Arc Morphology Barney Rickett University of California San Diego - PowerPoint PPT Presentation

Arc Morphology Barney Rickett University of California San Diego

Generic Features observed in Secondary Spectra Smooth symmetric shapes Parabola (arc) Forward Narrow Forward Broad Forward arc, sharp outer boundary, filled interior Reverse narrow (multiple arclets) Multiple forward arcs Asymmetry in Doppler Arc structure is often variable over time

Asymmetric (& faint fuzzy arc ?) Arecibo Observation at 1450 MHz from Stinebring et al. (2019) See his talk this afternoon For view at two frequencies

Multiple Forward Arcs in 6 Broad pulsars (Putney & Stinebring 2006) Forward filled Multiple narrow Forward interior forward Narrow

Forward filled Forward Bro ad interior. Asymmetric Sharp outer boundary - characteristic of weak scint Note how the arc is narrower at 825 than at 340 MHz where scattering is stronger See talk by Dan Stinebring

B0834+06 323 MHz 329 MHz Stinebring 2003, Arecibo See Hill, et al. (2005) for detailed analysis of such arclets in B0834+06 Note reverse arclets with apexes along forward Parabola Note same arclets in Independent bands at 323 & 329 MHz Note deep “valley”

Modulation index = 0.56 => weak scint ? But note narrow Dn ISS (How to define width Dn ISS ?) Forward Narrow See Stinebring et al. 2019, where we modelled the secondary spectrum by 1-dim brightness distribution B( q ) as follows:

B1133+16 1450 MHz MJD 57179 Arecibo (Stinebring et al. 2019) 1-dim model fitted dB

+ is the fitted model Dashed red line is an isotropic Kolmogorov model (+ delta fn) Dashed black line is a 1-dim Kolmogorov model (+ delta fn)

B1133+16 1450 MHz cross-cuts at fixed delay max/min 10-15dB Black line is 1D model fitted to secondary spectrum Note deficit in model in center at lowest delay 1-dim model imperfect …… Remedy requires width perpendicular to velocity ie 2-dim

B1133+16 1450 MHz Slices versus delay at small fixed Doppler Note the observed power law drop as S 2 ∝ t -2.5 Similar to weak Kolmogorov scint isotropic: S 2 ∝ t - 2.33 1-dim: : S 2 ∝ t - 1.83 Note also scattered pulse tail ∝ t - 2.33 Delay 0.01 0.1 1 µ sec

Random phase screen theory Consider the effects of: Strength of Scintillation m B2 <1 weak m B2 >1 strong Axial Ratio AR Orientation angle y relative to psr velocity More details were in talk by Bill Coles

