! Dark Matter and the Universe Topic 2 Dark Matter Observation Nearby and in Galaxies Why don’t Galaxies fly apart and how does this tell us that Dark Matter exists?! Contents of Topic 2 Following our introduction to the composition of the Universe and with some basic tools of cosmology in hand from Topic 1, we begin a survey of the observational evidence for Dark Matter, starting with the local neighbourhood and in galaxies. " Dark Matter observation on different scales " Quantifying dark matter using the Mass to Light ratio " Dark Matter near the Solar System and the Oort technique " Measuring Rotation Curves of Galaxies " The observation of flat rotation curves and implications " Derivation of the mass distribution in galaxies " The isothermal sphere model of galaxies halos " Modified Newtonian Dynamics (MOND) and dark matter " Galaxy structures, N-body simulations and the Milky Way Dark Matter Scale and Observation " We have seen from Topic 1 that our current view of the Universe is that it mostly contains Dark Matter and Dark Energy but what is the real observational evidence for the Dark Matter part and how widely is it spread? " It turns out that Dark Matter is found on a vast range of scales in the Universe - from the Solar System, Milky Way and Galaxies (covered here in Topic 2) to Galaxy Clusters, Super Clusters and beyond (covered in Topic 3). " By definition Dark Matter is dark, so studying its presence usually comes from observing its gravitational effects. " There are basically four techniques that can be used: (1) The Oort Technique (2) From Galaxy Rotation Curves (3) Use of the Virial Theorem (4) Gravitational Lensing " This Topic focusses on techniques (1) & (2). Dark Matter & the Mass to Light Ratio " In general we look to measure the mass around using one or other of these techniques, then compare the value with the mass inferred from the observed luminous material. " A good way to quantify this, as used by astronomers, is simply to determine the Mass to Light (luminosity) ratio: M M⊙ = " L L⊙ " Here M⊙ and L⊙ refer to the mass and luminosity of the Sun. Thus the Mass to Light ratio M/L for any system being studied (e.g. galaxy, cluster etc) is simply a number " in units of M⊙/L⊙. By definition " = 1.0 for the Sun. " The actual value of M⊙/L⊙ (for the Sun) is 5133 kg/W. Dark Matter & the Mass to Light Ratio " Measurement of the Mass to Light ratio M/L can tell is if there might be hidden dark matter around, for instance: (1) M/L < 1 likely implies we might have a system of luminous main sequence stars only. (2) M/L > 1 likely implies a system with hidden matter. " How you measure M/L depends where you are measuring. " e.g. near our Solar System you might count up the luminosity of nearby stars and objects and compare with the mass inferred from their motions (the Oort technique). " e.g. in a Galaxy Cluster you might measure the total luminosity of the galaxies and use the Virial Theorem to estimate the total mass of the cluster (covered in Topic 3). Dark Matter & the Mass to Light Ratio " It is important to distinguish stars or objects which are intrinsically so dim that we can not see them from those which we can not see just because they are far away. " i.e. there will always be stars that are intrinsically faint and so “hidden” just because of the luminosity rule: observed intensity of object distance to object 2 ls = Ls/4#d intrinsic luminosity of object " Examples of faint astronomical objects are: Brown Dwarfs, White Dwarfs, Black Holes and Neutron Stars. Dark Matter Nearby " As we found in Topic 1 with the mass of the Earth problem, the idea of “hidden” matter revealed by its gravitational effect is not new. Examples in and around the Solar System are: (1) Observation of the anomalous orbit of Uranus due to “hidden” matter led to discovery of Neptune by Galle (1846). (2) Observation of the anomalous motion of the star Sirius (a near neighbour of the Sun at 8.6 ly away) led to discovery of a companion star Sirius B by Clark (1862). The Oort Technique " One of the first techniques used to examine hidden mass in the Galaxy close to us was by Jan Oort (1932). The idea is to use the motion of nearby stars at right angles to the plane of the Galaxy to derive the total mass near the Sun. z direction motion of stars caused by the gravitational potential of the galactic disk is an up and down motion " This “vertical” motion of stars (let’s say in the z-direction) is expected to be like that of a Harmonic Oscillator with form F (= ma) = -kz where k is the restoring force constant due here to the gravitational potential of the