Chapter 8: Characterizing Stars

As the Earth moves around the Sun in its orbit, nearby stars appear in different apparent locations on the celestial sphere.

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 (link to 3d simulation)

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, 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: Sun and Earth at 1 m distance from each other, the Sun is a golf ball, 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. 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. ( )

Hipparcos spacecraft mission (European Space Agency, ) 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. The primary product from this mission was a set of stellar catalogues, The Hipparcos and Tycho Catalogues, published by ESA in Some of this data is available on the web site: “The Hipparcos Space Astrometry Mission” (link)(link)

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.

More on the Magnitude Scale The absolute magnitude is the apparent magnitude 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)(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  (radius) 2 x (temperature) 4 (where  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.

Chapter 10: Stars Part 2 - with a quick review of part 1 Answer questions on the worksheet as we go (for extra credit).

Stellar Parallax 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

Questions 1 and 2 Stellar Parallax The parallax angle is an angle in the triangle with a baseline of one astronomical unit (1 A.U.)

Question 1 One parsec corresponds to an angle of 1 arc second. 10 parsecs would correspond to an angle of 1/10 of an arc second. And 50 parsecs would correspond to an angle of 1/50 of an arc second. Star X is nearer and has the greater parallax angle.

Question 2 We measure the parallax angle in order to find the distance, so we can calculate the absolute magnitude.

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

Inverse-Square Law for Light - question 3.

Question 3 The farther star is 4 times as far away. Thus it is fainter. 4 times 4 is 16, so it is 16 times fainter. Imagine one more shell in the previous picture, with 4x4 or 16 squares.

Two unlike objects at different distances may appear the same – question 4

Question 4 Just like the picture, the closer star must be dimmer, if it appears as bright as the farther star. Thus the closer star has a lower luminosity (amount of light emitted).

Apparent Magnitude of some typical objects, along with some limits for seeing through various instruments. Question 5

Question 5 An 8 th magnitude star is one magnitude greater than a 7 th magnitude star, so it is dimmer. Each magnitude corresponds to a change in brightness of 2.5 times. So the 8 th magnitude star is 2.5 times dimmer than the 7 th magnitude star.

The absolute magnitude is the apparent magnitude 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 Question 6 Once we get the absolute magnitude from the apparent magnitude and the distance, we can get the luminosity compared to the Sun.

Question 6 The concept of absolute magnitude allows us to remove the effect of differing distance. Thus we can talk about the properties of the star itself, without needing to keep in mind the location (or distance from us).

Star Colors vary from red to blue – question 7

Question 7 The color of a star will not change if we look at it from a different distance … unless there is a dust cloud in the way. However, the angular size, parallax, apparent magnitude, and proper motion would appear to change at different distances.

spectral classification uses letters for the spectral classes: OBAFGKM (and LT) based on the star’s temperature.

Summary so far To measure the stars, we measure the 1. apparent magnitude 2. distance (by parallax) 3. spectrum (to find the temperature) and so we can deduce the luminosity and spectral class (OBAFGKM-LT)

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  (radius) 2 x (temperature) 4 (where  means “is proportional to”) Questions 8 and 9

Question 8 From the formula: luminosity  (radius) 2 x (temperature) 4 If the radius is not changed, but the temperature is increased from T to 2T then 2T times 2T times 2T times 2T gives a number 16 times greater than T 4

Question 9 From the formula: luminosity  (radius) 2 x (temperature) 4 If the temperature is not changed, but the radius is increased from r to 2r then 2r times 2r gives 4r 2 - which is 4 times greater than r 2