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Suddenly, without warning, a part of the Sun explodes, creating a solar flare. Some of them are the biggest explosions in the solar system, releasing energy of ten million, billion, billion joule, or 10<sup>25</sup> J, in just 100 s. This is comparable in strength to 20 million nuclear bombs exploding simultaneously, a... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.3.1 Solar Flares",
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Benz and Güdel ([2010\)](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR105) provided a review of magnetically driven flares on the Sun and other stars, whereas Zweibel and Yamada [\(2009](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR1159)) reviewed magnetic
Fig. 9.9 Solar flar... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.3.1 Solar Flares",
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For a sphere of radius, R, we have:
$$M = 4\pi R^3 N_e m_p / 3, (9.13)$$
where $\pi \approx 3.14159$ and the proton mass $m_p = 1.6726 \times 10^{-27}$ kg. The corona is a fully ionized, predominantly (90 %) hydrogen, plasma, so the number density of protons and electrons are equal, but since the protons are 1,... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.3.1 Solar Flares",
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Our planet is immersed within the hot, electrically charged solar wind that blows out from the Sun in all directions and never stops, carrying with it a magnetic field rooted in the Sun. Solar flares and coronal mass ejections create powerful gusts in the Sun's winds, producing space weather – the cosmic equivalent of ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.1 Earth's Protective Magnetosphere",
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The equatorial magnetic field strength of the Earth is $B_{0E} = 3 \times 10^{-5}$ tesla. Substituting these numbers into the equation for the standoff point, where the solar wind ram pressure equals the Earth's magnetic pressure, gives $R_{ME} \approx 7R_E$ , or seven times the Earth's radius.
The values of $R_{... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.1 Earth's Protective Magnetosphere",
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One of the first scientific discoveries of the Space Age was the finding, by James A. Van Allen (1914–2006) and his students, of high-energy electrons and protons that girdle the Earth far above the atmosphere (Van Allen et al. 1959). They move within two belts that encircle the Earth's magnetic equator but do not touc... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.1 Earth's Protective Magnetosphere",
"Header 3": "9.4.2 Trapped Particles",
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When directed at our planet or at humans in deep space, both solar flares and coronal mass ejections produce dangerous gusts and squalls in the Sun's winds. Here on the ground, we are shielded from many of the effects by the Earth's atmosphere and magnetic fields, but out in space there can be no protection, and both h... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.4 Solar Explosions Threaten Humans in Outer Space",
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Eight minutes after an energetic solar flare, a strong blast of x-rays and extreme ultraviolet radiation reaches the Earth and radically alters the structure of the planet's upper atmosphere, known as the ionosphere, altering its ability to reflect radio waves. During even moderately intense flares, long-distance radio... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.5 Disrupting Communication",
"token_count": 310,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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More than 1,000 commercial, military, and scientific satellites are now in operation, affecting the lives of millions of people. And the performance and lifetime of all of these satellites are affected by Sun-driven space weather.
Geosynchronous satellites, which orbit the Earth at the same rate that the planet spins... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.6 Satellites in Danger",
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Recognizing our vulnerability, astronomers use telescopes on the ground and in situ particle detectors or remote-sensing telescopes on satellites to carefully monitor the Sun, and government agencies post forecasts that warn of threatening solar activity. This enables evasive action that can reduce disruption or damage... | {
"Header 1": "Essential Astrophysics",
"Header 2": "9.4.7 Forecasting Space Weather",
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To determine the distance of a nearby star (other than the Sun), astronomers measure its angular displacement when viewed from opposite sides of the Earth's orbit, or from a separation of twice the AU. The AU is the mean distance between the Earth and the Sun, with a value of about 149.6 million km. This angle is known... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.1 How Far Away are the Stars?",
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This explains the spacecraft's name, which is an acronym for *HIgh Precision PARallax Collecting Satellite*; the name also alludes to the ancient Greek astronomer Hipparchus, who recorded accurate star positions more than 2,000 years ago. A successor to this mission is the ESA *GAIA* mission, short for *Global Astromet... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.1 How Far Away are the Stars?",
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The absolute magnitude is designated as M The luminosity classes are Ia Supergiant of high luminosity, Ib Supergiant of lower luminosity, II bright giant, III = Normal giant, IV = Subgiant, V Main-sequence star, or dwarf star, VI Subdwarf
M = 1.989 9 1030 kg, and the
The luminosity, L, is in units of the Sun's lumi... | {
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"Header 2": "10.1.1 How Far Away are the Stars?",
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Thus, the exceptional brightness of the brightest stars, as seen from the Earth, can be due
<sup>&</sup>lt;sup>a</sup> The luminosity is in units of the Sun's luminosity $L_{\odot}=3.828\times10^{26}~\rm J~s^{-1}$ , the mass is in units of the Sun's mass $M_{\odot}=1.989\times10^{30}~\rm kg$ , the radius is in unit... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.1 How Far Away are the Stars?",
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The Sun is the nearest star. It has a mean distance of 1 AU = 1.496 × $10^{11}$ m, an absolute luminosity of $L_{\odot} = 3.828 \times 10^{26}$ J s<sup>-1</sup>, an effective temperature of $T_{eff} = 5,780$ K, and a radius of $R_{\odot} = 6.955 \times 10^{8}$ m. The nearest star other than the Sun is Proxima C... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Distance, luminosity, temperature, and size of the nearest stars",
