arXiv subjects

Ari Laor

Publications and source records attributed to Ari Laor.

At least 19 recordsLinked to original sources

arXiv2026

The SKA-VLBI Perspective on Radio-Quiet AGN

The accretion-ejection mechanism in Active Galactic Nuclei (AGN) remains a central open problem in astrophysics, tied to the role of AGN feedback in galaxy formation and evolution. Radio-quiet AGN dominate the observed AGN population. Lacking luminous jets, their radio emission traces a rich set of processes spanning the host galaxy kpc scales down to the vicinity of the supermassive black hole: star formation, AGN-driven winds and shocks, free-free emission from photo-ionized gas, low-power jets, and coronal activity close to the inner accretion disk. The Square Kilometre Array (SKA) will probe these processes across a wide frequency range with unprecedented sensitivity, wide-field survey capability, and, critically, high-resolution VLBI imaging. Flux, spectral, and polarization monitoring will constrain dynamics and environmental coupling, while mapping nuclear regions on sub-pc to kpc scales will disentangle compact cores from host emission, resolving the diversity of radio activity across accretion regimes and jet powers from the local Universe to the cosmic dawn. At the full AA4 deployment, the SKA-MID phased into global VLBI arrays will deliver sub-milliarcsecond imaging and $\mu$Jy sensitivity over 0.35--15\,GHz, enabling the first population-level census of radio-quiet AGN nuclei. Earlier AA$\ast$ operations will support pilot studies of the brightest nearby systems.

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arXiv2026

Observation of A Solar Like Magnetic Reconnection Event in an AGN Corona with XRISM

The X-ray source in AGN is commonly referred to as the corona by analogy to stellar coronae. The similarities between the two suggest that the heating mechanism of AGN coronae is magnetic reconnection -- as in cool stars -- but this has not yet been directly observed. This work presents the first observational evidence for a magnetic reconnection flare in an AGN corona. We report on a flare in NGC 3783, which was observed with XRISM/Xtend and XMM-Newton/EPIC-PN exhibiting distinct temporal evolution in soft ($<2.0\,$keV) and hard ($>2.0\,$keV) X-rays. An Ultra-Fast Outflow (UFO) was detected during the event. The flare features the Neupert effect -- a temporal signature of the hard light curve correlating with the time derivative of the soft light curve, which shows that the flare is powered by magnetic reconnection, The Neupert effect is widely observed in the Sun, with Coronal Mass Ejections (CMEs) playing a role analogous to the UFO. We derive an upper limit of $30 \, R_g$ on the height of the magnetic loop from which the flare originates. Using the UFO's measured properties to characterize the magnetic field, we obtain $B > 1.3 \times 10^4\,$G for the field annihilated during the flare from total energy considerations, and $B \approx 500\,$G for the momentary magnetic field during reconnection from a dynamical consideration.

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arXiv2026

On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law

Power-law (PL) distribution functions (DF) are prevalent in highly diverse systems. The systems range in size from nanometer to mega light years, in complexity from dust grains to living organisms, and characterize the distribution of various events in nature and in various human activities. To gain some insight on why PL DF are so prevalent, we explore the conditions leading to the formation of a PL DF in a simple system of colliding hard sphere. We follow the time evolution of the energy DF through direct Monte Carlo simulations. In statistical equilibrium, the DF evolves into the Maxwell-Boltzmann (MB) DF. A transition to a PL DF occurs when: 1. The system is initially far from equilibrium. For example, a mix of light and heavy particles with the same velocity. 2. The system dynamics is scale-free, which holds in the intermediate asymptotic regime, far from the initial and the final equilibrium states. The scale-free dynamics leads to a DF which evolves in a self-similar form. 3. The system is open with a scale-free boundary condition. For example, a constant injection of particles far from equilibrium. The DF PL index is set by the time dependence of the self-similar DF and by the boundary condition. The PL index is independent of the self-similar DF form. Conditions 1-3 are common in a great variety of systems, which may explain why PL DF are so prevalent in nature.

