Active Galactic Nucleus Jet Model of the Sgr A Lobes at the Galactic Center

Li Sida 1,2, Guo Fulai 1,2

(1. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China; 2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China)

Volume 43, Issue 3, September 2025

Progress in Astronomy

Vol. 43, No. 3 Sept., 2025

doi: 10.3969/j.issn.1000-8349.2025.03.06

Keywords: Active Galactic Nuclei; Jets and Outflows; Bubbles; Interstellar Medium

China Library Classification: P145.2 Document Code: A

Received: 2024-09-01; Revised: 2024-10-14

Funding Projects: National Natural Science Foundation of China (12473010); CAS Project for Young Scientists in Basic Research (YSBR-061); Shanghai Branch of Chinese Academy of Sciences "Basic Research Special Zone Program" Project (JCYJ-SHFY-2021-013); Scientific Research Funding of China Manned Space Engineering Survey Space Telescope Special Project (CMS-CSST-2025-A10)

Corresponding author: Guo Fulai, fulai@shao.ac.cn

This version posted 2025-10-10.

1 Introduction

Multiple observational evidences indicate the existence of a supermassive black hole of approximately 4 × 10⁶𝑀⊙ at the Galactic center (Sgr A)[1, 2]. The evolution of supermassive black holes is associated with numerous extreme high-energy physical processes, potentially including outflow phenomena that inject substantial mass and energy into the surrounding environment. Although recent observational results show that Sgr A is currently in a relatively quiescent state, its historical active phases may have significantly influenced the gas distribution of the Milky Way across different temporal and spatial scales. For instance, the famous Fermi bubbles, with heights of approximately 10 kpc, might have been formed by AGN-driven outflows propagating through the circumgalactic medium (CGM) of the Milky Way several million years ago[3–7].

On a smaller spatial scale, recent X-ray and radio observations have discovered a pair of 15 pc high elliptical bubbles [8–11]. This pair of bubbles is commonly referred to as the Sgr A lobes. Both the Chandra and XMM-Newton telescopes have observed and analyzed the X-ray radiation from the hot gas in the bubble regions, indicating that the temperature of this hot gas ranges from 0.7 to 1.0 keV[8–10]. The surface brightness of the X-rays and the pressure of the hot gas in the bubbles decrease with increasing galactic latitude, suggesting that these outflowing gases are moving away from the galactic disk.

The bubble also has very clear boundaries, indicating that its outer boundary may be a shock wave generated by an outflow. Meanwhile, considering its perpendicular orientation to the silver disk and the symmetric characteristics about the Galactic center suggest that outflows originating from the region very close to the supermassive black hole at the center of the Milky Way are responsible for generating this pair of bubbles.

Possible mechanisms. The outflow phenomena that may produce such bubble structures can be divided into two categories: quasi-persistent outflows, including stellar winds from stars around the Galactic center black hole and past AGN jets; and intermittent explosive events, including tidal disruption events (TDEs) of the Galactic center black hole and supernova explosions of individual stars at the Galactic center[12]. Regarding the evolutionary process of supernova explosions occurring in the Galactic center environment, some hydrodynamic simulation studies have provided certain analyses[13, 14]. From their simulation results, it can be seen that the energy injected into the environment by a single supernova explosion is sufficient to produce a bubble structure of about 15 pc in size. However, since the supernova explosion process is nearly spherically symmetric energy injection, even with the confinement by stellar winds from other stars or gas disks, it is difficult to explain the formation of the highly symmetric double elliptical bubbles of the Sgr A lobes. Considering that the timescale for stellar winds at the Galactic center is much longer than the age of the Sgr A lobes, the model of continuous energy injection via stellar winds to form bubbles also faces challenges. Tidal disruption events of the black hole can generate strong winds and/or jets, injecting sufficient energy into the black hole's surrounding environment within a very short time to form the Sgr A lobes, making it a possible mechanism to explain their origin[15]. Currently, there are no specific research works on the AGN jet model for this pair of bubbles; therefore, in this paper, we choose to investigate the model where shocks generated by jets from the Galactic center black hole serve as the cause of the bubbles. Similar models can be used to explain the famous Fermi bubbles in the Milky Way[6].

