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Time-dependent modelling of the non-thermalemission in Eta Carinae
Vıctor Zabalza
Stefan Ohm, Jim Hinton, E. Ross Parkin
University of Leicester
Variable Galactic Gamma-ray SourcesHeidelberg 4–6 May 2015
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 1 / 19
Eta Carinae
▸ Distance 2.3 kpc▸ Period 5.54 yr▸ Last periastron: May 2014▸ Eccentricity: e ≃ 0.9▸ Semimajor axis: 16.16 AU▸ Separation at periastron: 1.66 AU
Primary star▸ Luminous Blue Variable (LBV)▸ M ∼ 120M⊙
▸ M ∼ 5 × 10−4M⊙/yr▸ vw,∞ = 500kms−1
Secondary star▸ O or WR▸ M ∼ 30M⊙
▸ M ∼ 10−5M⊙/yr▸ vw,∞ = 3000kms−1
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 2 / 19
The X-ray view of Eta Carinae
X-ray model▸ Hamaguchi et al. 2007:▸ A low temperature (T ∼ 1 keV) steady emitter enveloping thebinary (CCE)
▸ Hot (T ∼ 4 keV), variable emission from the wind-wind collisionregion (WWCR)
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 3 / 19
The X-ray view of Eta Carinae
RXTE PCU lightcurve
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 4 / 19
The GeV view of Eta Carinae: Flux variability
▸ Recent results from Reitberger et al. (2015)▸ Slow decrease in �ux after periastron▸ No evidence for wind collision region collapse!
55,000 55,500 56,000 56,500 57,000
Flux /
10
-7photo
ns
cm.2s-1
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Phase0 0.2 0.4 0.6 0.8 1
55,000 55,500 56,000 56,500 57,000
Flux /
10
-9photo
ns
cm.2s-1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Phase0 0.2 0.4 0.6 0.8 1
0.2 to 10 GeV 10 to 300 GeV
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 5 / 19
Spectral properties (Reitberger et al. 2015)
Two spectral components:▸ 1 GeV< E <10 GeV: Power lawwith a cuto� at
▸ periastron: Ec = 1.6 ± 1 GeV▸ apastron: Ec = 17 ± 6 GeV
▸ E > 10 GeV: Hard powerlawwith Γ = 2.0 ± 0.1 duringperiastron.
E²F
[erg
cm⁻²
s⁻¹
]
10−12
10−11
Energy [GeV]1 10 100
Periastron Apastron
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 6 / 19
Proposed scenarios for GeV phenomenology
▸ Reitberger et al. (2012)▸ Double spectral component arises from pair productionabsorption feature by circumbinary UV emiter.
▸ LUV ∼ 5 × 1037 erg s−1 required for this absorber, but noobservational evidence of its existence.
▸ Farnier et al. (2011)▸ Low energy component as IC emission, upscattering stellarphotons.
▸ High energy component as π0 decay in the dense shockedstellar wind.
▸ Acceleration of electrons to few tens of GeV requires superBohm acceleration around periastron
▸ No time dependence or particle distribution evolutionconsidered
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 7 / 19
Proposed scenarios for GeV phenomenology
▸ Reitberger et al. (2012)▸ Double spectral component arises from pair productionabsorption feature by circumbinary UV emiter.
▸ LUV ∼ 5 × 1037 erg s−1 required for this absorber, but noobservational evidence of its existence.
▸ Farnier et al. (2011)▸ Low energy component as IC emission, upscattering stellarphotons.
▸ High energy component as π0 decay in the dense shockedstellar wind.
▸ Acceleration of electrons to few tens of GeV requires superBohm acceleration around periastron
▸ No time dependence or particle distribution evolutionconsidered
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 7 / 19
Proposed scenarios for GeV phenomenology
▸ Reitberger et al. (2012)▸ Double spectral component arises from pair productionabsorption feature by circumbinary UV emiter.