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The brightest star in the sky is Sirius, the Dog Star, often denoted Sirius A to distinguish it from its faint companion Sirius B. Sirius A has an apparent magnitude of m=-1.47 and a distance of D=8.60 light-years. Divide by 3.26 to get the distance in parsecs, or D=2.64 parsecs, and the absolute magnitude is M=m+5-5 l... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: The absolute magnitude and luminosity of Sirius A and Sirius B",
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An understanding of the physical properties of a star requires knowledge of its temperature as well as its luminosity. The effective temperature of the Sun's visible disk, the photosphere, is inferred from the solar radius and luminosity, with a value of Teff = 5,780 K. However, we do not have direct knowledge of the r... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.4 The Temperatures of Stars",
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There are reddish stars like Betelgeuse and Antares, yellowish stars like the Sun and Capella, and whitish stars like Vega and Sirius. These colors provide a rough indication of the temperature of a star's photosphere. As the temperature rises, the colors change from red – near 3,000 K, to yellow – around 6,000 K, to w... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.5 The Colors of Stars",
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More than a century ago, astronomers noticed that stars of different colors exhibit different spectral lines. Strong absorption lines of hydrogen, for example, dominate the spectra of white stars like Vega and Sirius, whereas some blue stars have noticeable helium absorption lines. Yellow stars like the Sun have strong... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
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Michelson (1852–1931) was one of the first to describe the interferometer technique (Michelson 1890), and thirty years later, he teamed up with the American astronomer F.G. Pease (1881–1938) to use an interferometer to measure the size of Betelgeuse. They mounted two moveable mirrors and two fixed mirrors on a 20 foot ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
"token_count": 2009,
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5.2) is $V_{ther}$ $m_{mal} = (3kT/m_H)^{1/2} \approx 8.6 \times 10^3 \text{ m s}^{-1}$ , where the Boltzmann constant $k = 1.381 \times 10^{-23} \text{ J K}^{-1}, m_H = 1.66 \times 10^{-27} \text{ kg}, \text{ and the disk temperature}$ of the star is T = 3,000 K. Since the average thermal speed is just 10 times les... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
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There is a limit established when a star gets so big that the outward force of its internal radiation exceeds the inward gravitational force of the entire star.
Although the gas pressure of the hot, moving subatomic particles supports a star like the Sun, radiation pressure becomes important in more massive stars. As... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
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10.4 Alpha Centauri Two of the most brilliant stars in the southern sky appear as a single star, named Alpha Centauri, to the unaided eye, but they can be resolved into two stars with the aid of binoculars or a small 5 cm (2 inch) telescope. The yellowish Alpha Centauri A (lower left), also known as Rigil Kentaurus, an... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
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The analysis of binary stars usually assumes circular motion about a center of mass located between two stars. We have:
$$r_1 M_1 = r_2 M_2 \tag{10.30}$$
with M<sup>1</sup> and M<sup>2</sup> being the masses and r<sup>1</sup> and r<sup>2</sup> their respective distances to the center of mass. Thus, if a ¼ r<sup>1</... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
"Header 3": "Focus 10.2 Determining the stellar mass in a spectroscopic binary system",
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In his publication, Russell included a similar diagram for individual bright stars, the distances of which had been established from stellar parallax measurements. It closely resembled the diagram shown here with an exceptional point in the lower left-hand corner, which is included here with an ''x'' mark. This star is... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.1.6 The Spectral Sequence",
"Header 3": "Focus 10.2 Determining the stellar mass in a spectroscopic binary system",
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There was an unresolved uncertainty in the H-R diagram, which created a dilemma for specifying the physical characteristics of a star. A star could be small or large as well as hot or cold. A red cool star, for example, might be either much more luminous than the Sun or much fainter. Once the spectral type establishes ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.2.2 The Luminosity Class",
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Today, the H-R diagram remains a primary tool for tracing the path of stellar evolution, but the routes are more complex than initially supposed. Russell, for example, thought that most stars began life as hot, blue-white stars and ended their life as cool red ones, moving from upper left to lower right along the main ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.2.3 Life on the Main Sequence",
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The Sun's main-sequence lifetime, $\tau_{ms}$ , required to convert 12 % of its mass into helium is therefore:
$$\tau_{ms} = \left(\frac{E}{L_{\odot}}\right) = 0.12(0.007) \left(\frac{M_{\odot}c^2}{L_{\odot}}\right) \approx 3.92 \times 10^{17} \,\text{s} \approx 1.24 \times 10^{10} \,\text{years},$$
(10.46)
where ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.2.3 Life on the Main Sequence",
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After the low-mass, main-sequence stars, the most common type of star is the red giant found in the upper right side of the H-R diagram (Fig. [10.10](#page-344-0)). These lowtemperature stars are not exceptionally massive. They have an intermediate mass of roughly 1–10 times that of the Sun and are in a late state of s... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.2.3 Life on the Main Sequence",
"Header 3": "10.2.4 The Red Giants and Supergiants",
"token_count": 1922,
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We can determine the star's effective temperature, $T_{eff}$ , from the Stefan-Boltzmann law $L=4\pi\sigma~R^2~T_{eff}^4$ , where $\pi=3.14159$ and the Stefan-Boltzmann constant $\sigma=5.6704\times 10^{-8}$ J m<sup>-2</sup> K<sup>-4</sup> s<sup>-1</sup>, obtaining $T_{eff}\approx 10^4$ K.
