Transcript: The flat rotation curve of the Milky Way has profound implications for the mass distribution of our galaxy.  In the solar system the circular orbits of the planet decline with increasing distance from the Sun in accordance with Kepler’s Law and with the idea that the Sun contains essentially all the mass in the solar system.  In the Milky Way the situation is entirely different.  The velocities are constant or rising with increasing distance, and the implied mass scales proportionally to distance.  Out to the Sun’s radius the mass of the Milky Way is two times ten to the eleven solar masses.  Out to the edge of the halo measured by halo stars, forty kiloparsecs, the mass is five times ten to the eleven, and from the motions of satellite dwarf companions to the Milky Way to a distance of a hundred kiloparsecs the mass is two times ten to the twelve solar masses, two trillion times the mass of the Sun.  Thus most of the mass in the Milky Way galaxy is far out beyond the region of the disk, and most of it corresponds to material that does not emit light at any wavelength raising the issue of dark matter.

Total Mass of the Galaxy

Transcript: Newton’s law of gravity gives astronomers a way of estimating the mass of something from the motions of objects within it.  In the solar system or when an object has its mass concentrated in the center, the circular velocity declines with increasing distance from the center going as one over the square root of the distance.  This is the characteristic of Keplerian orbits, but in the Milky Way there’s a flat rotation curve which means that the velocity is not declining but it’s flat or even rising with increasing distance.  In this same formalism that means that the mass of the galaxy, estimated at different radii, would continue to increase.  The high speed of stars in orbits in the disk of the galaxy is apparently driven by a large amount of mass in an extended halo of the Milky Way.

Flat Rotation Curves

Transcript: The motions of stars and gas within the disk of the galaxy can be used to estimate the mass of the Milky Way galaxy, but the Sun is one of billions of stars, some of which are interior to the Sun’s orbit and some of which are far beyond the Sun.  So how is it possible to do this?  Isaac Newton had a fundamental insight calculating that the motion of an orbiting object is controlled only by the mass within its orbit.  This is obvious within the solar system where the planets’ motions are controlled by the Sun which sits at the center of the system.  In the Milky Way it means that the Sun’s motions are only governed by the mass within the orbit of the Milky Way.  All the regions outside the orbit of the Sun, the Sun does not feel those masses.  Applying Newton’s calculation to the situation of the Milky Way disk yields a mass interior to the orbit of the Milky Way of two times ten to the forty-one kilograms, a hundred billion times the mass of the Sun.

Mass of the Disk

Transcript: Maps of star and gas motions reveal the rotation curve of the Milky Way galaxy shown as a plot of orbital speed or circular velocity as a function of distance from the galactic center.  In the Milky Way the speed is zero at the center and it rises rapidly to two hundred kilometers per second one kiloparsec out.  Then there’s a slight decline and a steady rise to two hundred and twenty-five kilometers per second at the position of the Sun and a subsequent steady rise to two hundred and sixty kilometers per second fifteen kiloparsecs out from the center.  Beyond that the motions are difficult to detect.  This flat or slowly rising rotation curve is very different from Keplerian orbits which always decline steadily with distance from the center of mass.

Rotation Curve of the Galaxy

Transcript: Another idea to explain the existence of spiral arms is called the stochastic star formation theory.  In this theory the star formation in one region triggers star formation in neighboring regions of the disk like a chain reaction.  For up to a hundred million years a star formation region is lit up by young stars, and during this time differential rotation, the inner part of the region moving faster than the outer part, shears the star formation region into the segment of a spiral.  Overall a spiral pattern is seen, but the pattern is transient because different stars are coming and going and being born and dying over the long period of time of the lifetime of the Milky Way galaxy.

