The Family of Stars
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Transcript of The Family of Stars
The Family of StarsChapter 9
Science is based on measurement, but measurement in astronomy is very difficult. Even with the powerful modern telescopes described in Chapter 6, it is impossible to measure directly simple parameters such as the diameter of a star. This chapter shows how we can use the simple observations that are possible, combined with the basic laws of physics, to discover the properties of stars.
With this chapter, we leave our sun behind and begin our study of the billions of stars that dot the sky. In a sense, the star is the basic building block of the universe. If we hope to understand what the universe is, what our sun is, what our Earth is, and what we are, we must understand the stars.
In this chapter we will find out what stars are like. In the chapters that follow, we will trace the life stories of the stars from their births to their deaths.
Guidepost
I. Measuring the Distances to StarsA. The Surveyor's MethodB. The Astronomer's MethodC. Proper Motion
II. Intrinsic BrightnessA. Brightness and DistanceB. Absolute Visual MagnitudeC. Calculating Absolute Visual MagnitudeD. Luminosity
III. The Diameters of StarsA. Luminosity, Radius, and TemperatureB. The H-R DiagramC. Giants, Supergiants, and Dwarfs
Outline
D. Luminosity ClassificationE. Spectroscopic Parallax
IV. The Masses of StarsA. Binary Stars in GeneralB. Calculating the Masses of Binary StarsC. Visual Binary SystemsD. Spectroscopic Binary SystemsE. Eclipsing Binary Systems
V. A Survey of the StarsA. Mass, Luminosity, and DensityB. Surveying the Stars
Outline
The Amazing Power of StarlightWe already know how to determine a star’s
• surface temperature• chemical composition• surface density
In this chapter, we will learn how we can determine its
• distance• luminosity• radius• mass
and how all the different types of stars make up the big family of stars.
Distances to Stars
Trigonometric Parallax:Star appears slightly shifted from different
positions of the Earth on its orbit
The farther away the star is (larger d), the smaller the parallax angle p.
d = __ p 1
d in parsec (pc) p in arc seconds
1 pc = 3.26 LY
The Trigonometric Parallax
Example:
Nearest star, α Centauri, has a parallax of p = 0.76 arc seconds
d = 1/p = 1.3 pc = 4.3 LY
With ground-based telescopes, we can measure parallax p ≥ 0.02 arc sec, which is d ≤ 50 pc
This method does not work for stars farther away than 50 pc.
Proper MotionIn addition to the periodic back-and-forth motion related to the trigonometric parallax, nearby stars also show continuous motions across the sky.
These are related to the actual motion of the stars throughout the Milky Way, and are called proper motion.
Intrinsic Brightness/ Absolute Magnitude
The more distant a light source is, the fainter it appears.
Brightness and Distance
(SLIDESHOW MODE ONLY)
Intrinsic Brightness / Absolute Magnitude (2)
The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d)
Star AStar B Earth
Both stars may appear equally bright, although star A is intrinsically much brighter than star B.
Distance and Intrinsic Brightness
Betelgeuse
Rigel
Example:
App. Magn. mV = 0.41
Recall that:
Magn. Diff.
Intensity Ratio
1 2.512
2 2.512*2.512 = (2.512)2 = 6.31
… …
5 (2.512)5 = 100
App. Magn. mV = 0.14For a magnitude difference of 0.41 – 0.14 = 0.27, we find an intensity ratio of (2.512)0.27 = 1.28
Distance and Intrinsic Brightness (2)
Betelgeuse
Rigel
Rigel is appears 1.28 times brighter than Betelgeuse,
Thus, Rigel is actually (intrinsically) 1.28*(1.6)2 = 3.3 times brighter than Betelgeuse.
But Rigel is 1.6 times further away than Betelgeuse
Absolute Magnitude
To characterize a star’s intrinsic brightness, define Absolute Magnitude (MV):
Absolute Magnitude = Magnitude that a star would have if it were at a distance of 10 parsecs (pc).
Absolute Magnitude (2)
Betelgeuse
Rigel
Betelgeuse Rigel
mV 0.41 0.14
MV -5.5 -6.8
d 152 pc 244 pc
Back to our example of Betelgeuse and Rigel:
Difference in absolute magnitudes: 6.8 – 5.5 = 1.3
Luminosity ratio = (2.512)1.3 = 3.3
The Distance ModulusIf we know a star’s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes:
Distance Modulus
mV – MV = -5 + 5 log10(d)
distance in units of parsec
The Size (Radius) of a StarWe already know: flux increases with surface temperature (~ T4); hotter stars are brighter.
But brightness also increases with size.
A BStar B will be brighter than
star A.
Absolute brightness is proportional to radius squared (L ~ R2).
Quantitatively: L = 4 π R2 σ T4
Surface area of the starSurface flux due to a blackbody spectrum
Example: Star Radii
Polaris (F7 star) has just about the same spectral type (and thus surface temperature) as our sun (G2 star), but it is 10,000 times intrinsically brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This means its luminosity is 1002 = 10,000 times more than the sun.
Organizing the Family of Stars: The Hertzsprung-Russell Diagram
Stars have different temperatures, different luminosities, and different sizes.
