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It is to my understanding that one can measure the temperature of the universe by measuring cosmic microwave background radiation. Could we also use this method for calculating the average temperature of the heliosphere?

The average temperature of the universe has supposedly been measured in at 2.735 degrees above absolute zero. Presumably this measurement takes into account the massive amounts of 'empty' space which I imagine has a huge effect on the number.

My question, Can we measure the average temperature of the heliosphere, if so then what is it?

This might be quite hard to define as how do you determine when our solar system ends? So for the purpose of this question the following assumptions should be made:

-The Radius from the sun to the edge of the heliosphere is approximately 100AU (Roughly the size of the heliosphere as measured by voyager 1)

-Assume the heliosphere is a perfect sphere

-Assume we are measuring the Black body equivalent temperature (as this is what was measured to calculate the temperature of the universe)

If we don't know how to measure this average temperature (which is likely if we can't differentiate between microwaves from in and outside the heliosphere) then how could we theoretically measure this value assuming a perfect environment?

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You need to define what do you want to measure, as there are two things you can see as "Temperature": Black Body equivalent temperature for the radiation, and Statistical Thermodynamic temperature for particles. –  Envite Jan 23 at 9:34
    
@Envite Good point, Black Body equivalent temperature is what i am after, will edit in –  RhysW Jan 23 at 9:36
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up vote 5 down vote accepted

The heliosphere is mainly defined by the region dominated by solar wind against the interstellar medium.

"The solar wind is divided into two components, respectively termed the slow solar wind and the fast solar wind. The slow solar wind has a velocity of about 400 km/s, a temperature of $1.4–1.6×10^6 K$ and a composition that is a close match to the corona. By contrast, the fast solar wind has a typical velocity of 750 km/s, a temperature of $8×10^5 K$ and it nearly matches the composition of the Sun's photosphere."

Hence with 1 million Kelvin we get a good estimate of the average temperature of the heliosphere.

The temperature is the freeze-in temperature derived from carbon ion charge states measured by SOHO. Hence it's not the black-body temperature, but a reasonable definition of temperature for solar wind.

"Coronal temperatures are inferred from density ratios of adjacent charge states. The freeze-in temperature derived from a given density ratio is the electron temperature that reproduces this ratio in a static situation. For the analyzed iron charge states we use the ionization and recombination rates of Arnaud and Raymond [1992]". More details about SOHO's temperature measurement here.

If the heliosphere would be in the thermodynamic equilibrium, according to Planck's law or Wien's law, you would get the peak at about 3nm, in the soft x-ray range. But the equilibrium assumption probably doesn't hold.

For the hot interstellar medium extreme ultraviolet radiation measurements have been tried (CHIPSat), some successful (EUVE). Hence, in an ideal environment we would measure the radiation intensity across the electromagnetic spectrum, look for the peak intensity, apply Wien's law, and retrieve the effective temperature, which would be identical to the black body temperature in an ideal world.

The plasma of the heliosphere is very rare, therefore almost transparent. That's why we don't feel that heat of about 1 milion degrees. Microwaves play a minor role in that temparature range.

A temperature profile of Sun's corona and heliosphere is shown e.g. on pages 42 and 47 of this survey.

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It is too optimistic to expect that the wind which had been travelling for about a year and expanding by at least a factor of $10^6$ in volume would neither cool adiabatically, nor radiate away most of the energy. –  Alexey Bobrick Jan 23 at 21:39
    
@AlexeyBobrick It interacts with the magnetic field of the sun. The strange thing begins with the corona temperature of a million Kelvin, although Sun's surface is below 10,000 K. Where does the heat come from? The plasma cannot be treated as a gas. We have SOHO and Voyager data. The speed of the particles is slowed down at the heliopause by interstellar gas (voyager.jpl.nasa.gov/mission/interstellar.html). There seems to be a sharp (not necessarily convex) boundary between heliosphere and interstellar space (en.wikipedia.org/wiki/File:Solar_wind_at_Voyager_1.png) –  Gerald Jan 23 at 22:58
    
"The rapid and consistent changes in the freeze-in temperature calculated from four pairs of iron charge states confirm the patchy structure of the corona with length scales of some $10^4$ km and reveal the survival of these structures from a few solar radii throughout I AU." of the above referenced SOHO paper. I can't find a hint for adiabatic cooling or net loss of temperature due to radiation, as plausible as it would sound. –  Gerald Jan 23 at 23:13
    
It seems to me, that you don't differentiate between the bulk motion of the gas (plasma) and its thermodynamical properties, for example temperature and density. Solar wind surely expands till 100AU, as was pointed out already in the question, and it probably keeps the bulk velocity rather constant until gradually the shock from collision with ISM takes over. However, the temperature will go down almost immediately. You can check Kelvin-Helmholtz timescale of a mole of ideal gas in a reasonable volume. The wind will: 1) Cool down, 2) Possibly stop being in thermodynamical equilibrium. –  Alexey Bobrick Jan 24 at 11:37
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Thanks a lot! So it may be better, we leave the answer as it is. –  Gerald Jan 27 at 0:59
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