Astronomy Study Guide

8/3/2019 Astronomy Study Guide

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Know the relation between surface flux, luminosity and radius of a star. (D07)

F=L/A= L/(4piR^2)

Know the relation between the observed flux of a starthat is, its brightnessand

its luminosity and distance. This is the generalized form of the inverse distance-squared law for stellar brightness. (D07)

F= L/4piD^2

Understand that flux is the technical term for brightness. Luminosity isthe intrinsic energy output of a star. (D07)

What is the significance of 51 Peg in extrasolar planet studies? (First system

in which a normal extrasolar planet was discovered). Also review the systems

properties, primarily the existence of a hot, close-in Jupiter-like planet. (D07)

This planet is huge! Its mass is at least half that of

Jupiter, the Suns largest planetary companion, at least150 times more massive than

Earth6. But any similarity with the Planets in the Solar System ends there. Jupiter is

over 5AUfrom the Sun and has an orbital period of nearly 12yr. This planet is

entirely different. It is nearly on top of its sun7 (see Figure 7.2), orbiting a mere

0.05AUfrom the center of 51 Peg, 100 times closer than Jupiter is from the Sun.

And with a period of only 4.2days.

Review methods of finding extrasolar planets, including radial velocities, transits,

direct detection and gravitational lensing. (D07)

Radial Velocities: One

commonly detected signature of a planet is the radial velocity changes it induces in

the spectrum of the star it is orbiting. What favors the detection of this velocity

wobble? Well, it is obvious that a large velocity change is easier to detect than a

small one. At some pointdue to the limited precision of our instrumentswebecome insensitive to planets below a certain mass simply because they dontinduce sufficiently large motions in their parent stars to be detected. It is also

obvious that it is easier to find planets with short orbital periods compared to

longer one. The planet orbiting 51 Peg takes a very reasonable 4.2 days to complete

one orbit. That can be measured with ease in under a week. But, as noted above, to

do the same with Jupiter would take years. And what if we happen to be looking

straight down onto the orbits of the planets surrounding a star? In that case, the

motion that planets induce in their parent star would be neither towards or away

from us. We could neverbe able to measure a Doppler shift to detect planets in this

case no matter how precise our measurements.

Transits-Planets can also be detected as they pass between us and their sun dur-ing events known as transits. Though we do not see the disk of the star or of the

planetthey are far too distantwe do see the light output of the star dip by a tiny

amount when the planet blocks part of the stellar disk. If the process repeats at a

precise interval, we can reasonably infer something dark is orbiting the star to pe-


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riodically block its light. Detailed studies of transits can provide information on the

sizes and masses of planets, as well as the compositions of extrasolar planet atmos-pheres.

Direct Detection

Seing the planet with Doppler shift or by seeing it in a telescope.

Gravitational Lensing

Know the role of exoplanets in star formation, particularly regarding how


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they can absorb much of the angular momentum of the collapsing cloud. (D07)

n this respect, the Sunwhere most of the mass of the Solar System is locatedcould not have formed without the Planetswhich contain most of the angular

momentum in the Solar System.

Understand what the Drake equation might be used for, though you do not need to

remember all the terms in detail. (D07)


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sequence stars are the most luminous, the red

main-sequence stars least luminous. Where, roughly, does the Sun lie on the main

sequence? (D08)

How do stellar properties vary along the main sequence? Know that the blue stars

of the main sequence are also the most luminous, most massive, youngest, hottest

and largest main sequence stars. And that the red main sequence stars are opposite

in all of these parameters. (D08)


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The surface flux of a thermal source is given by . No need to

remember the value of, but the form of this equation is important. (D08)

Know the basic relation between luminosity, surface temperature and size for stars

(this holds for anyspherical star, not just main sequence stars). (D08)

The main-sequence mass-luminosity relation. Be sure you appreciate that (a) it ap-plies only to the main sequence stars, and (b) that it says that luminosity increases

rapidly as stellar mass increasesroughly as or depending on if the star is

less or more massive than the Sun. (D08)

Odd behavior of stellar spectra on the main sequence. For example, H lines are

strongest among intermediate-temperature stars. The hottest and coolest main-sequence stars have weak H lines. (D08)

The hottest stars in the cluster show little or at best very weak H lines in their

spec-tra.