galactic disk. Thus: d2z 2 = -4#$0Gz dt density of acceleration material in disk The Oort Technique " Integration gives the velocity and the Vertical Frequency %: dz = vz = vz,0 cos %t dt 1/2 % = (4#$0G) " So by measuring the Vertical Velocity of stars it is possible to determine #0. However, this is very hard in practice and you have to assume that vz depends only on #0. " Better is to assume that the number of oscillations made is much greater than the age of the galaxy. Then examine the distribution of stars away from the galactic plane. " Oort did such measurements of observed vertical distances of stars and derived #0 ~ 0.2 M⊙/pc-3. " This is about twice the visible matter near the Sun, hence the Mass to Light Ratio is "(near the Sun) = ~2. Mass to Light Ratio on Bigger Scales " The Oort measurement is hard and controversial and specific to our neighbourhood, near the Sun. The technique is also only really looking at mass in the disc of our galaxy. " However, it was a first hint from near the Galactic Centre that there is more matter than can be accounted for by the stars alone. Obviously this still could be gas and dust (at the time cold hydrogen could not be seen). " But we now know things get far more obvious as we move to larger scales and use new techniques, in summary: η(near Sun) = ~2 η(our Galaxy, inner part) = ~6 η(our Galaxy, outer part) = ~40 η(galaxy pairs) = ~80 η(galaxy local group) = ~160 η(galaxy clusters) = ~500 η(Abell clusters) = ~500 Mass to Light Ratio on Bigger Scales " Here is some data showing the Mass to Light Ratio for various objects going to greater and greater scale, out to galaxy clusters. " Note the lines marking the equivalent value of & and how at the largest scale the value appears to saturate at ~ & = 0.3. " This is suggestive that there is not enough matter in the Universe to give us a flat geometry with & = 1.0. The missing factor will eventually turn out to be Dark Energy. Dark Matter in Whole Galaxies " A big advance came in the 1970’s with the advent of Radio Astronomy. In particular, observations of the velocity of HI Hydrogen Clouds orbiting galaxies, started by Vera Rubin. " This is her paper and an early result. " This allowed production of Galaxy Rotation Curves - plots of circular radial velocities vc in the plane of the disc of a galaxy vs. distance r from the centre at distances beyond the visible. Basics of Rotation Curves " The concept and importance of Galaxy Rotation Curve measurements is illustrated below. Here we see a satellite HI cloud of mass m orbiting a galaxy of mass M at velocity vc with distance r from the centre. vc M m r mass m in orbit with circular velocity vc " Newton’s laws of gravity should tell us the relationship between the masses and the velocity. But first let’s consider how the measurement itself is possible. Rotation Curve Measurements " The measurement is possible because HI (atomic hydrogen) emits 21cm Wavelength Radio radiation (or 1.42 GHz). " This radiation arrises because the hydrogen 1s ground energy state is slightly split by the interaction between the electron spin and nuclear spin. " A 21cm photon is emitted when there is a transition from the state with nuclear and electron spin aligned parallel (the so- called F = 1 Hyperfine State) to the state where the nuclear and electron spins are antiparallel (F = 0 Hyperfine State). " This transition is sometimes called the Spin-flip Transition. Rotation Curve Measurements The 21cm Radio Line from HI is " Messier 83: 21-cm and Optical very useful because there is lots of HI rotating it at the edges of galaxies. towards us " The 21cm Radio Line also penetrates well through dust. " The figure here shows an example measurement from M83. Note how HI rotating away the radio emission extends to greater radius than the optical (lower image on the same scale). " Use of the Doppler Shift allows the velocities of the HI to be measured. (the blue in the top image signifies gas moving towards us, the red is moving away). Rotation Curve Measurements " The cartoon here illustrates how the Doppler Shift works to allow rotation of a Galaxy to be observed. 21cm Radio from the Milky Way " Below shows an image of 21cm Radio Line emission from our own Galaxy. Here we are looking through the disc. Caution Measuring Rotation Curves " Although the 21cm Line can be used in principle to measure the circular velocity of orbiting clouds via the Doppler Effect in practice caution is needed for several reasons: (1) There can be random Peculiar Motions of the clouds and the galaxy observed could also be moving away/towards us as a whole.