Astr 122 Exam 3

How many 21 cm photons are emitted by the above cloud, per second?

3.79x10^44

Molecular hydrogen is

H2

The most common nebula in the Galaxy is

HI clouds

Chapter 20 Einstein's theory of relativity deals with Newtonian physics when energies or velocities are near the speed of light. Relativity is usually thought of as modern physics since it was developed at the start of the 20th century and could only be tested in the realm available to scientists by high technology. However, relativity primarily completes the revolution that Newton started and is also highly deterministic as is much of classical physics. In the holistic viewpoint of relativity theory, concepts such as length, mass and time take on a much more nebulous aspect than they do in the apparently rigid reality of our everyday world. However, what relativity takes away with one hand, it gives back in the form of new and truly fundamental constants and concepts. The theory of relativity is traditionally broken into two parts, special and general relativity. Special relativity provides a framework for translating physical events and laws into forms appropriate for any inertial frame of reference. General relativity addresses the problem of accelerated motion and gravity. Special Theory of Relativity: By the late 1800's, it was becoming obvious that there were some serious problems for Newtonian physics concerning the need for absolute space and time when referring to events or interactions (frames of reference). In particular, the newly formulated theory of electromagnetic waves required that light propagation occur in a medium (the waves had to be waves on something). In a Newtonian Universe, there should be no difference in space or time regardless of where you are or how fast you are moving. In all places, a meter is a meter and a second is a second. And you should be able to travel as fast as you want, with enough acceleration (i.e. force). In the 1890's, two physicists (Michelson and Morley) were attempting to measure the Earth's velocity around the Sun with respect to Newtonian Absolute space and time. This would also test how light waves propagated since all waves must move through a medium. For light, this hypothetical medium was called the aether. The results of the Michelson-Morley experiment was that the velocity of light was constant regardless of how the experiment was tilted with respect to the Earth's motion. This implied that there was no aether and, thus, no absolute space. Thus, objects, or coordinate systems, moving with constant velocity (called inertial frames) were relative only to themselves. In Newtonian mechanics, quantities such as speed and distance may be transformed from one frame of reference to another, provided that the frames are in uniform motion (i.e. not accelerating). Considering the results of the Michelson-Morley experiment led Einstein to develop the theory of special relativity. The key premise to special relativity is that the speed of light (called c = 186,000 miles per sec) is constant in all frames of reference, regardless of their motion. What this means can be best demonstrated by the following scenario: This eliminates the paradox with respect to Newtonian physics and electromagnetism of what does a light ray `look like' when the observer is moving at the speed of light. The solution is that only massless photons can move at the speed of light, and that matter must remain below the speed of light regardless of how much acceleration is applied. In special relativity, there is a natural upper limit to velocity, the speed of light. And the speed of light the same in all directions with respect to any frame. A surprising result to the speed of light limit is that clocks can run at different rates, simply when they are traveling a different velocities. This means that time (and space) vary for frames of reference moving at different velocities with respect to each other. The change in time is called time dilation, where frames moving near the speed of light have slow clocks. Likewise, space is shorten in in high velocity frames, which is called Lorentz contraction. It is important to note that all the predictions of special relativity, length contraction, time dilation and the twin paradox, have been confirmed by direct experiments, mostly using sub-atomic particles in high energy accelerators. The effects of relativity are dramatic, but only when speeds approach the speed of light. At normal velocities, the changes to clocks and rulers are too small to be measured. However, near extreme objects, such as black holes and neutron stars relativity dominates over Newtonian physics. Special relativity describes changes in size and time through the use of Lorentz transformations. For an event that lasts to seconds in your frame, the same event will appear to last t in a frame that is moving with velocity v such that: to=t/(1-(v/c)2)1/2 where c is the speed of light. Spacetime: Special relativity demonstrated that there is a relationship between spatial coordinates and temporal coordinates. That we can no longer reference where without some reference to when. Although time remains physically distinct from space, time and the three dimensional space coordinates are so intimately bound together in their properties that it only makes sense to describe them jointly as a four dimensional continuum. Einstein introduced a new concept, that there is an inherent connection between geometry of the Universe and its temporal properties. The result is a four dimensional (three of space, one of time) continuum called spacetime which can best be demonstrated through the use of Minkowski diagrams and world lines.

Spacetime makes sense from special relativity since it was shown that spatial coordinates (Lorentz contraction) and temporal coordinates (time dilation) vary between frames of reference. Notice that under spacetime, time does not `happen' as perceived by humans, but rather all time exists, stretched out like space in its entirety. Time is simply `there'. Mass-Energy Equivalence: Since special relativity demonstrates that space and time are variable concepts from different frames of reference, then velocity (which is space divided by time) becomes a variable as well. If velocity changes from reference frame to reference frame, then concepts that involve velocity must also be relative. One such concept is momentum, motion energy. Momentum, as defined by Newtonian, can not be conserved from frame to frame under special relativity. A new parameter had to be defined, called relativistic momentum, which is conserved, but only if the mass of the object is added to the momentum equation. This has a big impact on classical physics because it means there is an equivalence between mass and energy, summarized by the famous Einstein equation: The implications of this was not realized for many years. For example, the production of energy in nuclear reactions (i.e. fission and fusion) was shown to be the conversion of a small amount of atomic mass into energy. This led to the development of nuclear power and weapons. As an object is accelerated close to the speed of light, relativistic effects begin to dominate. In particular, adding more energy to an object will not make it go faster since the speed of light is the limit. The energy has to go somewhere, so it is added to the mass of the object, as observed from the rest frame. Thus, we say that the observed mass of the object goes up with increased velocity. So a spaceship would appear to gain the mass of a city, then a planet, than a star, as its velocity increased. Likewise, the equivalence of mass and energy allowed Einstein to predict that the photon has momentum, even though its mass is zero. This allows the development of light sails and photoelectric detectors. Spacetime and Energy: Special relativity and E=mc2 led to the most powerful unification of physical concepts since the time of Newton. The previously separate ideas of space, time, energy and mass were linked by special relativity, although without a clear understanding of how they were linked. The how and why remained to the domain of what is called general relativity, a complete theory of gravity using the geometry of spacetime. The origin of general relativity lies in Einstein's attempt to apply special relativity in accelerated frames of reference. Remember that the conclusions of relativity were founded for inertial frames, i.e. ones that move only at a uniform velocity. Adding acceleration was a complication that took Einstein 10 years to formulate. Equivalence Principle: The equivalence principle was Einstein's `Newton's apple' insight to gravitation. His thought experiment was the following, imagine two elevators, one at rest of the Earth's surface, one accelerating in space. To an observer inside the elevator (no windows) there is no physical experiment that he/she could perform to differentiate between the two scenarios. An immediate consequence of the equivalence principle is that gravity bends light. To visualize why this is true imagine a photon crossing the elevator accelerating into space. As the photon crosses the elevator, the floor is accelerated upward and the photon appears to fall downward. The same must be true in a gravitational field by the equivalence principle. The principle of equivalence renders the gravitational field fundamentally different from all other force fields encountered in nature. The new theory of gravitation, the general theory of relativity, adopts this characteristic of the gravitational field as its foundation. General Relativity : The second part of relativity is the theory of general relativity and lies on two empirical findings that he elevated to the status of basic postulates. The first postulate is the relativity principle: local physics is governed by the theory of special relativity. The second postulate is the equivalence principle: there is no way for an observer to distinguish locally between gravity and acceleration. Einstein discovered that there is a relationship between mass, gravity and spacetime. Mass distorts spacetime, causing it to curve. Gravity can be described as motion caused in curved spacetime . Thus, the primary result from general relativity is that gravitation is a purely geometric consequence of the properties of spacetime. Special relativity destroyed classical physics view of absolute space and time, general relativity dismantles the idea that spacetime is described by Euclidean or plane geometry. In this sense, general relativity is a field theory, relating Newton's law of gravity to the field nature of spacetime, which can be curved. Gravity in general relativity is described in terms of curved spacetime. The idea that spacetime is distorted by motion, as in special relativity, is extended to gravity by the equivalence principle. Gravity comes from matter, so the presence of matter causes distortions or warps in spacetime. Matter tells spacetime how to curve, and spacetime tells matter how to move (orbits). There were two classical test of general relativity, the first was that light should be deflected by passing close to a massive body. The first opportunity occurred during a total eclipse of the Sun in 1919. Measurements of stellar positions near the darkened solar limb proved Einstein was right. Direct confirmation of gravitational lensing was obtained by the Hubble Space Telescope last year. The second test is that general relativity predicts a time dilation in a gravitational field, so that, relative to someone outside of the field, clocks (or atomic processes) go slowly. This was confirmed with atomic clocks flying airplanes in the mid-1970's. The general theory of relativity is constructed so that its results are approximately the same as those of Newton's theories as long as the velocities of all bodies interacting with each other gravitationally are small compared with the speed of light--i.e., as long as the gravitational fields involved are weak. The latter requirement may be stated roughly in terms of the escape velocity. A gravitational field is considered strong if the escape velocity approaches the speed of light, weak if it is much smaller. All gravitational fields encountered in the solar system are weak in this sense. Notice that at low speeds and weak gravitational fields, general and special relativity reduce to Newtonian physics, i.e. everyday experience.

