ASTROPHYSICS WORKSHEET,Cygnus A is one of the brightest radio galaxies in the extragalactic sky. The figure below shows the spectral energy distribution of Cygnus A over a wide range of frequencies across the electromagnetic spectrum.

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1. The Pinwheel Galaxy (M33, also called the Triangulum Galaxy) is a nearby (D = 690 kpc)
nearly face-on Sc-type spiral galaxy.
a. How many parsecs in M33 correspond to an angular size of 100 as seen from the Earth?
b. If the rotation curve is like our Milky Way (see your notes in Section 13), what is the
revolution period for a star 10 kpc from the galactic centre of M33?
c. What is the velocity of the star in b. in parsecs per year?
d. How far in arcseconds would the star appear to move in 100 years?
e. If astronomers can measure positions with an accuracy of 0.0100, comment on how long it
would take before the proper motion of the star in M33 could be readily detected.

2. Cygnus A is one of the brightest radio galaxies in the extragalactic sky. The figure below
shows the spectral energy distribution of Cygnus A over a wide range of frequencies across
the electromagnetic spectrum.
a. What can you say about the nature of the radiation of Cygnus A at low frequencies?
b. Use the figure below to calculate the spectral index (α) of Cygnus A at a radio frequency
of 1400 MHz. Hint: F(ν) = F0ν^−α.
1

3. A key observational parameter of stars is their distance. What is the best method you could
use to determine the distance to:
a. α Centauri (distance: 1.3 pc).
b. a globular cluster in the Milky Way (distance: ∼ 8 to 30 kpc).
c. an M0 Ia supergiant (distance: 5 kpc).
d. the Hyades open star cluster (distance: 46.3 pc).
e. a spiral galaxy in the Fornax cluster (distance: 17.2 Mpc).
f. the Large Magellanic cloud (distance: 48.5 kpc).
Motivate your answers.

4. The Hubble Space Telescope Key Project has used the Hubble Space Telescope to identify
and observe Cepheid variables in nearby spiral galaxies, in order to determine their
distances. These distances then allow the astronomers to determine the local value of the
Hubble constant (H0). The following table shows some observed parameters – period in
days and apparent V-band magnitude – of Cepheid variables identified in Messier 100, a
face-on spiral galaxy in the Virgo cluster.
Cepheid number Period (days) mV (mag)
10 50.0 24.81
23 39.7 25.69
48 24.7 25.92
60 17.1 26.15

a. Find the average distance modulus, and the average distance (in units of megaparsec) to
Messier 100. Take the Galactic foreground extinction (AV = 0.41 mag) towards Messier 100
into account.
b. Messier 100 has a measured radial velocity of 1571 km/s. What value of the Hubble
constant would you deduce from these observations alone?
c. What value of the Hubble constant would you have deduced if you did not take the
foreground extinction into account?
d. There are several sources of uncertainty when measuring the Hubble constant by looking
at cepheid variables in spiral galaxies in the Virgo cluster. Give two possible reasons why
there could be an error in the value you derived in part b of this question.
A type Ia supernova (SN2006X) was discovered in M100 on 7 February 2006.
e. Give two reasons why it is so important to observe a type Ia supernova in a galaxy with
a Cepheid-based distance

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