06 October 2011

Making Non-constants Constant

Title: The call to adopt a nominal set of astrophysical parameters and constants to improve the accuracy of funametnal physical properties of stars.
Authors: Petr Harmanec & Andrej Prša

Astrophysical parameters and constants are, admittedly, not the most exciting topic for a paper. Readily available in the back of most textbooks and compiled in every edition of Allen's Astrophysical Quantities, astrophysical parameters are of little concern, right? Well, it turns out this is not necessarily the case (if it was, we wouldn't be reading a paper about it). There are systems for which observational uncertainties are pushing below 1%, especially with the instruments aboard MOST, CoRoT, and Kepler. As detector noise is reduced, the precision of observational measurements encroaches a point where systematic sources of error in data analysis models begins to play a role.

Of primary interest to the authors are the definitions (in natural units) of the solar mass, solar radius, and solar luminosity units. Better instruments, data reduction procedures, and observational techniques have lead to more refined values for the said solar parameters. Tables 1 and 2 in the paper display the evolution of the solar mass, radius, and effective temperature (re: luminosity) since 1976, where the IAU defined a set parameters. The fluctuations are on the order of about half a percent, insignificant in most practical applications. However, for systems where observational uncertainties are being quoted as less than one percent, the difference in the adopted solar parameters begins to become a substantial source of uncertainty.

How, then, do we combat this? For one, the solar mass, radius, and luminosity are not strictly constant. The solar mass may as well be considered constant; mass loss due to the solar wind is a puny 10-14 solar masses per year - not a concern. Stellar evolution theory tells us that the solar radius and luminosity change significantly over the Sun's lifetime, but the time scales for these changes is far greater than anything we need to worry about - at least for the next 100 million years or so. There is also the question of the solar cycle, which may alter the solar radius and luminosity depending on whether the Sun is in an active or quiescient period. Results of such studies are contradictory. One group finds the radius and luminosity increase during active periods while another group finds the exact opposite. Either way, if we average observations over a solar cycle or just measure the Sun when it's in the middle of a solar cycle, we can come to an acceptable solution. That is, if we are careful. Observers need to be very meticulous and perform very precise observations, especially considering that defining the "radius" is difficult when looking at an image of the Sun. The boundary of the surface is rather hazy.

Either way, assuming the solar observers have made good observations over the years (which they have), the values are still a bit different. In order to set all models on a common base, the authors suggest adopteing a nominal set of values for each of these parameters. This way, even if the actual values change as the result of more precise measurements, models (and thus other observations) will be unaffected. The authors propose a set of nominal values, although their selection process and value determination method is not mentioned. It does get the conversation started, though. Unfortunately, to make this happen on a large scale, the IAU would have to set forth a committee (or several of them) to discuss and debate which set of values should be adopted as nominal. Do we use values determined by one observer or one research group? What about an average over several observations? These issues would have to be addressed in order to define the parameters in a rigorous manner.

As a final note, how many astronomers are actually concerned about this? Would the call to adopt nominal parameters be supported strongly enough to force the IAU to invest substantial resources into sorting out this issue? If only a small sample of astronomers are truly concerned, then the discussion is moot. We can simply imagine a situation where particular groups of researchers adopt standard parameters (e.g., eclipsing binary observers adopt their own set of parameters for the sake of consistency) or researchers can simply be forced to quote in their paper which values they utilize, essentially making them define, in natural units, the results of their work.

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