Measuring the Properties of Measuring the Properties of StarsStars

Warm UpWarm Up1.1. Where are bright, cool stars located on the H-R Where are bright, cool stars located on the H-R

Diagram? Diagram?

2.2. Where are bright, hot stars located on the H-R Where are bright, hot stars located on the H-R Diagram?Diagram?

3.3. Where are dim, cool stars located on the H-R Where are dim, cool stars located on the H-R Diagram?Diagram?

4.4. Where are dim, hot stars located on the H-R Where are dim, hot stars located on the H-R Diagram?Diagram?

5.5. What is the H-R Diagram?What is the H-R Diagram?

6.6. What is the H-R Diagram used for?What is the H-R Diagram used for?

7.7. What are the seven spectral classes of stars?What are the seven spectral classes of stars?

8.8. What is luminosity?What is luminosity?

Warm UpWarm Up

1.1. What is parallax?What is parallax?

2.2. What is an arc second?What is an arc second?

3.3. What is a parsec?What is a parsec?

4.4. How long is a parsec?How long is a parsec?

5.5. One degree of arc equals the thickness One degree of arc equals the thickness on a penny on its side from how far on a penny on its side from how far away?away?

Warm Up-11/04/12Warm Up-11/04/12

1.1. The angular shift from January to June of the The angular shift from January to June of the star Rigel is 0.25 arc seconds. How far away is star Rigel is 0.25 arc seconds. How far away is Rigel in parsecs? How far away is Rigel in light Rigel in parsecs? How far away is Rigel in light years?years?

2.2. The angular shift from January to June of the The angular shift from January to June of the star Alhambra is 0.345 arc seconds. How far star Alhambra is 0.345 arc seconds. How far away is Alhambra l in parsecs? How far away is away is Alhambra l in parsecs? How far away is Alhambra in light years?Alhambra in light years?

3.3. What is a standard candle?What is a standard candle?

Comet ISON SiteComet ISON Site

http://blogs.discovermagazine.com/http://blogs.discovermagazine.com/outthere/2013/10/25/novice-observers-outthere/2013/10/25/novice-observers-guide-comet-ison/guide-comet-ison/

Warm UpWarm Up1.1. Name two ways to determine the distance to a Name two ways to determine the distance to a

star.star.

2.2. Wein’s Law equates temperature with what?Wein’s Law equates temperature with what?

3.3. What is luminosity?What is luminosity?

4.4. What is apparent brightness?What is apparent brightness?

5.5. What is magnitude?What is magnitude?

6.6. List the 7 spectral classes and tell which List the 7 spectral classes and tell which direction stars are getting hotter?direction stars are getting hotter?

Wondering as You Look at the StarsWondering as You Look at the Stars

It’s impossible not to wonder as you look It’s impossible not to wonder as you look at the stars. What would that star look like at the stars. What would that star look like if you were close to it? How hot is that if you were close to it? How hot is that star? What is that star made of?star? What is that star made of?

Yet, scientists have developed ways to Yet, scientists have developed ways to answer many of these questions. Kepler answer many of these questions. Kepler gives us star’s masses, Wein’s Law gives gives us star’s masses, Wein’s Law gives us their temperature and Newton gives us us their temperature and Newton gives us spectra which is their chemical spectra which is their chemical composition.composition.

How far away is that star?How far away is that star?

But, one of the most fundamental questions But, one of the most fundamental questions about a star is…how far away is that star?about a star is…how far away is that star?

Measuring DistanceMeasuring Distance

Astronomers have several methods for Astronomers have several methods for estimating a stars distance.estimating a stars distance.

ParallaxParallax TriangulationTriangulation Method on standard candlesMethod on standard candles

TriangulationTriangulation

Using simple geometry, the distance Using simple geometry, the distance of stars can be determined given of stars can be determined given that you know thethat you know the

ParallaxParallaxParallax is the change in an object apparent Parallax is the change in an object apparent position caused by a change in the observers position caused by a change in the observers position.position.

ParallaxParallax

The shift in stars closer to us is The shift in stars closer to us is greater than for those far away. greater than for those far away. Regardless, the amount of shift is Regardless, the amount of shift is very small. Because of this, these very small. Because of this, these shifts are measured in shifts are measured in arc secondsarc seconds which 1/3600which 1/3600thth of a degree. of a degree.

