TWO SCREEN SCINTILLOMETRY OF FRBS

SACHIN PRADEEP

LISE MEITNER GROUP ON FRB'S, FUNDAMENTAL PHYSICS IN RADIO ASTRONOMY, MPIFR - BONN

Lise Meitner Max Planck Research Group, Max-Planck-Institut für Radioastronomie 

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AGENDA

• FRB AND SCATTERING
• TWO SCREEN MODELLING
• RESOLUTION ARGUMENT
• ACF AND MODULATION INDEX
• QUENCHING OF SCINTILLATIONS!
• SUMMARY

Multi Screen FRB

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FAST RADIO BURSTS

• Fast Radio Bursts (FRBs) are extra-galactic single pulses of micro to millisecond duration.
• Encounters Host galaxy ISM, Intergalactic Medium, Milkyway ISM.
• Propagation effects: Dispersion, Rotation Measure, Scattering and Scintillation.
• FRBs as an astrophysical tool. 

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FRB 20220207C (Zach) detected by DSA , MB. Sherman et al.2023

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Multi Screen FRB

SCATTERING AND SCINTILLATION

Multi Screen FRB

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• Multipath propagation of pulse causes delayed arrivals.
• Pulse Broadening due to scattering.
• Delays (τ) shorter than pulse duration interferes to produce scintillations of bandwidth 1/τ in frequency space . 
• Scattering material approximated to be distributed in thin screens/lens

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Courtesy - Dr. Robert Main

Scatter Tail

Interference

pattern

FRB

SCATTERING OBSERVABLES-SINGLE BURST

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Modulation index 

m_I - ACF Relation

Multi Screen FRB

t_{scatter, host}

Screen Parameters

Measure of screen modulation in pulse spectra. In a single screen case its 1, 

m_I = STD(𝜈)/ MEAN(𝜈)

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Sammons et al. 2023

𝜈_{scint, MW}

• Fourier uncertainty,  2πt_scatter𝜈_scint =1
• Violated by a number of FRBs (eg: Sammons et al. 2023)
• Major pulse scattering : Host galaxy screen.
• Scintillation effects : Milky Way (MW) screen.

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TWO SCREEN MODELLING

Multi Screen FRB

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• Total geometric delay  due to a path of multiple deflection is the sum of delay due to each deflection from straight line. Time delay from screen_j and screen_i,

• Image distribution: Random, overlayed with gaussian amplitude distribution.

• Stars twinkle, planets don’t.
• What happens when host galaxy screen is resolved? Will it be like resolving a planet?
• Presence of MW scintillation used to put limits on location of host galaxy screen (Masui et al. 2015)
• Resolution Power, RP = θ_host/θ_res  

RP > 1 : Resolved

    RP < 1 : Unresolved

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Unresolved

Resolved

RESOLVING SCREENS IN FRBS

SPECTRAL ACF AND MODULATION INDEX

• The two screen delay formula can written as:

Multi Screen FRB

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• FFT of the time series into the spectra. The spectral ACF in the two screen unresolved regime becomes

• N-Screen ACF and modulation index:

&

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NOW SIMULATIONS👉🏾

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ABRUPT QUENCHING OF SCINTILLATION?

Multi Screen FRB

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Just Resolved

Un-Resolved Screens

More Resolved

Completely Resolved screens

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DYNAMIC SPECTRA

Varying scintillation pattern!

Just Resolving 

(RP=1)

Completely Resolved (RP=10)

Un-Resolving Screens (RP=0)

Varying scintillation pattern!

