Persistent Radio Source (PRS)

• Persistent Radio Sources are compact, luminous non-thermal radio emitters associated with extragalactic repeating FRBs, characterized by flat spectral indices and high rotation measures.
• Systematic VLBI imaging and high-cadence radio monitoring reveal distinct variability patterns and spectral turnovers that distinguish PRSs from typical star formation sources.
• PRS studies enable precision cosmology and environmental diagnostics by correlating luminosity with Faraday rotation, aiding in measurements of H0 and host galaxy properties.

A Persistent Radio Source (PRS) is a compact, non-thermal radio continuum emitter spatially and physically associated with a subset of extragalactic, repeating Fast Radio Bursts (FRBs), notably in environments characterized by high magneto-ionic columns and extreme rotation measures. Systematic VLBI imaging and high-cadence radio monitoring have revealed that PRSs exhibit unique combinations of luminosity, variability, spectral properties, and environmental signatures, making them key observables for understanding FRB progenitors and host environments, as well as emergent tools in cosmological parameter estimation.

1. Definition, Identification, and Host Demographics

PRSs are defined as luminous ($L_\nu \sim 10^{28}$–$10^{30} \ \mathrm{erg\,s^{-1}\,Hz^{-1}}$ for $\nu \sim 1-5$ GHz), compact (size $R\lesssim1$ pc), non-transient radio sources precisely coincident with the FRB position on milliarcsecond scales and persisting over years (Snelders et al., 13 Oct 2025, Bhandari et al., 2023, Zhao et al., 2021, Yan et al., 2024, Law et al., 2021, Letsele et al., 2 Dec 2025). Empirically, they are discriminated from supernova remnants or AGN by radio luminosity orders of magnitude above what is expected from star formation given the galaxy's SFR and by flat or shallow spectral indices atypical for normal galaxy nuclei. Repeating FRBs such as FRB 20121102A, 20190520B, 20201124A, and 20240114A are canonical PRS hosts, predominantly residing in low-mass ($M_*\sim10^8$–$10^9\, M_\odot$), high-sSFR, often dwarf, starburst galaxies (Bruni et al., 2024, Bhusare et al., 2024, Bhandari et al., 2023, Vohl et al., 2023).

Common PRS identification criteria include:

• Compact morphology: unresolved with VLBI or e-MERLIN at $<1$ pc scale,
• Persistent emission with little or stochastic variability,
• Positional alignment with the FRB at sub-parsec offsets ($\lesssim$12 pc for FRB 20121102A (Snelders et al., 13 Oct 2025); $\lesssim$20 mas for 20190520B (Bhandari et al., 2023)),
• Radio spectral index $-0.2 \lesssim \alpha \lesssim 0.0$ (e.g., FRB 20121102A (Bhardwaj et al., 30 Jun 2025)),
• Host galaxy properties excluding AGN by optical line ratios and energetics.

2. Radio Continuum Properties and Temporal Variability

PRSs exhibit flux densities at GHz frequencies typically $50$–$300$ $\mu$Jy, with high radio luminosities contrasted to expected star formation rates (Yang et al., 2024, Vohl et al., 2023, Bruni et al., 2024). Long-term flux monitoring reveals that not all PRSs are stationary: FRB 20190520B's PRS decays as $F_\nu\propto t^{-3.3}$ over $\sim 4$ yr, punctuated by stochastic brightening and dimming episodes of $\sim$10–20% on timescales of days to weeks (Balaubramanian et al., 3 Jul 2025, Yang et al., 2024). At 3 GHz, marginal variability with strengths up to 25%, at significance $\eta=2.14$, has been observed (Zhang et al., 2023, Yang et al., 2024). In contrast, FRB 20121102A's PRS remains statistically stable (<15% intrinsic modulation) over $>7$ years; its observed variability is consistent with refractive interstellar scintillation alone (Bhardwaj et al., 30 Jun 2025, Snelders et al., 13 Oct 2025).

Time-resolved VLBI imaging, with mas resolution, confirms that PRS emission is not due to extended, diffuse galactic emission but arises in unresolved, likely parsec-scale nebulae (Snelders et al., 13 Oct 2025, Bhandari et al., 2023, Bruni et al., 2024).

