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Unformatted text preview: 1 Wednesday, November 16: Return of Syn- chrotron Both bremsstrahlung and synchrotron radiation can be emitted by hot ion- ized gas. How can you tell whether the light you observe from a distant galaxy is bremsstrahlung or synchrotron? One way of distinguishing, as we have seen, is by the spectrum of light emitted. Bremsstrahlung typically has a flux F ν that is nearly constant with frequency between the free-free ab- sorption cutoff at low frequencies and the exponential Planck cutoff at high frequencies. Synchrotron emission has a steeper dependence on frequency: F ν ∝ ν- s , with s ≈ . 7 for typical synchrotron emission from interstellar gas. If the distribution of relativistic electron energies is n ( ² ) ∝ ²- p , the relation between p and s is s = p- 1 2 . (1) Thus, s ≈ . 7 implies p ≈ 2 . 4. Another way of determining whether the source of light is bremsstrahlung or synchrotron radiation is to look at its polarization . Thermal bremsstrah- lung is unpolarized. Since the thermal motions of the free electrons and ions are random, there are no preferred axes in the problem. Thus, although the light from an individual electron – ion encounter is polarized, the light from many, many such encounters added together has no net polarization. How- ever, synchrotron radiation does have a preferred axis – the direction of the magnetic flux density ~ B . The calculation of the polarization of synchrotron radiation is a bit tedious, involving more modified Bessel functions, so I’ll let you work through that bit of the textbook at your leisure. It turns out that the synchrotron radiation has a net linear polarization. The axis of polarization is perpendicular to the magnetic field ~ B as projected onto the plane of the sky. The direction of polarization, as shown in Figure 1 for the galaxy M51, indicates the (projected) direction of the magnetic field. For electrons with n ( ² ) ∝ ²- p , the degree of linear polarization, integrated over all frequencies and all electron energies, is Π = p + 1 p + 7 / 3 . (2) If p ≈ 2 . 4, the degree of polarization is Π ≈ . 72. A 72 percent polarization is quite high; remember that the polarization of starlight scattered from 1 Figure 1: Synchrotron intensity at ν = 4 . 86 GHz (false color) and magnetic field orientation (straight lines) in M51; length of line is proportional to degree of polarization. dust was only a few percent. Synchrotron emission thus provides a powerful tool for studying the magnetic fields within galaxies. The linear polarization shows the projected direction of ~ B . Since the synchrotron power is (as we saw last week) dP dV dν ∝ n e B ( p +1) / 2 ν- ( p- 1) / 2 , (3) the intensity of synchrotron emission at a given ν tells you about the ampli- tude of ~ B ....
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This note was uploaded on 07/17/2008 for the course ASTRO 822 taught by Professor Ryden during the Fall '05 term at Ohio State.
- Fall '05