Stars: Properties and Classification

Stars:
Properties and
Classification

Announcements
n Homework # 5 starts today. Due Tuesday, Nov 15 th .
n Grades for Quiz # 4 are available in the OWL
Gradebook
n In-class Exam # 2 will take place on Tuesday, Nov
8 th .
– Please check www.astro.umass.edu/~calzetti/astro100 for
more infos

Assigned Reading
n Units 52.1-2-3, 54.1-2-3, 55, 56, 57.1-3

Goals for the Day
n To begin a study of stars – what theyre
made of, what kinds are out there, how
they are born, and how they die.
Are all stars similar to our Sun?
How far away are they?
Where did they come from?
What do they do?
Do they live forever?
How do they die?

n There are four principal characteristics
of a star:
– Luminosity
– Surface Temperature
– Size
– Mass
Three of them (luminosity, size, and mass) require
knowledge of the distance of the star from us.

Stellar Parallax
The measurements are taken six months apart.
The baseline is the diameter of the Earth’s orbit.
What is seen
What is seen
The ½ of the angle between the current location and the
6-month location is called the stellar parallax = P.

1 (AU)
D (in Parsecs) =
P (in arcseconds)
P, the parallax angle, is measured in arcseconds
60 arcseconds = 1 arcminute
60 arcminutes = 1 degree
There are 3600 arcseconds in a degree
The larger P, the smaller D
The smaller P, the larger D
1 parsec = 3.26 light years
= 3.086x10 16 meter
Parallax Distance

Parallax would be easier to measure if
1) the stars were further away.
2) Earth's orbit were larger.
3) Earth moved backwards along its
orbit.
4) none of these.

Parallax would be easier to measure if
1) the stars were further away.
2) Earth's orbit were larger.
3) Earth moved backwards along its
orbit.
4) none of these.

Star A has a parallax angle that is twice that
of Star B. What is the relationship between
their distances?
n Star A is closer than Star B
n Star B is closer than Star A
n The stars are at the same distance
n Not enough information is given

Luminosity
Luminosity is the total amount of power given off by
a star.
- Since its a power, Luminosity is measured in Watts
- For convenience, we often refer to the luminosity of
a star in terms of the luminosity of the Sun.
- Eg,
- That star has a luminosity of 22L Sun
- That galaxy has a luminosity of 2x10 12 L Sun

There is a Big Range of Stellar
Luminosities Out there!
Star
Luminosity (in units
of solar Luminosity)
Sun 1
Proxima Centauri 0.0006
Rigel (Orion) 70,000
Deneb (Cygnus) 170,000

The Sun radiates an enormous amount of energy
(L Sun =4 x 10 26 Watts). Only about 10 -9 of this
actually hits the Earth. Yet, the power of sunlight
that illuminates a patch of desert 100 km x 100 km
is equal to the total power consumption of the US.
4 x 10 26 Watts radiated
over entire surface
~10 17 Watts striking
the Earth
4 x 10 26 Watts generated
in core

Recall the inverse square law….

Brightness is different from Luminosity
n Luminosity – the total amount of power being released
from a star (this is an intrinsic property of the star).
n Brightness – the power from that star that actually gets
to us. This is the quantity we measure with a telescope.
A Stars brightness depends on its distance from us.
- there are stars much more luminous than our sun
in the sky, however, they are not nearly as bright because
they are far away.
A stars apparent brightness B = luminosity
4π (distance) 2 =
L
4π d 2

Surface Temperature
n We determine a stars surface
temperature by examining its blackbody
emission (a.k.a. its continuous
spectrum or color)
n No information on distance is
necessary!
n For reference: the Suns surface
(photosphere) temperature is 5,800 K

Surface Temperature

Another (more accurate) method to
measure Temperatures in Stars
Using spectra (recall the Fraunhofer spectrum of the Sun):
The `dark lines are created when the atoms in the photosphere
have energy levels that match the photons that are emitted
from the star.
1. They `reveal the composition of the star.
2. The strength of the lines (how `dark they are) depend on
the stars surface temperature.

Spectral Types
For historical
reasons, astronomers
classify the
temperatures of stars
on a scale defined by
spectral types, called
O B A F G K M L T,
ranging from the
hottest (type O) to
the coolest (type M)
stars.
The Sun has spectral type G2

Stellar Size
n Stars are very spherical so we
characterize a stars size by its radius.
R
Stellar Radii vary in size
from ~1500xR Sun for a
large Red Giant to
0.008xR Sun for a White
Dwarf.

