arXiv subjects

E. Ros

Publications and source records attributed to E. Ros.

At least 37 records · Page 2Linked to original sources

arXiv2024

Evidence for a toroidal magnetic field in the core of 3C 84

The spatial scales of relativistic radio jets, probed by relativistic magneto-hydrodynamic jet launching simulations (RMHDs) and by most very-long-baseline interferometry (VLBI) observations differ by an order of magnitude. Bridging the gap between these RMHD simulations and VLBI observations requires selecting nearby active galactic nuclei (AGN), the parsec-scale region of which can be resolved. 3C 84 is a nearby bright AGN fulfilling the necessary requirements: it is launching a powerful, relativistic jet powered by a central supermassive black hole, while also being very bright. Using 22 GHz global VLBI measurements of 3C 84 we aim to study its sub-parsec region in both total intensity and linear polarisation, to explore the properties of this jet, with a linear resolution of $\sim0.1$ parsec. We test different simulation setups by altering the bulk Lorentz factor $Γ$ of the jet, as well as the magnetic field configuration (toroidal, poloidal, helical). We confirm the persistence of a limb brightened structure, which reaches deep into the sub-parsec region. The corresponding electric vector position angles (EVPAs) follow the bulk jet flow inside but tend to be orthogonal to it near the edges. Our state-of-the-art RMHD simulations show that this geometry is consistent with a spine-sheath model, associated with a mildly relativistic flow and a toroidal magnetic field configuration.

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arXiv2024

Ordered magnetic fields around the 3C 84 central black hole

3C84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of VLBI above the hitherto available maximum frequency of 86GHz. Using ultrahigh resolution VLBI observations at the highest available frequency of 228GHz, we aim to directly detect compact structures and understand the physical conditions in the compact region of 3C84. We used EHT 228GHz observations and, given the limited (u,v)-coverage, applied geometric model fitting to the data. We also employed quasi-simultaneously observed, multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. We report the detection of a highly ordered, strong magnetic field around the central, SMBH of 3C84. The brightness temperature analysis suggests that the system is in equipartition. We determined a turnover frequency of $ν_m=(113\pm4)$GHz, a corresponding synchrotron self-absorbed magnetic field of $B_{SSA}=(2.9\pm1.6)$G, and an equipartition magnetic field of $B_{eq}=(5.2\pm0.6)$G. Three components are resolved with the highest fractional polarisation detected for this object ($m_\textrm{net}=(17.0\pm3.9)$%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017-2018. We report a steeply negative slope of the spectrum at 228GHz. We used these findings to test models of jet formation, propagation, and Faraday rotation in 3C84. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C84. However, systematic uncertainties due to the limited (u,v)-coverage, however, cannot be ignored.

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arXiv2024

TELAMON: Effelsberg monitoring of AGN jets with very-high-energy astroparticle emission -- I. Program description and sample characterization

Aims. We introduce the TELAMON program which is using the Effelsberg 100-m telescope to monitor the radio spectra of active galactic nuclei (AGN) under scrutiny in astroparticle physics, specifically TeV blazars and candidate neutrino-associated AGN. Here, we present and characterize our main sample of TeV-detected blazars. Methods. We analyze the data sample from the first ~2.5 years of observations between August 2020 and February 2023 in the range from 14 GHz to 45 GHz. During this pilot phase, we have observed all 59 TeV-detected blazars in the Northern Hemisphere (i.e., Dec. >0°) known at the time of observation. We discuss the basic data reduction and calibration procedures used for all TELAMON data and introduce a sub-band averaging method used to calculate average light curves for the sources in our sample. Results. The TeV-selected sources in our sample exhibit a median flux density of 0.12 Jy at 20 mm, 0.20 Jy at 14 mm and 0.60 Jy at 7 mm. The spectrum for most of the sources is consistent with a flat radio spectrum and we find a median spectral index ($S(ν)\proptoν^α$) of $α=-0.11$. Our results on flux density and spectral index are consistent with previous studies of TeV-selected blazars. Compared to the GeV-selected F-GAMMA sample, TELAMON sources are significantly fainter in the radio band. This is consistent with the double-humped spectrum of blazars being shifted towards higher frequencies for TeV-emitters (in particular for high-synchrotron peaked BL Lac type objects), which results in a lower radio flux density. The spectral index distribution of our TeV-selected blazar sample is not significantly different from the GeV-selected F-GAMMA sample. Moreover, we present a strategy to track the light curve evolution of sources in our sample for future variability and correlation analysis.

