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COSMIC RAY INDUCED COSMIC RAY INDUCED GALACTIC WINDSGALACTIC WINDS
S. Recchia
VHEPU 2018-Quy Nhon
APC-Paris 7
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● What are Galactic winds?● The role of CRs● Hydrodynamics of galactic winds● CR transport in a CR-driven wind● Diffusive halo● CR spectrum ● Role of the Galactic environment
OVERVIEWOVERVIEW
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WHAT ARE GALACTIC WINDS?WHAT ARE GALACTIC WINDS?
● Outflows from Galaxies
● (non)-stationary
● Flow subsonic near the gal. Disk
● Flow accelerated to supersonic speed by thermal, radiation, CR pressure gradients...
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WINDS IN GALAXIESWINDS IN GALAXIES
● AGN, Starburst Galaxies, ...
● Mass loss
● Flow speed
● Driven by , , , ...
M≃M S / yr
u≃100km / s
PTH PRAD PCR
● Galactic evolution
● Star formation rate
● Chemistry of ISM and IGM
● Missing barions
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WINDS IN THE MILKY WAYWINDS IN THE MILKY WAY
OBSERVED GALACTIC OBSERVED GALACTIC
HALOHALO
EVIDENCE OF EVIDENCE OF
WINDS?WINDS?
● X-ray em./abs.
● Oxygen lines
● Large (~ 100 kpc)
● Hot (~ millions K)
● Metallicity ~0.2-0.3
● From the disk
(Miller and Bregman (2015))
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THE ROLE OF CRsTHE ROLE OF CRs
● Thermal and radiation pressure not enough in the Milky Way ● Dynamical role of CRs● CR push against the gravitational force
● CR diffusive and advective motion● CR scattering and Effective coupling with ISM● Role of self-generation of plasma waves and wave damping ● Effective propagation region becomes energy dependent● Prominent effects on the CR spectrum
ECR≃ETH≃EMAG
(Ipavich (1975))(Breitschwerdt et al. (1991))
(Recchia et al. (2016))
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WINDS HYDRODYNAMICSWINDS HYDRODYNAMICS
● One-dim modelOne-dim model: the flow and the CR transport occur along the magnetic field lines, perpendicular to the disk
● Stationary flow
● Flux-tube geometry is preassigned
● CRs treated as a fluidCRs treated as a fluid, pressure contribution
● PPCR CR connected with the CR connected with the CR spectrumspectrum
● Damping of waves heats the gas
CR, THCR, TH
GRAVGRAV
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WINDS HYDRODYNAMICSWINDS HYDRODYNAMICS
MASS, MOMENTUM AND ENERGY CONSERVATION ρu A=const
dPg
dz=γ g
P g
ρd ρ
dz−(γ g−1)
vAu
dPc
dz
1ududz
=
cs2 1AdAdz
−g
u2−cs2
HYDRODYNAMIC CR TRANSPORT
dPcdz
=γeff
Pcρ [ 2u+v A
2(u+v A) ]d ρ
dz
γeff
γeff−1=
γcγc−1
−D
(γc−1)(u+v A)Pc
dPcdz
WIND EQUATION
c s2=γg
Pg
ρ +γeff
Pcρ [1−(γg−1)
v Au ] 2u+vA
u+v AGENERALIZED SOUND SPEED
EFFECTIVE CR ADIABATIC INDEX
CR DIFFUSIVITY
HEATING DUE TO WAVE DAMPING
z= distance from the galactic disk z= distance from the galactic disk
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WIND HYDRODYNAMICSWIND HYDRODYNAMICS
1ududz
=
c s2 1AdAdz
−g
u2−c s
2
WIND EQUATION:
CRITICAL POINTS OF
THE WIND EQUATION:
NUM=0
DEN=0
WIND BASE: n0e assigned.
