Download Astronomy Library wk 6.cwk (WP)

6–1
Transformation of Astronomy
Antiquity – 1700s:
Most astronomers were interested in the planets:
Stars remain fixed—it was the planets which moved
in interesting ways.
With the telescope planets could be resolved but
stars still looked like points of light.
Interest in the stars started to emerge in the 1700s:
Telescopic sights allowed the determination of stellar
positions with increasing accuracy.
Proper motions of the stars became measurable.
Astronomers actively searched for stellar parallax.
Astronomy shifted decidedly away from planets in
the 1800s and 1900s:
Advances in physics allowed astronomers to
determine various properties of stars (e.g.
temperature, composition) from their spectra.
Astronomy ==> Astrophysics
Only with the space program has there been renewed
interest in the solar system.
Astronomy: An Observational Science
Except for a few samples from planets, we have no
samples we can study in the lab.
Almost all the information we have about
astronomical objects comes from studying the light
(and other electromagnetic radiation) they emit.
Fortunately, quite a lot of information can be gleaned
from the light they emit. For example:
Atoms:
Temperature
An element is a substance which cannot be broken
down into other substances by chemical means.
Composition
Velocities
Size
Poor medieval alchemists!
An atom is the smallest possible particle which
retains the properties of an element.
Atoms are composed of two main parts:
To see how we can determine these properties we
need to explore the physics of the very small.
6–2
Quantum Mechanics
Excitation of Atoms
The behavior of things at small scales differs from
that at the larger scales of our common experience.
Atoms in which the electrons are in the lowest
energy level are said to be in the ground state.
e.g., planets can orbit the sun at any distance.
While electrons cannot be at intermediate energy
levels, they can jump from one permitted energy level
to another.
Not true of electrons in an atom:
They can only occupy certain orbits in an atom
called permitted orbits.
==> Electrons can only have certain amounts of
energy in atoms.
Electrons cannot have other energies.
Atoms can be excited from the ground state to higher
energy states in two major ways:
1. Collisions between atoms can excite electrons.
2. Electrons can absorb light (photons) if the photon
has just the right amount of energy.
The permitted energies are different for different
elements.
The energy of a photon of light depends on its
wavelength:
Atomic Spectra
E = hc/wavelength
As noted above, atoms are only good at absorbing or
emitting light of very specific wavelengths.
The shorter the wavelength, the more energetic the
photon.
Thus, atoms in a gas in front of a light source will
remove very specific wavelengths of light from the
source creating absorption lines:
Thus, because an atom can only absorb a photon of
just the right energy to excite an electron to a higher
energy level, it can only absorb light of just the right
wavelength.
Eventually, an excited atom will tumble back to its
ground state by emitting a photon of energy equal to
the difference in energy between the energy levels.
Alternatively, away from a light source, the atoms
will emit light at the same specific wavelengths
creating emission lines.
6–3
Recall that different elements have unique permitted
energy levels.
Blackbody Radiation:
==> Each element has a unique set of absorption or
emission lines.
As discussed earlier, the spectrum from a gas of
atoms will yield very specific wavelengths of light
(either in absorption or emission).
Thus spectral lines can be used much like a
fingerprint:
Not true of solid or liquid objects (or gases at high
density).
If a person’s fingerprint (or DNA) is present at a
crime scene it indicates they were there.
Such objects emit a continuous spectrum of light.
In just the same way the presence of an element’s
spectral lines in a spectra indicate it must be present
as well.
A blackbody is an ideal body which is a perfect
absorber (and emitter) of light.
While real objects are not perfect absorbers, most
objects emit light approximately like a blackbody.
Thus, it is useful to study how blackbodies emit
light.
Characteristics of Blackbody radiation:
Both very short (energetic) and very long (low
energy) wavelength photons are rare. Most of the
light is emitted at intermediate wavelengths.
Wien’s Law:
Specifically, the wavelength of the peak intensity is
inversely proportional to the temperature:
λ max (nm) = 3,000,000/T(K)
The amount of light emitted depends on the
temperature:
Do you think that hotter objects emit more or less
light than cool objects? Examples?
Examples of the peak intensity wavelengths:
The sun (6000K): λmax = ?
Cool star (3000K): λmax = ?
The peak wavelength of intensity also depends on
the temperature:
As a body is heated, the peak intensity occurs at
shorter (more energetic) wavelengths.
You (310K): λmax = ?
6–4
This explains why, for example, as iron is heated in a
forge it goes from emitting no light, to glowing a dull
red to glowing a brilliant white at very high
temperatures.
Stefan-Boltzman Law:
The power of light emitted per unit area by an object
depends strongly on its temperature:
It also explains the different colors of stars:
Cool stars (e.g. 3000K) will emit their light at what
wavelength (relatively short or long)?
E = σ T4
For example: doubling the temperature would lead to
how much more energy being emitted?
Thus they will appear what color?
tripling the temperature?
Somewhat warmer stars (like the sun)?
Hot stars?
==> a small change in the temperature can lead to a
large change in the energy emitted.
Color of a star can be used to determine temperature!
Formation of Spectra:
2. An excited low density gas will emit an emission
spectrum.