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arXiv2025

Radio Emission from Broad Absorption Line Quasars

Broad Absorption Line Quasars (BALQs) generally exhibit significant outflows that may interact with the surrounding medium, resulting in radio emission. We selected a sample of 13 powerful radio-quiet (RQ) BALQs, where the UV outflow kinetic power is measurable, and detected nine of them with the Very Large Array A configuration at 5.5 GHz and 9.0 GHz. The radio emission is mostly unresolved and is generally constrained within a scale of < 1--4 kpc. In the nine detected objects, the radio spectral slope alpha_5.5-9.0 is steep (< -0.5) in five objects and is flat or inverted (> -0.5) in four objects. We discuss how the steep-slope emission can be associated with the UV outflows, and how the flat-slope emission can be intrinsically steep but flattened by free-free absorption from the UV outflowing gas. However, we find no correlation between the radio luminosity and the estimated outflow kinetic power, which suggests that the outflows are likely not a major source of the observed radio emission. In addition, the radio loudness of these RQ BALQs is comparable to that of typical RQ quasars, implying that the UV outflows likely do not produce stronger radio emission compared to non-BALQs. Follow-up radio observations can test the free-free absorption interpretation and can be used as a new probe for outflows in AGN.

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arXiv2025

The CLASS Quasar Catalog: Coronal Line Activity in Type 1 SDSS Quasars

We conduct the first systematic survey of a total of eleven optical coronal lines in the spectra of a large sample of low redshift (z < 0.8) Type 1 quasars observed by the Sloan Digital Sky Survey (SDSS). We find that strong coronal line emission is rare in SDSS even in Type 1 quasars; only 885 out of 19,508 (4.5%) galaxies show at least one coronal line, with higher ionization potential lines ($>100$eV) being even rarer. The [Ne V] $\lambda$3426 line, which constitutes the majority of detections, is strongly correlated with the bolometric luminosity. These findings suggest that the optical coronal lines are significantly suppressed in the majority of local AGNs, possibly as a result of the presence of dust in the emitting regions. We find that the incidence of ionized outflows is significantly higher in coronal line emitters compared with non-coronal line emitters, possibly suggesting that dust destruction in outflows enhances coronal line emission in AGNs. Many coronal lines show line profiles that are broader than those of narrow lines, and are blue-shifted relative the lower ionization potential lines, suggesting outflows in the highly ionized gas. Given the limited number of detections, we do not find any statistically significant trends of detection statistics, or line ratios with black hole mass, Eddington ratio, or AGN bolometric luminosity. The catalog is publicly available and can provide a useful database of the coronal line properties of low redshift quasars that can be compared to the growing number of high-z AGNs discovered by JWST.

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arXiv2024

A dichotomy in the 1-24 GHz parsec-scale radio spectra of radio-quiet quasars

We present the pc-scale radio spectra of a representative sample of 13 Palomar-Green radio-quiet quasars, based on our new Very Long Baseline Array (VLBA) observations at 8.4 and 23.6 GHz and our earlier VLBA studies at 1.5 and 5.0 GHz. The radio core emission generally exhibits a flat spectrum at 1.5-5.0 GHz, which indicates a compact optically thick synchrotron source on a scale smaller than the broad-line region (BLR) radius R_BLR ~ 0.01-0.1 pc. The 8.4-23.6 GHz spectral slope remains flat in four objects indicating the inner radius of the radio source R_in < 0.1 R_BLR, and becomes steep in four other objects indicating R_in ~ 0.5 R_BLR. The flat 8.4-23.6 GHz slope sources may be associated with a continuous ejection starting at the accretion disk corona. The steep 8.4-23.6 GHz slope sources may be produced by an interaction of an AGN-driven wind with the BLR gas or a low-power jet extending to the BLR scale. Seven of these eight objects, which have a flat or steep 8.4-23.6 GHz slope, reside at the Eddington ratios L/L_Edd < 0.3, and four of the remaining five objects, where the 8.4-23.6 GHz fluxes are too faint to significantly constrain the slope, reside at L/L_Edd > 0.3. The 8.4-23.6 GHz radio emission in the high L/L_Edd objects may be weak due to more extended emission from a radiation pressure driven wind. Future sub-millimeter observations can further constrain the inward radial extent of the radio emission down to the coronal scale.

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arXiv2024

Windy or not: Radio pc-scale evidence for a broad-line region wind in radio-quiet quasars

Does a broad-line region (BLR) wind in radio-quiet (RQ) active galactic nuclei (AGN) extend to pc scales and produce radio emission? We explore the correlations between a pc-scale radio wind and the BLR wind in a sample of 19 RQ Palomar-Green (PG) quasars. The radio wind is defined based on the spectral slope and the compactness of the emission at 1.5-5 GHz, and the BLR wind is defined by the excess blue wing in the C IV emission line profile. The five objects with both radio and BLR wind indicators are found at high Eddington ratios L/L_Edd (> 0.66), and eight of the nine objects with neither radio nor BLR winds reside at low L/L_Edd (< 0.28). This suggests that the BLR wind and the radio wind in RQ AGN are related to a radiation pressure driven wind. Evidence for free-free absorption by AGN photoionized gas, which flattens the spectral slope, is found in two objects. Radio outflows in three low L/L_Edd (0.05-0.12) objects are likely from a low-power jet, as suggested by additional evidence. The presence of a mild equatorial BLR wind in four intermediate L/L_Edd (0.2-0.4) objects can be tested with future spectropolarimetry.

