Download Parallax - High Point University

The Sun and Stars
Chapters 10 and 11
Topics
• the Sun
–
–
–
–
Features
Structure
Composition
How do we know?
• Stars
–
–
–
–
–
brightness and luminosity
distance
temperature
mass
classification
Sun
• Photosphere
– the bright disc we see as “the Sun”
– the “surface”of the Sun
– causes the absorption lines in the Sun’s spectrum (called
Fraunhoffer lines)
– temperature 5800 K
– mostly hydrogen (94%) and helium (5.9%)
• Chromosphere
– thin layer above the photosphere
– 7000 K - 15,000 K
• Corona
– halo of high energy gas, very hot (2 MK)
– emits radiation (thus we can see emission lines), mostly x-rays
Sun
Activity on the Sun
• sunspots
– cyclic
– cooler region of the photosphere
– related to the Sun’s magnetic field
• prominences
•solar flares
–solar storm
–emits radiation and particles
–high temperature (>5 MK)
–affect radio communications on Earth
Sunspot cycle
• 11 year average cycle
• Time between maxima
can be as long as 15
years or as short as 7
years.
• Solar activity may
affect Earth’s climate,
but the mechanisms
are unknown.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
From http://sohowww.nascom.nasa.gov/
A comparison of two EIT images almost two years apart illustrates how the level of solar
activity has increased significantly. The Sun attains its expected sunspot maximum in the year
2000. These images are captured using Fe IX-X 171 Å emission showing the solar corona at a
temperature of about 1.3 million K. Many more sunspots, solar flares, and coronal mass
ejections occur during the solar maximum. The numerous active regions and the number/size
of magnetic loops in the recent image shows the increase.
General Theory of Relativity
• Newton’s theory of gravitation does not explain everything
– bending of light near massive objects (light is seemingly attracted
to mass?)
– precession of the perihelion of Mercury (now it’s known that the
perihelions of other planets precess as well)
• Local space-time is curved by the presence of mass
– light (and everything else) travels in a curved space-time.
– objects left to themselves travel in straight lines
– a straight-line on a curved surface is a geodesic, or great circle
• Early evidence that Einstein was right was the observation
that light from a star was bent as it passed near the Sun
(this could only be seen during a total solar eclipse of
course)
Are other stars like our Sun?
Let’s measure
• apparent brightness
– the amount of radiation we receive per second
• luminosity
– the amount of radiation emitted by the star per second
• distance
• temperature
• composition
Brightness and Luminosity
•Brightness: How bright a star appears.
Apparent Magnitude
•Luminosity: How much light the star is actually
giving off.
Absolute Magnitude
Apparent magnitude scale
• Introduced by Hipparchus (160-127 B.C.)
– Vega (0), Venus (-4), Sun (-26.8), Moon (-12.6),
Faintest objects observed with HST (+30)
• What does it measure?
– measures ratios of actual amount of light energy
received
– receive 2.5x more energy from a mag. 1 star than a
mag. 2 star
– difference of 5 magnitudes is 100x difference in
received energy
How does it work?
7.8
2.5X2.5 = 6.25 X
15.6 X
39.1 X
100 X
6.8
5.8
4.8
3.8
2.8
2.5 X
2.5 X
2.5 X
2.5 X
2.5 X
Difference of 5
Practice
•
•
•
•
Rigil Kentaurus (-0.01)
Spica (+1.0)
Which looks brighter?
How much more light do we receive from
it?
• One level of magnitude means 2.5 times
more light received!!
But...
• Spica is actually more than 1000x more
luminous than Rigil Kentaurus!!
• If Spica is putting out more light, why
might it appear dimmer in the sky?
Apparent brightness
• apparent brightness diminishes with
distance
• inverse-square law (brightness diminishes
as 1/D2)
2 feet
2 feet
A
?
A
B
4A
B/4
Practice
Both stars have apparent magnitude +4
A
4 ly
B
12 ly
What can you conclude about
their luminosities?
