DEEP CHANDRA X-RAY IMAGING OF A NEARBY RADIO GALAXY 4C+29.30: X-RAY/RADIO CONNECTION

Based on the soft and hard X-ray band images of the source, it is apparent that the unresolved nucleus, unlike the diffuse structure surrounding it, is bright at photon energies exceeding about 2 keV. Utilizing the hard band image (2–7 keV; see Figure 3), we measured a centroid for the nucleus at α(J2000) = 08^h40^m023, δ(J2000) = +29°49'0257. This position agrees with that of the galaxy centroid quoted in NED based on the Sloan Digital Sky Survey DR6.¹²

We defined the nucleus (core) region as a circle with a radius equal to 125 centered on the above position and extracted the X-ray spectra and response files for that region. A total of 5328 ± 73 counts (5303.7 ± 73.2 net counts) with photon energies between 0.5 keV and 7.0 keV were found. Approximately ∼90% of the detected counts have energies between 2 keV and 7 keV. We note that the expected pileup fraction for the counts in the nucleus is low, <2%, and we neglected the pileup effects in our analysis. To account for the local background contribution to the core emission, we assumed an annulus region centered on the core position with an inner radius of 15 and an outer radius of 10''. In fitting the background spectrum, we assumed a model composed of a thermal bremsstrahlung emission and power-law component, and the resultant fitted parameters are summarized in Table 3.

The Chandra spectrum of the core was poorly fitted with an absorbed power-law model, with χ²_ν = 2.56 in the standard χ² test applied to the binned data and ν = 453 degrees of freedom. Therefore, we attempted to fit the core spectrum with several parametric models that consisted of absorbed and unabsorbed emission components. All models included the Galactic absorption column density of N_H(Gal) = 3.98 × 10²⁰ cm⁻² (Dickey & Lockman 1990). Our selection of models and their best-fit parameters are listed in Table 3. We found that the nucleus is significantly absorbed with a relatively high intrinsic absorption column density of N_H(int) = 3.95^+0.27_−0.33 × 10²³ cm⁻² and that the unabsorbed lower energy X-ray spectrum constitutes a separate emission component. This type of a composite spectrum consisting of an unabsorbed soft X-ray emission and a highly absorbed hard X-ray component is often found in the centers of radio galaxies (Hardcastle et al. 2009).

To fit the hard band X-ray emission detected from the core, we assumed an absorbed power-law model. In this model, the best-fit photon index was Γ = 1.70^+0.38_−0.36 (N_H(int) as given above) and the resultant unabsorbed flux of (5.1 ± 0.5) × 10⁻¹² erg cm⁻² s⁻¹ corresponds to a 2–10 keV luminosity of (5.0 ± 0.5) × 10⁴³ erg s⁻¹. We note that the derived values of the photon index and luminosity of the nucleus in 4C+29.30 are similar to the ones found in the nuclei of Seyfert galaxies (Singh et al. 2011). In Section 5, we discuss implications of the luminous nucleus on the physical state of the environment in this object.

The observed soft (0.5–2 keV) unabsorbed emission component contains only about ∼10% of the total counts detected from the core. We first tried to model this emission with an unabsorbed power-law component, which was added to the absorbed power-law model discussed earlier, fitting both components simultaneously. We obtained a reasonable photon index of Γ_s = 1.60 ± 0.12 and a 0.5–2 keV flux of 6.4 × 10⁻¹⁵ erg cm⁻² s⁻¹ for this model. Next, instead of a power-law model, we tried two types of thermal models added to the intrinsically absorbed power-law component: a bremsstrahlung emission and the APEC plasma model. Both thermal models gave a good description of the soft emission. The best-fit temperature of the bremsstrahlung emission is equal to kT_b = 6.8^+9.9_−2.5 keV, while the APEC gave a slightly higher, but consistent (within the errors) temperature of kT_a = 9.6^+10.0_−4.8 keV and 3σ upper limit to the metal abundances of A < 1.35 with respect to the solar value. For the bremsstrahlung model, we measure a 0.5–2 keV flux of 7.1 × 10⁻¹⁵ erg cm⁻² s⁻¹ corresponding to a luminosity of 6.9 × 10⁴⁰ erg s⁻¹. Although we were unable to discriminate statistically between any of the above models for the soft component, we discuss a possible origin of this soft emission in Section 5.

