based on observations of the 21-centimeter line, a new system of galactic coordinates was adopted with the origin at the galactic center in Sagittarius at R.A. 17h 42.4m, Dec. -28° 55' (epoch 1950). The new system is designated by a superior Roman numeral II (i.e., bII, lII) and the old system by a superior Roman numeral I. Galactic coordinates are used to specify the position of objects in the Milky Way as observed from the Earth.

Figure 08-01h Galactic Co- ordinates [view large image]

Star Magnitudes⁴

The apparent magnitude m is a measure of the amount of light arriving on Earth from a star or other celestial objects. The brighter object has a smaller apparent magnitude. This curious property of "less is more" is a result of the work of Hipparchus (c130 BC) who classified stars into six magnitudes. The ‘first magnitude stars’ were the brightest in the heavens, which included Capella (alpha Aurigae), Sirius (alpha Canis Majoris), Vega (alpha Lyrae) and the like. Hipparchus categorized the other stars according to their relative brightness, down to the dimmest that the naked eye could see, which were called sixth magnitude.

Sky Charts

		latitude 10 to 15 degrees north or south of this) - suitable for viewing in the United States, Canada, Europe, and Japan. The Southern Hemisphere charts usually depict the sky from a latitude of 35oS. These are for use in the South Pacific, Australia, New Zealand, South America, and southern Africa.
Figure 08-01f Sky Chart, North [view large image]	Figure 08-01g Sky Chart, South [view large image]

		Figure 08-01h shows the entire Northern sky in late January. An one piece sky chart plots the sky with the North Pole at its center (see Figure 08-01i). An oval opening in an overlapping disc represents the heavens as seen from a certain latitude, e.g., 45oN. The time and date of viewing can be selected by rotating the disc around the center. This particular view is set at 22:00 h, January 20. The transparent cursor scale (from -50o to 90o) is used to calculate the declination of celestial objects. The right ascension is marked at the outer-most circle.
Figure 08-01h Sky Chart [view large image]	Figure 08-01i Star Finder [view large image]

		Sky charts computer software is perhaps the most versatile. It allows the user to specify any location and date/time as shown in Figure 08-01j, which displays a chart tailored to "Sample" with latitude 42o and longitude 270o at 22:00 h on January 20, 2004. The detail of objects can be adjusted by the user. It can display the ecliptic as well as the Galactic equator. The coordinate grids can be numbered. Outline of the Milky Way can be plotted on the chart. The name of each object (if not
Figure 08-01j Sky Chart, Computer Generated [view large image]	Figure 08-01k Sky Chart, Horizon [view large image]	already shown) can be obtained by clicking the pointer (such as NGC2539 in the sample chart). Figure 08-01k shows the same chart in horizon coordinate facing North. This free sky charts software is offered by Cartes du Ciel.

First Star⁵

The first stars appeared about 100 million years after the Big Bang. It formed in the denser regions of gas inside the protogalaxies. The protogalaxies in turn would be most likely located at the nodes of the filaments in the large structure. Since there was little metals present in the early universe, the production of nuclear energy is less efficient, the first stars were able to assemble more mass and still maintained a stable structure. The limit should be no more than 1000 solar mass. Figure 08-02 compares the calculated characteristics of the first stars with those for the Sun. The most iron-deficient star HE0107-5240 was discovered in late 2002. This primitive star has a measured abundance of iron less than 1/200000 that of the Sun. It seems to have formed shortly after the Big Bang.

Figure 08-02 First Stars [view large image]

Hertzspung-Russell (HR) Diagram^6,7,8

The Hertzspung-Russell diagram was introduced in the 1910s to plot a point representing a star with a certain values of luminosity and surface temperature as shown in Figure 08-03.

