## Homework Handout #7

7.01:  In the photosphere, the gas energy density dominates and can push magnetic field around until it becomes concentrated into tiny bundles of high field strength.  Given typical parameters for the photosphere: n = 1017 cm-3, T = 5770 K, estimate the magnetic field strength B in these bundles.  Magnetic field strength in cgs units is given in gauss (G).  [Hint: the gas can concentrate the field until b ~ 1.]

7.02:  A sunspot's umbra (darkest part of the sunspot) has a temperature of only 4000 K.  At an equal optical depth of t =1, the umbra is about 2600 K cooler than the photosphere.  Calculate the umbral intensity contrast Iu/Ip at 550 nm and at 1.0 mm in the infrared, and compare with the observed values of 0.1 at 550 nm and 0.23 at 1.0 mm.  Why is the contrast greater at 550 nm?  [Hint: You will need the Planck Function, eq'n 3.20 in the text.  Since you only need the ratio Iu/Ip you do not need to calculate the value of all of the constants!]

7.03:  Considering the Archimedean Spiral pattern of the interplanetary magnetic field (IMF),

r - ro = - v/w (q - qo),

(a) What is the rotation rate of the Sun (w) in radians/s, if it rotates once every 27.5 days?
(b) Which longitude at the Sun would be "best connected" to the Earth at 1 AU for a typical solar wind speed of 400 km/s?  For a slow wind speed of 300 km/s?  For a fast wind speed of 600 km/s?  Is this longitude east or west of the solar central meridian?