Pressure Balance and Energy Budget of the Nuclear Superbubble of NGC 3079

In this paper, we use three of the four Chandra archival observations covering NGC 3079 (ObsID 2038, 19307, 20947; ObsID 7851 is a snapshot observation with an effective exposure time of only 4.68 ks), with standard data calibration steps similar as those described in Li et al. (2019b; the Karl G. Jansky Very Large Array, VLA, radio image presented in Figure 1(a) is also described in this reference). The total effective exposure time is 124.2 ks after filtering out the abnormal count rate period. The exposure-corrected images are created using merge_obs with a bin size of 0.25 pixel (0123), adopting the Energy-Dependent Subpixel Event Repositioning algorithm (Li et al. 2004). The final background-subtracted and adaptively smoothed images in the 0.5–1.2 and 1.2–2.0 keV bands are presented in Figure 1(a).

As shown in Figure 1, the 0.5–1.2 keV emission from the superbubble shows some apparent coherent structures as the warm ionized gas traced by the Hα emission (see also in Cecil et al. 2002; Li et al. 2019b). The harder X-rays in 1.2–2.0 keV (black contours) concentrate at the base of the bubble on the galactic disk, which is probably associated with either the AGN or some nuclear starburst regions. There is a hard X-ray bright plume extending out of the nuclear region on the southwest side, which has been attributed to the synchrotron emission from the TeV CRs accelerated by the superbubble (Li et al. 2019b). We herein only focus on the extended soft X-ray emission on the northeast (NE) side, which is primarily from the hot gas.

We conduct spectral analysis of a few regions of prominent structures from the NE bubble (Figure 2(a)). Details of the spectral analysis, including the fitting models, uncertainties, and the derived physical parameters, are discussed in the Appendix. We herein only show an example of the spectra extracted from the entire NE superbubble after excluding the emission from the galactic nuclear region (Figure 2(b)). Apparently, the spectra from all the regions in the NE bubble are dominated by the thermal plasma with a characteristic temperature of kT ∼ 1 keV (Table 1; Figure 3).

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We also employ radio observations of NGC 3079 to probe the pressure of the magnetic field and the energy carried by the CR electrons in the superbubble. The radio data (Figure 1(a)) is taken from the Continuum Halos in nearby Galaxies—an EVLA Survey (CHANG-ES) project, observed with the VLA at C band (6 GHz) in C- and D-configurations and at L band (1.5 GHz) in B-, C-, and D-configurations. The details of this survey and data reduction are described in Irwin et al. (2012a, 2012b) and Wiegert et al. (2015). The D- (Wiegert et al. 2015) and B-configuration data (Irwin et al. 2019) are public, ¹ and the C-configuration data release is in preparation (R. A. M. Walterbos et al. 2024, in preparation).

We estimate the magnetic field strength of the NGC 3079 superbubble from the VLA radio observations. Estimating the magnetic field strength from the synchrotron emission requires an assumption on the energy equipartition between CRs and the magnetic field. This assumption is premised on an ideal scenario that CRs and magnetic field are strongly coupled and exchange energy until equilibrium is reached over a sufficient propagation timescale and length scale (typically ∼1 kpc; e.g., Beck & Krause 2005; Seta & Beck 2019). This length scale is comparable to the size of the superbubble in NGC 3079, so there is a risk that the energy equipartition assumption may not be satisfied. Under the energy equipartition assumption, Li et al. (2019b) estimated the magnetic field strength of ≈23 μ G for the NE bubble, leading to a magnetic pressure of ≈13 eV cm⁻³.

The SOFIA observations of the nuclear region of NGC 3079 were taken in February and March of 2017 with the Field-Imaging Far-Infrared Line Spectrometer (FIFI-LS; Klein et al. 2010; Fischer et al. 2018). The FIFI-LS observations cover four strong emission lines from ionized gas in two different channels: [O iii] λ58μm, [O iii] λ88 μm, [C ii] λ158 μm, and [N II] λ205μm. The [O iii] λ58 μm and [N ii] λ205 μm lines have too low signal-to-noise ratio (S/N), so we only focus on the [O iii] λ88 μm and [C ii] λ158 μm lines in the present paper. The [O iii] line was covered in the blue channel with a field of view (FOV) of ∼30''×30^'' and a spectral resolution of R ∼ 670, while the [C ii] line was covered in the red channel (FOV ∼1'×1', R ∼ 1200). The integral field spectra of the [O iii] and [C ii] lines combine over 30 and 50 exposures dithered in subpixel increments to boost the spatial sampling of the final data cube, which was resampled on a regular spatial grid with a pixel size of 1'' and 2'' for the [O iii] and [C ii] lines, respectively. The total effective exposure times are 1014 s and 1613 s for the two lines, respectively. The chop subtraction, flat correction, telluric correction, flux/wavelength calibration, and spectral rebinning are performed following the instrument data reduction pipeline.

