Preliminary

Three dimensional modeling of FR-II jets
using two-temperature MHD simulation

Ohmura Takumi,Machida Mami (Kyushu Univ.)
AGN jet workshop 2020 in Tohoku Univ. ,2020/01/20-22

1. Introduction - FR II Radio Galaxies Most of FR II sources have powerful jets
- Edge brightened sources ( hotspot, Radio-lobe )Synchrotron radiation from relativistic electrons in themagnetic fields of lobes.
- Diffuse thermal X-ray emitted like a rugby ball.

Blue:X-ray, Red: Radio1. Introduction - FR II Radio Galaxies -Classical theory of FR II jets (e.g., Scheuer 1974)- Jets convert kinetic energy into particles and internalenergy at the terminal shocks = Hotspots- The hot plasma through the hotspots back towards to thenucleus, spreading out = Radio-lobe (Cocoon)- The layer of shocked plasma emitted diffuse X-ray.

1. Introduction - Two-temperature plasma X-ray cavity in the galaxy cluster-> Jet plasma is hotter and lighter than ICM[ 𝑛ICM ∼ 10−2 − 10−3 cm−3 , 𝑇ICM ∼ 107 − 108 K ]- Relaxation time scale of electrons and ionsthrough Coulomb coupling is longer than thepropagation time scale.

𝜏ei ≥ 𝜏dyn−1 3/2
𝜏ei ∝ 𝑛 𝑇e

- Electrons and ions could be decoupled in jets.

𝑝electron ≠ 𝑝ion

1. Introduction - Energetics of radio-lobe -Cocoon

BeamBowshock

𝑃ion + 𝑃ele

External Pressure- Pressure balance of radio-lobe, 𝑃ext ≤ 𝑃ion + 𝑃ele
- The under-pressured lobe indicate the existence ofthe non-radiating ions in the FR-II jets.
(Belsole+ 2007)
𝑃ext + 𝑃ram
Under-pressured lobe

Lobe Internal Pressure

1. Introduction - Energetics of radio-lobe - Pressure balance of radio-lobe, 𝑃ext ≤ 𝑃ion + 𝑃ele- The under-pressured lobe indicate the existence of- We can only
estimateelectron
the non-radiating
ionsin the FR-IIjets. energythrough(Belsole+ 2007)
𝑃ext +𝑃ram radiation.
Under-pressured
Under-pressuredlobelobe

CocoonBeamBowshock

𝑃th + 𝑃mag

External Pressure- The ion energy are undetectable withcurrent observational techniques!!

Lobe Internal Pressure

1. Introduction - Motivations We investigate
・the spatial energy distribution ofelectron and ion through two-temperature
MHD jets simulation.

・the pressure balance between jet andsurrounding medium, especially possibilityof electron under-pressured lobe.

Method- Basic equations- The fraction of electron heating- Model2. Method - Basic equations Assumption- Electron-Ion plasma, 𝑛 = 𝑛i = 𝑛e
- One fluid approximation- Electron and Ion have distinct temperature
MHD Eqs. + Electron and Ion. energy Eqs.
𝑑𝑠i𝑛𝑇i= −𝑞 ie + 1 − 𝑓e 𝑞 heat𝑑𝑡
𝑑𝑠e𝑛𝑇e= +𝑞 ie + 𝑓e 𝑞 heat − 𝑞 rad𝑑𝑡[Colulomb] [Dissipation] [Radiation]

2. Method - The fraction of electron heating Model 1: Turbulent dissipation into the electron and ions.
( Kawazura+ 2019)𝑓e = 𝑓e (𝑇e /𝑇i , 𝛽i )Magnetic energy dominant region : 𝑓e → 1 (electron heating),
Thermal energy dominant region : 𝑓e → 0 (ion heating)Model 2: Dissipation in collisonless shock.
𝑓e = 0.05 Shocks heat ions (e.g., Ghavamian+2013, Matsukiyo+2010).

0 < 𝑓e < 1𝑢dis𝑓e𝑢ele.