• Broad Scintillation – MW Screen
• m_MW ≈ 1
• 𝜈_{MW,simulation} = 𝜈_MW,injected

Multi Screen FRB

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SPECTRAL ACF – RP=0

• Narrow Scintillation – Host screen
• Total two screen modulation, m_tot ≈ √3
• 𝜈_{host,simulation} = 𝜈_{host,injected}

• m_MW < 1
• 𝜈_{MW,simulation} > 𝜈_MW,injected

Multi Screen FRB

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SPECTRAL ACF – RP= 1

• Total two screen modulation, m_tot < √3
• 𝜈_{host,simulation} = 𝜈_{host,injected}

• m_MW < 1
• 𝜈_{MW,simulation} >> 𝜈_MW,injected

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SPECTRAL ACF – RP = 10

• Total two screen modulation, m_tot ≈ 1
• 𝜈_{host,simulation} = 𝜈_{host,injected}

INTRA-PULSE SCINTILLATION EVOLUTION

Spectrum (t)

ACF of each Spectrum (t)

Coherence length decreasing along the scattering tail

Multi Screen FRB

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 INTRA-PULSE MODULATION EVOLUTION

 Case-1: Unresolved Screens 

 Case-3: Resolving Screens 

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APPLICATION OF QUENCHING

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• Broadening and quenching of scintillation with increase in RP.
• Peak ACF value (ACF_MW) of the MW Scintillation fit gives an upper limit on the host galaxy screen distance from the host.

PROBING HOST GALAXY!

L_FRB,h – Distance between source and host screen

L_MW     – Distance to MW screen

𝜈_scint,MW  - MW scintillation bandwidth

T_scatt,h      – scattering time due to host screen

D_FRB    – Distance to FRB

Theoretically

Calculated Scint BW = 0.038MHz

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PREDICTION - BROADBAND STUDIES!

• Following θ_broadening ∝ 𝜈^-2 ; RP ∝ 𝜈^-3  for a two screen system.
• A broadband pulse could show the transition from unresolved screens to resolved screens. (Tim's talk!) 

2-Resolving Screens

Screen resolving incoherent emission region

• Screen resolves the emission region – Scintillation is quenched. Constant emission region size, RP ∝ 𝜈^-1.
• Observations: Nimmo et al 2024, observes this in FRB 20221022A. 

Multi Screen FRB

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SUMMARY AND FUTURE

• Multi-Screen Scattering Model: Incorporating cosmology for a general model for multi-screen scattering. 
• Scintillation Quenching in Two-Screen Systems: Evidence for gradual diminishing broad scintillation with increased resolution in two-screen systems.
• Host Screen Distance: New formula to position screens and proved through simulations. Caveat – does not work for 1-D screens.
• Broadband studies: Two resolving screens or screen resolve emission regions of FRBs/Pulsars have observable trends in 𝜈_scint ∝ 𝜈^a
• MW Screens: For two 1 AU screens at a separation of 1 kpc, RP = 750?!? -- means only one scale of scintillation survives.

THANK YOU!

ACKNOWLEDGEMENTS

• DR. TIM SPRENGER
• DR. OLAF WUCKNITZ
• DR. ROBERT MAIN
• DR. LAURA SPITLER

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FRB-SCINTILATOR – TWO SCREEN

• Starting from an image distribution over laid with a gaussian intensity distribution

• Total multi-screen effect: 

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HOST GALAXY SCREEN

MILKY WAY SCREEN

• Each pair of image points comprise a path of propagation

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Each path has an amplitude and phase

A_i . A_j

A_MW

A_host

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LOCATING HOST GALAXY SCREEN

The formulas proposed in literature so far to put an upper limit on host screen distance from FRB 

Top: 2 Screen systems of different resolving power. Error bars through itterative cacluations of observables at different pulse widths.

New Formula GOOD!

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1-D SCREENS

 Case-1: 1-D parallel screens 

 Case-1: 1-D perpendicular screens 

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1-D SCREENS

 Case-1: 1-D parallel screens 

 Case-1: 1-D perpendicular screens 

Caveat for distance formula

• Distance limit formula:

• Comparison of distance limit formula:

True value : 5 kpc

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INTERPRETATION - PHYSICS BEHIND!

FRB

Host galaxy screen

Milky Way screen

Larger delay

Smaller delay, Larger scintillation