Acceleration & Collimation Zone of
FSRQ 1928+738
Kunwoo Lee, Jongho Park, Sascha Trippe,
Nakamura Masanori
Seoul National University

Jets from Flat Spectrum Radio Quasars●Flat Spectrum Radio Quasar(Top View)●Relativistic jet (v ~ c)●Narrow angle ( θop <1 )●Massive Black Hole∘( 108 −10 9 M ⊙ )●High accretion rate˙˙( M BH / M Edd =0.1∼0.5 )●Image Credit : Sophia Dagnello, NRAO/AUI/NSF

Mostly in distant universe

Basic information of FSRQ 1928+738
MOJAVE 15 GHz Image

Optically thick core

●Common Name : 4C +73.18●

Radio Brightness S 43 >3 Jy●High Dec (+73)●→ Ease of observation●z ~ 0.3, M BH ∼10

Optically thin extended jet
8.57

M ⊙ , θv ∼12.8 ∘5→ 1 mas∼ 5×10 R s✔ Good target to explore inner jet
Nakamura-san’s talk
http://www.physics.purdue.edu/astro/MOJAVE/sourcepages/1928+738.shtml

KaVA Monitoring of FSRQ 1928+738
KaVA 43 GHz Image●KaVA Q band 43 GHz●2017 Feb ~ 2019 Jan (~2yr)●Monthly interval●Main Goals- (1) Exploring its jet kinematics- (2) its variability

KaVA Monitoring of FSRQ 1928+738(1) Jet kinematics → Proper motion analysis(2) Exploring its variability → Light curve analysis

KaVA Monitoring of FSRQ 1928+738

δ≡sD Lδ var =c Δ t decay (1+ z)

1γ(1−β cosθ)

Jorstad et al. (05, 17)

Jet Kinematics of FSRQ 1928+738●

Jet kinematics: βapp increases
as a function of distance

βapp=

β cos θ(1−β cos θ)●

β & θ : coupled- Real acceleration?
or projection effect?

Jet Kinematics of FSRQ 1928+738

β2app +δ 2 +1
Γ=2δ●●Observed Parametersβapp & δ increase●●

as a function of distance●Due to Real Acceleration!

θv =arctan2βapp
β2app +δ 2−1

Intrinsic Parameters

Real Acceleration→ Acceleration Zone∘

Hovatta et al. 2009●θv ∼12.8●

No significant jet bending !

Jet Kinematics of FSRQ 1928+738
22

β +δ +1
Γ= app2δ

●Γ×α=[0.15, 0.16, 0.25, 0.25]
Γ : Lorentz factor , α : half opening angle(de− projected)●

βapp =β cos θ(1−β cos θ)Γ×α=0.2 i n average: Acceleration & Collimation→ Causal Connected
Jorstad+ (05,17), Pushkarev+ (09,17)

Jet Kinematics of FSRQ 1928+738
2

2β +δ +1
Γ= app2δ

Cross-Check

βapp =β cos θ(1−β cos θ)●More knotty structure on 15 GHz●

Both data shows acceleration●Acceleration Zone (0 ~ 6 mas region)

Q1) Acceleration keep going?
Q2) Max of βapp ?
Q3) Collimation Zone ?

Jet Kinematics of FSRQ 1928+738
22

β +δ +1
Γ= app2δ

Cross-Check●

Jet Kinematics (~20 mas)
- Acceleration → Deceleration●βapp =β cos θ(1−β cos θ)Transition @~ 5 mas✔ Q1) Acceleration keep going?
✔ Q2) Max of βapp ?
✗ Q3) Collimation Zone ?

Jet Kinematics of FSRQ 1928+738
Park+ 2019

22β +δ +1
Γ= app2δ

Cross-Check●

Jet Kinematics (~20 mas)
- Acceleration → Deceleration●

βapp =β cos θ(1−β cos θ)Transition @~ 5 mas✔ Q1) Acceleration keep going?
✔ Q2) Max of βapp ?
✗ Q3) Collimation Zone ?

Jet Kinematics of FSRQ 1928+738
Nakamura+ 201822

β +δ +1
Γ= app2δ

Cross-Check●

Jet Kinematics (~20 mas)
- Acceleration → Deceleration●βapp =β cos θ(1−β cos θ)Transition @~ 5 mas✔ Q1) Acceleration keep going?
✔ Q2) Max of βapp ?
✗ Q3) Collimation Zone ?

