galactic center, 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 08-01i Sky Chart, North [view large image]	Figure 08-01j Sky Chart, South [view large image]

		Figure 08-01k 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 08-01l). 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 08-01k Sky Chart [view large image]	Figure 08-01l 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 08-01m, 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 08-01m Sky Chart, Computer Generated [view large image]	Figure 08-01n Sky Chart, Horizon [view large image]	already shown) can be obtained by clicking the pointer (such as NGC2539 in the sample chart). Figure 08-01n 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 08-02a 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 08-02a First Stars [view large image]

These oldest stars belong to the population III category opposing to the older population II objects in galactic halo and the young population I objects in galactic disk. It is not clear if the small trace of iron was generated within HE0107-5240 itself, or contaminated by materials from stars of later/earlier generations. Figure 08-02b compares the abundance of elements between the HE0107-5204 data (red circles) and those produced by the 25 Msun population III supernova model. Meanwhile, measurements of quasar absorption spectrum indicate that there is neutral hydrogen (not re-ionized) billion years after the Big Bang in contradiction to

Figure 08-02b HE0107-5240 [view large image]

the 100 million years derived from the observation of first star. Perhaps reionization was a slow process, which only gradually encompassed the whole universe. Further study is required to resolve the discrepancy.

Figure 08-02c presents the images of a portion of sky in the Hubble Deep Field North at two different infrared wavelengths, 3.6 m and 4.5 m, including an overlapping region as shown. The black pixels are bright sources masked off leaving extended fuzzy blobs glowing in the background. It is claimed that these could be fluctuations, due to nascent cosmic structure, in a bright pregalactic infrared background. The brighter, uniform, non-fluctuating component of the background is

Figure 08-02c First Stars Signatures as Infrared Blobs [view large image]

not directly detectable in these data, because it cannot be distinguished from other sources of noise and emission. In short, these puffy blobs are just the signatures of the early stars (not the real thing). See "Angular-Size Redshift Relation" for an explanation of the large angular size of the blobs.

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.

The HR diagram comes with many variations since luminosity and temperature are related to other quantities. For example, luminosity is related to the Absolution Magnitude; and 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 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 (yellow). It is a directly measurable quantity from photometer with colour filters.

Figure 08-03 HR Diagram [view large image]

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 collapse under the influence of gravity

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

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 08-05a. The variation of stellar radius can be traced with the curves 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

Figure 08-05a Post-Main-Sequence [view large image]

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 star). For star with mass greater than 15 Msun, no amount of support is sufficient to stop the collapse to a black hole. Figure 08-05b portrays the post-main-sequence evolutionary track for the Sun in details. While Figure 08-05c shows the post main-
Figure 08-05b HR Post-Main-Sequence [view large image]	Figure 08-05c HR Post-Main-Sequence, 3 Msun [view large image]	sequence evolution of a three solar mass star with metallic abundance Z = 0.02.

Figure 08-05a depicts the evolutionary tracks for stars with mass ranging from 0.3 - 30 Msun. The atomic element at each turning point indicates the beginning of nuclear burning for that particular species. Less massive stars don't have enough pressure to convert the elements all the way to irons. Only for stars with a mass of 30 Msun or more are able to complete the process of transforming silicons to irons (see top curve in Figure 08-05a). Figure 08-05d illustrates four different paths of stellar evolution depending on the stellar mass.

Figure 08-05d Stellar Evolution [view large image]

Brown Dwarfs

astronomers discovered the first definite brown dwarf in 1995. Now, a new analysis of Hubble Space Telescope data implies our galaxy has almost as many of these failed stars as it does normal stars like the Sun. Several brown dwarfs probably lurk unseen within just 12 light-years of the Sun. This volume of space contains more than two dozen main sequence stars like the Sun — but only two known brown dwarfs. Both these brown dwarfs orbit the orange dwarf star Epsilon Indi, which is 11.8 light-years from Earth. They are the closest known brown dwarfs to the Sun. Figure 08-06 shows an artist's conception on the relative size of a hypothetical brown dwarf-planetary system and the solar system.

