Astronomy 3500 Galaxies and Cosmology

1. Astronomy 3500Galaxies and Cosmology Examine the nature and morphology of galaxies of stars and their distribution in space, and to use that knowledge to understand the nature of the universe as a whole. Topics include the Milky Way Galaxy, the various morphological types of galaxies and their spatial distribution, exotic objects including active galaxies, and what the characteristics of galaxies and clusters of galaxies tell us about the nature of the universe as a whole. Emphasis is placed on the development of critical judgment to separate observational information from proposed physical models.

2. 24. The Milky Way Galaxy Goals: 1. Summarize the basic observational characteristics of the Galaxy and how they were established, distinguishing observational fact from physical models. 2. Introduce the dynamical equations for Galactic rotation and what they tell us about the nature of the Milky Way. 3. Characterize basic features of the Galaxy, the Galactic centre, the central bulge, the disk with its spiral features, and the halo.

3. Picturing the Galaxy: The proper study of the Milky Way Galaxy probably begins in 1610, when Galileo first discovered that the Milky Way consists of “innumerable” faint stars. In 1718 Halley discovered the proper motions of Arcturus, Sirius, and Aldebaran, and by 1760 Mayer had published proper motions for some 80 stars based upon comparisons of their recorded positions. His results established that the Sun and stars are not at rest relative to one another in the Galaxy. The obvious problem with trying to map our Galaxy from within is that the Sun is but one of many billions of stars that populate it, and our vantage point in the disk 8-9 kpc from the Galactic centre makes it difficult to detect objects in regions obscured by interstellar dust. But attempts have been made frequently.

4. In 1785 William Herschel derived the first schematic picture of the Galaxy from optical “star gauging” in 700 separate regions of the sky. He did it by making star counts to the visual limit of his 20 foot (72-inch diameter) telescope. He assumed that r ~ N1/3 (i.e. N ~ r3), and obtained relative thicknesses for the Galactic disk in the various directions sampled. No absolute dimensions were established. By 1817 Hershel had adopted a new picture of the Galaxy as a flattened disk of nearly infinite extension (similar to the modern picture).

5. In 1837 Argelander, of the Bonn Observatory and orginator of the BD catalogue, was able to derive an apex for the solar motion from studying stellar proper motions. His result is very similar to that recognized today. Also in 1837, Frederick Struve found evidence for interstellar extinction in star count data, which was considered necessary at that time to resolve Herschel’s “infinite universe” with Olber’s paradox (which had been published in 1823). By the turn of the century many astronomers felt that a concerted, detailed effort should be made to establish reliable dimensions for the Milky Way. The task was initiated by Kapteyn in 1905 with his plan to study in a systematic fashion 206 special areas, each 1° square, covering most of the sky — the well known “Selected Areas” for Galactic research. By then, separately-pursued research programs into the nature of the Milky Way system often produced distinctly different results.

6. In 1918, for example, Shapley noted the asymmetric location of the centre of the globular cluster system with respect to the Sun, and suggested that it coincided with the centre of the Galaxy. But the distance to the Galactic centre found in such fashion was initially overly large because of distance scale problems. Longitude distribution of globular clusters.

7. Kapteyn and van Rhijn published initial results from star counts in 1920, namely a Galaxy model with a radius of ~4.5 kpc along its major plane and a radius of ~0.8 kpc at the poles. Kapteyn published an alternate model in 1922 in with the Sun displaced from the centre, yet by less than the distance of ~15 kpc to the centre of the globular cluster system established by Shapley.

8. The issue reached a turning point in 1920 with the well known Shapley-Curtis debate on the extent of the Galactic system. The merits of the arguments presented on both sides of this debate have been the subject of considerable study over the years, but it was years later before the true extragalactic nature of the spiral nebulae was recognized. Although Shapley was considered the “winner” of the debate, it was Curtis who argued the correct points. A big step was Hubble’s 1924 derivation of the distance to the Andromeda Nebula using Cepheid variables. Somewhat less well-known is Lindblad’s 1926 development of a mathematical model for Galactic rotation. Lindblad’s model was developed further in 1927-28 by Oort, who demonstrated its applicability to the radial velocity data for stars. Finally, in 1930 Trumpler provided solid evidence for the existence of interstellar extinction from an extremely detailed study of the distances and diameters of open star clusters.

9. Perhaps the best “picture” of the Galaxy is that sketched by Sergei Gaposhkin from Australia, as published in Vistas in Astronomy, 3, 289, 1957. The lower view is Sergei’s attempt to step outwards by 1 kpc from the Sun.

