Revolution

While Kapteyn was occupied in Groningen measuring the positions of stars on photographic plates a revolution in physics was occurring elsewhere in Europe – a revolution that, over two decades, fundamentally changed the perception of the physical world that rested on the well-tested foundations of Newton's theory of dynamics and gravity and Maxwell's theory of electromagnetism. To say that these developments have had a profound impact on astronomy and astrophysics is a drastic understatement.

There were, in effect, two parallel revolutions. The first, following Max Planck, who in 1900 proposed that electromagnetic radiation came in discrete units of energy, was the quantum revolution. This permanently altered human perception of determinism and the fundamental limits of experimental precision and led to the concept of particle-wave dualism. The second revolution, the theory of relativity, forever changed the view of space and time as absolute entities and shook the foundations of Newtonian mechanics. The new theory of relativistic gravity, General Relativity, predicted phenomena that were discovered decades later, such as gravitational lenses, and, of particular relevance to this discussion, the existence of a new class of objects that are the consequence of gravitational collapse – black holes. It this second revolution that is most relevant to the discussion here.

It all began rather quietly in 1905 in Zurich where an obscure clerk in the patent office, Albert Einstein (Figure 3.1), wrote a fundamental paper dealing with the way in which the laws of particle dynamics and electromagnetism should be transformed between different reference frames moving at a constant relative velocity with respect to one another.

It is remarkable that a mere one hundred years ago most astronomers thought that the Universe was the Galaxy, a large flattened system of stars with the Sun near the center and various fuzzy objects scattered around it. This was the view supported by the systematic study of the positions and motions of stars began here in Groningen by Jacobus Kapteyn, a view that turned out to be wrong because no correction was made, or could made at that time, for the obscuration of star light by interstellar dust particles. The true scale of the Milky Way and the position of the Sun in the system became evident only after the pioneering work by Harlow Shapley on the spacial distribution of globular clusters in the halo of the Galaxy, work in turn based on the fundamental discovery of the period-luminosity relation for Cepheid variable stars by Henrietta Leavitt.

But Kapteyn's precise measurements of positions and motions of stars turned out to be extremely useful for his student, Jan Oort, who used the data to support the idea of Galactic rotation and accurately described the scale of the Milky Way and the Sun's true place, not in the center but on the outskirts of this vast system of stars. Oort, more than anyone, discovered the Center of the Galaxy – its direction and distance. Through radio astronomy and the 21-cm line of neutral hydrogen he and his students discovered the center of rotation, that there were expanding gas features moving away from that center, and that the center coincided with the source of continuum radio waves, the brightest radio source in the constellation of Sagittarius.

Kapteyn's Famous Student

Within five years of Kapteyn's death in 1922, his view of the Universe had been overturned. By 1930 it was generally accepted that the Milky Way Galaxy was one of many such systems supported against its own gravity by rotation, as had been supposed by Kant. This altered perception of the Galaxy was largely due to the work of the Swedish astronomer Bertil Lindblad and to Kapteyn's own student, Jan Oort (born 1900).

Oort (Figure 4.1) received his doctoral degree in Groningen in 1921 (the doctoral is roughly equivalent to a master's degree). After spending several years at Yale Observatory he was invited back to Leiden by de Sitter, and there he spent the remainder of his long active career.

For his PhD dissertation, defended in Groningen in 1926, Oort had studied the motions of halo stars, objects belonging to the Galaxy but distributed, as the globular clusters, in a large spheroidal halo surrounding the disk of the Milky Way. He was perplexed by the high velocities of these stars and the extremely skewed velocity distribution: they all seemed to be moving in the same direction. Then, in 1927, Lindblad demonstrated that Kapteyn's two star streams could be understood in terms of differential rotation of the Milky Way disk; which is to say, the system rotates not like a solid body, as a phonograph record, but the stars at any radial distance from the center revolved about the center at a rate determined by the Galactic gravitational force at that point.

