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REVIEW 5 major objections 7 minor 118 references

Sources and Radiations of the Fermi Bubbles

T0 review · 5 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper concludes that the Fermi Bubbles' gamma-ray and microwave glow comes from cosmic-ray electrons re-accelerated inside the bubbles, with protons contributing negligibly.

desk verdict A transparent synthesis of a decade of the authors' Fermi Bubble models, with a new but unquantified RT-turbulence-to-Alfven-wave link; worth reading as a review, not as a new result. read the letter →

arxiv 2411.14916 v1 pith:DO3VQT56 submitted 2024-11-22 astro-ph.HE

Vladimir A. Dogiel , Chung-Ming Ko This is my paper · ORCID
classification astro-ph.HE
keywords GalacticCenterFermiBubblestidaldisruptioneventsMHDturbulencestochasticre-accelerationcosmic-rayelectronsgamma-rayemissionmicrowavehaze
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to explain where the Fermi Bubbles come from and what makes them shine, arguing that routine tidal disruptions of stars by the Galactic center black hole release enough energy to drive an expanding cavity through the halo. Its central conclusion is that the observed gamma-ray and microwave radiation from the bubble envelope is generated by cosmic-ray electrons alone, with the proton contribution negligible. The preferred route is that GeV electrons from supernova remnants in the disk are re-accelerated in situ inside the bubbles to TeV energies by magnetohydrodynamic turbulence, and that a divergent outflow makes the re-accelerated spectrum reproduce both the Fermi-LAT and Planck data. If true, the bubbles are a leptonic, turbulence-powered system, and the same framework also lets protons escape the bubbles to account for the cosmic-ray spectrum from the knee to the ankle.

What carries the argument

The argument is carried by a chain: a Kompaneets-type hydrodynamic solution for a shock envelope expanding into an exponential halo, powered by repeated tidal disruption events; Rayleigh-Taylor instability at the accelerating top of the bubble, which destroys the thin swept-up shell and injects hydrodynamic turbulence with a Kolmogorov-Obukhov spectrum; the Lighthill mechanism, which converts part of that hydrodynamic turbulence into Alfvén waves; and a kinetic equation for cosmic rays whose spatial and momentum diffusion coefficients are derived from the MHD wave spectrum, yielding the re-accelerated electron spectra compared with Fermi-LAT and Planck data. The paper is explicit that the numerical values of the diffusion coefficients could not be independently calculated, because no observation of the wave spectrum in the Fermi Bubble envelope exists.

What would settle it

Measure the spectrum of magnetic fluctuations inside the bubble envelope, for example through Faraday rotation variations or radio scintillation across the bubble, and check whether it is strong enough to re-accelerate GeV electrons to TeV energies; alternatively, find a hadronic signature such as a pion-decay feature in the gamma-ray spectrum, which would falsify the claim that the emission is purely leptonic.

Watch

Extended reading notes

Core claim

The central claim is that the nonthermal gamma-ray and microwave emissions of the Fermi Bubbles are generated by cosmic-ray electrons only. The electrons are not freshly accelerated at a strong shock: the observed eROSITA shell moves at Mach number roughly 1.5, too weak for efficient diffusive shock acceleration. Instead, GeV electrons supplied by supernova remnants in the Galactic disk are re-accelerated in situ inside the bubble envelope by stochastic Fermi acceleration in magnetohydrodynamic turbulence, reaching about $10^{12}$ eV, with adiabatic losses in a divergent outflow shaping the spectrum so that it simultaneously fits the Fermi-LAT gamma-ray spectrum and the Planck microwave haze. The same supersonic-turbulence framework re-accelerates protons that escape the bubbles, producing the cosmic-ray spectrum from $10^{15}$ eV to several $10^{18}$ eV observed at Earth.

Load-bearing premise

The load-bearing premise is that the thin swept-up bubble shell remains turbulent enough for Rayleigh-Taylor instabilities to drive a turbulence cascade that couples to Alfvén waves with an efficiency of order unity, even though the wave spectrum inside the Fermi Bubble envelope has never been observed.