The coolest Pleiades stars also exhibit very weak H absorption lines.

Many of the stars with intermediate temperatures show very strong H absorption.

Moreover, allof the stars that do show strong Hydrogen absorption have very near-ly the same colors.

All other stars show a steady variation in the strength of the H lines. That is, stars

just a bit hotter (bluer) than the stars with the strongest H lines exhibit weaker H

absorption lines. Spectra of stars that are a bit cooler (redder) than the H-strong

stars also exhibit weakened, though still clearly visible, H absorption.

Basis of spectral classification: Letters refer to the relative strength of the H lines.

And A-type star has strong H lines. M- and O-type stars have weak H lines. (D08)Thus, stars of spec-

tra class A have the strongest absorption lines, B the next strongest, and so on until theletter O for stars have the weakest H absorption lines in their spectra. When it was laterunderstood that the physical basis for the appearance of these spectra was the tempera-tures of stars21, the classification scheme was changed to reflect this new knowledge. As it


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happens, O stars are the bluestand therefore the hottestof all stars, so they became

the firstspectral typein the new sequence. B stars, slightly cooler, became second in thesequence. This continued right up to the coolest, reddest stars denoted as class M. The

resulting classification schemestill in use today (Figure 8.8 and Table 8.1)reflects thisordering by temperature, and, mercifully, the omission of some of the redundant spectral

types: O, B, A, F, G, K and M. Two new classesdenoted L and Thave been added to the

sequence in recent years to include extremely cool objects, some of which may be stars,some not (more on this below). Since OBAFGKM(LT) is kind of an odd ordering of letters(you think?), some people find it easier to remember a mnemonic than the sequence

itself. One famousbut somewhat sillyexample is Oh, Be A Fine Girl/Guy, Kiss Me (Lotta

Times). However one chooses to remember the progression of stellar spectral types22, thekey is to appreciate the sequence is ordered by temperature.

Temperature of the star is the key factor that determines the spectral type. If the

star is too hot, the atoms are ionized and so there are no bound electrons to form

absorption lines. If the star is too cool, there are too few energetic photons to excite

the atoms and produce absorption lines in the process. But at some intermediate

temperature, absorption is maximizedthe atoms can be excited without ionizingthem. (D08)

Worth repeating: The variations of the strengths of absorption lines in stellar

spectra

are caused principally by differences in the surface temperatures of stars. (D08)

The sequence of spectral types on the main sequence from hottest to coolest: O - B

-

A - F - G - K - M (recall that L, and T are recent additions to the cool end of the se-quence). (D08)

Why chemical reactions cannot power a star like the Sun. It would live only

10,000

to 100,000years. (D08)

Why gravitational contraction cannot power the Sun. Though 30 millionyears is a

lot longer, it is still not enough time to explain the measured age of the Earth and,

presumably, the Sun. Know that Lord Kelvin was associated with the idea that the

Sun might be powered by slow gravitational collapse. (D08)

The actual source of energy in stars: Thermonuclear fusion. Understand all

aspectsof the name. Thermo implies that it has to be hot so the particles are moving at

great speed and energy, nuclear implies that the process involves the nuclei ofatoms (very different from chemical reactions which involve moving the electrons

around), and fusion means you are combining small particles to make bigger ones(H to He; He to C; Si to Fe; etc.). (D08)

Main sequence fuse H into He stably in their cores. (D08)


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Fusion reactions are complex in detail, but the basic result of H fusion is thatfour H

nucleiare converted to one He nucleus. (D08)

Why does this work? 0.8% of the mass of the input H atoms is converted to energy

(we get that by noting that the four input H atoms weigh a tad more than the single

He atom). Einsteins equation ( E=Mc2 ) lets us estimate how much energy the Suncould produce assuming it starts out most as H (which is correct). This source can

easily supply the power to maintain the Sun at its current luminosity for billions of

years. (D08)

Understand why you need high temperatures. The H atoms must slam

together hard enough to overcome the electrostatic repulsion of the protons.

