FIR-Radio Correlation (q_IR)

The FIR-radio correlation links a galaxy’s infrared luminosity to its 1.4 GHz synchrotron emission via the dimensionless parameter \(q_{\rm IR} = \log_{10}(L_{\rm IR} / 3.75\times10^{12} \, L_{\rm 1.4GHz})\). Higher \(q_{\rm IR}\) means relatively less radio per unit star formation. The canonical value for star-forming galaxies is 2.64 (Bell 2003).

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
import numpy as np

jax.config.update("jax_enable_x64", True)

from tengri.analysis.plotting import SWEEP_CMAPS, setup_style
from tengri.radio import radio_star_forming

setup_style()

# --- Wavelength grid: radio regime (1 mm to 10 m) ---
wave = jnp.logspace(7, 11, 600)  # Angstrom: 1 mm = 1e7 Å, 10 m = 1e11 Å

L_ir = 1e11  # L_sun — ULIRG-like

q_ir_values = [2.0, 2.3, 2.64, 3.0, 3.3]
cmap = plt.get_cmap(SWEEP_CMAPS["radio"])
colors = [cmap(i / max(len(q_ir_values) - 1, 1)) for i in range(len(q_ir_values))]

fig, ax = plt.subplots(figsize=(7, 4))

for q_ir, color in zip(q_ir_values, colors):
    # radio_star_forming takes q_ir as a parameter
    L_nu = radio_star_forming(wave, L_ir=L_ir, q_ir=q_ir, alpha_sf=0.8)
    nu_ghz = (3e18 / np.array(wave)) / 1e9  # convert Å → Hz → GHz
    ax.loglog(nu_ghz, np.array(L_nu), color=color, lw=2.0, label=rf"$q_{{\rm IR}}={q_ir}$")

ax.set_xlabel("Frequency [GHz]", fontsize=12)
ax.set_ylabel(r"$L_\nu$ [erg s$^{-1}$ Hz$^{-1}$]", fontsize=12)
ax.invert_xaxis()
ax.set_xlim(200, 0.1)
ax.set_ylim(1e-8, 1e2)
ax.legend(fontsize=10, frameon=False)
ax.set_title(
    r"FIR-Radio Correlation: $q_{\rm IR}$ sweep ($L_{\rm IR}=10^{11}\,L_\odot$)",
    fontsize=12,
)
plt.tight_layout()
plt.savefig("plot_q_ir_sweep.png", dpi=150, bbox_inches="tight")
plt.show()