Magnetically Driven Relativistic Jet in the High-Redshift Blazar OH 471

Understanding the jet launching mechanism in high-redshift active galactic nuclei (AGN) is crucial for unravelling the complex interplay between supermassive black hole (SMBH) accretion and feedback processes in the early Universe (e.g., Di Matteo et al., 2005, 2008; Dubois et al., 2014). The magnetically arrested disk (MAD) model proposes that relativistic jets can be powered efficiently when the magnetic flux threading the black hole reaches a critical threshold (Narayan et al., 2003). Previous studies have analysed AGN jets at redshifts up to 2.37, with most below $z\sim 2$ (Zamaninasab et al., 2014), however, confirming or refuting the MAD paradigm in higher redshift blazars can provide unique insights into the earliest epochs of SMBH accretion physics and jet formation mechanisms.

In this paper, we study the radio source OH 471 (0642+449, J0646+4451), a high-redshift ($z=3.396$) blazar that serves as a unique laboratory for testing MAD models and probing jet physics in the early Universe. It was one of the first distant ($z>3$) radio quasars identified in the 1970s (Gearhart et al., 1972; Carswell & Strittmatter, 1973; Crowther, 1973). Early radio observations of OH 471 revealed a complex spectral structure with multiple synchrotron self-absorption (SSA) components on different physical scales peaking between 0.5–20 GHz (Gearhart et al., 1974; Jones & O’Dell, 1974), indicating emission from several distinct regions in the relativistic jet. Very Long Baseline Interferometry (VLBI) observations established OH 471 as a blazar with a typical one-sided core-jet morphology on milliarcsecond scales (Marscher & Shaffer, 1980; Gurvits et al., 1992; Kellermann et al., 1998; Kovalev et al., 2005; Lister et al., 2013; Fey et al., 2015; Lobanov et al., 2015).

Multi-frequency VLBI observations reveal a compact core region with low (2%) fractional polarization and transverse magnetic fields (Lobanov et al., 2015). This contrasts with the substantially higher fractional polarization in a jet component located $\sim 4$ mas ($\sim$30 parsec) downstream the core, which displays magnetic fields aligning with the jet. Furthermore, an extremely high rotation measure (RM) of $9\times 10^{3}$ rad $\rm m^{-2}$ (redshift-corrected) is inferred in the inner jet just 0.5 mas from the core (Hovatta et al., 2012). This represents the largest redshift-corrected RM detected among similar high-redshift blazars.

A key motivation of this study is to explore the jet launching mechanism in OH 471 by estimating the magnetic flux and testing MAD models. Evidence for sufficient magnetic flux would strongly support magnetically-driven relativistic jets in this high-redshift radio-loud quasar.

A direct way to estimate the magnetic field strength is to fit the SSA spectrum of OH 471. The radio spectrum of OH 471 displays dramatic evolution over decades, with the SSA turnover frequency shifting from $\sim$1 GHz in early observations (Gearhart et al., 1974; Jones & O’Dell, 1974) to 10–20 GHz in recent monitoring data (Volvach et al., 2000; Sotnikova et al., 2021). This remarkable spectral variability likely implies substantial changes in the magnetic field strength, particle densities and opacity close to the SMBH. However, the spectrum has transitioned to an unusually flat shape between 1–22 GHz since 2015, representing a substantial departure from the earlier SSA-dominated spectrum. Such spectral flattening likely indicates the emergence of a newly generated jet component still embedded in the core.

By connecting changes in the jet structure and kinematics on milli-arcsec (mas) scales to this long-term spectral evolution, we expect to reveal the key structural changes in the inner jet responsible for the spectral change. Combining multi-epoch VLBI images over decades ¹¹1https://astrogeo.org/ maintained by Leonid Petrov. allow us to probe the jet kinematics. Identifying newly ejected components associated with the spectral flattening since 2015 could reveal essential clues to the particle acceleration and magnetic field evolution near the central engine.

In this paper, we provide an in-depth analysis of the jet properties and magnetic flux using multi-frequency radio variability modelling and up to three decades of VLBI image data from 1995 to 2022. The paper is organized as follows: Section 2 describes the data; Section 3 presents the results; Section 4 provides discussion; and Section 5 summarizes the conclusions. We assume a $\Lambda$CDM cosmology²²2Using this cosmological model, 1 mas angular scale corresponds to a projected physical size of 7.635 pc at $z=3.396$, and 1 mas yr${}^{-1}=109.5\,c$. with $\Omega_{\rm m}=0.27$, $\Omega_{\rm\Lambda}=0.73$, $H_{0}=70$ km s^-1 Mpc^-1.

