### Phys 728, Spring 2005            Homework Problem Set #11

11.1  The largest solar flare is about 105 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 103 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 107 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) = [3n(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.