Jet Collimation of FSRQ 1928+738
W ( z)∝ z●a

Extended Jet structure(~ 40 mas)

→ Jet collimation profile

Jet Collimation of FSRQ 1928+738
W ( z)∝ zaHigh-freq data●

Extended Jet structure(~ 8 mas)a●W ( z)∝ z , a∼0.553●

Jet collimationa∼0.553±0.025: parabolic jet (being collimated)Jet Collimation of FSRQ 1928+738
W ( z)∝ za

Low-freq data●

Extended Jet structure(~ 40 mas)a

●W ( z)∝ z , a∼1.142●

Jet collimationa∼1.142±0.051: conical (/ hyperbolic) jet(free expansion)Jet Collimation of FSRQ 1928+738
W ( z)∝ za∼1.03±0.013

Broken – Power Law Fit●W ( z)∝ z a 1 ( z<b)

●W ( z)∝ z a 2 ( z≥b)●b : transition sitea∼0.46±0.04
a∼1.142±0.051

4.73±0.30 mas

a→ parabolic to conical transition(Jet Geometry)

Acceleration & Collimation of FSRQ 1928+738
W ( z)∝ z

4.73±0.30 mas●

4.73±0.30 mas

Jet Geometry●

Jet Kinematics●Collimation Zone ~ Acceleration Zone●

Jet Kinematics : acceleration → deceleration●Jet Geometry: parabolic→ conical
1(= Jet Collimation Break)●

Both transition @ 5 mas→ ACZaJet Collimation Break @ Sphere Of Influence
W ( z)∝ z●

Jet Geometry
8.57●

M ⊙ , θv ∼12.8 ∘●M BH ∼10●

r S . O . I ≡ GM BH /σ 2star●σ star ∼σ [OIII ]= 128−166 km/ s

Jet Kinematics

Park 2017, Hovatta+ 09

6

Bian & Zhao 20046→ r S . O. I ∼ 1.6−2.8×10 r s , (r JCB = ∼ 2.7×10 r s ): coincident !!

aJet Collimation Break @ Sphere Of Influence
W ( z)∝ z4.73±0.30 mas●

Jet Geometrya

4.73±0.30 mas●

Jet Kinematics●Collimation Zone ~ Acceleration Zone

→ ACZ

●

JCB (& Kinematics transition) @ S.O.I●

ACZ : Inside S.O.I of the
1 SMBH●

JCB site (End of ACZ) : resembles HST-1 & S region ?
M87, 1H0323+342

JCB siteJCB site : Brightness Enhanced
W ( z)∝ zaJCB site : Limb-BrighteningW ( z)∝ za

Stacked Knot
positions

Stacked Knot
positions

VLBA 15GHz

VLBA 15GHz

JCB site : Limb-BrighteningW ( z)∝ za(1) Enhanced Intensity(2) Limb-brightening→ Re-collimation shock

NLS1 1H0323+342 : Doi+2018

ACZ & JCB : Conclusion
W ( z)∝ z

4.73±0.30 mas●

Jet Geometrya4.73±0.30 mas●

Jet Kinematics●Collimation Zone ~ Acceleration Zone

●JCB (& Kinematics transition) @ S.O.I●

ACZ : Inside S.O.I of the
1 SMBH●A re-collimation shock candidate @ S.O.I: pressure imbalance likewise→ ACZ

M87, 1H0323+342

JCB siteSummary●We discovered (spatially resolved) the ACZ in the jet of FSRQ.
- showing both acceleration & collimation- ACZ : inside the S.O.I of the SMBH●

We discovered the two transitions @ S.O.I- Acceleration → Deceleration in jet kinematics- Parabolic → Conical in jet geometry●

We detected re-collimation shock (candidate) @ S.O.I- Locally enhanced brightness- Limb-brightening feature

Deeper understanding the ACZ ?

Observational Strategy1 mas∼ 5×105 R s●GMVA / Space - VLBI
: ( in prep )●Polarimetry: ( in prep )Acceleration & Collimation Zone

●Multi-wavelength light curves: ( collaterally on-going )MWL analysis of FSRQ 1928+738●

Long-term perspective ( 10 yrs )- @ 225, 37, 15 GHz- large flares- flares with yr time scale→ Similar Global Trend●

Short-term perspective (~2 yrs)
- @ 225, 43, 37, 15 GHz- 2 (or 1) small flares- flares with month time scale

MWL analysis of FSRQ 1928+738●

Long-term perspective ( 10 yrs )- @ 225, 37, 15 GHz- large flares- flares with yr time scale→ Similar Global Trend●

Short-term perspective (~2 yrs)
- @ 225, 43, 37, 15 GHz- 2 (or 1) small flares- flares with month time scale: Well-constrained Eventshowing Δ t lag

MWL analysis of FSRQ 1928+738●

Long-term monitoring ( 10 yrs )- @ 225, 37, 15 GHz- large flares- flares with yr time scale→ Similar Global Trend●

Short-term monitoring (~2 yrs)
- @ 225, 43, 37, 15 GHz- 2 (or 1) small flares- flares with month time scale→ Well-constrained Event

Kudryavtseva+2011

Thank you