The Two-sided Jet Structures of NGC 1052 at Scales from 300 to 4 × 107 Schwarzschild Radii

Satomi Nakahara; Akihiro Doi; Yasuhiro Murata; Masanori Nakamura; Kazuhiro Hada; Keiichi Asada; Satoko Sawada-Satoh; Seiji Kameno

doi:10.3847/1538-3881/ab465b

1. Introduction

The structure of astrophysical jets plays an important role in accelerating the jet plasma flow in the surrounding interstellar/intragalactic medium. The jet width profile as a function of distance from the central engine in the nearby radio galaxy M87 (w_jet ∝ z^a; W_jet is the jet width, z is the distance from the central engine in the unit of R_S, and a is the power-law index) exhibits a parabolic structure (a ∼ 0.5) between a few hundred and 10⁵ Schwarzschild radii (R_S) from the central engine (Asada & Nakamura 2012). The region at which the jet acceleration is observed by monitoring observations (e.g., Nakamura & Asada 2013; Mertens et al. 2016) coincides with that of the parabolic streamline (Asada et al. 2014). The parabolic structure continues roughly up to the sphere of gravitational influence of the central black hole and is ended with a transition into a conical downstream. Similar properties with a parabolic-to-conical transition at similar scales (typically ∼10⁵R_S) have also been found in NGC 6251 (Tseng et al. 2016) and NGC 4261 (Nakahara et al. 2018). These results are thought to be observational evidence that a transverse pressure supports the external medium with a relatively shallow dependence in the core regions of galaxies and that magnetic energy is dissipated into kinetic energy as suggested by studies of numerical simulations (e.g., Komissarov et al. 2009). On the other hand, a parabolic jet structure that continues at least up to ∼10⁸R_S without a transition to a conical structure is also suggested for the jets in Cygnus A (Nakahara et al. 2019). Such results can be obtained by measurements over very wide physical scales beyond ∼10⁵R_S using both the Very Long Baseline Interferometry (VLBI) and connected array to cover the angular scales of interest for nearby radio galaxies. However, the number of examples investigated over such wide scales has been insufficient to examine the diversity of the evolution of the jet structure in active galactic nuclei (AGNs).

NGC 1052 is a nearby (a redshift of 0.005037 ± 0.000020; Denicoló et al. 2005) radio galaxy whose nuclear activity is classified as a low-ionization nuclear emission-line region (LINER). A well-defined double-sided radio jet is elongated by several parsecs with a position angle of approximately 70°. Eastern and western jets are considered as approaching and receding jets (jet and counter jet), respectively (Kameno et al. 2001; Vermeulen et al. 2003). Kiloparsecc-scale jet–lobe structures are also prominent on both sides in the images at 1.4 GHz at arcsec resolutions (Wrobel & Heeschen 1984; Kadler et al. 2004a). However, in the Very Large Array (VLA) image at 5 GHz the central core dominates against weak two-sided radio emissions (Jones et al. 1984). NGC 1052 shows a convex radio spectrum peaked at roughly 10 GHz, to be classified into the gigahertz-peaked spectrum (GPS) radio source (O'Dea 1998). The GPS radiation originates in the central core, which constitutes of parsec-scale jets. VLBI observations revealed the presence of water masers that distribute along the parsec-scale jets. The water masers were considered to be excited by shocks into circumnuclear molecular clouds, or amplification of the radio continuum emission of the jet by foreground molecular clouds (Claussen et al. 1998). On the other hand, the distribution of free–free absorption toward the nuclear region had been investigated in detail and suggests the presence of a surrounding obscuring torus with a radius of ∼0.5 pc around the nucleus (Kameno et al. 2001, 2003). The location of large opacity free–free absorption coincides with the distributions of water masers, HCN, and HCO⁺ molecular absorption lines, almost all of which are redshifted with respect to the systemic velocity of NGC 1052 (Sawada-Satoh et al. 2008, 2016, 2019). They argue that these materials around the NGC 1052 nucleus are associated with accreting flows onto the central engine. Thus, NGC 1052 is one of well-investigated nearby radio galaxies with apparent two-sided jets. However, a detailed analysis of the jet width profile has not previously been published.

