Helically Twisted Shocks in the M87 Jet

Philip Hardee1, Andrei Lobanov2 & Jean Eilek3

1 The University of Alabama, Tuscaloosa, AL, USA 2 Max-Planck Institut für Radioastronomie, Bonn, Germany

3 New Mexico Tech/NRAO, Socorro, NM, USA

RadioGals08, Cambridge, MA

IntroductionQuestions potentially answered by

studying jet structure

•Structure: What is the cause?

•Outflow: What are the jet plasma conditions?

•Dynamics: Are proper motions flow or pattern?

•Microphysics: Where are particles accelerated?

Basic facts: D ~ 16 Mpc, 1” ~ 77 pc

Nuclear region: Mbh ~ 3 x 109 Msol ; initial collimation < 100RG (Junor, Biretta & Livio 1999)radio: twisted structure & limb-brightened (Owen, Hardee & Cornwell 1989)

optical: brighter knots & spine than radio (Sparks, Biretta & Macchetto 1996)

X-ray: knots, interknot emission & spectrum steepens along jet (Perlman & Wilson 2005)

Marshall et al. (x-ray)

Zhou et al. (radio)

Perlman et al. (optical)

VLA 15GHz: (Biretta, Zhou & Owen 1995)

Similar Optical & Radio StructureHST R band: (Perlman et al. 2001)

Biretta, Sparks & Macchetto et al. (1999)

D E F IH

DE

F

I

H

Twisted Filament (?) & Filaments (?)

Filament Crossing (?) & Twist (?)

ED F

AA

Image Analysis & StructureSingle gaussian (SG): ridge line

Double gaussian (DG): internal550 slices

Dual twisted filament structure recovered by double Gaussian in VLA and HST images.

VLA

HST

SG 13.8” constant (HST-1 to Knot A)

DG 2”(HST-1 @ 1”) - 3”(Knot A @ 12”)

Typical Radio “Knot” Motions

<ob> (HST-1) < 0.25c (Cheung, Harris & Stawarz 2007)

<ob> (D) 0.40c (Biretta, Zhou & Owen 1995)

<ob> (F) 0.90c (Biretta, Zhou & Owen 1995)

Fast Optical Motions (Biretta, Sparks & Macchetto 1999)

• ob 6c through HST-1 Viewing angle j < 19o

• ob 5c through Knot D

• ob 4c through Knot E

Fast Radio Motions (Cheung et al. 2007; Biretta et al. 1995)

• ob > 3c through HST-1 Viewing angle j < 35o

ob 2.5c through Knot D

Implications• Superluminal speeds decrease bulk speed

• Subluminal speeds increase pattern speed

(Biretta, Sparks & Macchetto 1999)

subluminal optical

superluminal

optical

Observed Proper Motions/Viewing Angle

Accelerating Pattern/Viewing AngleJet Speed @ HST-1 & Viewing Angle

(A) 6c 7.5 (optical) @ = 150 viewing angle

(B) 3c 4 (radio) @ = 300 viewing angle

Pattern Acceleration (HST-1 to Knot A)

DG 2’ 3” Eob increase 50%

SG 13.8” Hob constant

Pattern Speed (radio motions) :(1) Knot D -- E

ob 0.4c – (slow pattern)

(2) Knot F -- Eob 0.9c – (fast pattern)

Case A: fast jet

Case B: slow jet

F

D

Observed change < Intrinsic change

Decelerating Jet/Accelerating SheathDecelerating Expansion (HST-1 to Knot D)

radius expansion factor 3.5

(Case A) 6c 7.5 to 5c 5 (optical) @ = 150 viewing angle

(Case B) 3c 4 to 2.5c 3.5 (radio) @ = 300 viewing angle

Jet Deceleration/Sheath Acceleration:• KH interface driven moving shocks• Jet energy flux transferred to sheath

Some Basic Assumptions:• Treat Jet like radial wind • Jet & sheath pressure balance• Sheath thickness 1.5 Rj (set by E mode)

jetsheath

Helically Twisted Sheath Shock

Helically Twisted Dual Filament Jet Shock: Kelvin-Helmholtz Elliptical Mode

KH Twisted Filaments

Theoretical Pressure structure of Elliptical surface mode

Theoretical Pressure structure of 1st Elliptical body mode

Intensity Image & Magnetic Pressure Cross Sections (Hardee et al. 1997)

30 36 42

Dual Helically Twisted filaments

Decelerating Jet/Accelerating SheathConserve Jet Energy/Mass Flux (to Knot A)

obtain jet deceleration

(Case A) 6c 7.5 to 3c 3 (fast jet)

(Case B) 3c 4 to 2c 2 (slow jet)

Case B: slow jet @ = 300 viewing angle

Lose Fraction Jet Energy Flux calculate sheath density & speed

1. E mode wavelength/speed increase & near resonance

2. Sheath energy flux = lost jet energy flux

(1) Slow Pattern (2) Fast Pattern

P0 : 10-9 dyne cm-2

L0 : ~ 1043 erg s-1

Msol : ~ 10-5 yr-1

Growth, Saturation & Structure

Pressure and velocity changes

Approximate Apparent Dual Filament Pressure Structure

Intrinsic Pressure & Velocity Structure (multiple modes shown)

Spatial Growth Rates

1D cuts along jet at fixed r/Rj

HST-1 Knot A

transonic

supersonic

Morphology HST-1 to Knot A

Slow Jet & Fast Pattern @ 30o viewing angle

Fast Jet & Slow Pattern @ 15o viewing angle

VLA @ 15GHz: (Biretta, Zhou & Owen 1995)

HST @ R band: (Perlman et al. 2001)

B nj2/3 ; = 0.7

ED F I

D

EF

Summary/Conclusions

1 pc

0.03 pc

• Dual twisted filament pair from HST-1 to Knot A.

• Radio/optical filament structure correlated (optical more compact).

• Oscillation described by SG = 13.8” (long wavelength Hs mode).

• Dual twisted filament pair DG = 2 - 3” (resonant frequency Es mode).

• Knots are not filament crossing projection. (other shock/adiabatic compression)

Energy/Mass Flux conserving models (~ 1043 erg s-1 , ~ 10-5 Msol yr-1) :

1) Decelerate jet/accelerate sheath, increase sound speed (Es mode resonant) 2) Pattern speed twisted shocks weaken & filling factor reduced 10s (HST-1) > shockMshock > few (knot I) @ jet surface particle injection energy spectrum steepens 3) Jet transonic at Knot A rapid destabilization

4) Morphology lower Lorentz factor, larger viewing angle, faster pattern. (fastest optical proper motions phase effects?)