Figure 08-06 Brown Dwarf [view large image]

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 eventually evolve to become a cold dark

Figure 08-11 White Dwarf [view large image]

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 08-12a 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 08-12a Nova [view

large image]

Wolf-Rayet Stars

		development from the massive blue supergiant star, which is on the verge of blowing apart by the enormous radiation pressure. It occupies a region in the H-R diagram, where the surface temperature is 30,000oK and the luminosity is 106 times that for the Sun. It throws off so much material that the inside of the star generated by nuclear fusion such as helium, carbon, nitrogen and oxygen, become visible. It is designated as WN, WC, or WO stars depending on whether it is enriched in nitrogen, carbon or oxygen (Figure 08-12b). Eventually, the successive nuclear fusions turn the core into iron. Then it will go supernova and collapse to either a neutron
Figure 08-12b Wolf-Rayet Star [view large image]	Figure 08-12c Eta Carinae [view large image]	star or black hole in a period as short as a week. Eta Carinae is an example of such star on the way to its final destruction (Figure 08-12c).

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 08-13a Crab Nebula, Visible Light [view large image]	Figure 08-13b Crab Nebula, Composite [view large image]	Figure 08-13c Crab Nebula, X-ray [view large image]	Figures 08-13a, 08-13b, and 08-13c are images of the Crab Nebula taken at different wavelength. The Crab Nebula is a supernova remnant after an explosion at 1054 AD.

		exceptionally massive star, it is suspected that an instability (produced by high temperature and pressure) could convert light into matter-antimatter pairs. This would cause a pressure drop, making the star contract and igniting a runaway nuclear reaction to obliterate the stellar core. Thus, unlike other massive star supernovae, neither neutron star, nor black hole, would remain.
Figure 08-14 SN200GY [view large image]	Figure 08-15a GRB080319B [view large image]	The record was broken by the detection of a more powerful supernova cataloged as GRB080319B in March 2008. It occurred at a distance of 7.5 billion light

years from Earth with a luminosity of 2.5 million times more than the brightest known supernova. The fading afterglow was captured in both X-rays and Ultraviolet light (Figure 08-15a). The farthest gamma-ray burst (GRB090423) was detected by the Swift Observatory in April 2009. At redshift z = 8.2, it occurred only 630 million years after the Big Bang and could be one of those first stars turning into a black hole. The infrared afterglow was captured by the Gemini Observatory as shown in Figure 08-15b. Observation on another cosmic blast GRB090102 indicates that there is a

Figure 08-15b GRB090423

considerable polarization of the order 10% in the optical radiation (unusually high for astrophysical sources). The most logical - but not the only - explanation for the high degree of polarization is that the emitting source is permeated by large-scale, ordered magnetic fields, and that the emission is

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
Figure 08-16 Electron Capture [view large image]	Figure 08-17 Neutron Star, Structure [view large image]	neutron star in several layers over a depth of ~ 10 km:

• 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.

		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 08-19a shows the
Figure 08-19a Pulsar Signal [view large image]	Figure 08-19b Pulsar Model [large image]	pulsar signal from the neutron star inside the Crab Nebula with a period of 0.03 sec in the X-ray range.

		"starquakes" that occur when the outer crust (a solid crystalline layer of heavy nuclei) slips to the fluid interior or by some abruptly adjustments. Extremely violent starquakes are believed to be induced when the intense magnetic fields of magnetars fracture their crusts. The energy released in such events may be responsible for producing the intense bursts of gamma rays that characterize objects called soft gamma-ray repeaters. Figure 08-19c shows the evolution of a neutron star to either a pulsar or magnetar. Figure 08-19d is an artist’s
Figure 08-19c Magnetar Pathway [view large image]	Figure 08-19d Magnetar [large image]	impression of a magnetar. A powerful explosion just beneath a magnetar's surface has been detected by the XMM-Newton orbiting X-ray observatory in 2007.

Quark Stars

A quark star (Figure 08-20a) is a hypothetical type of star composed of quarks. This is an ultra-dense phase of matter that is theorized to form inside particularly massive neutron stars. It is theorized that when the neutronium, which makes up a neutron star is put under sufficient pressure due to the star's gravity, the individual neutrons break down and their constituent quarks form strange matter. The star then becomes known as a "strange star" or "quark star". Strange matter is composed of up quarks, down quarks and strange quarks bound to each other directly, in a similar manner to how neutronium is composed of neutrons; a strange star is essentially a single gigantic nucleon. A quark star lies between neutron stars and black holes in terms of both mass and density, and if sufficient additional matter is added to a strange star it will collapse into a black hole as well.

