make_fig_shadow.py — src/21-gravity

1"""Figure: strong-field signatures vs current data (Fig.~\\ref{fig:shadow}).23Left: the Sgr A* shadow, FRC (b_c = 2e Gm/c^2) a parameter-free +4.6% wider than GR4(b_c = 3 sqrt3 Gm/c^2), 55.7 vs 53.3 uas. Right: fractional deviation from GR; the shadow5prediction +4.6% sits ~1 sigma above the EHT Keck/VLTI constraints; ringdown -4.4% (GW);6echoes absent. [approx] empirical comparison.7"""8import pathlib, math, matplotlib9matplotlib.use("Agg")10import matplotlib.pyplot as plt11from matplotlib.patches import Circle12FIG = pathlib.Path(__file__).resolve().parent.parent / "figures"13plt.rcParams.update({"font.family":"serif","mathtext.fontset":"cm","font.size":11,14                     "axes.linewidth":0.8,"figure.dpi":150})1516d_gr, d_frc = 53.3, 55.717r_gr, r_frc = d_gr/2, d_frc/218dshadow = 2*math.e/(3*math.sqrt(3))-1     # +0.046319dring   = 3*math.sqrt(3)/(2*math.e)-1     # -0.04422021fig, (axA, axB) = plt.subplots(1, 2, figsize=(7.6,3.7), gridspec_kw=dict(width_ratios=[1,1.32]))22# (a) shadow rings23axA.set_aspect("equal")24axA.add_patch(Circle((0,0), r_frc+3.0, facecolor="#fdf3da", edgecolor="none", zorder=0))25axA.add_patch(Circle((0,0), r_frc, facecolor="none", edgecolor="#1f4e79", lw=2.4, zorder=4))26axA.add_patch(Circle((0,0), r_gr,  facecolor="#3a3a3a", edgecolor="0.2", lw=1.0, zorder=3))27axA.annotate("GR  "+r"$b_c=3\sqrt{3}\,Gm/c^2$"+"\n"+r"$53.3\,\mu$as",28             xy=(0,-r_gr*0.18), ha="center", va="center", color="white", fontsize=8.0, zorder=5)29axA.annotate("FRC  "+r"$b_c=2e\,Gm/c^2$"+",  +4.6%"+"\n"+r"$55.7\,\mu$as",30             xy=(0, r_frc+4.6), ha="center", va="bottom", color="#1f4e79", fontsize=8.3)31axA.set_xlim(-r_frc-7, r_frc+7); axA.set_ylim(-r_frc-7, r_frc+11); axA.axis("off")32axA.set_title(r"Sgr A$^*$ shadow", fontsize=9.5)33# (b) deviation forest vs EHT34for i,(lab,c,lo,hi) in enumerate([("EHT Keck",-4.0,10.0,9.0),("EHT VLTI",-8.0,9.0,9.0)]):35    yy=3-i36    axB.errorbar(c, yy, xerr=[[lo],[hi]], fmt="o", color="0.30", ecolor="0.30", capsize=3, ms=5, lw=1.3)37    axB.text(c, yy+0.24, lab, ha="center", fontsize=8.0, color="0.25")38axB.plot(dshadow*100, 1.0, "s", color="#1f4e79", ms=7)39axB.text(dshadow*100, 1.0+0.24, "FRC shadow +4.6%", ha="center", fontsize=8.2, color="#1f4e79")40axB.plot(dring*100, 0.0, "D", color="#7a3030", ms=6)41axB.text(dring*100, 0.0+0.24, "FRC ringdown -4.4% (GW)", ha="center", fontsize=8.2, color="#7a3030")42axB.axvline(0, ls="--", lw=1.0, color="0.55")43axB.text(0, 3.75, "GR", ha="center", fontsize=8.5, color="0.4")44axB.set_ylim(-0.6, 4.05); axB.set_xlim(-21, 13)45axB.set_yticks([]); axB.set_xlabel(r"fractional deviation from GR,  $\delta$ (%)")46axB.set_title("Shadow size & ringdown vs current data", fontsize=9.5)47for s in ["left","right","top"]: axB.spines[s].set_visible(False)48axB.text(0.99,0.02,r"echoes: absent ($\Delta t\sim\Omega$)", transform=axB.transAxes,49         ha="right", va="bottom", fontsize=7.6, color="0.45")50fig.tight_layout()51fig.savefig(str(FIG/"fig_shadow.pdf"), bbox_inches="tight")52fig.savefig(str(FIG/"fig_shadow.png"), bbox_inches="tight", dpi=150)53print("wrote", FIG/"fig_shadow.pdf", " (+%.2f%% / %.2f%%)"%(dshadow*100,dring*100))54