In the present study, we report the measurements of the distance profiles of jet width for NGC 1052. Throughout this paper, we adopt a cosmology with H₀ = 70.5 h⁻¹ km s⁻¹ Mpc⁻¹, Ω_M = 0.27, Ω_Λ = 0.73, and the redshift corrected to a reference frame defined by the (Virgo + GA + Shapley) model, resulting in an angular size distance of 20.5 Mpc, calculated in the NASA/IPAC Extragalactic Database (NED). An angular size of 1 mas is equivalent to a linear scale of ∼0.099 pc. Assuming a viewing angle of 86° (Baczko et al. 2016), the angular scale 1 mas is equivalent to ∼6,700 R_S, given that the mass of the central black hole is 10^8.19 M_⊙ (Woo & Urry 2002). The sphere of gravitational influence of the central black hole is estimated to be ∼7 × 10⁵R_S from a central stellar velocity dispersion of 245 km s⁻¹ (e.g., Riffel et al. 2017). We uncover the structure of jets over a range of ∼300–4 × 10⁷R_S in distance from the central engine of NGC 1052 on both the approaching and receding jets. The present paper is structured as follows. In Section 2, the VLA and VLBI data we used in the present paper and image analysis for jet width measurements are described. In Section 3, we present the results of the jet width profiles. In Section 4 we briefly discuss the jet structure and its physical origin. Finally, our study is summarized in Section 5.

2. Data and Image Analysis

2.1. VSOP Data

We used space VLBI images obtained in the VLBI Space Observatory Programme (VSOP; Hirabayashi et al. 1998) at 1.6 GHz (observation code: W513A) and 4.8 GHz (W513B), which have already been published by Kameno et al. (2003). The observations were carried out on 2001 August 7 and July 31, respectively. Left-hand circular polarization was received with a bandwidth of 32 MHz. The spacecraft HALCA was linked to two tracking stations during each observation: Green Bank and Tidbinbilla for W513A and Green Bank and Usuda for W513B. The ground telescopes were the 10 antennas of the Very Long Baseline Array (VLBA). In addition to the original images, we remade images with uniform weighting and with restoring beams, as listed in Table 1. In preparation for subsequent slice analysis (Section 2.6), the restoring beam sizes at the major and minor axes were determined by the projection of the original synthesized beams perpendicular and parallel to the eastern jet's position angle of PA = 66°, respectively. The method to define the jet's position angle is described in Section 2.5. The VSOP images at 1.6 and 4.8 GHz shown in Figure 1 are the images convolved with the restoring beam; these images have been centered at the black hole position, which will be determined through the manner described in Section 2.4.

**Figure 1.** VLBI images of NGC 1052 at 1.6–15.4 GHz on epoch 2001. (a) VSOP 4.8 GHz, (b) VLBA 2.3 GHz, (c) VSOP 4.8 GHz, (d) VLBA 8.4 GHz, and (e) VLBA 15.4 GHz. Contours start from three times the image rms noise and increase by factors of $\sqrt{2}$ . Convolution was applied using restoring beam sizes ( ${\theta }_{\mathrm{maj}}^{\mathrm{re}}\times {\theta }_{\min }^{\mathrm{re}}$ and PA^re; see Table 1). Semi-transparent curves indicate where the solutions of Gaussian fitting for determining the jet width were successfully obtained. An angular size of 1 mas is equivalent to a linear scale of ∼0.099 pc. Images are centered at the determined black hole position (Section 2.4).
Download figure:
Standard image High-resolution image

**Figure 1.** VLBI images of NGC 1052 at 1.6–15.4 GHz on epoch 2001. (a) VSOP 4.8 GHz, (b) VLBA 2.3 GHz, (c) VSOP 4.8 GHz, (d) VLBA 8.4 GHz, and (e) VLBA 15.4 GHz. Contours start from three times the image rms noise and increase by factors of $\sqrt{2}$ . Convolution was applied using restoring beam sizes ( ${\theta }_{\mathrm{maj}}^{\mathrm{re}}\times {\theta }_{\min }^{\mathrm{re}}$ and PA^re; see Table 1). Semi-transparent curves indicate where the solutions of Gaussian fitting for determining the jet width were successfully obtained. An angular size of 1 mas is equivalent to a linear scale of ∼0.099 pc. Images are centered at the determined black hole position (Section 2.4).
Download figure:
Standard image High-resolution image

