284 lines
11 KiB
Python
284 lines
11 KiB
Python
#!/usr/bin/env python3
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"""
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Open Cluster Velocity Dispersion Analysis for Spin-Tether Hypothesis
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Author: Andre Heinecke & Claude
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Date: May 2025
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This script analyzes velocity dispersions in open clusters to test for
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the presence of a universal tethering acceleration sigma.
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"""
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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from astropy import units as u
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from astropy.constants import G, M_sun, pc
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import requests
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from io import StringIO
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# Constants
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G_SI = G.si.value # m^3 kg^-1 s^-2
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M_sun_kg = M_sun.si.value # kg
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pc_m = pc.si.value # meters
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class OpenCluster:
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"""Class to represent an open cluster with its properties"""
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def __init__(self, name, distance_pc, mass_msun, radius_pc,
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obs_dispersion_km_s, dispersion_type='3D'):
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self.name = name
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self.distance = distance_pc * pc_m # Convert to meters
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self.mass = mass_msun * M_sun_kg # Convert to kg
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self.radius = radius_pc * pc_m # Convert to meters
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self.obs_dispersion = obs_dispersion_km_s * 1000 # Convert to m/s
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self.dispersion_type = dispersion_type
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# Calculate expected virial dispersion
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self.calc_virial_dispersion()
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def calc_virial_dispersion(self):
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"""Calculate expected velocity dispersion from virial theorem"""
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# For a spherical cluster: σ_vir = sqrt(G*M/r)
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# This assumes a uniform density sphere, factor may vary for different profiles
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self.vir_dispersion = np.sqrt(G_SI * self.mass / (2 * self.radius))
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# If observed is line-of-sight, convert virial to line-of-sight
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if self.dispersion_type == 'LOS':
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# For isotropic velocities, σ_LOS = σ_3D / sqrt(3)
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self.vir_dispersion_los = self.vir_dispersion / np.sqrt(3)
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else:
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self.vir_dispersion_los = self.vir_dispersion
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def calc_sigma_tether(self):
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"""Calculate implied tethering acceleration from excess dispersion"""
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# From spin-tether theory: excess kinetic energy = sigma * r
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# Excess KE per unit mass = 0.5*(σ_obs^2 - σ_vir^2)
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# Therefore: sigma = (σ_obs^2 - σ_vir^2) / (2*r)
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dispersion_to_use = self.vir_dispersion_los if self.dispersion_type == 'LOS' else self.vir_dispersion
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excess_ke = 0.5 * (self.obs_dispersion**2 - dispersion_to_use**2)
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self.sigma_tether = excess_ke / self.radius
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# Also calculate what sigma would be needed to explain ALL the dispersion
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self.sigma_total = 0.5 * self.obs_dispersion**2 / self.radius
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return self.sigma_tether
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# Known open clusters with data from Gaia studies
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# Data compiled from multiple sources cited in the searches
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clusters_data = [
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# name, distance(pc), mass(Msun), radius(pc), obs_dispersion(km/s), type
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("Hyades", 47, 400, 10, 5.0, '3D'), # 3D dispersion for young stars
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("Pleiades", 136, 800, 15, 2.4, '3D'), # 3D dispersion from Gaia
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("Praesepe", 187, 600, 12, 4.2, 'LOS'), # Line-of-sight dispersion
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("Alpha Per", 170, 500, 13, 3.5, '3D'), # Estimated
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("IC 2602", 150, 300, 8, 2.8, '3D'), # Estimated
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("IC 2391", 150, 250, 7, 2.5, '3D'), # Estimated
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("NGC 2451A", 190, 350, 9, 3.2, '3D'), # Estimated
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("Coma Ber", 85, 200, 6, 2.0, '3D'), # Small, nearby cluster
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]
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def analyze_clusters():
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"""Analyze all clusters and calculate sigma values"""
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clusters = []
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for data in clusters_data:
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cluster = OpenCluster(*data)
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cluster.calc_sigma_tether()
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clusters.append(cluster)
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# Create results dataframe
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results = pd.DataFrame({
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'Cluster': [c.name for c in clusters],
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'Distance (pc)': [c.distance/pc_m for c in clusters],
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'Mass (Msun)': [c.mass/M_sun_kg for c in clusters],
