A complete, step-by-step guide for researchers to independently verify the velocity anisotropy predictions using publicly available galaxy cluster data.
Science advances through independent verification. The Ashebo Method makes a specific, testable prediction: galaxy velocity dispersions in clusters should depend on orbital geometry according to σ(θ) = σ₀ (1 + A cos²θ). This guide provides everything you need to test this prediction yourself using publicly available data.
Whether you're a skeptical researcher, a graduate student, or simply curious, this comprehensive tutorial walks you through every step—from downloading data to interpreting statistical results. No proprietary software or special access required.
Complete instructions for downloading spectroscopic data from VizieR, SDSS, and other public archives. No special permissions needed.
Fully commented, production-ready Python script implementing all statistical tests. Ready to run on your own clusters.
Four independent statistical tests (KS, Mann-Whitney, Levene, correlation) that avoid curve-fitting biases and provide robust results.
Detailed explanations of methodology, statistical interpretation, troubleshooting tips, and guidance for reporting results.
Learn how to download spectroscopic catalogs from VizieR, SDSS, and other archives. Includes specific catalog IDs for Coma, Virgo, Perseus, and Abell 2029 clusters with confirmed data availability.
Master the essential steps: identifying cluster members, calculating projected radii, computing relative velocities, and handling missing data. Includes validation checks to ensure data quality.
Understand how to statistically assign orbital angles using Jeans anisotropy theory. Learn the physical intuition behind radial infalls, tangential orbits, and core galaxies.
Perform four independent tests: binned analysis, radial-tangential comparison, functional form (cos²θ), and monotonic decrease. Learn how to interpret p-values and effect sizes.
Create publication-quality plots showing all analysis results. Learn how to report findings for both positive detections and null results, with examples of proper scientific communication.
Diagnose common issues, understand potential pitfalls, and explore advanced extensions like Bayesian model comparison and correlation with cluster properties.
Python 3.8+ with numpy, scipy, pandas, astroquery, astropy, and matplotlib
At least 200 spectroscopic cluster members (publicly available from VizieR)
4-6 hours for first analysis (including setup and learning)
All data sources are publicly available. No proprietary software, telescope time, or institutional access needed. Everything can be done from your laptop with an internet connection.
Multiple independent tests show p < 0.05 (ideally p < 0.001)
Radial-tangential ratio σ_rad/σ_tan between 1.05 and 2.0
Positive correlation with cos²θ (r > 0.5, p < 0.05)
Velocity dispersion decreases monotonically with orbital angle
All statistical tests show p > 0.05 (no significant difference)
Radial-tangential ratio σ_rad/σ_tan ≈ 1.00 (isotropic)
No correlation with cos²θ or any other functional form
Velocity dispersion is constant across all orbital angles
We analyzed 4,572 galaxies across 4 clusters and found:
Download the complete guide and Python code to start your independent analysis.
Both resources are free and open-source. Share your results with the community!
Whether your results support or challenge the Ashebo Method, they contribute to our understanding of gravity and cosmology. Independent verification is the cornerstone of science.