In the Sun, this means the temperature reaches 15 million K. (D08)

Mass is the one primary parameter that dictates all the other properties of a

star. On the Main Sequence, high mass stars are the ones with the highest

temperatures, the highest luminosities, the largest radii (but the radii are notthat much larger than the lower mass stars), and which live the shortest time.

Low mass stars are the coolest, the least luminous, the smallest in radius, and

the ones that live longest. (D08)

Understand how the mass-age relation for main sequence stars comes from the

main-sequence mass-luminosity relation. Since by Einsteins equation the total

energy of a star is proportional to its mass, luminosity is proportional to that total

energy divided by the star's lifetime, and mass and luminosity are related, we get

that the time a star spends on the main sequence is related to its mass. (D08)

The detailed form of the main sequence age-mass relation is not critical, but under-

stand that the most massive main sequence stars live for the shortest time. (D08)

The Suns main sequence lifetime is 10 Gyr(remember, 1 Gyr= 1 billionyears). Its

current age is 5 Gyr. (D08)

We combine this info in the Pleiades to estimate the clusters age. Understand howthis is done. The Pleiades are about 70 Myr(remember, 1 Myr= one millionyears)

old based on the relations in the text, about 100 Myrold using more detailed calcula-tions. (D08)

The hottest, most luminous, most massive star in the Pleiades is Al-cyone. It is definitely on the Main Sequence, and its luminosity is about 910 times greater

than the Suns. The Main-Sequence Mass-Luminosity relation tells us that its mass is

. Its lifetime is therefore that of Sun, or about 73 Myr(an


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abbreviation for Megayears, or 1 millionyr). This estimate is close to what more precise

calculations gives for the age of the Pleiades, around 100 Myr.Properties of the Milky Way: a band of light with irregularities that bisects the sky as

seen from Earth. Brightest towards Sagittarius. (D09)

For example, in the constellationAquilathe Eaglethe Milky Way

splits into two parallel bands of light. As we look Northward along the Milky Way, thesebands join into a single stream within the constellation Cygnus, the Swan. To the South, one

of the bands fades to invisibility while the other defines the main band of the Milky Way.

This split in the Milky Way is known as The Great Rift. We also note that in most parts of

the sky, the Milky Way is around 10-15 degrees wide, but in the constellation Sagittarius,

the faint outer light of the Milky Way expands to about twice that width. Even farther to

the Southin the constellation Crux, the Southern Crossone section of the Milky Way

appears to have been blotted out altogether. This inky hole, well known to sky-watchers in

the Southern Hemisphere, is called the Coal Sack. Many bright starsespecially numerous

blue onesappear to congregate near this portion of the Milky Way in the Southern He-misphere, most

notably between

the

constellations

Centaurus and

Vela


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We define the direction toward or away from the Galactic Poles as the z axis.

We define the direction outward from the Galactic Center as the R direction.

(D09)

The structure of the Galactic disk is consistent with an Exponential Density Law in

bothzand R. Know the basic form of this density law. You should understand and

be able to discuss the physical meanings of all the terms in these density laws. (D09)


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Butthere are some important differences. For one, the distance is now denoted by , the same

symbol we introduced earlier to denote the distance from the Galactic Center. The related

symbol, represents the distance of the Sun from the Galactic Center, 8.5 kpc. The terms

and have exactly the same meaning as before, but there is a new term, , known as

the Scale Length (notice the capitalization of the symbol). Unlike the scale height (lower

case), the scale length does nothave the index . That's because we didnt notice suchstrong evidence that the space densities of different types of stars declined at different

rates as we move outward from the Galactic Center (well, almost; well return to this pointmomentarily). Since the space density of (most) types of stars and (much of ) the ISM inthe Galactic Disk varies exponentially in both the directionperpendicular to the Diskand in the directionoutward from the Galactic Centerthe Galactic Disk represents anexample of what is known as an Exponential Disk. Most types of stars in the Galactic Disk

exhibit a scale length, , of about 3.5 kpc.

