The Mystery of Fast Radio Bursts and its possible resolution. Pawan Kumar

Transcription

1 The Mystery of Fast Radio Bursts and its possible resolution Outline Pawan Kumar FRBs: summary of relevant observations Radiation mechanism and polarization FRB cosmology Wenbin Lu Niels Bohr Institute, July 5, 2018

2 Transient sources in the universe Stellar explosions Supernovae and origin of elements have been observed for ~10 3 yrs. Gamma Ray Bursts (highest current redshift z=9.4) 1 st observed in Star falling into a massive black hole Tidal Disruption Events (1992) Gravitational waves black hole and neutron star mergers (2015 & 17) Origin of heavier nuclei (A > 40) Fast Radio Bursts (FRBs) the 1 st one found in 2007 Delete this slide for a general colloquium

3 Propagation of radio waves through ISM/IGM Dispersion Measure: t =(4.4 ms) 2 GHz DM Unit: pc cm -3 Pulse broadening due to scattering

4 Fast Radio Bursts (FRBs): History Discovered in 2007 Parkes 64m radio telescope at 1.4 GHz Duration (δt) = 5ms (3 o from SMC) Flux = 30 ± 10 Jy (3x10-22 erg s -1 cm -2 Hz -1 ) Lorimer et al. (2007) DM = 375 cm -3 pc (DM from the Galaxy 25 cm -3 pc high galactic latitude) Estimated distance ~ 500 Mpc δt(λ) / λ 4.4 (Consistent with pulse broadening due to ISM/ IGM turbulence)

5 Farah et al. (2018) Molonglo telescope UTMOST project 10 µs fluctuation 100 khz fluctuation

6 Burst duration (milli-second)

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8 One object (121102) had multiple outbursts (~10 2 in 4 yrs) (Spitler et al. 2016; Chatterjee et al. 2016; not a catastrophic event; VLBI 3 milli-arcsec) DM = ±3.3 pc cm -3 (same for all bursts) L iso = x10 43 erg s -1 Z=0.19 (3.2x10 9 light years ) No optical/x-ray counter-part Duration, δt ~ (1, 10) ms (no broadening) 10 < < 14 No optical/x-ray counter-part log E [erg] ~10 ~14 ~17 log ν [Hz] 45.7 Repeat rate for bursts detected by: Arecibo (red) & other telescopes (blue) Upper limit on repeat rate for non-repeater

9 Properties of FRBs (summary) Duration: t 1 ms Observed between 0.8 and 8 GHZ 10 2 < DM < ~ 10 3 pc cm -3 (>10 2 means outside our galaxy); 0.2 < z < 3 isotropic distribution About 40 bursts have been detected; the all sky rate is estimated to be ~10 4 /day. Some polarized some not. Isotropic energy energy release:

10 Models for FRBs Mergers (WDs, NSs) Collapsing NSs Galactic flaring stars Magnetar flares Giant pulses Question If FRBs are from catastrophic events then where did most of the erg energy go? Asteroids colliding with NSs Extra-terrestrial intellegent life communication

11 Rate: Progenitors? non-repeating: rate ~ 10 4 d -1 (~10% core-collapse SNa rate) Repeating: progenitor birth rate < 10-3 core-collapse SNe ~ Timescale: suggests NS or BH NS or BHs (t ff ~ 10-4 s) Relativistic jets Energetics: (for the repeater FRB ) NS B-field strength B > G ~ (for object size ~ c δt ~ 10 7 cm) (NS dipole spin-down cannot power FRBs)

12 Radiation Mechanism Brightness temperature Black body Flux: F = 2k BT B 2 T B = c 2 apple Rs d A F d 2 A c2 2(c t) 2 2 k B > k d 2 A28 2 for h k B T B coherent emission: E(x, t) Maser: Synchrotron, curvature, etc. negative absorption Collective plasma emission: Cherenkov, cyclotron-cherenkov etc. Beam instability, wave amplification Antenna mechanism: Coherent curvature radiation by charge bunches of size < λ

13 FRBs are more luminous by a factor >10 6 than radio sources in our galaxy Liso [erg/s] T B [K] δt dn/de FRBs > < ms Crab giant pulses ns Crab normal pulses μs log-normal Crab has spindown luminosity and by a factor ~10 2 compared to long-grbs at ~GHz!

