Mass of the Milky Way Galaxy
The mass of an object is one of the most fundamental properties of the
object. As such, reliable ways to measure mass are exceedingly important.
- One way
is to simply measure the optical emission (luminosity of a galaxy) and
to (independently) determine the average mass of a star in the galaxy.
This will then lead to an estimate for the mass of the galaxy if all
of the luminosity is in fact due to the stars and all material radiates
in a similar manner. This method has problems because it is
sometimes difficult to know whether all mass produces radiation.
- Another way to determine masses is to use
our knowledge of physics (in particular,
gravity). Since all mass is expected to interact gravitationally whether
or not we can see it, we should be able to measure the mass of objects
even if they are invisible to our eyes by their effects on
nearby objects. This is the tact we now
Rotation Curves ===> Masses
The gist of the method is to note that all objects are in orbit around
the center of our Galaxy. To see how this allows us to infer the mass of
our Galaxy, consider the
Earth in its orbit in our Solar System.
This is the basis of the method used to determine the mass of
the Milky Way galaxy (and other disk
galaxies). However, before we move on, we have one tweak to
A. In the Solar System, the planets orbit about the Sun. None of the
planets orbit within the body of the Sun. The planets closer to
the Sun feel stronger gravitational tugs due to the Sun and thus must
travel faster to maintain their orbits. For example, the Earth travels
with a speed of ~30 km per second. Pluto travels with a speed of
~4.6 km per second. This is typical of a sytem where bodies orbit outside
of the attracting mass.
B & C.
Suppose we lived in a spherical system where the mass was spread out and we
orbited inside of the body. Newton showed that only the mass contained
within our orbit contributed to the gravitational force on us.
So, if we approached the center of the object, the
gravitational force would, in general, vanish. In such an extended object,
the orbital speed would not fall-off as quickly as one moved away from
the center of the body
and, in fact, the orbital speed could stay the same and could
even increase in some cases.
For the Milky Way, we find that the orbital speed increases and then
remains roughly constant. This implies that we are still within the
body of the Milky Way, even at the largest distances from the center
of the Milky Way. We have not yet located the edge of the Milky
Way; the Milky Way extends much further than the edge of the disk
of stars (the visible disk)!
Oh my, the mass where we can see stars is only 1/3 of the mass of the
entire Galaxy. This suggests that a lot of mass in the Milky
Way is in some form which does not radiate large amounts of light
(Dark Matter). This interesting result keeps
popping up throughout
the rest of the course as we discuss mass determinations for the Universe.
Today, we believe that ~25 % of the Universe is made up of
Dark Matter! Recall that we believe that
~70 % of the Universe is Dark Energy,
so that only around 5 % of the Universe is made of stuff that
we have identified.
- The mass contained in the Milky Way (in the visible disk)
is 2x1011 M(Sun).
- the mass contained in the Milky Way galaxy (out to as far as we can
see HI gas) is 6x1011 M(Sun).