EFFECT OF MASS LOADING ON BOW SHOCK …EFFECT OF MASS LOADING ON BOW SHOCK NEBULAE Giovanni Morlino...

EFFECT OF MASS LOADINGEFFECT OF MASS LOADINGON BOW SHOCK NEBULAEON BOW SHOCK NEBULAE

Giovanni MorlinoGiovanni Morlino

Purdue University, INDIANACNRS/APC, Paris, FRANCE

In collaboration with:M. Lyutikov & M. Vorster

G. Morlino, Purdue – 12 May 2014

Workshop on Relativistic Plasma Astrophysics

Purdue University May 12-15 2014

Structure of bow-shock nebula

Hα emission

G. Morlino, Purdue University – 12 May 2014


Hα emission


If the ISM is partially ionized, Hydrogen atoms can suffer charge-exchange and collisional excitation emitting Balmer lines


Hα emission


If the ISM is partially ionized, Hydrogen atoms can suffer charge-exchange and collisional excitation emitting Balmer lines

Hα emission from J0437-4714

Structure of bow-shock nebula:simulations

Hα emission


[From Bucciantini, Amato & del Zanna 2005, A&A 434,189]

ISM

Supersonic wind

Subsonic wind

Shocked ISM

Unshockedwind

The wind is collimated in a cylindrical tale with constant area within the whole simulation box

Summary of pulsar with Hα bow shock

SN 1006 CYGNUS LOOP

Hα emission

Hα emission


- 6 over 9 known Hα bow shock nebulae show rapid expansion and/or contraction of the tale- These features are axisymmetric along the propagation axes of the pulsar

This suggest that the tale could be modified by internal dynamics rather than by external effects (non uniform ISM)

NEW

[From Brownsberger & Romani 2014, arXiv:1402.5465]

Cometary shape

OLD

Guitar nebula (powered by PRS B2224+65)

SN 1006 CYGNUS LOOP

Hα emission

Hα emission


From Palomar Observatory (1995)

[From Gautam A. et al. 2013]

Guitar nebula (powered by PRS B2224+65)

SN 1006 CYGNUS LOOP

Hα emission

Hα emission


Balmer emission:images from HST

From Palomar Observatory (1995)

[From Gautam A. et al. 2013]

PSR J2124-3358

SN 1006 CYGNUS LOOP

Hα emission


[ From Brownsberger & Romani 2014, ApJ accepted arXiv:1402.5465]

PSR J2124-3358

SN 1006 CYGNUS LOOP

Hα emission



New discovered with a survey for Hα bow shock emission around nearby FermiLAT γ-detected energetic pulsars

PSR J0742-2822

SN 1006 CYGNUS LOOP

Hα emission

Hα emission



Hα image with background star light subtracted

PSR J1509-5850

SN 1006 CYGNUS LOOP

Hα emission

Hα emission



Left: a median-filtered 3 Å~ 600 W012 SOI image of PSR J0742−2822, smoothed with a 0.45′′ Gaussian. The right panel shows an image with a scaled continuum (W014) image subtracted and 0.9′′ top-hat smoothing. The arrow indicates extent of the previous nebula detection.

New discovered!

Two bow shock nebulae in X-rays

SN 1006 CYGNUS LOOP

Hα emission

Hα emission


J1509 tail (in the 1–7 keV band, binned to the pixel size of 200). The blue line shows an approximate boundary of the PWN head within 15'' from the pulsar, but it does not fit the tail’s shape at larger distances. The white arrows show an approximate observed width of the tail.

[ From Kargaltsev, O. et al 2008, ApJ 684, 542]

Two bow shock nebulae in X-rays

SN 1006 CYGNUS LOOP

Hα emission

Hα emission


The Mushroom PWN powered by PSR B0355+54. Notice the sudden narrowing (transition from the “cap" to the “stem")

J1509 tail (in the 1–7 keV band, binned to the pixel size of 200). The blue line shows an approximate boundary of the PWN head within 15'' from the pulsar, but it does not fit the tail’s shape at larger distances. The white arrows show an approximate observed width of the tail.

[ From Kargaltsev, O. et al 2008, ApJ 684, 542]

Interaction length-scalesfor neutrals


d S=( Lwind

4π vNS2 ρ0 c )

1 /2

= 2.5⋅1015( Lwind

1034 erg )1/2

( V NS

500 km / s )( n0

cm−3 )−1/2

cm Stagnation distance

d S

Δ≈d S /3

d S

Δ≈d S /3


Hα emission


d S=( Lwind

4π vNS2 ρ0 c )

1 /2

= 2.5⋅1015( Lwind

1034 erg )1/2

( V NS

500 km / s )( n0

cm−3 )−1/2

cm

λcoll=V NS

xion n ISM ⟨σcoll vrel ⟩→

λCE=1.3⋅1015 cm ∼ d S

λ ion=7.0⋅1018 cm ≫d SNeutral Hydrogen from the ISM can easily penetrate into the wind region