Stochastic Star Formation

Transcript: Why does the galaxy have spiral arms?  Some analogies just don’t work.  A garden sprinkler sends out spiral patterns of water, but in this case the water is moving radially rather than the circular orbits within the Milky Way.  If you stir cream into your coffee it can give the illusion of a spiral pattern, but in the case of the Milky Way stars have made fifty orbits in the history of the Milky Way and so the spiral pattern would be hopelessly scrambled after that many windings.  The current idea for the spiral pattern is the idea of density waves, a pattern of enhanced activity traced by young stars but not the movement of the young stars themselves.  Increased general density leads to the tracers of star formation activity, and the spiral arms that result actually move more slowly than the constituent stars.  The best analogy is a traffic pileup that might occur on a freeway behind a slowly moving vehicle, say, painting the road stripe.  Cars approach at normal speed, they bunch up near the obstruction, and then they space out again as they reach their normal speed.  The result is a moving traffic jam where a high density of cars is created, but the set of cars involved in the high density concentration is constantly changing.

Density Waves

Transcript: Doppler mapping of the disk of the Milky Way by radio astronomers has revealed spiral arms.  Spiral arms are regions of enhanced star density, enhanced star formation, and large amounts of gas and obscuring dust.  We live on the inner edge of what’s called the Orion arm.  The arm beyond us is called the Perseus arm, and inside us is the Sagittarius and then the Centaurus arms.  These spiral arms coil outward from the galactic center, trailing the direction of rotation.

Spiral Arms

Transcript: If stars near the Sun share the same general motion around the center of our galaxy, and if visible light can only penetrate a kiloparsec or so which is a small fraction of the size of the disk, how do we know the overall motions?  Astronomers use the twenty-one centimeter line of neutral hydrogen which reveals the cold gas clouds where stars are forming.  They also use the carbon monoxide line at millimeter wavelengths.  Both of these techniques use long wavelength emission that can easily penetrate the disk of the galaxy.  It can arise that two clouds in the same direction might be at different distances from the Sun, so they will have different radial components of their circular motion.  By simply assuming that the motions of all clouds are circular, it’s possible to deconstruct the full map of the motions in the Milky Way galaxy.  The technique only fails in the directions very close to the galactic center and the galactic anti-center direction where there is no radial component to the motions.

Mapping the Disk

Transcript: Stars near the Sun have radial velocities measured by the Doppler shift in the range of ten to twenty kilometers per second.  Because us and the stars around us are all moving together at similar speeds around the center of our galaxy the differential speeds are small.  Further from the Sun the orbital speeds do vary.  The Milky Way does not rotate like a solid object with a constant angular velocity at every radius from the center.  Nor does it follow Kepler’s third law because unlike the situation of the planets orbiting the Sun, most of the mass in the disk is distributed and not concentrated at the center of the galaxy.  The situation in the Milky Way where the rotation speeds vary with distance is called differential rotation.  There is also some component of random motion superimposed on the circular rotation velocities.

Motions in the Disk

Motion of the Sun

Transcript: We view the Milky Way from a position within its enormous disk.  The Milky Way disk is thirty thousand parsecs across, roughly four hundred parsecs thick, and it’s packed with young stars, gas clouds, obscuring dust, open clusters, and active star formation regions.  The disk is imbedded within a spherical halo composed of galactic globular clusters and individual halo stars.  The halo looks diffuse, but it actually contains most of the mass of the Milky Way galaxy.  We’re located about eight thousand five hundred parsecs from the galactic center, and astronomers in talking about galactic distances use a different unit, the kiloparsec or a thousand parsecs.  In these terms the galactic center is eight and a half kiloparsecs away, and the Milky Way is thirty kiloparsecs across.  To give a sense of the scale of the Milky Way, if the galaxy were the United States, the stars would be individual microscopic specs separated by about a hundred yards each.

Location of the Sun

Transcript: Astronomers use a special set of coordinates to define the position of objects within the Milky Way galaxy.  The galactic equator runs along the center of the Milky Way band.  Galactic longitude, abbreviated by the small letter L, is the angular distance along the Milky Way with zero at the galactic center in the Sagittarius region.  L equals ninety degrees is in the constellation of Cygnus near the top of the Northern Cross.  L equals a hundred and eighty degrees, opposite to the galactic center, also called the anti-center direction, is in the constellation Taurus near the Pleiades and Hyades clusters, and L equals two hundred and seventy is south of Canis Major.  Galactic latitude, denoted by the small letter B, is defined to be zero on the galactic equator.  The direction B equals plus ninety is straight up out of the disk in the northern sky, and B equals minus ninety degrees is the opposite direction, straight out of the disk in the southern sky.

