Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mrao.cam.ac.uk/~krause/Dogliani2003.pdf Äàòà èçìåíåíèÿ: Mon Feb 14 21:58:51 2005 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 22:12:26 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ï ï ï ï ï ð ï c 1999 s4 linear

Large scale simulations of the jet-IGM interaction
Martin Krause Landesternwarte Heidelberg-KÆnigstuhl


Outline
· · ·
­

Pretty data: Cygnus A Parameters of jet simulations in the history Extension to very low jet densities
Blastwaves in the beginning

·
­ ­

Simulation to 100 kpc scale
Can we still use spherical approximation for the evolution of pressure and density? 3D structure rings, spots & filaments

·

Application to Cygnus A and 3C 317


Radio cocoon and shaped Xray gas (contours) in Cygnus A

Cygnus A (Chandra archive, courtesy P. Strub) large cocoon width elliptically shaped cluster gas marks bow shock axis ratio: 1.2


Outline
· · ·
­

Pretty data: Cygnus A Parameters of jet simulations in the history Extension to very low jet densities
Blastwaves in the beginning

·
­ ­

Simulation to 100 kpc scale
Can we still use spherical approximation for the evolution of pressure and density? 3D structure rings, spots & filaments

·

Application to Cygnus A and 3C 317


Parameter Space
Norman et al. 1983:

= too expensive


Tuning density contrast
/ =0.01-10 =j m M=6 Fatter cocoons for lower Jet head slower: vh=vj
Norman et al. 1983


Outline
· Pretty data: Cygnus A

· · ·

Parameters of jet simulations in the history Extension to very low jet densities
­ ­ ­ Blastwaves in the beginning Can we still use spherical approximation for the evolution of pressure and density? 3D structure rings, spots & filaments

Simulation to 100 kpc scale

·

Application to Cygnus A and 3C 317


Hydrodynamic Simulations
· Code: Nirvana (by Udo Ziegler) · Hydrodynamics equations (continuity, momentum & energy) · no magnetic fields · background gravity · constant density and King atmospheres


Parameter Study: ­5 M=2.6 Well known result: Smaller larger cocoon Lg[ =-3 ] Lg[ =-2 ] M=26

New result: Smaller (&M) wider bow shock

Krause (2003)


Spherical Bow Shocks: The Blastwave Solution (similar to stellar wind bubble)
Spherical force ballance at bow shock

General global solution for arbitrary mass profile M(r) and energy injection law E(t):


Special Solutions:
Constant external density: Castor et al. 1975 Power law density distribution:

King type density distribution:


Critical Radius for Spherical Symmetry
bow shock velocity caused by jet > blastwave velocity

r1//rj = 0.5

-¼

Confirmed by simulation results.


L g[ = -2 ]

Parameter Study: Axis Ratio
Small jets have spherical bow shocks! critical radius depends on . L g[ = - 4 ]

L g[ = - 3 ]


Outline
· · · · Pretty data: Cygnus A Parameters of jet simulations in the history Extension to very low jet densities
­ ­ ­ Blastwaves in the beginning Can we still use spherical approximation for the evolution of pressure and density? 3D structure rings, spots & filaments

Simulation to 100 kpc scale

·

Application to Cygnus A and 3C 317


0

BIPOLAR SIMULATION =10-4 core: 20Rj, size: >200 Rj


Pressure Distribution
· High pressure spots on axis despite jet disruption · But overall pressure is constant within factor 2

balanced by gravity


Pressure probability distribution: Very sharply peaked, declining


Average Pressure: Follows spherical approximation with 10% accuracy

Spherical formula: P(r)= (3L2 M(r) r dr) 4/3 3 r



Consequently: Radial bow shock position well described by the spherical approximation


Outline
· · · · Pretty data: Cygnus A Parameters of jet simulations in the history Extension to very low jet densities
­ ­ ­ Blastwaves in the beginning Can we still use spherical approximation for the evolution of pressure and density? 3D structure rings, spots & filaments

Simulation to 100 kpc scale

·

Application to Cygnus A and 3C 317


3D-Simulation (cylindrical coordinates) Bow shock shape: elliptical + cigars

Density Slice

core radius: 35 kpc, M=8, 7x10-3 =


Integrated X-ray emission Rings, spots, & filaments


Outline
· · · · Pretty data: Cygnus A Parameters of jet simulations in the history Extension to very low jet densities
­ ­ ­ Blastwaves in the beginning Can we still use spherical approximation for the evolution of pressure and density? 3D structure rings, spots & filaments

Simulation to 100 kpc scale

·

Application to Cygnus A and 3C 317


Comparison to observational data of 3C 317
Radio contours: jet died already Rings, elliptical, =>> inclination: 37 Bright spots at crossing points
[Blanton, 2001]
0


Radio cocoon and shaped Xray gas (contours) in Cygnus A
Well explained: 2. elliptica l deformation 3. filaments in cocoon 4. fork structure Consequence: 10 =
-4

Simulation:


Cygnus A : parameter determination

1. Bow shock observed, axis ratio 1.2 =>> model predicts (now 2h / ) 10-4 , since = 10-25 , =>> 2h =10-29 j0 0 j

2. =>>Sperical blastwave should be good approximation, calculat total Luminosity: L=k r2v3 , 0 k=3.7, 3.6, 4 for 0,-1,-2 =>> L= 8 x 1046 erg 0r 3. On the other hand (using magnetic from elsewhere): Lkin=2(h-1)hrj2c3 5x1045 (1-1/ h) j Lmag=5x1044 (u mag,jet/u mag,HS)2 2 =>> 20 (at least five, including uncertainties)


Conclusions
· Very light jets first form spherical bow shocks · Pressure approximately constant within jet bubble · After some time the bubbles get cigar shaped extensions · Spherical approximation is very exact in describing jet ´s pressure and expansion of inner (elliptical) bow shock part · 3D X-ray structure consists of (partial) rings, spots and linear filaments, depending very much on the viewing angle · Spherical approximation can be used to show that large scale jet in Cygnus a is highly relativistic