Editorial extensions

If this is right

  • If the leptonic re-acceleration model is correct, the gamma-ray and microwave emission share a single electron population, so their spectra should track each other as the bubble evolves.
  • The same turbulence-driven re-acceleration engine should operate in any large stellar-disruption-powered outflow, not just the Milky Way's.
  • The low Mach number of the eROSITA shell rules out shock acceleration at the bubble surface; acceleration must be stochastic and in-situ.
  • Protons re-accelerated by supersonic turbulence inside the bubbles and escaping to the disk would account for the cosmic-ray spectrum between the knee and ankle, making the bubbles a source of Galactic cosmic rays above $10^{15}$ eV.
  • The required re-acceleration power of about $2\times10^{38}$ erg s$^{-1}$ is a small fraction of the $3\times10^{41}$ erg s$^{-1}$ available from tidal disruption events, keeping the energy budget self-consistent.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An extension the paper leaves implicit: mapping Faraday rotation fluctuations across the bubble would probe the MHD wave spectrum directly, and a spectrum too steep to re-accelerate GeV electrons to TeV energies would contradict the leptonic engine.
  • A further implication: the re-acceleration model predicts a spatial gradient in the gamma-ray spectrum across the bubble as the balance of re-acceleration and adiabatic cooling shifts with height; future gamma-ray observations could look for that gradient.
  • If escaping protons from the bubbles really make the knee-to-ankle cosmic-ray component, the composition of cosmic rays in that energy range should reflect the bubble's seed population and magnetic field, giving a compositional test.
  • The same turbulence-to-Alfvén-wave-to-re-acceleration chain should apply to nuclear outflows in other galaxies whose shocks are too weak for diffusive shock acceleration, predicting electron-dominated gamma-ray and radio lobes in such systems.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 7 minor

Summary. The paper proposes a unified model of the Fermi Bubbles: repeated tidal disruption events at the Galactic center power an outflow whose envelope is shredded by the Rayleigh-Taylor instability; the resulting hydrodynamic turbulence radiates Alfvén waves through the Lighthill mechanism, and those waves stochastically re-accelerate cosmic-ray electrons injected by supernova remnants. The re-accelerated electrons are then claimed to produce both the Fermi-LAT gamma-ray and Planck microwave spectra, while re-accelerated protons escape to contribute to the cosmic-ray spectrum from the knee to the ankle. The central quantitative statement is in Section 8.2, where a set of transport parameters is said to reproduce the observed spectra, and in Section 10, where the authors conclude that the nonthermal bubble emission is purely leptonic.

Significance. If quantitatively established, the model would be a significant synthesis because it connects TDE-driven outflows, Rayleigh-Taylor instability, MHD turbulence, and cosmic-ray transport into a single framework and makes a sharp, testable claim that the gamma-ray and microwave emissions share one leptonic population. The paper is commendably candid about its main gap: Section 6 and the summary explicitly state that the wave spectrum in the bubbles is unobserved and that numerical values of the diffusion coefficients could not be derived from it. That candor is a strength, but it also means the successful spectral comparison in Section 8.2 is a fit, not an independent prediction, and the re-acceleration engine remains unquantified. The paper is therefore best read as a synthesis of prior work by the same authors and their collaborators, with the new contribution being the explicit RT-Lighthill-Alfvén chain and its asserted consequences.