Need to determine u0 that
gives smooth transition to
supersonic flow
distance from the GDdistance from the GD
Flow speedFlow speed
SONIC POINTSONIC POINT
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THE WIND LAUNCHING DEPENDS ONTHE WIND LAUNCHING DEPENDS ON:● input parameters at the wind base (n, T, B, Pc)
● flux-tube geometry
● Galactic gravitational potential (bulge, disk, Dark Matter halo)
RESULTS: HYDRODYNAMICSRESULTS: HYDRODYNAMICS
CONSTRAINT FROM OBSERVATIONS, DEPENDENCE ON THE
POSITION IN THE GALAXY
● Wind solution exists for closed intervals of n, T, Pc, g
● Small n and g, large T and Pc: non stationary outflows...
● Large n and g, small T and Pc: not enough energy for outflow...
● Stationary non transonic flows, non stationary flows...(Everett et al. (2008)) (Recchia et al. (2016))
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HYDRODYNAMICSHYDRODYNAMICS : TYPICAL CASE : TYPICAL CASE● PCR > PTH @ ~10kpc
● CRs push all along the wind profile
● Different adiabatic index
● Crucial for wind launching
SONIC POINTSONIC POINT
WAVE DAMPINGWAVE DAMPING
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HYDRODYNAMICS: DM HALOHYDRODYNAMICS: DM HALO
DM important also far
from the disk
models of DM halo:● Navarro-Frenk-White (NFW)
● Burkert (BUR)
● Innanen(INN)
● Similar DM densities at the SUNSimilar DM densities at the SUN
both u0 and u
f change
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CR TRANSPORT: SIMPLE MODELCR TRANSPORT: SIMPLE MODEL
Q0( p)∼p−γ
D (p)∼ pδ
−∂∂ z [D (p)
∂ f∂ z ]+u ∂ f
∂ z−dudz
p3
∂ f∂ p
=Q0 (p)δ(z)
γ∼4.1
δ∼0.6
CR TRANSPORT EQUATION
DIFFUSION ADVECTIONADVECTION COMPRESSIONCOMPRESSION
INJECTIONINJECTION
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CR TRANSPORT: SIMPLE MODELCR TRANSPORT: SIMPLE MODEL
f 0adv
( p)=Q0
2u∼p−γ
ADVECTION DOMINATETED REGIME● Low energies (below ~ 10 GeV)● Spectral slope same as injection
DIFFUSION DOMINATETED REGIME● High energies●
●
●
●
●
●
● Spectral slope depends also on D(p) ● Dependence on the halo size?
f 0diff
( p)=Q0
2HD
∼p−γ−δ
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WHAT SCATTERS CRsWHAT SCATTERS CRs
● Plasma (Alfvén) waves?
● Resonant scattering?
● Self-generation from CRs?
● Background turbulence?
● Damping mechanisms?
● Here we assume:
Self-generation by streaming instability
Damping by NLLD
Background Kolmogorov turbulence
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CR PROPAGATION : ISSUESCR PROPAGATION : ISSUES
CR DENSITY CR DENSITY GRADIENTGRADIENT
● Physical processes which determine D, u and H?Physical processes which determine D, u and H?
