1. Helically Twisted Shocks in the M87 Jet Philip Hardee 1, Andrei Lobanov 2 & Jean Eilek 3 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

2. Introduction Questions 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: M bh ~ 3 x 10 9 M sol ; initial collimation < 100R G (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)

3. VLA 15GHz: (Biretta, Zhou & Owen 1995) Similar Optical & Radio Structure HST R band: (Perlman et al. 2001) Biretta, Sparks & Macchetto et al. (1999) DEFIH D E F I H Twisted Filament (?) & Filaments (?) Filament Crossing (?) & Twist (?) E D F A A

4. Image Analysis & Structure Single gaussian (SG): ridge line Double gaussian (DG): internal 550 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”)

5. Typical Radio “Knot” Motions (HST-1) < 0.25c (Cheung, Harris & Stawarz 2007) (D)  0.40c (Biretta, Zhou & Owen 1995) (F)  0.90c (Biretta, Zhou & Owen 1995) Fast Optical Motions ( Biretta, Sparks & Macchetto 1999)  ob  6c through HST-1  Viewing angle  j < 19 o  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 < 35 o  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

6. Accelerating Pattern/Viewing Angle Jet Speed @ HST-1 & Viewing Angle (A) 6c    7.5 (optical) @  = 15 0 viewing angle (B) 3c    4 (radio) @  = 30 0 viewing angle Pattern Acceleration (HST-1 to Knot A ) DG  2’  3”   E ob increase 50% SG  13.8”   H ob  constant Pattern Speed (radio motions) : (1) Knot D --  E ob  0.4c – (slow pattern) (2) Knot F --  E ob  0.9c – (fast pattern) Case A: fast jet Case B: slow jet F D Observed change < Intrinsic change

7. Decelerating Jet/Accelerating Sheath Decelerating Expansion (HST-1 to Knot D)  radius expansion factor 3.5 (Case A) 6c    7.5 to 5c    5 (optical) @  = 15 0 viewing angle (Case B) 3c    4 to 2.5c    3.5 (radio) @  = 30 0 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 R j (set by E mode) jet sheath Helically Twisted Sheath Shock Helically Twisted Dual Filament Jet Shock: Kelvin-Helmholtz Elliptical Mode

8. KH Twisted Filaments Theoretical Pressure structure of Elliptical surface mode Theoretical Pressure structure of 1 st Elliptical body mode Intensity Image & Magnetic Pressure Cross Sections (Hardee et al. 1997) 303642 Dual Helically Twisted filaments

9. Decelerating Jet/Accelerating Sheath Conserve 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 @  = 30 0 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 P 0 : 10 -9 dyne cm -2 L 0 : ~ 10 43 erg s -1 M sol : ~ 10 -5 yr -1

10. 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/R j HST-1Knot A transonic supersonic

11. Morphology HST-1 to Knot A Slow Jet & Fast Pattern @ 30 o viewing angle Fast Jet & Slow Pattern @ 15 o viewing angle VLA @ 15GHz: (Biretta, Zhou & Owen 1995) HST @ R band: (Perlman et al. 2001) B  n j 2/3 ;  = 0.7 EDFI D E F

12. 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 ( ~ 10 43 erg s -1, ~ 10 -5 M sol 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) >  shock M shock > 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?)