Astro 10-Lecture 9:Properties of Stars

How do we figure out the properties

of stars?

We’ve already discussed the tools:•Light•Gravity (virtually impossible to measure).•Particles (might not get here).

Now let’s apply them to stars!

Chabot Trip

• Let's pick a Friday (Apr 1? Apr 16?)

• Meet at a BART station – Need volunteers to drive

• Planetarium show and telescope viewing

Observation + geometry or physics

Chemical Composition

• Presence of Absorption lines of a particular element indicates the presence of that element in the star!

• Absence of a spectral line doesn't necessarily mean an element is absent.

Chemical Composition

Temperature

Wavelength of Spectral Peak +

Blackbody Radiation

Absorption Lines+

Atomic Physics

Distance (1)

Trigonometric Parallax – You’ve all used it!

Animationlec9_pix\parallax.mpg

Distance (1)

Distance (3)

• Trigonometric Parallax – useful to 50pc (ground) and 500 pc (space)

• Parsec (pc) = Distance of a Star with a Parallax of 1 (one) arcsecond (ParSec)

• 1 pc is a little over 3 light years!

Space Velocity (1)

• Velocity = Speed + Direction• Space Velocity has 2 components

Radial Velocity (Towards/Away) Transverse Velocity (sideways)

Transverse Velocity:

PROPER MOTION + DISTANCEAnimation

Space Velocity (2)

• Radial Velocity:

DOPPLER EFFECT

carhorn.wav

Space Velocity (2)

Space Velocity (2)

Space Velocity (2)

Space Velocity (3)

Radial Velocity: Doppler Effect

ConcepTest

• Two stars lie in the same area of the sky. Star Gern has a parallax measurement of 1 arcsecond, while Star Zora has a parallax measurement of 0.5 arcseconds. – a) Star Gern is closer to us than star Zora– b) Star Gern has a larger space velocity than star

Zora– c) Star Gern and Star Zora are at the same distance– d) Star Gern and Star Zora have the same

temperature

Apparent Brightness vs. Luminosity

• Apparent Brightness: Energy we intercept per unit area per unit time (how bright it appears)

• Luminosity: Energy emitted per unit time (how bright it really is)

• Inverse Square Law: Projector Demo

The inverse square law

• Brightness proportional to 1/d2

Demo

LUMINOSITY: APPARENT BRIGHTNESS + DISTANCE

Inverse Square Law

Hertzprung-Russell (H-R) Diagram

• A Plot of Temperature vs. Luminosity

HR Diagram

Notice that theTemperature axis is reversed!(So is the magnitudeaxis, but we don’tuse it)

NOTE HUGE RANGEOF LUMINOSITIES!

MASS! (1)

• Period/Size of orbits are related to MASS by Newton’s version of Kepler’s Third Law

• Qualitatively, if two masses are orbiting about one another very rapidly, then the gravity between them must be stronger than if they were orbiting more slowly.

• SUM of MASSES: Orbital Period + Orbital Size + GRAVITY

MASS – Binary Stars (2)

• We can get stellar masses from observations of Binary Stars

Visual Binary (see the two stars move about one another on the sky)

Spectroscopic Binary (see the motion due to Doppler shifts of spectral lines)

Eclipsing Binary (see the light from one star periodically blocked by the other)

Visual Binaries

• Distance + angle measurement => orbital size

• Period + orbital size + gravity => sum of masses

• Center of mass determination gives individual masses

Spectroscopic Binaries

• Orbital velocity determined by Doppler shifts of lines in spectrum (OH 69)

• spbin.mov

• Period + Maxumum orbital velocity gives ~size of orbit

• INCLINATION PROBLEM

• Some stars in Big Dipper are Binaries!

Spectroscopic Binaries (2)

Eclipsing Binaries

• One star passes in front of the other at some point during the orbit, reducing the light that reaches us

• OH 70

• eclbin.mov

Eclipsing + Spectroscopic Binary => NO INCLINATION PROBLEMS

MASS RECAP

• Newton’s Laws of Gravity say that if we know 1) size of orbit 2) period of orbit then we can find the total mass of the system

• Size of orbit: need either distance, or eclipsing spectroscopic binary

• To find individual masses, must know where the Center of Mass of the system is

• Stellar masses are 0.01 to 100 times Sun’s mass

Mass-Luminosity Relation

Radius (size) from Binaries (1)

• In an eclipsing spectroscopic binary system, we can find the RADIUS of the stars too!