ParallaxParallax

By definition:By definition:DDpcpc = 1/p = 1/parc secondsarc seconds

Where:Where: D =D = distance in parsecs distance in parsecs

P = P = measure of angular measure of angular shift in shift in arc secondsarc seconds

One parsec equals 3.26 light-years or One parsec equals 3.26 light-years or 3.09 X 103.09 X 101313 kilometers kilometers

ParallaxParallax

A shift of one degree of arc is what you’d A shift of one degree of arc is what you’d see of a penny’s edge from 4 kilometers see of a penny’s edge from 4 kilometers (2.5 miles)(2.5 miles)

How Far is Sirius?How Far is Sirius?

Using the formula:Using the formula:

RR == pp where R = 1 AUwhere R = 1 AU

2pd2pd 360360 p = in arc p = in arc secondsseconds

P for Sirius is 0.377 arc seconds, so….P for Sirius is 0.377 arc seconds, so….

How Far is Sirius?How Far is Sirius?

d = 360 / 2d = 360 / 2p p

yields d = 360 AU/2yields d = 360 AU/2(.377) = (.377) =

Express p in arc seconds and d in Express p in arc seconds and d in parsecs and both cancel, leavingparsecs and both cancel, leaving

d = 1/p, therefore Sirius is 1/.377 or d = 1/p, therefore Sirius is 1/.377 or 2.65 parsecs away. Multiply times 2.65 parsecs away. Multiply times 3.26 to convert into light-years. The 3.26 to convert into light-years. The answer is answer is 8.6 light-years away.8.6 light-years away.

Method of Standard CandlesMethod of Standard Candles

Imagine having two 100-watt light Imagine having two 100-watt light bulbs in front of you. One is close bulbs in front of you. One is close and one is far away. You can learn and one is far away. You can learn to tell about how far away the distant to tell about how far away the distant light is. Indeed, driving at night, you light is. Indeed, driving at night, you use this to tell how far another car or use this to tell how far another car or a traffic light is away.a traffic light is away.

Standard CandleStandard Candle

Astronomers use the concept of the Astronomers use the concept of the standard candle to estimate distance. standard candle to estimate distance. They assign a given luminosity (or They assign a given luminosity (or brightness) as a reference. This brightness) as a reference. This reference is called a “standard reference is called a “standard candle”.candle”.

Measuring Properties of Stars Measuring Properties of Stars from Their Light: Temperaturefrom Their Light: TemperatureThe temperature of a star is often The temperature of a star is often indicated by its color. Just like you indicated by its color. Just like you look are a stove eye to determine look are a stove eye to determine how hot it is. how hot it is.

Measuring Properties of Stars Measuring Properties of Stars from Their Light: Temperaturefrom Their Light: TemperatureWein’s Law states that:Wein’s Law states that:

T = 3 x 10T = 3 x 1066//mm where T = temperature where T = temperature and and m is the frequency the star m is the frequency the star radiates at most strongly (in radiates at most strongly (in nanometers).nanometers).

Measuring Properties of Stars Measuring Properties of Stars from Their Light: Temperaturefrom Their Light: TemperatureSo, how hot is Sirius?So, how hot is Sirius?

T = 3 x 106 / T = 3 x 106 / mm Given that Sirius Given that Sirius radiates most strongly radiates most strongly at 300 nanometers at 300 nanometers

((m)m)

T = 3 x 106 / 300 nm, thereforeT = 3 x 106 / 300 nm, therefore

T = 10,000 KT = 10,000 K

Measuring Properties of Stars Measuring Properties of Stars from Their Light: Luminosityfrom Their Light: LuminosityLuminosity is the amount of energy a Luminosity is the amount of energy a star radiates each second. Our Sun star radiates each second. Our Sun has a luminosity of about 4 X 10has a luminosity of about 4 X 102626 watts. This a star’s luminosity is an watts. This a star’s luminosity is an indicator of how quickly it is indicator of how quickly it is consuming fuel. Astronomers use consuming fuel. Astronomers use stars luminosity to determine their stars luminosity to determine their distance and radius.distance and radius.

