1. Red Giants & White Dwarfs: Measuring the Stars
Star Chapter 17

2. Standards
Understand the scale and contents of the universe, including:
Objects in the universe such as stars
Describe how luminosity and temperature indicate a star’s age

3. It is estimated by astronomers that the number of stars in the visible universe outnumber all the grains of sand on all the beaches on Earth.

4. Distances to the Stars
Closest stars are measured using parallax – an object’s apparent shift relative to some more distant background as observer’s point of view changes.
Use Earth’s orbit as baseline to measure angle through which line of sight to the object shifts.

5. Parallax

6. Distances to the Stars
Measured in arc seconds, using units of parsec: 1 parsec = observed parallax of 1” = 206,265 a.u.
Note: ” = arc second:
tip of little finger held at arms length = 1 = 60’ = 3600”
This is 30,900,000,000,000 km (31 trillion km) or 19,200,000,000,000 mi (19 trillion mi)
The formula to determine distance to a star is:
distance (in parsecs) = _______1_________
parallax (in arc seconds)

7. Our Nearest Neighbors
Closest star, other than the sun, is Proxima Centauri, member of a triple star system known as the Alpha Centauri Complex.
Parallax = 0.76” = 1.3 parsecs = 270,000 a.u. = 4.3 light years
This is ~300,000 times the distance from Earth to the sun
This is typical for interstellar (between the stars) distances in the Milky Way.
Barnard’s Star, next closest, is 6 light years away.

8. Stellar Motion
In addition to apparent motion of parallax, stars have real motion.
They travel through space.

9. Stellar Motion Two components to the motion:
Transverse component – measures a star’s motion perpendicular to our line of sight (movement across the sky)
Radial component – measures the star’s movement along our line of sight (motion toward or away from us)
Transverse and radial components of motion are combined using the Pythagorean theorem to determine a star’s total velocity.

10. Stellar Sizes
Most stars are unresolved points of light, but a few are big enough, bright enough and close enough to measure size directly.
These stars are measured using speckle interferometry – an optical technique that combines many short-exposure images to make a high resolution map of the star.
By measuring the star’s angular size and knowing its distance from the sun, astronomers can determine its radius by simple geometry

11. Stellar Sizes A few dozen stars have been measured this way.
Most stars are too distant and must be measured using other techniques.
One technique is to use the relationship between a star’s radius, luminosity and temperature.
A star’s radius can be found by dividing the square root of its luminosity by its temperature squared.

12. Luminosity and Apparent Brightness
Luminosity is an intrinsic property of a star – it does not depend in any way on the location or movement of the observer.
It is sometimes called a star’s absolute brightness.

13. Luminosity and Apparent Brightness
When we look at a star, we don’t see its luminosity.
We see it’s apparent brightness – the amount of energy striking a unit area of a sight sensitive surface per unit time.
It is a measure of the energy flux produced by a star, as seen from Earth, and depends on our distance from the star.
A note on terminology:
apparent = what we see;
absolute = what it actually is

14. The Magnitude Scale
Magnitude scale is used for measuring apparent brightness.
Dates from 2nd century BC, when Hipparchus ranked naked-eye stars into 6 groups, with
1 = brightest and 6 = faintest.
A first magnitude star is 100 x brighter than a sixth magnitude star.
These numbers are called a star’s apparent magnitude.
They are no longer limited to whole numbers, and magnitudes outside the 1-6 range are allowed.

