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Stars: Their Properties. T. K. Prasad http://www.cs.wright.edu/~tkprasad (Adapted from a lecture by Daniel Wang of UMass). Twinkle, twinkle, little star, How I wonder what you are. Up above the world so high, Like a diamond in the sky. Stars. Are Stars similar to our Sun?
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Stars: Their Properties T. K. Prasad http://www.cs.wright.edu/~tkprasad (Adapted from a lecture by Daniel Wang of UMass)
Twinkle, twinkle, little star,How I wonder what you are.Up above the world so high,Like a diamond in the sky. Stars Are Stars similar to our Sun? How far away are they? Where did they come from? What do they do? Do they live forever?
The Four Basic Parameters of a Star • Luminosity • Size • Mass • Surface Temperature To infer these parameters, we need to know the distance!
Luminosity and Apparent Brightness • Luminosity is the measure of energy radiated by a star per second over all wavelengths. (Cf. Visual Luminosity) • Luminosity depends both on temperature and surface area. • This cannot be determined by direct observation. • Apparent brightness is the amount of energy coming from the star per square meter per second, as measured on Earth. (cf. Flux) • This can be determined by direct observation.
(cont’d) • Luminosity is an intrinsic property of a star, while apparent brightness depends on the distance to the observer. • Luminosity is how bright a star really is, while apparent brightness is how bright a star appears to an observer.
Distances by Triangulation We can measure distances by comparing the position of objects observed from two ends of the “baseline” of a triangle.
Parallax • Hold your thumb up, steadily in front of you. • Move your head from side to side and note the shift of your thumb with respect to background objects—this angular shift is called parallax. • Now look at your thumb while keeping your head steady but first closing one eye then the other. • Move your thumb closer to you—does it shift more or less with respect to the background?
Stereovision • You use parallax constantly to estimate distances. • Close your eyes. Have a neighbor dangle a pen in front of you, then open just one eye. Without moving your head, bring your hand in from the side and try to touch the pencil with just the tip of another pen. • Your brain processes the information from each eye and compares the angles to allow you to judge distances.
DA PB = DB PA The Geometry of Parallax p We use the Earth’s whole orbit as our baseline. 1 (AU) D (in Parsecs) = P (in arcseconds) 1 parsec (pc) = 3.26 ly. Other useful units: kpc and Mpc
Parallax from a Different Planet If we lived on Mars, orbiting 1.5 times farther away from the Sun, the parallax would be • the same as from Earth • 1.5 times smaller than from Earth • 1.5 times bigger than from Earth
100,000 yrs ago Digression:Proper Motion of Stars (Very Slow) Now Surprising Fact: It is easier to measure radial velocity using Doppler Effect than transverse velocity! 100,000 yrs in future Big Dipper
Stellar Parallax • Since ancient Greek times, astronomers expected that if the Earth moved through space, we would see the stars shifting due to parallax. • If the Copernican model is correct, parallax of stars was a necessary consequence, but it was undetected until the 1830’s because of the huge distances of stars. • The nearest stars shift by only about 0.7 arcsec 1 / 0.7 = 1.4 parsec This is about 4.3 light years or about 27,000,000,000,000 miles !
Survey Question: Stellar Parallax Suppose a star has a parallax of 0.01 arc seconds. How many parsecs away is it? distance (in parsecs) = 1 / parallax (in arcsec) Answer: 100
Brightness, Distance, and Luminosity L=4D2 B apparent brightness luminosity distance
B A Earth B A Apparent Brightness vs Luminosity • Luminosity depends on Brightness & Distance A appears brighter b = L / 4πd2 A appears brighter
How to measure the surface temperature of a star? Overall spectral shape (the peak of the blackbody continuous spectrum) is related to its temperature by Wien’s Displacement Law: T =2.9 × 106 K λmax (nm) More accurately, spectroscopically
Wein’s LawPeak frequency of radiation from a (star) blackbody is proportional to its (surface) temperature
Spectral Types of Stars • Spectral types are defined by the: • existence of absorption lines belonging to various elements, ions, & molecules in a star’s spectrum • the relative strengths of these lines • However, spectral type is not determined by a star’s composition. • all stars are made primarily of Hydrogen & Helium
Reason for Spectral Types • Spectral type is determined by a star’s surface temperature. • temperature dictates the energy states of electrons in atoms • temperature dictates the types of ions or molecules which exist • this, in turn, determines the number and relative strengths of absorption lines in the star’s spectrum
Spectral Type Classification System (L T) O BAFGKM Oh Be A Fine Girl/Guy, Kiss Me! 50,000 K 3,000 K Temperature Other Mnemonics: e.g., Officially, Bill always felt guilty kissing Monica Lewinsky tenderly
Stellar Size • Stars are spherical so we characterize a star’s size by its radius. Stellar Radii vary in sizefrom ~1500 RSun for a large Red Giant to 0.008 RSun for a WhiteDwarf. R How do we determine the radius of a star?
