•Homework #3 now due: March. 17 •Submit a .pdf copy of HW electronically to the email address that corresponds to your Section of ASTR 115:

sfsuastr115.2@gmail.com for Section 2 (TuTh at 3:30 PM)sfsuastr115.3@gmail.com for Section 3 (TuTh at 11:00 AM)sfsuastr115.4@gmail.com for Section 4 (Tu at 6:00 PM)

•Midterm postponed to April 7!•Review sheet for MT is on the class website: •http://physics.sfsu.edu/~chris/astro115

•Also, new “Reading & HW schedules” have been created. Please download them, and toss out the old ones

•Today: Chapter 11 -- Stars•Optional: Sec. 11:12-13 & Guided Discovery

•Office Hours will be held ONLINE. Email questions to: sfsuastro@gmail.com•(Questions answered immediately on Monday)

Voting Question

A.) The energy production increasesB.) There is an eclipseC.) The number of sunspots increases D.) The light output decreases significantly

What happens every 11 years on the Sun?

Voting Question

A.) The chemical burning of Hydrogen B.) The nuclear fusion of Hydrogen into Helium C.) Nuclear fission of Helium into Hydrogen D.) Nuclear fission of Uranium

The source of energy in the Sun is

Field of background stars: Parallax test

ParallaxBackground Stars

NearbyStar

! We obtain a different perspective on a star by observing it at different times of the year.

! The star is compared to distant background stars

! In 6 months, Earth moves 2 AU

! If a star is very far away (1000 light years or more) then parallax won’t work.

Parallax Measures Distance

! The larger the star’s distance, d, the smaller its parallax p.

! So distance and parallax are inversely related. ! d = 1 / p

Measuring Angles & Distances

! Most stars have a small parallax angle, p ! …. much smaller than 1 degree. ! So parallax angles are measured in units of arc seconds

! 1/60 of one degree = 1 arc minute

! 1 /60 of one arc minute = 1 arc second.

! Distances to stars are measured in either: light years, or parsecs.

! 1 parsec = 3.2 light years (parsec = PARallax of one arcSEC)

Parallax Example

! If a star has a parallax 1 arcsecond, then its distance is 1 parsec.

! Suppose a star has a parallax 0.1 arc seconds

! Question: what is its distance in parsecs? ! Answer: d = 1 / p ! d = 1 / 0.1

! d = 10 parsecs = 32 light years. ! (note: “p” = parallax angle, not parsecs)

Background Stars

NearbyStar

Parallax (p) is the angle a star appears to move by when Earth orbits the Sun.

(p measured in ‘arc seconds’)

It tells us the distance (d) to the star:(d measured in ‘parsecs’)

p = 1/d

Discussion Question Three stars have different parallaxes:

-Proxima’s parallax is: 0.8 arc sec

-Sirius’ parallax is: 0.4 arc sec

-Polaris’ parallax is: 0.008 arc sec

Q1: Which Star is closest, which is farthest?

Q2: Can you tell which star is brightest?

How Powerful Are the Stars?! “Power” is energy output per second. ! Power is measured in Joules per second, or Watts

! eg. a 100 Watt light bulb uses 100 Joules of energy per sec. ! We measure the power, or brightness, of stars in 2 ways:

luminosity and magnitude.

The Luminosity (L) of a star is just its wattage. The Sun’s luminosity is:

LSun = 380,000,000,000,000,000,000,000,000 = 3.8 x 1026 Watts!

=380 Yottawatts!

Other stars can be measured against the Sun.

Luminosities of Different Stars! Our Sun: L = 1.0 Lsun ! Sirius: L = 25 Lsun ! Polaris (North star): L = 1,300 Lsun ! Proxima: L = 0.002 Lsun

Instead of Watts, we’ll use the Sun’s Luminosity (LSUN = ) to measure other stars.

! Eta Carinae is the most luminous star known. ! L = 4 Million Lsun !!!!

! In ~5 seconds, it emits as much light as the Sun in 1 year!

The Most Luminous Star

Star Eta Carinae and surrounding nebula

Another way to measure the brightness of a star is its “Magnitude”

Ancient people put stars into 5 classes, from

“First Magnitude” (brightest) to “Fifth Magnitude” (dimmest)

This system is still in use today

Measuring Stars: Magnitudes

Magnitudes of stars in Orion

Magnitudes

• Lower magnitudes = brighter stars

• So a 1st magnitude star is brighter than a 2nd mag. star

•We use the symbol: m to mean magnitude.

