Download The Family of Stars

The Family of Stars
Distances to Stars
d in parsec (pc)
p in arc seconds
1
d = __
p
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.
1 pc = 3.26 LY
The Trigonometric Parallax
Example:
Nearest star, a 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
parallaxes p ≥ 0.02 arc sec
=> d ≤ 50 pc
This method does not work for stars
farther away than 50 pc.
Proper Motion
In addition to the
periodic back-andforth 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.
Intrinsic Brightness / Absolute
Magnitude (2)
More quantitatively:
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):
L
__
F~ 2
d
Star A
Star B
Both stars may appear equally bright, although
star A is intrinsically much brighter than star B.
Earth
Distance and Intrinsic Brightness
Example:
Magn.
Diff.
Intensity Ratio
1
2.512
2
2.512*2.512 = (2.512)2
= 6.31
…
…
5
(2.512)5 = 100
For a magnitude difference of 0.41
– 0.14 = 0.27, we find an intensity
ratio of (2.512)0.27 = 1.28
Betelgeuse
App. Magn. mV = 0.41
Rigel
App. Magn. mV = 0.14
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 pc.
Absolute Magnitude (2)
Back to our example of
Betelgeuse and Rigel:
Betelgeuse Rigel
mV
0.41
0.14
MV
-5.5
-6.8
d
152 pc
244 pc
Betelgeuse
Rigel
Difference in absolute magnitudes:
6.8 – 5.5 = 1.3
=> Luminosity ratio = (2.512)1.3 = 3.3
The Distance Modulus
If we know a star’s absolute magnitude, we
can infer its distance by comparing absolute
and apparent magnitudes:
Distance Modulus
= mV – M V
= -5 + 5 log10(d [pc])
Distance in units of parsec
Equivalent:
d = 10(mV – MV + 5)/5 pc
Organizing the Family of Stars:
The Hertzsprung-Russell Diagram
We know:
Stars have different temperatures,
different luminosities, and different sizes.
Absolute mag.
or
Luminosity
To bring some order into that zoo of different
types of stars: organize them in a diagram of
Luminosity
versus
Temperature (or spectral type)
Hertzsprung-Russell Diagram
Spectral type: O
Temperature
B
A
F
G
K
M
The Hertzsprung-Russell Diagram
The Hertzsprung-Russell Diagram (2)
Same
temperature,
but much
brighter than
MS stars
 Must
be much
larger
 Giant
Stars
The Radii of Stars in the
Hertzsprung-Russell Diagram
Rigel
Betelgeuse
Polaris
Sun
100 times smaller than the sun
Luminosity Classes
Ia Bright Supergiants
Ia
Ib
Ib Supergiants
II
III
IV
II Bright Giants
III Giants
IV Subgiants
V
V Main-Sequence
Stars
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 Mass
center 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.
Estimating Stellar Masses
Recall Kepler’s 3rd Law:
Py2 = aAU3
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:
3
a
____
AU
MA + MB =
Py2
(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:
163
____
MA + MB =
= 4 solar masses.
2
32
b) Any binary system with a combination of
period P and separation a that obeys Kepler’s
3rd Law must have a total mass of 1 solar
mass.
Masses of Stars in the HertzsprungRussell Diagram
The higher a star’s mass,
the more luminous
(brighter) it is:
40
L ~ M3.5
High-mass stars have
much shorter lives than
low-mass stars:
tlife ~
M-2.5
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
Masses in units of
solar masses
18
6
3
1.7
1.0
0.8
0.5
Maximum Masses of Main-Sequence Stars
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
h Carinae
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
Gliese 229B
At masses below
0.08 Msun, stellar
progenitors do not
get hot enough to
ignite thermonuclear
fusion.
 Brown Dwarfs
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 Stars
Faint, red dwarfs
(low mass) are
the most
common stars.
Bright, hot, blue
main-sequence
stars (highmass) are very
rare
Giants and
supergiants
are extremely
rare.