To bring some order into that zoo of different types of stars: organize them in a diagram of
Luminosity versus Temperature
or
Lum
inos
ity
Temperature
O B A F G K M Spectral type
“Hertzsprung-Russell (HR) Diagram”
Abs
olut
e m
ag.
The Hertzsprung-Russell Diagram AnalogyIt’s useful to compare an HR Diagram to a similar graph of cars with different weights and horsepower.
The Hertzsprung-Russell Diagram
Most stars are found along the
Main Sequence
The Hertzsprung-Russell Diagram (2)
“Giants” (and supergiants) are same temperature, but much brighter than main sequence stars.
Giants must be much larger than m.s. stars
Dwarfs are same temperature, but fainter and smaller than m.s. stars
Stars spend most of their
active life time on the
main sequence (m.s.)
The Radii of Stars in the Hertzsprung-Russell Diagram
10,000 times the
sun’s radius
100 times the
sun’s radius
As large as the sun
100 times smaller than the sun
Rigel Betelgeuse
Sun
Polaris
Luminosity Classes
Ia Bright Supergiants
Ib Supergiants
II Bright Giants III Giants
IV Subgiants
V Main-Sequence Stars
IaIb
IIIII
IVV
Spectral Lines of Giants
• Absorption lines in spectra of giants and supergiants are narrower than in main sequence stars
Pressure and density in the atmospheres of giants are lower than in main sequence stars, so:
• From the line widths, we can estimate the size and luminosity of a star.
• Distance estimate (spectroscopic “parallax”) is found using spectral type, luminosity class and apparent magnitude
Binary Stars
More than 50 % of all stars in our Milky Way
are not single stars, but belong to binaries:
Pairs or multiple systems of stars which
orbit their common center of mass.
If we can measure and understand their orbital
motion, we can estimate the stellar
masses.
The Center of Masscenter of mass = balance point of the system.Both masses equal => center of mass is in the middle, rA = rB.
The more unequal the masses are, the more it shifts toward the more massive star.
Center of Mass
(SLIDESHOW MODE ONLY)
Estimating Stellar MassesRecall Kepler’s 3rd Law:
Py2 = aAU
3
Valid for the Solar system: star with 1 solar mass in the center.
We find almost the same law for binary stars with masses MA and MB different
from 1 solar mass:
MA + MB = aAU
3 ____ Py
2
(MA and MB in units of solar masses)
Examples: Estimating Mass
a) Binary system with period of P = 32 years and separation of a = 16 AU:
MA + MB = = 4 solar masses.163____322
b) Any binary system with a combination of period P and separation a that obeys Kepler’s
3. Law must have a total mass of 1 solar mass.
Visual Binaries
The ideal case:
Both stars can be seen directly, and
their separation and relative motion can be followed directly.
Spectroscopic Binaries
Usually, binary separation a can not be measured directly
because the stars are too close to each other.
A limit on the separation and thus the masses can
be inferred in the most common case:
Spectroscopic Binaries
Spectroscopic Binaries (2)The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum.
Doppler shift Measurement of radial velocities
Estimate of separation a
Estimate of masses
Spectroscopic Binaries (3)Tim
e
Typical sequence of spectra from a spectroscopic binary system
Eclipsing Binaries
Usually, inclination angle of binary systems is
unknown uncertainty in mass estimates.
Special case:
Eclipsing Binaries
Here, we know that we are looking at the
system edge-on!
Eclipsing Binaries (2)Peculiar “double-dip” light curve
Example: VW Cephei
Eclipsing Binaries (3)
From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane.
Example:
Algol in the constellation of Perseus
The Light Curve of Algol
Masses of Stars in the Hertzsprung-Russell DiagramThe higher a star’s mass,
the more luminous (brighter) it is:
High-mass stars have much shorter lives than
low-mass stars:
Sun: ~ 10 billion yr.10 Msun: ~ 30 million yr.0.1 Msun: ~ 3 trillion yr.
0.5
18
6
31.7
1.00.8
40
Masses in units of solar masses
Low
masses
High masses
Mass
L ~ M3.5
tlife ~ M-2.5
Maximum Masses of Main-Sequence Stars
h Carinae
Mmax ~ 50 - 100 solar masses
a) More massive clouds fragment into smaller pieces during star formation.
b) Very massive stars lose mass in strong stellar winds
Example: h Carinae: Binary system of a 60 Msun and 70 Msun star. Dramatic mass loss; major eruption in 1843 created double lobes.
Minimum Mass of Main-Sequence Stars
Mmin = 0.08 Msun
At masses below 0.08 Msun, stellar progenitors do not get hot enough to ignite thermonuclear fusion.
Brown Dwarfs
Gliese 229B
Surveys of Stars
Ideal situation:Determine properties of all stars within a certain volume.
Problem:Fainter stars are hard to observe; we might be biased towards the more luminous stars.
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
stellar parallax (p)parsec (pc)proper motionfluxabsolute visual magnitude (Mv)
magnitude–distance formula
distance modulus (mv – Mv)
luminosity (L)absolute bolometric magnitude
H–R (Hertzsprung–Russell) diagram
main sequencegiantssupergiants
red dwarfwhite dwarfluminosity classspectroscopic parallaxbinary starsvisual binary systemspectroscopic binary system
eclipsing binary systemlight curvemass–luminosity relation
New Terms