Back to Basics: The Mass – Luminosity Relation in Main Sequence Stars

Posted: May 20, 2012 by Rog Tallbloke in Astronomy, Astrophysics, Cycles, Energy, Gravity, Solar physics, solar system dynamics, Tides

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.

Comments
  1. Tenuc says:

    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.

    Wow… this seems to go 180 degrees against the mainstream model of physics, which concludes that the particle nature of light is a virtual phenomenon with these virtual messenger photons mediating the scattering between two electrons by emission of a virtual photon (or some such explanation which I can’t quite follow or understand as I’m not an expert on magic).

    It does, however, support Mile Mathis conjecture that light photons have real mass, real size and real spin and interact with matter via the ‘bombardment’ pressure of the photonic charge field; this field being orthogonal to the direction of the apparent attraction of gravity.

    Time for mainstream physicists to see the light… :-)

  2. Scute says:

    Although this is so neat I would like it to be true, I have one concern that someone might be able to clear up. I read recently that it takes 100,000 years for the photons generated near the core to make it to the surface or it might have been for their energy to travel to the surface in multiple absorptions and emissions. Either way the decadal scale of the tides wouldn’t correlate to a near-simultaneous signature in luminosity if driven by the core activities.

    By the way, what is the lag time? I confess I only read some of the Scafetta paper.

    As I said, I would like to see this concern neatly laid to rest because it’s intuitively attractive to think of the sloshing of the core affecting criticality at the margins and therefore energy output.

  3. tallbloke says:

    Hi Scute: Section 5 of Scafetta’s paper says:

    The third objection is based on the Kelvin–Helmholtz time
    scale (Mitalas and Sills, 1992; Stix, 2003) that would predict that
    the travel time scale of an erratic photon in hot plasma from the
    core to the convective zone ranges between 10^4
    and 10^8 years.
    This argument is used to claim that even if the solar core gets
    warmer because of a tidal massaging, the luminosity perturbation
    would reach the surface on average after hundred thousand years.
    This time scale is very long compared to the historical astronomical record, and relatively small core luminosity variations would
    be practically smoothed out and disappear during the very long
    erratic photon transport journey to the surface. This topic is not
    directly addressed in the present paper because this paper focuses
    on the tidal heating effect in the solar core, not on how the energy
    may be transported to the surface.
    Preliminary attempts to solve the above problem have been
    already proposed in the scientific literature, where it is assumed
    that the solar core is not in a perfect hydrostatic equilibrium
    because of the tidal heating. For example, Grandpierre (1990,
    1996) proposed that planetary tides induce finite amplitude flows
    in the core that induce an electric field generation, which then
    produces some kind of gently local thermonuclear runaways
    which shoot up convective cells to the outer layers. Thermonuclear runaways processes move energy very fast at a speed of
    several kilometers per second, and are well known to cause
    supernova explosions. More recently, Wolff and Patrone (2010)
    argued that: ‘‘an event deep in the Sun that affects the nuclear
    burning rate will change the amount of energy going into the g-mode
    oscillations. Some information of this is transported rather promptly
    by g-modes to the base of the Sun’s convective envelope (CE). Once
    these waves deposit energy there, it is carried to the surface in a few
    months by extra convection, which should increase solar activity in
    the way described early in Section 1. This upward transport of
    luminosity by waves was also advocated by Wolff and Mayr (2004)
    to explain the east–west reversing flows detected by Howe et al.
    (2000) and Komm et al. (2003) with characteristic time scales of one
    to three years’’. Indeed, if the solar nuclear fusion rate oscillates
    because of an oscillating planetary tidal forcing, it should cause
    gravitational perturbations through buoyancy waves that should
    be felt by the entire Sun quite fast. Thus, it is possible that the
    energy output variation due to tidal forcing would propagate
    through the solar interior by means of pressure waves at a very
    high speed. An imperfect analogy would be given by sound waves
    and by the pressure propagation in a fluid, which is regulated by
    Pascal Principle that states that the pressure applied to an
    enclosed fluid is transmitted undiminished to every part of the
    fluid and that the perturbation propagates with the speed of the
    sound in that specific fluid. If the core warms a little bit, it
    expands, and all solar interior should rapidly feel the associated
    gravitational/pressure effects. These pressure perturbations
    together with the increased core luminosity may have the effect
    of modulating the luminosity flux toward the tachocline and
    induce a harmonic modulated forcing of the convective zone that
    produces the final TSI output. Consequently, the luminosity output could respond fast to oscillating changes in fusion rate
    occurring in the core without the need to wait hundred thousand
    years so that the surplus photons produced in the core come out
    of the radiative zone.
    It is through these wave pressure perturbations that the
    energy signal may be transferred from the core to the tachocline
    quite fast. For example, the internal solar g-wave oscillations
    could evolve as: GðtÞ ¼ ð1þa cosðoptÞÞcosf½1þb cosðoptÞogtg,
    where og is the average frequency of the g-waves, op is the
    planetary induced harmonic modulation, and a and b are two
    small parameters. Once at the tachocline, this energy anomaly
    would act as a modulating forcing of the solar dynamo and would
    tend to synchronize it (Gonza´lez-Miranda, 2004; Pikovsky et al.,
    2001; Scafetta, 2010) to its own frequencies generating a complex
    Schwabe cycle among other oscillations, as discussed above and
    in Scafetta (in press).