A New Constituent of the Universe

The demands of war lead to technological advances that have consequences for pure research long after. The development of radar during World War II is one such example. The German radar dishes left behind in Holland at the end of the war enabled Oort to make a beginning for Dutch radio astronomy which, as we have seen, led to an understanding of the overall structure and kimenatics of the Milky Way Galaxy. Ewing and Purcell, the discoverers of the 21-cm line of neutral hydrogen, both had strong backgrounds in microwave radar technology, Ewing as a naval radar officer and Purcell as director of the MIT Radiation Laboratory. In the United Kingdom the young radio engineer Martin Ryle made a major contribution to the development of radar and thus to the British defense effort. But after the war, he applied these skills at Cambridge in the development of radio astronomy, in particular, the technique of radio interferometry.

In astronomy whenever a new wavelength window opens, major discoveries follow. This was certainly the case in the early 1950s, when crude radio telescopes began mapping the sky in continuum radiation and, in addition to smooth radiation from the Galaxy, discovered a number discrete sources scattered about the sky. Some were clearly Galactic in origin (they were in the plane of the Galaxy and associated with known objects such as supernova remnants) but others were more uniformly distributed outside of the Galactic plane.

Nearby, “Normal” Galaxies

In 1964 shortly after the discovery of quasars, George Field, then at Princeton, was impressed by the fact that the high redshift of quasars implied that they must be prevalent in the past – that very possibly they were associated with galaxy formation and not the end of a long process of galaxy evolution. He wrote a paper, now largely forgotten, entitled “Quasi-stellar radio sources as spherical galaxies in the process of formation.” This was before the popularity, or even the respectability, of the black hole scenario, so Field's picture was that a collapsing protogalaxy could form a dense spheroidal cloud in which star formation would be rapid. This would lead to a quasar luminosity and flux variations due to frequent supernovae. He even pointed out that the density of quasi-stellar sources could be consistent with the present observed density of spheroidal galaxies. In many ways this was a very prescient contribution, but now we know that the energy source is likely to be accretion onto black holes, and the black holes do not disappear. They remain in the center of most reasonably massive galaxies as a generally quiet quasar remnant (Lynden-Bell's idea), waiting there to flare occasionally when a morsel of food drifts by.

Kapteyn's Universe

The “hondsrug” or “dog's back” passes for a mountain range in the Netherlands. It is a ridge of sand reaching an altitude of 30 m and stretching southeast to northwest from the German border through the wooded province of Drente into province of Groningen. In fact, the most northern point is the city of Groningen, which is certainly the reason why a city is there: it is the closest point to the North Sea that is still above sea level – that is to say, on a natural geological formation. To the north of the city there are ancient small villages built on “terps,” artificial small hills created over centuries from animal and human waste, usually with a church at the highest point. Long before the construction of dikes, local farmers would gather on these terps during storms or exceptionally high tides. It is a wet and grim climate: in winter low clouds hang over the flat green treeless landscape; sunny summer days can be disrupted by sudden downpours – soaking cyclists and sending them scurrying for bridges and highway overpasses.

Groningen is a large provincial town – the central market city of this rural region. It is, by Dutch standards, rather isolated – 200 km from Amsterdam and the other metropolises of crowded Holland. Basically it bears the same relation to the Netherlands as does Novo Sibersk to Russia; from the point of view of Holland, Groningen is in the far frozen and gloomy North. But because of this relative isolation, it has developed its own dialect and culture and bustling student life. For as unlikely as it might seem, the city has a university.

6.1 Introduction

It is appropriate to recall, in the context of this volume, that just over a century ago the first color-magnitude diagram (CMD) was published. The author of this landmark paper was not Ejnar Hertzsprung nor Henry N. Russell, but Hans O. Rosenberg, a colleague of Karl Schwarzschild at Göttingen. Rosenberg had been working since 1907 on getting spectral properties of stars by measuring plates obtained with the Zeiss objective prism camera (Hermann, 1994). To maximize the number of spectra per plate, he observed the Pleiades cluster and obtained spectra for about 60 of them, over 1907–1909, noting that their inferred effective temperatures correlated with their apparent magnitudes in the first ever published CMD (Rosenberg, 1910). His goal was to “make the most accurate determination of the spectral types of stars in the Pleiades” by using a “physiological blend” of the depth and width of the Ca II K line (393.37 nm) with the Balmer Hδ and Hζ lines. He excluded the Ca II H line at 396.9 nm as it was blended with H∈ in the very low dispersion spectra he used (1.9 mm from Hγ to Hζ). With an exposure time of 90 minutes he could measure spectra down to the 10th photographic magnitude, finding that for the actual members of the Pleiades “there is a strict relation between the brightness and the spectral type, with no exception in the interval from the 3rd to the 9th magnitude.”