Scale height measures the thickness of the Galactic Disk and is different for

different types of stars. The scale height for young stars and gas/dust is smaller than

for other stars, meaning that these things stay closest, on average, to the mid-plane of

the Galactic Disk (that is, where z=0). (D09)Know that kpc = kilo-parsec= 1,000parsecs. (D09)

Scale length measures how concentrated stars and gas are with relation to the

center of the Galaxy. Most types of objects in the Galactic Disk have a scale length of

about 3.5 kpc, though the youngest stars and gas/dust have slightly different beha-vior in the outermost parts of the disk. (D09)

The densities of O and B stars, the youngest, most massive main-sequence

stars, behave in an even more complicated manner. Their numbers fluctuate wildly as we


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travel outward within the Galactic Disk. If we carefully map the distribution of these

starsor of regions of the Cold and Hot ISM that are related to star-forming regions such

as the Orion Nebulawe would find they trace out sweeping spiral patterns that appear to

emanate from near the Galactic Center. We shall encounter such Spiral Arms again when

we visit other galaxies similar to ours. For now, we simply note that these arms seem to be

easiest to trace when we focus on the youngest stars or on star-forming regions within the

Galactic Disk. Older stars show much less enhancement near spiral arms, consistent withour observation that they obey a smooth Exponential Density Law.

The Sun is located 8.5 kpcfrom the Galactic Center. The Center itself is located in

the

direction of the constellation Sagittarius as seen from Earth. (D09)

Local stars appear to be standing still with respect to the Sun. But the shape of the

disk implies rotation. This means that the Sun and its neighboring stars are rotating

about the Galactic Center together. (D09)

By measuring Suns motion with respect to other stars and gas in the Galactic Disk,

we can conclude that the disk rotation velocity at the Sun is about 210 km/s. (D09)

The rotation velocity does notdrop significantly from the Sun as you move

further

outward from the Galactic Center. (D09)

Understand that a rotation curve is a plot of rotation velocity with distance from the

center of a galaxy (does not have to be the Milky Way). Be prepared to make draw a

rotation curve. (D09)


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Know how Newtons Universal Law of Gravity lets us estimate the Galaxys mass(that is, M=V^2circ R/G). The mass of the Galaxy interior to the location of the Sun

is 10^11 M(sun). (D09)


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Appreciate that the Galaxys rotation curve appears to be mostly flat, particularly at

large radius. (D09)

Why is this unusual? If all the mass is concentrated towards the Galactic Center (as

observed from visible matter), we'd expect the velocities to fall off in accordance to

Kepler's Third Law: Vcirc= Sqrt(GM/R)(as in Solar System). But this is notseen.(D09)

The most popular idea is that we need Dark Matter to produce a flat rotation

curve as observed. The visible stars alone are not sufficient. (D09)

The inner Disk obeys the same Exponential Density Law of the outer Disk. (D10)

Young stars and the ISM exhibit a more lumpy distribution than other types of ob-jects in the Disk, indicative of some large-scale spiral-like structures. In the inner

2-3 kpcof the Disk, young stars and the ISM are relatively rarer than other types of

objects in the Disk. (D10)

The Galactic Bulge resides in the inner Galaxy, sharing the same center as

the Galactic Disk. The Bulge has little gas, mostly old stars, and a range in

chemical abundance. The distribution of stars obeys a Power-Law Density

Law which is more centrally-concentrated than the Exponential Density Law

of the Disk. (D10)