Spectral analysis shows PRSs maintain flat or mildly steep indices over multi-GHz bands (e.g., $\alpha=-0.2$ to $-0.4$ for 20121102A, 20190520B), sometimes showing low-frequency turnover at $\nu_b\sim1$ GHz, consistent with synchrotron self-absorption or free-free absorption in the nebular environment (Bhusare et al., 2024, Balaubramanian et al., 3 Jul 2025).

3. Physical Interpretation: Nebular and Accretion Models

The principal models for PRS origin invoke synchrotron emission from a compact ($R\sim0.1-1$ pc), high-magnetic-field ($B\sim$ mG–10 mG), magneto-ionic nebula surrounding the FRB progenitor:

A. Magnetar Wind Nebula (MWN)/Composite SNR Models

A young, high-field magnetar ($B_\text{int}\sim10^{16}$ G), born in a core-collapse SN with $M_\mathrm{ej}\sim3-10\,M_\odot$ and $E_\mathrm{SN}\sim10^{50-51}$ erg, injects rotational and/or magnetic energy into its environment. Energy loss via magnetar wind inflates a pair nebula, producing persistent synchrotron emission and driving SN ejecta that supply high DM and RM. ISM and SNR shock interactions dictate nebular expansion and emission properties (Zhao et al., 2021, Rahaman et al., 1 Apr 2025, Balaubramanian et al., 3 Jul 2025). Key physical predictions include:

• Nebular radius $R_\mathrm{eq}\sim0.1$ pc at $t\sim10-100$ yr,
• Equipartition luminosity consistent with observed $L_\nu\sim10^{29}$ erg s$^{-1}$ Hz$^{-1}$,
• Cooling break in SED at $\nu_c\sim100$–$150$ GHz, SSA turnover near 200 MHz,
• Secular DM and RM decrease as $t^{-2}$ and $t^{-5/2}$, respectively.

B. Hyperaccreting Compact Object (Hypernebula) Models

Alternatively, super-Eddington accretion onto a compact object (black hole or neutron star) can drive powerful outflows, leading to a shocked, magnetized cavity. The hypernebula's synchrotron luminosity and time evolution depend on accretion rate, jet power, and wind structure (Bhandari et al., 2023, Balaubramanian et al., 3 Jul 2025). These models can replicate PRS luminosities, size, and the observed high and variable RM, but in some cases (e.g., FRB 20190520B), secular fading timescales exclude previously published hypernebula scenarios (Balaubramanian et al., 3 Jul 2025).

C. Low-Luminosity AGN/Wandering IMBHs

In several host galaxies, the properties of PRSs are generically compatible with compact AGN cores powered by low-Eddington accreting intermediate mass black holes (IMBHs). Their position on the fundamental radio–X-ray plane, flat spectra, and long-term stability offer a non-neutron-star alternative (Bhardwaj et al., 30 Jun 2025, Dong et al., 2024, Vohl et al., 2023). However, such scenarios must explain spatial coincidence with the FRB and often lack corroborating AGN spectral signatures.

4. Rotation Measure, PRS–RM–Luminosity Correlation, and Environmental Diagnostics

PRS-associated FRBs display high, often extreme, Faraday RMs (e.g., $2\times10^5$ rad m$^{-2}$ for FRB 20121102A (Snelders et al., 13 Oct 2025); $4.4\times10^4$ rad m$^{-2}$ in 2025), pointing to dense, magnetized local environments. Empirical and theoretical studies have established a tight correlation between PRS luminosity and $|{\rm RM}|$, often termed the "Yang relation" or YLZ relation:

$L_\nu \propto |{\rm RM}|$

with explicit formulation:

$$L_{\nu,\max} = \frac{64\pi^3}{27} \zeta_e \gamma_\mathrm{th}^2 m_e c^2 R^2 |{\rm RM}|$$

where $\zeta_e$ is the fraction of electrons radiating at the observed frequency, $\gamma_\mathrm{th}$ the typical Lorentz factor, and $R$ the emission region's size (Gao et al., 21 Apr 2025, Yan et al., 2024, Bruni et al., 2024, Yang et al., 2022).