major comments (5)
  1. [§6, §8.2] The central in-situ re-acceleration mechanism is unquantified: the momentum diffusion coefficient Dp = κp² used in Eq. (72) is not derived from the wave spectrum, and Section 6 explicitly states that the authors were unable to estimate numerical values for the bubbles because of the lack of available observation on the wave spectrum. The value κ = 2×10⁻¹⁴ s⁻¹ quoted in §8.2 is therefore selected so that the re-accelerated electron spectrum matches the same gamma-ray and microwave data it is meant to explain, making the agreement a fit rather than a test of the model.
  2. [§5, Eq. (35)] The Lighthill Alfvén-wave power in Eq. (35) scales as ηA (v/vA) ρ v³ k, so the injected wave power depends on the magnetic Mach number MA = v/vA; the manuscript never computes the RT-driven turbulent velocity v or MA in the bubble envelope. Since the quoted Alfvén speed is vA ≈ 3×10⁷ cm/s, the authors should provide an order-of-magnitude estimate of v and MA from Eq. (18), because if MA ≲ 0.1 the wave power available for re-acceleration drops by more than an order of magnitude relative to the order-unity estimate.
  3. [§8.2, Eq. (73)] The required re-acceleration power Ḏ ≈ 2×10³⁸ erg/s in §8.2 is estimated numerically from the observed gamma-ray and microwave fluxes, but it is never compared with the power available from the RT-driven turbulence, e.g., Eq. (18), or from the Lighthill radiation, Eq. (38). Without this energy-budget comparison, the paper does not demonstrate that the proposed engine can supply the electron population that produces the observed radiation.
  4. [§7, §8.2] The paper quotes inconsistent magnetic-field values: Section 7 lists the envelope magnetic field as B ∼ 8 μG, while the successful fit in Section 8.2 uses B = 3 μG. Because the synchrotron emissivity, the Alfvén speed, and the Lighthill power all depend on B, the manuscript should explain which value applies, whether they refer to different regions, and how sensitive the spectral fit is to this choice.
  5. [§9.1, §10] The claim that cosmic-ray protons escaping the bubbles explain the observed spectrum from the knee to the ankle is presented as a conclusion in Section 10, but Section 9.1 itself warns that the underlying numerical result of Cheng et al. (2012) 'has free parameters and some physics have been ignored' and 'might not be very solid.' The current paper does not supply the missing physics or a sensitivity analysis, so this part of the summary is not supported beyond the earlier work that the authors themselves qualify as tentative.
minor comments (7)
  1. [§10] In the final bullet of Section 10, 'greaterorsimilar' is a LaTeX error and should read '≥'.
  2. [Abstract, §10] The typesetting of '10 −4 ∼ 10−5 yr−1' in the abstract and '10 52 ∼ 1053 erg' in Section 10 is broken and should be fixed.
  3. [Figure 7] The axis labels in Figure 7 are garbled (e.g., '1. /Multiply 10 /Minus 16'), making the momentum diffusion coefficient plot difficult to read.
  4. [§5, Refs] The text and reference list use 'Hendriksen' for what is usually spelled 'Henriksen'; please harmonize the spelling throughout.
  5. [§1] The embedded YouTube links in Section 1 are not appropriate for a journal article and should be removed or replaced with proper references.
  6. [§3, §4] The symbol λ is used both for the Rayleigh-Taylor perturbation wavelength in Eq. (14) and for the turbulence eddy scale in Section 4; this notational overlap can confuse the derivation.
  7. [§8.2, Fig. 11] The caption of Figure 11 should state explicitly how the five curves are normalized and whether the gray band includes systematic uncertainties in the gamma-ray flux.

Circularity Check

3 steps flagged · score 7.0 of 10

The FB gamma-ray/microwave 'reproduction' is a self-admitted fit: Dp and Ė are estimated from the observed fluxes, then said to be reproduced; the preferred model also inherits its success from a same-group citation.

  1. fitted input called prediction [Section 6, paragraph after Eq. (54); Section 8.2, paragraph beginning 'In the phenomenological model...']
    "At present we are unable to derive reliable numerical values of these coefficients, and try to estimate roughly these parameters from the data ignoring the equation for the origin of MHD turbulence needed for CR scattering and propagation. ... In the phenomenological model, the power, ˙E, is estimated numerically from the observed FB gamma-ray and microwave fluxes, and it is about ˙E ∼ 2 × 10^38 erg s−1."

    The diffusion coefficients entering the re-acceleration equation (Eq. 72, Dp = κp²) are not computed from the RT-turbulence/Lighthill wave spectrum; the paper states it cannot. They and the required power are instead estimated from the observed FB gamma-ray and microwave fluxes. The successful 'reproduction' of those same fluxes in Fig. 8 is therefore a fit to the target data, not a prediction from the physical mechanism.

  2. self citation load bearing [Section 8.2, paragraph beginning 'Cheng et al. (2015b) showed...']
    "Cheng et al. (2015b) showed that the gamma-ray and radio emissions of the re-accelerated electrons reproduced nicely the Fermi-LAT and Planck data points for the parameters: the spatial diffusion coefficient Ds = 10^29 cm2 s−1, the energy loss rate ν = 2 × 10−16 s−1 GeV−1, the velocity gradient of the advection in the halo v′ = 10−15 s−1, the magnetic field strength is B = 3 µG, the thickness of the re-acceleration region (say, the FB envelope) is about ∆rFB = 60 pc, and the parameter of re-acceleration in the FBs is κ = 2 × 10−14 s−1."

