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Back to Basics: The Mass – Luminosity Relation in Main Sequence Stars
The novel aspect of Nicola Scafetta’s new paper which offers a viable physical mechanism which can potentially explain why we find correlations between planetary motion and changes in solar activity is its grounding in a well established observation concerning main sequence stars: The Mass – Luminosity Relation. In this post we’ll take a quick look at what it is, why it holds good for the class of stars which includes our Sun and why this is important to planetary-solar theory.
From Knoxville University:
Detailed observations, particularly in binary star systems where masses can be determined with some reliability, indicate that there is a correlation between the mass of a star and its luminosity.
The Relationship of Mass and Luminosity
The adjacent image illustrates for main sequence stars by plotting the logarithm of the luminosity (in units of solar luminosity) against the logarithm of mass (in units of solar mass).
We see that on this plot most stars fall very near a straight line. This is called the mass-luminosity relation for main-sequence stars.
The adjacent plot implies a very strong dependence of the luminosity on the mass, since the mass enters raised to the power 3.5. For example, if I double the mass of a main sequence star, the luminosity increases by a factor 2 3.5 ~ 11.3. Thus, stars like Sirius that are about twice as massive as the Sun are more than 10 times as luminous.
Caveats and Implications
This particular relation between mass and luminosity holds only for stars on the main sequence. It does not hold, for example, for white dwarfs or for giant stars. The observation of a correlation between mass and luminosity for particular classes of stars suggests important systematics relating the light output of stars to their intrinsic structure.
So what does this have to do with planets affecting solar variation? To understand this we need to consider why the Mass-Luminosity relation holds. From Penn State University:
Given our theory for the structure of stars, you can understand where this relationship comes from. Stars on the Main Sequence must be using the energy generated via nuclear fusion in their cores to create hydrostatic equilibrium. The condition of hydrostatic equilibrium is that the pressure is balancing gravity. Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase. So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars. At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star.
From Cliff’s Notes
The main sequence is bounded by upper and lower mass limits of about 80 solar masses and about 0.08 solar masses, respectively. Why should there not be more massive (and hence brighter) and less massive (hence fainter) stars? The upper limit ( Eddington limit) is set by radiation pressure in the star’s photosphere. An 80 solar mass star is not that much bigger than the Sun, but its luminosity is 106times greater. The radiation passing through each square meter of photosphere is perhaps 104 times greater than for the Sun. Radiation can apply a pressure (force per unit area) when it interacts with matter because photons of light can act as particles. In collisions with atoms, the atoms can be kicked away from the star. At the upper mass limit of main sequence stars, the addition of a bit more mass would increase the luminosity and radiative flux and simply blow away what has been added. Stable stars in a main sequence state with more than about 80 solar masses simply cannot exist.
The lower mass limit on stars seems to be about 0.08 solar masses. Below this mass limit, internal temperatures and pressures are too low to sustain thermonuclear conversion of hydrogen to helium. Without a thermonuclear energy source, an object is not self-luminous. It would be what has been called a failed star. Such objects actually exist and radiate at infrared wavelengths due to their store of heat energy generated when they contracted gravitationally — these are termed brown dwarfs. Less massive objects are planetary bodies like Jupiter.
So now we can see what Nicola Scafetta is driving at. As the planets revolve around the Sun, their tidal forces sometimes combine to produce spring tides, and sometimes partially cancel to produce neap tides. This action is effective right throughout the body of the Sun, from surface to core. Nearer the core the high pressure due to gravity makes the hydrogen act more like a metal than a gas in terms of its mechanical properties, so it is semi elastic, and will transmit pressure waves induced by the varying tidal forces produced by combined planetary motions. These pressure waves will, according to Scafetta’s hypothesis, affect the rate of nuclear fusion, thus amplifying the effect of the planetary tides and causing variation in solar output proportional to the tidal effects.
Read more at Tallbloke Talkshop
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