My researchDuring my PhD and my postdocs, I studied the motion of stars in galaxies, via the construction of (computer) dynamical models of galaxies. Studying the stellar motions in galaxies is a way to measure the galaxy mass distribution. Comparison of the total mass to the luminous mass of stars and gas sometimes gives surprising results. In the centers of galaxies, often the inferred mass distribution does not coincide with the stellar mass distribution, leading to conclude that there is some unseen (dark) material in the center. Through gravitational forces, this dark matter accelerates the stars: as a result, stars in the center move faster. Since this unseen material is very concentrated at the center, the best hypothesis is a black hole. In this section, you will find more detailed explanations (see below), my PhD and all my published articles.
The subjectThe study of stars and galaxies, their formation, their present properties and their evolution is one of the main goal of modern astronomy.
Astronomers are studying the orbital structure of nearby galaxies today, i.e. how stars move into them. This gives constraints on models of galaxy formation (and evolution), since these models should at least be able to match the dynamics of real galaxies after 14 billion years of evolution (assuming the galaxies were born shortly after the Big Bang, 14 ⋅ 109 years ago).
The dynamics links the real mass distribution within the galaxy with the observed stellar velocities, through the laws of (Newtonian) physics. In the solar system, where the gravitational potential is largely dominated by a "point-mass" in the center, the Sun, a measure of the circular velocity of a planet and its radius gives a direct estimate of the enclosed mass by the orbit, i.e. in this case the mass of the Sun. Let's see how:
Calculate the mass of the Sun with the planet velocity and radius
The planets in our Solar system follow approximately circular orbits around the Sun. To keep an object in a circular orbit requires a force that pulls toward the center of the circle. If this force ceases to exist, the object would fly off straight into space, like the hammer once the olympic champion has released it (the tension in the string does not exist any more, so nothing forces the hammer to curve its trajectory). In physics, this force is called the centripetal force Fc, centripetal meaning "toward the center". Using Newton's second law and a bit of geometry, one can easily show that this centripetal force is
Fc = mp v2/r
where mp is the mass of the planet, v its circular velocity and r its orbital radius. In the Solar system, the mass of the Sun creates the gravitational force Fgrav that keeps the planets on their circular orbits. Therefore, the centripetal force in this case is nothing but the gravitational force Fgrav.
Fgrav = G Msun mp / r2
where G is the universal gravitational costant G = 6.67 ⋅ 10-11 m3/(kg s2). Therefore, we have
G Msun mp / r2 = mp v2/r ==> Msun = v2 r/G.
If one has a way to measure the rotational velocity of the planets, with this short calculation the mass of the Sun can be evaluated. (BTW, the mass of the sun is Msun = 1.989 ⋅ 1030 kg, two thousand billion billion billion kg...)
For galaxies and black holes, it's not that different, except that the stellar mass distribution of galaxies is not point-like but is extended. Astronomers approximate the stellar density distribution with a smooth continuous function, as if the stars were a fluid, with its density increases dramatically toward the center. There are so many stars in a galaxy that the "spikyness" due to discrete nature of the stars is negligible. In reality, stellar distributions in galaxies are so concentrated at the center (especially in elliptical galaxies), that they are similar to point-mass density distributions, where all the mass is at the center.
Astronomers measure stellar velocities distribution in some locations of the 2D galaxy image, for example, along a slit on the symmetry axis of the galaxy. If they are observing a disk of stars, they can quickly derive the rotational velocity and solve for the mass distribution enclosed by the orbit. The problem for elliptical galaxies and bulges of spirals is that the dynamics is fare more complicated than the simple rotation of spiral discs or planetary systems. In these stellar systems, stars move in a disorganized and chaotic way, like the flight of the bumblebees around a beehive. No simplifying assumptions about their dynamical structure can be made, so it has to be solved simultaneously with the mass distribution.
Observing external galaxiesTo obtain the stellar velocities, astronomers observe a spectrum thanks to an instrument called a spectrograph. The spectrum is a one dimensional function, where the luminous Energy E is expressed as function of wavelength λ.