X-ray observations indicate that the internal energy within the Sgr A lobes is on the order of 10⁴³ J [8, 10]. Since the specific velocity of the outflow is unknown, the precise age of the bubbles cannot be determined; however, assuming the bubbles expand at the sound speed 𝑐𝑠 ≈ 500 km·s⁻¹, their age is approximately 3 × 10⁴ years [10], which can serve as an upper limit for the bubble age to constrain model parameters. In theoretical studies, the duration of AGN jets is typically on the order of millions of years, but the jet duration required to explain the formation of these bubbles using an AGN jet model is only on the order of a few hundred years—a value significantly lower than conventional estimates. However, recent observational evidence suggests that AGNs may indeed produce short-timescale, low-energy jet phenomena [16]. X-ray observations of molecular clouds in the Galactic center direction also indicate that these X-ray photons from molecular clouds may originate from the black hole region and reach Earth after being reflected by the molecular clouds, suggesting that the Galactic center black hole may have experienced a highly active phase in the recent past, with X-ray luminosity variability timescales far shorter than millions of years [17, 18]. Near the Galactic center black hole, candidate jet structures have also been identified in X-ray observations [19, 20]. These observational pieces of evidence collectively indicate that AGNs may produce the jets required by our model.

Another aspect supporting the plausibility of AGN jet models is the supply of accretion disk material. The numerous Wolf-Rayet stars in the galactic center region serve as potential material sources. These stars are in a phase of extremely strong stellar winds, typically lasting about 10⁵ years. Studies on the stellar winds of these Wolf-Rayet stars indicate they could indeed have played significant roles in past activities of the galactic center black hole and influenced the distribution of hot gas within 1 pc around the black hole[21–23]. Furthermore, supermassive black holes can capture material from molecular clouds or massive stars to form accretion disks. In this paper, we temporarily assume the existence of such an accretion disk, the specific material sources will not be discussed in detail.

In our work, we investigate the evolution of short-timescale AGN jets in the Galactic center environment through numerical simulations of fluid dynamics, and discuss whether they can serve as a formation mechanism for the Sgr A lobes. As a research basis, we compare the simulation-derived characteristics of the Fermi bubbles and Sgr A lobes, including their temperature, density, morphology, and X-ray surface brightness distribution. In Chapter 2, we introduce the basic setup of the numerical simulations. Chapter 3 compares the simulation results with observations, and finally, Chapter 4 provides a summary and discussion on certain issues related to the AGN jet model.

2 Research Methods

2.1 Simulation Basic Setup

We assume the entire simulated system is axisymmetric and employ the hydrodynamics simulation program ZEUS-MP[24] in two-dimensional spherical coordinates.

Solve the following system of equations:

\begin{cases}
+ 𝜌∇ · 𝒗 = 0
\[\frac{d\rho}{dt}\]
\[\rho\frac{d\boldsymbol{v}}{dt} = -\nabla P - \rho\nabla\Phi\]
\[\frac{\partial e}{\partial t} + \nabla \cdot (e\boldsymbol{v}) = -P\nabla \cdot \boldsymbol{v}\]
(1)

Among them, $\rho$, $\bm{v}$, $P$, $\Phi$, $e$, and $t$ represent density, velocity, pressure, gravitational potential, internal energy density, and time, respectively. Since the Sgr A lobes are overall perpendicular to the galactic disk and symmetric about the galactic center, we assume that the AGN jet injection is axisymmetric with respect to the Milky Way's rotation axis. Considering the density and temperature ranges of the hot gas in the galactic center and the bubble gas, their radiative cooling timescales are much longer than the gas age of the bubble, therefore, we neglect the radiative cooling term in the energy equation. Finally, we assume that all the gas is an ideal gas, satisfying ⟪P = k_B T ρ / (μ m_μ) = k_B T n⟫, where ⟪k_B⟫ is the Boltzmann constant, ⟪m_μ⟫ is the atomic mass unit, ⟪μ = 0.61⟫ is the mean molecular weight per particle, and ⟪T⟫ and ⟪n⟫ represent the temperature and number density of the gas, respectively.