The Inverse Square Law and a The Inverse Square Law and a Star’s LuminosityStar’s Luminosity

The inverse square law relates an The inverse square law relates an object’s luminosity to its distance object’s luminosity to its distance and apparent brightness. Like a and apparent brightness. Like a shotgun pattern, the farther away shotgun pattern, the farther away from an object the fewer number of from an object the fewer number of photons hit in a particular area.photons hit in a particular area.

The Inverse Square Law and a The Inverse Square Law and a Star’s LuminosityStar’s Luminosity

Astronomers have determined that Astronomers have determined that the relationship between brightness the relationship between brightness and distance is an inverse square and distance is an inverse square law:law:

B = L / 4B = L / 4dd22 where B is the apparent where B is the apparent brightness, L is luminosity brightness, L is luminosity

and d is the object’s and d is the object’s distance.distance.

Measuring Properties of Stars Measuring Properties of Stars from Their Light: Radiusfrom Their Light: Radius

If two stars have the same If two stars have the same temperature, but one is more temperature, but one is more luminous than the other, then the luminous than the other, then the brighter star must have a larger brighter star must have a larger radius.radius.

The Stephen-Boltzmann LawThe Stephen-Boltzmann Law

The Stephen-Boltzmann Law states that a The Stephen-Boltzmann Law states that a star’s luminosity equals its surface area star’s luminosity equals its surface area times times TT44::

L = 4L = 4RR22TT44 where L=luminosity, R = where L=luminosity, R = radius and radius and TT4 4 is the relationship is the relationship

between temperature and surface area. between temperature and surface area. You increase the temperature or radius You increase the temperature or radius and you increase the star’s luminosity.and you increase the star’s luminosity. = 5.6686 x 10- 6 (Watts/meters2Kelvins4).

The Stephen-Boltzmann LawThe Stephen-Boltzmann LawSo, what is the radius of Sirius?So, what is the radius of Sirius?

LLSunSun = = 44RRss22TTss

44 where R and T are where R and T are

LLSirius Sirius 4 4RRSrSr22TTSrSr

44 the Sun and Sirius the Sun and Sirius values respectively.values respectively.

Solved for RSolved for RSiriusSirius (25/1) (25/1)1/21/2/(6,000k/10,000k)/(6,000k/10,000k)22

RRSiriusSirius = 5(0.6) = 5(0.6)22

RRSiriusSirius = 1.8 Solar radii = 1.8 Solar radii

Page 359 textPage 359 text

What is a Parsec Anyway? What is a Parsec Anyway? By definition, one arc second spans 1 By definition, one arc second spans 1 AU at the distance of one parsec.AU at the distance of one parsec.

Aah, but I digress…Aah, but I digress…

So, back to Hipparcus. He wants to So, back to Hipparcus. He wants to classify stars. The characteristic he classify stars. The characteristic he decides to use is decides to use is apparent brightnessapparent brightness (or how bright a star looks to you and (or how bright a star looks to you and me). me).

It’s All About MagnitudeIt’s All About Magnitude

Hipparcus calls this apparent (or how Hipparcus calls this apparent (or how bright a star appears) brightness, bright a star appears) brightness, magnitudemagnitude. It is, with a few . It is, with a few changes, the same classification changes, the same classification system used today. system used today.

MagnitudeMagnitude

The system does have some The system does have some problems. First, it’s backwards, problems. First, it’s backwards, meaning that the more positive the meaning that the more positive the number, the fainter the star. So, number, the fainter the star. So, bright stars are like -1 or -2 and bright stars are like -1 or -2 and really dim stars are magnitude 10. really dim stars are magnitude 10. Our Sun is something whacked like -Our Sun is something whacked like -27 (I think). 27 (I think).

MagnitudeMagnitude

Hipparcus didn’t start out with Hipparcus didn’t start out with negative numbers on his scale. He negative numbers on his scale. He did, however, seriously misjudge how did, however, seriously misjudge how bright the brightest stars actually bright the brightest stars actually are. This pushed the scale negative are. This pushed the scale negative or brighter.or brighter.

