Mapping the narrow-line Seyfert 1 galaxy 1H 0323+342

Taking advantage of the most recent measurements by means of high-resolution radio observations and other multiwavelength campaigns, it is possible to elaborate a detailed map of the narrow-line Seyfert 1 Galaxy 1H 0323+342. This map will open the possibility of intriguing hypotheses about the generation of high-energy gamma rays in the narrow-line region.


Introduction
1H 0323 + 342, a.k.a. J0324 + 3410 (z = 0.063 1 ) is an active galactic nucleus (AGN) classified as jetted narrow-line Seyfert 1 Galaxy (jNLS1) [1], with a significant detection at high-energy γ rays [2]. It is the closest source of this type and, therefore, it offers a unique opportunity to dissect the AGN, as one milliarcsecond (mas) corresponds to ∼ 1.2 pc in a ΛCDM cosmology with H 0 = 70 km/s/Mpc, Ω Λ = 0.7, Ω m = 0.3. This means that the Very Long Baseline Array (VLBA) can probe the AGN on a parsec scale. Indeed, J0324 + 3410 has been the target of many studies at high-resolution radio frequencies [3,4,5,6,7], and is currently under monitoring in the framework of the MOJAVE program 2 [8]. It was found that the jet from J0324 + 3410 is one sided with a change in shape at about ∼ 7 mas from the core, being parabolic close to the central black hole, and becoming conical as the distance increases [5,6,7]. This quasi-stationary feature is similar to HST-1 in M87, although the radial distance from the central singularity is ∼ 10 7−8 r g , two orders of magnitudes farther than HST-1 from M87 [5,6,7]. Both Hada [6] and Kovalev [7] proposed that one solution could be to have a greater mass for the central black hole in J0324 + 3410, of the order of 10 8 M as suggested by [9].
The aim of the present work is to revise all the available information about the central mass black hole of J0324 + 3410, its surroundings and its jet, in order to obtain a consistent picture of this source.