Clocks inside a black hole

are stopped

Spiral patters are explained by

density waves

Interstellar dust is formed

in the atmospheres of red supergiants

Far-IR images of the Galaxy indicate that old stars are found

in the bulge

A neutron star's rotational energy is lost to

magnetic fields

Old neutron stars are found through

microlensing

Are there more or fewer stars in the night sky for a star in the Galactic core?

more

Nova is Latin for

new

Stars in the Galactic core move

slower than the Sun

The winding dilemma states

spiral patterns should be short lived

If the Sun were to become a black hole, the orbit of the Earth

stay the same

Same scenario, the Earth's year would

stay the same

The point of no return for a black hole is

the event horizon

Why does interstellar extinction prevent us from seeing optical tracers beyond a few 1,000 parsecs?

the light is blocked by the ISM

We deduce that there is a massive blackhole in the center of the Galaxy from

the motion of an inner gas ring

After a year, a nova shell is as big as (calculate this using the velocity of the shell from the lecture notes))

the solar system

Fusion in the higher mass nuclei shells proceeds faster than lighter elements because

the temperatures are higher

Dark nebula are dark because

they absorb the light striking them

We know that nova are not destroyed in their explosions because

they are recurrent

Dust is important in stellar astronomy because

they are the sites of star formation

Planetary nebula got their name because

they look like planets in a telescope

To escape from the inside of a black hole you need

to go faster than the speed of light

The wavelength to search for accretion disks is

x ray

) In a spacetime diagram, why can you not move in a horizontal line?

you would be moving faster than the speed of light

Which flashlight's light will be bluer?

yours

The mass of a photon is

zero

A bug at the center of a hard drive disk of 10 cm radius is moving at

0 cm/s

You see a spaceship zoom past at 285,000 km/s (0.95c). For one minute in your frame, how long do you see pass on the spaceship's clock?(click for an example)

0.3 min

A 2 solar mass star must lose mass to become a stable white dwarf with a Chandrasekhar mass. It must lose

0.6 solar masses

Another spaceship zooms by, you notice that for one minute that passes on your clock only 30 seconds passes on the space ship's clock. How fast is it going?(click for an example)

0.87 C

The change in size from a red supergiant star to a neutron star is a factor of

1 million

What will the surface gravity be on this white dwarf compared to the Earth's?(click for an example)

1,504,106 times greater

How many H atoms in a 100 solar mass gas cloud?

1.19x10^59

From the planetary nebula phase to the white dwarf phase, a star loses how much of its luminosity? (hint: use this diagram)

10 million

The typical hard drive spins at 6,000 rpm, what is its ω (angular velocity)?(click for an example)

100

A bug at the edge of the disk is moving at

1000 cm/s

The number of stars in the Milky Way is about

10^12

When the Sun becomes a white dwarf of 3,000 km in radius, how much will its density have increased

12,460,275 times

Modern telescopes can see down to 25 mag. How far away can we see supernova?

15.8 billion parsecs

A supernova equals the brightness of a galaxy, the typical galaxy has a magnitude of -21. If the star starts with an absolute mag of -5, how much does it increase in brightness when it goes supernova?

2.5 million times

The Sun is about 10,000 parsecs from the Galactic center. It moves at 200 km/s, what is its orbital period?

3.09x108 years

What is the cross section of a nebula that is 10 parsecs thick and a density of 10-12gm/cc?

3.1x107

If a dust grain has a density of 3 gm/cc, what is the typical mass of a dust grain?

3.39x10-4gms

In order to ionize hydrogen, a photon must have a wavelength of less than 912 Angstroms (1 Angstrom is 10-8centimeters). Use Wien's law to calculate the temperature of a star with this peak wavelength.

31,798K

The shock wave from a supernova moves at 1000 km/s, if the Sun goes SN how long till the Earth is squashed?

40 hours

A star of 0.5 solar masses will become a white dwarf of radius (hint: use the diagram in the lecture notes)

6000 km

If the Sun were to collapse at 100,000 km/s, how long would the collapse take?

7 secs

What is the Schwarzschild radius for the Earth?(click for an example)

8.9x10-3 meters

The mass of the Galaxy (using the orbital period above) is roughly

9.21x1010 solar masses

Chapter 21 The fact that light is bent by a gravitational field brings up the following thought experiment. Imagine adding mass to a body. As the mass increases, so does the gravitational pull and objects require more energy to reach escape velocity. When the mass is sufficiently high enough that the velocity needed to escape is greater than the speed of light we say that a black hole has been created. Another way of defining a black hole is that for a given mass, there is a radius where if all the mass is compress within this radius the curvature of spacetime becomes infinite and the object is surrounded by an event horizon. This radius called the Schwarzschild radius and varys with the mass of the object (large mass objects have large Schwarzschild radii, small mass objects have small Schwarzschild radii). The Schwarzschild radius is easy to determine for an object of mass M. It is simply the radius where a test particle of mass m must move at the speed of light to exceed the gravitational energy of the primary object. So, we equate the kinetic energy and the gravitational potential energy such that: mc2/2 =GMm/Rs which can be written as Rs= 2GM/c2 where G = 6.668x10-11 and c = 3x108 meters per second and mass is in kilograms. The visual image of a black hole is one of a dark spot in space with no radiation emitted. Any radiation falling on the black hole is not reflected but rather absorbed, and starlight from behind the black hole is lensed. So even though no radiation escapes a black hole, its mass can be detected by the deflection of starlight. In addition to mass, a black hole can have two other properties, electric charge and angular momentum. Even though a black hole is invisible, it has properties and structure. The boundary surrounding the black hole at the Schwarzschild radius is called the event horizon, events below this limit are not observed. Since the forces of matter can not overcome the force of gravity, all the mass of a black hole compresses to infinity at the very center, called the singularity.

A black hole can come in any size. Stellar mass black holes are thought to form from supernova events, and have radii of 5 km. Galactic black hole in the cores of some galaxies are built up over time by cannibalizing stars. Mini black holes formed in the early Universe (due to tremendous pressures) down to masses of asteroids with radii the sizes of grains of sand. Note that a black hole is the ultimate entropy sink since all information or objects that enter a black hole never returns. If an observer entered a black hole to look for the missing information, he/she would be unable to communicate their findings outside the event horizon. Of course if the objects falling into the black hole form an accretion disk, then we can detected the x-rays from the infalling gas. This is our only method of indirectly finding black holes, as companions to other stars. Wormholes: With the rubber sheet analogue of curved spacetime and gravity, it is possible to visualize a mass, such as a star, as a dent in the sheet and the orbit of objects around the star as objects following the curvature of the dent much like balls rolling on the inside of a bowl. With this same analogue, the greater the mass the deeper the dent. Black holes are objects which have an infinite well in the rubber sheet and effectively ``punch'' through the fabric of spacetime. It is mathematically possible to connect two black holes into a wormhole. Such a wormhole could be used as a shortcut from one part of the Universe to another, however, you would have to be able to travel faster than the speed of light to exit the wormhole, which is not possible. A wormhole can also be used to make a time machine. Imagine vibrating one end of a wormhole at close to the speed of light. Due to time dilation, that end would have a slower clock then the far end. Thus, you could enter the far end and exit the near end at a previous time. However, time travel is impossible since it is a violation of causality (see the grandfather paradox).