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arXiv2023

TELAMON: Effelsberg Monitoring of AGN Jets with Very-High-Energy Astroparticle Emissions -- Polarization properties

We present recent results of the TELAMON program, which is using the Effelsberg 100-m telescope to monitor the radio spectra of active galactic nuclei (AGN) under scrutiny in astroparticle physics, namely TeV blazars and neutrino-associated AGN. Our sample includes all known Northern TeV-emitting blazars as well as blazars positionally coincident with IceCube neutrino alerts. Polarization can give additional insight into the source properties, as the polarized emission is often found to vary on different timescales and amplitudes than the total intensity emission. Here, we present an overview of the polarization properties of the TeV-emitting TELAMON sources at four frequencies in the 20 mm and 7 mm bands. While at 7 mm roughly $82\,\%$ of all observed sources are found to be significantly polarized, for 20 mm the percentage is $\sim58\,\%$. We find that most of the sources exhibit mean fractional polarizations of $<5\%$, matching the expectations of rather low polarization levels in these sources from previous studies at lower radio frequencies. Nevertheless, we demonstrate examples of how the polarized emission can provide additional information over the total intensity.

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arXiv2023

The Impact of Southern-Hemisphere Radio Blazar Observations on Neutrino Astronomy

The origin of high-energy cosmic neutrinos detected by the IceCube observatory is a hotly debated topic in astroparticle physics. There is growing evidence that some of these neutrinos can be associated with active galactic nuclei (AGN) and especially with blazars. Several recent studies have revealed a statistical correlation between radio-bright AGN samples and IceCube neutrino event catalogs. In addition, a growing number of individual high-energy neutrinos have been found to coincide with individual radio-flaring blazars. These observational results strongly call for high-quality, high angular-resolution radio observations of such neutrino-associated blazars to study their parsec-scale jet structures. TANAMI is the only large and long-term VLBI monitoring program focused on the Southern sky. Within TANAMI, we put an emphasis on Southern IceCube neutrino candidate blazars at 2.3 GHz and 8.4 GHz. Here we present first results of the first high-quality, high angular-resolution VLBI observations of nine Southern-Hemisphere blazars that were associated to IceCube neutrino hotspots in the Southern sky. In the near future, the rapidly growing KM3NeT will complement IceCube by being sensitive to high-energy neutrinos mainly from the Southern Hemisphere. This will increase the importance of Southern-Hemisphere radio monitoring programs of neutrino-associated blazars, like TANAMI.

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arXiv2023

VLBI Probes of Jet Physics in Neutrino-Candidate Blazars

In recent years, evidence has accumulated that some high-energy cosmic neutrinos can be associated with blazars. The strongest evidence for an individual association was found in the case of the blazar TXS 0506+056 in 2017. In July 2019, another track-like neutrino event (IC190730A) was found spatially coincident with the well-known bright flat-spectrum radio quasar PKS 1502+106. PKS 1502+106 was not found to be in a particularly elevated gamma-ray state, but exhibited a remarkably bright radio outburst at the time of the neutrino detection, similar to TXS 0506+056. We have performed a multi-frequency VLBI study from 15 GHz up to 86 GHz on TXS 0506+056, PKS 1502+106 and one additional neutrino-candidate blazar (PKS 0215+015) to study the radio structure of neutrino candidate blazars in response to their neutrino association. We have obtained target of opportunity observations with the VLBA for all three sources within $\sim$1 month from their associated neutrino events and are performing multi-epoch studies of the jet kinematics at 15 GHz as part of the MOJAVE program. Here, we present first results on TXS 0506+056 at 86 GHz and one additional 43 GHz image obtained 27 days after IC170922A, closer in time to the neutrino event than previously published images. We also give an overview about our recent work on PKS 1502+106 and PKS 0215+015.