4.1 Introduction

Our understanding of the cosmological world relies on two fundamental assumptions: (1) The validity of General Relativity, and (2) conservation of matter since the Big Bang. Both assumptions yield the standard cosmological model according to which dark matter structures form first and then accrete baryonic matter that fuels star formation in the emerging galaxies. One important way to test assumption one is to compare the phasespace properties of the nearest galaxies with the expectations of the standard cosmological model.

Although the possibility of the existence of dark matter (DM) was first evoked more than 85 years ago (Einstein, 1921; Oort, 1932; Zwicky, 1933) and has been under heavy theoretical and experimental scrutiny (Bertone et al., 2005) since the discovery of flat galactic rotation curves by Rubin and Ford (1970) and their verification and full establishment by Bosma (1981), the DM particle candidates still elude both direct and indirect detection (Lingenfelter et al., 2009; Latronico and for the Fermi LAT Collaboration, 2009). Indeed, it appears that also the cryogenic dark matter search (CDMS) experiment fails to find significant evidence for the existence of cold dark matter (CDMS II Collaboration et al., 2010). Favored today is dark matter made of non-relativistic (“cold”) particles (cold DM, CDM) as it allows the correct degree of large-scale structure formation. Less-massive particles can perhaps account for the observed structures as long as the particles are not too light, leading to Warm DM (WDM) models, while light, relativistic (“hot”) particles (Hot DM, HDM) are excluded because structures on galactic scales cannot form sufficiently rapidly.

7.1 Introduction: exercise goals

The main goal of this practical course is to build up a theoretical representation (N-body model) of the observed properties of the stellar stream associated to the globular cluster Palomar 5. Our priors are (i) a static (simplified) representation of the Milky Way potential, (ii) the position on the sky of the cluster remnant core, (iii) its heliocentric radial velocity, and (iv) its heliocentric distance.

We use the position of the stellar stream as detected in the Sloan Digital Sky Survey (SDSS) (see Grillmair and Dionatos, 2006) as observational constraints on the free-parameters of our models, which in this simplistic exercise correspond to the 2D-tangential components of the current velocity vector (i.e., proper motions) of Pal 5. Note that there are available measurements of Pal 5 proper motions. However, measuring those quantities for stellar systems as faint MV = —4.77 ± 0.20 and distant (D ≃ 21 kpc) as Pal 5 is subject to large observational uncertainties that translate into poorly constrained Galactocentric orbital parameters. To illustrate this issue, we adopt the Galactocentric proper motions of Pal 5 (μα,μδ) as free parameters that we derive from fitting the orientation of the stellar stream on the sky, and compare their values with measurements available in the literature. The second main goal of the exercise is thus to inspect the reliability of the existing proper motion measurements for Pal 5.

2.1 Somewhat historical: overview of the Local Group, dwarf galaxies, and their observed structures

Before taking on a discussion of the dynamics of Local Group (LG) galaxies and the contributing and competing effects of dark matter and tides, it is useful to have an understanding of the spatial distribution of these galaxies, the distribution of their types and masses, and their morphologies – all of which play critical roles in defining how dark matter and tides play out their dynamical tug-of-war. The most common types of galaxies – the dwarfs – which are the most dark matter dominated as well as those among LG galaxies to show the greatest evidence for tidal effects, are the primary focus of this chapter.

2.1.1 The Local Group in context

Large-scale galaxy redshift surveys over the past decades (e.g., Davis et al., 1982; Geller and Huchra, 1989; Shectman et al., 1996; York et al., 2000; Colless et al., 2001; Strauss et al., 2002; Abazajian et al., 2009; Jones et al., 2009) have revealed clearly the filamentary structure of the distribution of galaxies in the Universe. The nearest 100 Mpc shows vast voids but several large mass concentrations, such as the Perseus-Pisces, Pegasus, Pavo, Coma, Hydra-Centaurus, and Virgo Superclusters. The Milky Way (MW) and the LG of galaxies live on the outskirts of the Virgo Supercluster, whose center lies about 15 Mpc away.