Table 1. Image Parameters of NGC 1052

Telescope	ν	Obs. Date	σ	${\theta }_{\mathrm{maj}}\times {\theta }_{\min }$	PA	${\theta }_{\mathrm{maj}}^{\mathrm{re}}\times {\theta }_{\min }^{\mathrm{re}}$	PA^re
	(GHz)	(yyyy mm dd)	(mJy/beam)	(mas × mas)	(deg)	(mas × mas)	(deg)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
VSOP	1.649	2001 Aug 7	0.83	1.98 × 1.68	−15.5	1.97 × 1.68	−22
	4.815	2001 Jul 31	1.18	0.92 × 0.78	−43.4	0.89 × 0.79	−22
VLBA	2.274	2001 Aug 17	0.49	6.34 × 2.58	−5.8	5.37 × 2.66	−22
	8.424	2001 Aug 17	0.56	1.86 × 0.77	−2.2	1.49 × 0.81	−22
	15.377	2001 Aug 17	0.52	1.40 × 0.55	−7.8	1.21 × 0.56	−22
	15.377	2000 Jul 24	0.37	1.33 × 0.52	−6.6	1.13 × 0.53	−22
	22.081	2000 Jul 24	1.25	0.86 × 0.34	−6.3	0.72 × 0.34	−22
	43.229	2000 Jul 24	0.91	0.46 × 0.20	0.2	0.35 × 0.20	−22
VLA	8.27	1998 Jun 20	0.06	694 × 521	88.3	680 × 520	80

Note. Columns are as follows: (1) telescope; (2) frequency; (3) observation date; (4) image rms noise; (5) original beam sizes in the major and minor axes; (6) position angle of the major axis for the original beam; (7) restored beam sizes in the major and minor axes; (and 8) position angle of the major axis for the restoring beam.

Download table as: ASCII Typeset image

2.2. VLBA Data

We used multifrequency images obtained using the VLBA, which are the same data sets that have already been published by Sawada-Satoh et al. (2008) and Kameno et al. (2003). NGC 1052 was observed using the VLBA at 2.3/8.4/15.4 GHz on 2001 August 17 (BK084; Kameno et al. 2003), and at 15.4/22.1/43.2 GHz on 2000 July 24 (BS080; Sawada-Satoh et al. 2008). The details of the observations and data reduction procedures were described in Sawada-Satoh et al. (2008) and Kameno et al. (2003). Natural weighting images were adopted at 15.4/22.1/43.2 GHz for investigating the jet structures including diffuse emission components, while uniform weighting images were adopted at 22.1/43.2 GHz for investigating the innermost structure of jets by taking advantage of the high spatial resolution. In addition to the original images, we remade images with restoring beams in the same manner as the VSOP cases (Section 2.1). The VLBA images shown in Figures 1 and 2 are the images convolved with the restoring beams (Table 1).

**Figure 2.** VLBA images of NGC 1052 at 15.4–43.2 GHz on epoch 2000. (a) VLBA 15.4 GHz, (b) VLBA 22.1 GHz, and (c) VLBA 43.2 GHz. Contours start from three times the image rms noise and increase by factors of $\sqrt{2}$ . Convolution was applied using restoring beam sizes ( ${\theta }_{\mathrm{maj}}^{\mathrm{re}}\times {\theta }_{\min }^{\mathrm{re}}$ and PA^re; see Table 1). Semi-transparent curves indicate where the solutions of Gaussian fitting for determining the jet width were successfully obtained. An angular size of 1 mas is equivalent to a linear scale of ∼0.099 pc. Images are centered at the determined black hole position (Section 2.4).
Download figure:
Standard image High-resolution image

2.3. VLA Data

The VLA data set AR0396 was retrieved from the data archive system of the National Radio Astronomy Observatory (NRAO). We chose the data that has the longest on-source time (33.85 ks) on NGC 1052 in the VLA archive. The observation was conducted on 1998 June 20 at 8.270 GHz using the VLA A-array configuration. Dual-circular polarization was received, with a bandwidth of 25 MHz. The data reduction procedures follow standard manners for VLA data using the Astronomical Image Processing System (AIPS). Data of the antennae 3, 7, 9, 19, and 27 were flagged because their system noises were apparently strange. We performed clean deconvolution using Difmap software for image construction. The image was made with natural weighting and a restoring beam, whose sizes at major and minor axes were defined by projection of the original synthesized beam along directions parallel and perpendicular to the jet's position angle of PA = 10° in the arcsec scale, respectively. The image with the restoring beam is shown in Figure 3.