We use a Python Graphical User Interface software SOSPEX (Fadda & Chambers 2018) to analyze the FIFI-LS data. We estimate the continuum level with a linear regression using the wavelength range with no significant line features on both sides of the emission lines. Such a continuum level is then subtracted from the data cube. We create the momentum maps by integrating the line emission in the velocity range of ±600 km s⁻¹ from the heliocentric velocity of NGC 3079 (v_helio = 1126 km s⁻¹, Hagiwara et al. 2004). The momentum maps are then cropped to discard the bad fittings with an intensity threshold of 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² for [O iii] and 2.5 × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² for [C ii]. The intensity maps of [O iii] and [C ii], as well as the velocity map of [C ii], are presented in Figure 1(b). Most of the far-IR line emissions concentrate in the nuclear region. As the highest-resolution [O iii] λ58μm line is lost, we cannot resolve the bubble with the existing [O iii] λ88μm and [C ii] λ158μm lines. The shorter wavelength [O iii] line is only firmly detected in the nuclear region, while it is quite marginal to use the stronger [C ii] line to study the spatial distribution of the ionized gas within the superbubble (Figure 1(b); the angular resolution of SOFIA at 158 μm is FWHM ∼13'', comparable to the size of the superbubble; Busch et al. 2018). Nevertheless, we found a [C ii] velocity gradient of ∼40 km s⁻¹ kpc⁻¹ on a larger scale along the major axis of the galaxy, which is consistent with a star-forming rotating disk.

The [C ii] line emission is the dominant coolant of the neutral interstellar gas, so often it is adopted as one of the best extinction-free tracers of the obscured star formation. There are a few factors affecting the accuracy of taking the [C ii] line as the star formation tracer, such as the presence of an AGN, the IR color of the galaxy, and the efficiency of converting the far-UV radiation into gas heating, etc. (e.g., Herrera-Camus et al. 2015). For example, in principle, the ionic emission lines could also be largely produced by the AGN. We measure the fluxes of the [O iii] and [C ii] lines from a circular region with a radius of 13'' centered at the galactic nucleus. The relatively low line ratio of [O iii]/[C ii] ∼ 0.1 disfavors a strong contribution from the AGN (Herrera-Camus et al. 2018). We then conclude that most of the line emission is produced by the starburst instead of the AGN. The [C ii] line flux in the central r = 13'' circle is 1.5 × 10⁴¹ erg s⁻¹, corresponding to an SFR of 1.3 M_⊙ yr⁻¹ (Herrera-Camus et al. 2015), which is consistent with the spatially resolved SFR estimate using the WISE 22 μm photometry (Vargas et al. 2018).

In this section, we examine the balance between the thermal pressure of the hot and warm gases, the radiation pressure provided by young stars, and the CR and magnetic pressures in and around the bubble. As summarized in Table 1, the thermal pressure of the hot gas in different parts of the NE superbubbble is in the range of (300–800) eV cm⁻³, with a reasonable assumption on the volume filling factor f_X ∼ 1. As the thermal pressure depends on f_X in the form of ${P}_{{\rm{X}}}\propto {f}_{{\rm{X}}}^{-1/2}$, the (300–800) eV cm⁻³ thermal pressure is a lower limit under the resolution of current X-ray observations. On the other hand, the density of the warm ionized gas measured from the [S ii] λ λ6717, 6731 doublets in the bubble is ≲10² cm⁻³ (Cecil et al. 2001), which results in a thermal pressure P_Opt ≲ 100 eV cm⁻³, assuming a typical warm gas temperature of T_e ∼ 10⁴ K. The thermal pressure of the hot gas could thus be about 1 order of magnitude higher than that of the warm ionized gas under current resolution of X-ray and optical observations.