Kirchhoff’s Laws:
Example: Emission Nebula
1. A hot solid, liquid, or dense gas will emit a
continuous spectrum.
Examples would include the filaments of light bulbs
and “red hot” metals.
Hot Star
Emission Nebula
Observer
6–5
3. A cool, low density gas between a continuum light
source and the observer will produce an absorption
spectrum.
Example: Most stars (including the sun) show an
absorption spectrum.
Spectral Classification
We expect that stars of similar temperatures will
have similar spectral features.
Stars have been classified into 7 major categories
based on the relative strength of their spectral lines.
Stellar Atmosphere
From hottest to coolest stars these are:
Star
O, B, A, F, G, K, and M
Observer
The main categories are subdivided into ten
subcategories:
For example, class A is subdivided into A0, A1,
A2...A8, A9
Most stars show absorption spectra, what does this
suggest about how temperature varies in such stars?
Determining Stellar Velocities:
For example, the sun is a typical G2 class star.
Stars
The Doppler Effect
Wavelength emitted by an object will be shortened if
approaching and lengthened if receding:
For the next couple of weeks or so we will be
discussing stars.
Following the scientific method we will first discuss
the properties of stars (initial observations).
Red
Shifted
Blue
Shifted
True of any waves including sound or light waves.
Shift in wavelength of spectral lines can be used to
measure the velocity of stars.
Also how radar guns determine the speed of cars.
How do we measure stellar properties?
Are there any patterns?
If so, how can we categorize stars?
We will then use these observed properties in
examining theories of stellar evolution.
6–6
Stellar Properties
Luminosity
Unfortunately, most properties of stars cannot be
determined directly.
It is straightforward to measure how bright a star
appears on the sky (apparent magnitude).
e.g. how would you measure the length of a table?
Is this enough?
We have seen how stellar spectra can be used to
determine stellar composition and temperature.
Here we will see how we can determine some other
stellar properties:
Luminosity: Energy emitted by a star per unit time.
Radius of a star
Measuring Distances:
Definition of the Parsec
Trigonometric (or Stellar) Parallax
Measuring distances to stars in AUs is unwieldy.
If one can determine the parallax of an object, one
can determine its distance.
A more convenient unit to use, especially when
measuring distances using parallax, is the Parsec:
“Triangulation”
It is defined as the distance at which a star would
exhibit a parallax angle of one arc second:
Technique used by surveyors to determine distance:
1 Parsec = 206,265 AU
With this definition, the distance to a star (in
parsecs) is given simply as:
d (Parsecs) = 1/p(")
6–7
Light Year
Another unit of distance which is often used is the
light year.
It is the distance light travels in a year:
1 Parsec = 3.26 light years
From the ground parallax angles can be measured
down to ~0.02".
Thus distances of stars out to what distance can be
reasonably accurately determined?
Hippacos satellite has done better measuring the
parallax angle down to about 0.001".
Once we have determined the distance to a star, we
can correct for the distance to the star and determine
its luminosity.
Absolute Magnitude:
The apparent magnitude of a star depends only on
the brightness of a star on the sky without regard to
its distance.
The absolute magnitude of a star is defined as the
apparent magnitude a star would have if it were at a
distance of 10 parsecs.
Provides a convenient way to compare the intrinsic
brightness of stars.
Absolute magnitude is basically a measure of stellar
luminosity.
Out to what distance can it accurately measure?
Stellar Sizes:
Because stars are nearly spherical, we can use the
surface area of a sphere, 4πR2:
As noted before, it is almost impossible
to measure the size of stars directly.
L = Area × Flux = 4πR2 × σT4
However, it can be inferred from
the luminosity and temperature of a star.
This equation can be simplified somewhat if we
compare the star to the sun:
The luminosity depends on two properties of the
stars: the temperature and the radius of a star.
 RStar  2  T Star  4
L Star
= 
 




LSun
RSun
TSun 
The amount of energy per second flowing through a
given area of a star’s surface (the flux) is given by
the Stefan-Boltzman equation:
We can determine the temperature of a star from its
color.
Flux = σT4
In order to get the total energy flowing out of a star
per second (the luminosity) we need to multiply the
flux by the surface area of the star.
We can determine the luminosity from the apparent
brightness and distance to a star.
Given these two quantities we can determine the
radius of a star from the above equation.
6–8
H-R Diagram
Early last century reliable distances and spectral
classifications were determined for the first time for
a significant number of stars.
Summary
We have examined how various properties of stars
can be determined:
Composition: Strength and presence of spectral
lines.
From these data, Russell plotted the luminosity vs.
temperatures of these stars.
Hertzsprung had done similar work looking at stars
in the Pleiades and Hyades star clusters.
Temperature: Color or strength of spectral lines.
Luminosity: Apparent brightness and distance
measurements (parallax).
Radius: Luminosity and Temperature.
Such a diagram is now known as a HertzsprungRussell, or H-R, diagram.
Do stars fall into distinct groups or are their
properties random?
HR-Diagram: Different classes of stars found from
plots of stellar temperatures vs. luminosity.
Why do stars have the properties they do?