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# ============================================================ # MONAD-FIELD SPARC – DWARF GALAXY FIT (DDO154) # Tests universality of γ in low‑baryon regime. # ============================================================ import numpy as np import pandas as pd import matplotlib.pyplot as plt from scipy.optimize import curve_fit from scipy.interpolate import interp1d # ------------------------------------------------------------ # Load your uploaded SPARC file (already done in previous code) # Instead of re-loading, assume df exists. If not, use the code from earlier. # ------------------------------------------------------------ # ------------------------------------------------------------ # 2. Select galaxy (change GALAXY name as needed) # ------------------------------------------------------------ GALAXY = "DDO154" # classic dark‑matter‑dominated dwarf # Alternative: "DDO52", "NGC2915", "IC2574", "UGC4325" df_gal = df[df['ID'].str.strip() == GALAXY].copy() if len(df_gal) == 0: raise ValueError(f"Galaxy {GALAXY} not found. Available: {df['ID'].unique()[:20]}...") print(f"\nLoaded {len(df_gal)} data points for {GALAXY}") # ------------------------------------------------------------ # 3. Compute baryonic and residual rotation curves (same as before) # ------------------------------------------------------------ df_gal['Vbary_sq'] = df_gal['Vgas']**2 + df_gal['Vdisk']**2 + df_gal['Vbul']**2 df_gal['Vbary'] = np.sqrt(df_gal['Vbary_sq']) df_gal['Vobs_sq'] = df_gal['Vobs']**2 df_gal['Vsub_sq'] = df_gal['Vobs_sq'] - df_gal['Vbary_sq'] df_gal['Vsub_sq'] = df_gal['Vsub_sq'].clip(lower=0) df_gal['Vsub'] = np.sqrt(df_gal['Vsub_sq']) df_gal['e_Vsub'] = df_gal['Vobs'] * df_gal['e_Vobs'] / df_gal['Vsub'] df_gal['e_Vsub'] = df_gal['e_Vsub'].replace([np.inf, -np.inf], 0).fillna(0) # ------------------------------------------------------------ # 4. Fit Monad‑Field static‑limit model # ------------------------------------------------------------ def sub_powerlaw(R, V0, gamma, R0=1.0): return V0 * (R / R0)**gamma mask = (df_gal['R'] > 0) & (df_gal['Vsub'] > 0) & (df_gal['e_Vsub'] > 0) R_fit = df_gal.loc[mask, 'R'].values Vsub_fit = df_gal.loc[mask, 'Vsub'].values e_fit = df_gal.loc[mask, 'e_Vsub'].values try: popt, pcov = curve_fit(sub_powerlaw, R_fit, Vsub_fit, p0=[20.0, 0.5], sigma=e_fit, absolute_sigma=True, bounds=([0, -0.5], [200, 2.0])) V0_fit, gamma_fit = popt perr = np.sqrt(np.diag(pcov)) print(f"\nFitted Monad‑Field substrate parameters for {GALAXY}:") print(f" V0 = {V0_fit:.2f} ± {perr[0]:.2f} km/s") print(f" gamma = {gamma_fit:.3f} ± {perr[1]:.3f}") except Exception as e: print(f"Fit failed: {e}") V0_fit, gamma_fit = np.nan, np.nan # ------------------------------------------------------------ # 5. Plot # ------------------------------------------------------------ plt.figure(figsize=(10, 7)) plt.errorbar(df_gal['R'], df_gal['Vobs'], yerr=df_gal['e_Vobs'], fmt='o', color='black', capsize=2, label='Observed') plt.plot(df_gal['R'], df_gal['Vbary'], 'b-', lw=2, label='Baryonic (Newtonian)') if not np.isnan(V0_fit): R_model = np.linspace(df_gal['R'].min(), df_gal['R'].max(), 200) Vsub_model = sub_powerlaw(R_model, V0_fit, gamma_fit) f_bary = interp1d(df_gal['R'], df_gal['Vbary'], kind='cubic', fill_value='extrapolate') Vbary_model = f_bary(R_model) Vtotal_model = np.sqrt(Vbary_model**2 + Vsub_model**2) plt.plot(R_model, Vtotal_model, 'r--', lw=2, label=f'Monad‑Field total (γ = {gamma_fit:.2f})') plt.xlabel('Radius (kpc)') plt.ylabel('Circular velocity (km/s)') plt.title(f'Rotation curve of {GALAXY}') plt.legend() plt.grid(True, alpha=0.3) plt.tight_layout() plt.savefig(f'MonadField_{GALAXY}_fit.png', dpi=150) plt.show() 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

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