• Originally there were only magnitudes 1-5

• However a very bright object can even have a negative magnitude.

Magnitude Examples

• The planet Venus’ magnitude is m = -4.0

• A very faint object can have a magnitude above 5.

• E.g.: A distant galaxy has a magnitude: m =20.

• Q: What object in the sky has the lowest magnitude?

Text

Magnitude

Some stars are a million times brighter than others. But, their magnitude difference is just 15.

Calculating Magnitude Differences

• Each magnitude is a factor of 2.5• So a difference of 3 magnitudes = 2.5 x 2.5 x 2.5 =

15.6 times brighter! • 5 magnitudes difference corresponds to a star which is

100 times brighter.

• Example:

• Star A’s magnitude is 1.0, Star B’s magnitude is 6.0• The difference in magnitudes is 6.0-1.0 = 5 Mags.• So, Star B is 100 times fainter than Star A.

Inverse Square LawAs the light from a star goes into space, it fills a larger and larger sphere. If “r” is the radius of the sphere, then the area of a sphere is given by : A = 4 π r2

The intensity of light decreases with the square of our distance from the star:

Brightness of a star ~ 1 / r2

demo

Distance & Brightness! If we view the same star from double the distance, it will appear

four times fainter. ! Its apparent magnitude will be higher. ! So, nearby stars can trick us into thinking they are truly bright. ! To compare stars fairly, we need to place them all at the same

distance...

! We need a way to measure the intrinsic (true) brightness of stars.

! The Absolute Magnitude does not depend on how far away it is. ! It is a measure of the star’s true energy output, not just its

brightness as viewed from Earth.

Absolute & Apparent MagnitudeApparent magnitude (m): the magnitude we see from Earth.

Absolute magnitude (M): the Intrinsic Magnitude (regardless of distance)

Absolute Mag. is defined as the magnitude that a star would have if we viewed it at a distance of 10 parsecs.

The Sun’s Apparent magnitude is: m = -27 !

The Sun’s Absolute magnitude is: M = 4.8

If the Sun were moved to a distance of 10 parsecs away, it would just barely be visible (Apparent Magnitude 4.8)

Example:Betelgeuse

Rigel

m = 0.45 mag

m = 0.15 mag

Betelgeuse Rigel

m 0.45 0.15

M -5.5 -6.8

d 152 pc 244 pc

Different Types of Star (How many are there?)

! To understand the diversity of stars, we first classify them. ! We can use the star’s spectrum to do this. ! This was first done in the early 1900’s at Harvard Univ. by

Annie Jump Cannon

! She was assigned the job of classifying stellar spectra into types (A,B,C ….)

! In her life she classified over 200,000 spectra!!!

Different Types of Star! Cannon found that most stars fell in to 7 different

categories

! A star’s spectral lines depend on what its temperature is.

! Cannon re-organized the spectral types to form a temperature sequence:

O,B,A,F,G,K,M

These absorption lines are used to distinguish the different spectral types

How Do We Classify Stars?! O type stars are the hottest ! M type stars are the coolest.

“Oh, Be A Fine Guy/Girl Kiss Me.”

Student Submissions....

OBAFGKM shows spectral types in order of decreasing temperature

! Oh Boy, An F Grade Kills Me! ! Octavius became Augustus, fighting gallantly, killing many.! Only Boys Accepting Feminism Get Kissed Meaningfully.! Oops! Bacon Appetizers for generally Kosher man.! On Break After Finals: Good, Key Moment

Spectral Sub-Types OBAFGKM

! A star’s spectral type can be specified more precisely using a subtype ranging from 0 to 9.

! Example: spectral type A is divided into A0, A1, A2 …. A9

! A0 is the hottest, and A9 is the coldest.

! F0 is cooler than A9. ! If you know a star’s spectral type, then you know its temperature.

! The Sun is a type G2 star, corresponding to a temperature of 5800 K.

Stars: What do We Know?

