Chapter 12
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 -Very large (10-1000x larger than Sun) stars reside here -Stars not on the main sequence are not happily converting hydrogen to helium. -Stars with lower T and higher L than main-sequence stars must have larger radii (giants and supergiants). -These stars were once on the main sequence.
Types of Binary Star Systems
-visual binary -eclipsing binary -spectroscopic binary -About half of all stars are in binary systems.
Properties of Thermal Radiation
2. Hotter objects emit photons with a higher average energy/shorter peak wavelength (Wien's Law).
What is the approximate surface temperature of a B star?
20,000 K
Why is a the birth mass of a star such an important quantity?
A star's birth mass is the most important predictor of a star's lifetime. A star born with high mass will have a short lifespan; a star born with low mass will have a significantly longer lifespan.
Which of the stars below is reddest?
A) M star
Suppose you see a star cluster with a turn-off point corresponding to the location of an O star (hottest star) on the H-R diagram. You know the cluster must be:
A) quite young -If the O stars are just leaving the main sequence, this cluster must have been formed very recently. THERE ARE NO OLD FLIES!!
How is the lifetime of a star affected by its mass?
More massive stars live much shorter lives than less massive stars.
Which star is the most luminous?
supergiants
Slide 17
-Most massive stars: 100 MSun -Least massive stars: 0.08 MSun
Slide 6
-Most luminous stars: 1 million LSun. -Least luminous stars: 0.0001 LSun (LSun is luminosity of the Sun).
Remembering Spectral Types
-(Hottest) O B A F G K M (Coolest) -Oversized Bananas Are Feeding Giant Killer Monkeys
Slide 37
-Amount of light passing through each sphere is the same. -Area of sphere = 4π (radius)2. -Divide luminosity by area to get brightness. -Light intensity needs to spread out over a larger area as it propagates out - star looks dimmer the farther one is from it. -Think of equal amounts of paint needed to paint walls of different sizes --- the larger wall gets a thinner layer of paint.
Apparent Brightness (or flux):
-Amount of light that reaches an observer (energy per second per square meter). -Depends on observer's location relative to light.
Luminosity:
-Amount of power an object radiates (energy per second, such as a Watt). -Intrinsic property of an object.
What is a Hertzsprung-Russell diagram?
-An H-R diagram plots the temperature and luminosity of stars. -Location of star on H-R diagram tells us about its size, temperature, luminosity, and nature. -Most stars (90%) fall somewhere on the main sequence of the H-R diagram. -Stars occupy a rather narrow path in luminosity temperature space. -Do not find hot, low luminosity or cool, high-luminosity stars on the main sequence. -Main sequence is a MASS sequence.
Slide 10
-Blue stars are hottest. -Red stars are coolest. -Color of star can tell us roughly its temperature.
Why Are More Massive Stars More Luminous?
-Core pressure and temperature of a higher-mass star need to be higher in order to balance gravity. -Higher core temperature boosts fusion rate, leading to larger luminosity.
Slide 28
-Detailed modeling of the oldest globular clusters reveals that they are about 12-13 billion years old.
Betelgeuse, Betelgeuse, Betelgeuse
-First star other than the Sun to be spatially resolved (because it is a supergiant star). -(Betelgeuse is not a main sequence star).
Slide 7
-Hottest stars: 50,000 K -Coolest stars: 3000 K (Sun's surface is 5800 K). -Surface temperature, not core temperature.
You have a bunch of stars, and for each of them you know luminosity and temperature, and sometimes mass. What do you do with them?
-Make a plot of luminosity vs. temperature. This is called a Hertzsprung-Russell (H-R) diagram. -Surprisingly, stars are not found with random, uncorrelated luminosities and temperatures.
Slide 25
-Massive blue stars die first, followed by white, yellow, orange, and red stars. -Pleiades now has no stars with total life expectancy less than around 100 million years. -To determine accurate ages, we compare models of stellar evolution to the cluster data. -Main-sequence turnoff point on the H-R diagram of a cluster tells us its age. -Older clusters have a turn-off point at a lower luminosity/ temperature/ mass than younger clusters. It occurs at a redder color for an older age.
