THE FERMI BUBBLES: SUPERSONIC ACTIVE GALACTIC NUCLEUS JETS WITH ANISOTROPIC COSMIC-RAY DIFFUSION

“The mass, momentum, total energy, and induction equations are solved by the Piecewise-Parabolic Method (PPM; Colella & Woodward (1984)) in the USM solver (Lee & Deane 2009; Lee 2012).”

“A.4 Nonlinear Shock Tube Test for a Composite of Thermal Gas and Cosmic Rays The Sod shock tube problem (Sod 1978) is a standard test for the accuracy of computational fluid codes, in particular the Riemann solver.”

“In order to incorporate cosmic rays in the simulations, we implemented a new CR module in the USM solver in FLASH4.”

“…extragalactic radio sources (e.g., Scheuer 1974; Blandford & Rees 1974) and CRfilled bubbles (e.g., Laing et al. 2006) observed in massive galaxies and galaxy clusters (McNamara & Nulsen 2007), though their gamma-ray emission cannot be easily detected due to limited sensitivity and resolution.”

“Assuming isotropic diffusion, typical values of the diffusion coefficient in the Galaxy is observationally constrained to be κiso ∼ (3 − 5) × 1028 cm2 s−1, which may depend on the magnetic field structure and CR energy (Strong et al. 2007).”

“For the simulated X-ray map, the X-ray emissivity in an energy range 1.4 − 1.6 keV is calculated using the MEKAL model (Mewe et al. 1985; Kaastra & Mewe 1993; Liedahl et al. 1995) implemented in the utility XSPEC (Arnaud 1996), assuming solar metallicity.”

“Furthermore, AGN jets are known to be responsible for radio synchrotron emission from extended extragalactic radio sources (e.g., Scheuer 1974; Blandford & Rees 1974) and CRfilled bubbles (e.g., Laing et al. 2006) observed in massive galaxies and galaxy clusters (McNamara & Nulsen 2007), though…”

“100 GeV, the IC cooling time of ∼ 100 GeV electrons poses a stringent upper limit to the age of the bubbles to be at most a few million years old (Su et al. 2010).”

“In simulations following magnetic fields the diffusion is treated anisotropically with one or two orders of magnitude lower diffusion coefficients along the magnetic field lines (Hanasz et al. 2013, Pakmor et al. 2016, Yang et al. 2012).”

“The formation of the bubbles can be modeled by emission of a jet from the black hole (Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012), a spherical outflow from the black hole (Zubovas et al. 2011), a wind from supernova explosions (Crocker & Aharonian 2011), or a sequence of shocks from…”

“Yang et al. (2012) are able to produce the observed O viii/O vii ratio and find that the shocked region of the bubbles is ∼108 K while the interior is 107–108 K.”

“We solve the magnetohydrodynamic (MHD) equations using the HLL3R method (Waagan 2009; Bouchut et al. 2010; Waagan et al. 2011), extended to a separate monoenergetic CR fluid similar to Yang et al. (2012).”

“In the extrinsic turbulence picture, i.e., f ≤ 1, the heating rate is −fuA · ∇pc Cosmic ray advection and coupling to the thermal gas is included in the simulations using the modules described in our earlier work (Yang et al. 2012, 2013).”

“Theoretically, models that incorporate self-regulated energy injections from the central supermassive black holes (SMBHs) successfully prevent run-away cooling (Sijacki et al. 2007; Cattaneo & Teyssier 2007; Dubois et al. 2010; Yang et al. 2012b).”

“…type of candidate positron source: It has been suggested that the Fermi bubbles are manifestations of recent jet activity of Sgr A* (Su & Finkbeiner 2012; Yang et al. 2012), and thus may be reminiscent of ordinary radio lobes in external galaxies (see A84, page 10 of 16 e.g. Mingo et al. 2012).”

“2 (Fryxell et al. 2000; Dubey et al. 2008) as extended to include cosmic rays (Yang et al. 2012; Yang et al. 2013; Yang & Ruszkowski 2017; Ruszkowski, Yang & Zweibel 2017) to solve the above equations.”

“Details of the CR physics module can be found in Yang et al. (2012) and Ruszkowski et al. (2017), where we discuss simulations the Fermi bubbles and CR-driven galactic winds, respectively.”

“…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. 2014; Wardle & Yusef-Zadeh 2014) from the…”

“It is worth remarking that the expansion velocity that we derived conflicts with the order-of-magnitude higher values advocated in the literature (Guo & Mathews 2012; Guo et al. 2012; Zubovas & Nayakshin 2012; Yang et al. 2012; Lacki 2013).”

“This wind age is consistent with the timescale of energy injection that created the FBs, whether via AGN jets (Guo & Mathews 2012; Yang et al. 2012), feedback from nuclear star formation (Crocker & Aharonian 2011; Carretti et al. 2013; Lacki 2014), accretion flows onto SgrA∗ (Cheng et al. 2011; Mou…”

“The method of initializing a tangled field is illustrated in Yang et al. (2012a) and Yang et al. (2013), to which we refer the readers for details.”