We also made a rough estimate of the radiation pressure of the UV photons produced by the nuclear starburst. Adopting an SFR of 1.3 M_⊙ yr⁻¹ and the stellar synthesis model (e.g., STARBURST99, Leitherer et al. 1999) with the metallicity of NGC 3079, we obtain an ionizing photon luminosity typically in the range of L_ion ∼ (0.6 − 1.1) × 10⁴³ erg s⁻¹ for a continuous star-forming process. The uncertainties come from the adopted metallicity and stellar evolutionary models. If the ionizing photons are absorbed by the gas on the bubble shell and reemitted isotropically in the optical and infrared regime (without further processing by the dust), the radiation pressure on a spherical bubble shell should be (e.g., Lopez et al. 2014)

$$\begin{eqnarray}&&{P}_{\mathrm{rad}}=\displaystyle \frac{{L}_{\mathrm{ion},\mathrm{escape}}}{4\pi {r}^{2}c}=\displaystyle \frac{{f}_{\mathrm{esc}}{L}_{\mathrm{ion}}}{4\pi {r}^{2}c},\end{eqnarray} \tag{ 1 }$$

in which f_esc is the escaping fraction of the ionizing photons from the nuclear region. The radiation pressure from the nuclear starburst is then ∼10 eV cm⁻³ and (0.4–0.8) eV cm⁻³ at the base and top of the NE superbubble, assuming f_esc ∼ 1.0. As f_esc is <1, the estimated radiation pressure is an upper limit and significantly lower than the thermal pressure of the hot and warm gases. The above discussions do not consider the radiation pressure on the dust, which could be higher if the reprocessed IR emission is stronger. It is not quite clear how the dust is coupled with different gas phases and affects the dynamics of the superbubble.

As discussed in Section 2.1, the magnetic field strength and the corresponding magnetic pressure of the NE bubble are ∼23 μ G and ∼13 eV cm⁻³, respectively. This is generally consistent with estimates from other literature (e.g., Li et al. 2019b; Sebastian et al. 2019). Apparently, the magnetic pressure is lower than the thermal pressure of both hot and warm ionized gases. However, a direct comparison between them may be more complicated, as there is no one-to-one correlation between specific radio/X-ray/optical emitting structures. The radio lobe is significantly more extended than the X-ray and optical emission line bubbles (Figure 1), so we cannot rule out the possibility that there is a pressure balance between them at the radio "cap." Considering the overall spatial distribution of the multiwavelength emissions from the NE side (radio "cap" above the X-ray and optical emission line "bubble"), we conclude that the magnetic pressure could at least play a role (if not dominant) in the overall dynamics of the galactic nuclear superbubble in NGC 3079.

The above examination of the pressure balance in the NGC 3079 superbubble could be compared to those in active star-forming regions, such as 30 Doradus in the Large Magellanic Cloud. Pellegrini et al. (2011) found that in most parts of 30 Doradus the P_hot/P_warm ratio is ∼1–10, while the radiation pressure is generally not important compared to the thermal pressures (also see Barnes et al. 2020). Combined with our analysis for NGC 3079, we then conclude that in star formation regions of scale less than kiloparsec (including the galactic nuclear region), the gas expansion and outflow are mainly thermal pressure driven, with the possibility of being affected by the magnetic pressure.

In this section, we further compare the energy detected in the superbubble to different energy sources from the galaxy. According to our X-ray spectral analysis, the total thermal energy of the hot gas in the NE superbubble is ${E}_{\mathrm{th},\mathrm{hot}}\,\sim 1.4\times {10}^{55}\,{f}_{{\rm{X}}}^{1/2}\,\mathrm{erg}$. The hot-gas radiative cooling timescale is typically in the range of τ_cool ≈ (2–7) × 10⁷ yr of the resolved features (Table 1; even longer for unresolved lower surface-brightness features), which is longer than the dynamical age of ≲1 Myr of the superbubble (see the next paragraph in this section). Therefore, the radiation loss of the hot gas is negligible during the evolution of the superbubble. For comparison, Cecil et al. (2001) reported a kinetic energy of the warm ionized gas of ${E}_{{\rm{k}},\mathrm{warm}}\sim 3\times {10}^{54}\,{f}_{\mathrm{warm}}^{1/2}\,\mathrm{erg}$, where f_warm is the volume filling factor of the warm ionized gas. We then expect E_k,warm < < E_th,hot, especially considering that the optical emission line features may have f_warm < < 1. However, caution should be taken that we may have overestimated E_th,hot, as a significant fraction of the soft X-ray emission may come from nonthermal processes such as the charge exchange (Zhang et al. 2014) although these processes may not qualitatively change our conclusions on the energy budget.