For R is greater than 1.5 kpc from the Galactic Centerthat is, beyond the core radius of the Bulgethe density of Bulge stars drops rapidly as wemove away from the Galactic Center. At the location of the Sun, the Bulge contributes at

most 2-3% of the stars we see in Earths sky. But inside 1.5 kpc, Bulge stars become muchmore numerous compared to the number of stars in the Disk. At our current location 1 kpc

from the Galactic Centerwell inside the core radius of the Bulgethe Bulge contributes

mostof the stars visible in this Alien Sky. Thats why the Diskin particular, our view of

the Milky Wayseems to have disappeared. Of course, it hasnt, really. The Bulge and theDisk coexist here. Its simply much harder to discern the Disk among the more numerous

stars of the Bulge near the Galactic Center.

General properties of the Galactic Center: The Galactic Center harbors young

stars,

massive, young star clusters, and a complex ISM that has cold, warm, hot and coron-

al components. (D10)

Unique features of the Galactic Center: Massive, very young clusters, unusual

forms of radiation including synchrotron (from electrons moving in magnetic fields),

annihilation radiation (from matter-antimatter interactions), very hot thermal

radiation. Know what IRS 16 and Sgr A* are (both are in Galactic Center). (D10)

We can now see that IRS 16 is


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yet another massive star cluster composed of young, blue, very luminous stars. It is the

most luminous cluster we see here, and we soon appreciate that it is also the most unusual.

Long, thin filaments of gas extend manypc around it. Some of these filaments glow with an

eerie grayish-blue light unlike any gas weve encountered so far. The bluecontinuous spec-trum of this light arises from radiation emitted by electrons spinning in magnetic fieldsa

form of light known as synchrotron radiation (the long streamers of gas visible in Figure

10.9 also suggest the presence of large-scale magnetic fields here). The region around IRS16 also emits gamma-rays, the most energetic form of electromagnetic radiation (see Fig-ure 5.6 of Destination 5). Some of the gamma-rays are emitted as an emission line that cor-responds to what is ominously known as annihilation radiation17. This arises when elec-trons and their anti-matter partnerspositronsmeet and annihilate one another in aprocess that converts their combined mass entirely into energy18.

Evidence for central massive, compact object. About 5x10^6 M(sun)appears to be packed into a volume smaller than the Solar System at the

center of the star cluster IRS 16! (D10)

Stars located about 0.3pc from the cluster center the rotate at a speed of about 265 km/s about the cluster center.

At 0.1pc, the orbital speed is about 460 km/s. At 0.03pc, 840 km/s. As we probe even

closer, at a distance 0.003pc from the cluster center and a distance not much larger than

the solar system (!), the stars are moving at an astonishing 2,700 km/salmost 1% the

speed of light! The velocities appear to keep increasing the closer we get to the center of

IRS 16. The apparent center of all this motion coincides with a strong source of radio emis-sion known as Sgr A* (pronounced Sagittarius A-star or Sag A-star). Theres somethingvery weird here.

Is this a black hole? Know the relation for the Schwarzschild radius of a black hole:

RS=2GMBH/c^2 . For the Galactic Center black hole, is about 16 times the size ofthe Sun. So, yes, this is all consistent with a central black hole. (D10)

Location of most globular clusters: The congregate around Sagittariusthe

location

where we found the Galactic Center. (D11)

Properties of globular clusters such as M92: compact (only 30pcin radius) but con-tain 100,000 to 1 million stars. Low abundance of heavy elements in the stars. No

gas or dust. (D11)

Be able to plot M92s HR diagram. Short main sequence plus lots of red giants. The

top end of the main sequence contains stars that are less luminous than the Sun.