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arXiv2024

Why are optical coronal lines faint in active galactic nuclei?

Forbidden collisionally excited optical atomic transitions from high ionization potential (IP$\geq$54.8\,eV) ions, such as Ca$^{\mathrm{4+}}$, Ne$^{\mathrm{4+}}$, Fe$^{\mathrm{6+}}$, Fe$^{\mathrm{10+}}$, Fe$^{\mathrm{13+}}$, Ar$^{\mathrm{9+}}$, and S$^{\mathrm{11+}}$, are known as optical coronal lines (CLs). The spectral energy distribution (SED) of active galactic nuclei (AGN) typically extends to hundreds of electron volts and above, which should be able to produce such highly ionized gas. However, optical CLs are often not detected in AGN. Here we use photoionization calculations with the \textsc{Cloudy} spectral synthesis code to determine possible reasons for the rarity of these optical CLs. We calculate CL luminosities and equivalent widths from radiation pressure confined photoionized gas slabs exposed to an AGN continuum. We consider the role of dust, metallicity, and ionizing SED in the formation of optical CLs. We find that (1) dust reduces the strength of most CLs by $\sim$three orders of magnitude, primarily as a result of depletion of metals onto the dust grains. (2) In contrast to the CLs, the more widely observed lower IP optical lines such as [O\, III] 5007\,\AA, are less affected by depletion and some are actually enhanced in dusty gas. (3) In dustless gas many optical CLs become detectable, and are particularly strong for a hard ionizing SED. This implies that prominent CL emission likely originate in dustless gas. Our calculations also suggest optical CL emission is enhanced in galaxies with low mass black holes characterized by a harder radiation field and a low dust to metal ratio. The fact that optical CLs are not widely observed in the early universe with JWST may point to rapid dust formation at high redshift.

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arXiv2023

A large jet narrow-line Seyfert 1 galaxy: observations from pc to 100 kpc scales

We present new 1.5-8.5 GHz Very Long Baseline Array (VLBA) observations and 0.32-1.26 GHz Giant Meterwave Radio Telescope (GMRT) observations of J0354-1340, which is the only known radio-quiet (RQ) or radio-intermediate (RI) narrow-line Seyfert 1 galaxy with a 100-kpc two-sided radio jet. A pc-scale one-sided jet in the southeast direction from the core emission is found in the VLBA observations, while the kpc-scale jet observed with Karl G. Jansky Very Large Array (VLA) and GMRT is in the south-north direction. The core spectra on pc and kpc scales are presented in combination with the archival VLASS observations at 3.0 GHz and the VLA C configuration observations at 5.5 GHz. The pc-scale emission dominates the kpc-scale emission above ~ 5 GHz, and the spectrum is inverted due to synchrotron self-absorption. This indicates a compact synchrotron source with a size of ~ 0.04 pc, which is associated with either the jet base or the corona. A sub-kpc scale jet, which is unresolved on scales of ~ 3 arcsec, probably dominates the emission below ~ 5 GHz. Future radio observations can explore the jet structure between the pc and 100 kpc scales, the origin of their direction mismatch, and the pc-scale jet proper motion. It remains to be explored how common such large-scale jets are in RQ or RI AGN.

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arXiv2023

The radio emission in radio-quiet quasars: the VLBA perspective

The origin of the radio emission in radio-quiet quasars (RQQ) is not established yet. We present new VLBA observations at 1.6 and 4.9 GHz of ten RQQ (nine detected), which together with published earlier observations of eight RQQ (five detected), forms a representative sample of 18 RQQ drawn from the Palomar-Green sample of low z (< 0.5) AGN. The spectral slope of the integrated emission extends from very steep (alpha < -1.98) to strongly inverted (alpha = +2.18), and the slopes of nine of the 14 objects are flat (alpha > -0.5). Most objects have an unresolved flat-spectrum core, which coincides with the optical Gaia position. The extended emission is generally steep-spectrum, has a low brightness temperature (< 10^7 K), and is displaced from the optical core (the Gaia position) by ~ 5-100 pc. The VLBA core flux is tightly correlated with the X-ray flux, and follows a radio to X-ray luminosity relation of log L_R/L_X = -6, for all objects with a black hole mass log M_BH/M_Sun < 8.5. The flatness of the core emission implies a compact source size (< 0.1 pc), which likely originates from the accretion disk corona. The mas-scale extended emission is optically thin and of clumpy structure, and is likely produced by an outflow from the center. Radio observations at higher frequencies can further test the accretion disk coronal emission interpretation for the core emission in RQQ.