We selected a narrow box region (marked in Figure 2 as SJet) to delineate the X-ray emission to the south of the nucleus to study the emission that could be associated with the known radio jet at that location. We fitted both an absorbed power law and an absorbed thermal model to the X-ray spectrum of this region (see Tables 4 and 5, respectively). In the power-law model, we obtained a photon index, Γ = 2.2 ± 0.2, when we fixed the absorption parameter at the Galactic value, and obtained only upper limits to both the absorbing column and photon index when the absorption parameter was left free in the fit. The upper limit to the absorption is consistent with the Galactic column, thus we conclude that there is no intrinsic absorption of the X-ray emission from this jet region. In the framework of the thermal model, we obtained the best-fit temperature of kT_b = 2.1^+0.9_−0.6 keV (68% uncertainties for 1 significant parameter). We could only obtain a 3σ upper limit of A < 0.13 of the solar values for the metal abundances in this region.

The total luminosity in the jet assuming the best-fit power-law model is equal to 1.4 × 10⁴⁰ erg s⁻¹ in the 0.5–2 keV range, which is comparable to the luminosity in the hard band (2–10 keV) of 1.2 × 10⁴⁰ erg s⁻¹. The thermal versus non-thermal origin for the X-ray emission detected from SJet is discussed in Section 5.

There are two enhanced regions of X-ray emission in the Chandra image located near the opposite extremes of the radio source. They appear to be associated with the radio hotspots, although the northern radio feature does not display a prominent hotspot in the VLA map. The X-ray images shown in Figure 3 indicate that the northern hotspot emission is rather soft, as it is very faint in the hard band image. In contrast, the hotspot to the south is quite prominent in the hard band image. We extracted the spectra of both features assuming circular regions with 12 radius each and fit the data assuming a single absorbed power-law model and a thermal emission model. In both cases, we both fixed the absorption column at the Galactic value and set it free in the fits.

4.3.1. Southern Hot Spot: The End of a Jet

4.3.2. Northern Hot Spot

We identified several distinct X-ray emission regions across the galaxy in addition to the main morphological features shown above. They are indicated in Figure 2 as EArm, HBranch, and HBranchS. These regions were modeled with both an absorbed power-law model and a thermal emission (see Tables 4 and 5, respectively). The best-fit model parameters for the EArm and HBranch regions are identical, with Γ = 3.53 for the power law and kT_b = 0.39 keV for a thermal model fit. The metal abundances are similar for both regions with A = 0.13–0.18 of the solar value for the temperature of kT_a = 0.7 keV. The HBranchS spectrum has a slightly higher best-fit temperature of kT_b = 0.52^+0.06_−0.05 keV and lower but consistent metal abundance of 0.09^+0.08_−0.04 for kT_a = 0.75 keV. The total 0.5–2 keV luminosities (corrected for absorption) of all three components are relatively high and equal to 9.1 × 10⁴¹ erg s⁻¹. The total contribution of these diffuse components to the total emission in the hard X-ray band is at least three orders of magnitude lower. The thermal origin of these regions is advocated in Section 5 below.

Even though the nucleus of 4C+29.30 was detected in X-rays already in the previous short Chandra observation (Gambill et al. 2003), only now can we study its properties in details using the new high-quality spectrum at keV photon energies. The new observations confirmed that the AGN is buried within a large amount of gas and the AGN emission is only visible at the high energy X-rays where the effect of the strong absorption is less substantial. The measured intrinsic absorption column of N_H = 3.95^+0.27_−0.33 × 10²³ cm⁻² is consistent with the values reported earlier by Gambill et al. (2003) and Jamrozy et al. (2007). This X-ray absorption is due to both the neutral and ionized gas. The neutral hydrogen column density of the infalling gas based on the redshifted H i absorption lines reported by Chandola et al. (2010) is equal to N_HI ≃ 5 × 10²¹ (T_s/100 K) cm⁻², where T_s is the spin temperature. The standard assumption of T_s ∼ 100 K results in almost two orders of magnitude smaller neutral column than the total one measured in X-rays, i.e., N_HI ≪ N_H. Only with much larger spin temperatures (which might in fact be expected in the AGN environment) could the neutral hydrogen column density around the nucleus of 4C+29.30 be comparable to the total equivalent hydrogen column density inferred from our X-ray observations (see in this context the discussion in Ostorero et al. 2010). Note that large amounts of infalling matter inferred from the redshifted H i absorption lines are usually observed in rejuvenated and newly born radio sources (e.g., Gupta et al. 2006; Saikia et al. 2007, and references therein), including also the case of Centaurus A (Morganti et al. 2008).

