26. Galactic Evolution Goals :

1. 26. Galactic Evolution Goals: 1. Examine the characteristics of clusters of galaxies and peculiar galaxies in search of potential mechanisms to explain the differences among them. 2. Determine the importance of various parameters in the creation and evolution of galaxies. 3. Consider clusters of galaxies as the observational test ground for various ideas about galaxy formation.

2. Evidence for Interactions of Galaxies: The centre of the Coma cluster of galaxies, a rich cluster.

3. The distribution of elliptical galaxies (filled circles) in the Coma cluster relative to spirals (open circles) peaks towards the centre of the cluster.

4. The Coma cluster of galaxies as viewed in X-rays.

5. The lower density Hercules cluster, on the other hand, appears to be more heavily populated by spiral galaxies in its central regions.

6. The Hercules cluster of galaxies as viewed in X-rays.

7. Dynamical Friction. Dynamical friction is a term related to loss of momentum and kinetic energy of moving bodies as a result of a gravitational interaction with surrounding matter in space. It is sometimes referred to as gravitational drag, as first discussed by Chandrasekhar (1943). The expression for dynamical friction on a moving object is related to its speed, vM, and mass, M, as well as the density, ρ, of the matter through which it is moving. In standard form: where C probably varies between 20 and 200. The time scale for dynamical capture is given by: where r is the orbital radius, with the obvious C dependence.

8. The Whirlpool Galaxy (M51) and its companion (M52).

9. The Whirlpool Galaxy and its companion as modeled by Toomre & Toomre (1972, ApJ, 178, 623).

10. The Antennae (NGC 4038/39), optical image.

11. The Antennae as modeled by Toomre & Toomre (1972, ApJ, 178, 623).

12. The ring galaxy II Hz 4, optical images.

13. The ring galaxy II Hz 4 modeled by Lynds & Toomre (1976, ApJ, 209, 382).

14. The polar ring galaxy NGC 4650A.

15. Centaurus A.

16. Starburst Galaxies. These are a group of strongly interacting galaxies that are bluer in colour than isolated galaxies, presumably because of the presence of recently-created hot young stars. Larson and Tinsley (1972) argued that the tidal interaction with another galaxy has induced star formation, although the resulting excess luminosity is hidden behind obscuring clouds of gas and dust. Such galaxies are bright at infrared wavelengths, however. Although the starburst activity was initially discovered in the galaxy nuclei, some spiral galaxies also exhibit disk-wide starburst activity. The star formation is assumed to have been induced by shock waves generated by the gravitational interaction. Starburst galaxies often exhibit strong X-ray emission. Does it originate from gas falling into a deep potential well at the centre of the galaxy, perhaps a “black hole”?

17. The starburst galaxy M82, which interacts with M81. M82 was previously believed to be an irregular galaxy (left), but in 2005 two symmetric spiral arms were discovered in near-infrared (NIR) images (right), detected by subtraction of an axisymmetric exponential disk from the NIR images. The arms emanate from the ends of a bar and can be followed for the length of 3 disk scales. Even though the arms were detected in the NIR images, they are bluer than the disk.

18. The rich galaxy cluster Abell 2199 and the multiple nucleus (cannibalistic?) cD galaxy near its centre.

19. The curious elliptical galaxy NGC 3923 and the multiple concentric rings (left, gas?) that surround it.

20. The butterfly galaxy NGC 6240 as viewed by the Hubble Space Telescope (left) and by the Chandra Orbiting X-Ray Observatory (right). What are the multiple strong sources of X-rays near the galaxy’s centre? How were the surrounding streams of gas produced?

21. Models for the Formation of Galaxies. Models for the formation of galaxies began with ideas on the formation of the Milky Way Galaxy. One of the first was that of Eggen, Lynden-Bell, and Sandage (1962), who suggested that the Galaxy initially collapsed rapidly from a proto-Galactic nebula, resulting in a collapsing spheroidal distribution of metal-poor stars in highly-elongated orbits. The collapse slowed as early generations of stars became supernovae, thereby enriching the gas content of the nebula and dissipating the spheroidal collapse. Combined with friction and the initial angular momentum of the cloud, it resulted in the development of a flattened metal-rich disk that eventually produced Population I stars (akin to ideas about the formation of the solar system).

22. Stellar Birthrate Function. How are stars created: at a constant rate or with an obvious time dependence as in the model below (Burkert et al. 1992, ApJ, 391, 651)?