14 Coherent curvature radiation Antenna mechanism Consider a charge bunch of longitudinal size λ moving along curved magnetic field Frequency of radiation: = c 3 2 : radius of curvature of field lines = 30 1/3 9 1/3 5 : Lorentz factor of particles L 8 2 c 5 q 2 n 2 e n e cm 3 L 1/2 43 B 0

15 Coherent curvature radiation (Antenna mechanism) L 8 2 c 5 q 2 n 2 e 6 n e cm 3 L 1/ Magnetic field produced by the current associated with particles streaming along the field lines B 0 B ind G L1/2 43 1/3 9 2/3 5 This induced field is perpendicular to the original field

16 Lower limit on B 0 The induced field will tilt the original magnetic field by different angles at different locations (because the induced field lines are closed loops in planes perpendicular to B 0 ) This will cause the particle velocities to be no longer parallel and that will destroy coherent radiation, unless B 0 B 0 > G This suggests that we are dealing with a magnetar

17 Particle acceleration The radiative cooling time of electrons is very short: t c = m ec 2 (n e`2 ) L lab s This time is much smaller than the wave period (1 ns for 1 GHz radiation) To prevent this rapid loss of energy, we need an electric field that is parallel to B 0 to keep the particles moving with Lorentz factor γ. The required electric field: E k esu L 1/

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19 Coherent radiation requires particle clumps of size ~λ Electrons & positrons moving in opposite directions due to the electric field suffer from 2-stream instability, which can generate particle clumps. e-p plasma e ± plasma γ=25 γ=25 γ=50 γ=75 The length scale for the fastest growing modes is of order 50 cm and the growth time is ~ a few µs.

20 Energetics The total energy release is modest: E = L t/(4 2 ) erg Whereas the total energy in the magnetic field is ~ erg So there is no problem powering a large number of bursts! The total number of electrons/positrons needed for producing a FRB radiation is ~ So about one kilogram of matter is producing the radiation we see at a redshift ~ 1.

21 Predictions of the model We should see FRB like bursts at much higher frequencies (mm and possibly higher) if the model I have described is correct. The reason for this is that the peak frequency for curvature radiation depends strongly on γ: = c 3 2 and / E 1/2 k L E 2 k 2 c / 2/3. The event rate / 2/3

22 Polarization Properties of the FRB Repeater Polarization has been measured for about 25 outbursts of the repeater (FRB ), in 4-8 GHz, during a seven month period (Michilli et al. 2018; Gajjar et al. 2018): All these outbursts were 100% linearly polarized The polarization angle varied by ±20 o from one burst to another over the 7 month period. The rotation measure was ~10 5 rad m -2 and varied by 10% Polarization has also been reported for several non-repeaters at 1.4 GHz and found to be between 0 and 80% linearly polarized the less than 100% polarization could be due to Faraday depolarization in finite channel width (0.4 MHz).

23 What is responsible for 100% polarization and nearly fixed direction for the electric field over a period of 7 months? The answer is strong magnetic field such that the cyclotron frequency is >> GHz, and plasma frequency of order 10 2 GHz. The mode that escapes to infinity is the X-mode: ~E w perpendicular to ~k and ~ B 0 X-mode ~E w ~k ~ B 0 ~E w (O-mode) ~ ~ As the wave travels outward it keeps the electric field k x B 0

24 The electric field direction is ~ k x ~ B 0 at the freeze-out radius. If the freeze out radius is >> R s then k r and ~ ~ Since, ~B 0 = 3ˆr(ˆr ~m) ~m r 3 ~ m: magnetic moment of the NS Then ~ E ~ k x ~ B 0 ~ k x ~ m The direction of ~ E changes from one burst to another if the magnetic & rotation (Ω) axes are miss-aligned. ±20 o swing in E w for suggests the angle between ~ m & ~ Ω ~20 o