The nuclear X-ray luminosity of 4C+29.30 is equal to L_2–10 keV ≃ 5 × 10⁴³ erg s⁻¹, a value typical of nearby Seyfert-type AGNs (Singh et al. 2011). This, together with the best-fit photon index for the hard X-ray nuclear continuum (Γ ≃ 1.7; representative of Seyferts and radio galaxies), suggests that the observed radiation is related to the standard AGN engine, i.e., X-ray emission from a hot corona reprocessing thermal optical/UV radiation from an accretion disk (see, e.g., Chiang 2002; Sobolewska et al. 2004a, 2004b). In the case of 4C+29.30, the exact level of the accretion-related UV luminosity is unclear because of the significant absorption affecting the observed central optical/UV radiation. However, assuming a typical value of the UV–to–X-ray luminosity ratio found in AGN samples corresponding to a power-law slope of α_ox ≡ −0.3838 × log [L_2 keV/L_2500 A] ≃ 1.5 (Kelly et al. 2007; Sobolewska et al. 2009), one can evaluate the optical/UV luminosity of the 4C+29.30 nucleus to be roughly ∼10⁴⁵ erg s⁻¹. On the other hand, if we assume a bolometric correction factor of 70 for Seyfert 2 galaxies, as advocated by Singh et al. (2011), we obtain a bolometric luminosity of 3.5× 10⁴⁵ erg s⁻¹.

We note that 4C+29.30 has recently been detected at photon energies exceeding 10 keV and up to ∼150 keV by the Swift/BAT (Baumgartner et al. 2010). The photon index of a power-law model reported in the Swift/BAT 58 month catalog¹³ of Γ_BAT = 1.65^+0.45_−0.42 agrees with the photon index we found in our Chandra spectra of the nucleus. We note that the reported Swift/BAT luminosity in 14–150 keV energy range is equal to 1.7 × 10⁴⁴ erg s⁻¹. This emission is most likely related to the disk corona in the Seyfert-type core of 4C+29.30. This provides additional evidence for the intrinsic high luminosity of the AGN buried in the 4C+29.30 center as we concluded based on the new Chandra data.

Our estimated AGN luminosity is comparable to the accretion-related luminosities observed in quasars (Hardcastle et al. 2009), and therefore exceeds by orders of magnitude the non-stellar nuclear optical–UV continuum in 4C+29.30 estimated by van Breugel et al. (1986). Yet it is in agreement with the required photoionizing flux for the observed equivalent width of the [O iii] emission-line in the extended emission-line region (a total required luminosity of the order of ∼10⁴³ erg s⁻¹). van Breugel et al. (1986) excluded collisional ionization of the line-emitting gas given the observed line ratios and speculated on the source of the ionizing photons. Our new results imply that the AGN can provide the required energy to efficiently photo-ionize the extended emission-line region gas. Further investigations of the nature of the AGN buried in the center of 4C+29.30 are given in M. A. Sobolewska et al. (2012, in preparation).

The one-sided radio jet of 4C+29.30 extends from the core to the south beyond the host galaxy and portions of it were detected in our deep Chandra image. Excluding the hotspot and core regions, a total radio luminosity of the jet is roughly ∼3 × 10⁴⁰ erg s⁻¹ (van Breugel et al. 1986). The X-ray spectrum is best modeled by an unabsorbed power-law continuum with a relatively large photon index of Γ = 2.2 ± 0.2 resulting in a total X-ray luminosity of ∼3 × 10⁴⁰ erg s⁻¹, i.e., comparable to the jet radio luminosity. Therefore the observed X-ray emission is most likely non-thermal in origin, although thermal scenarios cannot be definitively excluded. That is because the jet X-ray emission is relatively faint, and hence we were forced to extract the spectrum over a relatively large extraction region. This average spectrum may be oversimplified since there are several "blobs" or "patches" of diffuse X-ray radiation scattered across the entire galaxy, and there is a non-negligible probability that a few such blobs would fall into this extraction region. Indeed, the jet's X-ray morphology consists of several isolated knots, and it is unclear whether there is any continuous low-surface brightness emission associated with the inter-knot regions (see Figure 8). The only sign of possible continuous X-ray emission aligned with the radio jet can be found in the vicinity closest to the core. However, there is a similar X-ray feature extending on a similar scale in the opposite direction from the core (to the north) and both features coincide with the known emission-line filaments that indicate the presence of a warm medium (van Breugel et al. 1986).

