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ON THE NECESSITY FOR NON-STANDARD
MODELS OF INTERSTELLAR TURBULENCE THE
“CHAMPAGNE BOTTLE ” MODEL
S. Bonazzola, L. Celnikier, M. Chevreton
To cite this version:
Cl-136 JOURNAL DE PHYSIQUE Colloque Cl, supplément au n° 5, Tome 39, Mai 1978.
ON THE NECESSITY FOR NON-STANDARD MODELS
OF INTERSTELLAR TURBULENCE
THE « CHAMPAGNE BOTTLE » MODEL
S. BONAZZOLA, L. M. CELNIKIER and M. CHEVRETON Observatoire de Meudon, 92190 Meudon, France
Résumé. — Nous proposons une version complète du modèle écran mince de la scintillation
interstellaire des signaux pulsar ; ce modèle permet de mieux concilier la théorie avec l'observa-tion et nous amène à trouver des renseignements supplémentaires sur la turbulence du plasma interstellaire.
Abstract. — A complete treatment of interstellar pulsar scintillation by the Physically Thin
Screen phase changing model allows one to obtain better agreement with observation and thereby
extract new information about the turbulence structure of the interstellar plasma.
It is well known that the amplitudes of pulsar signals fluctuate over various time-scales — there are pulse to pulse variations as well as variations over tens of minutes and longer. It is generally considered that the multi-minute time scale fluctuations are induced by the interstellar plasma. The fluctuations may be observed at various frequencies co, and at a given frequency with different band-widths Aco. Pulsar signals have a number of features.
1) The fluctuations are characterized by a fluctua-tion index M(co, Act)), which is essentially the follow-ing quantity :
M = x U(.<») - ?] U(.<° +
Aro) - W
2•
many pulses
The actual calculation of this number from real data is often quite complicated.
It is observed (Lang [1]) that M often varies with Aco, as shown schematically in figure 1. Most theories of the scintillation phenomenon can reproduce this kind of behaviour. However, Shitov [2] has found a number of cases where the M — Aco curve has a drastically different behaviour — this is shown sche-matically in figure 2. He has also found 1 pulsar for which M exceeds 1.
From these observations, one can obtain (Aco)M=0>
which is the value of Aco at which M is zero. This is known as the decorrelation band-width, and for a given pulsar may be plotted as a function of co. It is observed that :
(Aco)M=0 GC co"
with a = 2 to 4 depending on the pulsar chosen. 2) At a sufficiently low frequency, it is often observed that the rise time of a pulse is finite.
M
A "
FIG. 1. — Schematic representation of M as a function of ACQ as is observed for many pulsars.
M
FIG. 2. — Schematic representation of Mas a function of Aw, as was observed by Shitov for several pulsars
3) Successive pulses sometimes have recognizable features which can be identified and followed. The
mouvement of such features within a pulse window
has been interpreted as due to scattering by the interstellar plasma (Wolszczan [3] et al.) ; analysis
CHAMPAGNE BOTTLE MODEL OF INTERSTELLAR TURBULENCE C1-137 of this phenomenon suggests that pulsar signals do
not scatter many times before reaching us.
The scintillation phenomenon has been interpreted in terms of the mouvement of an observer across a random interference pattern produced by irregulari- ties in the interstellar plasma : one should therefore be able to reconstruct the turbulence structure of the plasma. It turns out to be difficult to reconcile all existing data in a single model.
The simplest model is the so-called Physically Thin Screen : a thin plasma screen which intoduces random refraction effects is imagined to be placed somewhere between us and the pulsar. The model is clearly unphysical, but it has the advantage of being calcu- lable and is instructive.
The simplest version of the thin screen (see, for example Scheuer [4]) is associated with one typical length - that of a random irregularity - and with
the value of a typical fluctuation in electron density. Data shows that the value of the former is w 10" cm, and that of the latter w 5 x l o w 5 cmw3. This model also makes a number of predictions :
1) (Am),=,
cc
[distance of pulsar]-2.Observation shows that this prediction is not followed (Bonazzola and Celnikier [5]) ; this effect can be seen in figure 3.
FIG. 3. - Decorrelation band-with as a function of pulsar distance. The dotted line has gradient-2 ; the continuous line is a
fit to our equation (2).
2) (Am),=, K m4
-
strong scintillation (Am),,, K m2-
weak scintillation.Observation shows that for many pulsars (Am) cc m4. However, in the case of at least 2 examples (Am),=, cc m2, and in the case of one pulsar there is a continuous variation from 2 to 4 as a function of frequency (see Fig. 4). The simplest version of the thin screen can interpret the index 2 or 4, but not both using one and the same interstellar medium- supplementary ad-hoc assumptions for individual pul-
sars are necessary.
