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The heliopause is now estimated to be something around 100 AU (1 AU = Astronomical unit = about the earth sun distance). See the wikipedia article:
http://en.wikipedia.org/wiki/Heliosphere

From reading a book on NASA's Voyager mission, I learned that before the launch of these spacecraft, the expectation was that the heliopause was at around Jupiter or Saturn's orbit which is about 5 to 10 AU. The book says that as the spacecraft continued to move away from the sun, the space physicists kept increasing their estimate of the position of the heliopause. If it's about an energy or flux balance, then the estimate would be defined by a certain area of the sphere where the heliopause occurs, and since areas are proportional to the square of the radius they got the number wrong by as much as $(100/5)^2 = 400$. That's a huge underestimate of the sun's output or a huge overestimate of what goes on in interstellar space.

The book doesn't explain why it is that early estimates were wrong and I didn't see an explanation. Perhaps someone knows and will give a nice intuitive explanation for the estimates.

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Good question, Carl, +1. It would be nice to analyze some calculations - and their precision - to see what goes wrong in similar cases. –  Luboš Motl Jan 27 '11 at 7:08

3 Answers 3

up vote 14 down vote accepted

A brief history of the misapplication of magnetohydrodynamics to the analysis of the solar wind:

1959: Soviet satellite Luna 1 directly observed the solar wind for the first time and measured its strength.
http://en.wikipedia.org/wiki/Luna_1

So as of 1959, by direct experimental observation, it was known that the heliopause was at least the radius of the earth or R⊙.

Pneuman and Kopp 1971 Model: According to a more complex but still simplified MHD [MagnetoHydroDynamics] model of the coronal structure (ISP p. 114-117 etc., the model of Pneuman and Kopp 1971), the dipolar magnetic field lines form closed loops if they originate at solar latitudes of less than about 45° (above or below the solar equator). However, those arising greater than about 45° are open field lines that may curve around the closed region to some extent but eventually extend far into space in all directions, at least beyond a heliocentric distance of about 2 R⊙.

http://www.mcgoodwin.net/pages/spacephysics_ess471.pdf (page 36)

This is the only paper I've been able to find that approximately reads on the magnetopause question. This is a highly cited paper and it's early enough to influence the expectations at the Voyager launches (1977). So I believe that the Pneuman and Kopp paper gave the expectation that the heliopaue would be at around 2 R⊙ based on MHD calculations. Since this was a huge error, I've not been able to find any better detail.

The man who developed MHD was Hannes Alfvén. He got the 1970 Nobel prize in physics for this. His Nobel prize lecture was partially dedicated to the task of claiming that his theory was being abused. In particular, he noted that the space physics situation was out of control. From his lecture, I've italicized the parts having to do with space physics predictions:

Plasma physics, space research and the origin of the solar system
[ Nobel Prize Lecture, 1970, by Hannes Alfvén ]

... The cosmical plasma physics of today is far less advanced than the thermonuclear research physics. It is to some extent the playground of theoreticians who have never seen a plasma in a laboratory. Many of them still believe in formulae which we know from laboratory experiments to be wrong. The astrophysical correspondence to the thermonuclear crisis has not yet come. The reason for this is that several of the basic concepts on which the theories are founded, are not applicable to the condition prevailing in cosmos. They are "generally accepted" by most theoreticians, they are developed with the most sophisticated mathematical methods and it is only the plasma itself which does not "understand", how beautiful the theories are and absolutely refuses to obey them. It is now obvious that we have to start a second approach from widely different starting points.

If you ask where the border goes between the first approach and the second approach today, an approximate answer is that it is given by the reach of spacecrafts. This means that in every region where it is possible to explore the state of the plasma by magnetometers, electric field probes and particle analyzers, we find that in spite of all their elegance, the first approach theories have very little to do with reality. It seems that the change from the first approach to the second approach is the astrophysical correspondence to the thermonuclear crisis. ...

http://nobelprize.org/nobel_prizes/physics/laureates/1970/alfven-lecture.pdf

The above lecture includes a table with a detailed comparison between the "first approach" and "second approach".

Conclusion:

The problem in estimating the heliopause was mostly due to theoreticians overestimating their understanding of the limitations of MHD. In particular, the MHD equations fail when electric currents are strong enough to overcome the magnetic field. This breaks the MHD assumption that ions and electrons remain pinned to magnetic field lines.