    The central claim that the re-acceleration model 'reproduced nicely' Fermi-LAT and Planck data is imported from Cheng et al. (2015b), a paper by the same group (Cheng, Chernyshov, Dogiel, Ko). The parameter values quoted are the fitted ones, not derived in the present paper. Thus the paper's preferred conclusion leans on a self-citation carrying the fit rather than on externally verified evidence.

1 more flagged steps
  1. fitted input called prediction [Section 10, Summary bullets]
    "We estimated roughly the spatial and momentum diffusions of cosmic rays in the envelope from the data of gamma-ray and microwave radiations from the Fermi bubbles. We concluded that the observed gamma-ray and microwave radiations from the envelope of the Fermi Bubbles are generated by cosmic ray electrons only."

    The summary openly derives the transport coefficients from the gamma-ray and microwave radiations whose origin is the object of the conclusion. Estimating the electron population from the observed gamma-ray flux and then concluding that electrons (not protons) generate that gamma-ray flux is a self-definitional loop: the input data are the output claim.

full rationale

Most of the hydrodynamic machinery (Kompaneets envelope propagation, Rayleigh-Taylor instability, Lighthill radiation) is standard material and is not itself circular. The paper also invokes some genuinely external constraints: the eROSITA shock Mach number of about 1.5 disfavors strong diffusive-shock acceleration at the bubble surface, and the hadronic p-p model is rejected because its secondary-electron synchrotron spectrum is too soft and its normalization is too low. Those arguments give the leptonic-vs-hadronic discussion some independent content. However, the paper's preferred leptonic model is not independently predicted. Sections 4-6 do not deliver numerical values for the momentum-diffusion coefficient κ, the wave power, or the Alfvén-wave injection; Section 6 explicitly says the authors are 'unable to derive reliable numerical values' and instead estimate the parameters from the very gamma-ray and microwave data. Section 8.2 then fixes κ = 2e-14 s^-1, computes the required power from the observed fluxes, and normalizes the electron density to the observed gamma-ray flux. Reproducing Fig. 8 is therefore a fit to the same data, not a test. The 'reproduction' is also inherited from Cheng et al. (2015b), a same-group paper, so the self-citation is load-bearing for the central conclusion. This is partial but real circularity of the central claim, hence 7 rather than 0-2; it is not 10 because the hadronic exclusion and eROSITA shock-speed reasoning provide some independent, non-circular support, and the paper openly labels the model phenomenological.

Assumptions & free parameters 9 free parameters · 7 assumptions · 0 invented entities

All physically important inputs are either fitted to the very data the model claims to explain (Section 8.2 parameters and Edot) or imported from the authors' prior papers and galaxy-cluster turbulence literature. There are no new entities, but the chain from RT instability to Kolmogorov turbulence to Lighthill radiation to cosmic-ray acceleration is assumed without direct validation.