It soon became apparent that the HR diagram is not randomly populated, but that stars preferentially fall into certain regions. The majority of them occupy a strip called main sequence as depicted by the red line in Figure 08-03. This just reflects the fact that all the stars spend most of their time burning off hydrogen fuel with a constant luminosity and surface temperature. There are variable stars, which change their brightness, color, spectrum and other characteristics in the order of hours to few hundred days. They appear as a transient phenomenon in the HR diagram. The evolutionary track of an individual star with a given mass can be traced in the HR diagram as shown in Figure 08-04, 08-05, and 08-06. The age of the globular clusters can be estimated from the branch-off point in the HR diagram. The HR diagram comes with many variations since luminosity and temperature are related to other quantities. For example, in the vertical axis on the right of Figure 08-03, the label is Absolution Magnitude. Since different temperature of the stars generate different set of absorption lines, this scale can be translated into spectral types such as O, B, A, F G, K, and M as shown in the horizontal axis at the bottom of Figure 08-03. Each spectral type is further subdivided into numerals, e.g., G2 for the Sun, which is located in the middle of the main sequence. Sometimes the horizontal axis is labelled by the colour index B - V or mB - mV, i.e., magnitude in blue - magnitude in visual

Figure 08-03 HR Diagram

(yellow) with blue objects in the left and yellow objects to the right. It is a directly measurable quantity from photometer with colour filters.

Figure 08-04 is another version of the HR diagram. It shows the progression of mass along the main sequence, and the pre-main-sequence evolutionary track for different masses from 0.5 to 15 Msun. The mass of a star determines all its properties in the HR diagram. The observed upper limit for stellar mass is about 60 Msun, the star becomes unstable beyond this limit. The heavy star will be an O type located at the upper left corner of the main sequence. The observed lower limit is about 0.05 Msun occupying a position down in the lower right corner of the main sequence as M type stars. Protostar below this limit is not able to ignite hydrogen burning and becomes a brown dwarf. The contraction time to the main sequence is plotted as contours in range from 104 to 107 years. The pre-main-sequence stars begin their life as interstellar clouds (with a size of several light years), which

Figure 08-04 HR Pre-Main-Sequence [view large image]

collapse under the influence of gravity to a stage called T Tauri stars before settling down onto the main sequence (see Figure 08-07). In tabulation form, Table 08-01 lists some characteristics of main-sequence stars as a function of mass.

Table 08-01 Characteristics of Main-Sequence Stars

Stellar Evolution⁹

		The structure of a star is maintained in equilibrium via the balance of the gravitational attraction with a tendency to contract and the thermal pressure with a tendency to expand. When the star has exhausted its hydrogen fuel, it cools off and collapses until the pressure has risen sufficiently to ignite helium and other types of nuclear burning. This process of re-igniting fuel burning with different nuclear species is represented by the zigzag paths in Figure 08-05b. The variation of stellar radius can be traced with the curves
Figure 08-05a HR Post-Main-Sequence, Sun [view large image]	Figure 08-05b Post-Main-Sequence [view large image]	crisscrossing the loci of constant radius. It shows that the maximum extent can be 100 Rsun or more and hence the names of giant, and supergiant.

These stars have evolved to the terminal phase as shown in Figure 08-05a and 08-05b. Eventually, all the available fuels are consumed, there is no more source to supply the thermal pressure necessary to stop further collapsing. However, for star with mass smaller than 5 Msun the degeneracy pressure of the electrons lends its support to stop complete collapse and it forms a white dwarf with remnant less than 1.4 Msun. For star with mass in between 5 and 15 Msun the protons combine with electrons to form neutrons under the tremendous pressure. Then the degeneracy pressure of the neutrons can provide support up to 3 Msun (of the remnant) and it becomes a neutron star (or pulsar - spinning neutron

Figure 08-06 Stellar Evolution [view large image]

star). For star with mass greater than 15 Msun, no amount of support is sufficient to stop the collapse to a black hole. Figure 08-05a portrays the post-main-sequence evolutionary track for the Sun in details.

Variable Stars^10,11

The changes of brightness in (intrinsic) variable stars indicate that something is happening to them. The cause must be truly physical, because changes of color, spectrum, magnetic field, and radial velocity accompany the changes in light. Some variable stars display a more or less regular rhythm, or period, and are known as the periodic variables. Others, only roughly periodic, are know as the cyclic or semiregular variables, and then there are stars whose variations show no obvious pattern, the irregular variables. Far more spectacular are the changes shown by some stars that undergo some sort of explosion - the so-called cataclysmic variables. These include the novae (new stars), and the

Figure 08-07 HR, Variable Stars [view large image]

supernovae, which undergo the largest changes and attain the greatest luminosities recorded for any variable or nonvariable stars. Figure 08-07 shows the various types of variable stars in the HR diagram. Table 08-02 summarizes the properties of all the types.