Both the giant and ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.2.3 Life on the Main Sequence",
"Header 3": "10.2.4 The Red Giants and Supergiants",
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Although we cannot see the inside of a star, its internal structure can be explained by a few simple concepts, one of which is a star's equilibrium. Like the Sun, almost every star we see is neither collapsing nor expanding, and it remains the same size throughout most of its long life. At every point inside such a sta... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.1 The Internal Constitution of Stars",
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If the effective temperature was about the same as that of the Sun, and because the luminosity varies as the square of the radius, the star's radius will be $R_S \approx 10^{3.75} R_{\odot}$ , a large star, where the Sun's radius $R_{\odot} = 6.955 \times 10^8$ m. Assuming that the star is entirely composed of proto... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.1 The Internal Constitution of Stars",
"token_count": 1940,
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The total luminosity of a star, $L_S$ , with a radius, $R_S$ , is given by the Stefan-Boltzmann law $L_S = 4\pi\sigma R_S^2 T_{eff}^4$ where the Stefan-Boltzmann constant $\sigma = ac/4 = 5.6704 \times 10^{-8} \text{ J s}^{-1} \text{ m}^{-2} \text{ K}^{-4}$ and $T_{eff}$ is the effective temperature of the visi... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.1 The Internal Constitution of Stars",
"token_count": 783,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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All main-sequence stars generate energy by the thermonuclear fusion of hydrogen nuclei, the protons, into helium nuclei. Because the hydrogen is "burned up" or consumed to fuel the nuclear fires, we call this process *hydrogen burning*, although it is a chain of nuclear-fusion reactions rather than the combustion of an... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.1 The Internal Constitution of Stars",
"Header 3": "10.3.2 Two Ways to Burn Hydrogen in Main-Sequence Stars",
"token_count": 2037,
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It was Bethe who realized that the proton-proton reaction, which explains the luminous output of the Sun, fell short of the much greater luminosity of the hotter and more massive stars. So, he systematically examined a great number of nuclear reactions that would not operate within stars and eliminated them. He indep... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.1 The Internal Constitution of Stars",
"Header 3": "10.3.2 Two Ways to Burn Hydrogen in Main-Sequence Stars",
"token_count": 1871,
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The fact that giant stars are connected to the main sequence of the H-R diagram suggested that the giants are the next stage of stellar evolution. However, because giant stars have larger luminosities at lower disk temperatures than main-sequence stars, they seemed to shine by a different and unknown process. The enigm... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.3 Helium Burning in Giant Stars",
"token_count": 2020,
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Only the helium nuclei in the high-velocity tail of the Maxwellian speed distribution can merge together in a giant star, which means that most of the helium nuclei are not moving fast enough to merge and that the helium-burning reactions occur relatively slowly.
