How do we know the distance to these stars?

The Ping Pong Ball Challenge -Devise a method for determining the height of the ping pong ball above the floor. -You are restricted to the floor. -You can only measure things on the floor and up to one cinder block above the floor. -You can use what you can see 15 bonus points Due by the time we take the test for this unit.

When we look into the night sky, what are some things we can determine about the stars? What are some things we can not determine?

Which is brighter? What are the factors that need to be considered in order to answer this question?

Cosmic Distance Ladder

How do we measure the distance to NEARBY stars? We can use triangles.

Triangles The small triangle has the same shape as the large one. By measuring the two sides of the small triangle and the short side of the big triangle, we can calculate the length of the long side of the big triangle.

Measuring distance A a d D d D A a D A d a

p Take two telescopes some distance apart and observe the same star. Measure the tilt between the two telescopes this sets all the angles for the triangles. Then we can find the distance to the star from the distance between the telescopes and the angle of the tilt. p

Simple Trigonometry sin(θ) = Opposite / Hypotenuse cos(θ) = Adjacent / Hypotenuse tan(θ) = Opposite / Adjacent

A.U. = Astronomical Unit = distance from Earth to Sun

The largest distance is not by placing the two telescopes at opposite ends of the Earth. Instead, we can use one telescope and just let the earth move.

Stellar Parallax As Earth moves from one side of the Sun to the other, a nearby star will seem to change its position relative to the distant background stars. d = 1 / p d = distance to nearby star in parsecs p = parallax angle of that star, measured in arcseconds

There are 60 arc-seconds in one arc-minute, 60 arcminutes in one degree, and 360 degrees in a full circle.

Closer star larger parallax

Brightness of stars Hipparchus (Greek, 150BC) catalogued all stars he could see in the sky, which included how bright they were. He innocently thought up a brightness scale in which he designated the brightest stars as magnitude 1 ( first ranked ) ranging down to a magnitude of 5 for the stars he could barely see. Unfortunately this froze into astronomy for all time a brightness scale that runs backwards smaller numbers mean MORE flux.

What can we learn from a star s color? The color indicates the temperature of the surface of the star. The same is true for the filament in a light bulb or any other hot object.

Electromagnetic spectrum The spectrum of a particular star is how much light it produces at each wavelength.

Wien s law Cooler objects produce radiation which peaks at longer wavelengths (redder colors), hotter objects produce radiation which peaks at shorter wavelengths (bluer colors).

A star s color depends on its surface temperature

What color is our sun?

Stars are assigned a `spectral type based on their spectral analysis The spectral classification essentially sorts stars according to their surface temperature

Spectral type Sequence is: O B A F G K M O type is hottest (~25,000K), M type is coolest (~2500K) Star Colors: O blue to M red Sequence subdivided by attaching one numerical digit, for example: F0, F1, F2, F3 F9 where F1 is hotter than F3. Sequence is O O9, B0, B1,, B9, A0, A1, A9, F0, Useful mnemonics to remember OBAFGKM:

O B A F G K M

The spectrum of a star is most determined by 1. The temperature of the star s surface 2. Composition. 3. The star s distance from Earth 4. The density of the star s core 5. The luminosity of the star

Flux and luminosity A star produces light the total amount of energy that a star puts out as light each second is called its Luminosity. If we have a light detector (eye, camera, telescope) we can measure the light produced by the star the total amount of energy intercepted by the detector divided by the area of the detector is called the Flux.

Luminosity How, exactly, would we measure something like this?

Flux and luminosity To find the luminosity, we take a shell which completely encloses the star and measure all the light passing through the shell To find the flux, we take our detector at some particular distance from the star and measure the light passing only through the detector. How bright a star looks to us is determined by its flux, not its luminosity. Brightness = Flux = Apparent Magnitude

Luminosity So, the luminosity for a star is always the same. Distance, in regards to Luminosity, is irrelevant.

Luminosity Is it possible to actually take a direct measurement of something like this? What would you have to do? Do you think there is another way around this?