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arXiv2023

A Tight Correlation Between Millimeter and X-ray Emission in Accreting Massive Black Holes from <100 Milliarcsecond-resolution ALMA Observations

Recent studies have proposed that the nuclear millimeter continuum emission observed in nearby active galactic nuclei (AGN) could be created by the same population of electrons that gives rise to the X-ray emission that is ubiquitously observed in accreting black holes. We present the results of a dedicated high spatial resolution ($\sim$60-100 milliarcsecond) ALMA campaign on a volume-limited ($<50$ Mpc) sample of 26 hard X-ray ($>10$ keV) selected radio-quiet AGN. We find an extremely high detection rate (25/26 or $94^{+3}_{-6}\%$), which shows that nuclear emission at mm-wavelengths is nearly ubiquitous in accreting SMBHs. Our high-resolution observations show a tight correlation between the nuclear (1-23 pc) 100GHz and the intrinsic X-ray emission (1$σ$ scatter of $0.22$ dex). The ratio between the 100GHz continuum and the X-ray emission does not show any correlation with column density, black hole mass, Eddington ratio or star formation rate, which suggests that the 100GHz emission can be used as a proxy of SMBH accretion over a very broad range of these parameters. The strong correlation between 100GHz and X-ray emission in radio-quiet AGN could be used to estimate the column density based on the ratio between the observed 2-10keV ($F^{\rm obs}_{2-10\rm\,keV}$) and 100GHz ($F_{100\rm\,GHz}$) fluxes. Specifically, a ratio $\log (F^{\rm obs}_{2-10\rm\,keV}/F_{100\rm\,GHz})\leq 3.5$ strongly suggests that a source is heavily obscured [$\log (N_{\rm H}/\rm cm^{-2})\gtrsim 23.8$]. Our work shows the potential of ALMA continuum observations to detect heavily obscured AGN (up to an optical depth of one at 100GHz, i.e. $N_{\rm H}\simeq 10^{27}\rm\,cm^{-2}$), and to identify binary SMBHs with separations $<100$ pc, which cannot be probed by current X-ray facilities.

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arXiv2022

NGC 3147: a prototypical low-luminosity active galactic nucleus with double-peaked optical and ultraviolet lines

A previous narrow-slit ($0.1$ arcsec) Hubble Space Telescope observation unveiled a broad relativistic H$α$ profile in NGC3147, a low-luminosity ($\mathrm{L_{bol}}\sim10^{42}$ erg s$^{-1}$), low-Eddington ratio ($\mathrm{L_{bol}/L_{Edd}}\sim10^{-4}$) active galactic nucleus (AGN), formerly believed to be a candidate true type 2 AGN intrinsically lacking the broad-line region. The new observations presented here confirm the double-peaked profile of the H$α$ line, which further shows variability both in flux and in the inner radius of the emitting disc with respect to the previous epoch. Similar disc line profiles are also found in prominent ultraviolet (UV) lines, in particular Ly$α$ and C IV. The new data also allow us to build a simultaneous subarcsec optical-to-X-ray spectral energy distribution of NGC3147, which is characterized by the absence of a thermal UV bump, and an emission peak in the X-rays. The resulting very flat $α_{ox}=-0.82$ is typical of low-luminosity AGN, and is in good agreement with the extrapolation to low luminosities of the well-known trend with luminosity observed in standard AGN. Indeed, we are possibly observing the accretion disc emission in NGC3147 in the optical, close to the expected peak. On the other hand, the steep -2 UV power law may be Comptonization of that cold disc by a warm corona, what is instead generally observed as a `soft excess' in more luminous AGN.

