2. Milky Way Structure of the Milky Way: a brief history

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1 1 2. Milky Way We know a great deal, perhaps more than any other galaxy, about the Milky Way (MW) due to our proximity. However, our inside position also hampers our understanding of the Milky Way. Fore example, the spiral arms of the Milky Way have to be inferred, while for many external galaxies, we can often directly see these features. Another difficulty is that, at least in the optical, the Milky Way is heavily obscured by dust in the Galactic plane. Many questions about the Milky Way are still not completely understood. To name a few, we still do not completely understand the formation of the MW and the physical parameters of the Galactic bulge. We will discuss the formation of disk galaxies such as the Milky Way in Chapter 5 on Galaxy Formation Structure of the Milky Way: a brief history On a clear night, the Milky Way appears to like a band with dark patches. Greeks and Romans thought the Milky Way was like a fluid (Greeks: Galaxies Kuklos, and Romans: Via Lactea). In 1610, Galileo resolved the Milky Way into numerous stars. The structure of the MW was not properly understood until 1920 s. Our position inside the Milky Way made it more difficult to infer the spatial structure of the Milky Way. We only see the angular distribution of stars on the sky, as we do not know the distance to stars (particularly distant stars), so it is difficult to convert the two-dimensional angular distribution into a spatial distribution. Fig. 1. Panorama of the Milky Way (credit: Lund Observatory). Notice the dark patches caused by dust extinction. A Panorama of the Milky Way is shown in Fig. 1. The Galaxy appears as a thin band with dark patches which are caused by dust extinction. Many past astronomers often ignored such obvious dust extinctions! Under this assumption, if one further assumes that all stars have similar intrinsic luminosities, then their distances would be over-estimated, and the wrong structure for the MW would be inferred.

2 Photometric Model Herschel (1785) used star counts to infer a flattened distribution for the MW. A similar, but much larger survey of nearby stars was done by Kapteyn around He used parallax, proper motions, radial velocities and spectra to infer the distance to stars. He inferred that the size of the MW is about 10 kpc, and the MW is flattened with an axial ratio of 1/5. The Sun is about 650 pc offset from the centre. Kapteyn was aware of extinction problems. He searched for these, but did not find any significant effect. However, the mistake he made was at that time he was only aware of scattering by dust particles, but he did not consider absorption, which turns out to have a much more important effect. Shapley in 1920 s studied globular clusters and used the variables inside them as distance indicators. He found that globular clusters show a spherical distribution centred on a point 15 kpc away from the Sun (Fig. 2). He argued that globular clusters are massive systems made up of stars and hence they should trace out the structure of the MW. He reached the conclusion that the center of the MW is not at the solar position. Shapley ignored the effect of dust. So in order to explain Kapteyn s star counts, he had to add a local over-density of stars. Fig. 2. Distribution of globular clusters in the MW. The effect of dust was understood by Trumpler (1930) who used the angular size of open clusters as a distance indicator. If one assumes that open clusters have roughly the same luminosity, then one can estimate how bright the cluster would be without extinction. It turns out open clusters are much fainter than such inferred values. The difference is then attributed to the dimming caused by dust.

3 Kinematic model of the MW Kant (1755) considered the MW as a rotationally supported system. Lindblad (1927) realised stars with high velocities (v 250 km s 1 ) can not be bound by the Kapteyn s universe as its mass is too small. On the other hand, these stars cannot escape from the Shapley s universe as it has a much higher mass. Oort ( 1927) completed the picture. In this picture the high velocity stars and globular clusters form a different population (so called halo population, or pop II). They do not follow the Galactic rotation, and their spherical distributions are caused by their large random motions. In contrast, disk stars and open clusters follow the Galactic rotation and belong to the disk population (or pop I). The atomic hydrogen (HI) 21 cm emission line was predicted by Van de Hulst in 1944 and observed by Ewan and Purcell in It was soon realised that this line can used to map the MW. These observations indicate non-circular motions of the gas which were found to be due to perturbations of spiral arms. The central HI gas, in particular, shows large non-circular motions due to the Galactic bar (realised in 1970 s). Fig. 3. A schematic face-on view of the MW. Fig. 3 shows a schematic picture of the MW if it is viewed face-on. MW is now classified as an SBc or SBb spiral galaxy.

