Characterizing Stars

on the celestial sphere. As the Earth moves around the Sun in its orbit, nearby stars appear in different apparent locations on the celestial sphere. FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change the angle between their lines of sight as we look at things that are different distances away. Our eyes are adjusting for the parallax of the things we see. This change helps our brains determine the distances to objects and is analogous to how astronomers determine the distance to objects in space. (c) As Earth orbits the Sun, a nearby star appears to shift its position against the background of distant stars. The star’s parallax angle (p) is equal to the angle between the Sun and Earth, as seen from the star. The stars on the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale, the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us, the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of the parallax angle p (in arcseconds), d 1/p. (a, b: Mark Andersen/ JupiterImages)

This effect is called Parallax. It can be used to find the distance to nearby stars. FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change the angle between their lines of sight as we look at things that are different distances away. Our eyes are adjusting for the parallax of the things we see. This change helps our brains determine the distances to objects and is analogous to how astronomers determine the distance to objects in space. (c) As Earth orbits the Sun, a nearby star appears to shift its position against the background of distant stars. The star’s parallax angle (p) is equal to the angle between the Sun and Earth, as seen from the star. The stars on the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale, the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us, the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of the parallax angle p (in arcseconds), d 1/p. (a, b: Mark Andersen/ JupiterImages)

FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change the angle between their lines of sight as we look at things that are different distances away. Our eyes are adjusting for the parallax of the things we see. This change helps our brains determine the distances to objects and is analogous to how astronomers determine the distance to objects in space. (c) As Earth orbits the Sun, a nearby star appears to shift its position against the background of distant stars. The star’s parallax angle (p) is equal to the angle between the Sun and Earth, as seen from the star. The stars on the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale, the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us, the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of the parallax angle p (in arcseconds), d 1/p. (a, b: Mark Andersen/ JupiterImages)

Stellar Parallax (link to 3d simulation) A Parsec is the distance from us that has a parallax of one arc second (parsec = pc) 1 parsec = 206,265 A.U. or about 3.3 light-years

The Sun’s Neighborhood Each successive circle has a radius which is 0 The Sun’s Neighborhood Each successive circle has a radius which is 0.5 parsec larger About 21 systems are shown (some are binaries)

Some nearby stars Proxima Centauri, a companion to Alpha Centauri, is the nearest star. It has a parallax angle of 0.76” (arc seconds) so the distance is 1/.76 = 1.3 parsecs. 1 parsec = 3.3 light-years, so the Alpha Centauri system is about 4.3 light-years away, or about 270,000 A.U., a typical distance between stars. Barnard’s star is another example; it is 1.8 pc away. Analogy: Make a model with the Sun and Earth at one meter distance from each other: the Sun is a marble, the Earth a grain of sand, and the nearest star is 270 km away (St. Louis).

In addition to the apparent motion due to parallax, stars also have Real Space Motion. A study of Barnard’s Star over a period of 22 years reveals that it has a transverse velocity of 88 km/sec.

Hipparcos spacecraft being put into a huge vacuum chamber for environmental tests. This satellite was able to measure the positions of thousands of stars with very high accuracy. (1989-1993)

Hipparcos spacecraft mission (European Space Agency,1989-93) This space mission, named after the ancient Greek astronomer, was the very first space mission for measuring the positions, distances, motions, brightness and colors of stars. The science of astrometry is the measurement of astronomical objects. ESA's Hipparcos satellite pinpointed more than 100,000 stars, with measurements of position that were 200 times more accurate than ever before. The accuracy is equivalent to an angle of the height of a person standing on the Moon. Stars were measured out to a distance of 300 light years. The primary product from this mission was a set of stellar catalogues, The Hipparcos and Tycho Catalogues, published by ESA in 1997. Some of this data is available on the web site: “The Hipparcos Space Astrometry Mission” (link)

Gaia spacecraft mission (European Space Agency, 2015 - ) ESA's Gaia satellite was launched in 2015 and is still operating. It has measured the precise positions of more than 1 billion stars, and the distances of over 2 million of the nearer stars. For details, see their website at http://www.esa.int/Our_Activities/Space_Science/Gaia There is a virtual tour of the Milky Way which ends with some graphics showing the extent of the Hipparcos and Gaia surveys. The first major product is a 3-d map of a significant part of our Milky Way galaxy, out to about 30,000 light years from the Sun. (link)

The Inverse-Square Law for Light – means that the light is “diluted” or spread out over a larger area as it travels away.

FIGURE 11-3 The Inverse-Square Law (a) The same amount of radiation from a light source must illuminate an ever-increasing area as the distance from the light source increases. The decrease in brightness follows the inverse-square law, which means, for example, that tripling the distance decreases the brightness by a factor of 9. (b) The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in part (a). (b: Royalty Free/CORBIS)

Luminosity contributes to apparent magnitude, so two unlike objects at different distances may appear the same.

