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p476 1-20
1. How is parallax used to measure the distances to stars?
Parallax is an object's apparent shift relative to some more distant background as
the observer's point of view changes. By observing distant objects 6 months apart,
we extend the parallax baseline to the diameter of Earth's orbit around the Sun, 2
A.U. Only with this enormously longer baseline do some stellar parallaxes become
measurable.
2. What is a parsec? Compare it with the astronomical unit.
Astronomers measure parallax in arc seconds rather than in degrees. If we ask at
what distance a star must lie in order for its observed parallax to be exactly 1",
we get an answer of 206,265 A.U., or 3.1 1016 m. Astronomers call this
distance 1 parsec (1 pc), from "parallax in arc seconds." (NOTE: A star with a
measured parallax of 1" lies at a distance of 1 pc from the Sun. An object with a
parallax of 0.5" lies at a distance of 2 pc; an object with a parallax of 0.1" lies at
10 pc, and so on. 1 pc is approximately equal to 3.3 light years.)
ANOTHER NOTE: remember this the next time you see Star Wars Episode 4- A New
Hope (aka The Original Star Wars, aka Star Wars ’77) and you hear Harrison Ford
bragging that the Millenium Falcon can “make the Kessel run in less than 12
parsecs.” This is like saying “He ran a marathon in less than 12 feet.”) (YES BUT…if
the Kessel Run involves travel through super-strong gravitational fields (i.e.;, near a
black hole or neutron star) or at or beyond the speed of light (as we know the MF can
travel) such that significant relativistic effects can be observed, then there COULD be
a way to measure a timed trip by how much space you actually had to pass through. A
very nice dodge, I must admit, despite the timey-wimey complications at the startfinish when your spaceship crosses the finish line having aged far less than the
observers who both watched it depart and who are awaiting its arrival!)
3. Explain two ways in which a star’s real motion through space translates
into motion observable from Earth.
The transverse component of a star’s motion is that star moving laterally,
across the sky, and is measured by observing photographs taken certain times
apart. The radial component is the star moving toward or away from the sun
and can be measured by observing the star’s Doppler shift. (NOTE: Most of
the constellations will be unrecognizable in a few hundred centuries because
of the proper motion of our neighboring stars in the Milky Way.)
4. How do astronomers go about measuring stellar luminosities?
Determining a star’s luminosity is a twofold task.
1. determine the star’s apparent brightness by measuring the amount of
energy detected through a telescope over time. Then,
2. Measure the star’s distance (by parallax for nearby stars and by other
means for more distant stars.
The luminosity can then be found using the inverse-square law.
5. Describe how astronomers measure stellar radii.
If a star is close enough to measure its angular size though a telescope
(Betelgeuse measures 0.045", for instance) (that’s about 1/20 of an arcsecond, or 1/72,000˚ btw) we can use its distance (Betelgeuse being 130
parsecs away) to calculate its radius with basic . With a distance of 130 pc and
an angular diameter of Betelgeuse's radius is 630 times that of the Sun.
For stars to distant to be measured through a telescope, radiation laws are used to
determine star size. The radiation emitted by a star is governed by the StefanBoltzmann law: energy emitted per unit area per unit time increases as the
fourth power of the star’s surface temperature. To determine the star’s
luminosity, multiply by its surface area—large bodies radiate more energy than
do small bodies having the same temperature. Because surface area is
proportional to the square of the radius, we have
luminosity
radius2 temperature4
…and if you solve for radius you get: r2 = t4/L
6. Describe some characteristics of red giant and white dwarf stars.
A Red giant’s radius/diameter is between 10 and 100 times that of the Sun &
surface temperature is relatively low, so that it glows with a red color. A
white dwarf’s surface temperature is relatively high, so that the object glows
white. Dwarf stars are the size of the sun or smaller (Wait…Does that mean
the sun is a dwarf? Yup! Sure does! The sun is technically a yellow dwarf!)
7. What is the difference between absolute and apparent brightness?
Apparent brightness is how much of a star’s radiation reaches the earth
during a given amount of time, and it depends on our distance to the star. (In
other words, a star’s apparent brightness is how bright the star appears from
Earth.)
Absolute brightness is how bright a star would be if you were 10 pc (≈33
LY) away.
SO…if you want to know which of two stars appears brighter in the sky,
compare their apparent brightnesses. If you want to know which star would
be brighter if the two were side by side? Check their absolute brightnesses.)
8. How do astronomers measure stellar temperatures?
They compare the star’s radiation emission curve with that of the hypothetical
blackbody. This serves as a stellar thermometer. (this is sort of a review
question since we learned about about it way back in September’s Radiation
unit.)
9. Briefly describe how stars are classified according to their spectral
characteristics.
BRIEFLY would be something like this: stars are classified by surface temp.,
into the infamous O B A F G K M system, with O being bluest/hottest and M
being the reddest/coolest, and each letter being subdivied further into 0-9. You
can see this across the bottom (x axis) of any H-R diagram. (The sun is a G2.)
A BIT OF DETAIL, EXPLAINING THIS DAFFY LETTER SCHEME:
Astronomers initially (before 1920) classified stars by their hydrogen-line
intensities and labelled them alphabetically A through P. “As” had a stronger
hydrogen signature – hence were thought to have more hydrogen – than “Bs”, with
“Ps” theoretically having the least hydrogen of all.