This study utilizes two main radio datasets to investigate the spectral evolution and jet structure of radio OH 471.

The first dataset is comprised of radio flux density light curves monitored by the RATAN-600 radio telescope at the Special Astrophysical Observatory of Russian Academy of Sciences (Parijskij, 1993). Continuous monitoring of OH 471 has been carried out since 1997 at six frequencies: 1.1, 2.3, 4.7, 7.7/8.2, 11.2, and 21.7/22.3 GHz (Mingaliev et al., 2014, 2017). The mean time interval is approximately 65 days. Five epochs of data points observed by the RT-32 Zelenchukskaya and Badary radio telescopes (Shuygina et al., 2019) at 5.05 and 8.63 GHz are also included. In total, the RATAN-600 and single-dish light curves (Figure 1) include over 105 epochs spanning 15 years from 2009 to 2024 (Appendix A). This long-term multi-frequency monitoring provides excellent temporal sampling to quantify the evolution of the radio spectrum.

The second dataset consists of VLBI data at 2.3, 5, 8.4, and 15 GHz observed between 1995 and 2022. The 2.3, 5 and 8.4 GHz VLBI data are primarily obtained from the geodetic observations archived in the Astrogeo database (e.g. Beasley et al., 2002). The 15.4 GHz VLBI data are from the Monitoring Of Jets in Active galactic nuclei with VLBA Experiments (MOJAVE) programme ³³3https://www.cv.nrao.edu/MOJAVE/ (2018ApJS..234...12L). We used calibrated visibility data from these databases that had undergone initial calibration steps. We only performed a few iterations of self-calibration and made mode fitting to study the change of the jet structure over time. The details of VLBI data processing are described in Appendix B.

Combining multi-frequency light curves, VLBI imaging, and spectral modelling enables a robust investigation connecting the structural and spectral evolution of OH 471.

As one of the most distant blazars known, OH 471 provides a unique window into jet production and particle acceleration in the vicinity of an actively growing SMBH in the early Universe. Studying the variability, structural changes and magnetic field evolution of OH 471 is key to unravelling the physical processes driving powerful high-redshift jets.

The magnetic flux paradigm proposes that jet power is fundamentally determined by the accumulation of poloidal magnetic flux around the black hole (Sikora & Begelman, 2013). Poloidal flux refers to the vertical magnetic field component that threads both the black hole and the inner accretion disk. In MADs, strong poloidal fields obstruct the inner accretion flow, choking the accretion and creating a highly magnetized inner region (Tchekhovskoy et al., 2011). In MAD states, the strong vertical magnetic fields extract the spin energy of the black hole through the Blandford-Znajek process (Blandford & Znajek, 1977), generating jets with kinetic powers comparable to or exceeding the accretion power (Narayan et al., 2003). Without adequate magnetic flux accumulation, AGN cannot achieve MAD conditions, resulting in weaker jets compared to accretion power.

Observations support links between the magnetic flux and the jet power: e.g., MAD jets exhibit more ordered inner disk fields and higher core rotation measures (Zamaninasab et al., 2014); intermittent jet activity implies fluctuating magnetic flux levels (Sikora & Begelman, 2013); jet power correlates with radio core luminosity (Nemmen & Tchekhovskoy, 2015). These manifest that creating powerful jets relies on accumulating strong poloidal magnetic flux, beyond just black hole spin.

We can test if OH 471 has achieved the MAD state by comparing its estimated jet magnetic flux to the predicted MAD flux, thus assessing the role of magnetic flux in powering the powerful high-redshift jet in OH 471.