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arXiv2023

From binary to singular: the AGN PSO J334.2028+1.4075 under the high-resolution scope

PSO J334.2028+1.4075 (PSO J334) is a luminous quasar located at redshift z=2.06. The source gained attention when periodic flux density variations were discovered in its optical light curve. These variations were initially interpreted as the variability due to the orbital motion of a supermassive black hole binary (SMBHB) residing in a single circumbinary accretion disk. However, subsequent multiwavelength observations provided evidence against the binary hypothesis as no optical periodicity was found on extended time baselines. On the other hand, detailed radio analysis with the Karl G. Jansky Very Large Array (VLA) and the Very Long Baseline Array (VLBA) revealed a lobe-dominated quasar at kpc scales, and possibly a precessing jet, which could retain PSO J334 as a binary SMBH candidate. We aim to study both the large- and small-scale radio structures in PSO J334 to provide additional evidence for or against the binary scenario. We observed the source at 1.7 GHz with the European Very Long Baseline Interferometry Network (EVN), and at 1.5 and 6.2 GHz with the VLA, at frequencies that complement the previous radio interferometric study. Our images reveal a single component at parsec scales slightly resolved in the southeast-northwest direction and a lobe-dominated quasar at kiloparsec scales with a complex structure. The source morphology and polarization in our VLA maps suggest that the jet is interacting with dense clumps of the ambient medium. While we also observe a misalignment between the inner jet and the outer lobes, we suggest that this is due to the restarted nature of the radio jet activity and the possible presence of a warped accretion disk rather than due to the perturbing effects of a companion SMBH. Our analysis suggests that PSO J334 is most likely a jetted AGN with a single SMBH, and there is no clear evidence of a binary SMBH system in its central engine.

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arXiv2023

Radio jet precession in M81*

We report four novel position angle measurements of the core region of M81* at 5GHz and 8GHz, which confirm the presence of sinusoidal jet precession of the M81 jet region as suggested by \cite{Marti-Vidal2011}. The model makes three testable predictions on the evolution of the jet precession, which we test in our data with observations in 2017, 2018, and 2019. Our data confirms a precession period of $\sim7~\mathrm{yr}$ on top of a small linear drift. We further show that two 8 GHz observation are consistent with a precession period of $\sim 7~\mathrm{yr}$, but show a different time-lag w.r.t. to the 5 GHz and 1.7 GHz observations. We do not find a periodic modulation of the light curve with the jet precession, and therefore rule out a Doppler nature of the historic 1998-2002 flare. Our observations are consistent with either a binary black hole origin of the precession or the Lense-Thirring effect.

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arXiv2023

VLBI Scrutiny of a New Neutrino-Blazar Multiwavelength-Flare Coincidence

In the past years, evidence has started piling up that some high-energy cosmic neutrinos can be associated with blazars in flaring states. On February 26, 2022, a new blazar-neutrino coincidence has been reported: the track-like neutrino event IC220225A detected by IceCube is spatially coincident with the flat-spectrum radio quasar PKS 0215+015. Like previous associations, this source was found to be in a high optical and $γ$-ray state. Moreover, the source showed a bright radio outburst, which substantially increases the probability of a true physical association. We have performed six observations with the VLBA shortly after the neutrino event with a monthly cadence and are monitoring the source with the Effelsberg 100m-Telescope, and with the Australia Compact Telescope Array. Here, we present first results on the contemporary parsec-scale jet structure of PKS 0215+015 in total intensity and polarization to constrain possible physical processes leading to neutrino emission in blazars.

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arXiv2022

Jet kinematics in the transversely stratified jet of 3C 84 A two-decade overview

3C84 (NGC1275) is one of the brightest radio sources in the mm radio-bands, which led to a plethora of VLBI observations at numerous frequencies over the years. They reveal a two-sided jet structure, with an expanding but not well-collimated parsec-scale jet, pointing southward. High resolution mm-VLBI observations allow the study and imaging of the jet base on the sub-parsec scale. This could facilitate the investigation of the nature of the jet origin, also in view of the previously detected two-railed jet structure and east-west oriented core region seen with RadioAstron at 22 GHz. We produce VLBI images of this core and inner jet region, observed during the past twenty years at 15, 43, and 86 GHz. We determine the kinematics of the inner jet and ejected features at 43 and 86 GHz and compare their ejection times with radio and $γ$-ray variability. For the moving jet features, we find an average velocity of $β^\textrm{avg}_\textrm{app} = 0.055-0.22$c ($μ^\textrm{avg} = 0.04-0.18\,$mas/yr). From the time-averaged VLBI images at the three frequencies, we measure the transverse jet width along the bulk flow. On the $\leq 1.5$ parsec scale, we find a clear trend of the jet width being frequency dependent, with the jet being narrower at higher frequencies. This stratification is discussed in the context of a spine-sheath scenario, and is compared to other possible interpretations. From quasi-simultaneous observations at 43 and 86\,GHz we obtain spectral index maps, revealing a time-variable orientation of the spectral index gradient, due to structural variability of the inner jet.