Chapter 19 The idea of a neutron star was developed in 1939 when calculations were made of a star that was composed solely of degenerate neutrons. If the mass of a normal star were squeezed into a small enough volume, the protons and electrons would be forced to combine to form neutrons. For example, a star of 0.7 solar masses would produce a neutron star that was only 10 km in radius. Even if this object had a surface temperature of 50,000 K, it has such as small radius that its total luminosity would be a million times fainter than the Sun. As with white dwarfs, neutron stars have an inverse relationship between mass and radius. As a neutron increases in mass, its radius gets smaller. Their extremely small size implies that they rotate quickly, according to the conservation of angular momentum. Angular momentum is a measure of the momentum carried by an object because of its rotation about an axis. We define an angular velocity, ω, as how fast an object turns. For example, a record turns about once every two seconds, so we say that its ω = 1/2 or 0.5 secs-1. A car wheel turns about 100 times in a second, so we say that ω = 100. The speed of a wheel at its edge is determined by its linear speed and size such that: ω =v/r where v is linear velocity and r is radius from the center of rotation. Notice that a spinning record has a constant ω. A bug near the center of the record has a small, linear velocity compared to a bug near the edge because ω is a constant, but r increases. The interior of a neutron star is hard to calculate since the physics covers a new realm not testable in our laboratories. Models suggest that neutrons packed into such a dense configuration becomes a superfluid sea. Normally superfluids, such as liquid helium, occur at very low temperatures. But that normal matter has an electric charge (positive for the protons, negative for the electrons). A dense mixture of neutrons (with zero electric charge) can become a friction-free superfluid at high temperatures. The interior of a neutron star will consist of a large core of mostly neutrons with a small number of superconducting protons. Again, normally associated with low temperatures, superconducting protons, combined with the high rotation speeds of the neutron star, produce a dynamo effect similar to what creates the Earth's magnetic field. Surrounding the core is a neutron mantle, then a iron-rich crust. Pulsars: Every star has a magnetic field, usually a very weak one. However, when a stellar core is compressed into a neutron star during a supernova explosion, the weak magnetic field is also compressed. As the field lines squeeze together, the magnetic field becomes very powerful. A powerful magnetic field, combined with the rapid rotation, will produce strong electric currents on the surface of the neutron star. Loose protons and electrons near the surface of the neutron star will be sweep up and stream along the magnetic field lines towards the north and south magnetic poles of the neutron star. The magnetic axis of the neutron star does not necessarily have to be aligned with the rotation axis (like the Earth), they can be inclined from each other as shown below. The rotating neutron star has two sources of radiation: 1) non-thermal synchrotron radiation emitted from particles trapped in the magnetic field of the neutron star, and 2) thermal radiation from particles colliding with the neutron star surface at the magnetic poles. The thermal component contains x-rays, optical and radio radiation since the protons smashing into the surface of the neutron star at extremely high velocities. Given the geometry of the hotspots at the magnetic poles, the energy from the hotspots sweeps out into space like a lighthouse. Only when the Earth lies along the axis of the neutron star is the energy detected as a series of pulses, and the object is called a pulsar. Pulsars were discovered by accident in 1967 during a search for distant sources of radio radiation. A special telescope had been constructed to look at short timescales of radio waves. One object displayed extremely evenly spaced pulses of radiation. The period was 1.337 seconds with an accuracy of 1 part in 10 million. A typical pulsar signature is shown below. Notice that the shape of the pulses is similar from high energy photons down to the low energy radio photons. This indicates that the source of the radiation, over a range of wavelengths, is from the same region on the neutron star. The fact that the pulses of radiation are so sharp and regular allows an astronomer to make very accurate measurements of the period of the pulses. When this is done, it is found that pulsars are slowing down with time. The rapidly changing magnetic field produces some of the energy that is beamed outward. Therefore, each pulse takes rotational energy from the neutron star and sends it into space, i.e. the neutron star loses rotational energy and slows down. Typical changes are about 10-15 seconds per rotation. In other words, a neutron star with a rotation of 1 second will be slowed to 2 seconds in about 30 million years. Thus, the age of a pulsar is determined by its current rotation speed. Old pulsars are rotating slowly, young ones fast. Pulsars also display sudden speed-up's in their rotation rates in sharp `glitchs' of their timing curves. The surface gravity of a neutron star is millions of times greater than the surface gravity of the Earth. The tremendous weight causes the crust to shift and contract suddenly, a starquake. The contraction, even though only a 1 mm in depth, causes a resulting starquake that is about a billion times more powerful than any earthquake on the Earth. This is visible in the rotation rate since it can be measure with a high degree of accuracy.

Accretion Disks: If a supernova occurs in a binary system, the companion star will survive the blast (although it will lose some of its outer layers). A neutron star will be left in orbit around the secondary star. As the companion star evolves to become a red giant, its envelope will expand beyond the Roche limit and gas will spiral onto the neutron star. The gas flowing towards the neutron star forms a thick disk of orbiting material called an accretion disk. Since the infalling gas retains the direction of orbital motion of the companion, the stream of material forms a rotating disk. Friction between the gas in neighboring orbits cause the gas to spiral inward until it hits the surface of the neutron star. As the spiraling gas moves inward, gravitational energy is released in the form of heat into the accretion disk. The release of energy is greatest at the inner edge of the accretion disk where temperatures can reach millions of degrees. If the object at the center is very compact, then a highly energetic source is available with only a small accretion rate. This region will be the source of strong x-ray and UV radiation, the signature of an x-ray binary system such as seen in Puppisa shown below. If the gas is dumped in vast amounts from the accretion disk to the neutron star, then the energy can not be released fast enough and tremendous pressures build up. The pressure can only be relieved if the gas is ejected. Since its easier for the plasmas to be ejected through the thinner poles, two powerful jets of high velocity hot gases form perpendicular to the accretion disk. Microlensing : When old neutrons stars have slowed down to the point where they no longer emit radio or x-ray radiation, they are invisible. However, we can detect dark neutron stars by their tremendous gravitational fields as they bend of light of stars behind them, called gravitational microlensing. Surveys of microlensing will image a patch of the sky towards the center of the galaxy looking for sharp changes in light over a period of weeks. A computer monitors the brightesses of millions of stars looking for a variation. These changes in brightness mark the passage of a neutron star in front of the target star, and the lensing of the background star light by the neutron star. The period and shape of the microlensing event provides information on the mass of the neutron star.