free parameters (9)
  • Average GC power input Edot = ~3e41 erg/s
    Adopted from Ko et al. 2020, formed from TDE energy 1e52 to 1e53 erg times a rate of 1e-4 to 1e-5 per year; the model needs this value to support the bubbles.
  • Spatial diffusion coefficient D_s = 1e29 cm^2/s
    Chosen in Section 8.2 to reproduce the gamma-ray and microwave spectra of the re-accelerated electron model.
  • Energy loss rate coefficient nu = 2e-16 s^-1 GeV^-1
    Chosen in Section 8.2 for synchrotron and inverse Compton losses in the re-acceleration model.
  • Halo advection velocity gradient v' = 1e-15 s^-1
    Chosen in Section 8.2 to harden the electron spectrum enough to fit the Planck and Fermi-LAT data.
  • Magnetic field B = 3 uG
    Chosen in Section 8.2 for the re-accelerated electron model; differs from the 8.4 uG best-fit value used in the IC model from Ackermann et al. 2014.
  • Thickness of re-acceleration region Delta r_FB = 60 pc
    Chosen in Section 8.2 as the size of the re-acceleration region in the bubble envelope.
  • Momentum diffusion coefficient kappa = 2e-14 s^-1
    Chosen in Section 8.2 to define the Fermi re-acceleration strength; the resulting spectra are matched to the observed data.
  • Initial RT perturbation seed lambda(y0) = 0.01 d(y0)
    Used in Eq. 14 to set the turbulence pumping scale and therefore the injected turbulent power; no independent measurement is provided.
  • Lighthill radiation efficiency eta_A = order unity
    Set to order unity in Eq. 35 following Kato 1968; not independently measured for Fermi Bubble parameters.
assumptions (7)
  • domain assumption The halo gas distribution is exponential with scale height H = 2 kpc and base density n0 = 4e-3 cm^-3 (Eq. 1).
    Used throughout Section 2 to compute the bubble envelope evolution; the alternative beta-model is mentioned but not adopted.
  • domain assumption The strong-shock Kompaneets formalism describes the Fermi Bubble envelope evolution.
    Equations (3) to (9) are taken from prior works and assume strong shocks and an adiabatic index gamma_g for the halo gas.
  • standard math Rayleigh-Taylor instability growth is described by Eqs. (12) to (14) using the acceleration at the top of the bubble.
    Standard fluid instability theory, but applying it to the thin swept-up shell assumes the shell remains a coherent fluid interface.
  • domain assumption Hydrodynamic turbulence in the envelope follows the Kolmogorov-Obukhov spectrum (Eq. 16).
    Section 4 assumes a universal inertial-range spectrum without direct observational or numerical support for the Fermi Bubble envelope.
  • domain assumption Lighthill radiation converts hydrodynamic turbulence into Alfven waves with order-unity efficiency (Eqs. 35 to 38).
    Section 5 adopts this mechanism from galaxy cluster literature; no direct test in the Fermi Bubble envelope is provided.
  • domain assumption The cosmic-ray transport equation (Eq. 54) with momentum diffusion and advection is the correct description for the bubble envelope.
    Standard cosmic-ray kinetic theory, but the spatial and momentum diffusion coefficients are not independently known; Section 6 says numerical values cannot yet be derived.
  • domain assumption Tidal disruption event rate is about 1e-4 to 1e-5 per year and each event releases 1e52 to 1e53 erg.
    Taken from Ko et al. 2020 and Stone and Metzger 2016; the budget Edot ~ 3e41 erg/s depends on this rate and energy per event.

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Cite this review

Pith. "Pith review of Sources and Radiations of the Fermi Bubbles." pith.science (2026). https://pith.science/paper/DO3VQT56

@misc{pith2026241114916,
  author       = {Pith},
  title        = {Pith review of: Sources and Radiations of the Fermi Bubbles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DO3VQT56}},
  note         = {Machine review of arXiv:2411.14916}
}
read the original abstract

Two enigmatic gamma-ray features in the Galactic central region, known as Fermi Bubbles (FBs), were found from Fermi-LAT data. An energy release (e.g., by tidal disruption events in the Galactic center, GC), generates a cavity with a shock that expands into the local ambient medium of the Galactic halo. A decade or so ago, a phenomenological model of the FBs was suggested as a result of routine star disruptions by the supermassive black hole in the GC which might provide enough energy for large-scale structures, like the FBs. In 2020, analytical and numerical models of the FBs as a process of routine tidal disruption of stars near the GC were developed, which can provide enough cumulative energy to form and maintain large scale structures like the FBs. The disruption events are expected to be ten to hundred events per million years, providing the average power of energy release from the GC into the halo of 3E41 erg/s, which is needed to support the FBs. Analysis of the evolution of superbubbles in exponentially stratified disks concluded that the FB envelope would be destroyed by the Rayleigh-Taylor (RT) instabilities at late stages. The shell is composed of a swept-up gas of the bubble, whose thickness is much thinner in comparison to the size of the envelope. We assume that hydrodynamic turbulence is excited in the FB envelope by the RT instability. In this case, the universal energy spectrum of turbulence may be developed in the inertial range of wavenumbers of fluctuations (the Kolmogorov-Obukhov spectrum). From our model we suppose the power of the FBs is transformed partly into the energy of hydrodynamic turbulence in the envelope. If so, hydrodynamic turbulence may generate MHD-fluctuations, which accelerate cosmic rays there and generate gamma-ray and radio emission from the FBs. We hope that this model may interpret the observed nonthermal emission from the bubbles.