  4. Scute says:

    Thank you Tallbloke

    I’ve read that. Interesting. I should have read on at the time.

  5. Ray Tomes says:

    Scute asks what is the time for photonic energy to get from the centre of the Sun to the surface. I have seen a very wide range of figures from about 10,000 years to more than 10,000,000 years. I think the correct figure is near the upper end of that range. I cannot see why the answer should not be known to moderate accuracy from solar models.

  6. Brian H says:

    Interesting: there’s a kind of positive feedback sequence: tidal wave (gravity) induces more fusion at core, which increases heat, which increases pressure, which increases fusion … The dissipation of the pressure and heat also increases, a negative feedback which prevents runaway.

  7. Roger,
    very well done. The mass-luminosity relation may be the key for understanding the issue. Essentially, the planetary gravity add to the solar gravity. So the sun with the orbiting planets would be equivalent to a star with a mass sligthly larger than the solar mass. Thus. its luminosity needs to increase. Because the tides oscillate, the luminosity needs to oscillate as well.

    The propagation mechanism may be through wave mechanism like the sound. May there be a neutrino connection? Who knows.

    What it is evident to me is that arguments based only on classical physics (look at Leif) cannot be considered conclusive. As I wrote:

    The theoretical results of this paper, which are based on modern physics, would rebut the second major objection against the planetary-solar theory, which uses arguments based on classical physics alone to claim that planetary tides are too small to influence the Sun (de Jager and Versteegh, 2005;Callebaut et al., 2012). Indeed, the failure of the 19th century Kelvin-Helmholtz timescale theory claiming that the Sun is about 10 million years old instead of the currently accepted age of 4.7 billion years (Carroll and Ostlie, 2007) demonstrates that classical physics alone does not explain how the Sun works by a large factor. Indeed, the well-known fact that stars are not classical physical systems can invalidate any argument that uses classical physics alone to disprove a planetary tidal influence on the Sun.

    I have updated a short summary of my research here
    http://www.duke.edu/~ns2002/#astronomical_model

  8. gallopingcamel says:

    Tenuc says:
    May 20, 2012 at 12:36 pm

    “Wow… this seems to go 180 degrees against the mainstream model of physics, which concludes that the particle nature of light is a virtual phenomenon with these virtual messenger photons mediating the scattering between two electrons by emission of a virtual photon (or some such explanation which I can’t quite follow or understand as I’m not an expert on magic).”

    Nicola Scafetta works at the Duke University Free Electron Laser Laboratory that produces gamma rays by means of “Inverse Compton Scattering”. It would be hard to find a more convincing demonstration of the particle nature of light.

    A low energy photon (~2 electron Volts) meets an electron beam with an energy of 1 GeV. The electrons have a “gamma” of about 2,000 which means that their mass is 2,000 times the rest mass of an electron. The collision multiplies the energy of the photon by a factor of 16,000,000 (four times gamma squared). The scattered photon therefore has an energy of around 30 MeV. A photon with this energy can penetrate many feet of concrete. If you want a really bright and energetic gamma ray beam take a trip to Duke. They have a pretty good basketball team too.

    You are in good company if this puzzles you. Albert Einstein got a Nobel prize in 1921 for explaining the photo-electric effect which also convincingly demonstrates the particulate nature of light but he could not reconcile quantum mechanics with interference effects that demonstrate the wave nature of light.

    Fortunately, in difficult situations such as this, humor can help. Here is a little jingle by Gilbert Stead:
    http://www.haverford.edu/physics/songs/cavendish/hv.htm

  9. tallbloke says:

    Hi Ray: Nicola, is saying that although it might take a long time for the photonic energy to reach the surface, high speed waves caused by the fluctuations propogate quickly and affect the energy levels leaving the tachocline, which propagate to the surface much more quickly. See his paper here:
    http://www.duke.edu/~ns2002/pdf/ATP3610.pdf

    Nicola has done the heavy work on the mass-luminosity relation and the viable link with planetary tidal action on the Sun. I’ve just culled a few easy to understand snippets from the net which explain it. Thanks for the props though Nicola! The key to this is understanding that the important variable is differential pressure, which is induced by combinations of planetary tidal action. This is additional to the pressure induced by the action of the self gravity of the mass of the Sun compressing its core. The total mass of the planets is around 0.14% of the mass of the Sun. Coincidentally, the centennial variation in solar output is also around 0.15%.

  10. Tenuc says:

    gallopingcamel says:
    May 21, 2012 at 6:25 am
    “…You are in good company if this puzzles you. Albert Einstein got a Nobel prize in 1921 for explaining the photo-electric effect which also convincingly demonstrates the particulate nature of light but he could not reconcile quantum mechanics with interference effects that demonstrate the wave nature of light…

    Since the Copenhagen interpretation of theoretical quantum mechanics, back in the 1920’s, the science of physics lost its physical underpinnings, with ever more complex theories and heuristic maths needed to prop up this tottering edifice. Perhaps a return to the world of hard knocks and a simpler mechanical approach can help understanding…

    http://milesmathis.com/wave.mov

    Superposition
    http://milesmathis.com/super.html

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