# Day 23 - Ch. 8 - Characterizing Stars

Characterizing Stars This is the full version of the material I use in the Physics 101 class Introduction

to Astronomy As the Earth moves around the Sun in its orbit, nearby stars appear in different apparent locations

on the celestial sphere. This effect is called Parallax. It can be used to find the distance to nearby stars.

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 Suns 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. Barnards 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 Barnards 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.

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. 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) 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) Blackbody Curves for some typical star temperatures

Only two points are needed to determine the temperature. Stellar Spectra

These are simulated spectra. Real spectra have lots of fine structure. Simulated elemental

spectra: (link) 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 0.01 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. 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 0.01 times the size of the Sun. The smallest would therefore be about the size of Earth.

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