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arXiv2022

Quasi-simultaneous observations of radio and X-ray variability in three radio-quiet Seyfert galaxies

Radio variability in some radio-quiet (RQ) active galactic nuclei suggests emission from regions close to the central engine, possibly the outer accretion disc corona. If the origins of the radio and the X-ray emission are physically related, their emission may be temporarily correlated, possibly with some time delays. We present the results of quasi-simultaneous radio and X-ray monitoring of three RQ Seyfert galaxies, Mrk 110, Mrk 766, and NGC 4593, carried out with the Very Large Array at 8.5 GHz over a period of about 300 days, and with the Rossi X-ray Timing Explorer at 2-10 keV over a period of about 2000 days. The radio core variability is likely detected in the highest resolution (A configuration) observations of Mrk 110 and NGC 4593, with a fractional variability amplitude of 6.3% and 9.5%, respectively. A cross-correlation analysis suggests an apparently strong (Pearson r = -0.89) and highly significant correlation (p = 1 x 10^(-6)) in Mrk 110, with the radio lagging the X-ray by 56 days. However, a further analysis of the r values distribution for physically unrelated long time delays, reveals that this correlation is not significant. This occurs since the Pearson correlation assumes white noise, while both the X-ray and the radio light curves follow red noise, which dramatically increases the chance, by a factor of ~ 10^3, to get extremely high r values in uncorrelated data sets. A significantly longer radio monitoring with a higher sampling rate, preferably with a high-resolution fixed radio array, is required in order to reliably detect a delay.

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arXiv2022

The Nature of Luminous Quasars with Very Large C IV Equivalent Widths

We report results for a complete sample of ten luminous radio-quiet quasars with large C IV equivalent widths (EW > 150 A). For 8/10 we performed Chandra snapshot observations. We find that, in addition to the enhanced C IV line EW, their He II and Mg II lines are enhanced, but the C III] line is not. Their X-ray emission is substantially stronger than expected from their ultraviolet luminosity. Additionally, these large C IV EW quasars show small C IV blueshifts and possibly low Eddington ratios, suggesting they are "extreme low Eigenvector 1 (EV1)" quasars. The mean excess He II EW is well-matched by Radiation Pressure Compression (RPC) photoionization models, with the harder aox ionizing spectrum. However, these results do not reproduce well the enhancement pattern of the C IV, Mg II, and C III] EWs, or the observed high C IV/Mg II ratio. RPC calculations indicate that the C IV/Mg II line ratio is an effective metallicity indicator, and models with sub-Solar metallicity gas and a hard ionizing continuum reproduce well the enhancement pattern of all four ultraviolet lines. We find that the C IV/Mg II line ratio in quasars is generally correlated with the excess X-ray emission. Extremely high EV1 quasars are characterized by high metallicity and suppressed X-ray emission. The underlying mechanism relating gas metallicity and X-ray emission is not clear, but may be related to radiation-pressure driven disk winds, which are enhanced at high metallicity, and consequent mass loading reducing coronal X-ray emission.

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arXiv2022

Hard-X-ray-selected Active Galactic Nuclei -- II. Spectral Energy Distributions in the 5-45 GHz domain

A wide-frequency radio study of Active Galactic Nuclei (AGN) is crucial to evaluate the intervening radiative mechanisms responsible for the observed emission and relate them with the underlying accretion physics. We present wide frequency (5-45 GHz), high-sensitivity (few microJy/beam), (sub)-kpc JVLA observations of a sample of 30 nearby (0.003 < z < 0.3) AGN detected by INTEGRAL/IBIS at hard-X-ray. We find a high detection fraction of radio emission at all frequencies, i.e. > 95 per cent at 5, 10 and 15 GHz and > 80 per cent at 22 and 45 GHz. Two sources out of 30 remain undetected at our high sensitivities. The nuclear radio morphology is predominantly compact, sometimes accompanied by extended jet-like structures, or more complex features. The radio Spectral Energy Distributions (SEDs) of the radio cores appear either as a single or as a broken power-law, a minority of them exhibits a peaked component. The spectral slopes are either flat/inverted or steep, up to a break/peak or over the whole range. The sample mean SED shows a flat slope up to 15 GHz which steepens between 15 and 22 GHz and becomes again flat above 22 GHz. Significant radio-X-ray correlations are observed at all frequencies. About half of the sample features extended emission, clearly resolved by the JVLA, indicating low-power jets or large scale outflows. The unresolved cores, which often dominate the radio power, may be of jet, outflow, and/or coronal origin, depending on the observed frequency.

