Lecture 23: Distances to galaxies, Properties of Galaxies
The Cosmic Distance Scale
Early in the 20th century, the existence of other galaxies lying outside the Milky Way was a matter of dispute. Photographs had revealed "spiral nebulae" as well as "elliptical nebulae".
Spiral Nebulae were securely identified as extragalactic and as separate galaxies similar to but separate from the Milky Way by Edwin Hubble in 1924. He identified a number of Cepheid variables in M31 and used their period-luminosity relation to compute the distance to M31 which we now know to be ~680 kpc.
Hubble at 100-inch
What about Shapley's arguments?
--- Curtis was correct about the zone of avoidance
--- the "nova" of 1888 in M31 was actually a supernova and intrinsically much more luminous than a nova
--- Van Maanen had made a mistake in his measurements, no one else could duplicate his results
To appreciate the difficulty of observing other galaxies, consider trying to observe the Sun in M31, the nearest spiral galaxy:
The Hubble Space Telescope can detect an isolated star this faint (in a very long exposure), but a pixel on a galaxy will include 10s to 100s of stars so a star like the Sun cannot be seen as individual objects. Only very bright objects can be distinguished.
Distances to Galaxies
The same technique that Hubble used of observing Cepheids to determine the distance to M31 can be applied to relatively nearby galaxies.
However, Cepheids cannot be detected in very distant galaxies. To overcome this limitation, we have reached out by calibrating distance indicators useful over ever greater distances.
HST has contributed a large quantity of new data in this area because of its ability to observe faint objects at high spatial resolution (e.g. a pixel covers a relatively small area of a galaxy).
HST picture of globular cluster in M31
So the distance is inversely proportional to the flux/fluctuation ratio.
Most galaxies have nearly the same ratio of mass to luminosity so a measure of the mass is a measure of the luminosity. Not useful for ellipticals which have very little HI.
Brightest galaxies in cluster:
the brightest ellipticals in clusters of galaxies have nearly uniform brightness so they can be used as standard candles. Detectable over the greatest distances but galaxies too distant may have evolved (for example, if a galaxy is so distant that it takes light 5 billion years to reach us, will the same types of stars be on the main sequence in such a galaxy as in nearby galaxies?).
Coma cluster of galaxies:
By measuring the distance to a galaxy from Cepheids (or other distance indicators) and comparing with the Doppler shift of the galaxy, Hubble found some surprising facts:
1) Virtually all galaxies are moving away from us, e.g. they are redshifted.
2) The more distant the galaxy, the larger its redshift.
This second fact is summarized in Hubble's Law:
VR = H0 x d
VR = radial velocity, d=distance
H0 = Hubble's constant, about 75 Km/sec/Mpc
A galaxy is found to have H-alpha at 659.1 nm. We can compute its distance:
Hubble's Law, once it is calibrated, provides an easy way to measure the distance to a galaxy. Just take a spectrum and measure the redshift.Cepheids: directly calibratable in Milky Way, can be observed to ~20 Mpc. One drawback is that Cepheids are young stars and not seen in elliptical galaxies which consist almost exclusively of old stars.Brightest stars: relatively constant and useful over about 4x the distance that Cepheids areNovae: reach about the same peak brightness as the brightest stars and serve as a checkGlobular clusters: the brightest ones have about the same brightness and are visible over slightly greater distances than the brightest stars. Also useful for ellipticals.Surface brightness fluctuations: the number of stars in a fixed observing pixel will increase as the square of the distance to a galaxy assuming that galaxies have the same average surface density of stars. The variation (or fluctuation) in the number of stars depends on the square root of the number of stars being counted (observed). By comparing the surface brightness with the fluctuations between pixels, the distance can be derived if the average brightness of a star can be calibrated. Useful to ~200 Mpc.Supernovae: can be seen over huge distances (more than 5000 Mpc). Type I supernovae have been well-calibrated and are being used for distances.21-cm line width: the width of the HI 21-cm line reflects the rotation rate of the galaxy which in turn is a measure of the mass.