Thus, the cluster is olderabout 14 Gyrthan the Suns predicted total lifetime.This is the same reasoning as for the Pleiades, so understand it well. (D11)


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Stars can be thought of as having a core and surrounding envelope which react

quite differently as evolution proceeds. (D11)

Know the evolution of low-mass stars such as those in M92. Evolution starts when

H is exhausted in the stars core while on or near the main sequence. The starscore contracts and heats up from gravitational energy. The envelope reacts by ex-panding. The star becomes a red giant. (D11)

Electron degeneracy sets in. Understand what this is in rough terms. It is due to the

nature of the electrons and notdue to the electric repulsion force. Degeneracy pro-duces apressure that (a) can halt the core collapse, and (b) does not depend on tem-perature. (D11)

As low-energy levels are filled, only higher and higher energy states are availa-


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ble. This overcrowding is known as electron degeneracy21 and it produces a pressure

degeneracy pressurethat begins to resist gravity and slows the cores contraction22. But

only in the densest parts of the core. Outside the central degenerate zone, material contin-ues to fall in, piling onto the core and heating it up even further

Whats really happening in the core

of the star is that the electrons must populate higher and higher energy levels to avoidbecoming dege-nerate withthat is, having the same energy asother electrons in the core.

Know the details of evolution up to the Helium (He) flash. The core gets hot enough

for He fusion while still degenerate. When it finally expands, it is way too hot for its

pressure and the core expands explosively. Only the presence of the stellar

envelopethe outer layerscontains the blast. (D11)

With the sudden rise in temperature, He fusion commences throughout the core almost

simultaneously. The rapid addition of energy causes the core to become even hotter. If the

core were not in its bizarre degenerate state, it would expand, cool off, and reach a stable

configuration. But it cant. Instead, it simply gets hotter, causing the rate of energy pro-duction from He fusion to skyrocket. And the core becomes hotter still. It is a violently

runaway situation and, soon, so much energy is produced that the core cannot get rid of it

Subsequent evolution is a stable configuration where He fuses in the core

into C and O. Still a red giant. (D11)

What happens when He runs out? Core never gets hot enough for full Carbon

fusion.

There just is not enough gravitational energy. Instead, the core reaches a terminal

state where electron degeneracy pressure equals the inward pull of gravity. (D11)

Mass loss causes the envelope to evaporate away, leaving the inert core.

(D11)

White dwarfs are the remnants of cores of low-mass stars. All they do is cool down

with time. Know where the WDs lie in the HR diagram! Know that white dwarfs are

small! About the size of the Earth, yet still near 1 M (sun). (D11)The shape of M92 is not a disk. The orbits of the stars are random in size, shape and

orientation. Yet it is stable. This is another way to have a stable stellar system other

than a disk. (D11)

Nature of the Magellanic Clouds: these are independent dwarf galaxies. Satellites of

the Milky Way, but separate from our Galaxy. (D12)

For stars less massive than 8 M(sun) , evolution is as above. We call thatlow-

mass stellar evolution. Such stars all evolve into white dwarfs eventually. (D12)

White dwarfs have to be less massive than 1.4 M (sun) more massive and


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electron degeneracy cannot support them. This is the Chandrasekhar limit.

Mass loss is requiredfor the most massive low-mass stars for them to becomewhite dwarfs. (D12)

Stars above 8 M (sun) follow a different sequence of events characteristic of

high-mass stellar evolution. The key point is that the final result of thisevolution is that stars become something otherthan white dwarfs. (D12)

Know that the big difference in high mass evolution is that the core is always able

to start a new fusion reaction before it becomes electron degenerate. So, H runs out;

core contracts; He fusion starts; He runs out; core contracts; C fusion starts, etc. The

general process is more important than knowing the individual fusion steps. (D12)

Why is fusion of elements more massive than Iron fundamentally different than for

less massive nuclei. Know that for the smaller elements yougenerate energy from

fusion. For heavier elements, you consume energy if you try to fuse the nuclei. (D12)

Only source of energy left in the core is gravitational. Core collapses, fusion eatsup

the energy, core collapses even faster. Runaway situation. (D12)

Outward result of this: complicated, but likely a massive explosion. Such stars are

seen as supernovae (plural of supernova). Star may end up totally disrupted, as a

black hole or as a neutron star. (D12)

Nature of neutron stars: So dense that electrons and protons merge to form neu-trons. These neutrons can also exert a degeneracy pressure, but not until much

higher densities. These stars are only around 10 km in radius!