How do we find distance?
Parallax
Parallax - the apparent change in position of an
object due to the change in position of the
observer.
January
June
1
2
3
4
5
6
7
8
Observer
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Observer
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Would an object
here appear to move
more or less?
Parallax
But why would
stars do this?
Observer
1
2
3
4
5
6
7
8
Is p larger or
smaller for a
star farther
away?
p
1 AU
Jan
1 AU
July
Earth (Jan)
APPARENT
POSITION
1 AU
p
TRUE
POSITION
Earth (Jul)
Earth (Jan)
APPARENT
POSITION
1 AU
p
TRUE
POSITION
Earth (Jul)
TRIANGULATION
• the smaller the parallax angle the
greater the distance
• one arc second=1/3600 of 1 degree
• distance from Earth to a star where p=1
arc second is called the parsec
• a parsec=3.26 ly
Parallax Results:
• Closest star is Proxima Centauri, which is
located at 1.3 parsecs.
• Method good to about 250 parsecs!
• Gives knowledge of fraction of one percent
of stars in Milky Way
• About 1/100 of diameter of galaxy!!
Hipparcos
Satellite
HIgh
Precision
PARallax
COllecting
Satellite
(1989-1993)
Hipparcos
• Target: 118,000 stars
• Magnitude limit: 12.5
• Resolution: 0.001 arcsecond!!!
(about 200 parsecs)
Practice
Consider two stars (X and Y). If star X is 3
parsecs away and star Y is 5 parsecs away,
which has the greater parallax angle?
a) Star X
b) Star Y
c)
Not enough information
Comparing brightness
• How can we compare brightness if stars are
at varying distances?
• Calculate brightness as if the star is at a
distance of 10 parsecs (33 ly).
• This is called its absolute magnitude.
What magnitude would Antares (-0.1) appear if it
were at a distance of 10 parsecs? Take the current
distance to be 100 parsecs.
Are we expecting a number
greater or less than -0.1?
How many magnitudes is
100 x brighter?
1 mag = 2.5x
5 mag = 100x
- 5 = -5.1
absolute magnitude = -0.1 
10 x closer = _____
100 x brighter
brighter or dimmer?
Checkpoint
• What do we know now?
– apparent brightness is different than luminosity
and depends on distance to the star
– for the nearest stars, we can use parallax to
determine distance
– we describe apparent brightness with the
apparent magnitude scale and luminosity with
the absolute magnitude scale
• What else do we want to measure?
Temperature
• temperature can be directly measured for a
blackbody by plotting the brightness vs.
wavelength (i.e. a blackbody curve).
• temperature affects the color of the star
• peak wavelength depends on temperature
Blackbody curves
Temperature and brightness
As T increases,
the wavelength
for peak
brightness
decreases.
As T increases,
the brightness
increases.
How does temperature affect
aborption spectra?
• Absorption lines tell us about
the composition of the stars.
• Stars were originally grouped
according to similar
absorption spectra
• Later we realized that the
intensity (i.e. darkness) of
certain H lines were indicative
of temperatures
O
B
A
F
G
K
M
Classification of stars by
brightness
O
B
A
F
G
K
M
hotter than 25,000 K
11,000 - 25,000 K
7500 - 11,000 K
6000 - 7500 K
5000 - 6000 K
3500 - 5000 K
cooler than 3500 K
Each type is further divided into 10 subtypes (0-9)
H-R diagram
• A graph of stars’ luminosity (or absolute
magnitude since they are related) vs.
temperature (or spectral type since they are
related)
• short for Hertzsprung-Russell diagram
same
luminosity
same
luminosity
very
large
RED GIANTS
• Cool but VERY BRIGHT!
• Betelgeuse: 3500 K (10% as
bright/unit area as Sun) but 100,000
times as luminous--must have 1
million times the area
• radius must be 1000x that of Sun!
same
temperature
same
temperature
very
small
very
large
Globular Cluster in Scorpius