Table 08-02 Types of Intrinsic Variables

Red Giants

		high and the total luminosity is also high. Since the average luminosity is low, the star appears red. This big red star is a red giant. Figure 08-08a is a schematic diagram depicting this initial phase of a red giant with a (main-sequence) mass of 1 Msun.
Figure 08-08a Red Giant 1 [view large image]	Figure 08-08b Red Giant 2 [view large image]

Supergiants

an even larger volume. The much brighter, but still reddened star is called a red supergiant (it is blue supergiants for O, B stars). Some of these supergiants are unstable and form the very important Cepheid variables (as standard candles for determining distance to galaxies). In their final stages, supergiants will explode into supernovae. The collapse of these massive stars may produce a neutron star or a black hole.

Figure 08-09 Supergiant [view large image]

Planetary Nebulae¹² and White Dwarfs

			When a star with mass less than 5 Msun reaches the end of its life, it casts off its gaseous outer-envelope at high speed (1000-2000 km/sec) and leaves behind a planetary nebula as shown in Figure 08-10 (click on image to obtain larger view). The one on the left is the side view in bipolar appearance, while the Helix Nebula in
Figure 08-10	Planetary Nebulae		the middle is the end-on view. The right image shows ten different planetary nebulae in a

The shrinking core of a low mass star cannot contract far enough to raise its temperature high enough for carbon burning to commence. No further thermonuclear energy generation is possible. The shrunken remnant becomes a white dwarf with a size comparable to the Earth and is composed predominantly of carbon and oxygen. The structure is supported by electron degeneracy pressure. The matter in the white dwarf is packed very tight (up to 3x107 gm/cm3 in the core) in layers (see Figure 08-11). Under such conditions of high density the atomic electrons are no longer attached to individual nuclei. The electrons are ionized and form an electron gas. In the absence of nuclear energy sources, the star cools down, but, because degeneracy pressure is unaffected by the decreasing temperature, the cooling white dwarf does not contract. It instead continues to cool and to fade away gradually. Over ten billions years or more it will

Figure 08-11 White Dwarf [view large image]

eventually evolve to become a cold dark body called a black dwarf. This process takes so long that there has not been enough time since the origin of the universe for any star to reach the black dwarf state. Table 08-03 compares the properties of the Sun, the Earth, and Sirius B - a typical white dwarf.

Table 08-03 Properties of Sun, Earth, and a Typical White Dwarf

Novae

A nova can suddenly flares up in brilliance, by a factor of up to about one million, and then, over the next few months or years, fades back more or less to its original luminosity. It appears to be an event that occurs on the surface of a white dwarf in a close binary system when material flowing from the companion star onto the white dwarf's surface undergoes thermonuclear reactions, which trigger a violent explosion. The detonation blows surface material into space, leaving the underlying white dwarf unscathed. If the mass of the white dwarf is close to the Chandrasekhar limit of 1.4 Msun, hydrogen dragged from its companion burns to helium on its surface. The resulting increase in mass eventually triggers a Type Ia supernova explosion that completely destroys the white dwarf. Figure 08-12 is a recurrent nova in the constellation of Pyxis. It is surrounded by more than 2000 gaseous blobs packed into an area about 1 light year across.

Figure 08-12 Nova [view

large image]

Supernovae¹³, Neutron Stars¹⁴, and Pulsars

			When stars with mass greater than 5 Msun exhaust their nuclear fuel, they collapse suddenly in a process called supernova explosion, which flings off huge amount of heavy elements into interstellar space. Super- novae can be classified into two types. Their characteristics are listed in Table 08-04
Figure 08-13 Crab Nebula, Visible Light [view large image]	Figure 08-14 Crab Nebula, Composite [view large image]	Figure 08-15 Crab Nebula, X-ray [view large image]	below. Figures 08-13, 08-14, and 08-15 are images of the Crab Nebula taken at different wavelength. The Crab Nebula is a supernova remnant after an explosion at 1054 AD.