Mass of the central black hole
The estimate of the mass of the central black hole in narrow-line Seyfert 1 Galaxies is at the center of a long-standing debate (see [10] and references therein for the latest information). In the case of J0324 + 3410, the values are of the order of 10 7 M ( [1,2,11,13,12]), with two exceptions [9,14]. The available values and adopted methods are summarised in Table 1.
The mass estimates through the fit of an accretion disk model is generally overestimated (e.g. Fig. 6 in [15]), particularly when the jet contribution at infrared-to-ultraviolet frequencies is significant (e.g. see the case of J0948 + 0022, Fig. 6 in [11]). However, this seems not to be the case for J0324 + 3410, as the disk is quite strong and often prominent over the continuum of the jet (cf. the spectral energy distribution in [2]). This is confirmed by the polarisation measurements at optical wavelength, which are quite low (0.7 − 0.8% in V filter, [16]), and the X-ray emission (0.3 − 10 keV) is generally consistent with a thermal Comptonization (photon index ∼ 2) from the corona. Only during the jet activity, there is a hard tail (photon index ∼ 1.4) with a break at a few keV (see Fig. 1 in [17]; see also [18]). A rough estimate of the duty cycle of the jet can be done by selecting the X-ray observations where the broken power-law model was the best fit (jet active) and to compare with all the other observations best fitted by a powerlaw model consistent with the unsaturated Comptonization. From the data reported by [11], the global observing time was 208.5 ks, and 34.8 ks (∼ 17%) of data resulted to be best fitted by a broken power-law model (Fig. 1). This value of ∼ 17% could be taken as a rough estimate of the jet duty cycle. Therefore, it is not surprising to find an agreement between the estimate via accretion disk fit and that by using the reverberation mapping (RM).
The RM measurement is also in agreement with the second order moment (σ) of the Hβ emission line measured with one epoch spectrum. This quantity (σ) is known to be less affected than the full-width half maximum (FWHM) by the inclination and shape of the broad-line region (BLR), and the accretion rate of the disk (e.g. [10] and references therein). Therefore, we can also exclude a bias due to these factors.
In this work, we will consider as reference mass the average of the above cited values (∼ 2.2 × 10 7 M ), by excluding the two outliers [9,14]. One reason for the result in excess by [9] could be the difficulty to remove the background, to model the point spread function ([9] noted the lack of high S/N stars in the field of view), and also the presence of evident signatures of a recent merger, discovered by [19]. The discrepancies in the mass estimate via X-ray variability [12,14] could be due to the level of activity of the jet during X-ray observations: as previously noted (Fig. 1, see also [18,17]), the X-ray corona is dominating the 0.3 − 10 keV flux and only when the jet is Figure 1: Swift/XRT light curve of J0324 + 3410 from the analysis reported by [11]. Blue stars indicate a best fit with a power-law model; red circles are for a broken power-law model. The vertical lines for the years are placed on January 1st of each year. strongly active a hard tail above a few keV emerges.
Having set the most likely mass of the central black hole to the value of 2.2 × 10 7 M , it is possible to derive the structure of the AGN. The gravitational radius is: The size of the BLR is about 15 light days (3.9 × 10 16 cm or 0.013 pc), as derived from the measurements of Hβ and Fe II reverberation mapping (15 +4 −3 and 15 +7 −4 light days, respectively) [13]. This size is consistent with the expected external radius of the accretion disk (∼ 10 4 r g , [20]). From the radius-luminosity relationship [21] properly rearranged, it is possible to estimate the luminosity of the accretion disk: where L disk is the disk luminosity, R BLR = 15 light days, and κ is the factor to convert the λL 5100Å into the bolometric luminosity. This value is generally assumed to be 10, although in case of super-Eddington accretors, it could be as great as 150 [22,23]. In the above calculation, we assumed the conservative value of κ = 10. In the case κ = 150, then L disk ∼ 3.5 × 10 45 erg/s.
The boundary between the BLR and the molecular torus is given by the dust sublimation radius [24]: where L disk,45 is the disk luminosity in units of 10 45 erg/s. The dust sublimation temperature has been taken to be 1500 K, and different values imply an additional factor [24]. The outer boundary of the torus is given by [24]: The extension of the narrow-line region (NLR) can be measured from the luminosity of the [O III]λ5007 line emission [25]. This line has been carefully studied by [26], who found that the profile was significantly affected by turbulence, likely due to the interaction with the relativistic jet. The line luminosity was found to be log L [OIII] = 40.98 [26], which corresponds to a maximum extension of the NLR [25]: The ring/spiral arm structure observed by [1,19,9] has a radius of ∼ 7.5 , corresponding to a linear size of ∼ 9 kpc. The viewing angle is unknown, but, by considering this structure developed along the equatorial plane of the central black hole, and that the jet is perpendicular to the black hole equator, then the viewing angle of the ring/spiral arm should be the complementary angle of the jet viewing angle θ ∼ 9 • (see the next Section). Therefore, the deprojected size is almost equal to the above calculated linear size.

The jet structure
The structure of the relativistic jet from J0324 + 3410 has been studied at high-resolution radio frequencies [3,4,5,6,7]. Here we summarise their results. The jet shows a break at a quasi-stationary bright feature located downstream at ∼ 7 mas from the radio core. The inner region of the jet has a parabolic shape, while the outer region has a conical shape (see Fig. 2 in [6]). At the collimation break, the jet width is squeezed to half its value (see Fig. 5 in [5]). Taking as reference the radio core at 43 GHz, and assuming that the jet has the origin close to the black hole position, then the jet width as a function of the radial distance from the black hole W (r) [mas] is [6]: where r 0 = −41 ± 36 µas is the distance of the radio core at 43 GHz from the estimated position of the central black hole.
To calculate the linear distance, it is necessary to know the viewing angle of the jet. Many authors limited the viewing angle to θ ≤ 12 • [4,6]. Recently, by measuring the Doppler factor from the variability in 15 GHz OVRO 3 light curves (δ = 5.70 +1.01 −1.02 ) and the β app = 9.05 from the kinematic of the components as monitored by the MOJAVE project [27,8], a new value of θ = 9.06 +1.04 −8.91 degrees has been calculated [28]. The corresponding bulk Lorentz factor is then Γ ∼ 10.
We can now convert the angular distances to linear size by taking into account the redshift z = 0.063, which implies a projected linear size of ∼ 1.2 pc/mas, and the jet viewing angle θ ∼ 9 • , which in turn means a deprojected size of ∼ 7.7 pc/mas. A smaller viewing angle (says 4 • , [4] or even 3 • , [2]), implies a greater deprojected distance (∼ 23 pc/mas in the case of θ ∼ 3 • ). The results are summarised in Table 2.
Asada & Nakamura [29] suggested that the change in shape of the M87 jet is located close to the Bondi radius. In the case of 1H 0323 + 342, that quantity is [30]: where c s is the adiabatic sound speed of the X-ray emitting gas at the accretion radius r Bondi . If we assume a gas temperature similar to that of M87 (kT = 0.8 keV, [30]), then the sound speed is c s ∼ 305 km/s. The result is a radius much closer to the central black hole than the case of M87: in terms of gravitational radius, we have 2 × 10 4 r g for 1H 0323 + 342 vs 7.6 × 10 5 r g for M87 [29].