**Figure 3.** VLA image of NGC 1052 at 8.3 GHz. A strong point source was subtracted at the map center (2.57 Jy). Contours start from three times the image rms noise and increase by factors of $\sqrt{2}$ . Convolution was applied using restoring beam sizes ( ${\theta }_{\mathrm{maj}}^{\mathrm{re}}\times {\theta }_{\min }^{\mathrm{re}}$ and PA^re; see Table 1). Semi-transparent curves indicate where the solutions of Gaussian fitting for determining the jet width was successfully obtained. An angular size of 1'' is equivalent to a linear scale of ∼99 pc.
Download figure:
Standard image High-resolution image

2.4. Determination of the Central Engine Location

The central engine must be located at the upstream end of each side of the jet: the eastern/western jet is considered as the approaching/receding jet (or jet/counter jet). Radio emission from the innermost nuclear region of NGC 1052 suffers strong free–free absorption (Kameno et al. 2001, 2003; Kadler et al. 2004b; Sawada-Satoh et al. 2008). Kameno et al. (2003) proposed that a subparsec-scale circumnuclear torus consisting of dense plasma gas is responsible for observed convex radio continuum spectra due to free–free absorption. Therefore, there is frequency dependence in the apparent position of the upstream end in the jet. To determine the position of the central engine, it is necessary to measure the core shift, which is the frequency-dependent position shift of an observed core due to an opacity effect. However, the core shift for the NGC 1052 jets were determined with some ambiguity (Kadler et al. 2004b), unlike the core shift only due to synchrotron self-absorption in a jet (Lobanov 1998). It may be suggesting that the geometry and spatial profiles of dense obscuring materials is not simple (as a similar case, see Haga et al. 2015 for NGC 4261).

Alternatively, there is a method in which the ejection point of the approaching and receding jets on the basis of their proper motions is regarded as the central engine position. This method uses only simple kinematics. The present study adopts methods to determine the location of the central engine in the latter way. The proper motions in both sides have been intensively measured at 15 GHz, 15 GHz, and 43 GHz by Vermeulen et al. (2003), Lister et al. (2013), and Baczko et al. (2019), respectively. Apparent velocity for each blob shows variation in some levels. Because our images were taken in 2000 and 2001 (Table 1), we averaged the jet velocities reported in Table 2 of Vermeulen et al. (2003), which were based on VLBI monitoring during 1995–2001; we obtained 0.0781 ± 0.0022 pc yr⁻¹ for approaching jets and 0.0783 ± 0.0037 pc yr⁻¹ for receding jets. Therefore, the position to divide the separation between paired components in the approaching and receding jet sides into 0.0781:0.0783, and is considered to be the putative location of the central engine.

Before estimations for the location of central engine, we superimposed images of different frequencies. The positions of jet features were determined using the AIPS JMFIT task on all VLBA and VSOP images. Identified components were labeled as shown in Figures 1 and 2. Subsequently, we made pattern matching among the distributions of determined positions at different frequencies in the same manner presented in Kameno et al. (2003) and Sawada-Satoh et al. (2008). Because the data of Kameno et al. (2003) and Sawada-Satoh et al. (2008) were obtained at different epochs, jet structures changed. Hence, we made pattern matching for the multifrequency images of these two groups separately.