Under most circumstances, helium burning still would b... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.3.3 Helium Burning in Giant Stars",
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Entire stars have had a beginning, followed by a long period of growth and inevitable decay, eventually turning into something else, and we can use the H-R diagrams of star clusters to map out the stages of stellar transfiguration. As time elapses, the more massive stars evolve into the next phase of stellar life and t... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.4 Using Star Clusters to Watch How Stars Evolve",
"token_count": 1898,
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When Sandage's data were compared to the model results, it improved our understanding of evolution away from the main sequence and this provided a sound observational basis for stellar aging (Sandage and Schwarzschild [1952;](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR916) Sandage [1957;](http://dx.doi.org/10.100... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.4 Using Star Clusters to Watch How Stars Evolve",
"token_count": 1008,
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A supergiant star has a much greater mass, interior compression, central temperature, and luminosity than a giant star, which is why we call them ''super.'' Supergiants pass through the same early stages of stellar life as giants but at a faster rate. Unlike their counterparts of lesser mass, massive stars with a mass ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.1 Advanced Nuclear Burning Stages in Massive Supergiant Stars",
"token_count": 1398,
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What accounts for the origin of the chemical elements that make up our everyday world? The English astronomer Arthur Stanley Eddington (1882–1944) was one of the first to propose that the light elements are compounded into more complex elements within stars (Eddington [1920](http://dx.doi.org/10.1007/978-3-642-35963-7_... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.2 Origin of the Material World",
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An important key to understanding how stars synthesize the elements is obtained from their relative abundances, initially studied by chemists rather than astronomers. The American chemist William D. Harkins (1873–1951), for example, found an important clue to the mystery of the origin of the elements when he noticed th... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.3 The Observed Abundance of the Elements",
"token_count": 1016,
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The English astronomer Fred Hoyle (1915–2001) introduced the grand concept of nucleosynthesis in stars in the mid twentieth century (Hoyle [1946](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR493), [1954](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR495)). He showed that both theoretical and experimental conside... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.4 Synthesis of the Elements Inside Stars",
"token_count": 1183,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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The synthesis of elements inside stars is an incomplete scenario for it does not explain the origin of any of the hydrogen and most of the helium in the observable universe. Moreover, because deuterium is destroyed rapidly inside stars, there also must be another explanation for its cosmic existence. As proposed by the... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.5 Big-Bang Nucleosynthesis",
"token_count": 1411,
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Because big-bang nucleosynthesis produced no elements heavier than helium, the earliest stars had to be composed of the lightest abundant elements: hydrogen and helium. This first generation of stars is known as Population I stars. Then, as a result of ongoing stellar alchemy, the most massive first-generation stars fo... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.6 The First and Second Generation of Stars",
"token_count": 834,
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During the billions of years before the Sun was born, massive stars reworked the chemical elements, fusing lighter elements into heavier ones within their nuclear furnaces. Carbon, oxygen, nitrogen, silicon, iron, and most of the other heavy elements were created this way. The enriched stellar material then was cast ou... | {
"Header 1": "Essential Astrophysics",
"Header 2": "10.5.6 The First and Second Generation of Stars",
"Header 3": "10.5.7 Cosmic Implications of the Origin of the Elements",
"token_count": 356,
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The space between the stars, which looks like an empty black void is filled with cold atoms of hydrogen. Stars form out of this supposed emptiness and eventually return to it. We see some of this interstellar material when the brightest stars illuminate nearby regions (Fig. [11.1\)](#page-375-0). The energetic starligh... | {
"Header 1": "Essential Astrophysics",
"Header 2": "11.1 Gaseous Emission Nebulae",
"token_count": 1724,
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(Courtesy of KPNO/CTIA.)
Table 11.1 Bright named emission nebulae
| | RA | (2000) | Decem | nber (2000) | $\theta^a$ | Distance <sup>b</sup> (light-years) |
|-----------------------------|-------|-----------|----------|-------------|----------------|-------------------------... | {
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"Header 2": "11.1 Gaseous Emission Nebulae",
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At visible wavelengths, the most intense hydrogen emission line is the Balmer $\alpha$ transition at a red wavelength of 656.28 nm while the ultraviolet $\alpha$ transition is known as Lyman $\alpha$ at 121.567 nm.
