Temperature

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What is a Hertzsprung-Russell diagram?

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

Most stars fall somewhere on the main sequence of the H-R diagram

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

giants and supergiants

Large radius

Small radius

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

white dwarfs

Fig. 8-9, p. 141

Figure 8.9: Differences in widths and strengths of spectral lines distinguish the spectra of supergiants, giants, and main-sequence stars. (Adapted from H. A. Abt, A. B. Meinel, W. W. Morgan, and J. W. Tapscott, An Atlas of Low-Dispersion Grating Stellar Spectra, Kitt Peak National Observatory, 1968)

Spectral lines of supergiants, giants, and main-sequence stars

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

Fig. 8-10, p. 142

The approximate location of the luminosity classes on the H–R diagram.

Luminosity classes

Stellar Sizes

A few stars are big enough to resolve in the new telescopes.

Sizes for these can now be calculated directly.

Betelguese is 600X larger than the Sun.

Indirect Size determinations

Using the luminosity and the temperature of a star the area and hence the size of a star can be determined.

Example:

Polaris has just about the same spectral type (and thus surface temperature) as our sun, but

it is 10,000 times brighter than our sun.

Thus, Polaris is 100 times larger than the sun.

Temperature

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H-R diagram depicts:

Temperature

Color

Spectral

Type

Luminosity

Radius

Temperature

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Which star is the hottest?

A

BC

D

Temperature

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Which star is the hottest?

A

BC

D

A

Temperature

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Which star is the most luminous?

A

BC

D

Temperature

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Which star is the most luminous?

C

A

BC

D

Temperature

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Which star is a main-sequence star?

A

BC

D

Temperature

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Which star is a main-sequence star?

D

A

BC

D

Temperature

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Which star has the largest radius?

A

BC

D

Temperature

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Which star has the largest radius?

C

A

BC

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

The mass of a normal, hydrogen-burning star determines its luminosity and spectral type!

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

Main regions

For stars

Some HR diagrams use the magnitude instead of the luminosity. While it looks like a linear scale remember it’s really a log scale.

The Distance ModulusIf we know a star’s absolute magnitude or

luminosity, we can infer its distance by comparing absolute and apparent magnitudes:

Distance Modulus

= mV – MV

= -5 + 5 log10(d [pc])

Distance in units of parsec

Equivalent:

d = 10(mV – MV + 5)/5 pc

Stellar Distances. From parallax outward each new method is calibrated by data from the earlier method. The methods overlap.

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

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

(0.08 MSun) (100 MSun)

(100 MSun)(0.08 MSun)

The most visible stars

Notice the scales are log scales.

The diagonals are lines of constant radius, from the radius-luminosity-temperature relationship.

Nearby Stars

p. 151

A random sample of stars

There should be nothing special about our local neighborhood. It therefore is useful as a random sample of stars in the galaxy.

The larger our sample size the better our conclusions. So a complete sample out to greater distances gives a more accurate picture of the galaxy as a whole.

A Census of the StarsFaint, red dwarfs (low mass) are the most

common stars.

Giants and supergiants are extremely rare.

Bright, hot, blue main-sequence stars (high-mass) are very rare.

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% - 15% of total) is used up

Stellar Population Distribution Explained

Faint, red dwarfs (low mass) are the

most common stars. Long lived

Giants and supergiants are extremely rare.

Passing through a stage.

Bright, hot, blue main-sequence

stars (high-mass) are very rare. Short

lived

Main-Sequence Star SummaryHigh Mass:

High Luminosity Short-Lived Large Radius Blue

Low Mass:

Low Luminosity Long-Lived Small Radius Red

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

• The core of most stars ends up small and white after fusion has ceased: white dwarfs

Temperature

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Which star is most like our Sun?

A

B

C

D

Temperature

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Which star is most like our Sun?

B

A

B

C

D

Temperature

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

A

B

C

D

Temperature

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

C

A

B

C

D

Temperature

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Which of these stars can be no more than 10 million years old?

A

B

C

D

Temperature

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Which of these stars can be no more than 10 million years old?

A

A

B

C

D

Why do the properties of some stars vary?

Variable Stars

• Any star that varies significantly in brightness with time is called a variable star

• Some stars vary in brightness because they cannot achieve proper balance between power welling up from the core and power radiated from the surface

• Such a star alternately expands and contracts, varying in brightness as it tries to find a balance

Pulsating Variable Stars

• The light curve of this pulsating variable star shows that its brightness alternately rises and falls over a 50-day period

Pulsating Variable Stars

• Most pulsating variable stars inhabit an instability strip on the H-R diagram

• The most luminous ones are known as Cepheid variables

Cepheid Variable Stars

• Cepheid variable’s magnitude will vary between 0.5-2 magnitudes over a period from days to months.

• They have been show to have a period of variability that depends on luminosity.

• This allows Cepheid variables to be used as a standard candle to measure distance.

Cepheid Variable Stars• The accepted explanation for the pulsation of

Cepheids is called the Eddington valve• Doubly ionized helium is more opaque than

singly ionized helium.

Eddington valve cont.• The more helium is heated, the more ionized

it becomes. • At the dimmest part of a Cepheid's cycle, the

ionized gas in the outer layers of the star is opaque, and so is heated by the star's radiation

• Due to the increased temperature the fusion rate in the core increase resulting in an increase in radiation pressure causing the star to begin to expand.

Eddington valve cont.

• As it expands, the ionized helium cools, and becomes less ionized and therefore more transparent, allowing the radiation to escape cooling the star and slowing the fusion rate.

• Then the expansion stops, and reverses due to the star's gravitational attraction.

• The process then repeats.

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)

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 ceased

• Why do the properties of some stars vary?– Some stars fail to achieve balance between

power generated in the core and power radiated from the surface

Star Clusters

• Our goals for learning• What are the two types of star clusters?• How do we measure the age of a star cluster?

What are the two types of star clusters?

Open cluster: A few thousand loosely packed stars, typically found is galactic disk, and typically young in age <5 billion yrs.

Globular cluster: Up to a million or more stars in a dense ball bound together by gravity, most found in the galactic halo with some in the disk, some of the oldest objects found in the galaxy.

How do we measure the age of a star cluster?

Massive blue stars die first, followed by white, yellow, orange, and red stars

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

Pleiades now has no stars with life expectancy less than around 100 million years

Main-sequenceturnoff

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

What have we learned?• 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

• 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