Next, we presumed to make pairs of components in the approaching and receding jet sides. The region where very strong free–free absorption opacities are observed is located at the point between A1–R1 (Kameno et al. 2003) and near the component C4 (Sawada-Satoh et al. 2008). Therefore, the defined pairs are A1–R1, A2–R2, and A3–R3 for the epoch 2001 summer and B–C3a, A–C1, and Ba–C3 for the epoch 2000 July 24 at each frequency in the present study. Assuming the apparent jet speeds of 0.0781 (±0.0022) pc yr⁻¹ and 0.0783 (±0.0037) pc yr⁻¹ for the approaching and receding jet sides, respectively, we determined the location of the black hole as the jet production site by dividing the separation of each pair into 0.0781:0.0783. We obtained the four estimates of the black hole position using the pairs A3–R3, A2–R2, Ba–C3, and B–C3a, which are relatively young jet components. The four estimates included errors in R.A. and decl., which were propagated from the errors of apparent jet speeds and the image-based JMFIT procedure. Finally, we determined the position of the black hole by weighted means of the two estimates using the A3–R3 and A2–R2 pairs (only at 5, 8.4, and 15 GHz) with uncertainty to 22'' for the epoch 2001 summer (Figure 4), and of the two estimates using the Ba–C3 and B–C3a pairs with uncertainty to 13'' for the epoch 2000 July 24 (Figure 5).

**Figure 4.** JMFIT results of NGC 1052 at 1.6/2.3/5/8.4/15 GHz for observations on 2001 and the position determination of the jet origin. Data sets are the same as Kameno et al. (2003). Top: whole region; bottom: focused on the central region. The error bars are the fitting error of JMFIT and the determination error for the jet origins and the black hole (BH).
Download figure:
Standard image High-resolution image

**Figure 5.** JMFIT results of NGC 1052 at 15/22/43 GHz for observations on 2000 and the position determination of the jet origin. Data sets are the same as Sawada-Satoh et al. (2008). Top: whole region; bottom: focused on the central region. The error bars are the fitting error of JMFIT and the determination error for the jet origins and the black hole (BH).
Download figure:
Standard image High-resolution image

As a result, we obtained VLBI images centered at the determined black hole position at all frequencies (Figures 1 and 2). The location of the black hole coincides with the intensity peak in the 43 GHz image but is displaced significantly at 22 GHz. Our result indicates that the line of sight to the nucleus becomes optically thin between the two frequencies, which is consistent with conclusions based on intensive VLBI studies at 22–86 GHz for NGC 1052 (Baczko et al. 2016, 2019).

2.5. Determination of the Mean Jet Position Angle

In preparation for subsequent slice analysis (Section 2.6), we determined weighted-mean position angle of the jet axis. The position angles of the corrected positions of all components, except for innermost components (A3, R3, and C4), on both sides with respect to the black hole (Section 2.4) were weighted-averaged for each epoch separately. The propagated errors from the image-based JMFIT procedure and the determination of the black hole position (Section 2.4) was used for the weighting. We obtained 67 fdg 4 ± 2 fdg 3 and 68 fdg 3 ± 1 fdg 6 from the epochs 2000 and 2001, respectively. Therefore, we defined PA = 68° as the direction to measure the angular distance from the black hole in the VLBI scale. The minor axis of the restoring beams was set to have PA = 68°, while the major one was along PA = −22° (Table 1).

On the other hand, in the VLA scale, the jet appears toward PA = 80° (Kadler et al. 2004a). Therefore, we defined PA = 80° as the direction to measure the angular distance from the nucleus at the VLA scale. The minor axis of the restoring beams was determined along PA = −10°, while the major one was along PA = 80° (Table 1).

2.6. Jet Width Measurements

For jet width measurements, we adopted the method similar to those used in the previous studies for NGC 6251 (Tseng et al. 2016) and NGC 4261 (Nakahara et al. 2018), as described below. The NGC 1052 jet was assumed to extend at the position angle PA = 68° (Section 2.5). We rotated the VLBI images counterclockwise by 22 deg to make the mean jet axis parallel to the horizontal axis, and then, we defined a new coordinate system (z_a, r_a) centered at the position of black hole. z_a is the angular distance from the black hole along the mean jet axis, which is parallel to the minor axis of the restoring beam. r_a is the angular distance from the mean jet axis, which is parallel to the major axis of the restoring beam. The jet intensity profile was transversely sampled, i.e., along the r_a axis, using the AIPS SLICE task. Such slice sampling was performed at different distances, z_a. The pixel sampling rate on both the z_a and r_a directions was equivalent to approximately a fifth of the restoring beam with widths of θ_min^re and θ_maj^re, respectively. We adopted this sampling rate by following previous studies (Boccardi et al. 2016; Tseng et al. 2016; see also a study of angular resolution limit by Lobanov 2005).