This relation is consistent across all confirmed PRS–FRB pairs and is robust against microphysical variations, relying predominantly on the integrated magnetized column and energetics. A positive $L_\nu$–$|{\rm RM}|$ correlation is also predicted for turbulent nebular environments, whether powered by a magnetar or an accreting compact object (Yang et al., 2022).

Spectropolarimetric monitoring reveals time-correlated decline of both DM and RM, with the local DM decreasing by $\sim25$ pc cm$^{-3}$ and RM by $\sim75\%$ over five years in FRB 20121102A, pointing to an evolving, expanding, and weakening magnetized plasma in the local $\lesssim1$ pc environment (Snelders et al., 13 Oct 2025, Zhao et al., 2021).

5. Cosmological and Astrophysical Applications of PRSs

The empirical $L_\nu$–${\rm RM}$ relation underpins new methodologies for precision cosmology with FRBs (Gao et al., 21 Apr 2025, Zhang et al., 17 Apr 2025). By relating PRS luminosity, observed flux, and RM, one can derive the luminosity distance and calibrate $H_0$ independent of traditional dispersion measure ($DM$)–$z$ methods:

• Current samples yield $H_0=86_{-15}^{+18}$ km s$^{-1}$ Mpc$^{-1}$, with model uncertainties dominated by the nebula microphysics,
• Simulated samples ($N\sim400$ FRB-PRSs) can potentially constrain $H_0$ to $\sim$4% precision,
• Joint analysis with $DM$–$z$ samples breaks degeneracies in IGM baryon mass fraction and cosmological parameters by providing complementary observables (Gao et al., 21 Apr 2025, Zhang et al., 17 Apr 2025).

PRSs also serve as calorimeters for the long-term energy output of FRB engines and as environmental diagnostics of post-SN nebulae, SNRs, and compact object feedback in dwarf galaxies (Vohl et al., 2023, Zhao et al., 2021).

6. Variability, Population Statistics, and Open Challenges

Radio monitoring across repeaters indicates that significant $\sim 20$–$40\%$ amplitude variability on days to years is common (e.g., FRB 20190520B, FRB 20121102A), but intrinsic variability does not correlate with the FRB burst rate or other burst properties (Yang et al., 2024, Bhardwaj et al., 30 Jun 2025). Star formation alone cannot account for such luminosities, as demonstrated by radio-to-optical SFR disparity factors of $\sim$35–50 (Yang et al., 2024, Bhusare et al., 2024).

Current population constraints indicate that only $<5\%$ of known repeaters host PRSs with $L_\nu \gtrsim10^{40}$ erg s$^{-1}$ Hz$^{-1}$ (Ibik et al., 2024, Letsele et al., 2 Dec 2025). However, faint, compact PRSs may remain undetected in many repeaters due to sensitivity and frequency limitations (Bruni et al., 2024, Bhusare et al., 2024). The diversity in observed radio luminosities, host offsets, and host galaxy composition suggests multiple evolutionary channels or progenitor scenarios.

The lack of a correlation between PRS luminosity and FRB burst rate further supports models decoupling the persistent emission engine from the immediate FRB burst mechanism, implying that PRSs and FRBs may, in some systems, be physically distinct (Bhardwaj et al., 30 Jun 2025).

7. Future Prospects and Observational Agenda

Key future directions include:

• Systematic, high-sensitivity, multi-frequency, and VLBI monitoring to determine the lifetime and spectral evolution of PRSs,
• Deep, high-resolution searches in complete FRB samples to quantify PRS incidence and variability,
• Expanded low-frequency and sub-mm observations to identify spectral breaks (SSA, cooling),
• Comprehensive optical, IR, and X-ray follow-up to distinguish between AGN and neutron-star wind nebula origins (Letsele et al., 2 Dec 2025, Dong et al., 2024, Vohl et al., 2023),
• Direct tests of the RM–luminosity relation across broader environments and host types,
• Application of PRS observables in precision FRB cosmology and baryonic mapping (Gao et al., 21 Apr 2025, Zhang et al., 17 Apr 2025).

Continued progress is anticipated as next-generation facilities (e.g., SKA, ngVLA, DSA-2000) come online, providing the sensitivity and angular resolution required to both expand the known PRS population and definitively distinguish among magnetar, accretion, and AGN scenarios in the complex environments surrounding repeating FRBs.