Fermi Gamma-Ray “Bubbles” from Stochastic Acceleration of Electrons

“emission of a jet from the central black hole, wind from SN explosion close to the GC, 1st or 2nd order Fermi acceleration of CR electrons [143–147].”

“This model could be relevant in highly-turbulent environments, as exploited in [128] to study stochastic reacceleration inside the Fermi bubbles.”

“The CRs may be accelerated or reaccelerated in situ in these two bubbles (Mertsch & Sarkar 2011), but one potential problem for this scenario is to explain how turbulence is triggered roughly simultaneously in two bubble-shaped regions separated by such a large distance (∼ 10 kpc).”

“Various authors have proposed mechanisms for the origin of these energetic electrons, including, for example, recent (∼ 1–3 Myr ago) AGN jet activity from the central massive black hole [48–51], a spherical outflow [52], a sequence of shocks resulting from several accretion events (involving first order Fermi accelera…”

“For example, Mertsch & Sarkar (2011) argue that the spectral and morphological details of the emission are incompatible with hadronic radiation, leaving electrons as the main energy source.”

“Broadly speaking, the bubbles might be the signatures of a fairly recent (within a∼Myr timescale) explosive outburst (Su et al. 2010; Mertsch & Sarkar 2011; Zubovas et al. 2011; Guo & Mathews 2012; Yang et al. 2012; Zubovas & Nayakshin 2012; Fujita et al. 2013; Barkov & Bosch-Ramon 2014; Mou et al.…”

“On the other hand, Mertsch & Sarkar (2011) argued that the emission spectrum of the bubbles is inconsistent with CR protons and therefore the bubbles must be a recent, cosmic ray electron-powered, feature.”

“…(Crocker 2012; Crocker et al. 2014, 2015; Sarkar et al. 2015; Ruszkowski et al. 2016), or in-situ as the bubbles evolve (Cheng et al. 2011, 2015; Mertsch & Sarkar 2011; Fujita et al. 2014; Lacki 2014; Sasaki et al. 2015), and compare the non-thermal emission to the bubbles’ gamma-ray emission.”

“The precise mechanism of the γ-ray emission is unknown and, both, hadronic [71] and leptonic scenarios [72, 73] have been proposed in the literature as an explanation.”

“…the bubbles (∼10 kpc from the plane), these electrons either have to be delivered very quickly – presumably on a AGN-type outflow originating at Sgr A* (Guo & Mathews 2011) – or accelerated in situ by first- (Cheng et al. 2011) or second-order (Mertsch & Sarkar 2011) Fermi acceleration processes.”

“If there is turbulence within the wind bubble, second order acceleration might be able to solve this problem, but the model proposed by Mertsch & Sarkar (2011) proposes that the shock is growing instead of steadystate; any turbulence must be generated before the shock itself.”

“Also, similar distribution can produce radio emission in the galaxy [110, 114] due to the synchrotron radiation effect with the interaction of microgauss galactic magnetic field.”

“In contrast, models that are based on in-situ CR acceleration (Cheng et al. 2011; Mertsch & Sarkar 2011) assume that the shock fronts coincide with the bubble edges.”

“Mertsch & Sarkar (2011) argued that stochastic re-acceleration of CR electrons could account for the flat gamma-ray surface brightness if CR electrons are preferentially re-accelerated near bubble edges.”

“The high energy electrons or protons can either be accelerated in situ by internal shocks and turbulence (Mertsch & Sarkar 2011), or advected from the disc.”

“Although these models could bypass the age constraints, it has been challenging for the simplest models to produce the flat gamma-ray intensity profile (Mertsch & Sarkar 2011; Cheng et al. 2011) as well as the microwave haze emission (Fujita et al. 2014; Cheng et al. 2015).”

“[122] Philipp Mertsch and Subir Sarkar, “Fermi gammaray ‘bubbles’ from stochastic acceleration of electrons,” Phys.”

“This statement is nicely reinforced by the recent finding, in the Fermi data, of large scale bubbles extending away from the GC [131], to which astrophysical explanations have been proposed [131, 132, 133] — while the believer’s eyes could see a DM signal, as apparent as in Fig.”

“4 G, and there are independent estimates in the literature of B = 5–10 G [17] and B = 15 G [72].”

“Furthermore, as found by Mertsch & Sarkar (2011), for the required parameters to explain the gammas, the WMAP haze is underpredicted by an order of magnitude.”

“…to the current bubble location by either jets or winds, CRs can also be accelerated in situ by shocks (Keshet & Gurwich 2017; Cheng et al. 2011, 2015; Fujita et al. 2013, 2014; Lacki 2014) or turbulence (Mertsch & Sarkar 2011; Mertsch & Petrosian 2019; Cheng et al. 2014; Sasaki et al. 2015).”