Table 08-04 Types of Supernova

		When the core of the star collapses to a density of about 1014 gm/cm3 (of the order of that in the nuclei) it causes the atomic electrons to combine with the nuclear protons in the electron capture reaction as shown in Figure 08-16. This is the point where gravitational forces have won out over the pressure supplied by nuclear matter. Figure 08-17 shows the structure of a neutron star in several layers over a depth of ~ 10 km:
Figure 08-16 Electron Capture [view large image]	Figure 08-17 Neutron Star, Structure [view large image]

• Surface - There is an atmosphere of several centimeters thick. The ionized gas is highly compressed with a density gradually rising to 10³ gm/cm³. It may be in a condensed state (liquid or solid) in the presence of strong magnetic field (~ 10¹² gauss), which strongly affects the structure of atoms. The temperature at the surface is about 10^{7 o}K.
• Outer Crust (Envelope) - At the top of the crust, the nuclei are mostly iron 56 and lighter elements in lattice (solid) form, but deeper down the pressure is high enough that the equilibrium atomic weights rise, elements with Z=40, A=120 will form eventually. At densities of 10⁶ gm/cm³ the electrons become degenerate, meaning that electrical and thermal conductivities are huge because the electrons can travel great distances before interacting.
• Inner Crust and Outer Core - The "neutron drip" starts at a depth with a density around 4x10¹¹ gm/cm³. At this point, it becomes energetically favorable for neutrons to float out of the nuclei and move freely around, so the neutrons "drip" out. They pair up to form bosons, which compose the neutron superfluid. Even further down, there are mainly free neutrons, with a 5%-10% sprinkling of protons and electrons. As the density increases, a sequence dubbed the "pasta-antipasta" is in place (see Figure 08-17). At relatively low (about 10¹² gm/cm³) densities, the nucleons are spread out like meatballs that are relatively far from each other. At higher densities, the nucleons merge to form spaghetti-like strands, and at even higher densities the nucleons look like sheets (such as lasagna). Increasing the density further brings a reversal of the above sequence, where the nucleons change to holes (anti-particles) forming (in order of increasing density) anti-lasagna, anti-spaghetti, and anti-meatballs (also called Swiss cheese). Meanwhile the protons and electrons respectively couple into Cooper pairs to form the superconductive material in the outer core.
• Inner Core - When the density exceeds the nuclear density 3x10¹⁴ gm/cm³ by a factor of 2 or 3, really exotic elementary particles might be able to form, like pion condensates, lambda hyperons, delta isobars, and quark-gluon plasmas etc.

attached to the curve show what is happening to the microscopic matter as it is compressed from low densities to high. At normal densities, cold, dead matter is composed of iron. As the iron is squeezed from its normal density of 7.6 gm/cm3 up toward 100, then 1000 gm/cm3, the iron resists by the same means as a rock resists compression - the degeneracy-like motions of electrons. When the density has reached 100000 gm/cm3, the electron's degeneracy pressure completely overwhelm the electric forces with which the nuclei pull on the electrons. The electrons no longer congregate around the iron nuclei; they completely ignore the nuclei and form the electron gas moving around freely. At a density of about 107 gm/cm3 the motion of the electrons become relativistic (near the speed of light).

Figure 08-18 Equation of State [view large image]

The transition from white dwarf matter to neutron star matter begins at a density of 4x10¹¹ gm/cm³, according to theoretical calculation. It shows several phases to the transition:


• In the first phase: The electrons begin to be squeezed into the atomic nuclei, and the nuclei's protons absorb them to form neutrons. The matter, having thereby lost some of its pressure-sustaining electrons, suddenly becomes much less resistant to compression; this causes the sharp drop in the diagram.
• As the atomic nuclei become more and more bloated with neutrons, thereby triggering the second phase: Neutrons begin to drip out of the nuclei and into the space between them, alongside the few remaining electrons. These dripped-out neutrons create the degeneracy pressure of their own and start to resist further compression.
• In the third phase: At densities between about 10¹² and 4x10¹² gm/cm³, each neutron-bloated nucleus completely disintegrates, i.e., breaks up into individual neutrons, forming the neutron gas plus a tiny smattering of electrons and protons. From there on upward in density, the behaviour of the curve (dash line) takes on the Oppenheimer-Volkoff form for the non-interacting neutron gas. The solid curve is computed in the 1990s with nuclear interaction. A limit for the maximum mass of a neutron star can be obtained from such curve. It is called the Oppenheimer-Volkoff mass, and has been recalculated many times since. Because the exact properties of neutron gas is unknown the limit is usually said to be about 2 to 3 solar masses, and generally stays well below 4 or 5.

