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).”

“The energy input from these jets may have altered the properties of the multiphase gas in the Galactic bulge and halo, suppressed the accretion process, and regulated the co-evolution of the SMBH and the stellar bulge in the past.”

“However, the general success in reproducing the observed X-ray features provides a strong support for the hypothesis that both the Fermi bubbles and the ROSAT X-ray features originate from the same episode of jet activity from the central SMBH.”

“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…”

“In many situations where f is nearly isotropic in momentum space, f can be solved as a function of only r, |p|, and t (Skilling 1975; Miniati et al. 2001).”

“…pair of gamma-ray jets recently discovered by Su & Finkbeiner 2012), the detection of the Fermi bubbles, together with indications of past activity (Koyama et al. 1996; Revnivtsev et al. 2004), suggest that the central SMBH may have regularly undergone cycles of jet activity, or even was at a much…”

“Jets from SMBH are generally thought to carry magnetic field, as it plays an important role in jet collimation and acceleration (see Ferrari (1998) and references therein), and as suggested by observations of lobes of radio galaxies (Owen et al. 2000; Kronberg et al. 2001; Croston et al. 2005).”

“Cosmic rays may stream through thermal gas in regions where the magnetic field is locally aligned, with streaming speed limited by the Alfvén speed (Skilling 1971; Kulsrud 2005).”

“Moreover, such strong wind would have dominated over the gravitational restoring force (McCarthy et al. 2008) and stripped a significant amount of Milky Way gas away.”

“In this paper we adopt a more simplistic approach, which is to treat cosmic rays as a second fluid and solve directly for the evolution of CR pressure pcr as a function of r and t (Drury & Voelk 1981; Jones & Kang 1990; Ryu et al. 2003; Mathews & Brighenti 2008; Rasera & Chandran 2008).”

“The population of CR electrons is invoked to explain the hard-spectrum microwave synchrotron radiation spatially-correlated with the Fermi bubbles observed by the Wilkinson Microwave Anisotropy Probe (WMAP), also known as the ‘WMAP haze’ (Finkbeiner 2004; Dobler & Finkbeiner 2008; Dobler 2012).”

“Jets from SMBH are generally thought to carry magnetic field, as it plays an important role in jet collimation and acceleration (see Ferrari (1998) and references therein), and as suggested by observations of lobes of radio galaxies (Owen et al. 2000; Kronberg et al. 2001; Croston et al. 2005).”

“One may ask whether this is linked to the enhanced 511 keV radiation observed in the Galactic bulge (see a review by Prantzos et al. 2011).”

“One of the most important findings from the first two years of Fermi Gamma-ray Space Telescope observations are two large bubbles extending to ∼ 50◦ above and below the Galactic center (GC), with a width of ∼ 40◦ in longitude (Su et al. 2010; Dobler et al. 2010).”

“Jets from SMBH are generally thought to carry magnetic field, as it plays an important role in jet collimation and acceleration (see Ferrari (1998) and references therein), and as suggested by observations of lobes of radio galaxies (Owen et al. 2000; Kronberg et al. 2001; Croston et al. 2005).”

“21 Similarly, for the case of a hybrid fluid consisting of thermal gas and cosmic rays, an analytical solution of the shock tube problem has been derived by Pfrommer et al. (2006).”

“…from the decay of neutral pions produced during inelastic collisions between cosmic ray (CR) protons and thermal nuclei (the ‘hadronic’ model; Crocker & Aharonian 2011), and/or from inverse Compton (IC) scattering of photons in the interstellar radiation field (ISRF) and the cosmic…”

“In many situations where f is nearly isotropic in momentum space, f can be solved as a function of only r, |p|, and t (Skilling 1975; Miniati et al. 2001).”

“AGN are also considered to be a viable agent for distributing the fields into the intergalactic medium (IGM) and intracluster medium (ICM) by relativistic jets (e.g., Koide et al. 1999; Contopoulos et al. 2009; Sutter et al. 2012).”