“Others which include leptonic mechanisms or dark matter decay would produce lower neutrino emission or none at all [1,6,8–10].”

“…considered important for solar flares, γ-ray ? donnert@ira.inaf.it bursts and many other astrophysical environments (e.g. Hamilton & Petrosian 1992; Miller et al. 1996; Schlickeiser & Dermer 2000; Dermer & Humi 2001; Yan & Lazarian 2004; Chandran et al. 2010; Petrosian 2012; Mertsch & Sarkar 2011).”

“It could either be the forward shock or the reverse shock (Lacki 2014) or the contact discontinuity (Mou et al. 2015; Crocker et al. 2014b) or the region within the contact discontinuity (Mertsch & Sarkar 2011; Sarkar et al. 2015b).”

“In our model, CR electrons weakly accelerated at the shock are significantly reaccelerated in the turbulence (Markevitch et al. 2005; Mertsch & Sarkar 2011; ?”

“This arguments were used by (Mertsch & Sarkar 2011, SNS15) to assume that the FBs can be represented by the inner bubble extending all the way till the CD. Due to the lack of cosmic ray physics in the current simulations, I also follow the same arguments.”

“In a related issue, Mertsch & Sarkar (2011) showed that the gamma ray from the Bubbles can be produced by stochastic acceleration of electron throughout the Bubbles.”

“…from the central black hole, Sgr A*, in the past few million years (Su et al 2010; Guo & Mathews 2011; Zubovis et al 2011); the latter might be explained as due to all-pervading shocks (Cheng et al 2011) or distributed, stochastic, acceleration on plasma wave turbulence (Mertsch & Sarkar 2011).”

“…of electrons inside the bubbles itself, for instance, by multiple shock waves generated by periodic star capture by the central supermassive black hole (Cheng et al. 2011) or by second-order Fermi acceleration by the plasma wave turbulence present inside the bubbles (Mertsch & Sarkar 2011).”

“Phenomenological stochastic acceleration models have succeeded in reproducing photon spectra of blazars (Asano et al. 2014; Asano & Hayashida 2015; Kakuwa et al. 2015), and Fermi bubbles (Mertsch & Sarkar 2011; Sasaki et al. 2015).”

“…roughly a powerlaw from ∼1-1000 GeV suggesting that either the electrons have not had sufficient time to cool (the cooling time in this energy range is ∼ 106-107 yr; see Su et al. 2010) or are continuously being accelerated within the haze/bubbles (e.g., Dobler et al. 2011; Mertsch & Sarkar 2011).”

“The stochastic acceleration can be provided by interaction of charged particles with a hydromagnetic turbulence which is excited in the halo by jets (see e.g. Zubovas & Nayakshin 2012) or by a shock (as assumed by Mertsch & Sarkar 2011).”

“…Zubovas & Nayakshin 2012; Mou et al. 2014), or steady star-formation (Crocker 2012); and the CR acceleration mechanism as first-order Fermi accelera- tion, second-order Fermi acceleration (Mertsch & Sarkar 2011; Chernyshov et al. 2014), or injection at the GC (Guo & Mathews 2012; Thoudam 2013).”

“Stochastic Fermi acceleration in turbulent magnetic fields, inside the Bubbles, may yield the requisite population of high-energy electrons (Mertsch & Sarkar 2011; Cheng et al. 2014; Cheng et al. 2015).”

“Radio galaxies [2–7], clusters of galaxies [8–11], gamma-ray bursts [12, 13], extra-galactic large-scale jets [14, 15], blazars [16, 17], solar flares [18–20], the interstellar medium [21, 22], the galactic centre [23, 24], supernova remnants [25–27] and even the recently discovered “Fermi bubbles” [28] have been sugg…”

“A first SA model for the Fermi bubbles (Mertsch & Sarkar 2011) was presented quickly after their discovery.”

“Turbulent (re)acceleration behind shocks has beenconsidered for objects such as supernova remnants (e.g. Inoue et al. 2010; Zhang 2015) and the Fermi bubbles (e.g. Mertsch & Sarkar 2011; Sasaki et al. 2015).”

“If the volume emissivity is constant, the surface brightness should show a bump-like profile with gradually rising edges as a result of the projection effect (Mertsch & Sarkar 2011).”

“…can be provided either by a shock or shocks which are generated by tidal processes nearby the central black hole or by an MHD-turbulence which is excited behind a shock (for some aspects of the leptonic model see e.g. Cheng et al. 2011, 2014; Mertsch & Sarkar 2011; Yang et al. 2012, and others).”

“…& Nayakshin 2012; Mou et al. 2014), or steady star-formation (Crocker 2012); and the cosmic-ray (CR) acceleration mechanism as first order Fermi acceleration, second order Fermi acceleration (Mertsch & Sarkar 2011; Chernyshov et al. 2014), or injection at the GC (Guo & Mathews 2012; Thoudam 2013).”