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By the way, it took me a great deal of searching to find this. I'd given up when I managed to get lucky and read Alfvén's Nobel prize lecture. –  Carl Brannen Feb 7 '11 at 1:24
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Thanks, Carl. Very interesting post all around. +1 –  Gordon Feb 7 '11 at 2:05
    
The radius of the Earth's orbit, not the Earth itself? –  endolith Aug 15 '11 at 3:27

There was a considerable stretch when getting answers to within an order of magnitude was pretty good on topics like stellar structure and cosmology. Things improved---first slowly but later on quite markedly---so that now we are in the age of "precision cosmology" (a loss in terms of jokes about putting the error bar on the exponents, alas). But individual topics might have languished if they didn't attract much attention.

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This was helpful, but in order to estimate the size as "Jupiter's orbit" surely they must have done a calculation. They put some numbers in and something went wrong. –  Carl Brannen Jan 27 '11 at 2:38
    
@Carl: You're looking at a calculation involving the solar wind and magnetic fields on one hand and galactic particle flows and magnetic fields on the other. Lots of magnetohydrodynamics, therefore non-linearities. Hard problem, and if any of your inputs are shaky... –  dmckee Jan 27 '11 at 3:40

What book on Voyager were you referencing?

In any case, they started developing the Voyager spacecraft in the 1960's. The first measurement that a solar wind even existed wasn't reported until 1960-1961 [K. Gringauz using the Lunik 2 spacecraft]. They were able to determine a flux of particles (i.e., number per area per time), but did not determine speed or number density.

Biermann's hypothesis of the existence of the solar wind was between 1951-1957, thus, not much earlier. Though he did approximate the solar wind speed pretty closely with $\sim$500-1000 km/s, which would now be considered fast solar wind.

Mariner 2 was the first spacecraft to show that the solar wind was continuously emitted by the sun (observations and papers between 1962-1967). This is also the period when they first started to get semi-reliable estimates of the bulk flow speed, number density, temperature (i.e., Avg. kinetic energy in the bulk flow rest frame), etc. of the solar wind.

Once these parameters were found, and assuming that dynamic pressure $\propto$ $r^{-2}$ (assume V $\sim$ constant and adiabatic expansion, then n $\propto$ $r^{-2}$), the heliopause can be estimated using the dynamic pressure at 1 AU, $P_{1AU}$, combined with estimates of the interstellar pressure, $P_{I}$, to approximate a standoff distance, $R_{S}$.

If we use the following typical values n $\sim$ 5 $cm^{-3}$ and V $\sim$ 400 km/s, and $P_{I}$ $\sim$ 10$^{-13}$ Pa, then $R_{S}$ $\sim$ 100 AU. So MHD is not required, you can just use simple hydrodynamics to get a rough estimate. If the early estimates of $P_{I}$ were much higher or $P_{1AU}$ much lower, it is reasonable to understand why early estimates of $R_{S}$ may have been grossly inaccurate.

Remember, people weren't even comfortable with whether a solar wind existed until the 1950's. Paul Kellogg predicted the existence of the Earth's bow shock in 1962, which was controversial at the time due to the extremely low collision rates of tenuous plasmas and uncertainties about relevant speeds to use for Mach numbers.

My point is that it was only very recently that we had any measurements of the sun's atmosphere (technically, everything within the heliosphere is considered within the sun's atmosphere). At the time when Voyager was first starting to be discussed and designed, all of this stuff was less than a decade old. It wasn't even until the 1950's that we had a definitive estimate the age of the sun and solar system [e.g., Burbidge et al., 1957].

References
- Burbidge, E.M., et al. "Synthesis of the Elements in Stars," Rev. Mod. Phys. 29(4), pp. 547, 1957.
- Gringauz, K.I., et al. "Results of Observations of Charged Particles Observed Out to R = 100,000 km, with the Aid of Charged-Particle Traps on Soviet Space Rockets," Astronomicheskii Zhurnal 37, pp. 716, 1960.
- Kellogg, P.J. "Flow of Plasma around the Earth," J. Geophys. Res. 67, pp. 3805, 1962.
- Lang, K.R. The Sun From Space, Astronomy and Astrophysics Library (Springer, Verlag Berlin, Germany), 2000.
- Neugebauer, M. and C.W. Snyder "Solar Plasma Experiment," Science 138, pp. 1095-1097, 1962.

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