SO we have some conflicting information and data...
We know from the empirical record that we always see a spike in temperature prior to cooling. As the sun cools we indeed see a Spike in energy before quickly going towards zero. Wein's laws conflicts with other observed phenomena. Violating the laws of nature? Not hardly. As cooling begins there is indeed a spike in energy which quickly wanes and energy decreases in the longer wave length.
Let's see this empirical data ... I'm not aware of any circumstance where temperature decreases when energy increases ... by definition, temperature is the measure of (kinetic) energy, if something is gaining energy, then temperature will go up ... keep in mind, any exception to this will need to somehow relate to a single main sequence type G2 star, one that is average as average can be ... I know there's such things as Cephid variables, novae and type 1a supernovae, but all these are binary systems, the processes there don't occur at our own Sun ...
Ultraviolet catastrophe - Wikipedia
en.wikipedia.org
The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the
prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases. By calculating the total amount of radiated energy (i.e., the sum of emissions in all frequency ranges), it can be shown that a black body is likely to release an arbitrarily high amount of energy. This would cause all matter to instantaneously radiate all of its energy until it is near absolute zero – indicating that a new model for the behaviour of black bodies was needed. The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law. The phrase refers to the fact that the Rayleigh–Jeans law accurately predicts experimental results at radiative frequencies below 10 GHz,
but begins to diverge with empirical observations as these frequencies reach the ultraviolet region of the electromagnetic spectrum. Since the first appearance of the term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence.
Not sure why you're bringing up antiquated theories ... Max Planck proved the energy states in an atom are not smooth ... and any theory based on the assumption of smoothness is wrong ... these energy states are quantized, meaning an atom can only hold very specific energy states, and never exist outside these specific states ... and this is the reason we don't observe the UV catastrophe ... indeed it would be fair to say the whole of Quantum Mechanics started out by explaining why we don't observe this ...
I'm sorry ... Wein's Law is derived from Planck's Law and QM ... not Rayleigh–Jean's Law and Classical Physics ...
As plasma cools it does indeed spike in temperature but then quickly recedes to its new power level after the stored energy is expended. Are we violating Weins laws or are we diverging as has been observed? Is the law accurate when observations say it is not?
As above ... cooling matter and rising temperatures are mutually exclusive ... by definition ... it also sounds like you're using the words "power" and "energy" interchangeably ... ya can't do that, they are related, but are two different things ... the Sun's power level is 1,360 (± 5) W/m^2 and has been constant during the instrumentation era, and is called the Solar Constant ... the wavelength of peak energy from the Sun has also remained constant through this period to three significant digits ...
Yes, we can measure these values to a far more accurate level ... unfortunately we only measure temperature on Earth to the nearest whole kelvin, which is only three digits ... [shrugs shoulders] ... them are the rules, and I had no part making them up ...
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The OP is about the Solar Wind ... this isn't just energy, it's matter that contains energy ... matter plays no roll in the radiative transfer of energy; and the Solar Wind is much better described as the convective transfer of energy ... the Sun adds energy to a hydrogen atom, then flings the hydrogen atom (and it's energy) out into space ... what the atom crashed into then absorbs that energy, whether it's Earth, Mars ... or out of the solar system into an exoplanet as a cosmic ray ... some of this energy is radiated in transit, but it's a tiny tiny part of the radiative energy we receive from the Sun ...
i.e. this radiation is safely ignored when discussing the environment here on Earth ...