MagnitudeMagnitude

Here’s the part you’re going to hate. Here’s the part you’re going to hate. Magnitude differences correspond to Magnitude differences correspond to brightness ratios. Now, this whole brightness ratios. Now, this whole system is based on the first system is based on the first magnitude 1. This is half a ratio. magnitude 1. This is half a ratio. The other half of the ratio is 2.512 (or The other half of the ratio is 2.512 (or the fifth root of 100). the fifth root of 100).

MagnitudeMagnitude

Now naturally your first thought is, Now naturally your first thought is, hell, why didn’t I think of that. The hell, why didn’t I think of that. The idea is that a magnitude 1 star is 100 idea is that a magnitude 1 star is 100 times brighter than a magnitude 6 times brighter than a magnitude 6 star, so the star, so the 55thth root of 100, see? root of 100, see?

MagnitudeMagnitude

So, a magnitude 1 star’s ratio is:So, a magnitude 1 star’s ratio is:

2.5122.51211 = 2.512 : 1 = 2.512 : 1

A magnitude 2 star’s is 2.512A magnitude 2 star’s is 2.51222 = 6.31 : 1 = 6.31 : 1

A magnitude 3 star’s ratio is 2.512A magnitude 3 star’s ratio is 2.51233 = = 15.85:115.85:1

A magnitude 4 star’s ratio is 2.512A magnitude 4 star’s ratio is 2.51244 = 39.8:1 = 39.8:1

Yada, yada, yada…Yada, yada, yada…

Absolute MagnitudeAbsolute Magnitude

Still, given all this, we’re still Still, given all this, we’re still comparing apples to oranges. The comparing apples to oranges. The magnitude of a star is related to its magnitude of a star is related to its distance away from us. Astronomers distance away from us. Astronomers needed a better system to level the needed a better system to level the playing field where stars could be playing field where stars could be compared directly. compared directly.

Absolute MagnitudeAbsolute Magnitude

A new scale was invented that places A new scale was invented that places stars at a standard distance from us. stars at a standard distance from us. That distance is 10 parsecs (pc). That distance is 10 parsecs (pc). Absolute magnitude Absolute magnitude is a true is a true measure of a star’s luminosity.measure of a star’s luminosity.

The Dumbing it Down SlideThe Dumbing it Down Slideor it Gets Way Too Boring!or it Gets Way Too Boring!

Now, very quickly. Stars give off light that Now, very quickly. Stars give off light that can be divided into spectra. The spectra can be divided into spectra. The spectra indicate a star’s temperature. People have indicate a star’s temperature. People have studied these spectra since the early studied these spectra since the early 1800’s. One man, Henry Draper (1870’s) 1800’s. One man, Henry Draper (1870’s) studied the classification of spectra. He studied the classification of spectra. He died and his wife gave a fortune to Harvard died and his wife gave a fortune to Harvard to compile a book of these spectra called to compile a book of these spectra called the Henry Draper catalog. Remember the the Henry Draper catalog. Remember the HD catalog numbers from the constellations. HD catalog numbers from the constellations. This is a way to reference the spectra of This is a way to reference the spectra of stars in a constellation. Cool, eh?stars in a constellation. Cool, eh?

Oh Boy, A Fine Girl Kissed Me!Oh Boy, A Fine Girl Kissed Me!Star’s fit into one of seven distinct Star’s fit into one of seven distinct spectral classesspectral classes. Spectral classes . Spectral classes convey information on a star’s convey information on a star’s composition and temperature. The composition and temperature. The seven spectral classes are: O, B, A, F, seven spectral classes are: O, B, A, F, G, K and M. From O to M G, K and M. From O to M temperatures decline. temperatures decline.

Spectral ClassesSpectral Classes

Other mnemonics include: Only Other mnemonics include: Only Brilliant Artistic Females Generate Brilliant Artistic Females Generate Killer Mnemonics and my personal Killer Mnemonics and my personal favorite: Oh Big And Furry Gorilla, Kill favorite: Oh Big And Furry Gorilla, Kill My Roommate. Four other very rare My Roommate. Four other very rare spectral classes exist called R, N, S spectral classes exist called R, N, S and W. Can you include them in a and W. Can you include them in a mnemonic? mnemonic?

Summary of Stellar Summary of Stellar PropertiesProperties

QuantityQuantity MethodMethodDistanceDistance Parallax (up to about Parallax (up to about

250 parsecs250 parsecsTemperatureTemperature Wien’s LawWien’s Law

Spectral class (O- M)Spectral class (O- M)LuminosityLuminosity B = L / 4pd B = L / 4pd22

CompositionComposition Spectral linesSpectral linesRadiusRadius Stephen-Boltzmann lawStephen-Boltzmann law

InterferometerInterferometerEclipsing binariesEclipsing binaries

MassMass Kepler’s third lawKepler’s third lawRadial VelocityRadial Velocity Doppler shift of spectral Doppler shift of spectral

lineslines

Warm UpWarm Up1.1. Define a parsec.Define a parsec.2.2. Who had the idea for apparent brightness?Who had the idea for apparent brightness?3.3. What is another name for apparent brightness?What is another name for apparent brightness?4.4. Which is brighter, a magnitude 1 star or a Which is brighter, a magnitude 1 star or a

magnitude 6 star.magnitude 6 star.5.5. How much brighter is a magnitude 3 star than a How much brighter is a magnitude 3 star than a

magnitude 1 star.magnitude 1 star.6.6. What number is the base for the magnitude What number is the base for the magnitude

system? (Hint for number 5)system? (Hint for number 5)7.7. What is absolute magnitude?What is absolute magnitude?8.8. What are the 7 stellar classifications. What do What are the 7 stellar classifications. What do

they mean?they mean?

The Hertzsprung-Russell The Hertzsprung-Russell DiagramDiagram

While scientists could calculate the While scientists could calculate the mass, temperature, radius, mass, temperature, radius, luminosity and other characteristics luminosity and other characteristics of stars, they still understood of stars, they still understood practically nothing about how they practically nothing about how they worked. This changed in 1912 with worked. This changed in 1912 with the work of Ejnar Herstzsprung and the work of Ejnar Herstzsprung and Henry Norris Russell.Henry Norris Russell.

The H-R DiagramThe H-R DiagramIn a nearly simultaneous discovery, In a nearly simultaneous discovery, both men found that if you plotted both men found that if you plotted stars’ luminosities against their stars’ luminosities against their temperatures (or spectral classes) temperatures (or spectral classes) that the vast majority lay on a single that the vast majority lay on a single line. line.

The H-R DiagramThe H-R Diagram

Traditionally, on the H-R diagram, brighter stars Traditionally, on the H-R diagram, brighter stars appear at the top and hotter stars appear on the appear at the top and hotter stars appear on the

left axes.left axes.

The H-R DiagramThe H-R Diagram

This line that most (90%) stars fall on is This line that most (90%) stars fall on is called the “main sequence”. A minority of called the “main sequence”. A minority of stars appear in the upper right-hand and stars appear in the upper right-hand and lower left-hand corners.lower left-hand corners.Looking at the H-R diagram brings several Looking at the H-R diagram brings several questions to mind. How can stars ofquestions to mind. How can stars ofdifferent temperature have the same different temperature have the same magnitude? Conversely, how can stars with magnitude? Conversely, how can stars with the same temperatures have different the same temperatures have different magnitudes?magnitudes?The answer lies in the Stephan-Boltzmann The answer lies in the Stephan-Boltzmann law.law.

Analyzing The H-R DiagramAnalyzing The H-R DiagramWhen you look at the H-R diagram and see for When you look at the H-R diagram and see for one temperature that luminosities can range from one temperature that luminosities can range from 1010-3-3 to 10 to 1066, you get some idea of the great variety , you get some idea of the great variety is the sizes of stars.is the sizes of stars.

The Stephen-Boltzmann LawThe Stephen-Boltzmann Law

Stephen-Boltzmann (L = 4Stephen-Boltzmann (L = 4RR22TT44)) relates relates luminosity with a star’s temperature and luminosity with a star’s temperature and radius. So, if two stars, A and B, have the radius. So, if two stars, A and B, have the same luminosity , but the temperature of same luminosity , but the temperature of star A is higher, then the radius of star B star A is higher, then the radius of star B must be greater. Conversely, if stars A must be greater. Conversely, if stars A and B have the same luminosity but star A and B have the same luminosity but star A is larger than star B, then star B must is larger than star B, then star B must have a higher temperature. It’s all about have a higher temperature. It’s all about total luminous output. total luminous output.

Analyzing The H-R DiagramAnalyzing The H-R Diagram

To produce the same luminosity as very hot, To produce the same luminosity as very hot, smaller stars, cooler star must be 1000’s of times smaller stars, cooler star must be 1000’s of times larger. These stars are termed “giants” and larger. These stars are termed “giants” and appear at the top of the H-R diagram.appear at the top of the H-R diagram.

Analyzing The H-R DiagramAnalyzing The H-R Diagram

A similar look at the H-R diagram shows that A similar look at the H-R diagram shows that some stars that lie below the main sequence are some stars that lie below the main sequence are very hot, but have very small luminosities. These very hot, but have very small luminosities. These stars by contrast must be very small. They are stars by contrast must be very small. They are called “dwarf” stars.called “dwarf” stars.

Other Differences in StarsOther Differences in StarsGiants, main sequence stars and dwarfs Giants, main sequence stars and dwarfs differ in more ways than just temperature differ in more ways than just temperature and luminosity. They also differ greatly in and luminosity. They also differ greatly in density. For a given mass, a larger body density. For a given mass, a larger body must have a lower density, so giants have must have a lower density, so giants have densities millions of times less than main densities millions of times less than main sequence stars. Smaller stars must sequence stars. Smaller stars must therefore have much greater densities therefore have much greater densities than main sequence stars.than main sequence stars.

Other Relationships Revealed by Other Relationships Revealed by the H-R Diagramthe H-R Diagram

The H-R diagram reveals The H-R diagram reveals relationships between stars other relationships between stars other than just temperature and than just temperature and luminosity. It also reveals the stars’ luminosity. It also reveals the stars’ radii and masses as well.radii and masses as well.

The Luminosity-Radius RelationThe Luminosity-Radius Relation

I relationship can be inferred by the H-R I relationship can be inferred by the H-R diagram between the luminosity of a star diagram between the luminosity of a star and its radius. The greater the star’s and its radius. The greater the star’s luminosity the greater the star’s radius,luminosity the greater the star’s radius,

The Luminosity-Radius RelationThe Luminosity-Radius Relation

The Mass-Luminosity Relationship Luminosity vs. mass is plotted for the Sun and all Main Sequence stars that have good mass measurements shows that a Main Sequence star's luminosity is very strongly correlated with its mass:

The masses are

written in terms

of solar masses.

The relationship

is defined as:

L = M3, where

L= luminosity in

solar units and

M= solar masses.

Summary of the H-R Summary of the H-R DiagramDiagram

It offers a simple, pictorial summary of stellar It offers a simple, pictorial summary of stellar properties.properties.

Most stars lie on the main sequence with the hotter Most stars lie on the main sequence with the hotter stars being more luminous.stars being more luminous.

Blue stars are hottest while red stars are the coolestBlue stars are hottest while red stars are the coolest A star’s mass determines its location along the main A star’s mass determines its location along the main

sequence with more massive stars located at the sequence with more massive stars located at the top.top.

Stars masses range from about 30 solar masses to Stars masses range from about 30 solar masses to about 0.1 solar masses.about 0.1 solar masses.

It shows that stars fall within three main regions of It shows that stars fall within three main regions of the diagram: main sequence, giants and white the diagram: main sequence, giants and white dwarves.dwarves.

Variable StarsVariable StarsNot all stars have constant luminosity. Not all stars have constant luminosity. Some stars, called Some stars, called variable stars,variable stars, change change brightness over time. The time between brightness over time. The time between the intervals of maximum brightness is the intervals of maximum brightness is called the star’s called the star’s periodperiod. The graph of the . The graph of the star’s brightening and darkening cycle is star’s brightening and darkening cycle is called its called its light curvelight curve..

The Instability StripThe Instability StripVariable stars cluster together in the H-R Variable stars cluster together in the H-R diagram in a region known as the diagram in a region known as the instability stripinstability strip..

Analyzing The H-R DiagramAnalyzing The H-R Diagram

The H-R diagram shows the evolution The H-R diagram shows the evolution of stars. In the next section, we will of stars. In the next section, we will explore how and why stars evolve.explore how and why stars evolve.