Magnitudes of some stars in the vicinity of Orion. Sirius is the brightest star in the sky. FIGURE 11-2 Apparent Magnitude Scale (a) Several stars in and around the constellation Orion, labeled with their names and apparent magnitudes. For a discussion of star names, see Guided Discovery: Star Names. (b) Astronomers denote the brightnesses of objects in the sky by their apparent magnitudes. Stars visible to the naked eye have magnitudes between m 1.44 (Sirius) and about m 6.0. However, CCD (charge-coupled device) photography through the Hubble Space Telescope or a large Earth-based telescope can reveal stars and other objects nearly as faint as magnitude m 30. (a: Okiro Fujii, L’Astronomie)

Apparent Magnitude of some typical objects, along with some limits for seeing through various instruments. Each change in magnitude by 1.0 means a change in the amount of light seen, by a factor of 2.5 (times, less or more). Larger magnitudes mean a dimmer object.

More on the Magnitude Scale The absolute magnitude is the apparent magnitude of an object when viewed from 10 pc Our sun would appear to have an apparent magnitude of 4.8 if it were at 10 pc distance, so it has an absolute magnitude of 4.8

Magnitude Scale (This is inverted from the previous version) FIGURE 11-2 Apparent Magnitude Scale (a) Several stars in and around the constellation Orion, labeled with their names and apparent magnitudes. For a discussion of star names, see Guided Discovery: Star Names. (b) Astronomers denote the brightnesses of objects in the sky by their apparent magnitudes. Stars visible to the naked eye have magnitudes between m 1.44 (Sirius) and about m 6.0. However, CCD (charge-coupled device) photography through the Hubble Space Telescope or a large Earth-based telescope can reveal stars and other objects nearly as faint as magnitude m 30. (a: Okiro Fujii, L’Astronomie)

Star Colors vary from red to blue; an example is in Orion.

Many star colors are seen in dense regions near the center of the Milky Way galaxy.

The color of a star is due to its temperature. Blackbody spectra (continuous curve) for some representative objects (brown dwarf, Sun, Rigel) FIGURE 11-4 Temperature and Color (a) This beautiful Hubble Space Telescope image shows the variety of colors of stars. (b) These diagrams show the relationship between the color of a star and its surface temperature. The intensity of light emitted by three stars is plotted against wavelength (compare with Figure 4-2). The range of visible wavelengths is indicated. The location of the peak of a each star’s intensity curve, relative to the visible light band, determines the apparent color of its visible light. The insets show stars of about these surface temperatures. Ultraviolet (uv) extends to 10 nm. See Figure 3-6 for more on wavelengths of the spectrum. (a: Hubble Heritage Team/AURA/STScI/NASA; left inset: Andrea Dupree/Harvard-Smithsonian CFA, Ronald Gilliland/STScI, NASA and ESA; center inset: NSO/AURA/NSF; right inset: Till Credner, Allthesky.com)

Blackbody Curves for some typical star temperatures Only two points are needed to determine the temperature.

Stellar Spectra These are simulated spectra Stellar Spectra These are simulated spectra. Real spectra have lots of fine structure. Simulated elemental spectra: (link)

FIGURE 11-5 The spectra of stars with different surface temperatures. The corresponding spectral types are indicated on the right side of each spectrum. (Note that stars of each spectral type have a range of temperature.) The hydrogen Balmer lines are strongest in stars with surface temperatures of about 10,000 K (called A-type stars). Cooler stars (G- and K-type stars) exhibit numerous atomic lines caused by various elements, indicating temperatures from 4000 to 6000 K. Several of the broad, dark bands in the spectrum of the coolest stars (M-type stars) are caused by titanium oxide (TiO) molecules, which can exist only if the temperature is below about 3500 K. Recall from Section 4-5 that the Roman numeral I after a chemical symbol means that the absorption line is caused by a neutral atom; a numeral II means that the absorption is caused by atoms that have each lost one electron. (R. Bell, University of Maryland, and M. Briley, University of Wisconsin at Oshkosh)

Betelgeuse is large enough to be imaged and some features can be observed. So we get a direct measurement of its size.

Stellar Sizes: from 300 times the size of the Sun to only 0 Stellar Sizes: from 300 times the size of the Sun to only 0.01 times the size of the Sun.

Stellar sizes Some stars are close enough and big enough to be seen as disks, for example Betelguese. Most stars look like points, so we need to deduce the size from the luminosity (based on the apparent magnitude) and the temperature by a formula: luminosity a (radius)2 x (temperature)4 (where a means “is proportional to”)

Antares is 300 times the size of the Sun Antares is 300 times the size of the Sun. It would reach almost the distance to the orbit of Mars if it replaced the Sun in our solar system.

Some stars are near the size of the Sun.

Small stars (dwarfs) range from the size of the Sun to only 0 Small stars (dwarfs) range from the size of the Sun to only 0.01 times the size of the Sun. The smallest would therefore be about the size of Earth.