During the solution process, we established 600 exponentially growing grids in the 𝑟 direction and 400 uniform grids in the 𝜃 direction. In the 𝑟 direction, the position of the supermassive black hole Sgr A* was taken as the coordinate origin, with the inner grid boundary at 0.1 pc and the outer boundary at 30 pc, and Δ𝑟𝑖+1/Δ𝑟𝑖 = 1.007, indicating that the radial width of each grid is 0.7% larger than that of the previous grid. At the radial inner boundary, an inflow boundary condition was applied during the jet injection period, which was changed to an outflow boundary condition, the same as the outer boundary, after the jet ceased. Due to the symmetry of the system, we only need to simulate the jet evolution on one side, so the grid in the 𝜃 direction was set from 0◦ to 90◦, with reflective boundary conditions applied at both the inner and outer boundaries.

2.2 Gravitational Potential and Initial Gas Distribution

Observations indicate that the height of the Sgr A lobes is approximately 15 pc. Within a 20 pc radius around the black hole, the gravitational potential is dominated by the black hole itself and the nuclear stellar cluster. Therefore, in our simulations, we adopted a constant gravitational field composed of these two components. For the black hole's gravitational potential, we used the Newtonian gravitational field generated by a point source with mass 𝑀BH = 4 × 10⁶𝑀⊙. For the nuclear stellar cluster, we employed the gravitational potential model given in reference [25], where 𝛷 = 0.5𝑣² with 𝑅𝑐 = 2 pc, and 𝑟 denotes the radial coordinate.

(c + r^2)), where (v_0 = 98.6) km·s(^{-1}), 0lg(𝑅2)

In the Galactic Center environment, the interaction between pre-existing diffuse gas and material contributed by stellar winds from the nuclear star cluster collectively forms the circumnuclear medium (CNM) we assume existed prior to the jet's presence. Current observations cannot provide information on the distribution of the CNM before the bubble's existence. For simplicity, we assume that this medium was in hydrostatic equilibrium and its density followed an exponential distribution:

(2)
$n_r = n_0$
$n(r) = n_0 \left( \frac{r}{r_0} \right)^{-0.7}$ where $n_0 = 50$ cm$^{-3}$, $r_0 = 0.1$ pc.

When solving for hydrostatic equilibrium, we assume the gas temperature at $r = 50$ pc is $5 \times 10^6$ K. This density distribution and the resulting temperature distribution are consistent with X-ray observations and Wolf-Rayet stellar wind simulations in this region within 1 pc [21, 23, 26]. It should be noted that the exponent in Eq. (2) lacks clear observational constraints; the initial density distribution directly affects the simulated bubble's density and radiation intensity, and leads to changes in the required jet parameters. Within the 0.1 ∼ 1.0 pc range, the steady-state solution under the Wolf-Rayet stellar wind assumption gives an exponent of approximately −2. In this paper, we adopt −0.7 to ensure that the simulated gas density inside the bubble matches observational values, which is a weak constraint on the gas density in the simulated region. If we were to maintain the −2 exponent, the bubble density would be significantly lower than observed values, and its radiation would consequently be substantially lower than observed. Therefore, we select the parameter combination in Eq. (2) so that the hot gas density in the inner region is close to observational values or values from stellar wind solutions, while beyond 1 pc, most regions of the bubble can provide sufficient material to ensure that the resulting bubble density and radiation match observational values. However, more rigorous initial density and temperature distributions still require further research.

2.3 Jet Configuration

We utilize the inflow boundary condition in the ZEUS-MP code to implement jet injection. During the jet duration, the boundary condition at the inner boundary of the grid in the 𝑟 direction is set to the inflow boundary condition, and within the ghost zones, the density, energy density, and velocity of the jet are specified for grid cells within the jet half-opening angle. After the jet ceases, the inflow boundary condition is changed to an outflow boundary condition.