Recombination lines are also detected from emission nebulae, or H II regions, at radio frequencie... | {
"Header 1": "Essential Astrophysics",
"Header 2": "11.1 Gaseous Emission Nebulae",
"token_count": 1054,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
For the quantum number n = 109 and the $\alpha$ transition with m - n = 1, the frequency, $\nu$ , of the hydrogen recombination line, denoted H $109\alpha$ , is:
$$\nu = 3.28805 \times 10^{15} \left[ \frac{1}{(109)^2} - \frac{1}{(110)^2} \right] \approx 5.0089 \times 10^9 \,\text{Hz} \approx 5008.9 \,\text{MHz}.$... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: What is the recombination line frequency of the H $109\\alpha$ transition?",
"token_count": 1797,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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A star of spectral class O5 V has an effective $T_{eff} \approx 0.5 \times 10^5$ K for its visible disk, and it can ionize the surrounding hydrogen to a temperature of $T = T_e \approx 10^4$ K, where $T_e$ denotes the electron temperature, emitting $S = 3 \times 10^{49}$ ionizing photons every second. If the nu... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Temperature, extent, and mass of an emission nebula or H II region",
"token_count": 1969,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
What is this interstellar dust? The particles must be smaller than 1=10,000th of a meter, or 10-<sup>4</sup> m, across or they would completely block starlight and not scatter it; also they must be larger than gas molecules, the scattering of which depends strongly on wavelength (Oort and Van de Hulst [1946](http://d... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Temperature, extent, and mass of an emission nebula or H II region",
"token_count": 881,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The American radio engineer Karl Jansky (1905–1950) inadvertently discovered radio noise of cosmic origin in the early 1930s, when radio waves were being used extensively for global communications. At that time, the Bell Telephone Laboratories assigned Jansky the task of tracking down and identifying natural sources of... | {
"Header 1": "Essential Astrophysics",
"Header 2": "11.3 Radio Emission from the Milky Way",
"token_count": 2004,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The frequency, $v_s$ , of synchrotron radiation from high-speed electrons is amplified by an additional factor of $\gamma^3$ so $v_s = \gamma^2 v_g$ (see subsequent text).
High-speed electrons spiral about the interstellar magnetic field and emit nonthermal *synchrotron radiation* at radio wavelengths (Fig. 11... | {
"Header 1": "Essential Astrophysics",
"Header 2": "11.3 Radio Emission from the Milky Way",
"token_count": 1889,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Cosmic ray electrons that enter the Earth's atmosphere have an energy $E \approx 1$ GeV, where $1 \text{ GeV} = 1.6022 \times 10^{-10}$ J. The cosmic-ray electrons have a lower flux than cosmic ray protons, with comparable energies, but it is the electrons that give rise to synchrotron radiation, not the protons. T... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Synchrotron radiation of high-speed electrons in the Milky Way",
"token_count": 2033,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The H I regions do not emit visible light; hence they are invisible at optical wavelengths, but they do emit radio waves that are 21 cm long, with typical parameters given in Table 11.4.
As Van de Hulst pointed out, these spin transitions occur rarely in the tenuous interstellar gas; however, an observer might well... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Synchrotron radiation of high-speed electrons in the Milky Way",
"token_count": 2046,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Ho and Townes [\(1983](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR490)) have described interstellar ammonia; Combes [\(1991](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR229)) has reviewed the distribution of CO in the Milky Way – also see Gordon and Burton ([1976\)](http://dx.doi.org/10.1007/978-3-642-35963-... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Synchrotron radiation of high-speed electrons in the Milky Way",
"token_count": 1807,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Where did the Sun and its attendant planets come from? How and when did they form? The most likely explanation is provided by the nebular hypothesis, which states that the Sun and planets formed together, as a result of the gravitational collapse of an interstellar cloud of gas and dust also known as the solar nebula (... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.1.1 The Nebular Hypothesis",
"token_count": 853,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
If the nebular theory is correct, we might expect that all of the planets would have the same composition as the Sun because they all formed from the same interstellar nebula. After all, they should have the same ingredients as the material from which they formed – they do, but with a varying mix.
The abundance of el... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.1.2 Composition of the Planets",
"token_count": 1639,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The nebular hypothesis must also be adjusted to explain the current distribution of angular momentum in the solar system. Most of it is concentrated in the orbital angular momentum of Jupiter, and the rotating Sun has less than one percent of the amount of angular momentum carried by this giant planet. In other words, ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.1.3 Mass and Angular Momentum in the Solar System",
"token_count": 2019,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
These contemporary incubators of newborn stars have temperatures as low as 10 K, span tens of light-years, and each one has a mass of up to 1 million solar masses, mainly in the form of hydrogen molecules. These giant molecular clouds are now the dominant star-forming component of the interstellar medium.
