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Introduction to
Astronomy
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AST0111-3 (Astronomía)
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Semester
2014B
Prof. Thomas H. Puzia
Temperatures and Colors
WIEN’s Law
λ = b/T
The colors of the stars reveal their
surface temperature. For example, a
Sun-like star with a surface temperature
of 6000K is yellow. Taking images of stars
in a few wide-spectrum bands and taking
the ratio of intensities thus can be a very
CHEAP way of characterizing them.
Propagation of Light
f = L / d2 (ergs/s/cm2)
f=1
f = 1/4
f = 1/9
Apparent brightness or flux, f, depends both on true light output (luminosity)
and distance, and decreases as the square of the source distance.
Very important concept in astronomy
Apparent
Magnitude
Hipparchus, a century BC classified
the stars according to their brightness
in six categories:
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1-6 = 1-100 in brightness/flux
•scales
m=6 , brightest m=1
•weakest
The scale is logarithmic (which
•reflects
the response of the rods and
cones in the human eye).
Absolute Magnitude
Intrinsic Luminosity
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What magnitude will a star have if we put it at a distance of 10 parsec?
"
"
Example, for the Sun with apparent magnitude m=-26.5
Using the 1/d2 law, the Sun would provide only 1/2,000,0002 (1 pc ≈ 200,000 AU)
of the light we receive now.
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In general
i.e.,
Photometry
Measuring the flux of light in a given band. Shown here is the Johnson UBV system.
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The color Index measures the color of a star using two filters, e.g. B-V. It can be calibrated to the
temperature of the star.
★
V=Vo-2.5log(lV), B=Bo-2.5log(lB)
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B-V=(Bo-Vo)-2.5log(lB/lV)
✓
Sun:
V=-26.78, B=-26.16, U=-26.06, B-V=0.62, U-B=0.10
✓
Sirius: V= - 1.46, B= -1.46, U= -1.52, B-V=0.00, U-B=-0.06
The star YY has a temperature of 10000 K with a peak thermal emission at
290nm. The star ZZ has a temperature of 5000 K. Therefore, the peak
thermal emission from ZZ is at
A.
B.
C.
D.
E.
145nm
580nm
1160nm
4680nm
nowhere close to any of these.
Recall that WIEN’s Law states that the wavelength of the blackbody peak is
inversely proportional to temperature as λ = b/T where b = 2897768.5 nm·K
What is the difference between spectroscopy and photometry?
What are the advantages/disadvantages of each?
What is the difference between apparent and absolute magnitudes/fluxes?
What are the differences between an O star and a G star?
What do we mean when we say an object is a standard candle?
Independent Distance Determination
are very far away. How do we measure their distances so we can
• Stars
determine their intrinsic luminosities?
• The most direct and “cleanest” measures are geometric
• Parallax (only practically achievable for very nearby stars)
• Expansion Parallax (watch something expand with known speed)
the Greeks rejected the heliocentric theory because they did not
• Example:
detect stellar parallax. Tycho later realized that this is because stars are too
far away to measure with current precision.
•
Indirect measures are made using comparisons and calibrations.
• Comparing apparent vs. known intrinsic brightness of similar stars
• Variability tied to known luminosity (Cepheids, RR Lyrae, SNe)
• Can be applied out to great distances, although less accurate
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These are the first steps in the distance scale ladder (more later)
Stellar Parallax
Earth's orbit around the Sun provides the
base of a triangle with the star at the
apex. We can compare the shift of the
star with respect to background (“fixed”)
stars over the course of 6 months and use
that to measure its geometrical distance.
Parallax angle p is defined using the
triangle.
This angle p is very small.
When p = 1", the star is 1 parsec (Parallax
Second).
Note: 1 pc = 206,265 AU = 3.26 ly
Parallaxes of Nearby Stars
Parallax angles are very small because the stars are far apart.
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EXAMPLE: Proxima Centauri, the nearest star to us is measured to
have a parallax of p = 0.75 arcsec.
This yields a distance of d = 1 / p = 1.333 pc = 275000 AU = 4.3 ly.
The limit of ground-based telescopes is p > 0.01 arcsec, which
means the method is limited to stars with d < 100 pc.
The space mission Hipparcos measured parallaxes accurate to
d < 500 pc for 5000 stars. A new mission, GAIA, is doing this for
109 stars to d<50,000 pc from 2013-2018!
For scale, our galaxy is ~30,000 pc (100,000 lyr) wide.
If Alpha Centauri were placed at a distance ten times farther from the Earth
than it is now, its parallax would
A. increase
B. decrease
C. stay the same
D. change color
A star’s luminosity is the
A.
B.
C.
D.
E.
surface temperature of the star
total amount of light that the star will radiate over its entire lifetime
apparent brightness of the star in our sky
total amount of power that the star emits into space
lifetime of the star
Cosmic Dust
reddening
absorption
scattering/polarization
Causes several observational effects:
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Creates a problem for determining distances and temperatures!
What is Cosmic Dust?
Smooth chondrite interplanetary dust
particle.
Complex particles between ~0.1-10 µm in size and
consisting of a few molecules (“cores”) up to 100s
of molecules are generically called “dust grains”.
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There are many varieties, depending on where it
was formed: intergalactic, interstellar,
interplanetary and circumplanetary dust.
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Dust cores of Carbon, Silicon, or Iron-Sulfur-Nickel
need a dense and relatively warm environment to
initially form. But the cores can then accrete further
material at later stages in sparser, colder
environments.
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Its interaction with light depends on size and type.
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Grains can be destroyed by absorbing too much
UV radiation (leading to dust explosions), as well
as evaporation, sputtering, and grain-grain
collisions.
Porous chondrite interplanetary dust
V B U
UV
Extinction by dust is a major nuisance for optical astronomers, because it
means that an intrinsically red star with a considerable quantity of interstellar
dust between it and us will appear:
A.
B.
C.
D.
E.
redder with the same flux/magnitude
same color with fainter flux/magnitude
no change because it is already red
same temperature but redder and fainter
none of the above
Hertzsprung-Russell Diagram
Theoretical plane is H-R diagram
Observational plane is colormagnitude diagram.
Intrinsically brightest stars are highest.
Intrinsically hottest stars are to the left.
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Sequences:
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Main (Hydrogen burning stage)
Red Giant
Horizontal Branch
White Dwarfs
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The position of a star in a curve or
branch turns out to be related to their
state of evolution (AGE).
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The presence of clearly defined tracks
means that stars are simple,
predictable objects governed by
Determining other Stellar Parameters
Aside from temperature (color) and luminosity (absolute magnitude), what
other physical parameters are needed to characterize a star?
• Chemical composition
• Mass
• Radius
• Age
These parameters can be measured directly using:
• nearby/bright stars, (spectrum = composition)
• binary stars,
(binary orbit/separation = mass)
• variable stars,
(variation time + velocity = size)
• clusters of stars. (i.e., at the same distance = coeval age)
In general, the distance introduces the largest uncertainty. A large error in this
means the stellar parameters will be poorly known/constrained.
Stars are relatively “simple”: theoretical understanding + known constraints
can fill in gaps:
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w/ a ~ 3.5 for much of main sequence
(although ~1 - 4 at extremes)