The transverse jet profile of each slice was fitted with a Gaussian model to obtain the deconvolved angular size of jet width of

$\begin{eqnarray}&&{w}_{{\rm{a}}}=\sqrt{{\left({\theta }_{\mathrm{FWHM}}\right)}^{2}-{\left({\theta }_{\mathrm{maj}}^{\mathrm{re}}\right)}^{2}},\end{eqnarray} \tag{ 1 }$

where θ_FWHM is the FWHM of the fitted Gaussian profile and ${\theta }_{\mathrm{maj}}^{\mathrm{re}}$ is equivalent to the angular resolution along the jet transverse direction. The fitting error of θ_FWHM was also obtained, which presumably originated in the image noise, the deconvolution error on imaging processes, and the deviation of the slice profile from the Gaussian model. We calculated the error of w_a by considering the error propagation. The success criteria for the Gaussian fitting were as follows: (1) the jet brightness was more than three times the image noise; (2) ${\theta }_{\mathrm{FWHM}}\gt {\theta }_{\mathrm{maj}}^{\mathrm{re}}$ ; and (3) the determined value of θ_FWHM did not exceed its fitting error, which was the same as that used by Nakahara et al. (2018). As a result, we obtain the jet width profile, ${w}_{{\rm{a}}}({z}_{{\rm{a}}})$ , as a function of the distance from the black hole.

The slice analysis on the VLA image was performed in the same manner, but the different position angle PA = 10° was assumed. Note that the original beam was rather elongated roughly at the east–west direction. Hence, the major and minor axes of the restoring beam were swapped in Equation (1), and the jet width was obtained by deconvolution with ${\theta }_{\min }^{\mathrm{re}}$ for the VLA case. The lobe-like emissions seen in the VLA image at large scales ( $| {z}_{{\rm{a}}}| \gtrsim 6^{\prime\prime}$ ) were excluded for our analysis.

3. Results

3.1. Jet Width Profile for NGC 1052

The distance profiles of the jet width are shown in Figure 6 for the approaching jet side and in Figure 7 for the receding jet side. Figure 8 shows the comparison of them. The jet width w_a in the angular size was converted into w in units of Schwarzschild radii (R_S). The angular distance z_a was converted into the deprojected distance z in units of R_S assuming the viewing angle of 86°. The measurement range in distance resulted in z_a = 0.05 mas–6 farcs 1, corresponding to z = 0.005–610 pc or 3.3 × 10²–4.1 × 10⁷R_S from the black hole. As a result, our measurements distribute beyond the sphere of gravitational influence of r_SGI = 7 × 10⁵R_S for the black hole of NGC 1052.

**Figure 8.** Comparison between the approaching jet and the receding jet of NGC 1052. The horizontal axis shows the deprojected distance (z) from the central engine. The vertical axis shows the deconvolved jet width (w). Red and cyan circles represent measurements for the approaching and receding jet, respectively. Orange and blue squares represent the distance binning of the measurements for the approaching jet and receding jet, respectively. Orange, blue, and black solid lines are broken power-law fits for the approaching jet, receding jets, and combined data (approaching + receding), respectively. The parameters of fitting results are listed in Table 2.
Download figure:
Standard image High-resolution image

At first, the measurements of the jet width along the jet had been fitted with a single power-law model function (w∝z^a, where a is the power-law index). Since the density of the data sample is significantly higher in the upstream jet (≲10⁶ R_S) than in the downstream (≳10⁶ R_S), as can be seen in Figures 6 and 7, the upstream jet has a much greater influence on the fit. Therefore, we binned all the multifrequency data at intervals of the order of 10^0.25. Before the binning, we excluded data of z ≤ 10^4.75 R_S (∼8.4 mas) at 1.6/2.3/4.8 GHz because a significant deviation from the trend is seen. We consider that these deviations only at low frequencies are possibly caused by an interstellar broadening effect at our line of sight to the innermost jets, which will be studied in a separate paper. The single power-law fitting resulted in the power-law indices of a = 0.79 ± 0.06 and a = 1.07 ± 0.04 for the approaching side and the receding side, respectively. The reduced ${\chi }^{2}/{ndf}$ was 45.5/15 (p-value < 10⁻⁴) and 46.7/14 (p-value < 10⁻⁴), where ndf is the number of the degree of freedom indicating that the single power law does not fit the data well.