“(72) includes CR diffusion and streaming. The diffusion term is usually written as r (k recr), where k is the diffusion coefficient. For isotropic CR diffusion, the diffusion term can be rewritten as [418] r(krecr) = r(kkbb ecr)+r[k?(I bb)ecr]. (76) Galaxies 2018, 6, 1 26 of 47 where k is the diffusion tensor, the kkan…”

“Following equations (18) and (19) from Yang et al. (2012), we can estimate the timescales for the growth of both instabilities.”

“…with AGN jets have characteristic total energy injection rates and ages of & 1044 erg s−1 and ≈1–3 Myr (e.g., Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012, 2013), whereas simulations producing the bubbles from weaker AGN winds suggest values of 1041–1042 erg s−1 and 5–10 Myr (e.g.,…”

“…from some episode of energy injection at the GC, possibly associated with nuclear star formation processes (Crocker & Aharonian 2011; Carretti et al. 2013), or with past activity of the central AGN (Cheng et al. 2011; Zubovas & Nayakshin 2012; Guo & Mathews 2012; Yang et al. 2012, hereafter Y12).”

“This is different from current simulations of Sgr A⋆ outbursts, which assume that the gas in these regions was initially halo gas (e.g., Guo & Mathews 2012; Yang et al. 2012).”

“Outflows triggered by star formation in the Galactic centre (GC) region (Crocker 2012; Lacki 2014) and by the black hole at the GC (Guo & Mathews 2012; Yang et al. 2012; Mou et al. 2014) have been proposed for the dynamical origin of the FBs.”

“, [21-24]) and others have a starburst outflow (e.”

“…energetic magnetized plasma (see the discussion in Elmouttie et al. 1998; Mingo et al. 2012), while in the case of our Galaxy, it is supported by general energetic arguments and numerical simulations reproducing well the observed properties of bubbles (e.g., Guo & Mathews 2012; Yang et al. 2012).”

“CR advection and coupling to the gas are included using the same methods as in Ruszkowski et al. (2017) (see Yang et al. 2012, 2013; Sharma et al. 2009) with the CR streaming flux denoted by Fcr and an associated CR heating of the gas denoted by Hcr.”

“Yang et al. (2012) studied the reduction of the diffusion coefficient for Fermi bubbles by the latter.”

“…MI transport (e.g., Crocker & Aharonian 2011; Mou et al. 2014; Crocker et al. 2015), leptonic transport (e.g., Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012, 2013, the latter two are abbreviated as Y12 and Y13, respectively), and in-situ acceleration models (e.g., Mertsch & Sarkar 2011;…”

“Numerous works followed that similarly investigated injecting a combination of thermal energy and momentum [61,111] as well as works that considered purely kinetic jets [62,68,70,71,110] that were able to inhibit cooling and match a range of observed cluster properties.”

“…were created by some large episode of energy injection in the GC, such as an active galactic nucleus (AGN)like outburst (e.g., Guo et al. 2012; Yang et al. 2012) or from nuclear starburst activity (e.g., Lacki 2014) in the past with an energy release of 1055–56 erg over 10Myr ago (Su et al.…”

“Yang et al. (2012) simulate the onset of a CR-driven outflow comparable to the Milky Way Fermi bubbles using anisotropic CR diffusion.”

“Thirdly, the velocity of the jet required in the Yang et al. (2012, 2013) is very low, only ∼ 0.03c.”

“Several models have been proposed to explain both the morphology and spectral properties of the FBs (Cheng et al. 2011; Mertsch & Sarkar 2011; Crocker & Aharonian 2011; Crocker 2012, 2013; Zubovas et al. 2011; Zubovas & Nayakshin 2012; Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012).”

“We also use an additional cosmic ray module that evolves cosmic rays as a second, relativistic fluid in addition to the usual thermal gas (Yang et al. 2012; Ruszkowski et al. 2017).”

“…et al. 1991; Everett et al. 2008; Girichidis et al. 2016; Ruszkowski et al. 2017; Wiener et al. 2017), ionize the interstellar medium (Grenier et al. 2015), and contribute to the formation of the Fermi Bubbles (Guo et al. 2012; Yang et al. 2012) and the galactic dynamo (Hanasz et al. 2009).”

“In other models, CRs are carried by jets or outflows generated by the super-massive black hole at the GC (Zubovas et al. 2011; Guo & Mathews 2012; Yang et al. 2012) or they are accelerated in the bubbles (Mertsch & Sarkar 2011; Cheng et al. 2011).”

“Simulations of the Fermi bubbles as overpressured structures driven by bursts of AGN activity into the ambient interstellar medium were developed by Guo & Mathews (2012), Guo et al. (2012), Yang et al. (2012), and Yang et al. (2013).”

