Download Set 1

Ay 124: Structure and Dynamics of Galaxies
Problem Set 1
Handed out: January 28th; Due back: February 8th
1. The unusual radio source, Sgr A*, is thought to lie at the Galactic center. Rogers et
al (1994) quote its position as: RA=17h 45m 40.045  0.01s, Dec=-29 00’ 27”.9 
0”.2 (J2000).
Using the IAU-approved celestial coordinates of the North Galactic pole
(192.85948, 27.12825) and the Galactic longitude of the north celestial pole
(123.932), calculate the adopted Galactic coordinates (l, b) of Sgr A* . If the Galactic
center is 8.5 kpc away, calculate the distance discrepancy referred to in class.
Andrea Ghez (UCLA) wishes to observe the region of Sgr A* for as long as possible
from Mauna Kea (latitude +19 46’.9). She finds the Keck I telescope has an
elevation limit of 33.3 in the east and 18 in the west. Using spherical trigonometry,
estimate the maximum time the region can be observed. What is the optimum time of
year to make the observations?
2. The declination of a star is 42 57’ N and its proper motion components are:
 = -0.”0374,  = 1”.21. Calculate its total proper motion. If the spectrum reveals
a blueshift of 7.6 km s-1 and the parallax is 0.”376, calculate its space velocity relative
to the Sun and its total proper motion at the time of closest approach.
3. Smoot et al (1992) found a dipole anisotropy in COBE measurements of the
microwave background such that the background is higher by 3.36 mK (c.f. the 2.73
K average) in the direction  = 11h 09m, =-7. By subtracting the rotational motion
of the solar neighborhood, determine the direction (in celestial coordinates) and
peculiar speed of the Milky Way with respect to the microwave background. [Use the
coordinate data given in Q1]
4. Bahcall and Soneira’s (1980) star count analysis concluded that the disk and bulge
components of the Milky Way have integrated luminosities of 1.2 1010 and 1.9 109 L
respectively. If the Sun’s luminosity is MB is +5.48, calculate the blue absolute
magnitude of the Galaxy.
Kent et al (1991) assumed the luminosity density of the Galactic disk can be fit by an
exponential with Galactic radius. Using near-infrared (K-band) Spacelab 2 data, they
determined a central disk luminosity density of 1208 L pc-2 and a disk scale length
Rd=2.7 kpc. If Ro=8 kpc estimate the projected surface brightness K (in mags
arcsec2) of the Galactic disk in the solar neighborhood as viewed by an external
observer. (Solar MK=+3.28).
5. Salpeter’s Initial Mass Function (IMF) is of the form:
(M)  M–(1+x)
By considering only stars more massive than 1 solar mass (whose lifetimes are
shorter than the age of the Galaxy) and stellar luminosities L  M 4, find the slope x
such that equal numbers of stars are seen in a homogeneous isotropic region within
equal logarithmic ranges of luminosity. What type of star dominates the counts if the
slope x is flatter than this value?
6. The star formation history of a stellar population is often represented by an
exponential decay from an initial burst, viz:  (t)  exp (-t / ) where  is some time
constant. If the IMF (M) is invariant, obtain an expression for the observed number
of stars of a given mass at time t in terms of its main sequence lifetime. Comment
briefly on the differences you would expect to see in the H-R diagrams of a
population where  = 0.1 Gyr and  =  for a population viewed after 12 Gyr.
For a population formed instantaneously with a Salpeter IMF and an upper mass cutoff at 2 M, estimate the time after which most light comes from post-main sequence
stars. Assume the time a star spends on the main sequence is  M/L,