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arXiv2022

Radio spectra of narrow-line Seyfert 1 galaxies observed with ATCA and VLASS

We present radio spectral analyses for a sample of 29 radio-quiet (RQ) and three radio-loud (RL) narrow-line Seyfert 1 galaxies (NLS1s) detected with the Australia Telescope Compact Array at both 5.5 GHz and 9.0 GHz. The sample is characterized by L_bol/L_Edd > 0.15. The radio slopes in 25 of the 29 RQ NLS1s are steep (alpha_5.5-9.0 < -0.5), as found in earlier studies of RQ high L_bol/L_Edd AGN. This steep radio emission may be related to AGN-driven outflows, which are likely more prevalent in high L_bol/L_Edd AGN. In two of the three RL NLS1s, the radio slopes are flat or inverted (alpha_5.5-9.0 > -0.5), indicating a compact optically-thick source, likely a relativistic jet. Archival data at 3.0 GHz, 1.4 GHz, and 0.843 GHz are also compiled, yielding a sample of 17 NLS1s detected in three bands or more. In nine objects, the radio spectra flatten at lower frequencies, with median slopes of alpha_5.5-9.0 = -1.21 +/- 0.17, flattening to alpha_3.0-5.5 = -0.97 +/- 0.27, and to alpha_1.4-3.0 = -0.63 +/- 0.16. A parabolic fit suggests a median spectral turnover of ~ 1 GHz, which implies synchrotron self-absorption in a source with a size of only a fraction of 1 pc, possibly a compact wind or a weak jet. Two objects show significant spectral steepening to alpha < -2 above 3 GHz or 5 GHz, which may suggest relic emission from past ejection of radio emitting plasma, of the order of a few years to a few decades ago. Finally, two objects present a single spectral slope consistent with star-forming activity.

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arXiv2021

A New Iron Emission Template for Active Galactic Nuclei. I. Optical Template for the H$β$ region

We present a new empirical template for iron emission in active galactic nuclei (AGN) covering the $4000-5600$ A range. The new template is based on a spectrum of the narrow-line Seyfert 1 galaxy Mrk 493 obtained with the Hubble Space Telescope. In comparison with the canonical iron template object I Zw 1, Mrk 493 has narrower broad-line widths, lower reddening, and a less extreme Eddington ratio, making it a superior choice for template construction. We carried out a multicomponent spectral decomposition to produce a template incorporating all permitted and forbidden lines of Fe II identified in the Mrk 493 spectrum over this wavelength range, as well as lines from Ti II, Ni II, and Cr II. We tested the template by fitting it to AGN spectra spanning a broad range of iron emission properties, and we present a detailed comparison with fits using other widely used monolithic and multi-component iron emission templates. The new template generally provides the best fit (lowest $χ^2$) compared to other widely used monolithic empirical templates. In addition, the new template yields more accurate spectral measurements including a significantly better match of the derived Balmer line profiles (H$β$, H$γ$, H$δ$), in contrast with results obtained using the other templates. Our comparison tests show that the choice of iron template can introduce a systematic bias in measurements of the H$β$ line width, which consequently impacts single-epoch black hole mass estimates by $\sim0.1$ dex on average and possibly up to $\sim0.3-0.5$ dex individually.

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arXiv2021

Radiation pressure confinement -- V. The predicted free-free absorption and emission in active galactic nuclei

The effect of radiation pressure compression (RPC) on ionized gas in Active Galactic Nuclei (AGN) likely sets the photoionized gas density structure. The photoionized gas free-free absorption and emission are therefore uniquely set by the incident ionizing flux. We use the photoionization code Cloudy RPC model results to derive the expected relations between the free-free emission and absorption properties and the distance from the AGN centre, for a given AGN luminosity. The free-free absorption frequency of RPC gas is predicted to increases from $\sim$100 MHz on the kpc scale, to $\sim$100 GHz on the sub-pc scale, consistent with observations of spatially resolved free-free absorption. The free-free emission at 5 GHz is predicted to yield a radio loudness of $R\sim 0.03$, below the typical observed values of $R\sim 0.1-1$ in radio-quiet AGN. However, the flat free-free radio continuum may become dominant above 100 GHz. The suggested detection of optically thin free-free emission in NGC 1068, on the sub pc torus scale, is excluded as the brightness temperature is too high for optically thin free-free emission. However, excess emission observed with ALMA above 150 GHz in NGC 1068, is consistent with the predicted free-free emission from gas just outside the broad line region, a region which overlaps the hot dust disc resolved with GRAVITY. Extended $\sim$100 pc scale free-free emission is also likely present in NGC 1068. Future sub mm observation of radio quiet AGN with ALMA may allow to image the free-free emission of warm photoionized gas in AGN down to the 30 mas scale, including highly absorbed AGN.

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