Stagnation distance

Collisional length-scale in the shocked ISM

d S

Δ≈d S /3


Hα emission


d S=( Lwind

4π vNS2 ρ0 c )

1 /2

= 2.5⋅1015( Lwind

1034 erg )1/2

( V NS

500 km / s )( n0

cm−3 )−1/2

cm

λcoll=V NS


λCE=1.3⋅1015 cm ∼ d S

λ ion=7.0⋅1018 cm ≫d S

λ ion , wind=V NS

neσBethe c≈ 7⋅1023 ( V SN

500 km/ s )( ne

10−10 cm−3 )−1

cm

Neutral Hydrogen from the ISM can easily penetrate into the wind region

Stagnation distance

M pulsar=Lw

γw c2 = ne meπ d S2 c → ne≈10−10

Ionization scale of hydrogen inside the wind

Electron-positron density inside the wind


d S

Δ≈d S /3


Hα emission


d S=( Lwind

4π vNS2 ρ0 c )

1 /2

= 2.5⋅1015( Lwind

1034 erg )1/2

( V NS

500 km / s )( n0

cm−3 )−1/2

cm

λcoll=V NS


λCE=1.3⋅1015 cm ∼ d S

λ ion=7.0⋅1018 cm ≫d S

λ ion , wind=V NS

neσBethe c≈ 7⋅1023 ( V SN

500 km/ s )( ne

10−10 cm−3 )−1

cm

Neutral Hydrogen from the ISM can easily penetrate into the wind region

λ load= λ ion , wind

ρwindρN

=V NS

(1−xion)n ISM σBethe c

me

m p

≈ 1016 cm

Stagnation distance

Distance where mass loaded density = wind density

Ionization scale of hydrogen inside the wind


M pulsar=Lw

γw c2 = ne me π d S2 c → ne≈10−10 Electron-positron density

inside the wind

Our mathematical approach

MOMENTUM FLUX

ENERGY FLUX

∂∂ z

[ρw vw Aw ]= ϕN

∂∂ z

[(ρw vw2 +Pw)Aw ]= ϕN vNS

∂∂ z [(12 ρw vw

2 +γw

γw−1Pw)vw Aw]= 1

2ϕN vNS

3

Conservation equation along the flux tube for a stationary system

MASS FLUX

- Stationary approach- Single fluid (non relativistic) - Quasi 1-D along the propagation direction z- No magnetic field

ϕN= ρN ρw

⟨σ ion v ⟩me

Aw RATE OF MASS LOADING

Pw = P0PRESURE EQUILIBRIUMBETWEEN WIND AND SHOCK ISM

PN = 0

⟨σ ion v ⟩ f w(v)= const

Cold neutral fluid

Constant ionization rate


Analytical solution

∂ vw

∂ η = −12

vw(vw−V NS )

vw2−cs

2 [vw(γ+1)−V NS(γ−1)]

∂ cs

∂ η =c s

2 vw [∂ vw

∂ η (1−γvw

2

cs2 )−γ

vw(vw−V NS)

c s2 −1]

A(η)= A0 exp [−γ∫0

η vw(∂ηvw+1)−V NS

cs2 d η' ]

η = zλ load

= zλ ion

ρNρwind , 1

Coupled 1st order differential equations for flow speed and sound speed:

Solution for the flow cross-section:

vw ,1>V NS

∂vw

∂η <0 M

M 1>1∂c s

∂η >0 AIf

< <

>

M →1 ⇒∂ vw

∂ η → ∓∞ ⇒ ∂ A∂ η → ±∞

Expansion velocity > sound speed → stationary approach no more valid

Moreover:


Results

Initial supersonic flow Initial subsonic flow


M1> 1 M

1< 1

Results


M1=1.5 2 4

10

M1=0.8 0.7 0.57 0.54Γ

wind= 5/3; v

wind,1= 200 V

NS

c s

c s

vw

Results


M1=1.5 2 4

10

M1=0.8 0.7 0.57 0.54Γ

wind= 5/3; v

wind,1= 200 V

NS

Γwind

= 4/3; vwind,1

= 200 VNS

CONCLUSIONS

Neutral Hydrogen from ISM can easily penetrate into the relativistic wind of bow-shock pulsar wind nebulae

Internal dynamics of the wind can be strongly affected by neutrals on the typical mass loading scale

Mach > 1 → the flow slows down and expandsMach < 1 → the flow accelerates and contracts

Present results can explain the shape observed in many bow shock nebulae observed in Balmer emission (and X-rays)

The stationary approach fails when M → 1 Simulations are needed to get a comprehensive time dependent solution and to include magnetic field


Results


EFFECT OF MASS LOADING ON BOW SHOCK …EFFECT OF MASS LOADING ON BOW SHOCK NEBULAE Giovanni Morlino...

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