15. The Magnitude Scale
Absolute magnitude is a measure of a star’s absolute brightness, or luminosity (defined at a distance of 10 parsecs).
The numerical difference between a star’s absolute and apparent magnitude is a measure of the distance to the star.
The equation for this is:
apparent brightness = luminosity
distance2

16. Temperature and Color
A star’s temperature is determined by measuring its color
Hot stars (~15,000 K) are blue or white
Cool stars (~3000 K) are red
Our sun is a yellow star (~6000 K)

17. Stars of Different Temperatures

18. Classification of Stars
Stars are classified by color and temperature.
Based on this, they are assigned letters that designate their spectral class

19. Classification of Stars
Spectral Class
Color
Surface Temp (K)
Examples O
Blue
30,000
Naos B
Blue-white
20,000
Rigel A
White
10,000
Vega, Sirius F
Yellow-white
7,000
Canopus G
Yellow
6,000
Sun, Alpha Centauri K
Orange
4,000
Arcturus, Aldebaran M
Red
3,000
Betelgeuse
Temperature

20. Classification of Stars
Mnemonic to remember order of spectral classes:
“Oh, be a fine guy/girl, kiss me”
Each of the spectral classes are further divided into 10 subdivisions of 0-9.
The lower the number, the hotter the star.
Our sun is a G2 star.

21. The Hertsprung-Russel (H-R) Diagram
The H-R diagram plots a star’s luminosity vs. its temperature.
Temperature is plotted on the x-axis, and increases to the left (opposite of most graphs).
Luminosity is plotted on the y-axis and increases up.

22. The Main Sequence
There is a relationship between temperature and luminosity, such that most stars are confined to a well-defined band on the H-R diagram.
This band stretches from the top left (high temperature, high luminosity) to the lower right (low temperature, low luminosity).
In other words, cool stars tend to be faint (less luminous) & hot stars tend to be bright.
This band is known as the main sequence.

23. Main Sequence

24. The Main Sequence
At the upper end of the main sequence, stars are large, hot & bright.
These stars are known as blue giants or blue supergiants.
Giants are stars with radii between 10 & 100 times that of our sun.
Supergiants range up to 1000 solar radii.

25. The Main Sequence At the lower end, stars are small, cool & faint.
These are red dwarfs.
They are the most common type of star (80% of all stars in the universe) but are hard to see.
Dwarfs have a radius comparable to or less than the sun (including the sun itself)
Our sun is in the middle of the main sequence (G2V).

26. The Main Sequence
Stars are on the main sequence during their stable, hydrogen fusing lifetimes.
White dwarfs are found off the main sequence, at the bottom left corner of the H-R diagram.
Red giants are also off the main sequence in the upper right corner of the H-R diagram.

28. Luminosity Class
Stars are categorized into luminosity classes based on the width of their spectral lines.
Line width corresponds to the density of a star’s atmosphere.
The atmosphere of a red giant is less dense than a main sequence star, which is less dense than a white dwarf.
This allows astronomers to distinguish between these stars by studying the width of the spectral lines

29. Luminosity Class Luminosity Class Type of Star Ia Bright supergiantsIb
Supergiants II
Bright giants
III
Giants IV
Subgiants V
Main-sequence stars/dwarfs
(our sun = G2V)

30. Mass and Composition
A star’s mass & composition determine its position on the main sequence.
They are fundamental properties of a star that are set once and for all at a star’s birth.
They uniquely determine a star’s internal structure, external appearance & even its future evolution.

31. Mass and Composition
A star’s mass is measured by observing its gravitational influence on a nearby object and applying Newton’s laws:
F = Gm1m2 r2

32. Stellar Lifetimes
Can be estimated by dividing the amount of fuel available (star’s mass) by the rate at which fuel is being consumed (luminosity).

33. Stellar Lifetimes
Massive stars have short life spans because nuclear reactions proceed so rapidly that their fuel is quickly depleted despite their large masses.
O & B stars have life spans of 25 million years (1/400th the 10 billion year life of our sun).
K & M stars have sluggish nuclear reactions and have very long life spans (many we see in sky now will last at least another trillion years).

34. Estimated Lifetime (yrs)
Stellar Lifetimes
Star & Class
Solar Mass
Estimated Lifetime (yrs)
Rigel: B8Ia 10
20 million
Sirius: A1V
2.3
1 billion
Alpha Centauri: G2V
1.1
7 billion
Sun: G2V 1
10 billion
Proxima Centauri: M5V
0.1
>10 billion

35. Measuring the Stars: Table 17.5, p. 461