7. Comparisons of the Sun with Other Stars


Fig7_1 Prime Meridian

Fig7_1 Prime Meridian

Fig. 7.1 . Great circles through the North and South Poles of the Earth create circles of longitude. They are perpendicular to the equator where they intersect it. The circle of longitude that passes through Greenwich England is called the Prime Meridian. The longitude of any point, P, is the angle, l, measured westward along the equator from the intersection of the Prime Meridian with the equator to the equatorial intersection of the circle of longitude that passes through the point. The latitude is the angle phi, f, measured northward (positive) or southward (negative) along the circle of longitude from the equator to the point. In this figure, the point P corresponds to San Francisco.


Fig7_2 Celestial coords

Fig7_2 Celestial coords

Fig. 7.2 . Stars, galaxies and other cosmic objects are placed upon an imaginary celestial sphere. The celestial equator divides the sphere into northern and southern halves, and the ecliptic is the annual path of the Sun on the celestial sphere. The celestial equator intersects the ecliptic at the Vernal Equinox and the Autumnal Equinox. Every cosmic object has two celestial coordinates. They are the right ascension, designated by the angle alpha, a, or by R.A., and the declination, denoted by the angle delta, d, or Dec.. Right ascension is measured eastward along the celestial equator from the Vernal Equinox to the foot of the great circle that passes through the object. Declination is the angular distance from the celestial equator to the object along the great circle that passes through the object, positive to the north and negative to the south. Precession results in a slow motion of the Vernal Equinox, producing a steady change in the celestial coordinates.


Fig7_3 Precession

Fig7_3 Precession

Fig. 7.3 . The Earthís rotation axis traces out a circle on the sky once every 26,000 years, sweeping out a cone with an angular radius of about 23.5 degrees. The Greek astronomer Hipparchus (lived c. 146 BC) discovered this precession in the 2nd century BC. The north celestial pole, which marks the intersection of this rotation axis with the northern half of the celestial sphere, now lies near the bright star Polaris, but as the result of precession the rotational axis will point towards another bright north star, Vega, in roughly 13,000 years. This motion of the Earthís rotational axis also causes a slow change in the celestial coordinates of any cosmic object.


Fig7_4 Annual parallax

Fig7_4 Annual parallax

Fig. 7.4 . When a distant and nearby star are observed at six-month intervals, on opposite sides of the Earthís orbit around the Sun, astronomers measure the angular displacement between the two stars. It is twice the annual parallax, designated by pA, which can be used to determine the distance, D, of the nearby star. From trigonometry, sin pA = AU/D Ľ pA for small angles, where 1 AU is the mean distance between the Earth and the Sun. The distance D to the star in units of parsecs is given by 1/pA, if the parallax angle is measured in seconds of arc. This angle is greatly exaggerated in the figure, for all stars have a parallax of less than one second of arc or less than 1/3,600 of a degree. The German astronomer Friedrich Wilhelm Bessel (1784-1846) announced the first reliable measurement of the annual parallax of a star in 1838.


Fig7_5 Proxima Centauri

Fig7_5 Proxima Centauri

Fig. 7.5 . The red star centered in this image is the nearest star to the Earth, other than the Sun; it is at a distance of 4.24 light-years from us. Despite its closeness, the star has an absolute luminosity of just two thousandths, or 0.002 times, the Sunís luminosity, and is too faint to be seen with the unaided eye. Named Proxima Centauri, because of its proximity, the star is close enough for its angular diameter to be measured by interferometric techniques, yielding a radius of one-seventh the radius of the Sun. Proxima Centauri orbits the bright double star Alpha Centauri (see Fig. 7.9) at a distance of about 0.24 light-years and an angular separation of 2.2 degrees. All three stars are located in the southern sky, and cannot be seen from the northern hemisphere of the Earth. (Courtesy of David Malin/UK Schmidt Telescope/DSS/AAO.)


Fig7_6 VY Canis Majoris

Fig7_6  VY Canis Majoris

Fig. 7.6 . The exceptionally massive and luminous supergiant star VY Canis Majoris is nearing the end of its estimated life of 0.5 million years. As revealed in this image taken from the Hubble Space Telescope, the starís extended, outer atmosphere is being ejected into surrounding space in arcs, loops, filaments and knots. When this data is combined with spectroscopy using the ground-based Keck telescope, it is found that the numerous features are moving at different speeds and in various directions, and were hence produced from separate events and at different locations. One of the arcs is moving at a speed of 46,000 km s-1, close to the escape velocity of the star. (Courtesy of NASA/ESA/Roberta Humphreys, U. Minnesota.)


Fig7_7 The Flames of Betelegeuse

Fig7_7 The Flames of Betelegeuse

Fig. 7.7 . The red supergiant star Betelgeuse is slowly shedding it outer atmosphere, producing out-flowing gas that envelops the star and a much bigger nebula of gas and dust that surrounds it. The small circle in the middle of this composite image denotes the edge of the supergiantís optically visible disk; it has a diameter of about 4.5 AU, where one AU is the mean distance between the Earth and the Sun. The black disk masks the bright central radiation of the star, in order to detect the infrared radiation of the outer plumes. They stretch to about 400 AU, or 60 million million, or 6 x 1013, meters from the supergiant Betelgeuse. (Courtesy of ESO/VISIR/VLT/Pierre Kervella.)