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arXiv2021

Locating the $γ$-ray emitting region in the quasar 4C +01.28

Determining the location of $γ$-ray emission in blazar jets is a challenging task. Pinpointing the exact location of $γ$-ray production within a relativistic jet can place strong constraints on our understanding of high-energy astrophysics and astroparticle physics. We present a study of the radio- and $γ$-bright flat-spectrum radio quasar (FSRQ) 4C +01.28 (PKS B1055+018) in which we try to pinpoint the emission site of several prominent GeV flares. This source shows prominent high-amplitude broadband variability on time scales ranging from days to years. We combine high-resolution VLBI observations and multi-band radio light curves over a period of around nine years. We can associate two bright and compact newly ejected jet components with bright flares observed by the Fermi/LAT $γ$-ray telescope and at various radio frequencies. A cross-correlation analysis reveals the radio light curves systematically lag behind the $γ$-rays. In combination with the jet kinematics as measured by the VLBA, we use these cross-correlations to constrain a model in which the flares become observable at a given frequency when a plasma component passes through the region at which the bulk energy dissipation takes place at that frequency. We derive a lower limit of the location of the $γ$-ray emitting region in 4C +01.28 of several parsecs from the jet base, well beyond the expected extent of the broad-line region. This observational limit challenges blazar-emission models that rely on the broad-line region as a source of seed photons for inverse-Compton scattering.

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arXiv2021

Dual-high-frequency VLBI study of blazar-jet brightness-temperature gradients and collimation profiles

On the kiloparsec scale, extragalactic radio jets show two distinct morphologies related to their power: collimated high-power jets ending in a bright termination shock and low-power jets opening up close to the core and showing a more diffuse surface brightness distribution. The emergence of this morphological dichotomy on the parsec scale at the innermost jet regions can be studied with very-long-baseline interferometry (VLBI) radio observations of blazars in which the jet emission is strongly Doppler boosted due to relativistic bulk motion at small angles between the jet direction and the line of sight. We seek to characterize the geometry and emission profiles of the parsec-scale radio jets of flat-spectrum radio quasars (FSRQs) and BL Lacertae objects (BL Lacs) on parsec scales to derive properties of the magnetic field, environment, and energetics for different classes of extragalactic jets. We analyze the VLBI radio data of 15 FSRQs, 11 BL Lacs, and two radio galaxies contained in both the MOJAVE data archive and the Boston University BU blazar group sample archive at 15 GHz and 43 GHz, repectively. We derived the brightness-temperature and jet-width gradients along the jet axis from parameterizations of the jets using 2D Gaussian brightness distributions. In most BL Lac objects, the diameter and brightness-temperature gradients along the jet axis can generally be described well by single power laws, while the jets of FSRQs show more complex behavior and remain more strongly collimated on larger physical scales. We find evidence for a transition of the global jet geometry from a parabolic to a conical shape in the BL Lac objects 3C 66A, Mrk 421 and BL Lacertae, the radio galaxy 3C 111 and the FSRQs CTA 26, PKS 0528+134,4 C +71.07,4C +29.45, and 3C 279 outside the Bondi sphere.

