ETA Observations of Crab Pulsar Giant Pulses

Transcription

1 ETA Observations of Crab Pulsar Giant Pulses John Simonetti,, Dept of Physics, Virginia Tech October 7, 2005 Pulsars Crab Pulsar Crab Giant Pulses Observing Pulses --- Propagation Effects Summary

2 Pulsars --- Discovery Hewish and Bell dipole antennas (!) ν = 81 MHz Search for quasars by scintillation PSR (P = s) LGM, pulsars

3 Pulsars --- General ~ 1700 known (~20,000 observable in Galaxy) <P> = 0.79 s P max P min max = 8.5 s (PSR J ) 0.12 Hz min = 1.56 s (PSR B ) 642 Hz Pulses brief (typically few % of period) Normal Pulsars: P ~ 0.5s dp/dt ~ s/s P/(dP/dt dp/dt) ) ~ 10 7 y Handful: glitches P /P ~ 10-7 (e.g., Crab) < 1% found in binary systems Millisecond Pulsars: P ~ 3ms dp/dt ~ s/s P/(dP/dt dp/dt) ) ~ 10 9 y ~ 80% found in binary systems

4 Only a handful of Pulsars Emit radiation outside the radio, or Exhibit giant pulses, or Associated with a supernova remnant Crab has all of these attributes

5 Pulsars --- Pulse Profiles PSR (MPIfR) Mode switching Drifting subpulses Nulling B (Deich Deich et al. 1986)

6 Pulsar --- Sounds (Radio signals demodulated into audio) P(s) 1/P (Hz) B B (Vela) B (Crab) J B (Jodrell Bank)

7 Pulsars = Rotating Neutron Stars M ~ 1.4 solar masses R ~ 10 km (SN Type II) The only periodic phenomenon that can work! P rot,min ~ 0.5 ms (centrifugal accel ~ gravitational accel) dp/dt > 0 Lighthouse model B large, greater than about G (for a normal pulsar) (1G = 10-4 T) large induced E (F >> gravity) curvature radiation, pair production, relativistic beaming linear pol., angle sweeps through pulse Lower ν higher emission altitude (~ 100 km)

8 Crab Pulsar --- Crab Nebula

9 Crab Pulsar --- Optical Pulses

10 Crab Pulsar --- Pulse Profile, Flux Density P = s dp/dt = 4.21 x s/s D = 2 kpc S ν (W m -2 Hz -1 ) Moffett and Hankins (1996) Lyne and Graham-Smith (1998)

11 Crab Pulsar --- Discovery Staelin and Reifenstein 1968 (300ft tele.. at GB) MHz 0.1 MHz channels 0.6s sampling (0.06s? Time constant was 0.05s) Giant pulses! (slope due to dispersion)

12 Crab Pulsar --- Giant Pulses times the mean pulse intensity One 10x-mean GP per 10 3 pulses (30 seconds) Hankins and Rickett (1975), 430 MHz time scales t < 100 µs s Argyle and Gower (1972) S ν ~ 10 5 Jy Hankins et al. (2003), 5 GHz t ~ 2 ns S ν ~ 10 3 Jy nano-giant pulses S in units of mean pulse energy

13 Giant Pulse Brightness Temperature -- 1 Ι ν r Specific Intensity (W m -2 Hz -1 sr -1 ) Ι ν Flux density (W m -2 Hz -1 ) S ν = Ι ν πr 2 / D 2 (1 Jy = W m - 2 Hz - 1 ) D

14 Giant Pulse Brightness Temperature -- 2 Blackbody radiator Ι ν = (2hν 3 /c 2 ) (e( hν/kt 1) 1) -1 Rayleigh-Jeans Limit (hν( << kt) Ι ν = 2kT / λ 2 Radio astronomers define T b = brightness temperature : Ι ν = 2kT b / λ 2 T b = actual T, if the radiator is a blackbody

15 Giant Pulse Brightness Temperature -- 3 S ν = Ι ν πr 2 / D 2 = (2kT b / λ 2 ) πr 2 / D 2 Light-travel travel-time time size argument: r < ct T b S ν (λ 2 / 2k) 2 ) (D( / ct) 2 = (S ν / 2k) 2 (D / νt) ν 2 T b K S ν (Jy)) (ν( GHz t µs ) 2 (D / 2 kpc) 2 (Cordes et al. 2004) For t=100µs, S ν = 10 5 Jy, ν=430 MHz, get T b ~ For t=2ns, S ν = 10 3 Jy, ν=5 GHz, get T b ~ K 31 K T b = K is the largest for any astrophysical source

16 Crab Giant Pulses --- Cordes et al. 2004

17 Observing Pulsars --- Propagation Effects Looking through the ISM (n( e ~ 10-2 cm -3, irregular) Index of refraction at radio wavelengths n r = ( 1 ω p2 /ω 2 ) 1/2 ω p2 = 4πn4 e e 2 / m e ω p ~ 1 MHz for ionosphere ~ 1 Hz for ISM n r = 1 ω p2 /2ω 2 = plasma frequency Deviation of n r from vacuum value proportional to λ 2 V phase = ω/k = c/n r > c V group = dω/dk = n r c < c