As many as ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.1.3 Mass and Angular Momentum in the Solar System",
"token_count": 904,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Near the beginning of the 20th century, the English physicist and mathematician James Jeans (1877–1946) considered the stability conditions of a gas subject to perturbations in mass density, showing that a fluctuation greater than a critical size – now called the Jeans length – or a mass greater than a critical mass – ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.2.2 Gravitational Collapse",
"token_count": 2000,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The mass of the region is $M=4\pi R^3\rho/3\approx2.1\times10^{30}~{\rm kg}\approx M_\odot$ , the mass of the Sun. This shows that the mass of neutral, unionized hydrogen in the space between the stars is about equal to the mass of hydrogen in stars. The Jeans mass, $M_J$ , of the region is:
$$M_J = \frac{3kT}{Gm}R... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.2.2 Gravitational Collapse",
"token_count": 1434,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The ratio of magnetic pressure, $P_B$ , to gas pressure, $P_g = NkT$ , is $P_B/P_g = B^2/(2\mu_0NkT) = 2.88 \times 10^{28}\,B^2/(NT)$ for a magnetic field strength B, a gas number density N, and a gas temperature T, where the permeability of free space $\mu_0 = 4\pi \times 10^{-7} = 1.2566 \times 10^{-6} \text{ N ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Supporting interstellar clouds by gas pressure and magnetic pressure",
"token_count": 898,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
A star in the process of formation is commonly called a protostar. Such an embryonic star shines by the release of gravitational energy during the collapse of interstellar material, but it has not yet begun to shine by nuclear fusion in its core. Protostars are exceptionally bright at infrared wavelengths, which can be... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.2.4 Protostars",
"token_count": 1997,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The early stages of star life can be the most active. For example, young stars can have strong stellar winds that drive away protostellar material that may still envelop them. Even now, billions of years after its birth, the Sun generates a solar wind that removes about $10^{-14}$ solar masses every year; we suspect ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.2.5 Losing Mass and Spin",
"token_count": 1095,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Just as the ancient Greeks imagined that all matter consists of atoms, so they also believed that there were many planets like ours in the universe, created by the coalescence of atoms. In the second century BC, the Greek philosopher Epicurus of Samos (276–194 BC) proposed that the chance conglomerations of innumerable... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.1 The Plurality of Worlds",
"token_count": 359,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Planetary systems probably formed around many stars as a result of the gravitational collapse of an interstellar cloud of gas and dust that created the stars, all in accordance with the nebular hypothesis of the origin of the solar system. The collapsing cloud would rotate faster and faster, giving spin to the material... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.2 Proto-Planetary Disks",
"token_count": 1996,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Dullemand and Monnier ([2010\)](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR278) reviewed the inner regions of protoplanetary disks, and Blum
Fig. 12.7 Exoplanet on the move An exoplanet's orbital motion, denoted by the central white elliptical line, was imaged from an adaptive opt... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.2 Proto-Planetary Disks",
"token_count": 293,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Individual planets shine by reflecting light that is much fainter than the light of the star that illuminates them. The visible light reflected by Jupiter, for example, is about 1 billion or 10<sup>9</sup> times dimmer than the light emitted by the Sun, and that which is reflected by the Earth is 10 billion times faint... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.3 The First Discoveries of Exoplanets",
"token_count": 2018,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Under the assumption that $\sin i = 1$ and the star's mass is comparable to the Sun, with $M_1 \approx M_{\odot} = 1.989 \times 10^{30}$ kg, we obtain a planet mass of $M_2 = 7.55 \times 10^{26}$ kg, which is comparable to the mass of Jupiter $M_J = 1.90 \times 10^{27}$ kg. But the exoplanet is nowhere near as ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.3 The First Discoveries of Exoplanets",
"token_count": 872,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
After scientists realized that a large planet could be so near to its star, they knew where and how to look. By monitoring thousands of nearby Sun-like stars for years, American and European teams found hundreds of planets revolving about other nearby stars, most of them massive Jupiter-sized planets. The accelerating ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.4 Hundreds of New Worlds Circling Nearby Stars",
"token_count": 866,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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From a human perspective, the most interesting planets will be those as small as the Earth, in circular orbits at the precise distance from the heat of a Sun-like star to provide a haven for life. Scientists call this location a habitable zone, meaning that it could be inhabited – but not necessarily that it is. Such a... | {
"Header 1": "Essential Astrophysics",
"Header 2": "12.3.5 Searching for Habitable Planets",
"token_count": 1289,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
No material object can exist forever, and stars are no exception. Although their lives may be measured in millions or billions of years, stars do stop shining when all of the available sources of subatomic energy have been exhausted. Their central thermonuclear reactions, which keep the star hot inside, are then turned... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.1 A Range of Destinies",
"token_count": 2042,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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\tau_{\rm exp} = expansion age ≈ 16,000 years
```
photoionization recombine with protons to make hydrogen atoms, cascading through the atoms' various allowed electron orbits or energy levels and radiating the Balmer emission line (Menzel 1926; Zanstra 1927, 1928).