Relativity is only noticable at

All of the above

Chapter 24 The most violent, and therefore hottest, ejection of gas into the interstellar medium is from supernova explosions. A supernova remnant (SNR) is the structure resulting from the gigantic explosion of a star in a supernova. The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar material it sweeps up and shocks along the way. Many thin, arc-like nebula are found through out the Galaxy that are remnants of expanding shells of gas moving away from dead supernova at supersonic velocities. One such supernova remnant is the famous Tycho's Nova, observed in 1572. In either case, the resulting supernova explosion expels much or all of the stellar material with velocities as much as 1% the speed of light, some 3,000 km/s. When this material collides with the surrounding circumstellar or interstellar gas, it forms a shock wave that can heat the gas up to temperatures as high as 10 million K, forming a plasma. A close-up example is the Cygnus Loop shown below. Supersonic motion is always accompanied by a shock wave that compresses the medium in front of it. This compression causes the gas to heat and glow. The most recent supernova near the Earth was in 1024 A.D. and its remnant is seen as the Crab Nebula shown below. In the center of the Crab Nebula is a fast rotating pulsar. The shock wave from a supernova sweeps up matter in front of it and continues to heat this gas. Because supernova remnants are so hot, they emit a great deal of their energy in the x-ray region of the spectrum, shown in the x-ray picture of Cas A below. Notice that although the shock wave starts out as a symmetric explosion, the supernova remnant later develops structure and asymmetry. This is due to the fact that the density distribution of the interstellar medium is lumpy. The supernova remnant expands fastest in directions where the density is low. When pockets of dense gas are swept up, they radiate strongly and are visible as bright spots. So as a supernova remnant ages, it appears less round and regular. As millions of years pass, the supernova remnant slows down and merges with the interstellar medium. All the heavy elements produced in the original supernova explosion are mixed into newly forming molecular clouds enhancing the number of heavy elements in future stars and solar systems. A supernova remnant is a major source of energy for the interstellar medium. The region behind the shock wave is low in density, but very hot. Since its density is low, it cools at a very slow pace. The lumpy, foam-like nature to the interstellar medium is tracing the past history of supernovae. If the interstellar medium is dense, or the past supernova rate is small, then the interstellar medium has isolated bubbles of hot gas. If the interstellar medium is thin, or the supernova rate is high, then the interstellar medium becomes filled with connect bubbles or tunnels of hot gas.

Cosmic Rays: During both the day and night there is a continual shower of high speed particles into the Earth's atmosphere called cosmic rays. Most of these cosmic rays are protons and helium nuclei that have been accelerated to relativistic velocities (close to the speed of light). When cosmic rays collide with atoms in the Earth's atmosphere all their energy is converted back into matter (E=mc2) as a shower of particles that rains down to the Earth's surface. Supernova remnants are considered the major source of galactic cosmic rays. The connection between cosmic rays and supernovas was first suggested by Walter Baade and Fritz Zwicky in 1934. As cosmic rays move outward in all directions, most escape from the Galaxy. However, if the efficiency of cosmic ray acceleration in supernova remnants is about 10 percent, the cosmic ray losses of the Milky Way are compensated. This hypothesis is supported by a specific mechanism called "shock wave acceleration". Supernova remnants can provide the energetic shock fronts required to generate ultra-high energy cosmic rays. Cosmic ray showers are usually discovered with a cosmic ray detector, a large array of simply mirrors and phototubes to catch the Cerenkov radiation from the incoming particles. These array of detectors have shown that the cosmic rays arrive to the Earth from isotropic directions, meaning that there is no particular source to be deduced from their collisions with the Earth's atmosphere. A lack of a preferred direction implies that cosmic rays are deflected by the Galaxy's magnetic field and, thus, lose their orientation after many deflections over time. Cosmic rays strike all objects in outer space, not just the Earth. The image below is a picture of the Moon in gamma-rays, glowing from the impact of cosmic rays on it's surface (no atmosphere to block them). We can make some deductions about cosmic rays based on their frequency and energies. Since their energies and speeds are so high, they easily escape from the Galaxy's gravitational field. Since there are large numbers of cosmic rays seen everyday, this implies that they must be replenished at a steady rate. The only source in the Galaxy to produce particles at these energies are supernova explosions.

Chapter 22 When one looks up into the night sky we only see stars and the occasional planet. Most of outer space is empty, meaning that the density of atoms is much lower than even the best vacuums in our labs. Deep imaging of the skies showed that there are numerous regions where interstellar matter, in the form of gas and dust, collects to form clouds and nebula. Since these clouds are diffuse, they are difficult to see with the naked eye. The first indication that there was interstellar gas and dust was dark lanes in the Milky Way. Since we live in a disk galaxy, then looking outward we see a band of light in the sky which, if magnified, breaks down into the many stars in our Galaxy. A deep photo of the Milky Way shows that there are dark regions or lanes. We understand now that there is gas and dust blocking the starlight which produces these dark lanes, such as the CoalSack Nebula. In fact, most of our Galaxy is blocked from our view by patches of gas and dust. Interstellar Extinction: Astrophotograph in the 19th century showed that the dark lanes or holes in the Milky Way did not have sharp edges. That, in fact, detail studies of star clusters at various distances from us showed that the intensity of light from remote stars is reduced as it passes through the sparse material of the interstellar medium. Herschel tried to use star counts to measure the size of the Galaxy and where our position is within it. His result was the diagram below, but what he really discovered was that interstellar extinction limits our line of sight. Not only is the intensity of the light decreased, called interstellar extinction, it is also reddened, called interstellar reddening. The blue component of light is more easily scattered than the red component (which is why the sky is blue during the day, scattered sunlight). Thus, light from remote stars has part of its blue component scattered before it reaches the Earth. Maps of interstellar reddening demonstrated that the interstellar medium is composed mostly of hydrogen and helium gas (99%) and traces of dust. Dust, in an interstellar sense, is very small (few microns in size) particles of carbon and silicon. Dust is fragile because it can be broken down by UV photons, but is very important in dark nebula as sites for the formation of molecules. Neutral Hydrogen: Most of the interstellar medium is in the form of neutral hydrogen gas (HI). The typical densities of neutral hydrogen in the Galaxy is one atom per cubic centimeter. This gas is cold and the electron is usually in its ground state. However, protons and electrons can have spin. This spin produces a magnetic field such that when the spins are aligned the ground state has a slightly higher energy then when the spins are opposed. This is called hyperfine splitting of the ground state for hydrogen and results in the emission of 21 cm radio waves from HI clouds. The spins of the electron can be changed by collisions with other hydrogen atoms, although this is very rare because the densities are so low, or the transition can happen naturally after a few million years. On the other hand, there are billions and billions of hydrogen atoms in the typical cloud of gas. So the result is that 21 cm is a strong measure of the amount of HI gas in the Galaxy. A scan of our Milky Way galaxy at 21 cm shows that the distribution of neutral hydrogen is concentrated in the spiral arms. The Sun is marked as the yellow arrow, Galactic center is a blue dot. Notice how there is a cone of avoidance behind the Galactic center due to confusion in the HI signal. Interstellar Molecules: Atoms can bond together to form molecules. The most common atoms in the Universe are H, He, C, N, O, thus we have the expectation that the most common molecules are made from these atoms. However, the bonds between molecules is very weak (look how easy it is to breakdown water) and interstellar space is full of UV and x-ray photons which can break these bonds. So interstellar molecules are only found in the dark centers of dense nebula of gas and dust. Just as electrons orbit around the nucleus in quantized energy states, atoms can rotate around each other, also in quantized speeds. Changes in the rotation, by collisions or interactions, will emit photons. Radiation from interstellar molecules is a good tracer of the dense, thick regions of the interstellar medium. These dense regions are usually the sites of protostar formation and collapse of large clouds of gas to form into star clusters. Interstellar Dust: Interstellar dust is produced in the envelopes around red supergiant stars. Stellar winds and the planetary nebula phase eject this dust into the interstellar medium. Dust particles are mostly carbon and silicate grains that are a few microns in size. Although small, they completely absorb any light that strikes them and are heated by collisions with gas molecules. They will be warmed to the ambient temperature of the surrounding region and re-radiate that energy in the far infrared. Although solid objects, dust grains are not immune to destruction. Collisions with high speed gas particles, UV photons and other grains will breakdown dust grains. For this reason, dust is only found in the cores of dark nebula where they are shielded from destructive effects. Dust grains serve as sites for the formation of molecules and organic compounds. Their cold surfaces act as catalysts by allowing atoms to stick to them so there there is time for a second atom to land, interact, and form a molecule. Collections of dust and molecular gases are called molecular clouds.