4 Photometric model of the MW Galactic disk The surface brightness (luminosity per unit area) is approximately an exponential: I(R) = I 0 exp( R/R d ), (1) where I 0 is the central surface brightness and R d is called the scalelength. The total luminosity is: L tot = 0 I(R) 2π R dr = 2πI 0 R 2 d (2) For the MW, Kent et al. (1991) found in the K-band that R d 3 kpc, Σ B 1000L B, / pc 2, and L tot L. Using star counts from the SLOAN digital sky survey, Chen et al. (2001) found that the Sun is about 27 pc above the Galactic plane. Furthermore, the vertical distribution of stars in the solar neighborhood can be approximated by the sum of two exponentials. These were identified as a thin disk and a thick disk components. The stars in the thin and thick disks appear to have different ages and metallicities (see the Table below). component scale height (pc) mass (M ) V c ( km s 1 ) Metallicity (Z ) age (Gyr) thin disk z 0 = <10 thick disk z 0 = > Galactic bulge (bar) There is now substantial evidence for a Galactic bar HI observations indicate larger non-circular motions around the Galactic centre. Infra-light observations indicate asymmetry with longitude (see Fig. 4). Stars with near constant luminosity (standard candles) appear brighter on the positive longitude side (see Fig. 3). Unfortunately, the density distribution of the Galactic bulge is still rather uncertain. The total luminosity is about L in the K-band, uncertain by a factor of 2. The axial ratios are about 1.7 kpc : 0.6 kpc : 0.4 kpc. The minor axis coincides with the vertical axis, but the major axis is about 15 away from line of sight. The near-side of the bar is at positive longitude (the first quadrant). The size of bar is a few kpc, and the bar rotates with a pattern (angular) speed of Ω p = 60/ Gyr with a period of 10 8 yr. The bar causes non-circular motions and resonances in the stars and gas out to 4 kpc.

5 5 Fig. 4. Contours of the infrared light emission detected by the COBE satellite. Notice the asymmetry with longitude. This is due to the near-side of the bar being located in the first quadrant (positive longitude) Kinematics of MW Motions of stars and gas are important to understand the structure and mass distribution (including dark matter) in the MW. They also give strong hints about how the MW forms and evolves. Most stars and gas follow the Galactic rotation together with some random motions. In practice, we can measure the radial velocity (V r ) of stars using Doppler shifts and the proper motions µ (usually measured in arcsec/yr). The proper motion is equal to V t /d, where V t is the transverse velocity and d is the distance. If we know the distance, then we can measure V t (which is a vector and has two components), and hence we can measure all the three components of the velocity. The Galactic coordinate system is centred at the Sun, and the (x, y, z) is usually chosen such that the x-direction is toward the Galactic centre, the y-direction toward the Galactic rotation, and the z-direction is toward the North Galactic Pole, chosen to form a right-handed system. The angular coordinates of stars are labelled as (l, b), and the velocities are also often indicated by (U, V, W ). The line of sight toward the Galactic centre has l = Oort constants: rotation in the solar neighborhood The differential rotation of the MW implies that stars exhibit both radial, tangential and vertical motions. By studying these motions, we can infer the rotation curve of the Galaxy. We will assume that all stars rigourously follow the circular rotation of the Galaxy. The radial and tangential motions of an object in the Galactic plane at radius R from the Galactic centre are V r = R 0 sin l [ω(r) ω 0 ], V t = R 0 cos l [ω(r) ω 0 ] ω(r)d, (3) where ω(r) and ω 0 a1re the angular velocities at radius R and R 0, l is Galactic longitude, and d is the distance from the Sun to the object. Notice that these formulae are valid for any R.