In our primary AGN simulation, we assume that the jet direction is perpendicular to the galactic disk. Black hole jets are related to black hole spin, but the spin direction of the Galactic Center black hole is difficult to determine, which may pose a problem for AGN jet models. The jet duration is set to 500 years, and the jet half-opening angle is taken as 10°, meaning that within the grid from 0° to 10°, the density of the jet material is set to ρ = 5 × 10⁻²⁴ g·cm⁻³, the temperature to 10⁸ K, and the radial velocity of the jet to a constant value of 1.1 × 10¹⁰ cm·s⁻¹. The selection of jet parameters is primarily aimed at satisfying the observed properties of the Sgr A lobes. With this setup, the resulting total jet mass is 4 × 10⁻³ M⊙, and the total energy is 4.8 × 10⁴³ J.

3 Simulation Results

3.1 Bubble Evolution

The density and temperature distributions during the early and middle stages of the simulation are shown in Figure 1. After jet injection, a distinct shock front forms, and the shock front outer contour corresponds to the bubble's outline in the simulation. During the jet's active duration, the jet material undergoes multiple backflows, forming several recollimation shocks. After the jet ceases, at 𝑡 = 600 a, the shock has reached a height exceeding 10 pc in the 𝑧-direction. The overall shock front exhibits a slightly wider base and an elongated slender shape, which is consistent with most jet simulation results. Due to the absence of subsequent energy injection, the velocity of the jet material begins to decrease significantly, gradually concentrating at the apex of the shock wave, after which there is continuous backflow of material toward the base of the bubble. By 𝑡 = 1 500 a, a complex low-density region has formed in the lower half of the bubble, which is the area shaped by multiple intricate backflows. Overall, although the height of the shock front shows only a slight increase, however, as the jet material accumulates at the top and is accompanied by backflow and thermalization, the proportion of energy used for lateral expansion increases. Consequently, the width of the shock front shows a significant increase during this period, and the overall morphology gradually approaches the elliptical shape indicated by observations of Sgr A lobes.

Figure 1. Simulated density and temperature distributions of bubbles.

Note: From left to right are the density and temperature distributions of the simulated central region at 200, 600, and 1,500 a, respectively.

When the jet evolved to 𝑡 = 3 500 a, the shock front reached a height of 15 pc, and the overall morphology closely resembled the observed bubble structure. Figure 2 displays the density and temperature distributions of the simulated bubble at this stage. The high-density region along the bubble's outer contour represents the dense shell formed by compressed hot gas after the shock swept through the CNM, while a high-temperature, low-density cavity formed inside the bubble.

Figure 2 shows the density (a)) and temperature (b)) distributions of bubbles at 𝑡 = 3 500 a in the simulation.

The simulated bubble profile still differs from the observed profile, which may originate from uncertainties in the jet parameters. The width of the shock front is influenced by multiple factors. For instance, our parameter study reveals that jets with higher total mass and lower velocity decelerate and thermalize at higher altitudes, generating backflows that result in a broadening of the shock front in these regions. Large-scale AGN jet studies also indicate that variations in the jet's own power lead to changes in the width of the shock front [27].

3.2 Comparison with X-ray Observations

In this section, we obtain the thermal X-ray emission of bubbles through simulations, compare the resulting X-ray surface brightness with observational values, and then discuss the plausibility of AGN jet models as the origin of the bubbles. We assume that the hot gas in the simulations is optically thin and in collisional ionization equilibrium, and read the X-ray emissivity of the plasma in the 2 ∼ 4.5 keV energy range based on the astrophysical plasma emission code (APEC) [28]. The X-ray surface brightness is expressed as:

𝐼 (𝑥, 𝑧) = \( n e^{n H_{\epsilon}(T, Z)} dy \),
(3)
1 4π

Here, (n_e) and (n_{\text{H}}) are the number densities of electrons and hydrogen ions, respectively, and (\epsilon) is the emission coefficient obtained from APEC, which is a function of temperature (T) and metallicity (Z), with metallicity set to solar abundance. To calculate the surface brightness of X-ray radiation, we selected a spatial range of (-10) to (10) pc in the (y)-direction, projected the fluid density onto a uniform Cartesian grid with a width of (0.05) pc, and integrated along the (y)-direction as the line of sight. To compare with XMM-Newton observations, we converted the resulting X-ray radiation units to "(5 \times 10^{-5} \, \text{s}^{-1} \cdot \text{pixel}^{-1})". For this conversion, we adopted the parameters of the XMM-Newton telescope: an angular area per pixel of (4'' \times 4''), and an effective area in the (2) to (4.5) keV range approximated as a fixed value of (1,000 \, \text{cm}^2). Due to the distribution of neutral hydrogen along the line of sight, which absorbs a significant portion of the X-ray radiation, we assumed that (75\%) of the photons are absorbed. This absorption fraction corresponds to a neutral hydrogen column density range of (N_{\text{HI}} = (5 \sim 7) \times 10^{22} \, \text{cm}^{-2})[9], which is close to the neutral hydrogen column density values used in XMM-Newton observations ((N_{\text{HI}} = (6.3 \sim 8.0) \times 10^{22} \, \text{cm}^{-2}))[8]. Regarding the adopted neutral hydrogen column density, estimates from different observational methods vary, and our value is slightly lower than the column density estimated by Ponti et al. using dust[9].

Figure 3 Two-dimensional X-ray surface brightness distribution based on simulation results

Figure 3 displays the two-dimensional X-ray surface brightness distribution we calculated, where the white bright spots represent the outline of the Sgr A lobes observed by Chandra. The radiation calculated based on the simulation results is comparable to the XMM-Newton observations, and the bubble outline is consistent with the observed structure.

After calculating the radiation values, we can also provide the radiation-weighted average bubble temperature and density, respectively, as 𝑇ave = 1.02 keV, $n_{\text{ave}} = 6.23$ cm$^{-3}$, both of which are consistent with the results given by X-ray observations \cite{8, 10}.

Figure 4 Comparison of X-ray surface brightness distribution along the $z$-direction with observations

Note: Data are from XMM-Newton observations [8].

4 Summary and Outlook

In this paper, we analyze the possibility of AGN jet models as a formation mechanism for the Sgr A lobes at the Galactic Center through numerical simulations of fluid dynamics. A shock front generated by a single AGN jet lasting 500 years, when evolved to 3,500 years, can reproduce the observed bubble properties in terms of morphology, temperature, density, X-ray surface brightness, and other aspects. Based on current observational data, the AGN jet model can be considered a candidate formation mechanism for the Sgr A lobes.

However, relying solely on our simulation results cannot fully prove that the formation of Sgr A lobes originates from the shock evolution of AGN jets. On one hand, TDE outflows also possess the capability to form bubbles on the scale of Sgr A lobes; on the other hand, X-ray observations reveal several bright patch structures in the bubbles that are approximately symmetrically distributed about the galactic center. The specific origins of these radiative structures require further in-depth analysis, as our thermal X-ray radiation model alone is insufficient to explain them. Additionally, the short-timescale AGN jet model faces a significant issue: the required 500-year duration of jet activity in the model is shorter than the timescales indicated by the vast majority of AGN observations. Although some observations suggest that the galactic center black hole may have recently experienced a rapidly varying active phase, this is insufficient to demonstrate that the galactic center black hole Sgr A* previously erupted with a jet lasting only 500 years. There are numerous potential sources of material for the accretion disk that produces jets, such as stellar winds from a series of Wolf-Rayet stars in the galactic center, or partial mass stripping from certain massive stars by the black hole. Assuming a 10% energy conversion efficiency—meaning 10% of the accreted material's energy is converted into jet kinetic energy—the corresponding black hole accretion rate is approximately 10⁻⁵ M⊙/yr, corresponding to an Eddington ratio of 10⁻⁴. From simulations of Wolf-Rayet stellar winds, it is known that the Wolf-Rayet phase typically lasts 10⁵ years, and these stellar wind materials may have participated in past activities of the galactic center black hole [23]. However, based on existing observational evidence, we cannot determine the specific source of the accretion disk.

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