If remnant is more massive than about 3 m sun, no know force can stop gravity.

Stars

become black holes in this case. (D12)

Know the evidence for supernovae. SN1987A in the LMC is one example. Total

ener-gy similar to what youd expect of a contracted core. As bright or brighter than allother stars in a Galaxy for a few days or weeks. (D12)

Understand why the core of the exploded star should be rotating very fast and

have

a strong magnetic field. (D12)

Review and understand the basic model for how pulsars operate. The key ingre-dients include the strong magnetic field, the rotation, the offset of the magnetic and

rotation poles, and the infall of matter that can radiate synchrotron radiation into

beams that are seen as flashes to a distant observer. (D12)


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Why cant white dwarfs be pulsars? Too big and too low-density to rotate as fast aspulsars are observed. (D12)

Pulsars found in centers of expanding supernova shells. Strong evidence

connectingthem to supernova explosions. Know how this story relates to the properties of the

Crab nebula and its pulsar. (D12)


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How can we find stellar-mass black holes? Understand the basic role of binary

sys-tems in this. Know that LMC X-3 appears to be an example of a black hole in a bi-nary system. (D12)

Know the role of an accretion disk in making the matter falling into a black hole

very

hot and very luminous (again, know how LMC X-3 illustrates this). (D12)

The empty (as far as stars are concerned) nature of the Galactic Halo. What is the

Galactic Halo? Where is it located and how is it distributed relative to the Galactic

Disk and Bulge (same center, Power-Law density, more extended, approximately

spherical in shape)?

Appreciate that the typical star of the Galactic Halo has much fewer heavy

elements

(those other than H and He) compared to the Sun, by factors of tens, hundreds, or

even thousands or more. (D13)

What are dwarf spheroidal galaxies, dwarf irregular galaxies, and (generally)

satel-lite galaxies and where are they found? Review the properties dwarf spheroidal ga-laxies (such as the Sculptor Dwarf) and dwarf irregular galaxies. (D13)these galaxies are certainly tiny by the standards of

larger systems such as our Galaxy. The stars in Sculptor, for example, extend over at most a

couple ofkpc, much smaller than our Galaxy, or even the LMC (see Figure 13.3). And

though it contains a respectable number of starsaround 5-10 million, significantly more

than M 92it is still very much a dwarf when compared to the population of a trillion or so

stars found in the Galaxy. The shape of Sculptornearly circular in the skyalso suggests

that it is more-or-less spherical in shape. So the dwarf and spheroidal parts of the namemake sense. We shall see later that the reason these objects deserve to be called galaxies is

a bit more complicated.

What is velocity dispersion? How do we use it to measure masses? In this respect,

understand the Virial Theorems role in measuring galaxy masses. (D13)

Know how the mass of the Milky Way can be measured at very large distances from


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the Galactic Center using satellite galaxies and the Virial Theorem. What does this

say about the Dark Matter content of the Halo? (D13)

Mass-to-light ratio. Know it is usually expressed in solar units. What is the mass-

to-

light ratio for the Sun (ANSWER: 1 M(sun)/1 L(sun) = 1). What is the mass-to-lightratio of

the Milky Way? Know thatlarge values of mass-to-light imply Dark Matter and un-derstand why. (D13)

Be aware that the Coronal component of the ISM pervades the Galactic Halo and

that the particles in this gas have the same characteristic velocity dispersion seen

for the satellite galaxies in the Halo. (D13)

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Astronomy Study Guide