Transcript Luminosity - UCF Physics

Chapter 11
Surveying the Stars
How luminous are stars?
The brightness of a star depends
on both distance and luminosity
Luminosity:
Amount of power a
star radiates
(energy per
second=Watts)
Apparent brightness:
Amount of starlight
that reaches Earth
(energy per second
per square meter)
(not much) Thought
Question
These two stars have about the
same luminosity -- which
one appears brighter?
A. Alpha Centauri
B. The Sun
Luminosity
passing through
each sphere is the
same
Area of sphere:
4π (radius)2
Divide luminosity
by area to get
brightness
The relationship between apparent brightness
and luminosity depends on distance:
Apparent Brightness =
Luminosity
4π (distance)2
We can determine a star’s luminosity if we can
measure its distance and apparent brightness:
Luminosity = 4π (distance)2 x (Brightness)
Note that there is a huge range in stellar
luminosities
Proxima Centauri = 0.0006 Lsun
Betelgeuse = 38,000 Lsun
Thought Question
How would the apparent brightness of
Alpha Centauri change if it were
three times farther away?
A.
B.
C.
D.
It would be only 1/3 as bright
It would be only 1/6 as bright
It would be only 1/9 as bright
It would be three times brighter
Parallax and distance.
p = parallax angle in arcseconds
d (in parsecs) = 1/p
1parsec= 3.26 light years
Parallax and distance.
• Nearest Star: Alpha Centauri
•
distance = 4.3 light years
•
(since 1 parsec = 3.26 light years)
•
Distance (d) in parsecs = 4.3/3.26 = 1.32
• What is the parallax of this star?
•
•
d=1/p hence p=1/d (in parsecs)
p for nearest star is 0.76 arcseconds
• All other stars will have a parallax angle
smaller than 0.76 arcseconds
Laws of Thermal Radiation
hotter  brighter, cooler  dimmer
hotter  bluer,
cooler  redder
Hottest stars:
blue~50,000 K
Coolest stars:
Red~3,000 K
(Sun’s surface is
5,800 K)
An aside on “computers”
• In the old days an “Astronomical Computer” was
not a machine, but a person….often a woman.
• These were the people who calculated positions and
analyzed the photographic plates
• Women
did most
of the
work in
compiling
these huge
stellar
catalogues.
An aside on “computers”
•
•
•
What the “computers” did was sift through literally 100’s of
thousands of stellar spectra.
Established a classification scheme based on Hydrogen lines….
The types were alphabetical….letters were assigned in declining
strength of the H-lines
Stellar Classification
•
•
•
Like most early classification systems, they got it
wrong initially
Today we arrange spectral classes by temperature
Wien’s Law: The hotter the object, the bluer the
radiation it emits, and the more total energy is
emitted.
Stellar Classification
•
The hottest stars turned out to be (of course) the bluest.
•
Also the level of heat determined what sorts elements would be
prominent in the star’s spectrum
• For example only the hottest stars can ionize helium
• Only the coolest stars can have molecules
Remembering Spectral Types
(Hottest)
O B A F G K M
(Coolest)
• Oh, Be A Fine Girl/Guy, Kiss Me
• Only Boys Accepting Feminism
Get Kissed Meaningfully
A star’s full classification includes
spectral type (line identities) and
luminosity class (line shapes, related to
the size of the star):
I
II
III
IV
V
- supergiant
- bright giant
- giant
- subgiant
- main sequence
Examples: Sun - G2 V
Sirius - A1 V
Proxima Centauri - M5.5 V
Betelgeuse - M2 I
Star Types
Now we know temperature,
luminosity, and Distance……what
about mass?
Newton shows the way……
We measure mass using gravity
Direct mass measurements are
possible only for stars in binary
star systems
p = period
a = average separation
4π2
p2 =
a3
G (M1 + M2)
Most massive
stars:
100 MSun
Least
massive
stars:
0.08 MSun
(MSun is the
mass of the
Sun)
Stellar Properties Review
Luminosity: from brightness and distance
10-4 LSun - 106 LSun
Temperature: from color and spectral type
3,000 K - 50,000 K
Mass: from period (p) and average
separation (a)
of binary-star orbit
0.08 MSun - 100 MSun
Core pressure
and temperature
of a highermass star need
to be larger in
order to balance
gravity
Higher core
temperature
boosts fusion
rate, leading to
larger
luminosity
Mass & 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 104 times as fast
10 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years x 0.1 / 0.01
Stellar Evolution
•
Stars are like people in
that they are born,
grow up, mature, and
die.
•
A star’s mass
determines what life
path it will take.
•
The HertzsprungRussel Diagram is a
roadmap for following
stellar evolution.
Luminosity
An H-R
diagram
plots the
luminosity
and
temperature
of stars
Temperature
High-Mass Stars
Normal hydrogenburning stars reside on
the main sequence of
the H-R diagram
Low-Mass Stars
H-R diagram
depicts:
Temperature
Color
Spectral Type
Luminosity
Radius
*Mass
*Lifespan
*Age
C
Luminosity
B
Which star
is the
most
luminous?
D
A
Temperature
C
Luminosity
B
Which star
has the
largest
radius?
D
A
Temperature
C
Luminosity
B
D
A
Temperature
Which star
is the
main
sequence
star?
C
Luminosity
B
Which star
is the
hottest?
D
A
Temperature
C
Luminosity
B
D
A
E
Temperature
Which of
these
stars will
have
changed
the least
10 billion
years from
now?
Main-Sequence Star Summary
High Mass:
High Luminosity
Short-Lived
Large Radius
Blue
Low Mass:
Low Luminosity
Long-Lived
Small Radius
Red
Open cluster: A few thousand loosely packed stars
Globular cluster: Up to a million or more stars in a dense ball
bound together by gravity
How do we measure the age
of a star cluster?
Pleiades: no
stars with life
expectancy
of less than
100 million
years
Main-sequence
turnoff
Mainsequence
turnoff
point of a
cluster
tells us its
age
Detailed
modeling
of the
oldest
globular
clusters
reveals
that they
are about
13 billion
years old