23. The “G-dwarf problem” is the apparent conflict between the observed very small proportion of low-metallicity G dwarfs in the Galactic disk and model predictions for a sizable fraction (~½), given that the original population of low-metallicity stars from the Galaxy’s formation has not had time to evolve away from the main sequence. Perhaps the amount of matter in stars in the Galactic disk has increased significantly since the formation of the Galaxy? Or perhaps very few low-mass stars were formed early in the Galaxy’s history? Etc., etc.? And was the Galaxy’s initial collapse rapid or dissipative? Estimates for the various time scales based on applications of the Virial Theorem produce typical values like tff ≈ 200  106 years and tcool ≈ 8  106 years for the free-fall collapse time scale and cooling time scale, respectively, implying that tcool << tff. For tcool >> tff one predicts galaxy masses of 1081012M, much like what is observed, but implying that massive cD galaxies have formed through mergers (hierarchical merger model).

24. Galactic Disk Dynamics. The Galactic disk can be pictured as a thin plane of infinite dimension, with the density of stars and gas decreasing exponentially with height h above the Galactic plane, i.e. where z is the distance variation of the gas or stars and ρ0 is the density in the plane. The gravitational form of Gauss’s Law can be used to approximate the mass within a cylinder perpendicular to the plane: The dependence of gravitational acceleration with distance from the plane becomes:

25. The resulting height reached by the gas or stars can be related to their kinetic energy via the Virial Theorem to give: The scale height derived for the thick disk and thin disk is used to infer characteristics about the temperature of the gas from which the stars formed originally. The stars orbiting the Galactic centre appear to be blue in colour, but are not necessarily young. Demarque & Virani (2007, A&A, 461, 651), for example, argue that they are low-mass, low-metallicity, blue horizontal branch stars. The presence of high-velocity blue stars at high galactic latitude has been interpreted as stars being ejected from the Galaxy through interactions with the high-mass compact object at the Galactic centre.

26. The Formation of Elliptical Galaxies. While the Eggen, Lynden-Bell, and Sandage mechanism has been proposed for the formation of disk galaxies like spirals and lenticulars, the formation of ellipticals has generally been considered to have been a faster process in which star formation was extremely efficient, leaving nothing for the creation of a disk and later generations. The observational evidence, however, also suggests that galaxy collisions may also be important for the creation of giant ellipticals through cannibalism. Ellipticals are more abundant than spirals in rich clusters of galaxies, for example. Computer simulations have confirmed the possibility of such a mechanism, but keep in mind that computer simulations have reproduced a variety of possible galaxy scenarios, some of which have not yet been observed.

27. Sample Questions 1. The mass density of stars in the solar neighbourhood is estimated to be 0.05 M pc−3. If that value is constant in the Galactic plane and all of the stars are M dwarfs, estimate the fraction of the Galactic disk’s volume occupied by stars. Suppose that an intruder M dwarf moves perpendicularly through the Galactic disk. What are the chances of the intruder colliding with another star during disk passage? Assume a disk thickness of 1 kpc. Answer: An average M dwarf (Appendix G) has a mass of ~0.3M and a radius of ~0.4R. If the mass density of stars near the Sun is ρ = 0.05 M pc−3, the number density of M dwarfs can be estimated from:

28. The average volume occupied by a single M dwarf is therefore given by: The volume occupied by an M dwarf of radius ~0.4R is given by: The fraction of Galactic space occupied by M dwarfs is therefore given by:

29. If an intruder M dwarf traverses the Galactic plane, the mean free path between collisions is given by Equation 9.12, i.e. l = 1/nσ, where the collision cross-section is: The mean free path for the intruder is therefore: For a disk thickness of 1 kpc = 1000 pc, the probability of a stellar collision for the intruder star is given by:

30. 2. Equate the cooling time scale for a sphere of gas to its free-fall time scale to find the maximum mass of a protogalactic nebula. Note that anything less will not necessarily collapse on a free-fall time scale. Answer. See equations 12.26, 26.6, 26.7, and 26.8 of text. Equating tff to tcool yields:

31. The density ρ0 and number of particles n can be written as: and So: or or or

32. The minimum mass for a protogalactic nebula of radius 60 kpc for Λ 10−37 W m3 with μ = 0.6 is therefore given by: corresponding to about 35 Milky Way galaxies and fairly typical of giant ellipticals.

33. 3. The Large Magellanic Cloud has a distance modulus of 18.43, orbiting our Galaxy in the Magellanic Stream. If it has a mass of 2  1010M, what is the time scale for its dynamical capture by the Milky Way for C = 23? Answer. The distance to the LMC, its “orbital radius” r, is determined from: so: The orbital speed of the LMC can be inferred from Kepler’s 3rd Law: for m1 and m2 in M, a in AU, P in yrs. where:

34. Since 1 pc = 206265 AU, MMW 2  1011M, then: So: and:

35. The time scale for dynamical capture can now be evaluated: Which implies dynamical capture of the LMC in only half of its orbital period. But that assumes that Milky Way matter extends as far as the LMC so that there is friction occurring constantly, whereas there is some evidence that the LMC has orbited the Milky Way several times.