▸ LUV ∼ 5 × 1037 erg s−1 required for this absorber, but noobservational evidence of its existence.
▸ Farnier et al. (2011)▸ Low energy component as IC emission, upscattering stellarphotons.
▸ High energy component as π0 decay in the dense shockedstellar wind.
▸ Acceleration of electrons to few tens of GeV requires superBohm acceleration around periastron
▸ No time dependence or particle distribution evolutionconsidered
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 7 / 19
Proposed scenarios for GeV phenomenology
▸ Reitberger et al. (2012)▸ Double spectral component arises from pair productionabsorption feature by circumbinary UV emiter.
▸ LUV ∼ 5 × 1037 erg s−1 required for this absorber, but noobservational evidence of its existence.
▸ Farnier et al. (2011)▸ Low energy component as IC emission, upscattering stellarphotons.
▸ High energy component as π0 decay in the dense shockedstellar wind.
▸ Acceleration of electrons to few tens of GeV requires superBohm acceleration around periastron
▸ No time dependence or particle distribution evolutionconsidered
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 7 / 19
A time dependent particle acceleration,evolution and radiation model of η Car
Ohm, S., Zabalza, V., Hinton, J.A. & Parkin, E.R., 2015,On the origin of γ-ray emission in η Carina
MNRAS, 449, L132 arXiv:1502.04056
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 8 / 19
Dynamical model
▸ Analyticaldescriptionbased on Parkin& Pittard (2008).
▸ 82x100 Bins arefollowed as theymove outwardson the shock capand then shootout ballistically.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 9 / 19
Dynamical model
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 10 / 19
Shock and post-shock region properties
▸ Radiative regime can be estimated by(Stevens 1992):
χ = tcooltesc
≃ v43d12M7
▸ Primary wind:χprim = 10−4 − 10−3 → radiative
▸ Secondary wind:χsec = 10 − 100→ adiabatic
Density
x
ρp,w
4ρp,w
ρc
ρs,w 4ρs,w
CD
rc
rs,ps
rp,ps
Primary Secondary
CD
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 11 / 19
Shock and post-shock region properties
▸ Radiative regime can be estimated by(Stevens 1992):
χ = tcooltesc
≃ v43d12M7
▸ Primary wind:χprim = 10−4 − 10−3 → radiative
▸ Secondary wind:χsec = 10 − 100→ adiabatic
Density
x
ρp,w
4ρp,w
ρc
ρs,w 4ρs,w
CD
rc
rs,ps
rp,ps
Primary Secondary
CD
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 11 / 19
Shock and post-shock region properties
▸ Radiative regime can be estimated by(Stevens 1992):
χ = tcooltesc
≃ v43d12M7
▸ Primary wind:χprim = 10−4 − 10−3 → radiative
▸ Secondary wind:χsec = 10 − 100→ adiabatic
Density
x
ρp,w
4ρp,w
ρc
ρs,w 4ρs,w
CD
rc
rs,ps
rp,ps
Primary Secondary
CD
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 11 / 19
Shock and post-shock region properties
▸ Radiative regime can be estimated by(Stevens 1992):
χ = tcooltesc
≃ v43d12M7
▸ Primary wind:χprim = 10−4 − 10−3 → radiative
▸ Secondary wind:χsec = 10 − 100→ adiabatic
Density
x
ρp,w
4ρp,w
ρc
ρs,w 4ρs,w
CD
rc
rs,ps
rp,ps
Primary Secondary
CD
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 11 / 19
Primary wind
φ = 0.05
(E/eV)10
log6 7 8 9 10 11 12 13 14
time
(day
s)
-610
-510
-410
-310
-210
-110
1
10
210
310
410
cool,et
cool,pt
flowt
acct
Primary
tcool,p, tcool,e, tacct�ow: – – –
For each time step and shock cap bin:▸ Compute steady state spectrumfrom pp or Sync+IC+Bremss lossesfor protons and electrons,respectively, assuming ηacc = 10.