As time went on and astronomers got a better handle on how atoms generate
spectra and decided a better classification system would be based on SURFACE
TEMPERATURE. So they simply re-sorted all the stars’ by surface
temp……without changing the friggin’ letters! Thus we’re stuck with this
ridiculous
O B A F G K M system, with O (letter “oh”) being bluest/hottest and M being the
reddest/coolest, and each letter being subdivied further into 0(that’s zero)-9.
HENCE: (and here is a beautiful illustration of just how asinine this system is...) the
hottest possible star would be classified O0 (Yeah. That’s “oh zero.” What could
ever be confusing about that? No WAY could we ever make any easily preventable
mistakes with that!) while the coolest possible classification would be M9.
10.
Why do some stars have very few hydrogen lines in their spectra?
H is the most abundant element is ALL STARS, but if a star is hotter than
10,000K it’s H atoms are ionized and, with electrons swimming free,
independent of specific nuclei like that, they are not REALLY be hydrogen
atoms, and therefore do not generate hydrogen spectral lines.
11.
What information is needed to plot a star on the H–R diagram?
Stars’ luminosity (graphed on the vertical y axis) and surface temp (graphed
along the bottom x axis, OBAFGKM)
12.
What is the main sequence? What basic property of a star
determines where it lies on the main sequence?
The main sequence is the snaking line-shaped region on an H-R diagram that
runs diagonally from top left ot bottom right. All stars that are still fusing H
into He in their cores – like the sun -- lie on this line and are called Main
Sequence stars.
13.
How are distances determined using spectroscopic parallax?
Very complexly, and surprisingly inaccurately*, it turns out. The term
spectroscopic parallax refers to a complex mathematical process that uses
stellar spectra to infer distances.
But first thing’s first: Spectroscopic parallax is not “geometric” parallax (i.e.
binocular vision parallax, or “earth-on-either-side-of-the-sun” parallax)
that we learned about earlier in the year, and discussed up in question #1.
It’s actually sort of an abuse of the word parallax and makes things kind of
confusing since the other distance-measurement technique has the word
parallax in it.
We can read the star’s luminosity directly off a graph and determine its
distance by measuring the energy flux at Earth using the inverse-square
law. The existence of the main sequence allows us to make a connection
between an easily measured quantity (temperature) and the star’s luminosity,
which would otherwise be unknown. Again, the term spectroscopic parallax
refers to this whole process of using stellar spectra to infer distances.
*Distances obtained by spectroscopic parallax are probably accurate to no
better than 25 %. (Imagine being told that the best estimate of the distance between
L.A. and NYC is “between 3000 and 5000 km.” BUT: An estimate that is ±25 %
uncertain is better than no estimate at all!)
14.
Why does the H–R diagram constructed using the brightest stars
differ so much from the diagram constructed using the nearest stars?
Most of the nearest stars are cooler main sequence stars because these are the
most common type stars throughout the galaxy. (Any random sampling of stars
in the galaxy would show this distribution). The graph of brightest stars will
include stars that lie at great distances, since even very distant bright stars can be
seen by us more easily than most nearby stars can be seen!
15.
Which stars are most common in the Galaxy? Why don’t we see
many of them in H–R diagrams?
Red dwarfs are the most common (possibly 80% of stars in the galaxy) but
they don’t show up on an H-R diagram because they are very dim and hard to
observe from earth.
16.
Which stars are least common in the Galaxy?
Blue supergiants are the least common. Only 1 in 10,000 stars is a blue
supergiant.
17.
How can stellar masses be determined by observing binary-star
systems?
Remember that mass is determined based on distance between two objects ,
their orbital periods, and their corresponsing gravitational influence on each
other.
By observing the actual orbits of the stars, or the back-and-forth motion of the
spectral lines, or the dips in the light curve—whatever information is
available—astronomers can measure the binary’s orbital period.
If the distance to a visual binary is known, the semi-major axis of its orbit can be
determined directly, by simple geometry. (For spectroscopic binaries, it is not
possible to determine the semi-major axis directly. Doppler shift measurements give
us information on the orbital velocities of the member stars, but only on their radial
components. As a result, we cannot determine the inclination of the orbit to our line
of sight, and this imposes a limitation on how much information we can obtain
spectroscopically.)
18.
High-mass stars start off with much more fuel than low-mass stars.
Why don’t high-mass stars live longer?
Their higher mass means stronger gravity,
which makes fusion happen faster,
which makes them burn off (or rather “fuse off”) their fuel faster,
which makes them die sooner/younger!
19.
In general, is it possible to determine the age of an individual star
simply by noting its position on an H–R diagram?
Yes! We can be sure that all the O and B stars we now observe are quite
young—less than a few tens of millions of years old. At the opposite end of the
main sequence, the cooler K and M type stars have less mass than our Sun. The
small energy release per unit time leads to low luminosities for these stars, so
they have very long lifetimes. Many of the K and M type stars now seen in the
sky will shine on for at least another trillion years. (Yeah. That’s trillion, with a
T. Recall the known universe is “only” 13.7 billion years old, which is about 1%
of a trillion!)
20. Visual binaries and eclipsing binaries are relatively rare compared to
spectroscopic binaries. Why is this?
Visual and eclipsing binaries can only be detected from earth is the two
separate stars can be resolved visually from earth. Spectroscopic binaries are
detected with radio telescopes, which can see MUCH farther into space than
optical scopes.