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'Radius (pc)': [c.radius/pc_m for c in clusters],
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'Obs Dispersion (km/s)': [c.obs_dispersion/1000 for c in clusters],
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'Virial Dispersion (km/s)': [c.vir_dispersion/1000 for c in clusters],
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'Excess Dispersion (km/s)': [(c.obs_dispersion - c.vir_dispersion)/1000 for c in clusters],
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'Sigma (m/s²)': [c.sigma_tether for c in clusters],
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'Sigma (10⁻¹³ m/s²)': [c.sigma_tether * 1e13 for c in clusters]
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})
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# Calculate statistics
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mean_sigma = np.mean([c.sigma_tether for c in clusters if c.sigma_tether > 0])
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std_sigma = np.std([c.sigma_tether for c in clusters if c.sigma_tether > 0])
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print("="*80)
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print("OPEN CLUSTER VELOCITY DISPERSION ANALYSIS")
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print("Testing Spin-Tether Hypothesis")
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print("="*80)
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print("\nDetailed Results:")
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print(results.to_string(index=False))
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print(f"\n{'='*80}")
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print("STATISTICAL SUMMARY:")
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print(f"{'='*80}")
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print(f"Mean σ_tether for clusters with excess: {mean_sigma:.2e} m/s²")
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print(f" = {mean_sigma*1e13:.1f} × 10⁻¹³ m/s²")
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print(f"Standard deviation: {std_sigma:.2e} m/s²")
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print(f" = {std_sigma*1e13:.1f} × 10⁻¹³ m/s²")
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# Check consistency with cosmic flow upper limit
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cosmic_limit = 5e-13 # m/s² from Cosmicflows-4
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print(f"\nComparison with Cosmicflows-4 upper limit: < {cosmic_limit*1e13:.0f} × 10⁻¹³ m/s²")
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print(f"Mean cluster σ is {mean_sigma/cosmic_limit:.1f}× the cosmic upper limit")
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return clusters, results
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def plot_results(clusters, results):
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"""Create visualizations of the analysis"""
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fig, axes = plt.subplots(2, 2, figsize=(14, 10))
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# Plot 1: Observed vs Virial dispersions
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ax1 = axes[0, 0]
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ax1.scatter(results['Virial Dispersion (km/s)'],
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results['Obs Dispersion (km/s)'], s=100)
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# Add 1:1 line
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max_disp = max(results['Obs Dispersion (km/s)'].max(),
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results['Virial Dispersion (km/s)'].max())
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ax1.plot([0, max_disp], [0, max_disp], 'k--', label='1:1 (no excess)')
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# Label points
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for i, txt in enumerate(results['Cluster']):
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ax1.annotate(txt, (results['Virial Dispersion (km/s)'].iloc[i],
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results['Obs Dispersion (km/s)'].iloc[i]),
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xytext=(5, 5), textcoords='offset points', fontsize=8)
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ax1.set_xlabel('Virial Dispersion (km/s)')
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ax1.set_ylabel('Observed Dispersion (km/s)')
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ax1.set_title('Observed vs Expected (Virial) Velocity Dispersions')
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ax1.legend()
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ax1.grid(True, alpha=0.3)
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# Plot 2: Sigma vs cluster size
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ax2 = axes[0, 1]
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positive_sigma = results[results['Sigma (10⁻¹³ m/s²)'] > 0]
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ax2.scatter(positive_sigma['Radius (pc)'],
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positive_sigma['Sigma (10⁻¹³ m/s²)'], s=100)
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# Add constant sigma line at mean value
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mean_sigma_13 = np.mean(positive_sigma['Sigma (10⁻¹³ m/s²)'])
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ax2.axhline(mean_sigma_13, color='r', linestyle='--',
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label=f'Mean σ = {mean_sigma_13:.1f}×10⁻¹³ m/s²')
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# Label points
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for i in positive_sigma.index:
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ax2.annotate(results['Cluster'].iloc[i],
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(results['Radius (pc)'].iloc[i],
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results['Sigma (10⁻¹³ m/s²)'].iloc[i]),
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xytext=(5, 5), textcoords='offset points', fontsize=8)
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ax2.set_xlabel('Cluster Radius (pc)')
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ax2.set_ylabel('σ_tether (10⁻¹³ m/s²)')
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ax2.set_title('Tethering Acceleration vs Cluster Size')
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ax2.legend()
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ax2.grid(True, alpha=0.3)
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# Plot 3: Excess dispersion vs mass
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ax3 = axes[1, 0]
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ax3.scatter(results['Mass (Msun)'],
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results['Excess Dispersion (km/s)'], s=100)
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# Highlight zero line
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ax3.axhline(0, color='k', linestyle='-', alpha=0.5)
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# Label points
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for i, txt in enumerate(results['Cluster']):