Models of jet launching propose that relativistic jets can be efficiently powered once the poloidal flux surrounding the black hole exceeds a critical threshold via the Blandford-Znajek mechanism. Simulations indicate that the MAD state occurs when magnetic flux reaches $\sim 50\left(\dot{M}r_{\mathrm{g}}^{2}c\right)^{1/2}$ (Tchekhovskoy et al., 2011), in which $\dot{M}$ is the accretion rate, $r_{\mathrm{g}}$ the gravitational radius, and $c$ the speed of light. The mass accretion rate is $\dot{M}=L_{\mathrm{acc}}/(\eta c^{2})$, where $L_{\mathrm{acc}}$ is the accretion power, $\eta$ the efficiency (typically 0.1–0.4). The black hole mass ($M_{\mathrm{BH}}$) sets the gravitational radius via $r_{\mathrm{g}}=GM_{\mathrm{BH}}/c^{2}$, where $G$ is the gravitational constant. Combining these quantities, the predicted MAD magnetic flux is $\Phi_{\mathrm{MAD}}\approx 50\sqrt{L_{\mathrm{acc}}r_{\mathrm{g}}^{2}/\eta c}=2.4\times 10^{25}[\frac{\eta}{0.4}]^{-1/2}[\frac{M_{\rm BH}}{M_{\odot}}][\frac{L_{\rm acc}}{1.26\times 10^{47}\mathrm{erg\,s}^{-1}}]^{1/2}[\mathrm{G\,cm^{2}}]$. The accretion luminosity $L_{\mathrm{acc}}$ is calculated using the bolometric luminosity $L_{\mathrm{bol}}$ and an accretion efficiency, giving $L_{\mathrm{acc}}=\frac{L_{\mathrm{bol}}}{\eta}$. The bolometric luminosity was estimated from the optical C IV line luminosity. OH 471 presents strong optical emissions, which can be used to estimate $L_{\mathrm{acc}}\approx 10L_{\mathrm{BLR}}\approx 88.2L_{\mathrm{C\ IV}}\approx 6.5\times 10^{46}$ erg s^-1 (Liu et al., 2006; Francis et al., 1991; Ghisellini & Tavecchio, 2008). With $\eta\approx 0.4$ (Zamaninasab et al., 2014), the estimated MAD flux is $\Phi_{\rm MAD}\approx 1.7\times 10^{25}[\frac{M_{\rm BH}}{M_{\odot}}]$ [G cm²].

While we lack direct observations of the jet magnetic flux in OH 471, we can estimate it from synchrotron self-absorption magnetic field strength ($B_{\rm SSA}$) derived from the spectrum fitting and core size measurement. We estimate the SSA magnetic field strength following Marscher (1983) with details presented in Appendix E. $B_{\rm SSA}$ depends on turnover frequency, peak flux density, core size, and the Lorentz factor (Appendix D). The core size is derived from VLBI model fitting (Appendix B). Following Chamani et al. (2021), $\Phi_{\rm jet}=0.8\times 10^{25}f(a*)(1+\sigma)^{1/2}[\frac{M_{\rm BH}}{M_{\odot}}]B$ [G cm²], where $\sigma$ is the jet magnetisation parameter, $f(a*)$ is a dimensionless parameter related to the black hole spin, $B$ is the magnetic field strength at 1 parsec from the black hole. $f(a*)=[1+\sqrt{1-a^{2}}]/a$ is a function of the black hole spin $a$. For a rapidly rotating black hole, which is expected for powerful jet sources such as blazars, $f(a*)\approx 1$ (Appendix 6). The magnetic field strength at a distance of 1 pc from the black hole, $B_{\rm 1pc}$, was estimated using the relation $B_{\rm 1pc}=B_{\rm core}\times(h_{\rm core}/{\rm 1pc})^{-\beta}$, where $h_{\rm core}$ is the distance between the VLBI core and the central engine, $B_{\rm core}$ is the core magnetic field strength derived from the SSA fitting, and $\beta$ is the power-law index describing the magnetic field decay with distance, as expected for a conical jet geometry (1979ApL....20...15B). In this study, we adopt $\beta=1$, which corresponds to the magnetic field being inversely proportional to the distance from the black hole. Given the conical jet geometry, the angular size of a spherical homogeneous synchrotron source at the turnover frequency $\theta(\nu_{\mathrm{m}})$ is approximately equal to the angular size observed at another frequency $\theta(\nu)$ multiplied by the ratio of the frequencies. Further details on the calculation of $B_{\rm 1pc}$ can be found in Appendix E.