“The population of CR electrons is invoked to explain the hard-spectrum microwave synchrotron radiation spatially-correlated with the Fermi bubbles observed by the Wilkinson Microwave Anisotropy Probe (WMAP), also known as the ‘WMAP haze’ (Finkbeiner 2004; Dobler & Finkbeiner 2008; Dobler 2012).”

“…not necessarily aligned with the rotational axis of the galactic disks, and such misalignments are observed frequently in other galaxies (e.g., Middelberg et al. 2004; Giroletti et al. 2005; Gallimore et al. 2006; Kharb et al. 2010), and also recently found in the Milky Way (Su & Finkbeiner 2012).”

“The total pressure is ptot = (γ−1)eth+(γcr−1)ecr+B2/8π, where eth is the internal energy density of the gas, γ = 5/3 is the adiabatic index for ideal gas, and γcr = 4/3 is the effective adiabatic index of cosmic rays in the relativistic regime (Jubelgas et al. 2008).”

“…= 1 κ‖,i,j + 1 κ‖,i+1,j , 2 κ⊥ = 1 κ⊥,i,j + 1 κ⊥,i+1,j , (A9) and the transverse flux is sloped-limited in order to avoid negative CR energy densities when there is a large gradient (Sharma & Hammett 2007), ∂ecr ∂y = L { L [ ∂ecr ∂y ∣ ∣ ∣ ∣ i,j−1/2 , ∂ecr ∂y ∣ ∣ ∣ ∣ i,j+1/2 ] , L [ ∂ecr ∂y ∣…”

“Studies of ram pressure stripping of dwarf spheroidal galaxies orbiting the Milky Way give constraints to the value of ne,floor to be around 2.4 × 10−5 − 2.5 × 10−4 cm−3 (Blitz & Robishaw 2000; Grcevich & Putman 2009).”

“…recently discovered by Su & Finkbeiner 2012), the detection of the Fermi bubbles, together with indications of past activity (Koyama et al. 1996; Revnivtsev et al. 2004), suggest that the central SMBH may have regularly undergone cycles of jet activity, or even was at a much more active state…”

“Jets from SMBH are generally thought to carry magnetic field, as it plays an important role in jet collimation and acceleration (see Ferrari (1998) and references therein), and as suggested by observations of lobes of radio galaxies (Owen et al. 2000; Kronberg et al. 2001; Croston et al. 2005).”

“…not necessarily aligned with the rotational axis of the galactic disks, and such misalignments are observed frequently in other galaxies (e.g., Middelberg et al. 2004; Giroletti et al. 2005; Gallimore et al. 2006; Kharb et al. 2010), and also recently found in the Milky Way (Su & Finkbeiner 2012).”

“The fB is essentially a free parameter, and therefore in our simulations it is set such that the order of magnitude of the resulting magnetic field in the end of the simulations is consistent with observed values of & 50 µG at the GC (Crocker et al. 2010).”

“…of hot gas with temperature T ∼ 106 K extending out to the virial radius of the Milky Way halo with a scale height of a few tens of kpc (Blitz & Robishaw 2000; McCammon et al. 2002; Rasmussen et al. 2003; Fang et al. 2006; Bregman & Lloyd-Davies 2007; Grcevich & Putman 2009; Miller & Bregman 2012).”

“Because of the magnetic draping effect (Lyutikov 2006), the field lines are stretched and compressed in the draping layer, causing field alignment with the bubble surface as well as amplification of field strength.”

“…the main simulation code and is generated by 3D inverse Fourier transform (FFT) of magnetic field that, in k-space, has an amplitude given by (Ruszkowski et al. 2007) Bk ∝ k−11/6 exp(−(k/k1)4) exp(−k2/k), (12) where k = (k2x+k 2 y+k 2 z) 1/2, and k1 and k2 are the cutoff wavenumbers for…”

“Bending of radio jets in some cases can be explained by external ram pressure as galaxies move through an intracluster gas (e.g., Begelman et al. 1979; Balsara & Norman 1992).”