Fig7_8Alpha_Centauri_and_southerncross_cc.jpg

Fig7_8Alpha_Centauri_and_southerncross_cc.jpg

Fig. 7.8 . 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, and the blue Alpha Centauri B (upper right) are locked together in a gravitational embrace, orbiting each other every 80 years. The two components of this binary star system can approach each other within 11.2 AU and may recede as far as 35.6 AU, where the mean distance between the Earth and the Sun is 1 AU. Both stars have a mass and luminosity that are comparable to those of the Sun. They appear bright because they are very nearby, at a distance of just 4.37 light-years. A third and faint companion Proxima Centauri (also see Fig. 7.5) is located at about 15,000 AU or 2.2 degrees from the two bright stars. At a distance of 4.24 light-years from the Earth, Proxima Centauri is the closest star other than the Sun. (Courtesy of ESO/Yuri Beletsky.)


Fig7_9 Double stars

Fig7_9 Double stars

Fig. 7.9 . Two close stars are joined in a gravitational embrace, orbiting each other and forming a binary star system (top and bottom). The orbital period and linear star separation can be used to determine the sum of their masses. If the orbital plane of the two companions is sufficiently inclined and within the line of sight, the star system becomes an eclipsing binary (top), in which one star is observed to pass behind the other one and vice versa; this can provide additional information about the stars.


Fig7_10 Stellar mass luminosity relation

Fig7_10 Stellar mass luminosity relation

Fig. 7.10 . An empirical mass-luminosity relation for main-sequence stars of absolute luminosity, L, in units of the solar luminosity, L§, and mass, M, in units of the Sunís mass, M§. The straight line corresponds to luminosity that is proportional to the fourth power of the mass. The English astronomer Arthur Eddington (1882-1944) proposed a theoretical explanation for this relation in 1924.


Fig7_11 A star moves

Fig7_11 A star moves

Fig. 7.11 . The space velocity, V, of a star relative to an observer can be resolved into two mutually perpendicular components, the radial velocity, Vr, directed along the line of sight, and the tangential velocity, V^, which is perpendicular or transverse to the line of sight. From the Pythagorean theorem V2 = Vr2 + V^2. Over a given interval of time, shown here as one year, the star will move through a proper motion angle m, which depends on V^ and the starís distance, D, from the observer. In this figure, the proper motion m = V^/D is greatly exaggerated, by more than 10,000 for even the closest star. At a distance of only 6 light-years, Barnardís star has the largest known proper motion of 10.3 seconds of arc per year.


Fig7_12 Globular star cluster M80

Fig7_12 Globular star cluster M80

Fig. 7.12 . Hundreds of thousands of ancient stars are held together by their mutual gravitational attraction in this globular star cluster, which is designated M 80 or NGC 6093 and is located about 28,000 light-years from Earth. Most of the stars displayed in this Hubble Space Telescope image are about as old as the observable universe, with ages of nearly 14 billion years, much older than our Sun that is 4.6 billion years old. Stellar collisions result in more massive, and relatively young, ďblue stragglerĒ stars in the dense core of the globular cluster. (Courtesy of NASA/AURA/STScI/Hubble Heritage Team.)


Fig7_13 Faint stars globular cluster

Fig7_13 Faint stars globular cluster

Fig. 7.13 . This five-day exposure from an instrument aboard the Hubble Space Telescope includes the faintest detectable stars in the globular star cluster NGC 6397, which is located about 8,500 light-years away from Earth. Some of these objects are white-dwarf stars, the collapsed, burned-out relics of former stars like the Sun. White dwarfs cool down at a predictable rate, which can be used to measure the age of this globular cluster, estimated to be about 12 billion years old. The crossed lines radiating from the bright stars are diffraction spikes caused by the struts that support the telescope mirror. (Courtesy of NASA/ESA/Harvey Richer, U. British Columbia.)


Fig7_14 Globular star cluster NGC6934

Fig7_14 Globular star cluster NGC6934

Fig. 7.14 . Several hundred thousand stars swarm around the center of the globular star cluster NGC 6934, which lies at a distance of about 50,000 light-years from Earth. These ancient stars are estimated to be about 10 billion years old. This sharp image, obtained from the Hubble Space Telescope, is about 3.5 minutes of arc and 50 light-years across. (Courtesy of NASA/ESA.)


FIg7_15 Open Cluster

FIg7_15 Open Cluster

Fig. 7.15 . A brilliant cluster of bright blue-colored stars is located in the Small Magellanic Cloud, about 200,000 light-years away and about 65 light-years across. This Hubble Space Telescope image subtends an angle of about 70 seconds of arc. (Courtesy of NASA/ESA/E. Olszewski U. Az.)


Fig7_16 Pleiades Open Star Cluster

Fig7_16 Pleiades Open Star Cluster

Fig. 7.16 . These luminous blue-colored stars are members of the open star cluster known as the Pleiades or Seven Sisters, as well as M 45. It can be seen with the unaided eye, without binoculars or a telescope. The Pleiades contains about 3,000 stars, is only 440 light-years away, and about 13 light-years across. Interstellar dust reflects the blue light of the hot stars, creating the hazy nebulous appearance. The telescope causes the prominent, cross-shaped diffraction spikes. Astronomers estimate that the young Pleiades stars were formed just 100 million years ago, and that the cluster will survive for another 250 million years before dispersing. This color-composite image was taken in 1986 with a 48-inch Schmidt telescope as part of the second Palomar Observatory Sky Survey. (Courtesy of NASA/ESA/AURA/Caltech.)


FIG7_17 Runaway star

FIG7_17 Runaway star

Fig. 7.17 . A high-speed star slams into dense interstellar gas, creating a bow shock that may be a million, million kilometers wide. The star is thought to be relatively young, just millions of years old. Moving at a speed of about 100 km s-1, it has journeyed 160 light-years since its birth, most likely in a loosely bound stellar association. (Courtesy of NASA/ESA/R. Sahai/JPL.)