		to 1.6x10-6 sec. Only a tiny, dense neutron star could spin this fast; larger stars (including white dwarfs) would be torn to shreds by centrifugal force. The magnetic field at the surface of a collapsing star grows in strength as the surface area of the star decreases (decreases in radius / increases in magnetic field strength ~ 1 / 105). The magnetic field strengths at the surfaces of neutron stars are likely to be between 108 and 1013 gauss. In some extreme examples (known as magnetars) they may be as high as 1015 gauss. Figure 08-19 shows the pulsar signal from the neutron star inside the Crab Nebula
Figure 08-19 Pulsar Signal [view large image]	Figure 08-20 Pulsar Model [view large image]	with a period of 0.03 sec in the X-ray range.

Stellar Black Holes

Most black holes are said to be stellar: formed from stars. It is estimated that the Milky Way contains 10 million of these black holes. Their mass can be 10 times that of the sun and the radius of event horizon can be a few kilometers. Because not even light can escape from inside the event horizon, it is hard to detect black holes. Astronomers get around this problem by indirect observations on some signatures, which are peculiar to a black hole. It usually involves the interaction of the black hole with its environment, e.g., a companion star. Figure 08-21 is a model of a stellar black hole drawing material (the accretion stream) from the companion star. The accretion stream forms an accretion disc before finally spiraling into the black hole and generates bursts of X-rays.

Figure 08-21 Blackhole Model [view large image]

The observational techniques for identifying stellar black holes:


• Eclipsing Binary - Eclipsing binary stars are just one type of variable stars known as extrinsic variables. They are a special group of spectroscopic binaries. These stars appear as a single point of light to an observer, but based on its brightness variation and spectroscopic observations we can say for certain that the single point of light is actually two stars in close orbit around one another. The variations in light intensity from eclipsing binary stars are caused by one star passing in front of the other relative to an observer. A brightness versus time (or phase) plot for a variable star is know as light curve. In addition to the measurement of stellar masses, the light curves of eclipsing binaries give much information about the physical characteristics of the stars that compose the system. It points to the presence of a black hole if one of the star is small, invisible and has a mass greater than 3 M_sun.
• X-ray Binary¹⁵ - X-ray observations, coupled with optical identifications established that the bright X-ray sources in the Milky Way are binary systems containing a neutron star or black hole orbiting around a companion star. If the companion star is very young and massive, the system is called a High Mass X-ray Binary. These high mass O or B stars usually have an intense wind that is easily captured by the neutron star or black hole to release X-rays. Such is the case for the most famous X-ray binary, the black hole system Cygnus X-1, where a black hole with a mass of 10 M_sun orbits an O star called HD226868 (see Figure 08-22).
• Soft X-ray Transients - Soft X-ray transients (SXTs, also know as X-ray Novae) belong to a special class of X-ray binaries; they typically brighten by many orders of magnitude quickly, and decay exponentially over the next several months. SXTs probably experience such outbursts once every few decades. In quiescence, the mass-donor can be studied in detail, without the complication due to accretion. Typical orbital period is 5-20 hrs and the secondary are often low mass main sequence stars, which can shred material to the black holes only when they are close to each other. Recent theoretical work indicates that a black hole system with "advective accretion flows" (ADAFs - energy transferred as heat instead of radiation) would appear much darker than a similar neutron star system, because the energy would disappear into the black hole instead of transforming into radiation by the neutron star. Observations of V404 Cyg (see the animation in Figure 08-23) have yielded a spectrum much like an ADAF onto a black hole. This star seems to be swallowing nearly hundred times as much energy as it radiates, and the only way this can happen is if the star is a true black hole.
• Micro-quasar¹⁶ - Figure 08-24 is a series of radio images for GRS1915, which is a "Hard X-ray Transient" source probably associated with a 33 M_sun black hole and a high mass companion star. As the gas plunges into the black hole, the bubbles are formed from excessive matter moving along the rotational axis. It ejects one plasma bubble almost directly toward the line of sight at 90% the speed of light, and the other moving away. This kind of stellar black hole is also known as micro-quasar because it mimics, on a smaller scale, many of the phenomena seen in quasar. GRS1915

			is probably the largest stellar black hole discovered; while the X-ray source GRO J0422+32 near V518 Persei seems to be the smallest with a mass of 3 to 5 Msun.
Figure 08-22 Cygnus X-1 [view large image]	Figure 08-23 V404 Cyg	Figure 08-24 GRS1915 [view large image]