axial ratio orientation angle (deg) Scattering strength 0 30 60 AR m B2 ArcSim/mb2=0.2,ar=3,ph=0.mat ArcSim/mb2=0.2,ar=3,ph=30.mat ArcSim/mb2=0.2,ar=3,ph=60.mat 80 80 80 5000 5000 5000 4500 4500 4500 70 70 70 4000 4000 4000 Delay (1/freq0 units) Delay (1/freq0 units) Delay (1/freq0 units) 3500 3500 3500 60 60 60 3:1 3000 3000 3000 0.2 50 50 50 2500 2500 2500 2000 2000 2000 40 40 40 1500 1500 1500 1000 1000 1000 30 30 30 Kolmogorov 500 500 500 0 20 0 20 0 20 -100 0 100 -100 0 100 -100 0 100 θ x ( θ F units) θ x ( θ F units) θ x ( θ F units) Screen ArcSim/mb2=0.2,ar=10,ph=0.mat ArcSim/mb2=0.2,ar=10,ph=30.mat ArcSim/mb2=0.2,ar=10,ph=60.mat 80 80 80 5000 5000 5000 4500 4500 4500 70 70 70 4000 4000 4000 Delay (1/freq0 units) Delay (1/freq0 units) Delay (1/freq0 units) simulation 3500 3500 3500 60 60 60 10:1 3000 3000 3000 0.2 50 50 50 2500 2500 2500 2000 2000 2000 40 40 40 1500 1500 1500 1000 1000 1000 30 30 30 500 500 500 0 20 0 20 0 20 -100 0 100 -100 0 100 -100 0 100 θ x ( θ F units) θ x ( θ F units) θ x ( θ F units) ArcSim/mb2=1.0,ar=3,ph=0.mat ArcSim/mb2=1.0,ar=3,ph=30.mat ArcSim/mb2=1.0,ar=3,ph=60.mat 80 80 80 5000 5000 5000 4500 4500 4500 70 70 70 4000 4000 4000 Delay (1/freq0 units) Delay (1/freq0 units) Delay (1/freq0 units) 3500 3500 3500 60 60 60 3000 3000 3000 50 50 50 2500 2500 2500 1.0 2000 2000 2000 40 40 40 1500 1500 1500 3:1 1000 1000 1000 30 30 30 500 500 500 0 20 0 20 0 20 -100 0 100 -100 0 100 -100 0 100 θ x ( θ F units) θ x ( θ F units) θ x ( θ F units) ArcSim/mb2=1.0,ar=10,ph=0.mat ArcSim/mb2=1.0,ar=10,ph=30.mat ArcSim/mb2=1.0,ar=10,ph=60.mat 80 80 80 5000 5000 5000 4500 4500 4500 70 70 70 4000 4000 4000 Delay (1/freq0 units) Delay (1/freq0 units) Delay (1/freq0 units) 3500 Characterize the shapes by depth of valley in Doppler freq 3500 3500 60 60 60 3000 3000 3000 1.0 50 50 50 2500 2500 2500 2000 2000 2000 = dB difference between peak and valley 40 40 40 1500 1500 1500 10:1 1000 1000 1000 30 30 30 500 500 500 of a cross-cut at constant delay. 0 0 0 20 20 20 -100 0 100 -100 0 100 -100 0 100 θ x ( θ F units) θ x ( θ F units) θ x ( θ F units)

Depth of valley versus axial ratio 40 Asymptotic strong scint mb2=0.2 35 mb2=1 Depth of cross-cut valley (dB) mb2=5 30 mb2=0.2, =30 25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 Axial Ratio

Depth of valley in strong Kolmogorov scattering 60 50 40 max/min (dB) 30 20 = .15 s = .3 = .45 10 0 0 10 20 30 40 50 60 70 80 90 100 axial ratio Isotropic Kolmogorov spectrum 10 9 8 Depth of cross-cut valley (dB) 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 2 Scattering strength m B

From Stinebring GBT arc survey (2019) 1508+55,53632.55,scan20,340MHz 10 -3 1.2 100 -20 80 -25 1 60 -30 Forward 40 -35 0.8 Delay (microsec) Broad 20 -40 0.6 0 -45 -20 -50 0.4 -40 -55 0.2 -60 -60 -80 -65 0 0 10 20 -100 -70 (sec 3 ) -40 -20 0 20 40 Doppler Frequency (mHz)

Conclusions 1) Arcs are seen in a wide range of pulsars. But only few show deep valleys. e at angles y < 45 deg => 2) Arcs with deep valleys imply el elong ngated ed image 3) Arcs with sharp outer boundaries and filled interior are due to interference between an undeflected feature and outlying waves. Such as the un-scattered core in we weak statistical scattering . 4) Absence of deep valleys imply isotropic image => phase is isotropic 2-D => Isotropic fine structure OR superposition of randomly oriented 2-D fine structures 5) Asymmetry in Doppler is due to deflection by a plasma structure offset from the pulsar line of sight - OR due to refractive phase gradient covering pulsar 6) Reverse Arclets => deflection by plasma structures aligned parallel to the psr velocity. So Fine structure in plasma 7) Time variability in arcs imply very inhomogeneous fine structure in ISM

Curvature estimated vs theory