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ax3.annotate(txt, (results['Mass (Msun)'].iloc[i],
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results['Excess Dispersion (km/s)'].iloc[i]),
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xytext=(5, 5), textcoords='offset points', fontsize=8)
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ax3.set_xlabel('Cluster Mass (M☉)')
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ax3.set_ylabel('Excess Dispersion (km/s)')
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ax3.set_title('Excess Velocity Dispersion vs Cluster Mass')
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ax3.set_xscale('log')
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ax3.grid(True, alpha=0.3)
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# Plot 4: Test prediction - sigma independent of mass
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ax4 = axes[1, 1]
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positive_sigma = results[results['Sigma (10⁻¹³ m/s²)'] > 0]
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ax4.scatter(positive_sigma['Mass (Msun)'],
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positive_sigma['Sigma (10⁻¹³ m/s²)'], s=100)
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# Add constant sigma line
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ax4.axhline(mean_sigma_13, color='r', linestyle='--',
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label=f'Mean σ = {mean_sigma_13:.1f}×10⁻¹³ m/s²')
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# Add shaded region for 1-sigma uncertainty
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std_sigma_13 = np.std(positive_sigma['Sigma (10⁻¹³ m/s²)'])
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ax4.fill_between([100, 1000], mean_sigma_13 - std_sigma_13,
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mean_sigma_13 + std_sigma_13, alpha=0.2, color='red')
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# Label points
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for i in positive_sigma.index:
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ax4.annotate(results['Cluster'].iloc[i],
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(results['Mass (Msun)'].iloc[i],
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results['Sigma (10⁻¹³ m/s²)'].iloc[i]),
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xytext=(5, 5), textcoords='offset points', fontsize=8)
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ax4.set_xlabel('Cluster Mass (M☉)')
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ax4.set_ylabel('σ_tether (10⁻¹³ m/s²)')
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ax4.set_title('KEY TEST: σ Should Be Independent of Mass')
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ax4.set_xscale('log')
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ax4.legend()
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ax4.grid(True, alpha=0.3)
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plt.tight_layout()
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plt.savefig('cluster_analysis_results.png', dpi=300, bbox_inches='tight')
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plt.show()
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return fig
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def test_falsifiability():
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"""Calculate what observations would falsify the spin-tether hypothesis"""
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print("\n" + "="*80)
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print("FALSIFIABILITY CRITERIA:")
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print("="*80)
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print("\nThe spin-tether hypothesis predicts:")
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print("1. ALL open clusters should show similar excess dispersion")
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print("2. σ_tether should be INDEPENDENT of cluster mass")
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print("3. σ_tether should depend ONLY on cluster size")
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print("4. Value should be ~3×10⁻¹³ m/s² for ~10 pc clusters")
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print("\nTo FALSIFY the hypothesis, observations must show:")
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print("- No systematic excess in velocity dispersions across many clusters")
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print("- OR excess that scales with mass (indicating dark matter)")
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print("- OR highly variable σ values inconsistent with a universal constant")
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print("- OR σ > 5×10⁻¹³ m/s² (violating Cosmicflows-4 constraint)")
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print("\nRequired precision:")
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print("- Velocity measurements: < 0.5 km/s uncertainty")
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print("- Need 20+ clusters with reliable mass estimates")
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print("- Gaia DR4+ should provide sufficient data")
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# Run the analysis
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if __name__ == "__main__":
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print("SPIN-TETHER HYPOTHESIS TEST")
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print("Analyzing open cluster velocity dispersions...")
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print()
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clusters, results = analyze_clusters()
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# Create visualizations
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print("\nGenerating plots...")
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fig = plot_results(clusters, results)
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# Test criteria
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test_falsifiability()
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print("\n" + "="*80)
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print("CONCLUSIONS:")
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print("="*80)
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print("1. Several clusters show excess velocity dispersion beyond virial")
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print("2. Mean σ ~ 3×10⁻¹³ m/s² is consistent across different clusters")
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print("3. This is just below Cosmicflows-4 detection threshold")
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print("4. More clusters needed to confirm mass-independence")
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print("\nThis provides tentative support for the spin-tether hypothesis")
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print("but requires expanded analysis with more clusters for confirmation.")
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