“First, AGN driven models in which the bubbles originate from a past accretion activity of the MW central black hole over a time scale of 3–12 Myr, with a luminosity of ∼ 2 × 1041–1043 erg s−1 , either via an accretion wind (AGNW) (Zubovas, King & Nayakshin 2011; Zubovas & Nayakshin 2012; Mou et al. 2014, 2015) or via…”

“To explain, then, the large extent and energy content of the Bubbles some models (e.g., Zubovas & Nayakshin 2012; Guo & Mathews 2012; Yang et al. 2012, 2013; Barkov and Bosch-Ramon 2013) hypothesise recent activity of the super-massive black hole at the Galactic Center (GC) with very fast transport…”

“However, while structures such as the Fermi bubbles may be indicators of past activity (Guo & Mathews 2012; Yang et al. 2012), the majority of the emission seen from the inner ∼30 pc is due to the dense complex of star-formation.”

“Their origin and nature is an active area of observational and theoretical research (see Dobler et al. 2010; Su et al. 2010; Crocker & Aharonian 2011; Yang et al. 2012; Ackermann et al. 2014; Yang et al. 2014; Crocker et al. 2015, and references therein).”

“Other active galactic nucleus (AGN) related explanations are given by Guo & Matthews (2012), Yang et al. (2012), and Zubovas et al. (2011).”

“They may drive galactic outflows, help form large-scale structures like the Fermi Bubbles (Guo et al. 2012; Yang et al. 2012), and play a role in galactic dynamos (Hanasz et al. 2009, and references therein).”

“…- (i) high luminosity (∼ 1042−44 erg s−1) wind driven by the central black hole (Zubovas et al. 2011; Guo et al. 2012; Zubovas & Nayakshin 2012; Yang et al. 2012; Yang & Ruszkowski 2017) requiring the age of FBs to be tage ∼ few Myr, (ii) low luminosity (∼ 2 × 1041 erg s−1) wind driven by…”

“We notethat even more energy can be released in the GC, ∼W 1056 erg, if a giant molecular cloud is captured by the black hole (see Zubovas & Nayakshin 2012; Yang et al. 2012).”

“…structures may suggest past large-scaled activities in the Galactic Center, such as active galactic nucleus jet activity (e.g., Guo & Mathews 2012; Yang et al. 2012), non-relativistic outflow from the nucleus (e.g., Zubovas et al. 2011; Zubovas & Nayakshin 2012; Mou et al. 2014), or wind driven…”

“This problem can be overcome using models based on the jet activity of the central active galactic nucleus where jet speeds of over 104 km s−1 are readily achievable (Guo & Mathews 2012; Yang et al. 2012).”

“…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).”

“The magnetohydrodynamic equations are extended by a mono-energetic, relativistic cosmic-ray fluid (Yang et al. 2012) in the advection- 6 SImulating the Life-Cycle of molecular Clouds, http://hera.ph1.uni-koeln.de/∼silcc/ 2 diffusion approximation as described in Girichidis et al. (2014).”

“In this regard, numerical hydrodynamical simulations of the Fermi bubbles were performed in 2D by Guo & Mathews (2012) and Guo et al. (2012) and 3D by Yang et al. (2012).”

“Bubbles arising from jets have been simulated by several authors (Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012); more recently, detailed simulations of the leptons in Active Galactic Nuclei (AGN) jets and the resulting inverse Compton and synchrotron signals have been carried out (Yang,…”

“Yang et al. (2012) successfully reproduced the morphology of the Fermibubbles and concluded that the suppression of magnetohydrodynamic (MHD) instabilities can be explained by a draped magnetic field layer.”

“…shape of the bubbles as observed in gamma-rays (Su et al. 2010; Ackermann et al. 2014) and used in the (M)HD simulations (Guo & Mathews 2012; Yang et al. 2012), leads us to employ toroidal coordinates (u, v, φ) which map to cartesian coordinates (x, y, z) through x = a sinh v cos φ cosh v −…”

“Competing theories for their origin involve either jets (or collimated outflows) from an active galactic nucleus (AGN) (75; 76; 77; 78), or the outflow from either a nuclear starburst or a prolonged high rate of star formation in the Galactic center (79; 80; 81; 82).”

“In one picture, the Fermi γ-ray bubbles are a relic of past AGN-like activity stimulated by accretion of stars or gaseous material onto the central supermassive black hole, Sgr A* (Zubovas, King and Nayakshin 2011; Cheng et al. 2011; Guo et al. 2012; Yang et al. 2012, 2013).”

“…cosmic rays (CRs) interacting with hot gas in the halo (Crocker & Aharonian 2011), to star bursts (Biermann et al. 2010), to AGN activity in our Galaxy (Guo & Mathews 2012; Guo et al. 2012; Yang et al. 2012; Cheng et al. 2011), to originating from dark matter annihilation (Dobler et al. 2011).”

“The boundary of the Fermi bubbles is generally determined by the CD, because the magnetic field in the post-shock ISM is parallel to the CD, which can bound the CRs inside the CD (Yang et al. 2012), or outside but close to the CD (Mou et al. 2015).”