FIG. 4.
-
Decorrelation band-width as a function of frequency for CP808. The two dotted lines have gradients 2 and 4 ; thecontinuous line is a fit to our equation (1).
3) Infinitely fast pulse rise time at any frequency. In fact, one observes a finite rise time at a sufficiently low frequency.
A complete analysis of the physically thin screen
(Bonazzola, Celnikier, Chevreton [6]) leads to the following equation for the decorrelation band-width :
where :
D is the distance of the pulsar
/? is a constant, depending on a number of (known) physical parameters.
It turns out that :
1) Equation (1) can accomodate all observed indices in the (Am),=, - m plot using one and the same interstellar medium : the actual index obtained just depends on the value of
p ~ / m ~
for the pulsar concerned.2) The (Am),,, - D plot is still not followed.
3) The pulse shapes are of course still not
reproduced.
If one considers that the thin screen is just a pro-
C1-138 S. BONAZZOLA, L. M. CELNIKIER AND M. CHEVRETON bulence, one can try a phenomenological generaliza-
tion of equation (1) :
6 and y being constants to be determined from the data and which then contain information on how the
real medium scales with distance. Equation (2) can
of course fit the data, and one obtains 6 = 1.5,
.w = 3.5.
The most elementary 3-dimensional medium is in the form of a continuous distribution of random inho- mogeneities - a kind of swirlingfog. Such a medium
has been investigated theoretically by Uscinski [7] ; it turns out to be equivalent to a physically thin screen so far as the behaviour of the decorrelation band-width is concerned. With such a medium, one can easily obtain finite pulse rise times, since there is no longer a direct path to the observer (William- son 181) ; however, to obtain the observed pulse shapes, one needs :
1) the strong scintillation condition, whereas for at least two pulsars (Ao),,, K w2 ;
2) many scatters, which is inconsistent with the work of Wolszczan et a!.
The properties of figure 2 cannot be interpreted by any of the existing models. Using the general formu- lation in reference [6], we have fitted two different electron density correlation functions to the data of reference [ 2 ] .
The first function may be expressed as exp
(-
a1
xI),
x being a spatial variable. One can think of this function as being characteristic of the foggy plasma, in which a continuous distribution of inho- mogeneities is present : the distribution is characterized by a single length variable which represents some[I] LANG, K. R., Astrophys. J. 164 (1971) 249. [2] SHITOV, Yu. P., SOV. Astron. 16 (1972) 383.
131 WOLSZCZAN, A., HESSE, K., SIEBER, W. (1974) Preprint. [4] SCHEUER, P. A. G . , Nature 218 (1968) 920.
[5] BONAZZOLA, S., CELNIKIER, L. M., Astron. Astrophys. 45
(1975) 185.
kind of mean inhomogeneity size. This correlation function reproduces the shape of figure 1 ; however it cannot reproduce figure 2 whatever the value of a. The form of the second correlation function is given by exp (- a
I
x
1)
cos (bx). This function oscil- lates ; it can be thought of as representing a dis- continuous medium, consisting of bubbles having a high electron density separated by empty regions. The two length parameters a and b may be associated to the size of a bubble and to the separation ; the func- tion implies that the bubbles have a quasi-regular dis- tribution in space.This second correlation function gives a reasonable fit to the data of Shitov for CP808, with a = b. This
leads us to the following speculation.
The Physically Thin Screen is merely a two dimen- sional projection of an extended 3-dimensional medium. CP808 shows that in a limiting case, even the projection can have a bubbly structure. This would indeed be so if the interstellar plasma were organized in clusters of quasi-regular bubbles, a given pulsar being observed across one or more clusters, depending on the distance. As the pulsar distance increases, the projection changes its qualitative nature, since the bubbles will overlap to an increasing extent
- this can explain the necessity for the phenomeno-
logical version of the thin screen. We are currently working on a simulation study of just such a 3-dimen- sional bubbly medium, in order to investigate how it
projects as a thin screen. If this model turns out to
work, the physical nature of the turbulence will have to be investigated afresh a Kolmogorov type regime cannot account for a quasi-regular system of bubbles. In summary, we suggest that experimental data is in better agreement with a champagne bottle model of the interstellar plasma, than with the canonical swirl-
ing fog model.
[6] BONNAZZOLA S., CELNIKIER, L. M., CHEVRETON, M., Astro- phys. J. in press for 1978 January issue.
171 USCINSKI, B., J. Philos. Tvans. R. Soc. London A 262 (1968) 609.
[8] WILLIAMSON, I. P., Mon. Not. R. Astron. Soc. 166 (1974)