6 6 and In the solar neighbourhood, we can use approximations that are correct to first order of d, One can show that R R 0 d cos l, (4) ω(r) ω 0 = dω dr (R R 0 ), (5) R0 dω dr = 1 ( dv R0 R 0 dr V ) 0 R0 where A is Oort constant A. Using these relations, we find that R 0 2A R 0, (6) V r = A d sin(2l), V t = d [A cos(2l) + B], (7) where the Oort constants A and B are defined by A = 1 ( V0 dv 2 R 0 dr and Key points concerning the Oort constants: R0 B = 1 ( V0 + dv 2 R 0 dr R0 ) ) (8) (9) They can be determined by local measurements For flat rotation curves, i.e., V (R) =const., A = ω 0 /2 = B and hence A + B = 0. For solid-body rotations, i.e., ω(r) = ω 0 =const., A = 0, B = ω 0. Notice that there is no radial velocity for a solid-body rotation. Radial velocities can be measured using Doppler shifts, while tangential velocities can be measured using proper motions µ l = δθ δt = V t d = A cos(2l) + B, (10) which is independent of d. The proper motions are usually measured in arcseconds per year. The Hipparcos satellite has measured proper motions accurately for many nearby stars. Using these proper motions, Feast and Whitelock (1997) found: A = (14.8 ± 0.8) km s 1 kpc 1, B = ( 12.4 ± 0.6) km s 1 kpc 1 These constants imply that the rotation curve is about 218 km s 1 for R 0 = 8 kpc (see below) and slowly falling (see Problem set 2), in fact V R Distance to the Galactic centre The distances to the Galactic centre can be determined using a number of tracer populations. For example, the centre can be determined using the density peak of globular clusters, see Fig. 2. Observationally, we find from globular clusters that the distance determined using this method has a 10% uncertainty. R 0 = (8.0 ± 0.8) kpc, (11)

7 Rotation in the inner galaxy (R < R 0 ) The rotation curve of the Milky Way can be probed using both stars and gas. HI (atomic hydrogen) is particularly important due to its 21cm emission. The ground state of the H-atom is split into two hyperfine levels by the coupling between the spins of the electron and proton; the atom s energy is ev higher when the two spins are parallel than that when they are anti-parallel. The transition between these two hyperfine levels is forbidden, and has a wavelength of 21cm. As hydrogen is the most abundant element in the universe, HI emission can be observed in many places, including the MW. We can map the HI intensity as a function of longitude, latitude and radial velocity. In a given direction, the HI intensity is a function of the radial velocity. For lines of sight with 0 < l < 90, the intensity drops rapidly beyond a certain maximum radial velocity. This is because the angular velocity usually decreases as a function of radius, which immediately implies that the radial velocity is the largest at the tangent point when R = R 0 sin l. And the radial velocity at the tangent point is given by V c (R 0 sin l) = V (t) r + V 0 sin l, (12) where V r (t) is the radial velocity at the tangent point. Using this method, we can in principle determine the rotation speed for radius between 0 < R < R Rotation curve in the outer Galaxy (R > R 0 ) The Outer rotation curve cannot be determined using the method discussed above as there is no tangent point for 90 < l < 270. However, we can use a population of tracers with known distances. The distance between the tracers and the Galactic centre can be determined from R 2 = R d 2 2R 0 d cos l. (13) We can also determine the radial velocity of the tracers, then ω(r) and hence V (R) can be inferred using eq. (3). A prominent tracer population is Cepheid variables. They follow a so-called luminosity-period relation. These stars are very bright and so they can observed to large distances. Their periods can be measured from their periodic variable light curves. For a Cepheid variable, we can first determine its period, and then infer its intrinsic luminosity. Combined with the observed flux, we can infer its distance. Other tracer populations include globular clusters, planetary nebulae and Carbon stars. Fig. 5 shows the rotation curve out to roughly 20 kpc. Using this method, the Galactic rotation curve can be determined out to R 20 kpc. We can use halo stars and satellite galaxies to determine the mass distribution at even larger distances. From the motions of these satellite galaxies (see Fig. 6), we can infer the mass distribution as a function of radius, which can then be used to infer the rotation curve. Using this method, the rotation curve of the Milky Way is found to be flat all the way out to about 200 kpc.

