Surveying the Stars

Properties of Stars Our goals for learning How do we measure stellar luminosities? How do we measure stellar temperatures? How do we measure stellar masses?

How do we measure stellar luminosities?

The brightness of a star depends on both distance and luminosity

Light and Distance Light spreads with distance, expanding outward in a sphere The number of photons passing through each sphere is the same, but get spread over a larger area Thus light gets fainter with distance

To find the difference- Area of sphere: 4π (radius) 2 Divide luminosity by area to get brightness The “Inverse square” law

Luminosity: Amount of power a star radiates (energy per second = Watts) Apparent brightness: Amount of starlight that reaches Earth (energy per second per square meter)

The relationship between apparent brightness and luminosity depends on distance: Luminosity Brightness = 4  (distance) 2 We can determine a star’s luminosity if we can measure its distance and apparent brightness: Luminosity = 4  (distance) 2  (brightness)

Apparent Magnitude (how bright does an object seem?) Magnitude scale 1 st developed by Hipparchus to compare the different brightness of stars Brightest stars = 1 Dimmest stars = 6 (designed before invention of telescopes, so only naked eye observations initially possible)

So how far are these stars?

Parallax is the apparent shift in position of a nearby object against a background of more distant objects Distance Measuring by Parallax

Stellar Parallax: positions of nearest stars appear to shift as Earth orbits Sun

The amount of shift detected, depends on the distance to the stars

Parallax and Distance Use right-angled triangles to get distance

The Sun’s Neighborhood The distance to these stars was measured by parallax

The Magnitude Scale

Stellar Distances

Most luminous stars: 10 6 L Sun Least luminous stars: L Sun (L Sun = luminosity of Sun) Once we know the distance to stars by parallax, we can compensate for the drop in light levels caused by distance. We can then see the difference in light levels caused by differing power output

A star can be classified by 'luminosity class' (line shapes, related to the size of the star) More luminous stars = more surface area = larger star I - supergiant II - bright giant III - giant IV - subgiant V - main sequence

How do we measure stellar temperatures?

Every object emits thermal radiation with a spectrum that depends on its temperature

Properties of Thermal Radiation 1.Hotter objects emit more light per unit area at all frequencies. 2.Hotter objects emit photons with a higher average energy.

Hottest stars: 50,000 K Coolest stars: 3,000 K (Sun’s surface is 5,800 K)

Solid Molecules Neutral Gas Ionized Gas (Plasma) Level of ionization also reveals a star’s temperature 10 K 10 2 K 10 3 K 10 4 K 10 5 K 10 6 K

Absorption lines in star’s spectrum tell us ionization level

Lines in a star’s spectrum correspond to a spectral type that reveals its temperature (Hottest) O B A F G K M (Coolest)

Pioneers of Stellar Classification Annie Jump Cannon and the “calculators” at Harvard laid the foundation of modern stellar classification.

(Hottest) O B A F G K M (Coolest) Remembering Spectral Types Oh, Be A Fine Girl, Kiss Me Only Boys Accepting Feminism Get Kissed Meaningfully

(Hottest) O B A F G K M (Coolest) Remembering Spectral Types The letter types also get sub-divided further by numbers 0-9 0=hottest stars within the spectral type 9= coolest stars within the spectral type. Our Sun, Capella A and Tau Ceti are all G type stars. Capella A is a G0, the Sun is a G2, and Tau Ceti is a G8

A star’s full classification includes spectral type (line identities) AND luminosity class (line shapes, related to the size of the star): Examples:Sun - G2 V Sirius - A1 V Proxima Centauri - M5.5 V Betelgeuse - M2 I

How do we measure stellar masses?

Two stars in orbit of each other is called a binary system

The orbit of a binary star system depends on strength of gravity The gravity between those stars depend on their masses This means we can use Newton’s and Kepler’s laws to calculate the stars’ mass: About half of all stars are in binary systems!

Most massive stars: 100 M Sun Least massive stars: 0.08 M Sun (M Sun is the mass of the Sun)

What have we learned? How do we measure stellar luminosities? –If we measure a star’s apparent brightness and distance, we can compute its luminosity with the inverse square law for light –Parallax tells us distances to the nearest stars How do we measure stellar temperatures? –A star’s color and spectral type both reflect its temperature

What have we learned? How do we measure stellar masses? –Newton’s version of Kepler’s third law tells us the total mass of a binary system, if we can measure the orbital period (p) and average orbital separation of the system (a)

Patterns among Stars Our goals for learning What is a Hertzsprung-Russell diagram? What is the significance of the main sequence? What are giants, supergiants, and white dwarfs? Why do the properties of some stars vary?

What is a Hertzsprung-Russell diagram?

Enjar Hertzsprung (Danish)& Henry Norris Russell(American)

The H-R Diagram

Stars with higher luminosity than main- sequence stars must have larger radii: giants and supergiants Large radius

The H-R Diagram small radius Stars with lower luminosity than main- sequence stars must have smaller radii: dwarfs

Luminosity Classes and H-R Luminosity class has a clear correlation with the size of the star

Temperature Luminosity H-R diagram depicts: Temperature Color Spectral Type Luminosity Radius

Temperature Luminosity Which star is the hottest? A B C D

Temperature Luminosity Which star is the most luminous? A B C D

Temperature Luminosity Which star is a main-sequence star? A B C D

What is the significance of the main sequence?

