weak lensing measurements like those from LensMC for our understanding of fundamental physics and the nature of dark matter and dark energy?

Highly accurate weak lensing measurements, like those anticipated from LensMC and Euclid, hold the potential to revolutionize our understanding of fundamental physics and the nature of dark matter and dark energy. Here's how:
1. Precision Cosmology and Dark Energy:

Dark Energy Equation of State: Weak lensing is exquisitely sensitive to the properties of dark energy, particularly its equation of state, which describes how the pressure of dark energy relates to its energy density. Precise measurements of the growth of structure through cosmic shear can distinguish between different dark energy models, including the cosmological constant and more exotic scenarios like quintessence or modified gravity.
Neutrino Mass: Weak lensing can also constrain the sum of neutrino masses, a key parameter in both particle physics and cosmology. Massive neutrinos suppress the growth of structure on small scales, and accurate weak lensing measurements can detect this signature.
2. Dark Matter Properties:

Nature of Dark Matter: While weak lensing primarily probes the gravitational effects of dark matter, it can provide indirect constraints on its particle physics properties. For example, if dark matter interacts with itself or other particles beyond gravity, it could leave distinctive signatures in the matter power spectrum, which weak lensing can detect.
Dark Matter Substructure: High-resolution weak lensing measurements can probe the distribution of dark matter on small scales, potentially revealing the presence of subhalos, which are predicted by the standard cold dark matter paradigm. Detecting or ruling out these subhalos would have profound implications for our understanding of dark matter.
3. Tests of Gravity:

Modified Gravity: Weak lensing provides a powerful test of General Relativity on cosmological scales. By comparing the observed lensing signal to predictions from General Relativity and alternative theories of gravity, we can constrain deviations from Einstein's theory.
Cosmic Growth History: Accurate measurements of the growth of structure through weak lensing allow us to reconstruct the cosmic growth history, providing a sensitive probe of the nature of gravity and the expansion history of the Universe.
4. Synergy with Other Probes:

Cosmic Microwave Background (CMB): Combining weak lensing measurements with CMB observations provides a powerful cross-check and allows for breaking degeneracies between cosmological parameters.
Galaxy Clustering: Joint analyses of weak lensing and galaxy clustering can further tighten constraints on cosmological models and provide complementary information about the interplay between dark matter, dark energy, and baryonic matter.
Broader Implications:
The implications of highly accurate weak lensing measurements extend beyond cosmology and astrophysics. They have the potential to:

Advance our understanding of fundamental physics: By testing the fundamental laws of gravity and constraining the properties of dark matter and dark energy, weak lensing can provide insights into physics beyond the Standard Model.
Shape the future of cosmological research: The precision and accuracy of future weak lensing surveys will pave the way for new discoveries and drive the development of even more sophisticated observational and theoretical tools.
In conclusion, highly accurate weak lensing measurements have the potential to revolutionize our understanding of the Universe, from the properties of dark matter and dark energy to the fundamental laws of physics. LensMC, as a key component of Euclid's weak lensing analysis, will play a crucial role in this endeavor.