“The amount of cosmic rays that could be accelerated inside the shocks could be roughly estimated based on shock properties in our simulations and an assumed model for diffusive shock acceleration (Enßlin et al. 2007).”

“The anisotropic CR diffusion terms in the total energy and CR energy equations are updated explicitly using fluxes computed from the conservative ‘centered asymmetric differencing’ scheme (Parrish & Stone 2005; Sharma & Hammett 2007).”

“…to be due to some combination of fieldline wandering due to a random field component and magnetic field structure on scales less than the CR gyroradius, which allows the cosmic rays to migrate from one fieldline to another (Duffy et al. 1995; Jokipii 1999; Enßlin & Vogt 2003; Hauff et al. 2010).”

“Assumptions and Numerical Techniques We perform 3D MHD simulations of CR injections from the GC using the adaptive-mesh-refinement (AMR) code FLASH4 (Fryxell et al. 2000; Dubey et al. 2008).”

“…slower and wider jets are required to fulfill the constraints from the observed line ratios (§ 2.3), implying that the relativistic jets from the AGN may have slowed down a little by interacting with the interstellar medium during propagation from pc to kpc scales (e.g., Middelberg et al. 2004).”

“These values are unreasonably large for estimated properties of the Local Group (e.g., McConnachie et al. 2007; Cox & Loeb 2008).”

“…of hot gas with temperature T ∼ 106 K extending out to the virial radius of the Milky Way halo with a scale height of a few tens of kpc (Blitz & Robishaw 2000; McCammon et al. 2002; Rasmussen et al. 2003; Fang et al. 2006; Bregman & Lloyd-Davies 2007; Grcevich & Putman 2009; Miller & Bregman 2012).”

“This model is based on the magnetic ‘tower’ model of Li et al. (2006), in which the magnetic field is composed of a poloidal flux that presumably comes from the dynamo process in black hole accretion disks, as well as a toroidal component that may be generated by shearing of the poloidal flux lines…”

“It is known that the Milky Way moves in the intragroup medium (IGM).”

“However, we note that there are still large uncertainties in the current constraints on the observed profiles of the hot gaseous halo (Fang et al. 2006; Miller & Bregman 2012).”

“This misalignment could either arise from an intrinsic effect, such as jet precessions (e.g., Falceta-Gonçalves et al. 2010), or could be due to jet interactions with the surrounding medium as the jet travels from pc to kpc scales (e.g., Fanaroff-Riley type I radio sources).”

“In this paper we adopt a more simplistic approach, which is to treat cosmic rays as a second fluid and solve directly for the evolution of CR pressure pcr as a function of r and t (Drury & Voelk 1981; Jones & Kang 1990; Ryu et al. 2003; Mathews & Brighenti 2008; Rasera & Chandran 2008).”

“…the detection of the Fermi bubbles, together with indications of past activity (Koyama et al. 1996; Revnivtsev et al. 2004), suggest that the central SMBH may have regularly undergone cycles of jet activity, or even was at a much more active state for the past 1-10 Myr than now (Totani 2006).”

“These values are unreasonably large for estimated properties of the Local Group (e.g., McConnachie et al. 2007; Cox & Loeb 2008).”

“AGN are also considered to be a viable agent for distributing the fields into the intergalactic medium (IGM) and intracluster medium (ICM) by relativistic jets (e.g., Koide et al. 1999; Contopoulos et al. 2009; Sutter et al. 2012).”

“…not necessarily aligned with the rotational axis of the galactic disks, and such misalignments are observed frequently in other galaxies (e.g., Middelberg et al. 2004; Giroletti et al. 2005; Gallimore et al. 2006; Kharb et al. 2010), and also recently found in the Milky Way (Su & Finkbeiner 2012).”

“The hot gas distribution in the inner galaxy is also well fit by a galactic wind (Everett et al. 2008, 2010) emanating from a ring with inner galactocentric radius about 3 kpc.”