Use Temperature and Luminosity
to Measure Size
A stars luminosity, surface temperature, and size are all
related by the Stefan-Boltzmann Law:
A refresher: the Stefan-Boltzmann Law
L=4πR 2 σT 4
Luminosity
Stellar
radius
Surface
temperature

L=4πR 2 σT 4
Survey Question
Two stars have the same surface temperature, but
the radius of one is 10 times the radius of the other.
The larger star is
1) 10 times more luminous
2) 100 times more luminous
3) 1000 times more luminous
4) 1/10 th as luminous
5) 1/100 th as luminous

L=4πR 2 σT 4
Survey Question
Suppose two stars are at equal distance and have the same
radius, but one has a temperature that is twice as great as the
other. The luminosity of the hotter star is ____ as
the other.
1) 1/2 as great
2) 1/4 as great
3) the same
4) 4 times as great
5) 16 times as great

L=4πR 2 σT 4
Survey Question
Suppose two stars are at equal distance and have the same
radius, but one has a temperature that is twice as great as the
other. The apparent brightness of the hotter star is ____ as
the other.
1) 1/2 as great
2) 1/4 as great
3) the same
4) 4 times
5) 16 times as great

Stellar Properties Survey Questions
1) Luminosity 2) Radius
3) Surface Temperature
Question #1:
Which property do we determine by first measuring
the stars apparent brightness and distance?

Stellar Properties Survey Questions
1) Luminosity 2) Radius
3) Surface Temperature
Question #2:
Which property do we determine by measuring
the wavelength of peak emission (i.e., its color)?

Mass: How do you measure the
mass of a star?
n Mass is the single most important
property in determining how a stars life
and death will proceed.
n We can weigh stars that are in binary
systems (two stars orbiting each other).
Fortunately, most stars (about 70%) fall
into this category.

Center of Mass (or Barycenter)
n Stars orbiting
each other orbit
around their
`center of mass
or barycenter
n They behave
like children on a
seesaw
M a
M b
C.M.
R b
R a
C.M. (center of mass) is where:
R a M a = R b M b

Binary Stars: use the Generalized Keplers Third Law
Star A
- Binary stars are in orbit around
each other.
- They orbit around their C.M.
C.M.
R b
R a
- Their orbital period depends on
their separation and their masses.
Star B
Generalized Keplers Third Law
(M a +M b ) P 2 = a 3
Keplers Third Law
G/4π 2 M sun P 2 = a 3
a= (R a +R b )/2
Big P = Small Masses
Small P = Big Masses

I. Visual Binaries

Summary
n There are four principal characteristics
of a star:
– Luminosity (brightness and distance)
– Surface Temperature (black-body spectrum)
– Size (Stefan-Boltzmann Law)
– Mass (generalized Keplers Third Law)
Are these quantities related with each other?

Lets recall:
Hydrostatic Equilibrium of Stars
Thermal
Pressure
Gravitational
Contraction

Nuclear fusion rate
rises dramatically
The Stellar Thermostat
Outward thermal pressure of core
is larger than inward gravitational
pressure
Core expands
Expanding core cools
Contracting core heats up
Nuclear fusion rate
drops dramatically
Core contracts
Outward thermal pressure
of core drops (and becomes
smaller than inward grav. pressure)

What happens if we increase the
mass of the star?
n More mass = more gravitational
contraction
n = need for more balancing pressure =
higher temperature at the center (and
on the surface)
n Higher temperature = more hydrogen
fusion = higher energy production =
more luminous

Thus…
n More massive =
n Higher Temperature
(bluer color) =
n More luminous
L ~ M 3.5
A star 10 times more massive than the Sun is ~3000
times more luminous!

The Hertzsprung-Russell Diagram

The Hertzsprung-Russell Diagram

The Hertzsprung-Russell Diagram
The Main Sequence
- all main sequence
stars fuse H into He
in their cores
- this is the defining
characteristic of a
main sequence star.
- more massive stars
are more luminous and
hotter: L=4πR 2 σT 4

The Hertzsprung-Russell Diagram
L=4πR 2 σT 4
Red Giants
- Red Giant stars
are very large, cool
and quite bright.
Ex. Betelgeuse is
100,000 times more
luminous than the Sun
but is only 3,500K on
the surface. Its radius
is 1,000 times that of the
Sun.

The Hertzsprung-Russell Diagram

The Hertzsprung-Russell Diagram
White Dwarfs
- White Dwarfs
are hot but since
they are so small,
they are not very
luminous.
L=4πR 2 σT 4

The Hertzsprung-Russell Diagram
Mass of
Star
Size of Star