To independently estimate the magnetic field strength in the VLBI core region, we performed a joint analysis of the simultaneous 8.4 and 15.4 GHz images on 2011 March 5 to determine the core shift. We found a typical core shift of ($0.09\pm 0.01$) mas between these frequencies. Using the method given by 1998A&A...330...79L, assuming equipartition between the particle and magnetic field energy densities, and assuming a viewing angle of $0.25\degr$, we estimate a magnetic field strength at a distance of 1 pc from the black hole of $B_{\rm 1pc}=(4.2\pm 0.8)$ G. This is slightly lower than the value of ($10\pm 2$) G derived from the SSA fitting, but the two values agree to within $3\sigma$. The core shift estimate thus provides an independent confirmation of the high magnetic field strength in the OH 471 jet, although both methods rely on several simplifying assumptions, so the true uncertainties are likely to be larger than the formal errors reported here. In addition, we have only one epoch of quasi-simultaneous data, so the core-shift calculation here represents a rough assessment of the magnetic field strength derived from the SSA spectrum fit. Higher-resolution multi-frequency VLBI observations are desirable to refine these magnetic field estimates and to probe the magnetic field structure of the jet in more detail.

The calculated $B_{\mathrm{SSA}}$, $B_{\mathrm{1pc}}$, and magnetic flux $\Phi_{\mathrm{jet}}$ are shown in Figure 4. $B_{\mathrm{SSA}}$ does not exhibit systematic variations over time. $B_{\mathrm{SSA}}$ depends on multiple parameters ($B_{\mathrm{SSA}}\propto\nu_{\mathrm{m}}^{5}\theta^{4}S_{\mathrm{m}}^{-2}\delta$) that vary differently over time. These combined effects essentially cancel out, leading to a relatively stable $B_{\mathrm{SSA}}$. Physically, $B_{\mathrm{SSA}}$ represents the magnetic field strength right at the SSA photosphere. This photosphere likely moves inward/outward as the jet conditions evolve, sampling different field strengths across a range of radii. In contrast, $B_{\mathrm{1pc}}$ approximates the field strength at a fixed 1 parsec distance. This single location maintains a higher field when the jet is actively flaring with fresh particle acceleration. As the flare fades over time, the field decreases at that fixed point. As $B_{\mathrm{1pc}}$ is more heavily dependent on $\nu_{\mathrm{m}}$ through the $\nu_{\mathrm{m}}^{5}$ scaling, $B_{\mathrm{1pc}}$ follows a similar evolution trend with $\nu_{\mathrm{m}}$.

The inferred $\Phi_{\mathrm{jet}}$ exceeds the predicted $\Phi_{\mathrm{MAD}}$ in 2009–2012, when the source was in a declining phase after the large 2008 flare and the newly generated jet had not yet dimmed. From 2015–2020, $\Phi_{\mathrm{jet}}\approx\Phi_{\mathrm{MAD}}$, indicating magnetic flux accumulation between flares. The period of 2021 December – 2024 February represents the rising phase of a new flare whose peak is yet to be determined, and in this period $\Phi_{\mathrm{jet}}$ is significantly higher than $\Phi_{\mathrm{MAD}}$, indicating that the magnetic flux has now exceeded the critical threshold needed to trigger a new jet ejection episode. The strong magnetic flux explains how OH 471 is able to launch such a powerful jet.

The temporal evolution of $\Phi_{\mathrm{jet}}$ relative to $\Phi_{\mathrm{MAD}}$ implies a cyclical flux accumulation process, where sufficient magnetic flux builds up to launch a new jet component, followed by a declining phase as the new jet expands and fades. Monitoring the magnetic flux over multiple flaring cycles can further test this magnetic paradigm for powering recurring jets.

To maintain the MAD state for long periods of time, significant magnetic flux is likely to have accumulated early on near the event horizon of the black hole. This type of accretion is thought to fuel the rapid growth of SMBHs at high redshifts. This scenario suggests a link between the jet’s current activity and the AGN’s early accretion history. The large reservoir of magnetic flux from past accretion builds up over timescales much longer than the jet variability, enabling the AGN to periodically reach MAD conditions and drive powerful jets intermittently. Despite fluctuations in magnetic flux, the stored flux near the black hole ensures continued jet activity following accretion episodes.

