Stellar Measurements AST 112 Lecture 6

Off to the stars! Thus far, we have relied upon the Sun for our discussions of stars. In order to study other stars, many of which are clearly different from the Sun, we have to turn our observations to points of light that are no less than 25 trillion miles away. Even at these distances, we can make accurate measurements of numerous properties. And incredibly, it all forms a “big picture” that leads to our understanding of a star’s entire life.

Stars Each one is unique, but… They have common characteristics

Stars We see a snapshot of the universe – Stars evolve, but we can’t watch stellar evolution! – But… we can see patterns in the properties of stars that allow us to piece together their evolution

Stars This is not unreasonable! Cosmic Perspective, Page 519: – Imagine an alien spaceship flies by Earth and has one second to figure us out.

Stars So yes, we only see them at one instant in their lives. But we can see vast numbers of them, and they are at different stages of their lives.

Plan of Attack This lecture: – Luminosity / Apparent Brightness – Distance – Mass Next lecture: – Spectra And then: – Organize it all into a scheme! Finally: – Use the scheme to predict and understand the life cycles of stars

Measuring Stellar Luminosities As we see them, some stars are brighter than others.

Measuring Stellar Luminosity Apparent Brightness: – How bright the star APPEARS to our eyes – Depends on distance and light output Luminosity: – How much light energy the star is giving off – Does NOT depend on distance Luminosities expressed in terms of L Sun

Measuring Stellar Luminosity 60 Watt bulb at 10 ft 60 Watt bulb at 100 ft What do you perceive? Apparent brightness or luminosity? What depends on distance? Apparent brightness or luminosity? What do you get charged for? Apparent brightness or luminosity?

Measuring Stellar Luminosity Conservation of energy: – Star is emitting photons – Photons are energy – Spherical symmetry They spread out.

Measuring Stellar Luminosity This leads to an equation for apparent brightness: – L is Luminosity – d is the distance from the object Apparent Brightness = L ________ 4  d 2

Measuring Stellar Luminosity Cosmic Perspective, Page 520: Suppose Star A is four times as luminous as Star B. How will their apparent brightness compare they are both the same distance from Earth? How will their apparent brightness compare if Star A is twice as far from Earth as Star B?

Luminosity: Size and Color Temperature sets the color – Temperature increases from red to blue – For two stars that are the same size: Blue one is more luminous than red one The surface of a star emits light. – For a given temperature: If Star A has twice the surface area of Star B, Star A has twice the luminosity of Star B

Luminosity: Summary To measure luminosity: – We can measure apparent brightness. – If we can measure the distance, we can calculate the luminosity. Luminosity depends on: – Temperature of the star – Size of the star

Measuring Distance How do we measure the distance to nearby stars?

Measuring Distance Parallax.

Measuring Stellar Masses To find the mass of a star: – Apply Kepler’s 3 rd Law (relates period to orbital distance) But Kepler’s 3 rd Law requires two objects orbiting each other…? So we need to observe binary star systems

Binary Star Systems Three classes of binary star systems: – Visual Binary – Eclipsing Binary – Spectroscopic Binary The differences between these classes are not in the stars, but how we are able to measure them.

Visual Binaries You can SEE the stars orbiting each other.

Eclipsing Binaries The orbiting stars cross in front of one another

Spectroscopic Binaries See Doppler shift if the stars move toward or away from us If stars are so close that we see them as one: – One spectrum superimposed on the other – Lines shift in opposite directions

Step by Step: Masses of Spectroscopic Binary Stars We can get the orbital period of orbit from the spectra. How? We can obtain the size of the orbit from spectra. – Know speeds and orbital period. Then use Kepler’s 3 rd Law to find the total mass of the system. Depending on the relative masses of the stars: – Lines of less massive star shift more – Lines of more massive star shift less