Angular Radius of Star The angular radius of the Sun is about 103 arc seconds. If another star like the Sun was 5 parsecs away (about 106 AU), what would its angular radius be? • 109 arc seconds • 100 arc seconds • 10-3 arc seconds • 10-9 arc seconds
Temperature, Luminosity, and Size – pulling them all together A star’s luminosity, surface temperature, and size are all related by the Stefan-Boltzmann Law: Stefan-Boltzmann Law L=4πR2 σT4 Surfacetemperature Stellarradius Luminosity
L=4πR2 σT4 Two stars have the same surface temperature, butthe radius of one is 10 times the radius of the other.The larger star is 1) 10 times more luminous 2) 100 times more luminous 4) 1/10th as luminous 5) 1/100th as luminous
L=4πR2 σT4 L=4πD2 B Suppose two stars are at equal distance and have the sameradius, but one has a temperature that is twice as great as theother. The apparent brightness of the hotter star is ____ as the other. 1) 1/2 as great 2) 1/4 as great 4) 4 times 5) 16 times as great
Measurements of Star Properties Direct measurent Parallax Distance + apparent brightness ( L=4D2 B) Spectral type (or color) Luminosity + temperature (L=4R2 T4) Apparent brightness (B) Distance Luminosity Temperature Radius Luminosity and temperature are the two independent intrinsic parameters of stars.
How do you weigh a star? • Mass is the single most important property in how a star’s life and death will proceed. • The mass of a star can only be measured directly by observing the effect of its gravity on another object • This is most easily done for two stars which orbit one another --- a binary star!
Newton’s Version of Kepler’s Third Law Star A Newton was able to derive Kepler’s Third Law from his own Law of Gravity. In its most general form: a P2 (mA + mB)= a3 The orbital period of two objects (P) depends on the distance between them (a) and the sum of the masses of both objects (mA + mB). So if P and a can be measured, mA + mB can be estimated. Star B Each star in a binary system moves in its own orbit around the system's center of mass.
Orbits and Masses of Binaries The primary importance of binaries is that they allow us to measure stellar parameters (especially mass). We get the sum of the masses unless we see both stars moving.
Visual Binaries But for most binaries, one cannot separate the stars even with most powerful telescopes. For them, we need to use the spectroscopic information.
Sirius – the brightest star in the sky. Visual Binary Star Images Mizar – in the handle of the Big Dipper. Albireo – The “Cal” star
Spectroscopic Binaries 4 1 2 5 • The total spread (size) of the Doppler shift gives velocities about center of mass orbit sizes, a • The time to complete one repeating pattern period, P 3 Recall: Doppler Shift tells only if it is moving toward or away
Eclipsing Binaries • Binary orbiting edge-on to our line of sight. • The stars alternately eclipse each other changing the apparent brightness. From the eclipse duration, and orbital speed, we can also find the size of the star. Thus one typically can tightly constrain the star masses in eclipsing binaries.
In Review • There are four principal characteristics of a star: • Luminosity • Surface Temperature • Size • Mass How may we classify stars? We can take a census of stars and see what’s out there. But first, let’s do some sociology in the classroom.
Star A has a parallax that is twice that of Star B. What is the relationship between their distances? • Star A is closer than Star B • Star B is closer than Star A • The stars are at the same distance • Not enough information is given
Discussion Question Make a plot that shows the generalrelationship between height and weight for humans. - now add to your plot the population of basketball players who are very tall and very thin. - now add the population of obese wrestlers
How can we classify stars • Collect information ona large sample of stars. • Measure their luminosities(need the distance!) • Measure their surface temperatures(need their spectra)
The Hertzsprung-Russell Diagram Around 1910, Ejnar Hertzsprung (Dane) and Henry Norris Russell (American) had the idea of plotting the luminosity of a star against its spectral type. For a star cluster, all the stars are at the same distance. So, apparent brightness vs spectral type is basically the same as luminosity vs temperature. They found that stars appeared only in certain parts of the diagram.
