Transcript Interstellar turbulent plasma spectrum from multi

Interstellar turbulent plasma
spectrum from multi-frequency
pulsar observations
Smirnova T. V.
Pushchino Radio Astronomy
Observatory
Astro Space Center
P.N. Lebedev Physical Institute
1. Relations of pulsar observations to the
turbulent plasma spectrum
2. Construction of the structure function
• from multi-frequency observations
3. Measurements of the ISM spectrum in the
directions to PSR 0329+54, 0437-47, 0809+74,
0950+08, 1642-03
• 4. Conclusions
Diffractive scintillation
Inhomogeneities of size sd = /2sc ~ 107  1010
cm
Time scale td = sd/V ~ sec  min
Frequency scale fd = c/(Rsc2) ~ KHz  MHz
Modulation index, m  1
Refractive scintillation
Inhomogeneities of size sr = Rsc ~ 1012  1015 cm
Time scale Tref = sr/V ~ weeks  months
srsd ~ R (Frenel scale)2
Dispersive arrival times, angular broading,
time of arrival fluctuations, pulse broading
Electron density irregularities in the plasma cause random phase
perturbations of the wavefront. These are characterized by the phase
structure function:
Ds() = <[S(1 +) – S(1)]2>
S = const(f0/f)DM
For a power-law spectrum
Ne (q) = CNe2q-n, 2/li  q  2/lout
n = 11/3 for Kolmogorov spectrum
Ds() =const2CNe2()n-2, q = 1/
Diffractive scintillation
Correlation function of flux variations I(t) is described by the equation
BI(t) = <I>2exp[- DS(t)] .
If t0 is the characteristic scale of intensity variations we have
DS(t0) = 1
DS(t)  [BI(0) – BI(t)]/<I>2  (1/2) DI(t)/<I>2, t << t0
DS(t)  DS() by  = Vt
In frequency domain:
DS(f)  (n-2) [BI(0) – BI(f)]/<I>2
To reduce DS(f) to frequency f0 :
DS(f , f0) = (f/f0)2 DS(f,f)
f(f0) = (f0/f)2 f(f)
For the case of strong angular refraction, ref >> dif:
f(f0) = (f0/f)3 f(f),
ref = 3Vf/R(t/f)
The slope of DS(f ) is the same as DS(t)
Refractive scintillation
For homogeneous medium
Ds() = mref2/(6(4-n))(Tref/tdif)2
 = VTref
Variations of DM
DDM() = A (f0 / f)2 <[DM(1+ ) – DM(1)]2> ,
A = 6,38.1014 pc-2cm6
Pulsar timing
Ds(t) = (2f)2 2τ2
dash line: n = 3.5
straight line: n = 11/3
Interstellar plasma spectrum in the direction to
PSR 0329+54, Shishov, Smirnova, Siber et al., 2003
R = 1 kpc, V = 95 km/s (parallax)
Data:
f = 102, 610, 4860 MHz
Flux variations, Tref =17 days, m=0.37 at 610 MHz
(Stinebring et al., 2000)
Timing during 30 years, residuals t = 0.7 ms at
103 MHz (Shabanova, 1995)
Reference frequency f0 = 1000 MHz
 = 1.47
straight line: 1.5
dash line: 1.67
Interstellar plasma spectrum in the direction to
PSR 1642-03, Smirnova, Shishov, Siber et al., A&A,
2006.
Data:
f = 102, 340, 610, 800, 4860 MHz
 = 30 mas/year (Brisken et al., 2003), R – 160 pc ?
R = 160 pc, V = 22 km/s; R = 2.9 kpc, V = 400 km/s
sc = 6.8 mas at 326 MHz (Gwinn et al., 1993)
Flux variations, Tref = 0.9 days, m = 0.46 at 610 MHz
(Stinebring et al., 2000)
Timing during 8.5 years, residuals t = 1 ms at
103 MHz (Shabanova et al, 2001)
Interstellar plasma spectrum in the direction to
PSR 0437-47 (Smirnova, Gwinn, Shishov,
A&A, 2006
R = 150 pc, V = 100 km/s (parallax)
Data:
f = 152, 327, 436 MHz
fdif = 16 MHz, tdif = 17 min at 328 MHz
(Gwinn et al. 2006)
cross Gothoskar&Gupta
(2000), f = 327 MHz
triangle Issur (2000),
f = 150 MHz
star Gwinn et al. (2006),
f = 328 MHz
circle Johnston et al (1998),
f = 436 MHz
 = 1.44  0.03
scattering layer near to Sun
PKS 0405-385: m=0.1, t= 33 min
at 4.8 GHz (Rickett et al. 2002)
predicted time scale 23 min at 330 MHz
PSR 0809+74
R = 433 pc, V = 102 km/s (Brisken et al. 2002)
Observations: f = 41, 62.43, 88.57 and 112.67 MHz
December - January 2001, 2003, 2004
DKR: time duration 35.3 min
BSA: T = 12 min
Time resolution 2.56 ms or 5.12 ms
B = 12820 KHz and 128 1.25 KHz at 41 MHz
Time averaging 19.4 s (15 P1) at 113 MHz, 39 s at 88 MHz,
62 and 41 MHz
PSR 0950+08
R = 262 pc, V = 36.6 km/s (Brisken et al. 2002)
Observations: f = 41, 62.43, 88.57 and 112.67 MHz
December - January 2001, 2003, 2004
DKR: time duration 15.63 min
BSA: T = 3.2 min
Time resolution 2.56 ms or 5.12 ms
B = 12820 KHz and 128 1.25 KHz at 41 MHz
Time averaging 15.2 s (60 P1) at 113 MHz, 20.24 s at 88
MHz,
62 and 41 MHz
Conclusions
1. Multi-frequency observations of pulsar interstellar
scintillation give us new and more accurate information
about the shape of turbulent spectrum in the definite
directions of the sky.
2. Interstellar plasma spectrum for 4 from 5 pulsars is well
described by a power law with n from 3 to 3.5 for scales
from 107 to 1010 cm which is different from Kolmogorov
one.
3. We detected strong angular refraction of radiation in the
direction to 3 pulsars: 0329+54, 0437-47 and 0950+08.
4. The spectrum in the direction to PSR 1642-03 has a changing
of slope from n = 3.3 for scales less than 109 cm to n = 3.7
for scales from 109 to 1015 cm (Kolmogorov spectrum).