MadSci Network: Astronomy

Re: Is there a maximum surface brightness for an object?

Date: Sat Nov 30 08:15:47 2002
Posted By: Joseph Lazio, Radio Astronomer
Area of science: Astronomy
ID: 1022109689.As

For a blackbody emitter, it is fairly easy to show that the amount of energy coming out in the visible part of the spectrum is a strong function of the temperature of the emitter. (Its functional dependence is something like T4.) Consider two blackbodies, with temperatures T1 and T2 with T1 > T2. (That is, the temperature of the first blackbody is higher than the temperature of the second.) The first blackbody will radiate more energy in the visible part of the spectrum than will the second blackbody.

The above is in principle. In practice, if we consider stars, which are reasonable approximations to blackbodies, we find some physical limits. There appear to be no stars with (surface) temperatures much greater than 50,000 K. The reason for this is because stars are a balancing act. They shine because of nuclear fusion in their cores, which produces heat (i.e., temperature) and pressure, to balance the gravitational force from their mass. Conversely, it is their mass that produces enough gravitational force to increase the pressure to the point that nuclear fusion reactions can commence.

Extremely hot stars, for instance a hypothetical star with a surface temperature of 200,000 K, need a huge rate of nuclear fusion reactions in their cores. For any such star, the resulting pressure would be so large as to overwhelm the gravitational force from its mass. That is, if a star were formed with enough mass to begin nuclear fusion reactions that would produce a surface temperature of 200,000 K, the pressure from the nuclear fusion reactions would blow away the outer layers of the star. Reducing the mass of the star lowers its central temperature, so the temperature of the surface layers would fall as well.

There are objects, however, that have surface brightnesses well in excess of what one might expect if they had blackbody spectra. Pulsars are an example. These objects also have nonthermal spectra, that is, the shape of their spectra is not in agreement with a blackbody spectrum, indicating that some other process must be producing their radiation.

Unfortunately, for pulsars, we do not have a good understanding of how they radiate. We know that it must be due to their strong magnetic fields (which are typically estimated to be 109 Gauss or stronger) and the motions of subatomic particles (most likely electrons) moving within these fields, but the exact details are not known.

Your hypothesis for the Crab pulsar, while inventive, suffers a couple of problems. First, the Crab pulsar is observed to pulsate at wavelengths from the radio to the gamma-ray. Moreover, the pulses arrive at the same time. This indicates that the mechanism by which the pulsar emits must be tied strongly to the pulsar. It may not arise at the pulsar's surface, but it must be fairly close to it---certainly not in a distant nebula. Second, the Crab pulsar is not the only known pulsar. Any model for pulsars must explain all (or at least a large majority). There are many other known pulsars (over 1000), several are observed to pulse at wavelengths other than the radio, and not all are surrounded by nebulae.

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