Absolute Magnitudes of Supernovae
Summary Using the Hubble Law,
determine the absolute magnitudes of Type
Ia supernovae occurring in distant galaxies.
Background - During a three-week period
in 1997, the Hubble Space Telescope was
used to observe a supernova - an exploding
star in a distant galaxy. These exploding
stars appear suddenly, as they increase
rapidly in brightness, and then fade slowly
over weeks or months. The fuzzy red object
that appears at constant brightness in each of
the six frames in this image is a distant
galaxy, and the bright spot that is visible in
the first frame in the upper left is the
supernova, which gradually fades away. For
a time, the supernova is so bright that it
rivals the brightness of an entire galaxy of
stars. Supernovae are of several types, and
we will be considering supernovae of type
Ia.
Figure 1: Six views of a distance galaxy with a supernova to the
lower left of the galaxy. Notice the decreasing brightness and
changing color of the supernova with time. (Hubble Space
Telescope)
Determining Absolute Magnitudes. On the accompanying pages are the light curves of
nine Type Ia supernovae that appear in galaxies during the years 1994-1996 (Type 1a
supernovae are a particular type of exploding star that contains no hydrogen lines in its
spectrum). The units on the x-axis are days, and on the y-axis are apparent magnitude. Each
supernova was monitored for several weeks so that its rise to maximum light and its
subsequent decline in brightness were well-determined. For each, the apparent magnitude at
which the supernova was brightest can be determined from the light curve. Our goal is to
determine the absolute magnitude of each supernova.
Record the brightest magnitude reached for each supernova in the table on the following
page.
The recession velocities of the host galaxy of each supernova were measured from the
redshift of spectral lines. The recession velocity must be measured from the host galaxy,
rather than from the supernova itself, because the gas from which the supernova spectrum
arises is expanding explosively from the original supernova progenitor.
Use the value of the Hubble Law to compute the distance of the host galaxy (and the
supernova) from the recession velocity. Remember that the distance = velocity / Ho.
Now you can calculate the absolute magnitude from the distance and the apparent magnitude
using the inverse square law. Recall that the distance in parsecs is related to the difference
between the absolute and apparent magnitude as follows:
Distance in parsecs = 10(m-M+5)/5
In this case, we know the distance and apparent magnitude and want to determine the
absolute magnitude. The expression can be rewritten as
M = m – 5 log(distance in parsecs) + 5
Use your calculator to obtain the logarithm of the distance in parsecs (the distance in parsecs
is 106 times larger than the distance in megaparsecs. The absolute magnitudes of the
supernovae should be negative, since the supernovae are very bright compared to ordinary
stars. Remember that astronomical magnitudes become smaller, and then negative, as
objects become brighter. Each 5 magnitudes is a factor of 100 in brightness.
Supernova
1994S
1995D
1994ae
1995al
1995ac
1995bd
1996X
Host
Galaxy
NGC
4495
NGC
2962
NGC
3370
NGC
3021
Anon
UGC
3151
NGC
5061
z
Recession
velocity
(km s-1)
0.01610
4,463
0.00655
1,998
0.06700
1,279
0.00514
1,536
0.04900
14,615
0.01520
4,758
0.00681
2,034
1996bl
Anon
0.3480
10,598
1996bo
NGC
673
0.01650
5,063
Mean Absolute Magnitude
Median Absolute Magnitude
Distance in Mpc for
Ho=72 km s-1 Mpc-1
App
Mag
(mmax)
14.8
Absolute
Magnitude
(M)
How does the brightness of a Type Ia supernova compare to the brightness of the Sun? The
Sun's absolute magnitude is approximately 5. (The Sun's apparent magnitude is -26.)
What can you conclude about the absolute magnitudes of Type Ia supernovae?
What is peculiar about the supernova 1995bd? What explanation might account for its
difference from other Type Ia supernovae?
How might your conclusions about Type Ia supernovae be useful for determining the
distances to other galaxies?
This exercise is based on one developed by Lindsay Clark (see
http://www.astro.princeton.edu/~clark/SNLab.html), and has been revised for use in the "Exploring
the Dark Universe" workshop for teachers at Indiana University. The original data used in the
exercise were obtained from Riess et al. 1999, AJ, 117, 707.