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arXiv2021

Ambilateral collimation study of the twin-jets in NGC1052

With the increased sensitivity and resolution of radio interferometry the study of the collimation and acceleration region of jets in Active Galactic Nuclei (AGN) has come into focus within the last years. Whereas a large fraction of AGN jets reveal a change from parabolic to conical collimation around the Bondi radius, a small number of sources deviate from this standard picture, including the radio galaxy NGC1052. We study the jet width profile, which provides valuable information about the interplay between the central engine and accretion disk system and the collimation and acceleration zone of the jets. We observed the double-sided active galaxy NGC1052 at six frequencies with the VLBA in 2017 and at 22GHz with RadioAstron in 2016. These data are combined with archival 15, 22, and 43 GHz multi-epoch VLBA observations. From ridge-line fitting we obtained width measurements along the jet and counter-jet which were fitted with broken power-laws. We find a break in the jet collimation profile at ~10^4 R_s (Schwarzschild radii). Downstream of the break the collimation is conical with a power-law index of 1.0 - 1.2 (cylindrical 0; parabolic 0.5; conical 1). The upstream power-law index of 0.36 for the approaching jet is neither cylindrical nor parabolic and for the receding jet with 0.16 close-to cylindrical. Both jets have an opening angle of ~30 degree at a distance of ~10^3 R_S and are well collimated with an opening angle of <10 degrees downstream of the break. There are significant differences in the upstream collimation profile between approaching (Eastern) and receding (Western) jet. Absorption or scattering in the surrounding torus as well as an accretion wind may mimic a cylindrical profile. We need to increase the observing frequencies, which do not suffer from absorption to find the true jet collimation profile upstream of 10^4 R_s.

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arXiv2021

MOJAVE XIX: Brightness Temperatures and Intrinsic Properties of Blazar Jets

We present multi-epoch, parsec-scale core brightness temperature observations of 447 AGN jets from the MOJAVE and 2cm Survey programs at 15 GHz from 1994 to 2019. The brightness temperature of each jet over time is characterized by its median value and variability. We find that the range of median brightness temperatures for AGN jets in our sample is much larger than the variations within individual jets, consistent with Doppler boosting being the primary difference between the brightness temperatures of jets in their median state. We combine the observed median brightness temperatures with apparent jet speed measurements to find the typical intrinsic Gaussian brightness temperature of (4.1 +- 0.6)*10^10 K, suggesting that jet cores are at or below equipartition between particle and magnetic field energy in their median state. We use this value to derive estimates for the Doppler factor for every source in our sample. For the 309 jets with both apparent speed and brightness temperature data, we estimate their Lorentz factors and viewing angles to the line of sight. Within the BL Lac optical class, we find that high-synchrotron-peaked (HSP) BL Lacs have smaller Doppler factors, lower Lorentz factors, and larger angles to the line of sight than intermediate and low-synchrotron-peaked (LSP) BL Lacs. We confirm that AGN jets with larger Doppler factors measured in their parsec-scale radio cores are more likely to be detected in gamma rays, and we find a strong correlation between gamma-ray luminosity and Doppler factor for the detected sources.

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arXiv2021

MOJAVE: XVIII. Kinematics and Inner Jet Evolution of Bright Radio-Loud Active Galaxies

We have analyzed the parsec-scale jet kinematics of 447 bright radio-loud AGN, based on 15 GHz VLBA data obtained between 1994 August 31 and 2019 August 4. We present new total intensity and linear polarization maps obtained between 2017 January 1 to 2019 August 4 for 143 of these AGN. We tracked 1923 bright features for five or more epochs in 419 jets. A majority (60%) of the well-sampled jet features show either accelerated or non-radial motion. In 47 jets there is at least one non-accelerating feature with an unusually slow apparent speed. Most of the jets show variations of 10 to 50 deg in their inner jet position angle (PA) over time, although the overall distribution has a continuous tail out to 200 deg. AGN with SEDs peaked at lower frequencies tend to have more variable PAs, with BL Lacs being less variable than quasars. The Fermi LAT gamma-ray associated AGN also tend to have more variable PAs than the non-LAT AGN in our sample. We attribute these trends to smaller viewing angles for the lower spectral peaked and LAT-associated jets. We identified 13 AGN where multiple features emerge over decade-long periods at systematically increasing or decreasing PAs. Since the ejected features do not fill the entire jet cross-section, this behavior is indicative of a precessing flow instability near the jet base. Although some jets show indications of oscillatory PA evolution, we claim no bona fide cases of periodicity since the fitted periods are comparable to the total VLBA time coverage.