“…the applied regression procedures (,see for instance Linden & Profumo 2010; Mertsch & Sarkar 2010, and) and proposing possible physical mechanisms (Bottino et al. 2010; Dobler et al. 2011; Guo et al. 2011; Guo & Mathews 2011; Biermann et al. 2010; Crocker & Aharonian 2011; Mertsch & Sarkar 2011).”

“While in the leptonic models, inverse Compton scattering of relativistic electrons on optical and UV photons produce the gamma rays [2,3,13,14].”

“…namely the inverseCompton scattering of interstellar radiation field and the cosmic microwave background by electrons (e.g. Cheng et al., 2011; Mertsch & Sarkar, 2011; Lacki, 2014) or the hadronuclear process of protons (and ions) colliding with ambient gas in the bubbles (e.g. Crocker &…”

“In spite of its low efficiency, stochastic acceleration may be essential for particle acceleration in solar flares (see e.g., Miller et al. 1990; Petrosian 2012), in the interstellar medium of the Galaxy (Berezinskii et al. 1990) and near the Galactic center (see e.g., Mertsch & Sarkar 2011).”

“Re-markably, random time-varying environments or fluctuating force fields have been identified as a major driving force for particle acceleration in outer space, explaining the existence of high-energy cosmic rays [28–31].”

“…has been invoked to model the origin of high-energy particles and radiation in extreme environments as diverse as the Galactic center [2–4], accretion flows [5–11] and black hole coronae [12–15], extragalactic jets [16–22], intracluster gas [23–27], gamma-ray bursts [28–31], pulsar…”

“Finally, the study of quantum Fermi acceleration [8, 30] could be a promising avenue for quantum information science, as there is concrete potential for the development of new tools for the manipulation of quantum wavepackets .”

“If the real bubble age is around 4 Myr, to keep their hard spectra CR electrons in the Fermi bubbles should be continuously reaccelerated by the second order Fermi acceleration (Mertsch & Sarkar 2011) or other mechanisms, unless the gamma ray emission from the bubbles is dominated by CR protons.”

“This activity may be leptonic (Cheng et al. 2011; Crocker et al. 2011; Mertsch & Sarkar 2011; Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012; Carretti et al. 2013; Lacki 2014) or hadronic (Crocker & Aharonian 2011; Crocker et al. 2011; Lacki 2014; Crocker et al. 2015).”

“…VHE particles has been proposed for a wide variety of astrophysical objects, including — with a highly incomplete list of references — black hole accretion discs [3], galactic outflows [4], galaxy clusters [5], large-scale relativistic jets [6] and compact object mergers [7], among (many) others.”

“In order to explain the γ -ray emission from the FBs, a re-acceleration of electrons is necessary (Mertsch and Sarkar 2011).”

“However, despite these challenges, more involved diffuse acceleration models supporting a scenario in which both the radio and gamma-ray emission are leptonic in origin are currently viable [27].”

“[20], the electron spectrum was computed analytically by using a hierarchy of times-scales: For the parameters adopted the dynamical time was found to be always larger than the acceleration and energy-loss times, such that the electron spectrum would be in a quasi steady-state at fixed distances from the (expanding) s…”

“However, this can be overcome in the case that there is reacceleration due to turbulence inside the bubble outflow [58], or if the electron transport is dominated by fast advection (with speed & 10 000 km s−1) [57].”

“Other which include leptonic mechanisms or dark matter decay exclude the neutrino emission or yield lower fluxes [Su et al., 2010; Lacki, 2013; Chernyshov et al., 2011; Mertsch and Sarkar, 2011; Dobler et al., 2011].”

“…given the vast extension of the Bubbles, these electrons either have to be delivered very quickly – presumably on an AGN-outflow originating at Sgr A* (Guo & Mathews(2011)) – or accelerated in-situ by first (Cheng et al.(2011)) or second-order (Mertsch & Sarkar(2011)) Fermi acceleration processes.”

“While some authors have criticized the original analysis procedure [7], or the synchrotron nature of the haze [8], both arguments have been rebutted in detail [9, 10].”

“Despite such challenges, however, more involved diffuse acceleration models supporting a scenario in which both the radio and γ-ray emission are leptonic in origin are also presently viable [21].”

“Alternatively, Mertsch and Sarkar[26] assumed that this emission is produced by electrons in-situ accelerated by MHD-turbulence behind the shock.”

“In order to reproduce the spatial distribution of γ-ray emissivity in the bubble Mertsch & Sarkar (2011) assumed arbitrarily that: a) the acceleration is nonuniformly distributed inside the bubbles and its efficiency increases near the shock which excited the MHD-turbulence inside the bubble; b)…”