ASPD

Cosmic Distance Ladder

Remember: What is the Flux of a star? a.k.a. Apparent Magnitude a.k.a. Brightness a.k.a. Intensity

What About Flux? Can we use the FLUX of a Star to determine its distance? How? Flashlight graphing activity

Inverse Square Law

Inverse Square Law Light from any source diminishes by an amount equal to the inverse of the square of the distance from the source. This makes things predictable.

INVERSE SQUARE LAW

Calculating Distance So what do we need to do it? Do we have it?

Flux and luminosity Flux decreases as we get farther from the star Distance 2 = 1 / (Flux/Luminosity) Mathematically, if we have two stars A and B Flux Flux A B Luminosity pr Luminosity A B Distance Distance B A 2

So, can we calculate the distance to a star using its brightness? What do we need?

The luminosity / distance relationship can be used to determine distances throughout the universe. The problem is, it is often difficult to determine the total luminosity of a star, therefore a distance cannot be calculated. Unless... We have a STANDARD CANDLE A Standard Candle is an object in the universe with a known luminosity. If there are objects with a known luminosity, and we can observe their flux, the distance to that object can be easily calculated.

Cosmic Distance Ladder

Classifying stars We now have two properties of stars that we can measure directly: Flux (apparent magnitude) Color / surface temperature Using these two characteristics has proved extraordinarily effective in understanding the properties of stars the Hertzsprung-Russell (HR) diagram

Two Astronomers independently came up with a graph that represents a stars luminosity, temperature, and magnitude. Danish astronomer Ejnar Hertzsprung American astronomer Henry Norris Russell (2 years later) The Hertzsprung-Russell diagram is a statistical plot of luminosity and spectra.

Hertzsprung-Russell diagram

If we plot lots of stars on the HR diagram, they fall into groups

So how do we know where to plot the stars on this diagram? We use the PARALLAX METHOD to calibrate the diagram. In other words, all of the stars you see have distances determined by the Parallax Method, therefore we can determine their luminosity, therefore we can place them on the graph.

So what? Big deal, right? Well, we already established that if we have the luminosity, we can calculate the distance.

So how do we know whether it s a main sequence or a giant star? Won t that effect the determined luminosity?

The spectrum also tells us the composition. For example, if a spectrum tells us the star has mostly hydrogen, that s a good clue that it should be a main sequence star. If the spectrum tells us it has a lot of helium with some other heavier elements, then it could be in the GIANT phase of its life.

O B A F G K M

The spectra tells us their composition, thus their likely stage of evolution, thus where on the H-R diagram they belong.

Once they are on the graph, a pattern is established and we can use the pattern to determine the luminosity of any star we see in the sky. We look at it, determine its spectral class, place it on the trend line of the H-R diagram, and we then have its luminosity. Once the luminosity is determined, we can calculate the distance.

HR diagram

The third rung Identification of spectral class will determine a stars luminosity. Once we have the luminosity, we can calculate the distance.

Luminosity classes Class Ia,b : Supergiant Class II: Bright giant Class III: Giant Class IV: Sub-giant Class V: Dwarf The Sun is a G2 V star

A0III 4000K and -7 Ab Mag F2IV O9II Type F with a +15 AbsMag K2II Type G with +5 AbMag

We use the PARALLAX METHOD to calibrate this technique. In other words, we calculate the distance to one of these standard candles, measure their flux, and then calculate their luminosity. If this is done for hundreds of these particular type of star, then we have a STANDARD by which we compare to others.

Cepheid Variables are a standard candle Young, massive, bright stars undergo periodic changes in luminosity (i.e. they blink). The period of the blinking is directly proportional to their size, thus their luminosity. If you measure the period of the blinking, and thus determine its luminosity, you can easily calculate the distance because you know the flux by direct observation.

Cepheid variable

Type 1a supernovae are a standard candle All type 1a supernovae have the same luminosity when they reach critical mass and explode. Once again, it is easy to measure their flux, therefore it is easy to measure the distance to the 1a supernova.

Type 1a supernovae are a standard candle The great things about this are: type 1a supernovae occur repeatedly with the same star, and the critical mass is the same each time it explodes, so the luminosity will not change from explosion to explosion. They are extremely bright, so can be used for very far objects, such as other galaxies.