chapter 11 surveying the stars the brightness of a star depends on both distance and luminosity how...

Chapter 11Surveying the Stars

The brightness of a star depends on both distance and luminosity

How luminous are stars?

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)

(not much) Thought Question

These two stars have about the same luminosity -- which one appears brighter?

A. Alpha CentauriB. The Sun

Luminosity passing through each sphere is the same

Area of sphere:

4π (radius)2

Divide luminosity by area to get brightness

The relationship between apparent brightness and luminosity depends on distance:

Luminosity Apparent Brightness = 4π (distance)2

We can determine a star’s luminosity if we can measure its distance and apparent brightness:

Luminosity = 4π (distance)2 x (Brightness)

Note that there is a huge range in stellar luminosities

Proxima Centauri = 0.0006 Lsun

Betelgeuse = 38,000 Lsun

Thought Question

How would the apparent brightness of Alpha Centauri change if it were three times farther away?

A. It would be only 1/3 as brightB. It would be only 1/6 as brightC. It would be only 1/9 as brightD. It would be three times brighter

Parallax and distance.p = parallax angle in

arcseconds

d (in parsecs) = 1/p

1parsec= 3.26 light years

Parallax and distance.

• Nearest Star: Alpha Centauri • distance = 4.3 light years• (since 1 parsec = 3.26 light years)• Distance (d) in parsecs = 4.3/3.26 =

1.32

• What is the parallax of this star?• d=1/p hence p=1/d (in parsecs)• p for nearest star is 0.76

arcseconds

• All other stars will have a parallax angle smaller than 0.76 arcseconds

hotter brighter, cooler dimmer

hotter bluer, cooler redder

Laws of Thermal Radiation

Hottest stars:

blue~50,000 K

Coolest stars:

Red~3,000 K

(Sun’s surface is 5,800 K)

An aside on “computers”• In the old days an “Astronomical Computer” was

not a machine, but a person….often a woman.• These were the people who calculated positions and

analyzed the photographic plates

• Women did most of the work in compiling these huge stellar catalogues.

An aside on “computers”• What the “computers” did was sift through literally 100’s of

thousands of stellar spectra.• Established a classification scheme based on Hydrogen lines….• The types were alphabetical….letters were assigned in declining

strength of the H-lines

Stellar Classification• Like most early classification systems, they got it

wrong initially• Today we arrange spectral classes by temperature• Wien’s Law: The hotter the object, the bluer the

radiation it emits, and the more total energy is emitted.

Stellar Classification• The hottest stars turned out to be (of course) the bluest.

• Also the level of heat determined what sorts elements would be prominent in the star’s spectrum• For example only the hottest stars can ionize helium

• Only the coolest stars can have molecules

(Hottest) O B A F G K M (Coolest)

Remembering Spectral Types

•Oh, Be A Fine Girl/Guy, Kiss Me

•Only Boys Accepting Feminism Get Kissed Meaningfully

A star’s full classification includes spectral type (line identities) and luminosity class (line shapes, related to the size of the star):

I - supergiantII - bright giantIII - giantIV - subgiantV - main sequence

Examples: Sun - G2 VSirius - A1 VProxima Centauri - M5.5 VBetelgeuse - M2 I

Star Types

Now we know temperature, luminosity, and Distance……what about mass?

Newton shows the way……

We measure mass using gravity

Direct mass measurements are possible only for stars in binary star systems

p = period

a = average separation

p2 = a3 4π2

G (M1 + M2)

Most massive stars:

100 MSun

Least massive stars:

0.08 MSun

(MSun is the mass of the Sun)

Stellar Properties Review Luminosity: from brightness and distance

10-4 LSun - 106 LSun

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 MSun - 100 MSun

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

Mass & Lifetime

Sun’s life expectancy: 10 billion years

Life expectancy of 10 MSun star:

10 times as much fuel, uses it 104 times as fast

10 million years ~ 10 billion years x 10 / 104

Life expectancy of 0.1 MSun star:

0.1 times as much fuel, uses it 0.01 times as fast

100 billion years ~ 10 billion years x 0.1 / 0.01

Until core hydrogen(10% of total) is used up

Stellar Evolution

• Stars are like people in that they are born, grow up, mature, and die.

• A star’s mass determines what life path it will take.

• The Hertzsprung-Russel Diagram is a roadmap for following stellar evolution.

Temperature

Lu

min

osi

tyAn H-R diagram plots the luminosity and temperature of stars

Normal hydrogen-burning stars reside on the main sequence of the H-R diagram

Low-Mass Stars

High-Mass Stars

H-R diagram depicts:

Temperature

Color

Spectral Type

Luminosity

Radius

*Mass

*Lifespan

*Age

Temperature

Lu

min

osi

ty

Which star is the most luminous?

A

BC

D

Temperature

Lu

min

osi

ty

Which star has the largest radius?

A

BC

D

Temperature

Lu

min

osi

ty

Which star is the main sequence star?

A

BC

D

Temperature

Lu

min

osi

ty

Which star is the hottest?

A

BC

D

Temperature

Lu

min

osi

ty

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

A

BC

D

E

Main-Sequence Star Summary

High Mass:

High Luminosity Short-Lived Large Radius Blue

Low Mass:

Low Luminosity Long-Lived Small Radius Red

Open cluster: A few thousand loosely packed stars

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

How do we measure the age of a star cluster?

Pleiades: no stars with life expectancy of less than 100 million years

Main-sequenceturnoff

Main-sequence turnoff point of a cluster tells us its age

Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old