The map
It is now possible to summarise the linear deprojected size of all the structures of the jNLS1 J0324 + 3410 in terms of gravitational radius, thus mapping this cosmic source. Table 3 lists all the structures of the AGN starting from the central black hole to the outer part of the galaxy, while Fig. 1 displays the corresponding schematic.
As noted earlier, some authors [6,7] suggested that a central black hole with a greater mass, consistent with the measurements by [9], would imply the overlap of the jet profile of J0324 + 3410 with that of M87. However, this line of reasoning is the classical post hoc, ergo propter hoc. Indeed, the scalability of the jet is a consequence of the self-similar shape, as proven by [31]. High-resolution radio observations of M87 and J0324 + 3410 proved that the jet shape is self-similar (paraboloidal and conical) in both sources. Therefore, it is possible to scale the jet according to [31], but it is not useful to set the mass of the central singularity, because it is the normalisation quantity. This also means that we can make the two jet profiles overlap by setting a smaller mass for the black hole in M87.
We note from Table 3 that the 43 GHz core is placed at a distance comparable with that of the torus 4 . It is worth noting that, in case of super- 794 Ring/Spiral Arm 9.0 × 10 9 9 × 10 3 Jet length 9.6 × 10 10 9.6 × 10 4 Eddington accretion, the greater disk luminosity (L disk ∼ 3.5 × 10 45 erg/s), would imply a farther torus (R d,sub ∼ 0.75 pc), much farther than the radio core. Moreover, if we assume the upper limit of the BLR (15 + 7 = 22 light days) and a super-Eddington disk (κ = 150), then L disk ∼ 7 × 10 45 erg/s, which in turn implies R d,sub ∼ 1 pc and R out ∼ 32 pc. Therefore, in this case, the radio core would be still at the scale of the BLR, but the jet nozzle remains always outside the torus, whatever the combination of measurements and errors we could consider. The quasi-stationary feature at ∼ 5 × 10 7 r g , which is clearly in the NLR, is much more interesting. On one side, this is not surprising: the [O III] emission line profile reveals features indicating high turbulence, likely due to the interaction of the jet with the NLR gas [26]. On the other side, this is surprising when we linked this information with the observed activity at high-energy γ rays [5,6]. The jet width at the convergence is 0.39 ± 0.17 mas [5], corresponding to ∼ 0.47 pc (or 4.5 × 10 5 r g ). The fastest variability at high-energy γ rays was measured to be ∼ 3.1 hours [32], which implies a size of the emitting region r < τ cδ/(1 + z) ∼ 1.8 × 10 15 cm. This is clearly too small for the jet size at the convergence shock. The observed width of the jet is more consistent with a time scale of months (∼ 97 days), and invoking a greater, but still reasonable, Doppler factor is not sufficient to mitigate the requirements (for δ = 50, the time scale could be 11 days). A dedicated  Table 3). multiwavelength campaign with an intense sampling (hours time scale) would be necessary to better understand the behaviour of the quasi-stationary shock and the possible production of high-energy γ-rays.
If confirmed, it would open a really intriguing possibility. The debate about the site of γ-ray generation was always confined between the BLR [33], the torus [34,35], or both cases, depending on the epoch, as in the case of PKS 1222 + 216 [36]. Perhaps, now it is time to add one more competitor: the NLR. In this case, being the seed photons co-spatial with the relativistic electrons of the jet as shown by the turbulence in the [O III] line emission [26], it is necessary to study the new dynamics of interactions in order to understand the possible implications.