Model 1𝑢
1 − 𝑓 ion

Model 2e

2. Method - Model MHD CODE : CANS+ (Matsumoto+2019, Ohmura+ 2019)
Uniform Grids: (800,800,1200)
Jets parameter𝑛 [g/cm]
1010𝐿kin = 2.0 × 1046 erg/s
𝑇e = 𝑇i = 3.0 × 109 K−1−2𝑣jet = 0.2𝑐
𝐵tol = 50𝜇𝐺
𝑟jet = 1kpc

Initial ICM profile
𝛽-profile (King+ 1972)
𝜌(𝑟) = 𝜌0 1 + 𝑟/𝑟c 2 −3𝛽/2𝑇e = 𝑇i = 2.3 × 107 K (2KeV)
𝜌0 = 8.35 × 10−26 g/cc , 𝑟c = 30kpc, 𝛽 = 1/2

Results- Overview- Energetics in jets
- Under-pressured lobe

3. Results - Overview - Beam can reach termination, and form the terminal shocked.
- The most of heating energy goes to ions.
130MyrIonEle.

3. Results - Energetics in jets Volume-weighted pressure in radio-lobe.
‫ ׬‬2𝜋𝑟𝑑𝑟𝑑𝑧

𝑝𝐵 = 𝐵2 /8𝜋Lobe
Ion
ElectronMagnetic

Z [kpc]Z [kpc]Pressure [Code Unit]

𝑃i,e,B 𝑧 =‫𝑝 ׬‬i,e,B 2𝜋𝑟𝑑𝑟𝑑𝑧

3. Results - Energetics in jets -Lobe vs. Shocked-ICM

Ion

Z [kpc]Pressure [Code Unit]- In shocked-ICM, Ions and electrons decouple by bowshock.
But, Coulomb interaction is effective because density is high.
- The lobe electron pressure is lower than shocked-ICM.

ElectronZ [kpc]3. Results - Energetics in jets -Shocked-ICM electron

Lobe electronZ [kpc]Z [kpc]Pressure [Code Unit]- Shocked-ICM electron pressure is higher than surrounding
electron pressure everywhere.
- Lobe electrons have lower energy than ICM electrons (z<80).

3. Results - Under-pressured lobe - Shocked-ICM electron pressure is higher than surrounding
electron pressure everywhere.

Under-pressured lobe
z=30 kpc

𝑃lobe
𝑃ICM

z=30 kpc

𝑃shocked ICM
𝑃ICMz∼ 100 kpcz∼ 80 kpc

Internal electron Pressure

Z [kpc]External electron Pressure- On the other hand, lobe electron pressure is low.

Discussion4. Discussion - Under-pressured lobe - The bow (cocoon) shocks of Cyg.A are clearly seen in highresolution Chandra observations.
- Shock compression is clearly observed at these shocks.
0.5-7.0 KeV X-ray (Chandra), contour 4.5 GHz (VLA)(de Vries+ 2019, Snios+2018)

Cocoon shock4. Discussion - Under-pressured lobe - However, the pressure of the eastern lobe, which isestimated by X-ray Inverse Compton, is lower than
the rim pressure, i.e., Under-pressured lobe.
- These observational analysis indicates that𝑃lobe < 𝑃ICM < 𝑃shocked−ICM(de Vries+ 2019)4. Discussion - Under-pressured lobe - However,pressure of the eastern
lobe, which
Ourthetwo-temperature
jets modelcouldis
estimatedbyX-ray
InverseCompton,islowerthanexplain this pressure condition.
the rim pressure, i.e., Under-pressured lobe.
𝑃lobe < 𝑃ICM < 𝑃shocked−ICM- These observational results indicate thatPressure

𝑃lobe < 𝑃ICM < 𝑃shocked−ICM
Shocked-ICM electron

Lobe electronz [kpc]5. Summary- We have carried out high-resolution two-temperature
MHD jets propagate simulations.
- Beam, which propagating up to 100 kpc, can reachtermination of jets, and terminal shock (hotspot) is formed.
- The magnetic energy is much less than the ion thermalenergy, and hence most of heating energy goes to ions.
- The lobe electron pressure is lower than that of shockedICM and surrounding ICM, and under-pressured lobe isformed .