Slide 26-27
-Massive stars are blue, hot, and luminous (upper left). --Low mass stars are red, cool, and dim (lower right). -Sun-like stars are somewhere in between. -Stars on the main sequence are happily converting hydrogen to helium in their cores -stable (for now). -Stars not on the main sequence (giants, white dwarfs, etc.) are not happily converting hydrogen to helium in their cores.
Star Clusters and Stellar Lives
-Our knowledge of the life stories of stars comes from comparing mathematical models of stars with observations. -Star clusters are particularly useful because they contain stars of different mass that were born about the same time and at the same distance. -All cluster stars have same distance, same age, so we can study effect of mass of stars
Slide 5
-Parallax: apparent positions of nearest stars shift as Earth orbits Sun. -Relies on simple geometry - no assumptions needed. --Just need to know Earth-Sun distance (AU). -This is the (very small) angular shift the ancient Greeks could not measure using just their eyes. -Parallax angle depends on distance: the closer the object, the greater the angular shift. -Measure angle - GET DISTANCE
Slide 9
-Stars on the main sequence are happily converting hydrogen to helium in their cores - stable (for now). -O stars have the shortest lifetimes (less than 10 million years). -M stars have the longest lifetimes (more than a trillion years) -Initial mass determines nearly every property of a star.
Slide 13
-Stars with higher T and lower L than main-sequence stars must have smaller radii (white dwarfs). -These stars used to be main sequence and then giant stars, but are now at the end of their stellar lifetimes.
Mass and Lifetime
-Sun's life expectancy: 10 billion years -Until core hydrogen (10% of total) is used up. -Life expectancy of 10 MSun star: 10 times as much fuel, uses it 10,000 times as fast as Sun 10 billion years × 10/104 ~ 10 million years. -Rock stars -Life expectancy of 0.1 MSun star: 0.1 times as much fuel, uses it 0.001 times as fast as Sun 10 billion years × 0.1/0.001 ~ 1 trillion years - Penny pinchers
How do we measure the age of a star cluster?
-The hottest, most massive stars on the main sequence age (use up their core hydrogen) first and leave the main sequence first. -They are followed by successively lower mass stars. -Place where main sequence of a cluster ends: turnoff point. - younger clusters have bluer turnoff points on the H-R diagram
Slide 3
-The relationship between apparent brightness and luminosity depends on distance: Brightness =Luminosity /4π (distance)2. -We can determine a star's luminosity if we can measure its distance and brightness: Luminosity = 4π (distance)2 x (Brightness) -This makes finding the distances to astronomical objects crucial!
Luminosity Versus Brightness
-Two observers looking at a 100 Watt light bulb. -Both observers must agree the luminosity of the bulb is 100 Watts. -The observers measure a different apparent brightness for the bulb.
Sizes of Stars
-Very, very few star sizes measured directly (too far away and/or are too small) even with modern instrumentation. -Most sizes deduced from modeling of stellar emission or eclipses. -Note: these are all main sequence stars -Remember: Sun is a G star (yellow circle) -Note: you CANNOT tell that the gold star is larger simply from looking at the photo - the gold star only appears larger because of the imperfect focus of a telescope -Neither star can be resolved into a disk by the telescope!!
Visual Binary
-We can directly observe the orbital motions of both stars (need stars to be wellseparated). -Analogous to direct imaging method of finding extrasolar planets (where you actually see the planet).
Eclipsing Binary
-We can measure periodic eclipses when one star passes in front of another star. -We don't actually see two stars, we just measure dips in light from one apparent star, when one star blocks light from the other star. -Analogous to transit method for finding extrasolar planets.
Spectroscopic Binary
-We determine the orbit by measuring Doppler shifts of emission/absorption lines in the spectrum of one star (or both). -Analogous to Doppler method for finding extrasolar planets.
Slide 11
-We learn a lot more about stars by obtaining their spectra (dispersing their light). -Lines in a star's spectrum correspond to a spectral type that reveals its temperature (spectral type is just another way of expressing the temperature of a star). -(Hot-Blue) O B A F G K M (Cool-Red)
Slide 18
-We measure mass using gravity. -Direct mass measurements are possible only for stars in binary star systems.