▸ Epmax ≈ 100 GeV
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 12 / 19
Secondary wind
φ = 0.05
(E/eV)10
log6 7 8 9 10 11 12 13 14
time
(day
s)
-610
-510
-410
-310
-210
-110
1
10
210
310
410
cool,et
cool,pt
flowt
acct
Companion
tcool,p, tcool,e, tacct�ow: – – –
▸ The secondary post-shock densityis low enough that protons do notinteract during their �ow along theshock cap→ not a steady state.
▸ Maximum energy is set by the totaltime the particles remain in theshock before they �ow away.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 13 / 19
Acceleration in the Secondary shock
▸ Acceleration conditions change along the shock-cap withinloss timescale: Time-dependent acceleration needed!
▸ Lagrangian acceleration scheme, based on DSA in a strongshock, to track the particle populations at the shock anddownstream of the shock with time:
▸ At each time step ∆t << tacc , low energy particles are injected.▸ The existing particles in the shock gain a factor exp(∆t/tacc) inenergy, and
▸ A fraction (1 − exp(−∆t/tacc)) of the particles in the shock areadvected downstream. These are transported with the �ow andlose energy through pp interaction.
▸ When a given bin reaches the edge of the shock cap, the twoshock layers mix within 1011 cm and radiate.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 14 / 19
Acceleration in the Secondary shock
▸ Acceleration conditions change along the shock-cap withinloss timescale: Time-dependent acceleration needed!
▸ Lagrangian acceleration scheme, based on DSA in a strongshock, to track the particle populations at the shock anddownstream of the shock with time:
▸ At each time step ∆t << tacc , low energy particles are injected.▸ The existing particles in the shock gain a factor exp(∆t/tacc) inenergy, and
▸ A fraction (1 − exp(−∆t/tacc)) of the particles in the shock areadvected downstream. These are transported with the �ow andlose energy through pp interaction.
▸ When a given bin reaches the edge of the shock cap, the twoshock layers mix within 1011 cm and radiate.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 14 / 19
Acceleration in the Secondary shock
▸ Acceleration conditions change along the shock-cap withinloss timescale: Time-dependent acceleration needed!
▸ Lagrangian acceleration scheme, based on DSA in a strongshock, to track the particle populations at the shock anddownstream of the shock with time:
▸ At each time step ∆t << tacc , low energy particles are injected.
▸ The existing particles in the shock gain a factor exp(∆t/tacc) inenergy, and
▸ A fraction (1 − exp(−∆t/tacc)) of the particles in the shock areadvected downstream. These are transported with the �ow andlose energy through pp interaction.
▸ When a given bin reaches the edge of the shock cap, the twoshock layers mix within 1011 cm and radiate.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 14 / 19
Acceleration in the Secondary shock
▸ Acceleration conditions change along the shock-cap withinloss timescale: Time-dependent acceleration needed!
▸ Lagrangian acceleration scheme, based on DSA in a strongshock, to track the particle populations at the shock anddownstream of the shock with time:
▸ At each time step ∆t << tacc , low energy particles are injected.▸ The existing particles in the shock gain a factor exp(∆t/tacc) inenergy,
and▸ A fraction (1 − exp(−∆t/tacc)) of the particles in the shock areadvected downstream. These are transported with the �ow andlose energy through pp interaction.
▸ When a given bin reaches the edge of the shock cap, the twoshock layers mix within 1011 cm and radiate.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 14 / 19
Acceleration in the Secondary shock
▸ Acceleration conditions change along the shock-cap withinloss timescale: Time-dependent acceleration needed!
▸ Lagrangian acceleration scheme, based on DSA in a strongshock, to track the particle populations at the shock anddownstream of the shock with time:
▸ At each time step ∆t << tacc , low energy particles are injected.▸ The existing particles in the shock gain a factor exp(∆t/tacc) inenergy, and
▸ A fraction (1 − exp(−∆t/tacc)) of the particles in the shock areadvected downstream. These are transported with the �ow andlose energy through pp interaction.
