time-dependent modelling of the non-thermal emission in ... · v´ıctor zabalza (university of...

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


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)


The X-ray view of Eta Carinae

RXTE PCU lightcurve


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


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


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


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


http://adsabs.harvard.edu/abs/2015MNRAS.449L.132O

http://www.arxiv.org/abs/1502.04056

Dynamical model

▸ Analyticaldescriptionbased on Parkin& Pittard (2008).

▸ 82x100 Bins arefollowed as theymove outwardson the shock capand then shootout ballistically.


Dynamical model


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


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


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.


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.





▸ 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







▸ 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.






▸ 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




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


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


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


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.


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 <


http://adsabs.harvard.edu/abs/2015MNRAS.449L.132O

http://www.arxiv.org/abs/1502.04056

time-dependent modelling of the non-thermal emission in ... · v´ıctor zabalza (university of...

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