Galactic Coordinates

Transcript: The third component of the Milky Way is the bulge of our galaxy.  This concentration of stars is centered on the galactic center but is much smaller than the halo.  The stars in the bulge are mostly old and red, but many are younger than the halo stars with ages of only a few billion years.  The bulge is best seen with infrared observations that can penetrate the obscuring dust that lies in the plane of the disk of our galaxy.

Galactic Bulge

Transcript: The halo of the Milky Way galaxy is traced by the globular clusters and by individual stars that are dim and which contain a far lower metal abundance than the Sun or stars in the solar neighborhood.  The distribution of globular clusters on the plane of the sky gives a clue both to the shape of the galaxy and to the Sun’s position within that distribution.  For example, if we were at the center of a spherical cloud of globular clusters, we would count equal numbers in each direction in the sky, but if we were offset from the center, we would count more clusters in the direction towards the center.  This simple technique was used by Harlow Shapley in the 1930s to show that the Milky Way was indeed spherical in the shape of its halo and that the Sun was not at the center of the distribution but was offset by eight or nine thousand parsecs from the center which was in the direction of the constellation Sagittarius.

Galactic Halo

Transcript: The disk of our galaxy is traced by the band of stars in the Milky Way and also by the open star clusters which contain mostly young stars.  The concentration of stars in the Milky Way is greatest in the direction of the Sagittarius constellation in the southern sky.  This represents the direction towards the center of our galaxy.  In visible light we cannot see much further than about a thousand parsecs in the plane of the Milky Way due to the obscuring effects of dust.  This explains the patchy variations of brightness across the Milky Way caused by clouds of gas and dust that obscure the stars beyond.  However, in near infrared radiation it’s possible to see all the way to the galactic center, and also the distribution of older and cooler stars becomes visible.  Far infrared emission shows the distribution of cool dust and very cool stars and makes the thinness of the galactic disk clear.  At twenty-one centimeters, radio waves, the neutral hydrogen can be traced, and in addition to the thin disk it shows wisps and filaments rising far above the plane of the Milky Way that represent energy deposited by supernovae and gas that leaves the disk and then eventually falls back onto the disk.

Galactic Disk

Transcript: The sky is not the same in all directions.  The Milky Way is a band of stars and gas and obscuring dust that encircles the entire sky.  Away from the direction of the Milky Way the stars are more sparsely scattered.  Even the Milky Way is not the same in every direction.  There’s a greater concentration of stars in the southern sky near the constellation of Sagittarius.  A long time ago it was realized that the distribution of stars might give a sign as to the shape of the galaxy we inhabit.  In 1750 the English theologian Thomas Wright speculated that the Sun was just one member of a huge slab-like arrangement of stars.  German philosopher Immanuel Kant had the same idea at a similar time, and by the late eighteenth century several people had realized the Sun may be part of a large disk of stars.

The Shape of the Galaxy

Transcript: William Herschel was born in 1738 in Germany to a musical family.  He was a professional musician himself.  He deserted the German army during the seven years war and made his way to England where he became the organist in the cathedral in Bath.  While studying music and building his own musical instruments he read books by Robert Smith on musical harmony, then on mathematics, and then on astronomy which attracted his interest in that subject.  Working with his sister Caroline he beautifully hand-crafted telescopes from wood and brass and observed every clear night.  A self-taught astronomer, he avidly watched the sky every clear night of the year including the winter, often working in temperatures so cold that he had to break the ice on his inkwell to make his notes.  He discovered Uranus and set the stage for the understanding of the nebulae.  With a grant from King George III he built larger and larger telescopes culminating in a telescope of 1.2 meters aperture, the largest telescope for another century.

