Unit 10: Measuring the Properties of Stars Mr. Ross Brown Brooklyn School for Law and Technology

In this unit we will learn about: How we measure stars’ distances using parallax Why a star’s color indicates temperature & how to use Wien’s law to determine temperature The difference between luminosity and brightness How we can measure radius using temperature The magnitude system of star brightness Stellar spectra and how it indicates surface temperature Luminosity classes How we estimate stellar masses The H-R diagram for inferring a star’s size and evolutionary state

How do we measure a star’s distance 7 March 2016 Do now: Why is it important to know a star’s distance from Earth? What other things can we calculate if we know the distance?

How do we measure a star’s distance For nearby stars…. Triangulation Lay out a right triangle, whose one side we know

How do we measure a star’s distance Parallax Method of triangulation that uses an apparent change in an object’s position as the observer’s position changes.

How do we measure a star’s distance Parallax is small across such large distances. Rather than measure it in degrees, we measure it in fractions of degrees called “arc seconds” (1/3600 of a degree, 1/60 of an arc minute)

Homework #17 7 March 2016 How is a parsec defined? How big is a parsec compared to a light year?

How do we measure a star’s distance We define a parallax (p) as ½ the angle by which it appears to shift. From this, we measure a star’s distance (d) as 1/p where p is in arc seconds and d is parsecs. dpc=1/parc seconds One parsecs = 3.26 light-years (3.09*1013 km)

How do we use a star’s light to learn about its properties? 14 March 2016 (Happy Pi Day!) Do now: How can we tell how hot something is without using a thermometer or touching it?

How do we use a star’s light to learn about its properties? Temperature Stars are VERY hot Hotter  blue, cooler  red

How do we use a star’s light to learn about its properties? Using color more precisely Wien’s Law: longer wavelength = cooler temperature

How do we use a star’s light to learn about its properties? Luminosity: the amount of energy an object radiates Lightbulb = 60-75 watts Sun = 4* 1026 watts Luminosity measures how fast an object consumes its fuel

How do we use a star’s light to learn about its properties? Luminosity measured via inverse-square law Its distance and apparent brightness

How do we use a star’s light to learn about its properties? Radius If two stars have the same temperature but one is more luminous, the more-luminous star must have a larger surface area, thus a larger radius

How do we use a star’s light to learn about its properties? Stefan-Boltzmann Law If two stars have the same size but the surface of one is hotter, the hotter star will have greater luminosity

In what other ways can we measure a star’s properties? 15 March 2016 (Beware the Ides of March!) Do now: Which star is cooler and many times brighter than Earth’s Sun? a) Barnard’s Star b) Betelgeuse c) Rigel d) Sirius

In what other ways can we measure a star’s properties? Direct measurement of radius (Yesterday we used luminosity and Stefan-Boltzmann Law to arrive at radius) We can be more precise by using Angular Size

In what other ways can we measure a star’s properties? Challenges to using angular size Due to distance, fuzzy images, even with telescopes Large ground-based telescopes get better images, but the atmosphere blurs them some Computer can de-blur it a little

In what other ways can we measure a star’s properties? We need a HUGE telescope Or TWO telescopes, far apart, combined with computers

In what other ways can we measure a star’s properties? Star radii differ greatly Most are roughly the size of our Sun Some, like Betelgeuse, are hundreds of times larger. These are Giants Smaller stars, including our Sun, are Dwarfs, or Dwarves

In what other ways can we measure a star’s properties? The Magnitude System of measuring brightness 150 BCE, Greek astronomer Hipparchus Brightest is magnitude 1, dimmest is magnitude 6

In what other ways can we measure a star’s properties? Is the Magnitude System the best system? Apparent magnitude is a function of luminosity and distance The scale is “backward,” with the lowest number representing the brightest stars Magnitude differences represent ratios Each magnitude represents a factor of 2.512

Homework #18 15 March 2016 What is the H-R Diagram? What are its axes?

How can we differentiate between classes of stars? 16 March 2016 Do now: What are dimensions across which we can differentiate one star from another?

How can we differentiate between classes of stars? The Hertzsprung-Russell Diagram (H-R) 1912 If we plot stars according to luminosity and temperature, the follow a smooth curve

How can we differentiate between classes of stars? The H-R Diagram Bright stars on top, dim on bottom Hot stars on left, cool on right Blue on left, red on right Temperature-wise, this is opposite other graphs The curve on which most stars (90%) are depicted is the Main Sequence

How can we differentiate between classes of stars?

How can we differentiate between classes of stars?

How can we differentiate between classes of stars? 17 March 2016 Do now: On what factors does the luminosity of a star depend?

How can we differentiate between classes of stars? Luminosity depends on a star’s surface area and temperature If stars are the same temperature and one is brighter, it must have a larger radius This is a Giant Cool giants are Red Giants Hot stars that are dim must have smaller radii Dwarfs If it’s hot yet dim, White Dwarf

How can we differentiate between classes of stars? What can we surmise about mass and density and luminosity? The Mass-Luminosity Relation Larger mass = greater luminosity

How can we differentiate between classes of stars? Luminosity Classes

How can we differentiate between classes of stars? 18 March 2016 Do now: What are the various methods we use for determining stellar quantities?

How can we differentiate between classes of stars? Methods of determining stellar quantities Distance Temperature Luminosity Composition Radius Mass Radial Velocity

How can we differentiate between classes of stars? The Method of Standard Candles Think about oncoming headlights as you drive

How can we differentiate between classes of stars? Method of Standard Candles If we know luminosity and brightness, we can calculate distance

How can we differentiate between classes of stars?