Figures

Figures reproduced from arXiv: 2411.14916 by the authors.

Figure 1
Figure 1. Two superbubbles in the galaxy NGC 3079 observed in X-ray (purple and pink). Image obtained from https://chandra.harvard.edu/photo/2019/ngc3079 . Im￾age credit: X-ray: NASA/CXC/University of Michigan/J-T Li et al.; Optical: NASA/STScI. The total energy needed to generate large Galactic outflows is assumed to be in the range up to about 1056 erg. This energy release in the GC may be com￾pelling evidence for a huge en… view at source ↗
Figure 3
Figure 3. A thermonuclear explosion in the terrestrial at￾mosphere. Image credit: United States Department of En￾ergy. Image from https://commons.wikimedia.org/wiki/ File:Castle Bravo nuclear test (cropped).jpg . Kahn (1998), Baumgartner & Breitschwerdt (2013), Ko et al. (2020) and Schulreich & Breitschwerdt (2022) developed analytical solutions of a hydrodynamic model for the shock wave propagation in non-uniform atmo￾sphere… view at source ↗
Figure 4
Figure 4. Illustration of the double-bubble shock envelope in the halo evolving with time. The gas distribution in the halo in the left panel is exponential and in the right panel is power-law. Figure adapted from Ko et al. (2020) with permission. with r(z, t) or r(z, y) as the bubble radius at the altitude z, ρ0 = n0mp is the mass density corresponding to n0 (the number density at the base z = 0), E is the energy released by… view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: Temporal variation of the shock velocity of the top of the bubble for the case of exponential halo with H = 0.67 kpc and n0 = 0.03 cm−3 . Left panel: One single input of energy from the GC. Right panel: Multiple TDEs with different values of the power release at the GC…
Figure 6
Figure 6. Figure 6: Density distribution of numerical simulations of the FBs in an exponential halo. The two panels on the left column are results of multiple explosions (e.g., TDEs) and the right column are results of a single huge explosion. In the upper left panel, “Me0.05-3e52erg 18.0…
Figure 7
Figure 7. Figure 7: The solid line shows the momentum diffusion coefficient derived for the bubble parameters when the CR absorption is taken into account. The dash-dotted line is the results ignoring the CR absorption. Figure reproduced from Cheng et al. (2014) with permission. momenta p…
Figure 8
Figure 8. Figure 8: Spectrum of radio (left) and gamma-ray (right) emission from the FBs (see Cheng et al. 2014). The microwave data was taken from Planck Collaboration (2013), and gamma-ray from Ackermann et al. (2012, 2014). Figure adapted from Cheng et al. (2014) with permission. 7.2. …
Figure 9
Figure 9. Figure 9: X-ray emission from the Galactic plane whose excess emission is above the equilibrium Maxwellian spec￾trum. Dash-dotted line is a simple combination of ther￾mal plus nonthermal spectrum. Solid line is the spectrum with the effect of runaway flux. Figure reproduced from…
Figure 10
Figure 10. Figure 10: The spectrum of electrons accelerated from background plasma (see Chernyshov et al. 2012). The solid line is the density of electrons, f(p). The thick solid line is the pure thermal Maxwellian distribution. The dashed line is the power-law approximation of the nonther…
Figure 11
Figure 11. Figure 11: The spectrum of SNR electrons from the Galactic disk that have been re-accelerated in the FBs. The five spectra in the figure correspond to different cases of the model: (1) thick solid line: without re-acceleration, es￾cape and advection; (2) thick dash-dotted line: …
Figure 12
Figure 12. Figure 12: CR spectrum at the Earth as a combination of the contributions from the SNRs in the Galactic disk and the stochastic acceleration in the FBs. Figure reproduced from Cheng et al. (2012) with permission [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: A possible multiple-shock structure in the FBs resulting from multiple TDEs at the GC. The figure shows the pressure (left panel) and kinetic energy (right panel) dis￾tributions of a numerical simulation of the FBs in an expo￾nential halo. In the panels, “Me0.05-1e53”…

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