Stars come in all sizes, small, large

and even larger.

(2) Effective Temperature (T) - determined from continuous spectrum (blackbody curve), Wien’s Law. Stellar Properties: (1) Distance – measure parallax for closer stars There are 6 important properties of stars.: (3) Luminosity (L) - determined from apparent magnitude and distance, or from spectrum (luminosity class).

(4) Chemical composition - determined from line spectrum. (5) Radius (R) - determined from luminosity and temperature, or from distance. (6) Mass (M) - determined from binary stars

The distance to a star in parsecs is: We can get some accurate distances by Stellar Parallax One arcsecond = 1’’and, is the angular size of a dime seen from 2 miles or a hair width from 60 feet. 1 parsec = 3.26 light-years = 3.09x10 13 km The nearest star, aside from the Sun, is called Proxima Centauri with a parallax of 0.77 arcsecond. Its distance is therefore: 1.3 pc

Inverse Square Law of Brightness The Apparent Brightness of a source is inversely proportional to the square of its distance: The apparent brightness of a light source varies inversely with the square of the distance Brightness = 1/D 2 = 1/D 2 2-times Closer or 1/2 distance = 4-times Brighter 2-times Farther = 1/4-times as Bright

Black Body Radiation A Blackbody is a perfect absorber, an object that absorbs light at all wavelengths, and it heats up. It is also the perfect radiator: emits at all wavelengths (continuous spectrum) characterized by its Temperature. Energy emitted depends strongly on Temp. Stars act nearly like Black Bodies.

Radiation Laws Three Laws Characterize Continuous Spectra Planck Wien Stefan-Bolzman With these laws we can determine the temperature & other characteristics of stars.

1.The Planck radiation law assumes that the object observed is a perfect radiator and absorber of energy (black body). 2. Stars, although not perfect black bodies, are close enough so that Planck curves are useful descriptions of their radiation.

Wien’s Law for Black Bodies : The peak of a black body curve shifts toward shorter wavelength if the temperature is increased.

Black Body Temperature Star B is cooler Our Sun A cooler star will have a lower, flatter peak closer to the red end. Star A is hotter According black-body radiation, the spectrum of a hotter star will have a higher, sharper peak closer to the blue end of the spectrum.

Continuum & Lines Real stars usually have a blackbody-like continuous spectrum, upon which absorption lines are superimposed

Hydrogen Continuum Absorption Lines A spectrum can be converted to a trace spectrum.

Wien’s Law Is measured in nm which is m or The p eak wavelength of a Black Body depends upon the Temperature. The higher the temperature, the shorter the wavelength of the peak radiation. So, we can get the temperature of a star form its spectrum. Needs to be in meters (m)

The sun’s max intensity is at a wavelength of about 500nm or Using Wien’s Law, calculate the sun’s surface temperature. Problem

F R It only depends upon the temperature of the object and a constant. It’s the rate of heat flow/sec. Stefan-Boltzmann Law If you know the temperature of a Black Body then the total energy emitted from from each square meter, called Energy Flux (F), can be calculated. This is only for a square meter and stars are different sizes, so to find the total energy, which is called Luminosity, we change the formula to :

Luminosity Temperature Surface Area (how hot) (how big) So,Luminosity depends upon Radius(R) & Temperature(T) Luminosity is, the total amount of e nergy per second emitted. The Star’s total Wattage! The area of a sphere is, A= So, the total energy emitted by the object each second is called the Luminosity (L).

Brightness: How bright something appears to us,depends on temperature, size, and the distance. These 2 will put out the same energy per square unit because: This one is much bigger (R) So the total L is much more. Greater Temperature Greater Luminosity Same Size same temperature

L = 4   R 2 T 4 This formula relates a Star’s Temperature and Surface Area (its size) to its Luminosity. It’s more natural to compare an object to a known object. Comparing a star to the Sun would be easier and more helpful, since we know a lot about the Sun and it is a star. L = 4   R 2 T 4 looks rather messy  is a constant that you will not have to use. Let’s get rid of the constants !

Since 4  and  are constants, in the next formula they cancel each other when compared to the sun. Giving

Betelgeuse has a Luminosity of 60,000 L and a surface temperature of 3500 K. Find the radius compared to the Sun. Example Problem

Suppose a star is 10 times the Sun’s radius, but only ½ as hot.Find the luminosity of the star compared to the Sun. The star is 6.25 times the Sun’s Luminosity

The next two formulas are for Main Sequence stars only ! M is the mass of the star in solar mass. L is the Luminosity of the star in solar Luminosity. Life Time is the approximate life time of a MS star in solar life times. What is the Luminosity of a MS star that has a mass 4 times the sun ? Life

How long can a 4 solar mass MS star live ? Solar life times Or, since the sun will live for 10 billion years

Over half of the stars in the sky have stellar companions, bound together by gravity and in orbit around each other.

Visual Binaries Optical Binaries Optical Binaries- are chance superpositions, where two stars appear close together but do not actually orbit one another. (Like Mizar & Alcor) Types of Binaries Physical Binaries Physical Binaries- where one star orbits another, and each star can be seen in the telescope.

OPTICAL DOUBLES Not a true binary system Stars only appear close together in the sky Mizar & Alcor in the Big Dipper While Alcor and Mizar are Optical Double stars and only appear to be near each other, Mizar is actually a Physical Binary star.

Types of Physical Binaries Eclipsing Binary –(If the angle is good ) two stars that regularly eclipse one another causing a periodic variation in brightness. Spectroscopic Binary - two stars that are found to orbit one another through observations of the Doppler effect in their spectral lines. At least half of the stars in the sky are binaries. Eclipsing Binary stars are also referred to as Extrinsic Variable Stars.

Orbits and Masses of Visual Binaries The primary importance of binaries is that they allow us to measure stellar parameters (especially mass). The center of mass is the location where a fulcrum would be placed to balance the stars on a seesaw.

Masses of Binary stars Newton’s Modification of Kepler’s Law P must be in years, a in AU M in solar mass, where Sun = 1

A nearby star Epsilon Eridani has a planet circling the star at a distance of 3.4 AU. The period of the planet is 7.1 years. Find the mass of the star, assuming the mass of the planet to be negligible. Problem - Ignoring the mass of one object.

When dealing with binary stars, the mass of the two stars are similar, and cannot be simply ignored. Sirius b is a white dwarf, and its orbital period around Sirius takes 50 years.If the distance between the the stars is 20 AU, find the mass of the stars.

But we happen to know that Sirius’ mass 1.99 Msun and so, Sometimes we might be able to get information about one of the stars from the H- R diagram to help us determine the mass of both stars. So,

Eclipsing Binaries Sometimes the orbital plane is lined up so that the stars pass in front of each other as seen from the Earth. Each eclipse will cause the total light from the system to decrease. The amount of the decrease will depend on how much of each star is covered up (they can have different sizes) and on the surface brightness of each star.

Some binaries are too close together to be resolved, you may still be able to detect the binary through the Doppler shift (in one or both stars). They must be relatively close to each other (short orbital period). If you can see both stars’ spectrums, you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge- on, etc.). This is usually useful information. Spectroscopic Binaries

Thank goodness, my brain is full