Dark Nebula: We divide the interstellar medium into three types dependent on their temperature (called the phase of the interstellar medium): cold (10's K), warm (100 to 1000's K), hot (millions K). The colder a cloud of gas, the more of its output emission is in the long wavelengths; radio and microwave. Hot regions of interstellar gas are bright in their own optical emission. Note also that the various temperatures determine the type of matter that will exist. Cold temperatures are suitable to the formation of molecules. Warmer temperatures will find only atoms, such as neutral hydrogen. Under higher temperatures, atoms become ionized (HII regions). The coldest regions of space are the dark nebula. Some dark nebula are found through star counts, such as the Coalsack. Others are visible because an emission nebula is behind them, so they are illuminated from behind, such as the Horse Head Nebula shown below. This happens often because the same gas that is associated with the dark nebula can also be heated by nearby stars to glow as an emission nebula. The Horse Head Nebula is several tens of parsecs across and would envelop the local neighborhood of stars around our solar system. Stars seen in the image are foreground stars since the nebula is opaque. Some dark nebula are surrounded by emission regions, giving the impression that the dark cores are being dissolved by the hotter gas as in the Eagle Nebula shown below. A great deal of information is contained in the above image, the irregular shape of the dark regions, the hot vapor off the edges heated by nearby stars, the straight rays of dissolved gas. This nebula indicates that the interaction between dark nebula and bright, hot gas is dynamic and ongoing. Molecular Clouds: Often in the centers of dark nebula are dense concentrations of gas and dust called molecular clouds. They are called molecular because the temperatures are so low (only a few 10's K) that H2 and CO can form on the surface of dust grains. Dense gas makes for instability to gravity, and large pieces of the cloud can collapse to form protostars. Thus, molecular clouds are important as `nurseries' for young star clusters. Molecular clouds are probed with far infrared and sub-millimeter telescopes to study the conditions that lead to star formation and the details of protostar evolution. As the young stars evolve and heat the leftover gas, the molecular cloud will be destroyed and turned into a HII region such as the Orion Nebula. A perspective plot of the location of molecular clouds towards the center of the Galaxy is shown below. The location of the Sagittarius and Scutum spiral arms are clearly outlined. There are many processes that go on inside a molecular cloud that can enhance or inhibit the formation of stars. For example, turbulence in the core of a cloud would compress some regions and enhance star formation. Magnetic fields would retard the collapse of a cloud and slow down the production of new stars.

Chapter 17 As an asymptotic giant branch star becomes larger and more luminous, the rate at which is loses mass also increases. For stars less than 8 solar masses, a strong stellar wind develops and the outer layers of the star are removed to expose the hot degenerate core. As the gas is expelled and the core is visible, the color of the star becomes much bluer and moves to the left in the HR diagram at constant luminosity. Only a few 1,000 years are needed for the temperature of a star to grow to 30,000K. At this temperature, the star begins to emit large quantities of UV radiation. This UV radiation is capable of ionizing the hydrogen shell of matter that escaped from the star during the AGB phase. This shell of ionized hydrogen glows deep red as a planetary nebula. In the center of the planetary nebula is the remnant core. Stars above 25 solar masses end their time as AGB stars by becoming supernovae. White Dwarfs: Our knowledge of white dwarfs began in 1850 with the discovery of a companion to Sirius, called Sirius B. It was 10,000 times fainter than Sirius A, however its mass was 0.98 a solar mass. Since its temperature was measured to be 10,000K, its small mass and faint luminosity did not make sense in the context of the mass-luminosity relation for stars. The only way it could be both hot and faint was for Sirius B to be very, very small, and so they were called white dwarf stars. White dwarf stars are much smaller than normal stars, such that a white dwarf of the mass of the Sun is only slightly larger than the Earth. It was soon realized that the gas inside a white dwarf was too dense to behave as an ideal gas and, instead, was degenerate. For normal stars, if you increase the mass, the star gets larger, its radius increases. However, for white dwarfs, the opposite is true, increasing the mass shrinks the star. Notice that at some mass the radius of the star goes to zero. The size of a star is a balance between pressure and gravity. Gravity pulls the outer layers of the star inward. Pressure pushes those layers upward. In a degenerate gas, increasing the density does not increase the pressure (opposite to a normal gas). But increased density does increase gravity. So, as you add mass to a white dwarf, the gravity increases, but the pressure only changes a small amount. Gravity wins and the star shrinks. Notice that the mass-radius relation for white dwarfs means you cannot keep adding mass to a star, for eventually its radius goes to zero. This also means the massive stars (with masses greater than 1.4 solar masses) must shed most of their mass as planetary nebula or the final contraction to a white dwarf cannot be stopped by the degenerate electrons. If the mass can not be shed they will become neutron stars or black holes.

Evolution of White Dwarfs: White dwarfs are quite common, being found in binary systems and in clusters. Since they are remnants of stars born in the past, their numbers build up in the Galaxy over time. It is only because they are so faint that we fail to detect any except for the very closest ones. Once a white dwarfs contracts to its final size, it no longer has any nuclear fuel available to burn. However, a white dwarf is still very hot from its past as the core of a star. So, as time passes, the white dwarf cools by radiating its energy outward. Notice that higher mass white dwarfs are small in size, and therefore radiate energy slower than larger, small mass white dwarfs. Radiative cooling is one way for a white dwarf to cool, another way is neutrino cooling. At very high temperatures, around 30 million degrees K, gamma-rays can pass near electrons and produce a pair of neutrinos. The neutrinos immediately escape from the white dwarf (because they interact very weakly with matter) removing energy. On the other hand, as a white dwarf cools, the ions can arrange themselves in a organized lattice structure when their temperature falls below a certain point. This is called crystallization and will release energy that delays the cooling time up to 30%. The cooling process is very slow for white dwarfs. After a billion years the typical white dwarf is down to 0.001 the luminosity of the Sun. But the endresult is unstoppable as the white dwarf will eventually give up all its energy and become a solid, crystal black dwarf. Nova: Once a decade, on average, we observe a `new' star in the heavens. These stars, named nova from the Latin word for new, are visible only for a few weeks, then fade from view. Comparing before and after images of that region of the sky demonstrates that novae are old stars that dramatically increase in brightness, such as Nova Herculis shown below: The change is brightness is typical a factor of 106 (whereas a supernova is 108, a different object all together). The light curves for a nova look like the following: There are many reasons why a star might increase in brightness in a sudden and explosive-like manner; the collision of two stars, core changes, unstable pulsations. However, novae are often recurrent, meaning that after 50 to 100 years the nova will go off again. This means that whatever causes the brightness changes must be cyclic (i.e. it doesn't destroy the star). The best explanation for novae is surface fusion on a white dwarf. By definition, white dwarfs no longer have any hydrogen to burn in a fusion reaction. They have used all there hydrogen at earlier phases of their life cycle. However, a white dwarf in a binary system can `steal' extra hydrogen from its companion by tidal stripping. A binary system with a normal main sequence star and an old white dwarf will look like the following: Eventually the main sequence star will evolve to become a red giant star. As the red giant star continues to expand it will exceed its Roche limit and hydrogen gas will stream across to the white dwarf, spiraling inward to form an accretion disk. Hydrogen gas will build up on the surface of the white dwarf where the surface gravity is extremely After the shell is fused, the process starts over again, thus explaining why we see recurrent novae. Observations of old novae, several years after the event, demonstrates our theory is correct with the discovery of expanding shells of gas around DQ Her and GK Per. These shells are moving away from the binary at about 1,000 km/sec. We will see a similar scenario around binaries where one of the pair is a neutron star. Since the pressures on the infalling gas are so much higher, most of the energy is released in the x-ray, called an x-ray burster. Because most stars evolve to white dwarfs, novae are relatively common in the Galaxy. About 200 have been discovered in the last few 100 years.