In Figure 4, we plot the measured jet magnetic flux $\Phi_{\rm jet}$ versus $L_{\rm acc}^{1/2}M_{\rm BH}$ for OH 471 compared to the sample from Zamaninasab et al. (2014). Their sample consists of 76 radio-loud AGN, including 68 blazars and 8 nearby radio galaxies. Zamaninasab et al. (2014) used published measurements of the core-shift effect to calculate the jet magnetic flux for each source. Since $\Phi_{\rm jet}$ varies with time and $M_{\rm BH}$ is not determined for OH 471, we show the range that spans the $\Phi_{\rm jet}$ variations and $M_{\rm BH}=10^{8-10}M_{\odot}$. The ($\Phi_{\rm jet}$) value derived for OH 471 broadly aligns with the previously established relationship between jet magnetic flux and the combined quantity ($L_{\rm acc}^{1/2}M_{\rm BH}$) for powerful jets from $z=(0.07-2.37)$. While our calculation involves uncertainties discussed before in this section, the overall consistency with lower-redshift AGN jets suggests the magnetic flux paradigm remains applicable to powerful jets at higher redshifts. The agreement between OH 471 and the relation for lower-$z$ sources hints at the potential universality of magnetically-driven launching processes of powerful jets from the local Universe to earlier cosmic epochs. Further studies of additional high-redshift jetted AGN can solidify the connection between magnetic flux and jet power from the early AGN population to their modern counterparts.

The magnetic field estimates presented in this paper are based on the SSA spectrum fitting of the entire source. However, this approach has some limitations due to the mixing of the core and inner jet components at lower frequencies (e.g. 2.3 and 5 GHz), which can introduce uncertainties in the derived magnetic field strengths. To obtain more accurate magnetic field estimates and to probe the magnetic field structure of the jet in detail, high-resolution multi-frequency VLBI observations are needed. These observations will allow us to more precisely determine the core shift between different frequencies, providing an independent constraint on the magnetic field strength. By comparing the magnetic field estimates derived from the core shift analysis with those obtained from the SSA spectrum fitting, we will be able to assess the robustness of our results and better constrain the uncertainties. Furthermore, the high-resolution images will allow us to study the evolution of the magnetic field along the jet, providing insights into the collimation and acceleration processes of the jet.

As a radio-loud quasar at $z>3$, OH 471 provides a unique window into jet formation and evolution in the early Universe. It shows multiple observational signatures that are consistent with the predictions of a magnetically arrested disk based on the magnetic flux paradigm for powering relativistic jets – a system in which strong magnetic flux accumulation enables efficient extraction of black hole spin energy to power relativistic jets. These indications include: extremely high brightness temperatures exceeding $10^{13}$ K measured with VLBI on parsec scales (Lobanov et al., 2000), implying efficient jet formation from the core region; large rotation measures detected in the inner jet (Hovatta et al., 2012; O’Sullivan et al., 2011), which could arise from ordered magnetic field components and/or dense magnetised plasma screens local to the jet formation region; long-term variability in the radio flux density and spectral shape (Lister et al., 2019; Sotnikova et al., 2021, and the present paper), consistent with the recurrent ejection of new synchrotron self-absorbed components seen in many AGN jets including OH 471, which potentially arise from episodic accumulation and release of magnetic flux driving transient MAD episodes near the black hole; and an estimated jet magnetic flux that surpasses theoretical predictions for the critical MAD threshold needed to power a relativistic jet (the present paper). All these observations support a scenario where cyclic magnetic flux accumulation likely enables this high-redshift blazar to periodically achieve magnetically arrested states that give rise to energetic jet ejections from the vicinity of the central SMBH.

This finding provides important insights into existing models of the earliest growth of supermassive black holes. Powerful flares and extremely relativistic jets observed in high-redshift AGN likely require achieving MAD conditions early, allowing time to accumulate magnetic flux. We expect other high-$z$ jetted AGN to follow this magnetic paradigm, with the most powerful systems already reaching MAD levels. Studying a large statistical sample for correlations between jet power, accretion rate, and magnetic flux can firmly establish the importance of magnetic flux accumulation in generating the earliest AGN jets. Future multi-band observations are crucial to understanding if the jet dynamics in OH 471 differ from similar lower-$z$ objects, potentially revealing changes in jet production and collimation over cosmic time.

While the MAD model provides rich qualitative predictions for the accretion and jet dynamics around black holes, it does not provide universal quantitative relations directly linking magnetic flux accumulation and jet cycles to system parameters. The complex interplay between black hole mass, accretion rate, disk properties, and GRMHD processes makes accurate quantitative modelling a challenge. Nevertheless, the MAD framework provides important insights into the physical mechanisms likely to drive the episodic powerful jets observed from sources such as OH 471. Despite the limitations of quantitative modelling of individual objects, multi-wavelength observations may help to distinguish MAD signatures.