▸ When a given bin reaches the edge of the shock cap, the twoshock layers mix within 1011 cm and radiate.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 14 / 19
Acceleration in the Secondary shock
▸ Acceleration conditions change along the shock-cap withinloss timescale: Time-dependent acceleration needed!
▸ Lagrangian acceleration scheme, based on DSA in a strongshock, to track the particle populations at the shock anddownstream of the shock with time:
▸ At each time step ∆t << tacc , low energy particles are injected.▸ The existing particles in the shock gain a factor exp(∆t/tacc) inenergy, and
▸ A fraction (1 − exp(−∆t/tacc)) of the particles in the shock areadvected downstream. These are transported with the �ow andlose energy through pp interaction.
▸ When a given bin reaches the edge of the shock cap, the twoshock layers mix within 1011 cm and radiate.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 14 / 19
Acceleration: CR Shock modi cation
▸ In the outer part of theshock-cap, ram pressure islow, and cosmic ray pressureat the shock is high.
▸ We apply nonlinearmodi cation to accelerationscheme following Berezhko& Ellison (1999).
(E/eV)10
log9 9.5 10 10.5 11 11.5 12 12.5 13R
elat
ive
Ener
gy C
onte
nt in
Rel
ativ
istic
Par
ticle
s
1
10
210
310
2
3
4
6
8
11
162230425880
Annulus
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 15 / 19
Results: SED
(Energy/eV)10
log7 8 9 10 11 12
)-1
s-2
dN
/dE
(er
g cm
2E
-1210
-1110
-1010
< 0.06ϕ0.91 <
(Energy/eV)10
log7 8 9 10 11 12
)-1
s-2
dN
/dE
(er
g cm
2E
-1210
-1110
-1010
< 0.44ϕ0.06 <
10 months around periastron 5 to 28 months after periastron
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 16 / 19
Results: Lightcurve)
-1 s
-2dN
/dE
(ph
cm
-710
0.2 GeV < E < 10 GeV
ϕ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
)-1
s-2
dN/d
E (
ph c
m
-1110
-1010
-910
10 GeV < E < 300 GeV
Secondary Primary
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 17 / 19
Conclusions
▸ The GeV phenomenology of η Car is well charaterised byemission from protons accelerated in the primary andsecondary stellar wind shocks.
▸ Where are all the other gamma-ray emitting wind collidingbinaries?
▸ Looking forward to the observational results during the 2014May periastron: NuSTAR, Fermi, HESS-II.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 18 / 19
Conclusions
▸ The GeV phenomenology of η Car is well charaterised byemission from protons accelerated in the primary andsecondary stellar wind shocks.
▸ Where are all the other gamma-ray emitting wind collidingbinaries?
▸ Looking forward to the observational results during the 2014May periastron: NuSTAR, Fermi, HESS-II.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 18 / 19
Conclusions
▸ The GeV phenomenology of η Car is well charaterised byemission from protons accelerated in the primary andsecondary stellar wind shocks.
▸ Where are all the other gamma-ray emitting wind collidingbinaries?
▸ Looking forward to the observational results during the 2014May periastron: NuSTAR, Fermi, HESS-II.
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 18 / 19
Full details
Ohm, S., Zabalza, V., Hinton, J.A. & Parkin, E.R., 2015,On the origin of γ-ray emission in η CarinaMNRAS, 449, L132 arXiv:1502.04056
(Energy/eV)10
log7 8 9 10 11 12
)-1
s-2
dN
/dE
(er
g cm
2E
-1210
-1110
-1010
< 0.06ϕ0.91 <
(Energy/eV)10
log7 8 9 10 11 12
)-1
s-2
dN
/dE
(er
g cm
2E
-1210
-1110
-1010
< 0.44ϕ0.06 <
Vıctor Zabalza (University of Leicester) Time-dependent modelling of Eta Carinae 19 / 19