Next, we made the fit with a broken power-law model in the same manner as in the previous study for NGC 4261 (Nakahara et al. 2018). The fitting function is

$\begin{eqnarray}&&w(z)={W}_{0}\ {2}^{({a}_{u}-{a}_{d})/s}{\left(\displaystyle \frac{z}{{z}_{b}}\right)}^{{a}_{u}}{\left(1+{\left(\displaystyle \frac{z}{{z}_{b}}\right)}^{s}\right)}^{({a}_{d}-{a}_{u})/s},\end{eqnarray} \tag{ 2 }$

where W₀ is the scale factor, a_u is the power-law index for the upstream jet, a_d is the power-law index for the downstream jet, z_b is the break location, and s is the sharpness of the profile at the break (here, we use the fixed value s = 10). The fitting results are represented in Table 2 and the reduced χ² was improved from single power-law fitting.

Table 2. Results of the Broken Power-law Fit to Jet Structures of NGC 1052

Case	W₀	z_b	a_u	a_d	χ²/ndf	ndf	p-value
	(×10³R_S)	(×10⁴R_S)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Approaching jet	1.5 ± 0.5	0.99 ± 0.49	−0.03 ± 0.12	0.96 ± 0.04	1.10	13	0.35
Receding jet	1.3 ± 0.2	0.96 ± 0.23	−0.05 ± 0.07	1.02 ± 0.03	0.43	12	0.95
Approaching + receding jets	1.3 ± 0.2	0.90 ± 0.26	−0.05 ± 0.07	0.98 ± 0.03	0.75	29	0.83

Note. Columns are as follows: (1) cases of fitting analyses; (2) jet width at structural transition; (3) distance of structural transition; (4) power-law index of the jet structure at upstream; (5) power-law index of the jet structure at downstream; (6) reduced chi-squared value; (7) the number of degree of freedom; and (8) probability in the χ² distribution.

Download table as: ASCII Typeset image

4. Discussion

On the basis of our investigation for the distance profile of the jet width along the jet, we found that the approaching and receding jets are symmetric within errors (Table 2). Following the case of NGC 4261 (Nakahara et al. 2018), NGC 1052 is the second example for the confirmation of symmetry in the two-sided jet structure throughout very wide ranges of physical scales. The maintenance of the of symmetry suggests that the distributions of the interstellar medium in these host galaxies are spherically symmetric or that the jets have developed with its overwhelming power without being affected by the interstellar medium. Another important result is that both sides of the jet structure change from a cylindrical (a ∼ 0) to a conical (a ∼ 1) structure at ∼10⁴R_S in NGC 1052. Consequently, we found a structural transition in the NGC 1052 jets, as well as those seen in M87 (Asada & Nakamura 2012), NGC 6251 (Tseng et al. 2016), and NGC 4261 (Nakahara et al. 2018) of nearby radio galaxies.

However, the characteristic feature in the NGC 1052 case is that the jet exhibits a cylindrical-to-conical (from a ∼ 0 to ∼1.0) structure, not a parabolic-to-conical (from a ∼ 0.5 to ∼1.0) structure as seen in the other these AGNs. The profile at <1 × 10⁴R_S in NGC 1052 becomes flat, rather than parabolic, from a conical outer profile (Figure 8). The physical scale of the transition is significantly less than 7 × 10⁵R_S as the sphere of gravitational influence of the central black hole for NGC 1052. The flat profile continues at least ∼1.5 orders of magnitude of the distance scale. Baczko et al. (2016) estimated the jet width to be ∼0.2 mas at distances of ∼0.2 mas on both sides and to be ≲0.15 mas at the innermost component at a distance of ≲15 μarcsec for the NGC 1052 jets, on the basis of the global millimeter-VLBI array observation at 86 GHz. These are corresponding to ∼1 × 10³R_S at a distances of ∼1 × 10³R_S and ≲1 × 10³R_S at a distance of ≲100R_S. Their estimates are consistent with our result. A cylindrical structure (a ∼ 0) is also inferred at the distance of ≲1 mas (corresponding to ≲0.7 × 10⁴R_S) based on size measurements of each jet component on 43 GHz VLBA images of NGC 1052 at 29 epochs (Baczko et al. 2019). Some physical mechanism to form the flat profile in the inner region is required.