Herschel

Transcript: In the eighteenth century astronomers began using larger and larger telescopes to map the galaxy to begin to learn the distribution of stars far from the Sun.  The astronomer William Herschel was prominent in this effort.  The discoverer of Uranus used his telescope to sweep the sky in parallel strips night after night.  This was in the days before telescopes had motorized drives so Herschel just used the rotation of the Earth to have stars scan across his visual field, and he counted them and kept careful notes.  In this way he was able to see the different distributions and densities of stars on the plane of the sky.  He also developed a technique to compare the brightness of two stars.  Pointing two identical telescopes at stars of different brightness he covered the aperture of one telescope partially until the apparent brightness of the images was the same.  The ratio of the covered aperture to the uncovered aperture then gave the relative brightness of the stars.  By assuming stars had the same intrinsic luminosity, the relative brightness could be used to give the relative distances.  This is a crude assumption because stars do not all have the same luminosity, but it allowed Herschel to combine his counts of stars in areas of the sky with the sense of depth so he could map out the third dimension.  In this way Herschel was like a cartographer mapping out the galaxy for the first time.

Mapping the Galaxy

Transcript: The night sky blazes with light.  Far from a city you can see six thousand stars, and long before the invention of the telescope people could plainly see a band of diffuse light that arches across the sky.  Twenty-five hundred years ago Democritus, the Greek philosopher, attributed this glow to unresolved stars.  It was called the Via Lactea or the Milky Way.  Soon after the invention of the telescope Galileo confirmed Democritus’ idea and showed that the diffuse light is in fact comprised of the pinpoint light of many distant stars.  A galaxy is a large collection of stars held together by gravity.  The Milky Way galaxy contains the Sun, all the stars in the night sky, and billions more beyond.

The Milky Way

Transcript: The ages of stars are derived from stellar models.  The physics is complex so computers are used to simulate energy transport mechanisms.  The details depend on heavy element abundance and on the mechanism for helium diffusion in the atmosphere of the stars.  Thus there are uncertainties attached to the prediction of luminosity from stellar models.  There are also uncertainties attached to the determination of luminosity from observation of stars.  This can include the effect of interstellar extinction and uncertainties in the distance estimates.  Since luminosity is proportional to distance squared, a ten percent error in the distance leads to a twenty percent error in luminosity.  For all of these reasons it’s difficult to measure ages more accurately than ten or twenty percent.

Ages From Stellar Models

18. Galaxies

Transcript: The HR diagram is a plot of stellar properties, luminosity and photospheric temperature.  It’s a frozen snapshot in time, but over tens of millions to billions of years the main sequence population changes as stars exhaust their hydrogen and leave the main sequence to become giants, dwarfs, supernovae, and collapsed objects.  This process can be used to measure age.  Remember that when astronomers talk about stars, their position on the main sequence, and their movement on an HR diagram, they’re referring to a plot of stellar properties.  The stars themselves are not moving in physical space.  This is just the statistical way of discussing the properties of a set of stars.

Evolving HR Diagrams

Transcript: In the early part of the twentieth century, astronomers calculated the distances to stars by assuming that interstellar space was perfectly transparent.  But eventually comparisons of distance to clusters in different directions in the sky yielded inconsistent results, and in 1930 Robert Trumpler showed that interstellar extinction or obscuration dims the light from all stars, groups, and clusters, that are larger than a distance of a few dozen parsecs.  What this means is that the intensity of light falls off more rapidly than would be predicted by the inverse square law.  We see a star as dimmer than it truly is, and we overestimate its distance.  Without taking into account interstellar obscuration it’s impossible to correctly measure distances to stars, groups, and clusters, and map out the Milky Way galaxy.

Distance and Obscuration

Transcript: Main sequence fitting can be applied in principle to any cluster.  However, the rare variable stars like RR Lyraes and Cepheid variables are particularly valuable because the physics of their variations allows their luminosities to be estimated, and their luminosities allow them to be seen to large distances.  RR Lyraes are a hundred times more luminous than the Sun, so they can be seen ten times further away than a Sun-like star could.  Cepheid variables are ten thousand times more luminous than the Sun and so can be seen at distances a hundred times that of a Sun-like star.  But we really need a large cluster to be able to detect even a few versions of these very rare stars, and that is a practical limitation.

Distances and Rare Stars

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