25 General constraints on Maser & Plasma mechanisms These mechanisms are favored for radio pulsars, and so are obvious possibilities to consider for FRBs. Magnetic field energy converted to Particle beam kinetic energy 2 L beam < R B 2 c/4π = erg s B 14 /R 6 L beam > L frb ~ erg s -1 ) -1/4 1/2 The outflow launch radius: R ~ < 10 7 cm L frb,43 B 14

26 Synchrotron maser in plasma, and plasma waves produce radiation at a frequency ~ ν p γ a Observed frequency: ν = Γ ν p γ a (ν ~ 1 GHz) We can eliminate n e in terms of ν p (ν p n 1/2 / e ) 0 < a < 1 γ: e - LF ν p : plasma frequency Γ: source Lorentz factor Kinetic luminosity of the beam converted to GHz radiation: L beam =4 R 2 n e m c 3 2 L beam (4x10 39 erg s 1 ) R a L beam > L frb ~ erg s -1 =) R>10 14 a 1 cm >> R LC Stimulated-IC loss limits brightness temperature: R LC = 5x10 9 P cm T B < τ T -1 γ 5 << K (or the radiative efficiency < 10-8 )

27 Curvature Maser frequency: strong B-field inside NS magnetosphere (only possible when there is torsion) negative This also applies to collective plasma emission ψ is the angle between electron & photon momenta.

28 Synchrotron Maser (vacuum) Consider a jet with Lorentz factor Frequency: = qb0 2 sin 2 m e c Luminosity: L iso apple 4 r 2 n 0 e(b 02 Γ 2 sin 2 /6 ) 2 c Emission radius: population inversion nearly uniform B-field narrow pitch-angle distribution negative ψ is the angle between LoS & electron momentum vector α ~ γ -1 pitch angle

29 Synchrotron Maser (plasma) v v population inversion p ( e / B ) 1/4 dn e /d 0 / 0>2 (in shock) Sagiv & Waxman (2002) v ε B < ~ 10-9 Γ 3 Luminosity: Emission radius: 4 (for ν ~ 4 GHz) r 3x10 10 cm L 1 2 iso, x10 12 cm apple e B 1 4 Duration: t r 2c 2 0.1ms 2 3 number of particles: N 4 r3 n 0 5x !! induced Compton scattering limit: Waxman (2017) has =) T B apple K (T FRB ~ K)

30 Collective Plasma Emission Plane-wave perturbation Wave dispersion relation: For real k, If ω = real, wave propagation If Im(ω) < 0, wave damping If Im(ω) > 0, wave growth and there is an instability aka plasma maser, because it is a maser-like process with exponential growth rate = Im(ω)

31 Collective Plasma Emission B-field constraint: Particles are in the lowest Landau level and have: 1-D distribution function Consider a plasma moving towards the observer: v Another beam runs through this plasma instabilities where Im(ω)>0 v Two-stream instability: impossible to grow at v Cyclotron-Cherenkov (anomalous Doppler) instability: v Cherenkov instability: curvature cooling growth rate too low at

32 z FRBs as probe of Dark Energy & Intergalactic Medium Dark energy equation of state DM = Z d` n e à distance Localize to within arc-sec à z of the host galaxy à Baryons in intergalactic medium (DM) Intergalactic medium magnetic field Turbulence spectrum in IGM (duration) Macquart et al. (2015)

33 Summary FRBs are from extra-galactic NSs with magnetic field > G. The radiation is likely coherent curvature radiation; e ± are accelerated in magnetic reconnection. Multiple outbursts from the same object is a natural expectation of this model. The model predicts FRB like bursts (ms duration) at larger frequencies with L, at a decreasing rate (ν -2/3 ). / 2/3 Polarization properties of the repeater (FRB ) are consistent with the coherent curvature model.