A relatively flat profile had also been reported in the jet width distance profile of very young radio galaxy 3C 84. A limb-brightening structure is apparent with a nearly cylindrical flow showing power-law indices of a = 0.25 ± 0.03 (at z ∼180–4000R_S; Giovannini et al. 2018) and a = 0.17 ± 0.01 (at z ∼ 10⁴–10⁵R_S; Nagai et al. 2014) in those researches on the basis of RadioAstron and VLBA 43-GHz observations, respectively. If the magnetized jets are collimated by the pressure of external medium as theoretical studies suggest, the pressure gradient of ambient gas is required to be b < 2, where the pressure profile is p_ism ∝ r^−b (Komissarov et al. 2009; Porth & Komissarov 2015), to make an over-collimation with the power-law index of the jet width profile a < 0.5. Nagai et al. (2014) discussed that the over-collimation in 3C 84 could be responsible for making the ambient pressure gradient shallower. Alternatively, it may be controlled by different physics because the jet might not have reached a pressure balance with the surrounding medium for this very recent outburst (∼10 yr).

The common property of NGC 1052 and 3C 84 as AGNs is that these nuclei are surrounded by the parsec-scale distribution of dense obscuring material, part of which is ionized and causes heavy free–free absorption. For 3C 84, nondetection of a receding jet at low frequencies cannot be explained entirely by the Doppler debeaming effect, and therefore, free–free absorption due to the ionized gas is inferred (Walker et al. 2000). For NGC 1052, Kameno et al. (2001) found the presence of a torus-like ionized absorber around the nucleus in addition to molecular gas at outer radii with very high column densities (Sawada-Satoh et al. 2016, 2019). It has been argued that these distributions suggest a transition from spherical radial accretion flow to rotational accretion orbits (see also, Kameno et al. 2003, 2005; Sawada-Satoh et al. 2008). The physical size of the high-density ionized region in the center of NGC 1052 is estimated to be ∼0.5 pc in radius (Kameno et al. 2001), corresponding to ∼3 × 10⁴R_S; this is consistent with the locations of transition at ∼1 × 10⁴R_S in the jet width profiles. Hence, we consider that the external pressure by the obscuring material is attributed to the observed over-collimation making cylindrical shapes in the innermost jets of NGC 1052, as well as 3C 84. After escaping the area of the dense obscuring material, at the outer region the jets would become conically expanding in the surrounding ambient medium with a much steeper profile in the host galaxy and/or become overpressured by sufficient magnetic dissipation. More detailed studies are required to understand the observed jet width profile by numerical simulation including the relationship between a jet and the distribution of a circumnuclear torus (e.g., Fromm et al. 2018).

5. Summary

We found the symmetric distance profiles of the jet width along the jet throughout scales from 300 to 4 × 10⁷R_S on the approaching and receding jet sides in the nearby radio galaxy NGC 1052. The jets show cylindrical-to-conical structures with transitions at ∼10⁴R_S. The distance of the transitions is consistent with the subparsec-scale distribution of dense obscuring material as a free–free absorber surrounding the central region of NGC 1052. We suggest a picture that the transverse pressure by the accreting matter in the dense obscuring material supports the over-collimation of the innermost jets in NGC 1052.

The VLBA and VLA are operated by the National Radio Astronomy Observatory, which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The authors gratefully acknowledge the VSOP Project, which is led by the Japanese Institute of Space and Astronautical Science in cooperation with many organizations and radio telescopes around the world. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. This study was partially supported by the Sasakawa Scientific Research Grant from The Japan Science Society (SN) and by Grants-in-Aid for Scientific Research (B) (24340042, AD) from the Japan Society for the Promotion of Science (JSPS).

The Two-sided Jet Structures of NGC 1052 at Scales from 300 to 4 × 10⁷ Schwarzschild Radii

Article metrics

Permissions

Author e-mails

Author affiliations

ORCID iDs

Dates

Abstract

1. Introduction