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Phys 728, Spring 2005
Homework Problem Set #11

11.1 The largest solar flare is about 10^{5} sfu (solar flux
units), while the weakest detectable flare from a flare star is about 1
mJy (10^{-3} Jy). At what distance could the largest solar
flare be detected, in pc? Compare this distance with the distance
to the nearest star (about 1.3 pc). A typical solar burst is about
10^{3} sfu. At what distance could such a typical flare be
detected?
11.2 Our VLA observations in 1980 ("First detection of nonflare microwave
emissions from the coronae of single late-type dwarf stars," Gary, D. E.;
Linsky, J. L. 1981, ApJ, 250, p284) showed the star UV Cet to have a flux
density of 1.55 mJy at a wavelength of 6 cm. The stellar radius is
about 0.25 Rsun, and its distance is 2.7 pc. If we assume that the
source has a brightness temperature of 10^{7} K, what is the radius
of the source (assumed circular) that would account for this flux density?
If the emission is optically thick due to gyroresonance emission, what
magnetic field strength would be required (say it is x-mode at the 4th
harmonic of the gyrofrequency)? Given the expression from Jackson *Classical Electrodynamics* for the magnetic field from a magnetic dipole *B*(**x**) = [3**n**(**n** . **m**) - **m**]/|**x**|^{3}, where **n** is the unit vector in the direction of **x**, and **m** is the dipole moment, what field strength at the surface
of the star would this correspond to, if the dipole is centered at the
center of the star? Use the "on-axis" expression. Note that all you need is a ratio--the value of **m** is not required.