“…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 their gamma-ray emission cannot be easily…”

“…to be due to some combination of fieldline wandering due to a random field component and magnetic field structure on scales less than the CR gyroradius, which allows the cosmic rays to migrate from one fieldline to another (Duffy et al. 1995; Jokipii 1999; Enßlin & Vogt 2003; Hauff et al. 2010).”

“…the main simulation code and is generated by 3D inverse Fourier transform (FFT) of magnetic field that, in k-space, has an amplitude given by (Ruszkowski et al. 2007) Bk ∝ k−11/6 exp(−(k/k1)4) exp(−k2/k), (12) where k = (k2x+k 2 y+k 2 z) 1/2, and k1 and k2 are the cutoff wavenumbers for…”

“The population of CR electrons is invoked to explain the hard-spectrum microwave synchrotron radiation spatially-correlated with the Fermi bubbles observed by the Wilkinson Microwave Anisotropy Probe (WMAP), also known as the ‘WMAP haze’ (Finkbeiner 2004; Dobler & Finkbeiner 2008; Dobler 2012).”

“Bending of radio jets in some cases can be explained by external ram pressure as galaxies move through an intracluster gas (e.g., Begelman et al. 1979; Balsara & Norman 1992).”

“In this paper we adopt a more simplistic approach, which is to treat cosmic rays as a second fluid and solve directly for the evolution of CR pressure pcr as a function of r and t (Drury & Voelk 1981; Jones & Kang 1990; Ryu et al. 2003; Mathews & Brighenti 2008; Rasera & Chandran 2008).”

“This estimate is likely only a lower limit, because the condition for the onset of RT instability becomes more stringent for inflating bubbles (Pizzolato & Soker 2006).”

“In this paper we adopt a more simplistic approach, which is to treat cosmic rays as a second fluid and solve directly for the evolution of CR pressure pcr as a function of r and t (Drury & Voelk 1981; Jones & Kang 1990; Ryu et al. 2003; Mathews & Brighenti 2008; Rasera & Chandran 2008).”

“Assuming the Fermi bubbles are tilted by α degrees from the rotational axis of the Galaxy, the required ram pressure from the wind (Burns et al. 1979) is Pram,wind = Pram,jet tanα, where Pram,jet = ρjv 2 jet is the ram pressure of the jets.”

“Here we present results of a 2D test of a sound wave propagating in a composite of thermal gas and cosmic rays (Rasera & Chandran 2008).”

“Since in a tangled field the effective diffusion coefficient (κiso) can be suppressed compared to that along the field lines (κ‖), likely by a factor of ∼ 3 (Tao 1995), we choose to vary the parallel diffusion coefficient in the range of (0.4− 1.2)× 1029 cm2 s−1.”

“At t = tFermi, the magnetic field within the shells is amplified to & 10 µG, comparable to the equipartition field strength inferred by radio polarization mea- 9 10 surements (Jones et al. 2012).”

“The latter is associated with the turbulent interstellar medium, which has a typical coherence length of ∼ 5 − 50 pc (see a recent review by Noutsos (2012)).”

“For both simulations, the initial tangled field has an average strength of ∼ 1 µG, which corresponds to plasma β = ptot/(B 2/8π) ∼ 1 in the ambient galactic halo (note that pcr = 0 for the ambient gas), in agreement with observations (e.g., Haverkorn & Heesen 2012).”

“Accordingly, the sound speed of the combined fluid of gas and cosmic rays, which is used when solving the Riemann problem in the PPM method as well as when computing the hydrodynamic timestep, is replaced by the effective sound speed (Miniati 2007), c′s = √ γpth + γcrpcr ρ .”

“AGN are also considered to be a viable agent for distributing the fields into the intergalactic medium (IGM) and intracluster medium (ICM) by relativistic jets (e.g., Koide et al. 1999; Contopoulos et al. 2009; Sutter et al. 2012).”

“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…”