Chapter 12 Astronomy

Remembering Spectral Types

(Hottest) O B A F G K M (Coolest) Remembering Spectral Types • Oh, Be A Fine Girl/Guy, Kiss Me • (Oh Boy, An F Grade Kills Me) • There are extended types such as "L", "T" etc., which are beyond the scope here • Caution: spectral classification still does not capture the whole picture; there is one more dimension to be discussed later (soon)

Remembering Spectral Types

(Hottest) O B A F G K M (Coolest) Remembering Spectral Types • Oh, Be A Fine Girl/Guy, Kiss Me • There are extended types such as "L", "T" etc., which are beyond the scope here • Caution: spectral classification still does not capture the whole picture; there is one more dimension to be discussed later (soon)

Life expectancy of a 10MSun star:

- 10 times as much fuel, uses it 104 times as fast - 10 million years (<= 10 billion years × 10/104)

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

How do we measure stellar temperatures?

- A star's color and spectral type both reflect its temperature

What are giants, supergiants, and white dwarfs?

- All stars become larger and redder after core hydrogen is exhausted: giants and supergiants. - Most stars end up as tiny (but very dense) white dwarfs after fusion has ceased

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 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)

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)

What are the two types of star clusters?

- Open clusters are loosely packed and contain up to a few thousand stars. - Globular clusters are densely packed and contain hundreds of thousands of stars

Life expectancy of a 0.1MSun star:

0.1 times as much fuel, uses it 0.01 times as fast 100 billion years ~ 10 billion years × 0.1/0.01

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. Level of ionization also reveals a star's temperature Absorption lines in a star's spectrum tell us its ionization level (the Sun's spectrum shown here as an example Different levels have different number of electrons, whose excitation states are different - hence different absorption features Lines in a star's spectrum correspond to a spectral type that reveals its temperature: (Hottest) O B A F G K M (Coolest)

Need two out of three observables to measure mass:

1. Orbital period (p) 2. Orbital separation (a or r = radius) 3. Orbital velocity (v) For circular orbits, v = 2πr / p r M v (Actually in this way only (M1+M2) is measured If we can further determine M1/M2, we can get the individual masses - beyond the scope here)

Sun's life expectancy

10 billion years

Least luminous stars:

10-4LSun (LSun is luminosity of the Sun)

Most luminous stars:

106LSun

Coolest stars:

3000 K (Sun's surface is 5800 K)

Hottest stars:

50,000 K

Open cluster

A few thousand loosely packed stars

Star's full classification

A star's full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star): I — supergiant II — bright giant III — giant IV — subgiant V — main sequence Examples: Sun — G2 V Sirius — A1 V Proxima Centauri — M5.5 V Betelgeuse — M2 I

Luminosity:

Amount of power a star radiates (energy per unit time; for example: =>joule/sec = watts)

Apparent brightness:

Amount of starlight that reaches Earth (energy per unit time per unit area; for example, => j/s/m2)

What is a Hertzsprung-Russell diagram?

An H-R diagram plots the stellar luminosity of stars versus surface temperature (or color or spectral type)

The Magnitude Scale for Brightness

Apparent mag = -2.5*log10(Brightness) + const. Absolute mag. is the magnitude of an object put at 10 pc away The larger the magnitude, the fainter the object

These two stars have about the same luminosity— which one appears brighter? A. Alpha Centauri B. The Sun

B

How do we measure stellar luminosities?

Brightness of a star depends on both distance and luminosity Luminosity passing through each sphere is the same. Total area of a sphere is: 4πr2, Where r is the radius Divide luminosity by area to get brightness ("luminosity per unit area" - luminosity density) 1) The relationship between apparent brightness and luminosity depends on distance: Luminosity Brightness = 4π (distance)2 (because the distance is the radius of the sphere enclosing the target) 2) We can determine a star's luminosity if we can measure its distance and apparent brightness: Luminosity = 4π (distance)2 × (Brightness)

How would the apparent brightness of Alpha Centauri change if it were three times farther away? A. It would be only 1/3 as bright. B. It would be only 1/6 as bright. C. It would be only 1/9 as bright. D. It would be three times as bright.