18 Propagation: Dispersion --- Pulse Delay t DM delay delay = 4.1 ms DM ν GHz GHz -2 DM = nedl (pc cm -3 ) = 2.8 s DM (ν( / 38 MHz) -2 for ETA = 160 s (DM / 56.8 pc cm-3) (ν( / 38 MHz) -2 for ETA Crab obs. Across B = 18MHz bandwidth: 170 s

19 Propagation: Dispersion --- Pulse Smearing t DM smear = 8.3 µs s DM ν GHz -3 GHz ν MHz = 0.15 s DM (ν( / 38 MHz) -3 ν ν MHz MHz for ETA = 8.6 s (DM / 56.8 pc cm-3) (ν( / 38 MHz) -3 ν for ETA Crab observation ν MHz = 0.13 s (DM / 56.8 pc cm-3) (ν( / 38 MHz) -3 ( ν ν / 15 khz) For ETA Crab obs., with smallest ν

20 Propagation: Scattering Thin Screen Model (Lorimer and Kramer 2005; Cordes 2002) φ rms proportional to λ 2 >1 radian for ν < 5 GHz, D > 1kpc (roughly) ( strong scattering ) θ d proportional to λ 2 for single-sized sized blobs (or a Gaussian size distribution) λ 2.2 for a Kolmogorov power spectrum of blob sizes

21 Scattering Effects: Pulse Broadening θ d τ d ~ D θ d2 / 2c λ 4.4 λ D For ETA Crab obs: τ d = 4.4 s (ν( / 38 MHz) -4.4 θ d = 1.4 (ν( / 38 MHz) -2.2 (using Cordes et al. 2004: τ d ~ GHz for Crab) (MPIfR Pulsar Group website)

22 Scattering Effects: Diffractive Scintillation Twinkling Stars twinkle, planets don t. Twinkling requires θ source < θ critical < l / D d so diffraction patterns of different parts of source don t blur each other (l d = characteristic length scale in diffraction pattern; see later) θ source < θ critical well satisfied for pulsars. (Other transient sources?) Then, in strong scattering case: m = σ Ι / <Ι> < > = 1 ( modulation index is unity) Probability (Ι( > S) = e -S/< S/<Ι> Ι < 0.5 <Ι> < > occurs 40% of the time Ι > 2 <Ι> < > occurs 14% of the time (unless instrumental parameters t and/or ν suppress scintillation*)

23 Scattering Effects: Diffractive Scintillation Scintles seen in dynamic c spectrum t d ~ 10 minutes scintillation illation time scale ν d ~ 2 MHz scintillation illation bandwidth for B , 810 MHz (Cordes)

24 Diffractive Scintillation Bandwidth Typical ray path length difference ~ c τ d Typical phase difference ϕ d ~ 2π2 c τ d / λ = 2π ν τ d For ϕ d = (dϕ( d / dν) ν = 2π ν τ d ~ 1 radian get major change in diffraction pattern at observer s plane Therefore ν d ~ 1 / 2πτ2 d For ETA Crab obs: 4.4 ν d ~ 3.6 x 10-5 khz (ν( / 38 MHz) 4.4

25 Diffractive Scintillation Time Scale Depends on transverse velocity V, scintillation length scale l d l d = λ / θ d (see diagram at right) θ d t d = l d / V = λ / θ d V λ / λ2.2 ν 1.2 Cordes et al. 2004, Crab: 1.2 GHz t d = 20 s ν GHz For ETA Crab obs: 1.2 t d = 0.4 s (ν( / 38 MHz) 1.2 λ l d observer s plane

26 Diffractive Scintillation: Modulation Index For observations smoothed over t and ν,, the number of scintles expected in one t or ν are approximately (Cordes( and Lazio 1991): N t = t / t d N ν = ν / ν d The observations therefore average over these scintles producing a modulation index m m = 1 / (N( t N ν ) Many scintles in one t and/or one ν will quench diffractive scintillations (m 0)

27 Scattering Effects: Refractive Scintillation Focusing/defocusing effects of blobs with sizes ~ D θ d m = σ Ι / <Ι> < > ~ 0.05 to 0.3 ν r ~ ν t r ~ l r / V ~ D θ d / V λ 2.2 Recall t d = λ / θ d V and τ d ~ D θ d2 / 2c Therefore t r ~ (D θ d2 / λ) t d ~ 2 τ d ν t d t r ~ 10 8 s (ν( / 38 MHz) -2.2 ~ 3 y (ν / 38 MHz) -2.2

28 Summary of Observing Parameters ETA design parameters B = 18 MHz, centered on ν = 38 MHz ν = 15 khz (at smallest; therefore 1200 freq. channels at most) t = 66 µs s (at smallest) Propagation t DM delay = 160 s DM 56.8 ν38 ( t DM delay = 170 s across B = 18 MHz) t DM smear = 0.13 s DM 56.8 ν ν 15 (>> P, single pulses; ; >> small t) τ d = 4.4 s ν (>> smallest t; best t ~ a few seconds) ν d = 3.6 x 10-5 khz ν (<< smallest ν; diffractive scintillations quenched) t d = 0.4 s ν (irrelevant since diff. scint.. quenched) t r = 3 y ν (> grant period! Can t worry about it.)