Question 10
-Where on this diagram do we find stars that are cool and dim? in the lower right hand corner. -Where on this diagram do we find stars that are cool and luminous?in the upper right hand corner. -Where on this diagram do we find stars that are hot and dim?in the lower left hand corner. -Where on this diagram do we find stars that are hot and luminous?in the upper left hand corner.
So How Far Away Are These Stars?
Are the brightest ones luminous and far away or just dim and nearby? Need to get their distances to know.
How would the brightness of Alpha Centauri change if it were 4 times farther away from us than it is now?
B) It would be 1/16 as bright as now Brightness changes like 1/(distance)2
Which star is on the main sequence?
D
How would the apparent brightness of Alpha Centauri change if it were 3 times closer to us than it is now?
D) It would be 9 times brighter than now -Brightness changes like 1/(distance)2, NOT 1/(distance).
Which of the following main sequence stars is least massive?
D) M star
Which combination of properties go together for a high mass star?
Hot, blue, luminous, short life time
What is the main-sequence turnoff point of a star cluster, and why is it important?
It is the spectral type of the hottest main sequence star in a star cluster, and it tells us the cluster's age.
If we triple our distance from an object, how does the apparent brightness of the object change?
Its apparent brightness will decrease by a factor of 9.
Question 5
Look back in homework.
Which comparison between low-mass stars and high-mass main-sequence stars is accurate?
Low-mass stars are cooler and less luminous than high-mass stars.
Slide 23
Massive blue stars die first, followed by white, yellow, orange, and red stars - that is, first O, then B, A, F, G, K, M stars in order.
Which star is the hottest star?
O
Which of the stars below is hottest?
O star
From hottest to coolest, the order of the spectral types of stars is _________.
OBAFGKM
Based on the description of the appearance of an H-R diagrams for four different star clusters, which cluster is the youngest?
The diagram shows main-sequence stars of every spectral type except O, along with a few giants and supergiants.
What do all main sequence stars share in common?
They generate energy through hydrogen fusion in their core.
Which star below has a spectrum that peaks at the shortest wavelength?
a blue star
Which of the following stars has the longest lifetime?
a main-sequence M star
Which of the following stars is the most massive?
a main-sequence O star
Which of the following stars has the coolest surface temperature?
an M star
Which group represents hydrogen-burning stars with the shortest lifetimes?
c
What two quantities allow one to determine a star's luminosity?
apparent brightness and distance
The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note that (a) represents the entire main sequence while (c) and (d) represent only small parts of the main sequence. Which group represents stars that have no ongoing nuclear fusion anywhere in the star?
b
Star X is identical to Star Y, except that Star X is twice as far from us as Star Y. As a result, ________.
both stars have the same luminosity, but the apparent brightness of Star Y is four times that of Star X
On an H-R diagram, stellar masses _________.
can be estimated for main sequence stars but not for other types of stars.
The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note that (a) represents the entire main sequence while (c) and (d) represent only small parts of the main sequence. Which group represents stars that are cool and dim?
d
The sketch above shows groups of stars on the H-R diagram, labeled (a) through (e); note that (a) represents the entire main sequence while (c) and (d) represent only small parts of the main sequence. Which group represents stars with the longest main-sequence lifetimes?
d
Which group includes stars that are burning elements besides hydrogen in their cores?
e
If the star Alpha Centauri were 10 times farther away from us than it is now, its parallax angle would
get smaller.
If the distance between a star and us is doubled, with everything else remaining the same, its luminosity
remains the same, but its apparent brightness is decreased by a factor of four.
Where on a Hertzsprung-Russell diagram are white dwarfs located?
lower left
The total amount of power, or energy per time, emitted by a star is called its _________.
luminosity
Since all stars begin their lives with more or less the same basic composition, which property is most responsible for how they will differ throughout their lives?
mass they are formed with
Which two quantities are required to calculate the masses of stars in a binary system?
orbital period and average orbital distance
A star's luminosity is the
total amount of energy that the star radiates each second.
Where on the main sequence on a Hertzsprung-Russell diagram do the stars with the greatest mass reside?
upper left
Which star is the hottest?
white dwarfs