Preamble The mass-to-light ratio is a useful measure of how much mass there is c

Question

Preamble The mass-to-light ratio is a useful measure of how much mass there is compared to how much light there is in a galaxy. The mass-to-light ratio is simply defined as mass/luminosity, where mass is expressed in units of Mo and luminosity is expressed in units of Lo (see question 2.3) The Tully-Fisher relationship for spiral galaxies L V4 can be rewritten as Mg =-9.9510g 10Vmax + 3.15 for Sa galaxies Mg =-10.21081°Vmax + 2.71 for Sb galaxies MB-11.0log10Vmax 3.31 or Sc galaxies which come from linear fits to data where Vmax has intrinsic units of km/s For spiral galaxies, radius increases with increasing luminosity regardless of Hubble type. Therefore, a useful quantity is the radius of a galaxy corresponding to a surface-brightness of 25 mag/arcsec2 in the B band. This radius is defined as: og1o(R25)0.249M-4.00 where R25 is measured in kiloparsecs.

Explanation / Answer

Given: Vmax = 324 km/s, mB =12.22

a) NGC 2639 is a Sa galaxy

MB = -9.95log10Vmax + 3.15 = -21.83

b) Distance Modulus

m - M = 5 log d - 5

d = 65 Mpc

c) Galaxy's radius at a surface brightness of 25 mag/arcsec2 is R25

log10(R25) = - 0.249MB -4.00

MB = -21.83

R25 = 27 kpc

d) M = R25V2/ G = 1.3 x 1042 kg = 6.5 x 1011 Msun

e) MB = MB,sun - 2.5log(L/Lsun)

MB,sun = 5.47

-21.83 = 5.47 - 2.5 log(L/Lsun)

L/Lsun = 8.3 x 1010

L = 8.3 x 1010 Lsun = 3.17 x 1037 W    (Lsun = 3.828 x 1026 W)

f) mass-to-light ratio is

M/L = 1.3 x 1042 kg / 3.17 x 1037 W = 4.1 x 104 kg/W

M/L = 6.5 x 1011Msun /8.3 x 1010 Lsun = 7.83 (Msun/Lsun)

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