10. Sergei Gaposhkin’s drawing is crucial for the insights it provides into the size and nature of the Galactic bulge, that spheroidal (or bar-shaped?) distribution of stars surrounding the Galactic centre. Keep in mind that all such attempts rely heavily upon the ability of the human eye (and brain) to distinguish a “grand design” from the confusing picture posed by the interaction of dark dust clouds, bright gaseous nebulae, and rich star fields along the length of the Milky Way (see below).

11. The present picture of the Galaxy has the Sun lying ~20 pc above the centreline of a flattened disk, ~8.5±0.5 kpc from the Galactic centre. The spheroidal halo is well established, but the existence of a sizable central bar and the nature of the spiral arms are more controversial.

12. Another schematic representing the present view of the Galaxy.

13. An outdated picture of the Galaxy by the instructor prior to 2010 had the Sun lying ~20 pc above the centreline of a flattened disk, ~9±1 kpc from the Galactic centre. The spheroidal halo is well established, and there is an obvious warping of the Galactic disk in the direction of the Magellanic Clouds that is best seen in the fourth Galactic quadrant.

14. Star Count Analysis: Define, for a particular area of sky: N(m) = total number of stars brighter than magnitude m per square degree of sky, and A(m) = the total number of stars of apparent magnitude m ±½ in the same area (usually steps of 1 mag are used). N(m) increases by the amount A(m)m for each increase m in magnitude m.  dN(m) = A(m) dm, or A(m) = dN(m)/dm. Star counts in restricted magnitude intervals are usually made over a restricted area of sky subtending a solid angle = . The entire sky consists of 4 steradians = 4 (radian)2 = 4 (57.2957795)2 square degrees = 41,252.96 square degrees ≈ 41,253 square degrees. Thus, 1 steradian = 41,253/4 square degrees = 3283 square degrees.

15. In order to consider the density of stars per unit distance interval of space in the same direction, it is necessary to consider the star counts as functions of distance, i.e. N(r), A(r). If the space density distribution is D(r) = number of stars per cubic parsec at the distance r in the line of sight, then: . If D(r) = constant = D, then: Cumulative star counts in a particular area of sky should therefore increase as r3 for the case of a uniform density of stars as a function of distance. For no absorption: m – M = 5 log r – 5, 0.2(m – M) + 1 = log r, or r = 10[0.2(m – M) + 1] . Thus, , if M and D are constant.

16. i.e. log N(m) = 0.6m + C. A(m) = dN(m)/dm = d/dm [10C 100.6m] = (0.6)(10C)(loge10)100.6m = C'100.6m. Denote lo = the light received from a star with m = 0.  l(m) = lo10–0.4m [m1–m2 = –2.5 log b1/b2]. or –0.4 m = log l(m)/lo . The total light received from stars of magnitude m is therefore given by: L(m) = l(m) A(m) (per unit interval of sky) = loC'10–0.4m + 0.6m = loC'100.2m . The total light received by all stars brighter than magnitude m is given by: Ltot(m) = ∫ L(m')dm' = loC'∫100.2m'dm' = K 100.2m, where K is a constant. Thus, Ltot(m) diverges exponentially as m increases (Olber’s Paradox).

17. The results from actual star counts in various Galactic fields are: i. Bright stars are nearly uniformly distributed between the pole and the plane of the Galaxy, but faint stars are clearly concentrated towards the Galactic plane. ii. Most of the light from the region of the Galactic poles comes from stars brighter than m ≈ 10, while most of the light from the Galactic plane comes from fainter stars (maximum at m ≈ 13). iii. Increments in log A(m) are less than the value predicted for a uniform star density, no interstellar extinction, and all stars of the same intrinsic brightness.

18. It implies that D(r) could decrease with increasing distance (a feature of the local star cloud that could very well be true according to the work of Bok and Herbst), or interstellar extinction could be present (or both!). The existence of a local star density maximum is also confirmed by the star density analysis of McCuskey (right).

19. Actual star counts were done in the past using (m, log p) tables (magnitude, parallax), which were simple to use with experience. For each value of m, the entries reach a maximum at some value of log pk. The summation of the entries for each column gives the values for the predicted counts. The values can be compared with actual star counts in a particular area, which are usually much smaller. They must be reduced by the values for the apparent density function D(rk) for each shell. It is therefore necessary to reconstruct the (m, log p) table including an estimated D(rk) function. A solution for the observed counts generally requires a number of iterations with a variable D(rk) function until a best match is obtained. Experience is particularly helpful. Once a solution for D(rk) is obtained, one still needs to know a(r) to obtain D(r) from the results. Such a(r) estimates can come from various sources, e.g. Neckel & Klare (A&AS, 42, 251, 1980).