Table 08-05 End of Stars

Stellar Models¹⁷

In most cases, the density, the temperature, and the chemical composition of a star change appreciably only over very long time intervals. For the Sun, only 1% of the hydrogen is depleted and converted into helium in one billion years . Thus the change induced by nuclear fuel depletion is entirely negligible. A static stellar model is appropriate for the Sun and most of the main sequence stars. Time does not appear in any equation under this circumstance. Whether it is static or dynamic, the stellar structure is governed by five basic equations. In mathematical terms, they are a set of inter-dependent differential equations (see Figure 08-25). A verbal description is given below for simulating the structure of a main sequence star.

Figure 08-25 Stellar Model [view large image]

• The equation of hydrostatic equilibrium - it is essentially the balance between the gaseous pressure and gravity as a function of the distance from the center of the star. An additional term to describe the acceleration of a layer (within the star) is required if it undergoes an expansion/contraction phase.
• The equation of mass - this equation calculates the mass within a certain distance from the center of the star.
• The equation of conservation of energy - this equation governs the generation of energy (luminosity) from the nuclear fuel and gravitation as a function of the distance from the center of the star. It is applicable to the core only as indicated in Figure 07-03. In the pre-main-sequence phase, nuclear fuel would not be available; only the gravitational energy is converted to heat as the protostar contracts. In the post-main-sequence phase, the nuclear energy production rate would become more sensitive to the progress of time.
• The equation of radiative transport - it describes temperature variation related to the propagation of the luminosity in the radiative zone of the star as shown in Figure 07-03.
• The equation of convective transport - it describes temperature variation related to the change of pressure in the convective zone of the star as shown in Figure 07-03.



In addition to these equations which characterize general conditions, there are three explicit relations to describe more specifically the behavior of the interior gases.


• The equation of state - this is a formula to describe the relationship between the pressure, the density, the temperature, and the composition of the gases.
• The equation for the absorption coefficient - this is a formula to describe the opacity of the gases.
• The equation for energy generation - this is a formula to determine the energy production rate by the nuclear fuel and gravity.

References:

1. Constellations, a List of the Eighty Eight -- http://www.physics.csbsju.edu/astro/sky/constellations.html
2. Constellations, Details -- http://www.dibonsmith.com/stars.htm
3. Constellations and Stars -- http://www.astro.wisc.edu/~dolan/constellations/
4. Stellar Magnitudes -- http://cobalt.golden.net/~kwastro/Stellar%20Magnitude%20System.htm
5. First Star, Computer Simulation -- http://www.space.com/scienceastronomy/first_star_011115.html
6. Hertzspung-Russell Diagram -- http://zebu.uoregon.edu/~soper/Stars/hrdiagram.html
7. Hertzspung-Russell Diagram, Globular Cluster -- http://www.dur.ac.uk/ian.smail/gcCm/gcCm_intro.html
8. Hertzspung-Russell Diagram, Variable Stars -- http://www.astro.wesleyan.edu/~anna/Astro211/0411a.html
9. Stellar Evolution -- http://www.tim-thompson.com/hr.html
10. Variable Stars -- http://www.astro.utoronto.ca/~percy/info.htm
11. Variable Stars, more details -- http://www.astro.wesleyan.edu/~anna/Astro211/0411a.html
12. Ends of Stars -- http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit3/extreme.html
13. Supernova, Crab Nebula -- http://www.obspm.fr/messier/m/m001.html
14. Neutron Stars -- http://www.astro.umd.edu/~miller/nstar.html
15. X-ray Binaries - http://lheawww.gsfc.nasa.gov/users/white/xrb/xrb.html
16. Micro-quasar -- http://www.gsfc.nasa.gov/gsfc/service/gallery/fact_sheets/general/1997/97-07.htm
17. Stellar Model -- http://www.physics.uq.edu.au/people/ross/ph3080/extra/ulrich2.pdf

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