Figure 08-20a Quark Star [view large image]

1. The origin of gamma-ray bursts.
2. The energy requirement for the r-process, which make elements heavier than zinc.
3. The two velocity groups with ~125 km/sec and ~ 700 km/sec respectively for the neutron stars - they would be produced by either the one- or two-burst event when the explosions are off-centre.

		Baksan neutrino observatory (in the Caucasus). Their data are shown in Figure 08-20c. A research report in 2009 indicates that there is a significant time delay between the two bursts. It is suggested the first burst was released when a neutron star formed, while the second was triggered seconds later by its collapse into a quark star. High-resolution X-ray observatories, due to fly in space in the next decade, may be able to verify such claim. Neutron
Figure 08-20b SN1987a [view large image]	Figure 08-20c SN1987a Data [view large image]	stars and quark stars should look very different at X-ray wavelengths.

Preon Stars

of superstring. More recently in the 2000s, confidence in string theory has waned in some quarters, leading to renewed interest in alternative approaches, including preon models (see Wikipedia for more about preon theory). There are now several proposed methods to test the preon theory and preon star. An obvious test is for the LHC to break up the quark into its constituent preons. While preon star can be detected via gravitational lensing or gravitational waves with its special signatures. Figure 08-20d compares the size and density of the various degeneracy stars. The data for the preon star are highly speculative especially when no one knows the

Figure 08-20d Degeneracy Stars [view large image]

mass of the preons. It is also suggested nevertheless that preon stars could possibly account for some of the dark matter in the universe.

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 08-24a 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
Figure 08-22 Cygnus X-1 [view large image]	Figure 08-23 V404 Cyg	Figure 08-24a GRS1915	smallest with a mass of 3 to 5 Msun.

Table 08-05 End of Stars

For high mass stars, there are three ways to end their life. Depending on the initial mass and the metallic content Z (elements other than hydrogen and helium), their fates are depicted in Figure 08-24b. The Iron-core-collapse supernova turns the iron core into neutrons and neutrinos leaving a neutron star behind. The pair-instability supernova (as discussed earlier) blows the whole thing apart leaving nothing behind (as recently observed in SN2007bi). The dotted line marks the point above which pair-unstable stars are thought to form black hole instead of exploding. The blue shaded area denotes a transition region in which stars first become 'pair unstable', but eventually undergo iron-core collapse. Triangles and squares denote values obtained by different theoretical studies; green triangles for zero metallicity.

Figure 08-24b High Mass Supernovae

Black Stars

		The novel mechanism is related to the zero point energy, which normally has a value near to zero by almost complete cancellation of the positive and negative contributions. A semi-classical investigation reveals that if the collapse proceeds significantly slower than free falling, the zero point energy is disturbed in such a way that a large repulsive force would be generated near the event horizon and the collapse might come to a complete halt just short of forming an event horizon, or it might continue forever at an ever slower pace, becoming ever closer to forming an event horizon but never actually producing one. Such scenario is similar to the vacuum polarization
Figure 08-25 Black Star Formation [view large image]	Figure 08-26a Black Star [view large image]	by electric charge, but the virtual particles surrounding the mass now carry negative mass (Figure 08-25). This object is called black star as shown in Figure 08-26a.

Electroweak Stars

hasn't happened within the visible universe anytime in the last 10 billion years, except perhaps in the core of these electroweak stars. But it could happen at the extreme temperatures and densities when a star begins to collapse into a black hole. The energy generated could halt the collapse, much as the energy generated by nuclear fusion prevents ordinary stars like the Sun from collapsing. In other words, an electroweak star is the possible next step before total collapse into a black hole. If the electroweak burning is efficient, it could consume enough mass to prevent what's left from ever becoming a black hole. Most of the energy eventually emitted from electroweak stars is in the form of neutrinos, which are hard to detect. A small fraction comes out as light, and this is where the electroweak star's signature will likely be found. Further study is required to understand such star better. And until then, it is hard to tell an electroweak star from the other varieties. There's time, however, to learn. The theorists have calculated that this phase of a star's life

Figure 08-26b Electroweak Star [view large image]

can last more than 10 million years - a long time for us, though just an instant in the life of a star. Figure 08-26b shows some of the massive stars in a nebula that could be electroweak 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 08-27). A verbal description is given below for simulating the structure of a main sequence star.

Figure 08-27 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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