Multiple-Dish Pulsar Scintillation Studies Dana Simard, Caltech Scintillometry 2019 MPIfR @ Bonn, November 2019
Scintillometry is a powerful tool Pulsar scintillation provides a way to study • Plasma structures in the ISM • By testing models of scintillation • By comparing locations of screens to other tracers • Pulsar magnetospheres • Screens can resolve pulsar magnetosphere • Compare separation of components or emission heights to beam models • The distribution of scattering screens in the ISM • Understand the prevalence of screens • Compare to other structures and tracers of ionized or neutral gas Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
Scintillometry is a powerful tool Pulsar scintillation provides a way to study • Plasma structures in the ISM • By testing models of scintillation • By comparing locations of screens to other tracers • Pulsar magnetospheres • Screens can resolve pulsar magnetosphere • Compare separation of components or emission heights to beam models • The distribution of scattering screens in the ISM • Understand the prevalence of screens • Compare to other structures and tracers of ionized or neutral gas For all, we need the distance to the screen! Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The secondary spectrum doesn’t give us distances B0834+06 What information do we have? η = λ 2 D e ff Curvature of the arc: V 2 2 c e ff , k Locations of the apexes: Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The secondary spectrum doesn’t give us distances B0834+06 What information do we have? η = λ 2 D e ff Curvature of the arc: V 2 2 c e ff , k Locations of the apexes: What information do we need? The locations of the images: θ or The velocity of the scintillation pattern: V e ff Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The secondary spectrum doesn’t give us distances B0834+06 What information do we have? η = λ 2 D e ff Curvature of the arc: V 2 2 c e ff , k Locations of the apexes: What information do we need? Measured with VLBI and used to reconstruct a The locations of the images: θ scattering screen by Brisken et al. (2010 ApJ 708 232) or Measured with simultaneous observations by The velocity of the scintillation pattern: V e ff eg. Galt & Lyne (1972 MNRAS 158 281); Rickett & Lang (1973 ApJ 185 945) Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The conjugate spectrum phases are dominated by dispersive ones V Each point in the conjugate spectrum also has a phase: Φ jk = φ j − φ k + 2 π D e ff 2 ( θ 2 j − θ 2 k ) λ 𝜾 2 , LoS Phases imparted 𝜾 2 , 𝜾 1 by the lens. Typically dominate 𝜾 1 , LoS the phase and 𝜾 1 cause phase f D wrapping. 𝜾 2 LoS, 𝜾 1 𝜾 1 , 𝜾 2 LoS, 𝜾 2 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The secondary spectrum has no phase information V Each point in the conjugate spectrum also has a phase: Φ jk = φ j − φ k + 2 π D e ff 2 ( θ 2 j − θ 2 k ) λ In the secondary spectrum: S ( τ , f D ) = ˜ I ( τ , f D )˜ I ( − τ , − f D ) Each point has a phase: 𝜾 1 Φ S,jk = Φ jk + Φ kj = 0 𝜾 2 And there is no remaining phase information. Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The FT of the Visibilities is no longer symmetric V ~ V AB* ( 𝜉 ,t) = FT[E A ( 𝜉 ,t) E* B ( 𝜉 ,t)] 𝜾 2 , 𝜾 1 2 observed by A correlated with 1 observed by B 𝜾 1 𝜾 1 , 𝜾 2 𝜾 2 1 observed by A correlated with 2 observed by B b A B Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the VLBI secondary cross-spectrum depends on 𝜄 V Φ jk,AB ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ shorter by 𝜾 1 𝜾 2 ・ b /2 shorter by 𝜾 1 ・ b /2 𝜾 2 b A B Brisken et al. 2010 ApJ 708 232 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the VLBI secondary cross-spectrum depends on 𝜄 V Φ jk,AB ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ Φ kj,AB ∗ = Φ kj, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ 𝜾 1 Longer by longer by 𝜾 1 ・ b /2 𝜾 2 𝜾 2 ・ b /2 b A B Brisken et al. 2010 ApJ 708 232 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the VLBI secondary cross-spectrum depends on 𝜄 V Φ jk,AB ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ Φ kj,AB ∗ = Φ kj, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ 𝜾 1 equal but opposite 𝜾 2 b A 0 B Brisken et al. 2010 ApJ 708 232 