A K star seen through a region of the interstellar medium will have the color of a

M star

Chapter 18 For stars less than about 25 solar masses the end of their lives is to evolve to white dwarfs after substantial mass loss. Due to atomic structure limits, all white dwarfs must mass less than the Chandrasekhar limit. If their initial mass is more than the Chandrasekhar limit, then they must lose their envelopes during their planetary nebula phase till they are below this mass limit. An example of this is the Cat's Eye Nebula shown below: At what stage a star leaves the AGB (Asymptotic Giant Branch) and becomes a white dwarf depends on how fast it runs out of fuel in its core. Higher mass stars will switch from helium to carbon burning and extend their lifetimes. Even higher mass stars will burn neon after carbon is used up. However, once iron is reached, fusion is halted since iron is so tightly bound that no energy can be extracted by fusion. Iron can fuse, but it absorbs energy in the process and the core temperature drops. After evolving to white dwarfs, stars with original masses less than 25 solar masses slowly cool to become black dwarfs and suffer heat death. Stars greater than 25 solar masses undergo a more violent end to their lives. Carbon core burning lasts for 600 years for a star of this size. Neon burning for 1 year, oxygen burning about 6 months (i.e. very fast on astronomical timescales). At 3 billion degrees, the core can fuse silicon nuclei into iron and the entire core supply is used up in one day. An inert iron core builds up at this time where successive layers above the core consume the remaining fuel of lighter nuclei in the core. The core is about the size of the Earth, compressed to extreme densities and near the Chandrasekhar limit. The outer regions of the star have expanded to fill a volume as large as Jupiter's orbit from the Sun. Since iron does not act as a fuel, the burning stops. The sudden stoppage of energy generation causes the core to collapse and the outer layers of the star to fall onto the core. The infalling layers collapse so fast that they `bounce' off the iron core at close to the speed of light. The rebound causes the star to explode as a supernova. The energy released during this explosion is so immense that the star will out shine an entire galaxy for a few days. Supernova can be seen in nearby galaxies, about one every 100 years (therefore, if you survey 100 galaxies per year you expect to see at least one supernova a year). One such supernova (1991T) is shown below in the galaxy M51. Supernova Core Explosion: Once the silicon burning phase has produced an iron core the fate of the star is sealed. Since iron will not fuse to produce more energy, energy is lost by the productions of neutrinos through a variety of nuclear reactions. Neutrinos, which interact very weakly with matter, immediately leave the core taking energy with them. The core contracts and the star titers on the edge of oblivion. As the core shrinks, it increases in density. Electrons are forced to combine with protons to make neutrons and more neutrinos, called neutronization. The core cools more, and becomes an extremely rigid form of matter. This entire process only takes 1/4 of a second. SN ball bounce With a loss of pressure from core, the unsupported regions surrounding the core plunge inward at velocities up to 100,000 km/s. The material crashes into the now-rigid core, enormous temperatures and pressures build up, and the layers bounce upward. A shock wave forms, which accelerates and, within a few hours, explodes from the surface of the star rushing outward at thousands of km/sec. This entire process happens so fast that we can only follow it using supercomputer simulations. Maps of density and flow show the details in regions where observations can not be made. As the outer layers are blasted into space, the luminosity of the dying star increases by a factor of 108 or 20 magnitudes. In 1987, a supernova exploded in our nearest neighbor galaxy. That supernova, designated SN1987A (the first one discovered in 1987) was visible to the naked eye, rising to a maximum brightness 85 days after detonation with a slow decline over the next 2 years. The light curve for SN1987A is shown below: Although a supernova is extremely bright, only 1% of its energy is released as optical light. The rest was released as neutrinos and kinetic energy to explode the star. Most of the initial luminosity is the shell of the star expanding outward and cooling. After a few hundred days, this shell of expanding gas has cooled to be almost invisible and the light we see at this point is due to the radioactive decay of nickel and cobalt produced by nucleosynthesis during the explosion.

Neutrinos and Gravity Waves: Supernova are the most energetic events in the Universe and provide an opportunity to observe two very elusive phenomena, neutrinos and gravity waves. The collapse of a supernova core produces a flood of those very strange particles, neutrinos. Neutrinos interact very weakly with matter. Under most conditions, matter is transparent to neutrinos. During the high densities of a supernova core collapse, some of the neutrinos provide the pulse to starts the outward moving shock wave. But most of the neutrinos zip out of the supernova core. Thus, when a supernova explodes, huge numbers of neutrinos pour into space, streaming across the Galaxy passing through dust, gas, nebula unhindered. Even if the supernova is obscured, the neutrinos will rain down on the Earth. However, because neutrinos are weakly interacting, they are also just as difficult to detect. Our best neutrino `telescopes' are large tanks of water buried deep underground such as the Super Kamiokande in Japan. Water contains lots of protons in the form of hydrogen atoms. Neutrinos from a supernova explosion travel at or very near the speed of light and carry a lot of energy. On rare occasions, a neutrino will hit a proton in the tank of water (the more water, the greater the chance). This collision will produce a positron which recoils with such high speed that it emits a brief flash of light known as Cerenkov radiation. The detector tank of water is buried deep in the Earth to eliminate cosmic rays and other interactions that would distort the detection of the neutrinos. Only neutrinos can reach to such depths. The supernova SN1987A was the first recorded neutrino detection of an astronomical event (most neutrinos detected are from the Sun). Twelve neutrinos were detected 3 hours after the supernova was seen in the optical. The neutrino detections also give us valuable information on the neutrino itself. Until recently, we did not know if the neutrino has zero mass (like the photon and, therefore, travels at the speed of light) or if it has a small mass and must travel less than the speed of light. If neutrinos are massless, then they would arrive at the Earth at the same time. The more massive the neutrino, the more spread out their arrival times. The results from these experiments showed that the neutrino has a very small mass, a surprise to the world of particle physics. Another exotic technique to study supernovae is through the use of gravitational radiation. During the core collapse of the supernova, vast amounts of matter are moved about at enormous speeds. The dense mass is surrounded by a strong gravitational field. Einstein's general theory of relativity describes gravity as curves in the fabric of space. Vigorous changes in gravity will produce `ripples' in the geometry of space, and these ripples can propagate outward at the speed of light, called gravity waves. Gravity waves can be detected by the effects they have on other masses. For example, two masses will vibrate when a gravity wave passes, so sensitive measurements of their motion with lasers will detect the motion. Currently our technology is unable to detect gravity waves, but a new system (LIGO) is currently under construction for use at the turn of the century. Nucleosynthesis: There are over 100 naturally occurring elements in the Universe and classification makes up the periodic table. One of the great successes of stellar evolution theory was the explanation of the origin of all these elements. Some of the elements were formed when the Universe was very young. The era immediately after the Big Bang was a time with matter was densely packed and temperatures were high (ten's of millions of degrees). Fusion in the early Universe produced hydrogen, helium, lithium, beryllium and boron, the first 5 elements in the periodic table. Other elements, from carbon to iron, were formed by fusion reactions in the cores of stars. The fusion process produces energy, which keeps the temperature of a stellar core high to keep the reaction rates high. The fusing of new elements is balanced by the destruction of nuclei by high energy gamma-rays. Gamma-rays in a stellar core are capable of disrupting nuclei, emitting free protons and neutrons. If the reaction rates are high, then a net flux of energy is produced. Fusion of elements with mass numbers (the number of protons and neutrons) greater than 26 uses up more energy than is produced by the reaction. Thus, elements heavier than iron cannot be fuel sources in stars. And, likewise, elements heavier than iron are not produced in stars, so what is their origin? The construction of elements heavier than iron involves neutron capture. A nuclei can capture or fuse with a neutron because the neutron is electrically neutral and, therefore, not repulsed like the proton. In everyday life, free neutrons are rare because they have short half-life's before they radioactively decay. Each neutron capture produces an isotope, some are stable, some are unstable. Unstable isotopes will decay by emitting a positron and a neutrino to make a new element. Neutron capture can happen by two methods, the s and r-processes, where s and r stand for slow and rapid. The s-process happens in the inert carbon core of a star, the slow capture of neutrons. The s-process works as long as the decay time for unstable isotopes is longer than the capture time. Up to the element bismuth (atomic number 83), the s-process works, but above this point the more massive nuclei that can be built from bismuth are unstable. The second process, the r-process, is what is used to produce very heavy, neutron rich nuclei. Here the capture of neutrons happens in such a dense environment that the unstable isotopes do not have time to decay. The high density of neutrons needed is only found during a supernova explosion and, thus, all the heavy elements in the Universe (radium, uranium and plutonium) are produced this way. The supernova explosion also has the side benefit of propelling the new created elements into space to seed molecular clouds which will form new stars and solar systems.