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arXiv2021

TELAMON: Effelsberg Monitoring of AGN Jets with Very-High-Energy Astroparticle Emissions

We introduce the TELAMON program, which is using the Effelsberg 100-m telescope to monitor the radio spectra of active galactic nuclei (AGN) under scrutiny in astroparticle physics, namely TeV blazars and candidate neutrino-associated AGN. Thanks to its large dish aperture and sensitive instrumentation, the Effelsberg telescope can yield radio data superior over other programs in the low flux-density regime down to several 10 mJy. This is a particular strength in the case of TeV-emitting blazars, which are often comparatively faint radio sources of the high-synchrotron peaked type. We perform high-cadence high-frequency observations every 2-4 weeks at multiple frequencies up to 44 GHz. This setup is well suited to trace dynamical processes in the compact parsec-scale jets of blazars related to high-energy flares or neutrino detections. Our sample currently covers about 40 sources and puts its focus on AGN with very-high-energy astroparticle emission, i.e., TeV blazars and neutrino-associated AGN. Here, we introduce the TELAMON program characteristics and present first results obtained since fall 2020.

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arXiv2021

Persistent Non-Gaussian Structure in the Image of Sagittarius A* at 86 GHz

Observations of the Galactic Center supermassive black hole Sagittarius A* (Sgr A*) with very long baseline interferometry (VLBI) are affected by interstellar scattering along our line of sight. At long radio observing wavelengths ($\gtrsim1\,$cm), the scattering heavily dominates image morphology. At 3.5 mm (86 GHz), the intrinsic source structure is no longer sub-dominant to scattering, and thus the intrinsic emission from Sgr A* is resolvable with the Global Millimeter VLBI Array (GMVA). Long-baseline detections to the phased Atacama Large Millimeter/submillimeter Array (ALMA) in 2017 provided new constraints on the intrinsic and scattering properties of Sgr A*, but the stochastic nature of the scattering requires multiple observing epochs to reliably estimate its statistical properties. We present new observations with the GMVA+ALMA, taken in 2018, which confirm non-Gaussian structure in the scattered image seen in 2017. In particular, the ALMA-GBT baseline shows more flux density than expected for an anistropic Gaussian model, providing a tight constraint on the source size and an upper limit on the dissipation scale of interstellar turbulence. We find an intrinsic source extent along the minor axis of $\sim100\,μ$as both via extrapolation of longer wavelength scattering constraints and direct modeling of the 3.5 mm observations. Simultaneously fitting for the scattering parameters, we find an at-most modestly asymmetrical (major-to-minor axis ratio of $1.5\pm 0.2$) intrinsic source morphology for Sgr A*.

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arXiv2021

Probing the innermost regions of AGN jets and their magnetic fields with RadioAstron IV. The quasar 3C 345 at 18 cm: Magnetic field structure and brightness temperature

Context. Supermassive black holes in the centres of radio-loud active galactic nuclei (AGN) can produce collimated relativistic outflows (jets). Magnetic fields are thought to play a key role in the formation and collimation of these jets, but the details are much debated. Aims. We study the innermost jet morphology and magnetic field strength in the AGN 3C 345 with an unprecedented resolution using images obtained within the framework of the key science programme on AGN polarisation of the Space VLBI mission RadioAstron. Methods. We observed the flat spectrum radio quasar 3C 345 at 1.6 GHz on 2016 March 30 with RadioAstron and 18 ground-based radio telescopes in full polarisation mode. Results. Our images, in both total intensity and linear polarisation, reveal a complex jet structure at 300 $μ$as angular resolution, corresponding to a projected linear scale of about 2 pc or a few thousand gravitational radii. We identify the synchrotron self-absorbed core at the jet base and find the brightest feature in the jet 1.5 mas downstream of the core. Several polarised components appear in the Space VLBI images that cannot be seen from ground array-only images. Except for the core, the electric vector position angles follow the local jet direction, suggesting a magnetic field perpendicular to the jet. This indicates the presence of plane perpendicular shocks in these regions. Additionally, we infer a minimum brightness temperature at the largest $(u,v)$-distances of $1.1\times 10^{12}$ K in the source frame, which is above the inverse Compton limit and an order of magnitude larger than the equipartition value. This indicates locally efficient injection or re-acceleration of particles in the jet to counter the inverse Compton cooling or the geometry of the jet creates significant changes in the Doppler factor, which has to be $>11$ to explain the high brightness temperatures.

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