In a brilliant piece of detective work, the America... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.1 A Range of Destinies",
"token_count": 1820,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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(2000) | (000 | $D^{\mathrm{b}}$ (1y) | R (1y) | $V_{exp} \; ({\rm km \; s}^{-1})$ | m <sup>o</sup> d | $T^{\mathrm{d}}\left(\mathrm{K}\right)$ |
| | | h | ш | 0 | , | | | ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.1 A Range of Destinies",
"token_count": 2044,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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The first white dwarf to be known is a companion of a much brighter star, 40 Eridani, also known as Omicron Eridani from its Greek letter designation. The fainter star is designated 40 Eridani B to distinguish it from the brighter member, A, of the pair. The American astronomer Walter S. Adams (1876–1956) first drew at... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.3.1 The Discovery of White Dwarf Stars",
"token_count": 805,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Having depleted the hydrogen in their cores, the central regions of solar-mass stars contract to become hot enough to fuse helium into carbon and oxygen; however, there is not enough mass to generate a temperature hot enough to fuse carbon into neon, at about 1 billion K, and an inert carbon–oxygen core is surrounded b... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.3.2 Unveiling White Dwarf Stars",
"token_count": 1990,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The gravitational redshift, $z_g$ , caused by this loss of photon energy is given by
$$z_{g} = \frac{V_{r}}{c} = \frac{\Delta v}{v} = \frac{v_{L} - v_{observed}}{v_{observed}} = \frac{\Delta \lambda}{\lambda_{L}} = \frac{\lambda_{L} - \lambda_{observed}}{\lambda_{L}} = \frac{GM}{Rc^{2}}$$
$$= 2.12 \times 10^{-6} \... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.3.2 Unveiling White Dwarf Stars",
"token_count": 1980,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
The matter deep inside a white dwarf star is completely ionized and composed of equal numbers of atomic nuclei and electrons. Because most white dwarfs are the crushed remnants of red giant stars, which previously fused helium into carbon, their collapsed cores consist mainly of carbon nuclei and electrons. Stars that ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.4.1 Nuclei Pull a White Dwarf Together as Electrons Support It",
"token_count": 1978,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
\tag{13.8}$$
where the Planck constant $h = 6.626 \times 10^{-34}$ J s, the electron mass $m_e = 9.109 \times 10^{-31}$ kg, and $N_e$ is the electron density. Notice that the degenerate electron pressure does not depend on the temperature. An equivalent expression for the equation of state of non-relativistic d... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.4.1 Nuclei Pull a White Dwarf Together as Electrons Support It",
"token_count": 324,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
A white dwarf star has a mass density of $\rho = 10^9$ kg m<sup>-3</sup> and an initial temperature of $T = 10^7$ K. The gas pressure, $P_G$ , is given by:
$$P_G = N_i k T = \frac{\rho}{A m_p} k T, \qquad (13.11)$$
where $N_i$ is the ion number density, the mass number A=4 for helium, A=12 for carbon and A=1... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Example: Gas pressure, degenerate electron pressure, and magnetic pressure in a white dwarf",
"token_count": 973,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
A higher-mass white dwarf will be squeezed into a smaller space by its gravity, so the star's radius decreases with increasing mass. For a large enough mass, we might imagine that the star's radius would become very small, perhaps even shrinking to almost zero; however, this is preposterous and there must be a limit to... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.4.2 Radius and Mass of a White Dwarf",
"token_count": 1302,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
For at least 2,000 years, astronomers, hunters, mariners, and others familiar with the brightest stars must have been amazed by a nova, or ''new star'', that would appear suddenly at a place in the sky where no star previously had been seen. For a few days, the nova might be among the brightest stars in the dark night ... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.1 Guest Stars, the Novae",
"token_count": 1146,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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A major new understanding of novae occurred in the 1950s and 1960s when a few American astronomers began to examine the total light and spectra of ex-novae, long after the intense light of the nova outburst had faded to a relatively weak level. It then was discovered that a nova is not one star but rather two stars ver... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.2 What Makes a Nova Happen?",
"token_count": 2037,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
A runaway thermonuclear explosion then occurs, and a white dwarf that normally would cool and fade away if left alone suddenly shines as brightly as 100,000 Suns (Starrfield et al. [1974](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR997), [1985\)](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR998). The explosion... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.2 What Makes a Nova Happen?",
"token_count": 392,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
On rare occasions, an entire star is annihilated and suddenly becomes so bright that it can be seen easily in daylight rather than just at night like the novae. The Chinese emperor's astronomers in the Sung dynasty recorded one on July 4, 1054, near the constellation now known as Taurus, the Bull. The Chinese chronicle... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.3 A Rare and Violent End, the Supernovae",
"token_count": 2032,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Because there are many of these extragalactic spirals, now called galaxies, Zwicky realized that a systematic photographic survey quickly would catch at least one star in the act of supernova explosion – and he was right. He detected the first one in 1937, with a camera attached to a modest telescope placed on the ro... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.3 A Rare and Violent End, the Supernovae",