Hubble Law from brightest cluster galaxies:
Galaxies come in a variety of shapes:
Spiral Elliptical Irregular
The irregular category is a catchall that includes a variety of galaxy types ranging from small, amorphous galaxies to mergers and collisions between large galaxies.
Galaxy shapes or morphologies have been categorized into a shorthand system:
Sa (large bulges, less prominent spiral arms)
Sc (small bulges, prominent arms) M51
SBa (large bar)
E7 quite flattened
A transition class, S0 or SB0 has also been defined which might be loosely described as an elliptical with a disk but without either spiral arms or readily detectable interstellar material.
An irregular galaxy:
Galaxies in any of the morphological classes exist with a range of brightnesses and masses. Ellipticals range from objects hardly any larger than globular clusters to objects with 10-100 times the mass of the Milky Way. Spirals also show a large size range. Big galaxies are often referred to as "giants" and small ones as "dwarfs". In general, small galaxies are more numerous than large galaxies.
Many galaxy properties vary systematically with morphological type:
|Morphology||Disk + bulge,
|All bulge||Huge variety|
|Stellar population||Young and old stars||Old stars only||Young and old stars|
|Interstellar material||Present||Virtually none||Very abundant|
|Star Formation||Present||None||Usually vigorous|
|Kinematics||Disk rotating, Bulge and halo have random 3-D orbits||Little rotation, mostly random 3-D orbits||Huge variety|
Hubble attempted a systematic explain of the shapes of galaxies via his "Tuning Fork" where he postulated that irregulars become spirals which become ellipticals.
This model of galaxy evolution is now generally discredited because all galaxies appear to have a tleast a few very old stars implying that one type does not turn into another type. Note however, that mergers of spiral galaxies could produce galaxies with elliptical shapes but it is unclear whether all ellipticals form this way.
Why Do Galaxies Have These Shapes?
In trying to understand spiral arms, several issues must be understood:
"The Winding Problem":
obviously either galaxies have a method of regenerating new spiral arms or arms do not rotate as units.
"Leading versus Trailing"
The only way to determine which case is correct is to appeal to the fact that interstellar dust will make the more distant side of an arm appear dimmer. Such considerations have lead to the discovery that virtually all spiral arms are trailing arms. (Note that studies of the Milky Way also show it to have trailing arms).
What Causes Spiral Arms?
At least in the case of "grand design" spirals where the arms are strong and well-defined, density waves appear to explain the shapes. A wave propagates through the galaxy compressing material which then is seen as an arm where star formation occurs because of the compression of the gas. The stars orbit the center of the galaxy on nearly circular orbits.
"Flocculent" spirals where only portions of arms can be traced out may result from self-propagating star formation.
Surface Brightness Profiles
One method of quantifying the stellar content of a galaxy is to measure the distribution of the star light. If a galaxy is a self-gravitating object, then the distribution of stars should trace the gravitational field in a galaxy.
Ellipticals have very similar profiles all obeying a law of this form:
where I is the surface brightness (usually expressed as flux per square arc sec or magnitude per square arc second), Ie and re are the surface brightness at a fiducial distance and re is this fiducial distance called the effective radius within which half of the galaxy's total luminosity is contained. This law is often called the "r to the one-quarter law" or the de Vaucouleur's Law.
Observationally it is a very good description of the brightness profile for an elliptical galaxy or the bulge of a spiral, but it has never been derived theoretically from a gravitational model of galaxy.
Spirals have more complicated profiles with the bulge following the r.25 law while the disk component follows an exponential law:
Io is the central surface brightness of the disk and r0 is usually called the "disk scale length". Again, this is a very good empirical description of the light in a spiral galaxy but does not yet have a firm basis in theory.
Measuring Velocities in Galaxies
Dispersion refers to the broadening of a spectral line when stars with random velocities in all three dimensions contribute to the observed light from a galaxy. Velocity dispersions are used to characterize ellipticals and spiral bulges.