8 8 Fig. 5. The rotation curve for the Milky Way. Notice that the vertical scale starts from 150 km s 1, not from zero. Fig. 6. A dozen or so Satellite galaxies in the Milky Way. The bar at the top of the figure shows the scale for 10 5 light years.

9 Dark matter in the MW Dark matter distribution in the MW is still not completely understood. We shall consider the dark matter distribution in the solar neighbourhood, in the inner galaxy (for R < R 0 ) and in the outer galaxy (for R > R 0 ). Kinematics of nearby stars yield Dark matter in the solar neighbourhood Σ tot ( z < 1.1 kpc) = (71 ± 6)M / pc 2. (14) HST star counts give Σ = 26.9M / pc 2. (15) And the gas surface density is roughly And hence the dark matter surface density is given by Σ gas = 13.7M / pc 2. (16) Σ DM = Σ tot Σ Σ gas = (30 ± 15)M / pc 2. (17) Notice that the error bar is quite large. Around the solar neighbourhood, there is weak evidence for dark matter Dark Matter in the inner galaxy (R < R 0 ) Recall that in the K-band (see 2.2.1) the Galactic disk has a central brightness of I L pc 2 and a disk scalelength of R d = 3 kpc, so for the solar neighbourhood, the mass-to-light ratio in the K-band is given by M L = Σ tot I = 71M pc 2 I 0 exp( R 0 /R d ) 1M L. (18) If we assume the mass-to-light ratio is the same throughout the Galactic disk, then the total disk mass is about M disk = L tot M L = M. Similarly, the total mass of the bulge is about which is uncertain by 40%. M bulge = M, (19) For a spherical mass distribution, we have for the solar neighbourhood 1, Vc 2 (R 0 ) = G(M DM + M disk + M bulge ) M DM = V c 2 R 0 R 0 G M disk M bulge, (20) 1 We ignored the complication that for a flattened disk system, its circular velocity diffs from that of a spherical distribution.

10 10 where M DM, M disk and M bulge are the dark matter, disk and bulge masses within R 0, respectively. And hence M DM = V c 2 R 0 G M disk M bulge M. (21) So within the solar circle, the fraction of dark matter is about 30%, although this number is still quite uncertain. Most of the mass ( 70%) within the solar circle is therefore made up stars and gas. Of course, baryons (protons and neutrons) dominate the mass of stars and gas (the mass of electrons is negligible), so we can say that most of the mass within the solar circle is in baryons Dark Matter in the outer galaxy (R > R 0 ) The mass distribution can be inferred using halo stars, tidal streams and satellite galaxies. These studies indicate that the total mass is roughly a linear function of radius ( ) M = r M. (22) 200 kpc One interesting question is that within 200 kpc, the baryon fraction is only of the order f baryon = M disk + M bulge M 3.2%, (23) much lower than the average baryon fraction (16%) in the universe from, e.g., observations of the microwave background observations. It appears that the Milky Way is quite inefficient in gathering baryons. Fig. 7. Sagittarius dwarf galaxy, angular (left panel) and spatial positions (right panel). This dwarf elliptical galaxy is is being ripped apart by tidal forces into long streams of stars that will eventually be merged into the Milky Way. One important discovery in the last decade or so was the Sagittarius dwarf galaxy. This galaxy was initially discovered just behind the centre of the MW (see Fig. 7). Infrared-observations of M-giants further reveal a stream of stars associated with this galaxy (see Fig. 8). The dwarf galaxy is being tidally disrupted by the intense gravitational field of the MW and stars are being stripped off the galaxy which produce the tidal streams. The stars are observed to be in a plane almost pole-on with a tilt of about 15.