20. An Example of a m-log p Table. As tied to Van Rhijn’s luminosity function.

21. The use of star counts inside and around the Veil Nebula in Cygnus (part of the Cygnus Loop) to determine the distance to the dust cloud and the amount of extinction it produces at photographic (blue) wavelengths.

22. Well-recognized characteristics of the Galaxy: 1. Gould’s Belt, consisting of nearby young stars (spectral types O and B) defining a plane that is inclined to the Galactic plane by 15 to 20. Its origin is uncertain. The implication is that the local disk is bent or warped relative to the overall plane of the Galaxy. This is not to be confused with the warping of the outer edges of the Galaxy.

23. 2. An abundance gradient exists in the Galactic disk and halo, consistent with the most active pollution by heavy elements occurring in the densest regions of these parts of the Galaxy. See results below from Andrievsky et al. A&A, 413, 159, 2004 obtained from stellar atmosphere analyses of Cepheid variables.

24. The abundance gradient is also seen in the halo according to the distribution of globular clusters of different metallicity relative to the Galactic centre (below).

25. 3. The orbital speed of the Sun about the Galactic centre is about 251±9 km s–1, as determined from the measured velocities of local group galaxies, as well as from a gap in the local velocity distribution of stars corresponding to “plunging disk” stars (Turner 2014, CJP, 92, 959). This fact is actually NOT “well recognized” by most astronomers.

26. 4. The Galactic bulge is spheroidal, although some researchers believe it displays a boxy structure at infrared wavelengths suggestive of a central bar viewed nearly edge on. A mapping (right) of Milky Way planetary nebulae in Galactic co-ordinates (Majaess et al. MNRAS, 398, 263, 2009) suggests a more spheroidal structure typical of galaxies like NGC 4565 (top). The nature of the Galactic bulge is still unclear. The surface brightness follows a de Vaucouleurs law.

27. 5. The Galaxy is a spiral galaxy. But does it have 2 arms or 4, and can it be matched by a logarithmic spiral? A “grand design” spiral pattern is not obvious in the plot of the projected distribution of Cepheids (points) and young open clusters (circled points) below (Majaess et al. 2009).

28. A schematic representation of what are considered to be major spiral features. How would you connect the points? Most recent studies consider the Cygnus feature to be a spur or minor arm, and the Perseus feature is considered to be a major arm! There is an “Outer Perseus Arm” in many deep surveys. It lies >4 kpc from the Sun In the direction of the Galactic anticentre.

29. 6. The Galactic disk is warped, presumably from a gravitational interaction with the Magellanic Clouds. The warp is evident in 21cm maps of neutral hydrogen restricted (by radial velocity) to lie at large distances from the Galactic centre (below).

30. 7. The Galaxy has a magnetic field that appears to be coincident with its spiral arms (or features), with the likely geometry of the magnetic field lines running along the arms. Weak fields of ~tens of mGauss are typically measured. The evidence for the presence of a magnetic field comes from the detection of interstellar polarization in the direction of distant stars (see below).

31. 8. Note features in the textbook that are NOT included in the list: spiral structure the Milky Way’s central bar 3-kpc expanding arm dark matter halo evidence of dark matter Can you understand why?

32. Kinematics of the Milky Way: The Galactic co-ordinate system is defined such that the Galactic midplane is defined by main plane of 21cm emission. The zero-point is defined by the direction towards the Galactic centre (GC), which is assumed to be coincident with Sagittarius A*.

33. The Galaxy’s rotation is observed to be clockwise as viewed from the direction of the north Galactic pole (NGP). Galactic co-ordinates are Galactic longitude, l, measured in the direction of increasing right ascension from the direction of the GC, and Galactic latitude, b, measured northward (positive) or southward (negative) from the Galactic plane.

34. The velocity system for objects in the Galaxy is defined by: Θ = Rdθ/dt, the velocity in the direction of Galactic rotation Π = dR/dt, the velocity towards the Galactic anticentre Z = dz/dt, the velocity out of the Galactic plane.

35. The equations of motion are derived relative to the Local Standard of Rest (LSR), a fictitious object centred on the Sun and orbiting the Galaxy at the local circular velocity; the Sun orbits at a faster rate. The radial velocity of an object in the Galactic plane is given by: vR = Θ cos α – Θ0 cos (90°–l) = Θ cos α – Θ0 sin l . where Θ is the circular velocity at distance R from the Galactic centre and Θ0is the circular velocity at R0, the Sun’s distance from the Galactic centre.