● CR gradient
● CR induced diffusion
● Advection with self-generated waves
● CR-driven large scale flows (WINDS)
● Free escape boundary? Size of the propagation region
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● u(z) grows with zu(z) grows with z
● At a given z*(p) advection overcome diffusionAt a given z*(p) advection overcome diffusion
● The size of the diffusive halo becomes energy dependent
● No need to impose H by hand output from the transport model
● Additional effects if z* is in the region of flux tube opening
SIZE OF THE DIFFUSIVE HALOSIZE OF THE DIFFUSIVE HALO
H 2( p)D
=H (p)u
→H ( p)∼√D
(Ptuskin et al. (1997)) (Recchia et al. (2016))
u∼u0 z
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CR TRANSPORT IN A CR-DRIVEN WINDCR TRANSPORT IN A CR-DRIVEN WIND
WIND HYDRODYNAMICS: determine the wind velocity, the
gas density and pressure, the CR pressure and the magnetic field
CR TRANSPORT: determine the CR distribution function and
the CR-induced diffusion coefficient
PROBLEM BADLY NON LINEAR
CR DISTRIBUTION
FUNCTION
DIFFUSION COEFFICIENT
WIND VELOCITY
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CR SPECTRUM AT EARTHCR SPECTRUM AT EARTH
● Wind lanched near the disk at Sun position
● launching param. within observations
● advection vadvection vAA(z)+u(z)(z)+u(z)● Hard spectrum at low
energies
U0 = 93 km/s
U0 → HARD
(Recchia et al. (2016))
f 0adv
( p)=Q0
2u∼p−γ
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CR SPECTRUM AT EARTHCR SPECTRUM AT EARTH
U0 = 30 km/s
● wind launched at z0 = 100 pc
● launching param. within observations
● UU00 = 30km/s VS 93km/s = 30km/s VS 93km/s
● smaller advection, better smaller advection, better agreement at low energyagreement at low energy
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CR SPECTRUM AT EARTHCR SPECTRUM AT EARTH
● steep diffusion coefficient (self generation)● wind expansion, H(p) in the expansion region● very steep spectrum at high energyvery steep spectrum at high energy● Need additional source of turbulence
D ~ pD(p) → STEEP
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CR SPECTRUM AT EARTHCR SPECTRUM AT EARTH
● Role of pre-existing Role of pre-existing turbulenceturbulence
● Spectral hardening at Spectral hardening at high energieshigh energies
HARDENING
TRANSITION FROM
SELF-GEN. D TO
KOLMOGOROV
(D(p) ~ p1/3)
(Aloisio et al. (2015))
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● Winds ubiquitous and important for galaxies● Winds maybe also in the Milky Way
(observation of the halo)● CRs are likely to drive winds in the MW ● Strong dependence on the Galactic
environment● CR transport in CR driven winds ● Self-generation, advection, halo size● Important implication for the CR spectrum
SUMMARYSUMMARY
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● Non stationary flows (fountains, winds, …)
● Other stationary flows (Breezes)
● CR distribution in the Galaxy
● Transport of metals etc with the wind
● Implications on the CR grammage
● Reacceleration of CRs at the wind termination shock
● Self consistent determination of the flux tube geometry
● Application to other galaxies
INTERESTING DEVELOPMENTSINTERESTING DEVELOPMENTS
(Dorfi et al. (2013))
(Taylor et al. (2017))
(Ruszkowski et al.(2016))
(Zirakashvili et al. (2006))
(Recchia et al. (2016))
(Zirakashvili et al. (1996))
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R < 10 kpcR < 10 kpc
nCR
> than at R> 10 kpc
nCR
peak at 2-5 kpc
CR slope 2.5-2.6 at 3 kpc
CR DISTRIBUTION: GAMMA-RAY DATACR DISTRIBUTION: GAMMA-RAY DATA
● FermiLAT data
● Gamma-Rays → nCR (R)
● Catalogs → CR Sources(R)
R > 10 kpcR > 10 kpc
nCR
flatter than SN(R)
“radial gradient problem”
CR slope 2.8-2.9
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A DIFFICULT INTERPRETATIONA DIFFICULT INTERPRETATION [Acero et al. ArXiv:1602.07246]
