FRB emission mechanisms

Maxim Lyutikov (Purdue, McGill)

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What FRBs are not• msecs long (not AGNe)

• > 104 per day (not prompt GRBs)

• repetitive (not catastrophic events like NS-NS mergers)

• isotropic (extra-Galactic); D ~ 1 Gpc - (cosmological)

• coherent emission, (not just synchrotron)

• local DM ~ 100, constant over few yrs (not through early SN)

• Polarization - no clear idea (Petroff ’s talk)Chatterjee + 2017

Tendulkar + 2017

Tb ⇡ 1034 K

- If there is a road to Perytons-II, polarization is a suspect-Very unfortunately, there is no clear evidence for two or (18) !different populations

Origin: only NS magnetospheres

• Instantaneous luminosity for the Repeater: !

• duration (assume intrinsic)-> size • Equipartition B-field (lower limit): !!

• NS magnetospheres! (Clean, relativistic) - Stellar-mass BHs (?) - accretion-supplied B-field is dirty.

- WD magnetosphere(?)

4

Liso

= 4⇡D2(⌫F⌫) ⇠ 1041ergs�1

Beq =p8⇡

p⌫F⌫D

c3/2⌧= 3⇥ 108⌧�1

�3 G (Lyutikov + 2016)

Oh, this murky business of pulsar/NS radio emission mechanisms… !50 years of intense research, there are books published - please no cheesy order-of-magnitude “scale this with that”…

(Lyutikov, 2017)

Radio emission from NSs• There are three types of coherent

emission from NS: type-I, type-II, type-III

• Type I: log-normal dist., Crab precursor, polar caps, rotationally-driven

• Type II: GPs, power-law, Crab MP&IP, border between open/closed field lines, rotationally-driven

• Type III: magnetars, on close field lines, crustal shear-driven (reconnection, ~ Solar)

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Crab

1810

Serylak+ 2009

FRBs from NS magnetospheres

• Model I: Giant pulses (Crab on steroids) - rotationally powered (type ii radio emission)

!

• Model II (hypothetical): magnetar flares - magnetically powered (type iii radio emission)

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Pulsar radio emission: theory

• Let's never again talk about coherent curvature emission by bunches.

• Yes, there are wigglers (FELs) !!!!!!

• But: generally, plasma process in astrophysics are in kinetic regime (random phase), while in laboratory in reactive regime (finely tuned, all in phase)

• (Extra slide at the end of the talk, during the discussion part)

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(c.f. Goldreich-Keely 1971)

Plasma astrophysics primer: Plasma Maser.

• Plasma maser: non-equilibrium distribution f(p) (in momentum space, not physical space) results in coherent emission of plasma normal modes. Population inversion: there is more particles willing to emit a wave than willing to absorb it

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� /✓s!B

��?

@

@p?+ kk

@

@pk

◆f(pk, p?)

s > 0

Landau levels

s = �n > 0

s = �n < 0✏ = (n+ 1/2)~!B

meff,k ⇠ �3me

meff,? ⇠ �me

need > 0 for growth

� / 1

! � kkvk � s!B/�

f(p?) / �(p?)/p?@p?f < 0

A roadmap for radio emission theory:

• Guess (justify) the distribution functions (parallel, perp, curvature drift also might be important)

• Find dispersion relation for normal modes omega (k) • Find resonant condition - are there any resonant particles? • Find growth rate • Find saturation level (quasilinear?) !!

• Or just do PICs - not yet, but we are getting close

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• BTW, Hessels' talk: Narrow spectral features (and their drifts) - narrow range of velocities where resonant conditions are satisfied

• We are not yet in a position to construct microscopic models of radio emission

• we are left only to discuss the macroscopic limitations • (Still, Later on - my favorite microscopic model of radio-X-

gamma emission model for pulsars)

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Macroscopic Model I (type ii emission): Rotationally powered super-Giant Pulses

• very young SNRs, 10-100 years • free-free absorption in new SN shell (no LOFAR)

• DM through the shell

!• Crab’s GPs reach ~ 1% efficiency • If need ~ 104 higher peak power from 100 Mpc

• Few msec period, with Crab-like B-field - reasonable to expect

• Spin-down times ~ 10-100 yrs

• Rates within 100 Mpc are OK.

• Injection rate (observed - consistent with observed distribution of fast pulsar)

• Very flat distribution of distances to a given brightness (type of Malmquist bias)

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⌧ff ⇠ 1@300MHz

DM ⇡ 100s

✓t

yrs

◆�2

⌫F⌫ / Lsd

finj / E�1 f / E�3/2

Lyutikov + 2016

It was a good model, but not from ~ 1 Gpc

• Radio power cannot be larger than the spin-down (must be magnetospheric, hard to store much more energy in the magnetosphere) !!

• Need high B - short P (at least few msec) !!

• Constant DM: t >100 yrs • eta ~ 1 + 1 msec spin at birth + 100 yrs< age < 600 yrs - NO.

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⌫F⌫ = ⌘Lsd

4⇡D2

⌧SD = ⌘⇡INS

2D2⌫F⌫P 2min

⇡ 600 ⌘ yrs

The most powerful Crab’s GP have eta = 10-2

For Crab: 6 yrs if all in GPs

Repeating FRB at 1 Gpc + constant large DM !excludes rotationally powered emission

FRB 160102 could be even worth

• It is truly amazing that radio power starts to contradict the limits on the total power!