The type of stars that produce a Stromgren sphere are

O and B stars

Chapter 25 A galaxy is a collection of stars and interstellar material held together by gravity. The galaxy our Sun lives in is called the Milky Way or the Galaxy (note the capital 'G'). The name `Milky Way' comes from the band of light that is seen overhead on very dark nights. The ancients called it the Celestial River. Galileo showed that the band is actually an edge-on concentration of stars seen looking through the disk of our Galaxy from the inside. That same band looks very different when imaged at different wavelengths. For example, below is an image of the sky in the near-IR, sensitive to giant stars and dust. The same region imaged in gamma-rays shows where all the neutron stars and x-ray binaries are found The x-ray picture of our Galaxy shows where the hot supernova remnants are found (notice the partial arcs) A deep optical picture shows where the dark nebula are found near the axis of the disk. An image in the far-IR shows the concentration of old stars in the center of the Galaxy (called the bulge) An an image taken at the 21-cm wavelength of neutral hydrogen shows how neutral gas avoids the center of the Galaxy and is found mostly out in the arms. Size of the Milky Way: Mapping of the Galaxy using star counts was shown to be ineffective due to the extinction of starlight by the interstellar medium. A Harvard astronomer, H. Shapley, mapped the distribution of globular clusters in the Galaxy's halo to see where the Sun was with respect to the Galactic center. The distance to a globular cluster is found by main sequence fitting, where a HR diagram of a cluster is made and `slide' up and down to match the globular cluster main sequence luminosity to the absolute luminosity of the main sequence of nearby stars. The difference between the apparent and absolute luminosity determines the distance to the globular cluster. When Shapley did this for 150 globular clusters he had the following plot. The globular clusters orbit the center of the Galaxy, so where their centroid is on the plot is the Galactic center. The Sun is shown to be off center from the Galactic center by about 8 kiloparsecs or 25,000 light-years. Later mapping of variable stars, neutral hydrogen radio maps and star clusters gives us our current view of the shape of our Galaxy shown below.

The key components of our Galaxy is a bulge of old stars in the center, a disk of stars and gas and a halo of globular clusters. The disk of our Galaxy is whirlpool shaped with numerous spiral arms spanning out from the center of the Galaxy. In the very center of the bulge of our Galaxy lies a nucleus, possibly a million solar mass black hole. Notice that the total size of the Milky Way is about 50,000 light-years in radius, with the Sun a little over halfway from the center. Since the Galaxy is similar in shape to the solar system, we use a Galactic coordinate system where the plane of the disk forms the galactic equator. Angular distance from the center of the Galaxy eastward is galactic longitude, angular distance above or below the plane is galactic latitude The orbital period of an object is just how far an object traveled divided by its velocity. In a circular orbit, how far is the circumference of the orbit such that the period, P, is P = 2 π r/v where r is the distance from the center and v is the velocity. Since the Sun orbits the center of the Galaxy, we can use this knowledge to determine the mass of the Galaxy. Remember that Kepler's 3rd law states that the sum of the masses of two objects in orbit around each other is given by MGalaxy+ MSun= r3/P2 Notice that the mass of the Sun is really, really small compared to the mass of the Galaxy. So MGalaxy + MSun becomes just MGalaxy. Rotation Curve of Galaxy: The orbital period of the Sun around the Galaxy gives us a mean mass for the amount of material inside the Sun's orbit. But a detailed plot of the orbital speed of the Galaxy as a function of radius reveals the distribution of mass within the Galaxy. The simplest type of rotation is wheel rotation shown below. Rotation following Kepler's 3rd law is shown above as planet-like or differential rotation. Notice that the orbital speeds falls off as you go to greater radii within the Galaxy. This is called a Keplerian rotation curve. To determine the rotation curve of the Galaxy, stars are not used due to interstellar extinction. Instead, 21-cm maps of neutral hydrogen are used. When this is done, one finds that the rotation curve of the Galaxy stays flat out to large distances, instead of falling off as in the figure above. This means that the mass of the Galaxy increases with increasing distance from the center. The surprising thing is there is very little visible matter beyond the Sun's orbital distance from the center of the Galaxy. So the rotation curve of the Galaxy indicates a great deal of mass, but there is no light out there. We call this the dark matter problem, and states that the halo of our Galaxy is filled with a mysterious dark matter of unknown composition and type.

Chapter 23 Often there is found a blue haze around bright, hot stars. This haze is called a reflection nebula and is caused by scattering of blue light off a background cloud of dust. The most famous is the Pleiades (UKS 18, see below), a cluster of young stars in front of a dust cloud. Remember that only the blue component of a star's light is scattered, so the reflection will look bluer than the original star. Emission nebula look dense, but they are actually thinner than the best vacuum in any laboratory on the Earth. To see this consider the typical density, ρ, from the mass and size of a nebula such that ρ =M/V where M is the mass of the nebula and V is the volume of the nebula. Notice that it is not how dense a nebula is to detect it, but what is its cross section. Since a nebula is so thin, you basically can see through its core. thus, it is not the volume density at the surface that determines how bright a nebula is, but rather the total number of atoms through the line of sight into the nebula. This is called the cross section, σ, and is expressed as σ = ρL where L is the length or depth of the nebula. Masers: Near regions of star formation are often found powerful sources of microwave radiation, called OH or H2 masers. The radiation from newborn stars causes collisions with the molecules and `pumps' them into excited energy states. Some of these energy states are meta-stable, meaning that they will only transition downward when stimulated by a passing photon. The electromagnetic field of the passing photon causes the excited electron to transition downward emitting another photon of the same energy and wavelength. This is the process behind the laser. If many molecules in the cloud are pumped to their excited states, then one photon can cause a downward transition of billions of molecules. The released radiation would have a particular wavelength signature instead of being spread out in a thermal spectrum. HII regions: Once stars are formed in the center of a molecular cloud, the stars will emit large amounts of UV radiation and heat the cloud. The gas will ionize and become an HII region, a region of ionized hydrogen (HII) surrounded by cooler, neutral hydrogen (HI).

The largest example of an HII region in the sky is the Orion Nebula. The size of the HII region is directly proportional to the number of UV photons emitted to ionize the gas. You can increase the number of UV photons by either have large mass stars or simply more stars. The glow from an HII region is the recombination of ionized hydrogen, so the size of an HII region is simply the point in space where the rate of recombination equals the rate of photoionization from the central stars. This region is called a Stromgren sphere and is a useful method of calculating the number of hot O and B stars that are produced in the Galaxy by measuring the sizes of HII regions (i.e. the current star formation rate). Also found in bright HII regions are new stars, and with them supernova. Supernova explosions over thousands of years will send shock waves back into the molecular cloud where they were born from. This will cause compression in the cloud and enhance the formation of even more new stars as shown below. The style of star formation will lead to the spiral patterns we see in galaxies, where star formation travels along the dense clouds found in the spiral arms. Planetary Nebula: Hotter and more compact than HII regions are planetary nebula, which got their names cause they look like distant fuzzy planets in old telescopes. Since planetary nebula are the ejected envelopes of AGB stars, the regions around them are empty, unlike the dense clouds around HII regions. The planetary nebula are heated solely from the interior AGB core. Thus, planetary nebula offer a unique chance to watch the interaction of radiation and low density gas. Most planetary nebula are spherically symmetric shells with some icicle shapes on the inner edge of the outrushing shell, such as IC 3568. The green color is from emission lines of oxygen. If the original star was rotating, then a disk can form with holes along the long axis for radiation to escape, such as NGC 6826, NGC 7009 and NGC 3918. `Fliers' develop where there is a leak of UV light. Often a remnant disk shell or old solar system will form a disk near the star. In this case, the expanding gas moves faster out the poles of the solar system to develop a dumbbell shape as in Hubble 5. The strangest case is where the core star has a hotspot not aligned with the rotation axis. This hotspot could be ejected charged particles which are falling back onto the magnetic poles of the stars. The result is a beam or jet of UV radiation which will paint helix shaped wobbles on the planetary nebula, as in NGC 5307.