Since the galaxy appears on the sky as a 2D image, ideally we would need a 3D detector to register the 2 spatial dimensions x' and y' and the wavelength λ. This is difficult because astronomical detectors (CCDs) are bidimensional.
One solution is to record only the light that passes through a thin slit: one spatial dimension is neglected, because we know its value. For example if the slit is positioned along the x'-axis (the major axis), we know that for all these observations y'=0. In that case, the position x' along the slit is one of the coordinates on the CCD and the wavelenghth λ is the other. Each line of the CCD records then the spectrum E(λ) for a given spatial position along the slit.
The picture on the left shows M31 (NGC 224) and its small companions M32 (NGC 221), lower center, and NGC 205 (sometimes designated M110), to the upper right. To illustrate the concept of long-slit spectroscopy, two long-slits have been added over the galaxy image. In this case, only the stellar light from the major and minor axes of the galaxy can pass through the slits and be recorded on the CCD (Credit for the M31 image: Bill Schoening, Vanessa Harvey/REU program/NOAO/AURA/NSF).
More modern techniques are now able to register the spectra of all the positions x' and y' by cleverly packing spectra diagonally on the CCD. These techniques are called Integral Field Spectroscopy, like the SAURON spectrograph.
Once the spectrum has been recorded, astronomers rely on absorption lines and the Doppler effect to derive the velocity of the stars in the galaxy (see here).
Schwarzschild modelsIn the case where we do not know a priori the type of stellar motion (like e.g. simple circular rotation), we need a model that can adapt freely its internal dynamical structure to match a set of observations. The aim is to construct a model of a particular galaxy, as accurately as possible, with its luminous profile and observed stellar velocities. There are various ways to construct dynamical models, but only one that has the flexibility and the complexity required here. It was devised by M. Schwarzschild in the 1980s, in which one computes a large of set of orbits in a given mass distribution. In a second step, one solves for the weight of each orbit (or the number of stars traveling on each orbit) in order to match the observations: luminous density profile and velocities.
If no good match between the models and the data can be obtained, the galaxy may contain some dark mass that contributes to the gravitional forces, but not to the luminous distribution. It can be easily added in the model, but entirely new libraries of orbits have to be computed. Repeating this game a few times, one can study what is the amount of dark mass that provides the best fit to the data. In general, dark matter in galaxies is in the form of a central black hole or an extended dark halo.
Black holesWhat is a black hole? How does it form and grow? Is a black hole a giant cosmic vacuum cleaner? There are many excellent websites about black holes. Look at this nice Black Hole Encyclopedia, or at the list of the 10 basics questions regarding BHs. If you still didn't find the answer to your question, you might want to have a look here.
Rotation curves of many spiral galaxies show a surprising feature: since most of the stellar mass lies within 10 kpc, one would expect that the rotation curve decreases for even larger radii, but many observed rotation curves remain flat out to a very large radius. In NGC 6503 (figure to the left) the data points with error bars are the observed velocities. The contribution to the rotation curve of the disk stars (dashed line) and the contribution of the gas (dotted line) are also shown. The rest is attributed to an invisible dark and extended halo. (Credit for the figure: Kamionkowski 1998, astro-ph/9809214).
This dark material acts on the stars through classical gravitational forces, but a part from that, we do not know what it is made of. The dark halo makes up most of the mass of the galaxy, around 90%. It means that we have no idea of at least 90% of the mass in the universe. For the detailed construction of the stellar, gas and dark halo rotation curve of a spiral galaxy (NGC 2403), look here.
The presence of dark halos around spiral galaxies is well established. For ellipticals, the situation is much less clear, because of their complicated dynamics. Only in a few cases, where a general dynamical model has been applied to the galaxy, can we say with certainty that there is a massive dark halo around the galaxy (see Rix et al. 1997, Gerhard et al. 2001, but also Romanowsky et al. 2003.)