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Macroscopic Model II: magnetar flares (type-iii)

• Solar type-III radio emission in magnetars (Lyutikov 2006) • Initial stage of a “reconnection flare” - jets of particles, hence

coherent emission - like Crab flares (Lyutikov et al. 2016) • Best case - observe radio burst associated with magnetar

burst and flares. • Constraining limits from SGR 1806-20 flare

• SGR flare was 1047 erg/s -> radio efficiency 10-6 - OK? • But would give a GJy from 10 kpc - not seen in Parkes side-lobes

(Tendulkar + 2016) • No radio from PSR J1119-6127 X-ray (radio efficiency < 10-8)

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Glitches?• There are no bright EM signals with glitches • Magnetospheric changes are tiny, 10-6 • Time scales - crustal shear ~ 100 msec (for ~ msec time

scale the energy must be stored in the magnetosphere).

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• Juste pour rire/just for laughs, let’s make a glitch FRB model • Imagine you are walking at 1 m/sec. And then, “suddenly” a

glitch: on human reaction time of 100 msec, you change your speed by 10-6 to (1 m - micrometer)/sec. And then you convert all that energy into radio waves at 1 GHz.

• Boom! - Mega-Jy signal 3 km away!

• This is obviously ridiculous, but astrophysically, scaling “this with that”, it makes sense, right?

• Not for radio (could be OK for high energy) • (Mechanical to radio vs EM to radio)

Best hope: other wavebands

• Radio: > 1040 erg/s • Optical > 1045 erg/s • X-rays> 1050 erg/s, GRB-like rates - not correct • All sky X-rays monitors can see magnetar-type flare to ~ 40 Mpc,

but targeted observation (eg. of the Repeating FRB) can detect with Chandra/NuStar magnetar-type flare to z ~1.

• Afterglows: jetted magnetar post- burst outflows (Keane 2016, Lyutikov 2006)?)

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Lyutikov 2006

for flat (nu Fnu )

Counter-part strategy: optical

• Optical energetics >> radio (If !)

• Peak flux ~ 9m (but only for few msec - fast read-outs!)

• m~ 15 image in 60 sec PTF, ASAS-SN,

EVRYSCOPE (LSST!) - PTF might have seen, as star-like points in single exposure.

• Optical would look at FRB every ~ 10 hours (10 sq. degrees field of view)

• fast readout is good

• Radio and optical - stare at the same patch

• But: For The Repeater, the optical power is in the 1045 erg/sec

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Lyutikov & Lorimer 2016

Best observational strategy

• Simultaneous Radio - Optical • Simultaneous pointed X-rays (The Repeater - e.g. NuStar) • Multi-frequency radio (triggered LOFAR obs.)

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My favorite pulsar radio emission mechanism for Type II radio

emission (giant pulses)

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Crab

20

Rad

io in

tens

ity (a

u)

0

0.5

1

1.5

2 Radio (Nancay telescope, 1.4 GHz) (a)

Nor

mal

ized

cou

nt ra

te

00.5

1

1.5

22.5

3

3.54

4.5 Optical (SCam-3) (b)

Cou

nts/

s

0

500

1000

15002000

2500

3000

3500

4000

4500 X-rays (RXTE, 2 - 16 keV) (c)

Phase0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

)3C

ount

s (x

10

1.57

1.58

1.59

1.6

1.61 Hard X-rays (INTEGRAL, 100 - 200 keV) (d)

Soft gamma-rays (Comptel, 0.75 - 30 MeV) (e)

Cou

nts

65000

66000

67000

68000

69000

70000

71000

72000

73000

Gamma-rays (EGRET, >100 MeV) (f)

Cou

nts

0

50

100

150

200

250

300

350

400

450

Gamma-rays (Fermi LAT, >100 MeV) (g)

Cou

nts

0

500

1000

1500

2000

Phase0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

VHE gamma-rays (MAGIC, >25 GeV) (h) )3C

ount

s (x

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182182.5183183.5184184.5185185.5186186.5

Aligned from radio to VHE gamma - common origin

What excites gyration: anomalous cyclotron resonance

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B-fieldn > 1 γ

γ

γ

γ

γ

γ γ

γ

v> c/n

- A particle can emit a cyclotron photon with no initial gyration

!- Particle goes up in Landau levels and

emits a photon - radio - Spontaneous down cyclotron

boosted in UV-X-rays - IC - VHE gamma rays

! � kkvk = �!B/�

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What excites gyration: anomalous cyclotron resonance

23

B-fieldn > 1 γ

γ

γ

γ

γ

γ γ

γ

v> c/n

- A particle can emit a cyclotron photon with no initial gyration

!- Particle goes up in Landau levels and

emits a photon - radio - Spontaneous down cyclotron

boosted in UV-X-rays - IC - VHE gamma rays

! � kkvk = �!B/�

10-4 0.01 1 100 104 10610321033103410351036

eêHmec2L

eF e,ergês

From ~100 MHz to ~ 2 TeV - 20 orders in energy

Lyutikov 2012, also in prep.

Conclusion

• Amazingly, radio power (+ constant DM and non-changing properties of The Repeater) puts energetic limits on the type of emission (rotationally vs magnetically powered; does not yet constrain particular instability that drives radio emission). Neither looks too promising for now - Mystery!

• Perhaps there is some slack left in either: • Highly non-stationary processes in pulsar outer magnetospheres

• Explosive reconnection events in magnetar magnetospheres - can they generate unstable distributions and radio bursts?

• PICs ?

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• Please no “ - FRB comes from here” models

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A point on terminology: magnetar vs high B-field NS

• Let’s not call rotationally powered effects from high-B NS “a magnetar” - just “high-B NS” !

• Leave the magnetar term for B-field powered effects.

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(Also: non-linearity parameter “a”)

• EM non-linearity parameter !!

• If no B: • Actually, !

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a =eE

mec!⇡ 105 � 1

� ⇠ a

a =eE

mec!B 1

huge radiative losses (eg. induced Compton)

Coherent emission by bunches - critique

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