[ Yang, Aharonian & Evoli, 2016]
● difficult to explain in a standard leaky-box model
● D constant in the Galaxy. Cannot explain nCR(R) and slope(R)
● Several extension of the leaky box have been proposed
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PROPOSED SOLUTIONSPROPOSED SOLUTIONS ● Extended halo, H > 4 (Dogiel, Uryson, 1988; Strong et al.,1988; Bloemen,
1993, Ackerman et al., 2011)
● Flatter distribution of SNR in the outer Galaxy (Ackerman et al., 2011)
● Enhancement of CO/H2 density ratio (X ) in the outer
Galaxy (Strong et al., 2004)
● Injection dependence on the ISM temperature (Erlykin et al., 2015)
● Advection effects due to the Galactic wind (Bloemen, 1993; Breitschwerdt, Dogiel, Voelk, 2002)
None of these ideas can simultaneously account
for the both the CR density and spectral slope
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● Natural radial dependence in non-linear CR propagation, in particular with winds
● Standard CR prop. Models → D constant in the Galaxy. Cannot explain nCR(R) and slope(R) Evoli et al. (2012), Gaggero et al. (2015a,b)
● Galactic magnetic field and ISM density
● Injection of CRs, Galactic distribution of sources
RADIAL DEPENDENCE RADIAL DEPENDENCE
v A(R)=B (R)
4 πρ(R)D self−gen(v A ,B , nCR )
Q0( p , R)
uwind
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ASSUMPTIONSASSUMPTIONS
● D is self generated ● VA constant along z (perp. to
the disk)
● Free escape boundary at z=H
● n(R)=const● B(R) varies
f SNR∝( RRS)α
e−β
R−R s
Rs
BB00(R)(R) : const R<5 kpc
1/R R>5 kpc
[exp. cut-off R> 10 kpc]
SOURCE DISTRIBUTION
(GREEN 2015)
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TRANSPORT EQUATION: SOLUTION TRANSPORT EQUATION: SOLUTION WITHOUT WINDSWITHOUT WINDS
f 0diff
(R)∼(Q0(R)
B0 (R) )3
f 0adv(R)∼(Q0(R)
B0(R ))
● Injection Spectrum
● Diffusive regime
● Advective regime
f 0diff
(p)∼p7−3γ
f 0adv
( p)∼p−γ
Q0adv
( p)∼p−γγ≈4.3
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CR RADIAL GRADIENT(NO WINDS)CR RADIAL GRADIENT(NO WINDS) CR density at 20 GeVCR density at 20 GeV spectral slope at 20 GeVspectral slope at 20 GeV
f 0adv
∼(Q0
B0)
● B~const
● peak Q0 ====> many waves =====> CRs well confined
● peak CR density
● advective regime =====> hard spectrum
ADVECTION
ADVECTION
f 0adv
( p)∼p−γ
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CR RADIAL GRADIENT(NO WINDS)CR RADIAL GRADIENT(NO WINDS) CR density at 20 GeVCR density at 20 GeV spectral slope at 20 GeVspectral slope at 20 GeV
DIFFUSION
DIFFUSION
f 0diff
∼(Q 0
B0)
3
f 0diff
(p)∼p7−3γ
● B~1/R
● small Q0 ====> few waves =====> CRs poorly confined
● low CR density
● diffusive regime =====> steep spectrum
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CR RADIAL GRADIENT(NO WINDS)CR RADIAL GRADIENT(NO WINDS) CR density at 20 GeVCR density at 20 GeV spectral slope at 20 GeVspectral slope at 20 GeV
DIFF. + B cut-off
DIFF. + B cut-off
● B~1/R with exponential cut-off above R=10kpc
● small Q0 + small B ====> D smaller despite few sources
● better confinement of CRs, higher CR density
● B and Q0 same R dependence ====> flatter CR density
Mixed diffusion/advection regime ====> harder CR spectrum
Cut-off scale ~ 3kpc
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● At the source peak: larger advection with wind → smaller CR density
● At the source peak: larger advection with wind VS larger D(less waves)
● At R > 10 kpc wind not launched (for the chosen input parameters)
● Results at R< 10 kpc depend on the Dark Matter halo potential
CR RADIAL GRADIENT(WINDS)CR RADIAL GRADIENT(WINDS)
ADVECTION
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WIND HYDRODYNAMICSWIND HYDRODYNAMICS
1ududz
=
1AdAdz
−g/c s2
M2−1
WIND EQUATION: DE LAVAL NOZZLE:
1ududz
=
1AdAdz
M 2−1