Main-sequence stars are fusing hydrogen into helium in their cores like the Sun Luminous main- sequence stars are hot (blue) Less luminous ones are cooler (yellow or red)

Mass measurements of main-sequence stars show that the hot, blue stars are much more massive than the cool, red ones High-mass stars Low-mass stars

Core pressure and temperature of a higher-mass star need to be larger in order to balance gravity Higher core temperature boosts fusion rate, leading to larger luminosity

Stellar Properties Review Luminosity: from brightness and distance L Sun L Sun Temperature: from color and spectral type 3,000 K - 50,000 K Mass: from period (p) and average separation (a) of binary-star orbit 0.08 M Sun M Sun

What have we learned? What is a Hertzsprung-Russell diagram? –An H-R diagram plots stellar luminosity of stars versus surface temperature (or color or spectral type) What is the significance of the main sequence? –Normal stars that fuse H to He in their cores fall on the main sequence of an H-R diagram –A star’s mass determines its position along the main sequence (high-mass: luminous and blue; low-mass: faint and red)

Mass & Lifetime Sun’s life expectancy: 10 billion years

Mass & Lifetime Sun’s life expectancy: 10 billion years Life expectancy of 10 M Sun star: 10 times as much fuel, uses it 10 4 times as fast 10 billion years x 10 / 10 4 ~ 10 million years

Mass & Lifetime Sun’s life expectancy: 10 billion years Life expectancy of 10 M Sun star: 10 times as much fuel, uses it 10 4 times as fast 10 billion years x 10 / 10 4 ~ 10 million years Life expectancy of 0.1 M Sun star: 0.1 times as much fuel, uses it 0.01 times as fast 10 billion years x 0.1 / 0.01 ~ 100 billion years

Main-Sequence Star Summary High Mass: High Luminosity Short-Lived Large Radius Blue Low Mass: Low Luminosity Long-Lived Small Radius Red

How do we Measure Stellar Diatances? Based on our knowledge of star behavior, we can observe the spectra of stars then calculate their properties, including luminosity. We can take a star, calculate its luminosity, then the difference between this and the star's observed brightness, must be caused by distance.

Stellar Distances We now know both luminosity and apparent brightness, we can re-use the inverse square law Using the H-R diagram this way is called Spectroscopic Parallax. Distance =

Stellar Distances

Stellar Mass Distribution

What are giants, supergiants, and white dwarfs?

Off the Main Sequence Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence All stars become larger and redder after exhausting their core hydrogen: giants and supergiants Most stars end up small and white after fusion has ceased: white dwarfs

Temperature Luminosity Which of these stars will have changed the least 10 billion years from now? A B C D

Temperature Luminosity Which of these stars can be no more than 10 million years old? A B C D

What have we learned? Why is a star’s mass so important? –A star’s mass controls how fast it consumes fuel. –High mass stars are short-lived, low mass stars are long-lived –Over 70% of stars are less than the mass of our Sun How do we measure stellar distances? –A star's luminosity can now be estimated by it's spactral type and main-sequence postion. –The luminosity and measured brightness can be combined to calculate the star's distance. –This technique is Spectroscopic parallax

What have we learned? What are giants, supergiants, and white dwarfs? –All stars become larger and redder after core hydrogen burning is exhausted: giants and supergiants –Most stars end up as tiny white dwarfs after fusion has cease

Star Clusters and the HR Diagram Our goals for learning: What is a star cluster? How do we find the distance to a star cluster? How do we measure the age of a star cluster?

A group of stars clustered together, because they are formed from the same initial gas cloud. The stars were formed at about the same time, so have about the same age and distance from Earth. What is a star cluster?

The stars of the cluster will have different luminosities. So they will fall on the line of main sequence. The light falls off with distance, so the cluster has an apparent brightness. How do we find the distance to a star cluster?

The apparent brightness of a star cluster’s main sequence, compared to the true main sequence line tells us its distance. This technique is called Main Sequence Fitting

main sequence fitting and spectroscopic parallax are both 'Standard Candles' A standard candle is an object whose luminosity we can determine without needing to measuring its distance first.

How do we measure the age of a star cluster?

Massive blue stars die first, followed by white, yellow, orange, and red stars. -The age of a cluster can be first recognized by its color!

When stars start to die, they leave the main sequence. The short- lived ones do so first, the longer-lived stars remain on the main sequence.

This cluster now has no stars with life expectancy less than around 100 million years. Thus, the cluster must be over 100 million years old.

The main- sequence turnoff point of a cluster tells us its age.

This cluster has lost it's yellow sun- like stars, so it must be about billion years old.

What have we learned? What is a star cluster? A groups of stars with similar age and distance. How do we measure the distance to a star cluster? ‒ A cluster’s main sequence line will fall below where it should be, because it has dimmed with distance How do we measure the age of a star cluster? A star cluster’s age roughly equals the life expectancy of its most massive stars still on the main sequence