To understand how to translate the velocity dispersion into the mass of the galaxy, start with the Virial Theorem:
From conservation of energy,
Total Energy = Potential Energy + Kinetic Energy
Total Energy = PE + KE
For system involving objects moving under the influence of gravity only and following circular orbits:
The last relation, that one-half the potential energy of a gravitational system equals the negative of its kinetic energy is the Virial Theorem and be proven in a general case where objects move on any allowed orbit.
In the case of our galaxy, we can equate the kinetic energy we are measuring via our velocity dispersion to the gravitational potential:
The factor of square root of three results from our measuring only the radial velocity. The subscripts "e" indicate that we are measuring these quantities at some effective radius usually chosen to include 50% of the galaxy.
Recall from our study of the Milky Way that the rotation rate of the galaxy does not decline with distance nearly as rapidly as the case of "Keplerian" rotation. This fact along with the fact that the disk of the Milky Way is quite thin has led to the suggestion that the Milky Way is surrounded by a "halo" of unseen or dark matter.
Measuring Rotation Curves:
The entrance to a spectrometer, the slit, is placed along a diameter of a galaxy. Velocities can then be obtained by measuring the wavelength shifts along the slit:
Either hydrogen emission lines at visible wavelengths such as H-alpha (656.3 nm) or the 21-cm line at radio wavelengths have been used to obtain rotation curves.
"Flat" rotation curves are common among spirals:
so dark matter appears to be common.
Note that in the case of ellipticals, gravitational lensing has been used to measure the mass of the entire galaxy which leads to the need for dark matter surrounding them as well.
On What Scales Is Dark Matter Required?
This need comes from measuring velocities of galaxies within clusters, and was the first discovery of dark matter by Zwicky in the 1930s. He appealed to the spherical shapes of clusters to prove that they are bound together by gravity. Modern data reveal gas in clusters with T~107° K (detected by x-ray satellites). This gas would escape unless the cluster contains a large amount of dark matter.
Review of Assumptions Leading to Need for Dark Matter
Dark matter appears to be required as the result of comparing a gravitational force (e.g. velocities of stars) with the number of objects visible. No dark matter required if
bound system = one which obeys the Virial Theorem
Candidates for Dark MatterNeutrinos or other exotic sub-atomic particles: Any widely distributed particle which accounts for dark matter must not interact very well with regular (baryonic) matter or they would have already been found. Alternatively, they must be virtually absent from the Solar neighborhood (very unattractive possibility given the sensitivity of searches so far). Two types of exotic particles could solve the missing mass problem: those which have been postulated to exist to solve some other issue and those which are postulated solely to explain the missing mass.
Examples of the first class: axions (possibly required to explain some aspects of the strong nuclear force), massive neutrinos, supersymmetric particles (required for some theories in particle physics)
Examples of the second class: WIMPS (Weakly Interacting Massive Particles), CHAMPS, etc.Baryonic Matter which is not luminous: possibilities include ancient white dwarfs, brown dwarfs, chunks of cold matter significantly larger than the wavelength of visible lightOther exotica: Included in this category are objects such as small black holes that formed outside the process of stellar evolution
Searched for axions or WIMPS have been negative so far; there is evidence that some neutrinos may have a non-zero mass but if the massive type if neutrinos are present in sufficient quantities to solve the missing matter problem, other problems may arise.
Searches for Baryonic Dark Matter:
Use repeated observations of a rich field of stars lying beyond the dark matter halo of the Milky Way to search for gravitational microlensing by "MACHO"s, Massive Compact Halo Objects. MACHOs might be brown dwarfs or dim white dwarfs or other low mass stars. The Large Magellanic Cloud is ideal for such studies because is lies just far enough away that some of the Milky Way's halo lies between us and the LMC but isn't so far away that individual stars can't be seen.
So results so far suggest that the Milky Way's halo may consist of ~50% MACHOs with masses around 0.1 to 0.5 MSun.
Other Searches for Halo Matter
Look for the halo around an edge on spiral galaxy. NGC5907 has been a favorite target of such searches because it is relatively nearby, very thin, and has a small bulge. Light from the halo has been detected at 700nm to 2200nm at levels which could account for the missing mass.