"token_count": 1245,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Both types of supernovae involve the explosive conversion of a star's entire mass into energy but by different physical mechanisms. A Type Ia stellar explosion is due to external causes. It involves a white dwarf star pushed into nuclear explosion by too much mass overflow from a nearby companion. The other, Type II, s... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.4 Why do Supernova Explosions Occur?",
"token_count": 564,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Like the novae, there is one type of supernova that gets assistance from the outside, being pushed over the edge into explosion, shattering an entire star. Such a supernova – now known as Type Ia and characterized by the absence of emission from hydrogen – occurs in a close binary-star system, with a white dwarf star –... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.5 When a Nearby Star Detonates Its Companion",
"token_count": 715,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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There is more than one way to explode a star, and some of the supernovae are gravity-powered, catastrophic outbursts from very old massive stars. This method of shattering a star applies to an isolated star with the right mass – between about 8 and 20 times the Sun's mass – that blows itself apart. This Type II superno... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.6 Stars that Blow Themselves Up",
"token_count": 854,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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For more than three and a half centuries, nobody was fortunate enough to see a supernova with the unaided eye. Then, late in the evening of February 24, 1987, astronomers discovered one (Fig. [13.6\)](#page-456-0), which was designated SN 1987A (SN is for supernova; 1987A denotes the first one discovered that year). Th... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.7 Light of a Billion Suns, SN 1987A",
"token_count": 2033,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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#### Example: Energy of a supernova
During the supernova explosion of SN 1987A, about a solar mass, or $1.0 M_{\odot} = 1.989 \times 10^{30} \text{ kg}$ was ejected with a velocity V of about $10^7$ m s<sup>-1</sup>. The kinetic energy of the ejected mass is equal to $0.5 M_{\odot} V^2 \approx$ 10<sup>44</sup>... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.5.7 Light of a Billion Suns, SN 1987A",
"token_count": 994,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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In their explosive death, stars that go supernova blast their outer layers into surrounding space, expelling much or all of the stellar material at supersonic speeds of up to 30,000 km s-<sup>1</sup> , or 1=10th of the speed of light. A strong shock wave forms ahead of the ejected material, colliding with the surroundi... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.6 Expanding Stellar Remnants",
"token_count": 2042,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Wilson 2.5 m (100 inch) telescope in the early 1940s indicated that the visible nebula consists of two 446 13 Stellar End States
Fig. 13.8 The Crab Nebula supernova remnant The optically visible light of the Crab Nebula, designated as M 1 and NGC 1952, consists of two distinct parts: (... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.6 Expanding Stellar Remnants",
"token_count": 2013,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Because the more energetic electrons lose their energy faster and also radiate at shorter wavelengths, the synchrotron radiation mechanism provides a natural explanation for the nonthermal emission of the Crab's inner regions and for the fact that its radio emission is a thousand times more intense than its visible lig... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.6 Expanding Stellar Remnants",
"token_count": 1786,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
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Walter Baade (1893–1960) and Fritz Zwicky (1898–1974) proposed the possibility that neutron stars might exist just two years after James Chadwick's (1891–1974) discovery of the neutron (Chadwick [1932a,](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR202) [b\)](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR203). T... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.6 Expanding Stellar Remnants",
"Header 3": "13.7.1 Neutron Stars",
"token_count": 1891,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
Before discussing the discovery of pulsars, we provide references to modern reviews for further reading. Lyne and Graham-Smith [\(2012](http://dx.doi.org/10.1007/978-3-642-35963-7_16#CR671)) have discussed many aspects of pulsar astronomy, and Taylor and Stinebring [\(1986](http://dx.doi.org/10.1007/978-3-642-35963-7_1... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.7.2 Radio Pulsars from Isolated Neutron Stars",
"token_count": 2011,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
So a typical surface magnetic field on a visible-light star, with a strength of 0.01 tesla, would be strengthened by a factor of a ten thousand million, or to 10<sup>8</sup> tesla, if collapsing to a neutron star.
#### Example: Period and magnetic field of a rotating neutron star or white dwarf star
We can infer th... | {
"Header 1": "Essential Astrophysics",
"Header 2": "13.7.2 Radio Pulsars from Isolated Neutron Stars",
"token_count": 1214,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
A neutron star with a dipolar magnetic field will behave as a rotating magnetic dipole, with radiation luminosity $L_{NS}$ given by:
$$L_{NS} = \frac{\mu_0 m_\perp^2 \omega^4}{6\pi c^3},\tag{13.24}$$
where the magnetic constant $\mu_0 = 1.2566 \times 10^{-6} \text{ N A}^{-2}$ , the symbol $m_{\perp}$ denotes t... | {
"Header 1": "Essential Astrophysics",
"Header 2": "Focus 13.3 Luminosity, rotational energy, and magnetic field strength of a radio pulsar",
"token_count": 1301,
"source_pdf": "datasets/websources/Astronomy_v1/Astronomy/978-3-642-35963-7.pdf"
} |
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