Consistent with the above estimates, we then compare our measurements to the analytical model of the superbubble evolution in the intermediate stage, developed by Castor et al. (1975) and Weaver et al. (1977). This model accounts for a steady mechanical energy injection, and the growth of the bubble is driven by the adiabatic expansion of the shock-heated hot gas. The shocked ambient medium forms a dense shell around the hot bubble under the circumstance of rapid cooling. The age of the bubble in the adiabatic expansion stage is linked to the current radius and velocity in the following form:

$$\begin{eqnarray}&&{t}_{\mathrm{Myr}}=0.59{R}_{\mathrm{kpc}}/{v}_{\exp ,3},\end{eqnarray} \tag{ 2 }$$

where t_Myr, R_kpc, and ${v}_{\exp ,3}$ are the age in Myr, radius in kilopsarsecs, and expansion velocity in 10³ km s⁻¹, respectively. Adopting the velocity measured via the shift of optical emission lines (typically ∼(500–1000) km s⁻¹); Veilleux et al. 1994) and a radius of R = 0.75 kpc, we obtain the range of the age of the bubble t ∼ (0.4–0.8) Myr. On the other hand, the hot bubble model predicts that the thermal energy of the hot gas takes 5/11 of the total mechanical energy (Mac Low & McCray 1988). Therefore, the observed total amount of thermal energy of hot gas requires an average energy injection rate of ${\dot{E}}_{\mathrm{hot}}\approx (1.2\mbox{--}2.5)\times {10}^{42}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

We then estimate the energy provided by nuclear starburst and AGN. We use the stellar synthesis model STARBURST99 to estimate the mechanical energy injection rate in the case of a continuous star-forming process. At an SFR of ∼1.3 M_⊙ yr⁻¹ for the nuclear region of NGC 3079 (Section 2.2), the stellar synthesis model predicts a growing mechanical energy injection rate of ${\dot{E}}_{\mathrm{SF}}$ due to the accumulation of supernova events at the early stages. ${\dot{E}}_{\mathrm{SF}}$ stabilizes at ∼(5–6) × 10⁴¹ erg s⁻¹ at the age of ≳ 40 Myr. This ${\dot{E}}_{\mathrm{SF}}$ could thus be adopted as an upper limit of the star-formation energy injection, which is still below the required energy injection we estimated above, let alone the fact that the cold gas may carry kinetic energy of similar amount (e.g., Cecil et al. 2001). Besides that, the energy loss due to radiation, thermal conduction, or even breakout at the top of the superbubble may consume a significant fraction of the injected mechanical energy. Therefore, we conclude that current nuclear starburst is not powerful enough to drive the expansion of the superbubble.

The parsec-scale jet revealed by radio very long baseline interferometry observations may provide additional power to drive the superbubble. Shafi et al. (2015) reported a power of ${\dot{E}}_{\mathrm{jet}}\sim 4\times {10}^{41}$ erg s⁻¹ for the parsec-scale jet, according to its radio continuum luminosity and empirical relations (e.g., Bîrzan et al. 2008; Cavagnolo et al. 2010). This jet power, however, is still not enough to match the requirement of the observed hot-gas thermal energy of the superbubble. If neither the current nuclear starburst or the parsec-scale jet can be energetic enough to account for the observed hot-gas thermal energy, we speculate that the past AGN activity may help to inject more mechanical energy to drive the expansion of the nuclear superbubble. Such a scenario has also been employed to explain the "Fermi bubble" in the MW (e.g., Guo & Mathews 2012) and supported by the discovery of the ionization cones toward the Magellanic stream, which could be a fossil imprint of a powerful flare from the MW center (Bland-Hawthorn et al. 2013).