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the VLBI secondary cross-spectrum depends on 𝜄 V Φ jk,AB ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ Φ kj,AB ∗ = Φ kj, 00 ∗ + 2 π 1 2( θ j + θ k ) · b λ Φ [ ˜ V AB ∗ ( τ , f D ) ˜ V AB ∗ ( − τ , − f D )] 𝜾 1 = Φ jk,AB ∗ + Φ kj,AB ∗ 𝜾 2 = 2 π λ ( θ j + θ k ) · b b A 0 B Brisken et al. 2010 ApJ 708 232 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the VLBI secondary cross-spectrum depends on 𝜄 1200 1000 Φ [ ˜ V AB ∗ ( τ , f D ) ˜ 150 V AB ∗ ( − τ , − f D )] 100 = Φ jk,AB ∗ + Φ kj,AB ∗ 800 = 2 π 50 phase (deg) λ ( θ j + θ k ) · b τ ( µ s) 600 0 − 50 400 − 100 − 150 200 60 0 − 60 − 40 − 20 0 20 40 60 f D (mHz) Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
First reconstructions of scattered image with VLBI PSR B0834+06 Brisken et al. 2010 ApJ 708 232 AR-GBT Distance to the screen: 0.65 D psr Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
First reconstructions of scattered image with VLBI Vela Kirsten et al. in prep. Distance to the screen: 0.73 D psr Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The secondary spectrum doesn’t give us distances B0834+06 What information do we have? η = λ 2 D e ff Curvature of the arc: V 2 2 c e ff , k Locations of the apexes: What information do we need? Measured with VLBI and used to reconstruct a The locations of the images: θ scattering screen by Brisken et al. (2010 ApJ 708 232) or Measured with simultaneous observations by The velocity of the scintillation pattern: V e ff eg. Galt & Lyne (1972 MNRAS 158 281); Rickett & Lang (1973 ApJ 185 945) Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
Correlating 2-station dyn spec measures the scintillation velocity • Galt & Lyne 1972 (MNRAS 158 281): Measured the delay in the scintillation pattern of PSR B0329+54 between DRAO and Jodrell Bank over more than day to measure the velocity of the scintillation pattern Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
Correlating 2-station dyn spec measures the scintillation velocity • Bignall et al. 2006 (ApJ 652 1050): Used the delay between the scintillation pattern of PKS 1257-326 to constrain the direction and amount of anisotropy in the scattered disk Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
Correlating 2-station dyn spec measures the scintillation velocity • Fadeev et al. 2018 (MNRAS 480 4199): Measure the scintillation pattern velocity for PSR B0823+26 using the delay between GBT and WB and combine this w/ the arc curvature to measure distance to the screen Velocity of the pattern: 610 km s − 1 Distance to the screen: 0.77 +/- 0.03 Dpsr Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the intensity cross secondary spectrum depends on 𝜄 V Φ jk,AA ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j − θ k ) · b λ 𝜾 1 longer by shorter by 𝜾 2 ・ b /2 𝜾 1 ・ b /2 𝜾 2 b 0 A Simard et al. 2019 MNRAS 488 4952 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the intensity cross secondary spectrum depends on 𝜄 V Φ jk,AA ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j − θ k ) · b λ Φ kj,BB ∗ = Φ kj, 00 ∗ + 2 π 1 2( θ j − θ k ) · b λ 𝜾 1 shorter by longer by 𝜾 2 ・ b /2 𝜾 1 ・ b /2 𝜾 2 b 0 B Simard et al. 2019 MNRAS 488 4952 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the intensity cross secondary spectrum depends on 𝜄 V Φ jk,AA ∗ = Φ jk, 00 ∗ + 2 π 1 2( θ j − θ k ) · b λ Φ kj,BB ∗ = Φ kj, 00 ∗ + 2 π 1 2( θ j − θ k ) · b λ Φ [˜ I AA ∗ ( τ , f D )˜ I BB ∗ ( − τ , − f D )] 𝜾 1 = Φ jk,AA ∗ + Φ kj,BB ∗ 𝜾 2 = 2 π λ ( θ j − θ k ) · b b A 0 B Simard et al. 2019 MNRAS 488 4952 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
The phase of the intensity cross secondary spectrum depends on 𝜄 1200 Φ [˜ I AA ∗ ( τ , f D )˜ I BB ∗ ( − τ , − f D )] 1000 = Φ jk,AA ∗ + Φ kj,BB ∗ 150 100 = 2 π 800 λ ( θ j − θ k ) · b 50 phase (deg) τ ( µ s) 600 0 − 50 400 − 100 − 150 200 60 0 − 60 − 40 − 20 0 20 40 60 − f D (mHz) Simard et al. 2019 MNRAS 488 4952 Dana Simard SKA VLBI KSP Workshop 16 October 2019
Phase pattern is different for two analyses Visibilities: ∗ ∗ = 2 π λ ( θ j + θ k ) · b Intensities: = 2 π λ ( θ j − θ k ) · b Simard et al. 2019 MNRAS 488 4963 Dana Simard Scintillometry 2019 @ MPIfR 4 November 2019
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