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We note that our Chandra image may not be deep enough for a detection of the continuous X-ray jet emission. For example, in the case of the X-ray jet of Centaurus A (Hardcastle et al. 2003), there are many surface brightness enhancements embedded in a faint diffuse continuous emission (less than ∼10% of the knots' peaks). Many of these X-ray enhancements (though not all) have corresponding radio knots, and some of them also show offsets between the radio and X-ray peak brightnesses. In 4C+29.30, the limits to the inter-knot X-ray emission are of the order of 30%–40% of the knots' peaks. It is then possible that the jet X-ray diffuse emission is present but just below our detection limits and we are only able to detect X-ray knots.

We present a zoomed-in X-ray image of the jet overlaid with the radio contours at two different frequencies in Figure 8. The lower-resolution 1.4 GHz radio map shows a continuous and slowly expanding outflow flaring at the position of the southern hotspot. The higher-resolution 5 GHz radio map reveals instead a very knotty structure, with the innermost 43 scale (or 5 kpc long) linear feature terminating at the position of the X-ray enhancement located at the boundary of the 1.4 GHz jet. An isolated 5 GHz knot is present further away (∼8'' from the core), and downstream of the strongest X-ray peaked bright feature. Some faint enhancements in the X-ray emission are seen all along the radio jet further downstream up to the terminal hotspot where both the radio and X-ray emission peaks are well aligned.

We cannot exclude some significant thermal contribution to the jet X-ray emission spectrum given the limited quality of the current data. However, in the case of a non-thermal origin for the bulk of the detected jet X-rays, two main processes can be invoked—synchrotron emission from high-energy relativistic electrons and the inverse Compton (IC) process involving low-energy particles only. There is strong evidence for the synchrotron origin of the X-ray emission in all FR I jets detected by Chandra (see Harris & Krawczynski 2006, and references therein) in general, including the Centaurus A radio galaxy (Kataoka et al. 2006; Worrall et al. 2008; Goodger et al. 2010). The synchrotron process has also been advocated for the X-ray jets in some FR II sources, such as Pictor A and 3C 353 (e.g., Hardcastle & Croston 2005; Kataoka et al. 2008). The X-ray photon index and luminosity, and the radio–to–X-ray flux ratio inferred for the 4C+29.30 jet are similar to those established for the other FR I objects, supporting the synchrotron interpretation also in this case.

In the synchrotron model, the Lorentz factors of the X-ray-emitting electrons in the jet need to be as high as γ ≃ (1/2) δ^−1/2 (ν/10¹⁸ Hz)^1/2 (B/μG)^−1/2 ∼ 10⁸, for the equipartition magnetic field, B ≃ 30 μG, and the expected jet bulk Doppler factor, δ ∼ a few. Stawarz & Ostrowski (2002) argued that 100 TeV energy electrons could be produced by turbulent acceleration within the whole jet volume but especially at the jet boundaries where the interactions between the radio jet and the ISM can generate substantial turbulence (De Young 1986). There is strong observational evidence for such interactions to take place in 4C+29.30 and in the other low-power FR I systems in general. Electrons accelerated in this way could then be compressed by shocks at the positions of the knots.

Although, the synchrotron process is likely responsible for the jet X-rays, the IC scenario, favored by many authors in the case of powerful and X-ray-bright quasar jets (Tavecchio et al. 2000; Celotti et al. 2001), remains a formal possibility. There are several sources of seed photons for the IC scattering located at tens of kpc distances from the nucleus: (1) the cosmic microwave background, (2) starlight of the elliptical host (Stawarz et al. 2003; Hardcastle & Croston 2011), and (3) the beamed emission of the misaligned blazar core (Celotti et al. 2001; Migliori et al. 2012). The relevance of different photon fields depends on the velocity structure of the jet, while the resulting X-ray IC spectrum reflects the energy spectrum of the low-energy tail of the electron distribution (Harris & Krawczynski 2006). In this regard, one challenge to the IC hypothesis is that the observed spectral index of the jet-related X-ray emission in 4C+29.30 is larger than the spectral index of the jet radio continuum (α_r ≃ 0.8; see van Breugel et al. 1986; Jamrozy et al. 2007). This is because the higher-energy electrons involved in producing synchrotron radio emission are not expected to be characterized by a flatter spectrum than the low-energy electrons IC upscattering starlight/nuclear photons to the X-ray frequency range.