! Temperature (T) & Spectral Type

! Distance

! Brightness ! Luminosity (Lstar) - energy output of a star ! Apparent Magnitude (m) - how bright a star appears ! Absolute Magnitude (M) - how bright a star really is

So many stars…so little time

Organizing the Family of Stars" To understand the huge diversity of stars, we organize them according to their:

" Temperature (T)" Luminosity (Lstar/LSun)

" How are these properties related?" To find out, each star is plotted as a point on a graph

"The x-coord. is Temperature (T)"The y-coord. is Luminosity (Lstar)

•Midterm will happen April 7!•You will be sent the exam by email. •You will submit your answers by email.•Follow the directions in the email very carefully.

•Review sheet for MT is on the class website: •http://physics.sfsu.edu/~chris/astro115

•

Download the HR Diagram Worksheet,Print it out, and fill it out yourself. You’ll need to do some graphing.

Hertzsprung-Russell (HR) Diagram

Star LSTAR LSUN

Temp

Sun 1 5800

Proxima 0.002 3000

Vega 40 10,000

δ Orion.

70000 30,000

Arcturus 200 4300

Main Sequence

HR Diagram

Most stars are found along the

main sequence, including the Sun

L. vs. T.

! Stars on the main sequence are called dwarfs, so the Sun is a “dwarf star”

HR Diagram

But not all stars are on the Main Sequence:

Giant Stars have greater luminosity.

Supergiants are even more luminous.

White Dwarfs are fainter and bluer. They are hotter than the Sun, but less luminous.

L. vs. T.

HR Anim

Giant Stars

Giant stars can be 100 times the size of the Sun!

If they were in our solar system they would swallow Mercury and Venus!

Supergiant stars are even bigger! 1000 times the size of the Sun!!!

H-R DiagramsHRDiagrams

Nearest Stars

Brightest Stars

Proxima Centauri --The Nearest Star to the Sun is a faint M star on the Main Sequence

Use of H-R Diagrams

! H-R Diagrams are the astronomers “most useful tool”

! They quickly tell us which kind of star (giant or dwarf)

! They can also reveal the mass, age & lifespan of the star.

! We can use them to determine the ultimate fate of a star…including the Sun.

The most important characteristic of a star is its MASS

Mass determines the fate of the star: whether or not it will explode.

Mass is measured in units of MSun

For Main Sequence Stars: more massive stars are hotter and more luminous.

but how do we measure a star’s Mass?

Solar Masses

Solar Masses

Solar Masses

anim.

Binary Stars in AstronomyMost of our knowledge of stars’ Masses comes from binary stars

In a binary star system two stars orbit each other.

Alberio, a double star in Cygnus

Alpha Centauri A & B,The nearest star system to the Sun

Binary Stars in Movies

Tatooine, a planet orbiting a binary star, in Star Wars

Motion Measures MassIn a binary star system, both stars orbit around the Center of Mass, or balance point.

By measuring the motions of the stars, (their orbits) we can determine their mass.

Kepler’s 3rd Law & MassUsing his theory of gravity, Newton improved Kepler’s 3rd Law. It can be applied to a binary star system:

�

a = semi-major axis (AU)P = orbital period (in years)MTOT=Total Mass of both stars (In MSun)

So, if we measure the size of the orbit (semimajor axis, a) and the period (P), we can find the masses of stars in a binary system.

P2 =a3

(MTOT)

Binary Star ExampleIf Luke observes his binary star has a period of 4 years, and a semi-major axis of 2 AU, what is the combined mass of the two stars?

�

MTOT = a3 /P2 = 23 /42 = 8/16 = 0.5 Msun

P2 =a3

(MTOT)

The combined mass is 1/2 the mass of the Sun.

The more massive star is closer to the center of mass

Main Sequence Stars: M & L are Related

Binary star measurements revealed the mass of many stars on the “Main Sequence”

We find :

More massive stars are also more luminous...

...much more luminous

The Mass-Luminosity Relationon the Main Sequence

L ~ M3.5

Chapter 11 Summary

! Distances to stars: Parallax method

! Luminosity of stars (Lsun)

! Absolute (M) and Apparent (m) magnitudes.

! Organizing stars: HR Diagrams

! Measuring stellar masses: Binary Stars

HR Diagram

...Is a graph of a star’s Luminosity vs. its Temperature

Most stars fall on a single line, The Main Sequence

L. vs. T.

Other stars:

Giants

Supergiants

White Dwarfs