Chapter 26 It is difficult to measure the structure of our Galaxy since we are inside it (trying to see the forest from the trees). One method is to plot the position of tracers, such as young stars or molecular clouds. One such plot is shown below, the position of nearby HII regions and young clusters of stars. Since their age is young, then they will not have drifted far from their formation places. Interstellar extinction prevents a map much larger than the one above for optical tracers, but even this plot is enough to show that there are distinct arms of material in the Galaxy. Maps of neutral hydrogen show the global spiral pattern throughout the Galaxy. It is somewhat surprising that we even see a spiral pattern since the Galaxy does not rotate as a solid body. After a few rotations, the spiral pattern would be wound up very tight, as shown in the diagram below. This is known as the winding dilemma. One explanation for the winding dilemma is to use density waves. Imagine a scenario such as shown below. DENSITY WAVE Even though all the cars and trucks are moving at different velocities, there is an apparent overdensity near the slow moving truck. A similar explanation is proposed for spiral arms in our Galaxy, they exist because they exert a gravitational influence on stars and gas that orbit the Galaxy. In particular, gas clouds will orbit slower in the arms and, thus, the density goes up in this region. The spiral arms don't wind up because they are not made of material arms, but rather density patterns that shift like cars in traffic. The concentration of gas in the spiral arms explains why neutral hydrogen maps trace spiral structure, but why do young stars occur in spiral arms. Higher density of gas means more gas clouds and cloud collisions. This sparks star formation, which leads to HII regions and young clusters. As the young stars age, they drift out of the spiral pattern. Center of the Galaxy: The center of the Galaxy is obscured from us by thick interstellar clouds of gas and dust. We can observe the Galactic bulge as an ellipse of stars above and below the Galactic plane. In the solar neighborhood, the stellar density is about one star per cubic parsec (one parsec is 3.26 light-years). At the Galactic core, around 100 parsecs from the Galactic center, the stellar density has risen to 100 per cubic parsec, crowded together because of gravity. Very near the center of the Galaxy, the stellar densities rise to several hundreds of thousands of stars per cubic parsec. The stars are separated by light-weeks rather than years. Starlight at night is bright enough to read by, although there is a great deal of dust in the Galactic core and much of the energy is radiated in the IR. As one approaches the Galactic center, not only does the number of stars increase, but a thin ring of gas and dust forms visible by its radio radiation. Streamers of gas are visible in the image below, suggesting an accretion disk over 10 parsecs in size. The rotation speeds of this inner gas ring indicates that the object located at Sgr A is less than 13 A.U.s in size and masses over 1 million solar masses. Only a black hole of massive proportions would satisfy these requirements. Given all above information, the following is a trip to the Galactic core. Stellar Populations: A group of stars within the Galaxy that resemble each other in spatial distribution, chemical composition or age are called a stellar population. Stellar populations are not discrete in their properties, but rather have a continuum of characteristics that reflect the changes in star formation with time. Stellar populations are tracers of events in our Galaxy's past and formation. There are basically three stellar populations in our Galaxy, corresponding to the three distinct dynamical components to the Galaxy; the disk population, the bulge population and the halo population. The disk population inhabits the rotating, flattened region of our Galaxy. The bulge population is restricted to the rounded, central region of the Galaxy, also rotating. And the halo population inhabits the far outer regions of the Galaxy, on long ellipisodal orbits that takes it into the disk and bulge.

The three components not only have distinct kinematic properties, but the types of objects in them also varied. The disk contains all the gas and young stars, although old stars are also found there. The bulge is dominated by old stars and a violent core. The halo contains very old stars and globular clusters. The reason for this separation of stellar types is a clue to how the Galaxy formed. Once the distinct kinematic components of the Galaxy had been isolated, an interesting fact arose in that the chemical composition of the stars in those components also varied in a regular manner. Disk and bulge stars tend to be rich in heavy elements (above helium on the periodic table). Halo stars tend to be very poor in heavy elements. Changes in the chemical composition of a star are due to the initial chemical composition of the gas cloud that it was born from. This heavy elements are mostly produced by supernova explosions, gas clouds become enriched by the ejecta of supernova. The larger the number of supernova near a cloud, the richer in heavy elements it will become. As time passes, each of the gas clouds in the Galaxy will increase in the abundance of elements such as carbon, iron, etc. So the more recent a star has been formed, the richer in heavy elements it is. This is a form of dating system for stars and we deduce that halo stars are the oldest stars in the Galaxy since they have the lowest chemical abundances. The disk stars are the youngest since they are the most metal rich. Formation of Our Galaxy: The key to understand how our Galaxy formed is the location, ages and chemical composition of the various stellar populations. The oldest stars are in the halo and bulge. The most metal rich stars are in the disk and bulge. From this we deduce that the halo formed first, followed by the bulge then disk. All the gas is located in the disk (which is rotating) because gas clouds can undergo inelastic collisions. Inelastic collisions occur when two objects collide and share momentum as a single body. Stars are too small to collide within the Galaxy (their cross section is very, very low). But gas clouds are large and can 'stick' together. Even the above facts, the formation and evolution of our Galaxy must have taken place through a series of continuous stages. First, the Galaxy began as a large single gas cloud a few hundred of thousand light-years across. Passage near other proto-galaxies caused this large cloud to spin. This rotation was far from organized as currents and smaller clouds formed within the proto-Galaxy. Spheres of gas containing about a million solar masses of material collapsed first, this will become the future halo globular clusters. These first clouds were very weak in chemical abundance, but the first supernovae in the halo stars begins to enrich the interstellar medium. Cloud-cloud collisions steadily eliminated those clouds with the greatest inclination and those moving in the opposite directions until the distribution of gas clouds became flatter and flatter. Most of the gas is directed to the bulge regions where the high densities produce a highly dense core region. Lastly, the remaining gas settles into the disk where the rotation slows the formation of new stars until spiral density wave form to dominate the appearance of the Galaxy today.

More stars will produce

a larger hill region

The Sun lives

a little over halfway from the Galactic center

A nova returns to its normal brightness in

a month

If a nebula is blue in color it is probably

a reflection nebula

Maps of neutral hydrogen display

a spiral shaped galaxy

Dark matter is

all of the above

Shock waves from supernova will

all of the above

Stars in the disk are

all of the above

Relativity means

all the above

The Michelson-Morley experiment

all the above

Krypton has more protons than neon, therefore the fusion shell of krypton would

be lower than the neon shell

Why is the Milky Way hard to see in cities?

because the city lights make the sky bright

You are running towards a wall, as you pass a friend you both turn on a flashlight, which beam hits the wall first?

both hit the wall at the same time

Which of the following is not a stellar population component of the Galaxy?

central blackhole

With time, a white dwarf becomes

fainter and redder

Black holes cannot be detected in space.

false

Stars with chemical compositions rich in heavy elments

formed later

A accretions disk's rotation energy is lost to

friction

Galaxies form from

gas cloud collisions

Neutron capture will

increase the atomic mass

Which of the following is not a part of the maser process?

ionization

Angular momentum is conserved when a neutron star forms, this means

it spins faster

Time travel is impossible because

it violates causality

How does the escape velocity of a black hole the mass of the Earth compare to the escape veolcity of the Earth?

its greater

How does the escape velocity of the Earth compare to the escape velocity of the Moon?

its greater

In relativity, gravity is warped spacetime, therefore, more mass means

move curvature

If 14C6 undergoes beta decay, it becomes (hint: google on beta decay)

nitrogen

All white dwarfs are nova.

no

If a neutron star has an orbital period of 1 year around its primary, would you expect to find an accretion disk?

no

The Sun lives on

orion arm

An electron in orbit around a proton must be either spin up or spin down, not in-between, because of

quantum pyshics

Interstellar clouds are examined with

radio telescopes

The r and s in r/s-processes stands for

rapid and slow

Globular clusters orbit

the center of the galaxy

Stars in the outer regions of the Galaxy move

the same speed as the sun