• Time spent in eclipse + orbital velocity of star (from Doppler) => SIZE OF STAR

Radius from Blackbody Radiation (2)

• Blackbody radiation law says that the energy emitted / area / time by the star is determined only by its TEMPERATURE

• So if we can determine the LUMINOSITY (energy emitted / time) of the Star, we can combine this with its TEMPERATURE to determine the RADIUS

• TEMPERATURE + LUMINOSITY + BLACKBODY RADIATION => RADIUS

Radius from Blackbody Radiation (2)

• Giants: ~10 x size of sun (~1000 x size of Earth)

• Supergiants: ~10-1000 x size of sun (~1000-100,000 x size of Earth)

• White Dwarfs: ~ size of Earth

Radius from Blackbody Radiation (2)

• L=4R2T4

• Giants: ~10 x size of sun (~1000 x size of Earth)

• Supergiants: ~10-1000 x size of sun (~1000-100,000 x size of Earth)

• White Dwarfs: ~ size of Earth

Now What?

• Notice that most of these quantities rely in some way upon a determination of DISTANCE

• Remember Trigonometric Parallax is only good to ~500 pc, while the Milky Way Galaxy is ~17,000 pc across!

• How do we learn anything about more distant stars?

Spectroscopic Parallax (1)

• Previously: Measurement + geometry or physics => Quantity

• NOW – Let’s USE what we’ve learned to bootstrap our way to more distant stars!

• Suppose we KNEW the intrinsic luminosity of a star – then a measure of its apparent brightness would tell us its DISTANCE (remember the INVERSE SQUARE LAW?)

Spectroscopic Parallax (2)

• If all stars were on the “Main Sequence” in the HR diagram, then a measurement of the TEMPERATURE of the star would allow you to determine its LUMINOSITY from the H-R diagram

• LUMINOSITY + APPARENT BRIGHTNESS + INVERSE SQUARE => DISTANCE

• Notice that this only works AFTER we have found the luminosities of many stars other ways, and “calibrated” the H-R diagram

• I

Spectroscopic Parallax (3)

• NOTE: We’re assuming more distant stars are just like nearby ones!

• BUT WAIT! Not all stars lie on the Main Sequence• Subtle differences in the widths of the star’s absorption

lines can determine its “Luminosity Class” (WD, MS, giant, supergiant)

• Measure spectrum + blackbody + atomic physics => TEMP and LUMINOSITY CLASS

+ CALIBRATED HR DIAGRAM => LUMINOSITY + APPARENT BRIGHTNESS + INV SQ => DISTANCE

• What does the Population of Stars look like?• What makes a star shine (model)?• How can we TEST this model with observation?

Observation + geometry or physics

ConcepTest

By looking at the spectra of two stars, we learn that they are both main sequence stars, and they have the same temperature.

1) If we can measure the distance to ONE of the stars using trigonometric parallax, can we find the distance to the other star? (A=yes, B=no)

1) If we could not measure the distance to ANY stars using trigonometric parallax, can we find the luminosity of these stars? (A=yes, B=no)

Population of Stars

• The Sun isn’t special!• Nearest star is ~ 4 ly away• Temperatures: 2,000-30,000K (sun 5800)• Luminosities: 1/100,000 to > 1,000,000 x sun• Fall into “classes” on the H-R diagram

• Main sequence (sun), white dwarfs, red giants, supergiants

Population of Stars (2)• Radii:

• WD ~ Earth-sized (1/100 of Sun)• Giants ~ 10-100 x size of sun (~Earth orbit in our scale

model of the solar system)• Supergiants ~ 100-1000 x size of sun

• Mass:• ~0.1 Msun to 55-100 Msun

• Mass + Radius => Density (DEMO)• MS: density sun ~ 1g/cm3 ~ density water• Giants: 0.1 – 0.01 x density sun• Supergiants: 0.001 – 0.000001 x density sun• WD: ~ 3 000 000 x density sun (1 tsp ~ 15 tons on Earth)

Mass-Luminosity Relation

• For MAIN-SEQUENCE STARS ONLY:• A relationship between MASS and LUMINOSITY

Most luminous main-sequence stars are also the most massive ((L ~ M3.5)

POPULATION STATISTICS

What stars do we see as bright in the night sky? LUMINOUS ONES

What stars are the nearest? DIM (RED) ONES

How many stars of each kind per cubic parsec? LUMINOUS RARE, NEAREST DIM

Comparing HR Diagrams for nearest and brightest stars

Nearest Stars Brightest Stars

IN-CLASS EXERCISE