11 11 Fig. 8. Sagittarius dwarf galaxy tidal streams. Another view, from Martnez-Delgado et al (2003). Computer simulations can reproduce the observed stream (see Fig. 9). The stars in the Sagittarius stream seem to be distributed in a plane. If the halo is highly flattened, then the stars will precess due to torques and hence can not stay in the same plane for a long time. The fact that they are more or less in the same plane implies that the dark matter distribution (which dominates the mass budget) is quasi-spherical. Fig. 10 shows a MW-type halo found in numerical simulations. There are many striking substructures in the simulations. The number of substructures seems to exceed the number ( a dozen) of luminous satellite galaxies we observe in the MW. It is unclear at present how this discrepancy (if there is one) can be resolved. Summary: components of the Milky Way The following table summarises all the components of the Milky Way. component size (kpc) mass (M ) V c ( km s 1 ) Metallicity (Z ) age (Gyr) thin disk r d z < 10 thick disk z >10 bulge few (1 2) mostly old globular clusters tens few >10 stellar halo < 200 < >10 dark matter halo < HI < H Notice that the metallicity (commonly written as Z) refers to the fractions of mass in elements heavier than hydrogen and helium. The solar metallicity (Z ) is approximately 0.02 and this is often used as the units.

12 12 Fig. 9. Sagittarius dwarf galaxy: computer simulations by Dr. K. Johnston. The satellite moves counter-clock-wise in this figure. The ages and metallicities of different populations in the MW provide clues how different components were assembled. We will return to this issue when we discuss the theoretical models of galaxy formation.

13 13 Fig. 10. A Milky Way type dark matter halo in computer simulations. Notice the large number of substructures present. Galaxies: Problem Set 2 1. Revision questions: how do we know that a) the Milky Way has spiral arms? b) the Sun is about 8kpc from the centre of the Milky Way? c) the Milky Way has a bar at the centre? d) the Milky Way has a massive dark matter halo? e) Milky Way has dust extinction? 2. What is the typical angular size of a Milky-Way sized galaxy at a distance of 1Gpc? Can the Hubble Space Telescope (with a resolution of about 0.05 arcsecond) resolve it? 3. What is the acceleration experienced by the Sun in its orbit around the Galactic centre? How does that compare with acceleration experienced by the Earth around the Sun? 4. Given the definitions of Oort s constants A and B A = 1 ( V0 dv 2 R 0 dr and R0 B = 1 ( V0 + dv 2 R 0 dr where R 0 (= 8kpc) and V 0 are the distance to the Galactic centre and the rotation velocity, show that the rotation curve falls off as V r β, where β = (A + B)/(A B). What is the β-value for the solar neighbourhood? 5. Consider the density profile (so-called Navarro, Frenk and White profile) of a dark matter halo found in computer simulations with ρ = A r(r + r s ) 2, R0 ) ) for r < 200kpc

14 14 where the scale radius r s is 20 kpc. Integrate and find its mass within radius r Assuming the rotation velocity is 200 km/s at r = 200 kpc, plot the rotation curve and comment on its flatness. 6. (From Binney & Merrifield 1998) Show that for any spherical Galactic potential, the escape velocity from the solar neighbourhood, V e, and the local circular speed, V c, are related by V c V e 2 (24) with equality in the case that there is no mass at R > R 0. Stars are observed that have Galacto-centric speeds up to 400 km s 1. From this observation, obtain an upper limit on V c. Why might this upper limit be misleading? 7. (From Binney & Merrifield) The vorticity of a fluid flow v( x) is v. In the case of a disk galaxy such as the Milky Way this flow represents the differential rotation of the stars. Show that locally ω is simply related to the Oort constants by ω = 2B.