We conclude that the synchrotron scenario for the jet X-ray emission is the most likely option, even though some contribution due to the IC scattering of the starlight or of the blazar emission illuminating the jet from behind, or even a thermal origin of some fraction of the detected X-ray flux, cannot be excluded. A more in-depth understanding of the broadband emission of various jet features in the source would, however, require more detailed modeling than considered here.

In Figure 9, we show the radio and X-ray profiles along the radio source axis (P.A. = 24°; here, the bulk of the AGN core emission is absorbed, and hence the X-ray core peak in the figure is dominated by the soft unabsorbed component). The emission at the two frequencies appears correlated, with the brightest radio and X-ray peaks aligned. The characteristic double structures of the radio features noted first by van Breugel et al. (1986) for the brightest knots in the radio jet and the hotspot regions can easily be seen in the radio profile. Note that the brighter peaks in these doubles are always located upstream of the outflow and that the X-ray counterparts have only been detected for these upstream features. In the observed profiles, the radio flux asymmetry between the prominent southern hotspot and the counter-hotspot to the north is also evident and this asymmetry is followed in the X-rays.

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Positional offsets between X-ray and radio peaks (with the X-ray peaks located upstream relative to the radio ones) and double structures of radio knots in general have been seen in large-scale jets observed by Chandra, e.g., the cases of Centaurus A (Hardcastle et al. 2003), PKS 1127−145 (Siemiginowska et al. 2007), and 3C 353 (Kataoka et al. 2008). The origin of such offsets is still debated. Kataoka et al. (2008) suggested that such a morphology cannot be linked to stationary jet features (like nozzles of reconfinement shocks, for example), but instead could be due to moving portions of the plasma generated by the central engine during epochs of enhanced activity. Kataoka et al. (2008) further speculated that a complex double-shock structure may form as a result of the interaction between the two phases of the ejecta, with the reverse shock (propagating within the faster portion of the jet) being associated with the peak of the X-ray emission. This scenario may also possibly account for the properties of the 4C+29.30 jet and hotspots. If so, it is also of particular relevance for understanding the intermittent/modulated jet activity in this source (see discussion in Jamrozy et al. 2007).

The non-thermal (synchrotron, in particular) character of the X-ray emission of the southern hotspot advocated by Tavecchio et al. (2005) and supported by our spectral analysis (Section 4) fits the above model well. However, a possible thermal origin of the X-ray emission associated with the northern hotspot (on the counterjet side) would then be puzzling. There have only been a few detections of thermal X-ray emission from the hotspots of powerful radio sources. In these cases, the emission was apparently enhanced by interactions between a radio jet and dense ISM clouds (Ly et al. 2005; Young et al. 2005). Indeed, the northern hotspot of 4C+29.30 coincides with the region of a significant amount of observed line-emitting gas, so it may be an example of such a relatively rare phenomenon. But then the question remains why the X-ray peak brightness coincides with the upstream radio peak rather than with the outer (downstream) one. On the other hand, the soft X-ray spectrum of the northern hotspot may be alternatively described by the high-energy tail of the synchrotron continuum shaped by severe aging due to radiative losses of the underlying electron energy distribution. The spectral asymmetry between the southern and the northern hotspots could then possibly be related to the brightness asymmetry, and hence accounted for by relativistic effects (difference in relativistic beaming of the plasma at the reverse shocks on the jet and the counterjet sides, light-travel effects, etc.) in the framework of the modulated jet activity scenario.

Even more likely, the differences in the local ISM between the regions north and the south of the nucleus could lead to distinctive source morphologies in these two directions of the outflow. The radio jet extending toward the south implies a possibly less disturbed outflow than the one to the north characterized by enhanced optical emission features due to interaction between the radio source and the dense medium (van Breugel et al. 1986). Such environmental differences were observed in other galaxies, although very high signal-to-noise data from deep Chandra observations were required to accurately determine the nature of the X-ray emission as was performed for Centaurus A (Kraft et al. 2009; Croston et al. 2009). Interestingly, the very recent numerical simulations by Gaibler et al. (2011) confirm that interactions of bi-polar relativistic jets with the asymmetrically distributed multi-phase ISM can indeed result in an asymmetric morphology of the entire system, with the jet that propagates into the denser environment being restrained (at least for some time), and affecting at the same time the line-emitting clouds themselves in various ways. Future X-ray and other multi-waveband observations of 4C+29.30 are needed to fully understand the structure of the outflows and the two hotspots in the source.

In addition to the core, jet, and hotspots, our Chandra image reveals diffuse X-ray emission covering large parts of the galaxy and extending beyond the radio-emitting plasma. Some structures correlate with the extended emission-line region while others might be related to a recent merger event. For example, the two X-ray filaments perpendicular to the radio axis and extending from the core toward the SE and NW directions (HBranch and HBranchS regions in Figure 2) seem to be aligned with colder gas mixed with the dust seen in the archival optical images of the host galaxy, resembling the famous dust lane in the Centaurus A galaxy (Israel 1998). On the other hand, these two filaments may also be related to the jet activity. In particular, they may be a signature of gas compressed by the expanding lobes to form a quasi-linear structure perpendicular to the jet axis. Similar structures has been seen in Cygnus A (Wilson et al. 2006), although the horizontal structures (named "cold belts" by Wilson et al. 2006) were not as straight as observed in 4C+29.30.

The diffuse X-ray structures seen to the north of the nucleus overlap with the clouds of line-emitting gas associated predominantly with the boundaries of the counterlobe (van Breugel et al. 1986). Our spectral analysis indicate that the X-ray emission of these diffuse components is most likely thermal, with gas temperatures ranging from ≃ 0.4 keV up to ≃ 0.6 keV (see Table 5), with the possible exception of the southern regions located around the radio lobe downstream of the hotspot, for which either a non-thermal contribution or higher gas temperatures (≃ 0.8 keV) remain valid options.

Given the normalization in the best-fit thermal model and the fixed emitting volumes (assuming 1 kpc depths for their third dimensions), we estimated the densities of the hot X-ray-emitting gas in different regions (see Table 6). These densities vary roughly between n_e ∼ 0.02 cm⁻³ in the southern regions, and ∼0.2 cm⁻³ around the center and in the northern regions. It is interesting to note that the denser material is located in the regions with prominent optical line emission. The estimated values are consistent with the densities of hot gas found in other elliptical galaxies located in poor groups (Mathews & Brighenti 2003). 4C+29.30 might be located in such a group. We checked the NED for known galaxies located within 20 arcmin (∼1 Mpc) of 4C+29.30 and with the velocities within ±1000 km s⁻¹, which would be close enough to be possibly associated with a group. Only four galaxies with known redshifts met these selection criteria. One galaxy is closer than ±500 km s⁻¹ and only ∼4.5 arcmin away, so possibly indicative of a group. Future observations are needed to confirm this conclusion.

The average pressures of the hot X-ray-emitting gas are p_th ≃ 2 n_e kT ≲ 10⁻¹⁰ dyne cm⁻² (see Table 6 for the pressure values of the individual features). This pressure is then comparable to/lower than the minimum non-thermal pressures of the jet, hotspots and the lobes (all estimated assuming energy equipartition between the radio-emitting electrons and the magnetic field), as well as the pressure of the line-emitting clouds calculated by van Breugel et al. (1986), i.e., ∼10⁻¹⁰–10⁻⁹ dyne cm⁻². We note that the pressure estimates for the line-emitting clouds are rather uncertain, and that our calculations assumed one size for the depth of all the analyzed regions, while van Breugel et al. (1986) used different scales for different components. Also, the minimum pressure calculations do not take into account the possible contribution of non-radiating particles (cosmic-ray protons in particular) to the jet/lobes' pressure (see, e.g., Dunn & Fabian 2004).

We conclude that it is most likely that the expanding radio source in 4C+29.30 is slightly overpressured with respect to the ambient medium (i.e., the hot ISM component), but it is likely in pressure equilibrium with the denser clouds of the colder material emitting the optical lines. We also note that van Breugel et al. (1986) found a velocity structure of the gas along the jet with increasing velocity toward the outer regions of the galaxy. The outermost gas is outflowing with velocities of ≳ 500 km s⁻¹, exceeding the escape velocity for the host galaxy. The largest velocities (and the broadest emission lines) were found at the boundaries of the radio lobes and hotspots. Thus, it is natural to conclude that the entire outflow is driven by the jets.

The analysis of our X-ray data and the above pressure estimates also indicate that not only the colder line-emitting gas but also the hot X-ray-emitting gas can be pushed out by the expanding radio-emitting plasma. The process may be accompanied by the formation of weak shocks around the lobes, as witnessed in several other analogous systems (such as Centaurus A, M 87, or NGC 1275; e.g., Croston et al. 2009; Million et al. 2010; Fabian et al. 2011, respectively). The shocks should then compress and heat the surrounding X-ray-emitting gas and this may be the origin of the slightly hotter diffuse emission observed around the southern lobe of 4C+29.30.

We can estimate the Mach number of a shock that could heat this southern region. Assuming the standard shock jump condition, one gets the temperature jump:

$$\begin{equation} {T_+ \over T_-} = { [ 2 \, \hat{\gamma } \, \mathcal {M}^2 - (\hat{\gamma } - 1 ) ] \, [ (\hat{\gamma } - 1 ) \, \mathcal {M}^2 + 2 ] \over (\hat{\gamma } + 1 )^2 \, \mathcal {M}^2} , \end{equation} \tag{ 1 }$$

where T₊ and T₋ are the downstream and upstream gas temperatures, respectively, $\mathcal {M} \equiv v / c_{\rm s}$ is the Mach number (as measured in upstream region), and the adiabatic index of the gas (assumed to be the same for the upstream and downstream medium) is $\hat{\gamma }$ = 5/3, as appropriate for a non-relativistic fluid. For the observed temperatures of 0.5 keV for the ambient medium and 0.8 keV for the hotter component, the resulting Mach number reads as $\mathcal {M}=1.6$. This is a very reasonable Mach number and such weak shocks have been discovered in radio galaxies located in clusters of galaxies, such as Hydra A, Cygnus A, and Perseus A (Nulsen et al. 2005; Wilson et al. 2006; Fabian et al. 2006, respectively). However, a much stronger shock was associated with the southern lobe of Centaurus A ($\mathcal {M} \simeq 8$; Croston et al. 2009). Also, slightly higher Mach numbers ($\mathcal {M} \simeq 4$) have been claimed for the shocks driven by the radio structures expanding in the group environments of a low-power FR I radio galaxy NGC 3801 and a Seyfert galaxy Markarian 6, albeit at smaller scales (≲ 10 kpc; see Croston et al. 2007; Mingo et al. 2011, respectively).

We can check the velocity of the shock since we determined the temperature and density of the different regions in our X-ray data. For a kT = 0.5 keV, the sound velocity in the upstream medium is $c_{\rm s} = \sqrt{\hat{\gamma } \, k T / \mu m_{\rm p}} \simeq 360$ km s⁻¹, assuming a non-relativistic gas ($\hat{\gamma }=5/3$) and the mean molecular weight of the gas μ = 0.6. A $\mathcal {M} \simeq 1.6$ shock propagating within the gas characterized by this sound velocity implies the radio lobes driving the shocks have an expansion velocity, $v_{\rm exp} = \mathcal {M} \times c_{\rm s} \simeq 580$ km s⁻¹. This is in excellent agreement with the highest velocity measured for the line-emitting gas ≳ 500 km s⁻¹ and strongly supports the idea that feedback is operating in this galaxy.

The implied shock velocity of 580 km s⁻¹ can be used to estimate a size for the region influenced by the shock during the source lifetime. Assuming the source dynamical age of ∼33 Myr (Jamrozy et al. 2007), the calculated source size is consistent with the extension of the SLobe (∼20 kpc). We conclude that during the lifetime of the source, the whole SLobe region could indeed be shock heated.

We also comment on the northern X-ray emission region we identified as EArm. This structure is located outside and along the eastern boundary of the northern radio lobe and is slightly offset from the strongest radio emission. Interestingly, van Breugel et al. (1986) reported a large velocity jump (by ∼300 km s⁻¹) in the optical-line-emitting gas in this region. In an X-ray surface brightness profile across EArm (Figures 10 and 11), we found that the surface brightness increases by a factor of ∼2–2.5 at the location of EArm over the projected width of ∼3 kpc. Although it is tempting to associate the surface brightness increase as due to shock heating and compressing the background plasma, we were unable to constrain the temperature profile in this region in our current data. However, we note that EArm could be similar to the X-ray emission observed at the boundary of the southern lobe of Centaurus A (Kraft et al. 2007; Croston et al. 2009) where the evidence for the shock exists in a deep Chandra image. The shock in Centaurus A is resolved on parsec scales (1'' ∼18 pc) and the change in the surface brightness is measured across a ∼1 kpc region. The EArm "width" is much larger, and the enhancement covers about 3 kpc, but its morphology seems to relate this structure to the radio lobe. Future higher signal-to-noise data are necessary to properly assess the presence of a shock in the EArm feature.

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We conclude that signatures of weak shocks due to an expanding radio source are present in the X-ray data. The radio-emitting outflow in 4C+29.30 therefore clearly interacts with the ambient medium, not only accelerating denser and colder optical-line-emitting clouds present within the ISM as found before, but also heating and displacing the warm phase of its gaseous environment, thus providing strong evidence for a complex jet-related feedback in a post-merger galaxy. We note that interactions of a relativistic magnetized jet with a multi-phase ISM are rarely subjected to detailed numerical simulations (but see Krause & Alexander 2007; Sutherland & Bicknell 2007; Wagner & Bicknell 2011), even though the problem is particularly relevant in the context of high-redshift (z > 1) radio galaxies.

The intrinsic luminosity of the nucleus of 4C+29.30 of ∼10⁴⁵ erg s⁻¹ implies an accretion power of order ∼10⁴⁶ erg s⁻¹, assuming a standard value of 10% for the radiative efficiency. It also implies a mass of the central SMBH that exceeds ∼10⁸ M_☉. The observed non-thermal X-ray luminosities of the jet and hotspots put a strict lower limit on the source radio power of >10⁴¹ erg s⁻¹.

The minimum jet power can also be calculated from the radio measurements. The total energy of the southern radio lobe (tail) calculated under the equipartition condition is equal to E_ℓ ∼ 10⁵⁷ erg.¹⁴ The north and south radio structures (excluding the southern tail) have similar minimum energy estimates of ∼10⁵⁷ erg. If we now take the age of the radio source, t_j ∼ 30 Myr (Jamrozy et al. 2007), we can obtain a lower limit to the jet kinetic energy required to power the radio lobes of L_j ∼ E_ℓ/t_j ∼ 10⁴² erg s⁻¹. Interestingly, this is also the minimum power needed for heating the surrounding thermal gas required by our Chandra observations. The thermal energy in the diffuse X-ray-emitting component is E_th ∼ 10⁵⁶–10⁵⁷ erg, which is also in agreement with the minimum energy estimates for the radio structures given above and would require a continuous energy supply of ∼10⁴¹–10⁴² erg s⁻¹ over the radio source lifetime.

A total ionized hydrogen mass in the line-emitting clouds of 4C+29.30 estimated by van Breugel et al. (1986) is about ∼10⁶ M_☉ and their total kinetic energy is of order E_kin ∼ 10⁵⁴ erg. This is much smaller than the total energy deposited by the jets within the lobes. Thus, we can conclude that only a small fraction of the available jet power is needed to drive the gaseous optical outflow, while a much higher fraction (>10%) of the total jet power (∼10⁵⁶ erg) is used to heat the surrounding medium to the X-ray temperatures (>0.1 keV).

We can also compare the energy stored in the outer lobes formed during the previous outburst of the radio source to the current jet power. Approximating the outer lobes as a cylinder with a height h = 640 kpc and a radius r = h/4, the source volume is V = πr²h. Assuming the minimum energy magnetic field B = 0.7 μG (U_B = B²/8π) and lifetime t_out ⩾ 200 Myr given by Jamrozy et al. (2007), the required jet power is equal to L_j ∼ 2 U_B V/t_out ∼ 10⁴³ erg s⁻¹. This is a lower limit to the jet power in the previous outburst as the duration of the active phase might be shorter than t_out. However, this jet power indicates that the previous outburst of the jet activity might have been more powerful than the current one, in agreement with the powers derived for other double–double radio sources.