C

Which of the stars below is hottest? A. M star B. F star C. A star D. K star

C

How do we measure stellar temperatures?

Every object emits thermal radiation with a spectrum that depends on its temperature An object of fixed size grows more luminous as its temperature rises

What is a Hertzsprung-Russell diagram?

Hertzsprung and Russell independently discovered that stars occupy only some distinctive regions in the color-luminosity plot (c.a. 1911-1913) An H-R diagram (HRD) plots the luminosities and temperatures of stars. A broader term is "Color-Magnitude Diagram (CMD); in special case it can be treated as an HRD (e.g. when stars are at more or less the same distance) Most stars fall somewhere on the main sequence of the H-R diagram. It was later found that the HRD reveals a mass sequence (owing largely to Arthur Eddington; c.a. 1920)

Main-Sequence Star Summary

High-mass: High luminosity Short-lived Large radius Blue Low-mass: Low luminosity Long-lived Small radius Red

Stellar Properties Review

Luminosity: (derived from brightness and distance) (0.08MSun) 10-4LSun - 106LSun (100MSun) Temperature: (derived from color and spectral type) (0.08MSun) 3000 K - 50,000 K (100MSun) Mass: (derived rom period (p) and average separation (a) of binary-star orbit) 0.08MSun - 100MSun

Which star is most like our Sun?

Main Sequence

Basic idea of stellar evolution

Massive blue stars die first, followed by less massive white stars, and then even less massive yellow, orange, and red stars. Higher mass stars always evolve faster than lower mass ones One cannot wait for billions or even millions of years; however star clusters provide a different route

Binary Star Orbits

Orbit of a binary star system depends on the strength of gravity

Ages

Pleiades now has no stars with a life expectancy less than around 100 million years The mainsequence turnoff point of a cluster tells us its age To determine accurate ages, we compare models of stellar evolution to the cluster data Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old - this puts a very strong constraint to the age of the universe

white dwarfs

Stars with higher T and lower L than main-sequence stars must have smaller radii

giants and supergiants

Stars with lower T and higher L than mainsequence stars must have larger radii

Which star has the largest radius?

Supergiants

Which star is the most luminous?

Supergiants

H-R diagram depicts

Temperature Color Spectral type Luminosity Radius

Globular cluster

Up to a million or more stars in a dense ball bound together by gravity

Which of these stars will have changed the least 10 billion years from now

White Dwarf

Which star is the hottest?

White Dwarf

Main-sequence stars

are fusing hydrogen into helium in their cores, like the Sun. Luminous mainsequence 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. The mass of a normal, hydrogenfusing star determines its luminosity and spectral type The core temperature of a higher-mass star needs to be higher in order to balance gravity. A higher core temperature boosts the fusion rate, leading to greater luminosity

Parallax

is the apparent shift in position of a nearby object against a background of more distant objects Apparent positions of the nearest stars shift by about an arcsecond as Earth orbits the Sun. The size of parallax angle depends on distance Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star, against a fixed background (basically more distant objects whose parallaxes are negligible)

Stars within a cluster

were born at the same time - looking at its HRD thus gives a snapshot of the life stages of stars with different masses

How do we measure stellar masses?

• Direct measurement - using Kepler's Law! • (More properly, Newton's Law) • Applicable to binary stars p = period a = average separation

Not to confuse Parallax with Proper Motion

• Parallax measures the positional shift of a star due to the difference of the Earth's location - the star in question will "return" to the same place after one year (Earth's rotation around the Sun) • Proper motion is due to the star's movement in space - it will not return to the same place ever

Pioneers of Stellar Classification

• Pickering pioneered a method to photograph the spectra of multiple stars simultaneously • Annie Jump Cannon and the "calculators" at Harvard laid the foundation of modern stellar classification

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 (- that's the end of it: they cool off gradually) Giants and supergiants are far larger than mainsequence stars and white dwarfs

Types of Binary Star Systems

• Visual binary • Eclipsing binary • Spectroscopic binary About half of all stars are in binary systems