36. By the Sine Law: So . Therefore, since Outside the Galactic plane the radial velocity becomes: .

37. The observed tangential velocity of the object relative to the LSR is given by: vT = Θ sin α – Θ0 cos l (where vT is positive in the direction of Galactic rotation). But R sin α = R0 cos l – d, where d is the distance to the object. So and These are the general equations of Galactic rotation.

38. If Ω decreases with increasing distance from the Galactic centre, then for any given value of l in the 1st (0° < l < 90°) and 4th (270° < l < 360°) quadrants, the maximum value of Ω occurs at the tangent point along the line-of-sight, i.e. at Rmin = R0 sin l. In that case, d = R0 cos l, so: Rmin = R0 cos (90° – l) = R0 sin l . vR(max) = Θ(Rmin) – Θ0 sin l .

39. Approximations to the general formulae can be made for relatively nearby objects, where d << R0, in which case: and . But And, for d << R0, R0 R≈ d cos l . So, for nearby objects in the Galactic plane vR becomes:

40. or vR = Ad sin 2l = Ad sin 2l cos2b, outside the plane, where: is Oort’s constant A.

41. For the tangential velocity: or vT = Ad cos 2l + Bd, where: is Oort’s constant B.

42. Expectations from the equations of motion are that radial velocities (solid line) and proper motions(dashed line) for nearby stars should a double sine wave variation with Galactic longitude. They do. The proper motion relationship is a modified version of the vT relation:

43. In the 1st Galactic quadrant (0° < l < 90°) stars are receding from the Sun. In the 2ndGalactic quadrant (90° < l < 180°) stars are approaching from the Sun. In the 3rdGalactic quadrant (180° < l < 270°) stars are receding from the Sun. In the 4th Galactic quadrant (270° < l < 360°) stars are approaching the Sun.

44. Note that: Also: So evaluation of Oort’s constants permits one to specify the velocity gradient and local vorticity of local Galactic rotation. It can also provide a solution for R0 if the local rotational velocity can be found. Can that be done?

45. Use of the equations for Galactic rotation is predicated upon the establishment of an accurate value for the Sun’s motion relative to the LSR. That is not an easy chore because of the nature of stellar orbits in the Galaxy, which are neither circular nor elliptical, but more like a roseate pattern. The general direction of the Sun’s motion relative to nearby stars is readily detected in stellar proper motions, and lies roughly towards RA = 18h and Dec = +30°, i.e. towards the constellation of Hercules.

46. A typical orbit for a star in the Galaxy can be pictured as epicyclic motion of frequency κ superposed on circular motion of frequency Ω. When κ = 2Ω the orbit is an ellipse. Since κ(R) ≠ 2Ω(R) in most cases, the orbits are roseate, something like what is produced by a spirograph. Cyclical motion perpendicular to the Galactic plane also occurs.

47. The random motion of nearby stars relative to each other produces the observed velocity dispersions for various stellar groups. Stars in the Galactic bulge appear to exhibit no preferred direction or orbital inclination, so define a spheroidal distribution.

48. The Local Standard of Rest: In the gravitational field of the Galaxy, stars near the Sun orbit the Galactic centre with velocities that are close to the local circular velocity Θc. A star at the Sun’s location that describes roughly a circular orbit about the Galactic centre has velocity components: (Π, Θ, Z) = (0, Θc, 0) km/s. A velocity system centred on such a fictitious object is used to define the LSR. That is, the LSR is defined by an axial system aligned with the Π, Θ, and Z axes and with an origin describing a circular orbit about the Galactic centre with a velocity Θc. Nearby stars have peculiar velocities relative to the LSR described by: u = Π – ΠLSR = Π, v = Θ – ΘLSR = Θ – Θc , w = Z – ZLSR = Z .

49. The peculiar velocity of the Sun is therefore given by: (u, v, w) = (Π, Θ–Θc, Z) . The velocity of any star with respect to the Sun has three components: i. a peculiar velocity relative to the star’s LSR, ii. the peculiar velocity of the Sun with respect to the Sun’s LSR, and iii. the differential velocity of the LSR at the star with respect to the solar LSR resulting from differential Galactic rotation (usually negligible). Since (iii) is indeed negligible for d ≤ 100 pc, the observed velocity of a star relative to the Sun is given by the velocity vector (U*, V*, W*), where: U* = u* – u = Π* – Π , V* = v* – v = Θ* – Θ , W* = w* – w = Z* – Z .

50. For any particular group of stars belonging to the disk and having nearly identical kinematic properties, one can define a kinematic centroid of their velocities by: For disk stars not drifting either perpendicular to the Galactic plane or in the direction of the Galactic centre, it is reasonable to expect that: