Transcript Answer to question 1 - Northwestern University

Brane power to the max, cont
Besides the existence of another universe, BPM has
two special features (at least);
1. We won’t find and non-baryonic dark matter
because there isn’t any. Rather the gravitational
interaction with the other Universe mimics this
effect.
2. We won’t find gravitational radiation
General Considerations continued
• How long is it going to take me?
• How much is it going to cost?
• Are the time and money worth it?
Other Considerations
• When to hold’em and when to fold’em
• What are the cost drivers in my design?
• Do I need any instrument development
to allow me to achieve my goals?
• Do I have all the skills I need?
• If not, can I assemble a winning team?
Technical Considerations
• What limits the accuracy of my
measurement?
• How will I calibrate my measurements so
that somebody else can judge the results.
• What assumptions will I have to make
from theory or experiment to build my
case.
• If I’m looking for an effect (such as
WIMPs), will my result be interesting even if
I don’t find the effect?
Why Distance
• Why bother with the distance scale?
• Because nearly every thing we derive in
astronomy depends on knowing the distance.
• For cosmology, we want to know:
• The expansion rate (Hubble constant) which
requires distance versus velocity measurements.
• We want to measure the mass density of the
universe, we need to know the mass within a
given volume, which means a knowledge of the
distance.
Why Distance
• For cosmology, we want to know:
• The distance along with a measure of the redshift
so we can test different geometries of the
Universe
• The distance to objects can tell us how these
objects form and evolve.
• The spatial distribution objects is another test of
cosmology.
Back to distance
• Overall design calls for a “bootstrap”
approach.
• Begin with small distances we can
effectively measure with a ruler.
• Then use “parallax” can tell us distances.
• Parallax is the effect of noting you can
discern the distance to an object if you
can measure how much it appears to
move around as you do.
• Overall
design calls for a “bootstrap”
approach.
• We start with small distances we can
effectively measure with a ruler.
• Next step in the design is to figure out that the
“parallax” can tell us distances.
• Parallax is the effect of noting you can discern
the distance to an object if you can measure how
much it appears to move around as you do.
Parallax Demo
• Take a piece of paper and draw a stripe on it.
• Hold the paper at arm’s length with your nose
pointed at the stripe.
• Hold 1 finger a 1 - 1.5 feet in front of your nose
• Then close your left eye. Then open it and close
your right eye. Notice how much your finger
appears to move RELATIVE to the stripe.
• Move finger until it is almost touching the stripe
and try again.
• Won’t be much apparent motion relative to
stripe.
•The effect is caused by moving your vision
relative to your finger and you have
accomplished the “motion” by using different
eyes.
•Same as using one eye and moving it the
distance between you two eyes perpendicular
to the line-of-sight.
• How far can we determine distances that
way? Need to answer:
•(1) How far apart are our eyes ?
•(2) How small a change in apparent motion
can we measure?
OK now what, cont.
• My eyes are separated by about 7 cm, and I
know also I can see an angular separation of
about 1 arc minute. So the diagram I draw is
like this:
Using
Apparent motion trigonometry,
Each right
d*sin(1.0 arc min)
triangle has a
= 3.5 cm or d =
base of 3.5
q
d
120 meters “tops,”
cm and the
l
q = 1 arc min.
apex angle of
s
l about = d,
eyes
1 arc minutes
s = 3.5 cm
Parallax cont.
• => If we know s and q we can calculate d (and or
l). This give us the distance. A person’s distance or
depth perception via binocular vision” is about 7
times worse than what I’ve calculated = about
50-60 feet (15-18 meters) .
(cf., http://online.sfsu.edu/~psych200/unit6/66.htm)
• Where did I go wrong? (a) Our eye needs a
reference frame and the reference frame should be
distant enough not to show parallax; (b) the eye
doesn’t have the luxury of being able to accumulate
data for hours and to look at objects with extremely
well defined centers.
Parallax and astronomy
• Need equivalent of “s” to be as large as possible
and accurately measured. =>
• Here to Chicago won’t “do it.”
• One side of earth to the other can allow us a low
tech way of measuring the distance to the Moon.
• Fine, but the closest star besides the sun is four
million times further away. We need a larger “s.”
This is
Parallax and astronomy
• The Earth’s orbit around the sun!
• Our most accurate measure now is by?
Radar!
And 1 arc second for q in our diagram with
the earth’s motion around the sun to define
s, we find that 1 arc second gives a distance
called a Parsec (for parallax and arc
second!)
The parsec
Taking s = 1.50 x 1013 cm and q = 1 arc second and
sin(1 arc second) = 4.85 x 10-6. Or, d = (1.50
x1013)/(4.85 x 10-6) = 3.09 x 1018 cm! Or in round
numbers, 3 x 1018 cm = 1 par sec. A year = p x 107
sec of time=> p x 107 sec x 3 x 1010 cm/sec = 1018
cm, or 1 par sec = about 3 light years, where speed
of light = c= 3 x 1010 cm/sec
1 parsec (pc) = 3 x 1018 cm
3 light years = 1 parsec
But will parallax work beyond
the stars in our galaxy?
• NO! => We need to determine parallax to
a standard candle, if we can get it.
• What do we need? Precise, small images, the
better to find the centers of, and a well defined
non-moving background for reference.
• Stars are good for making small images,
and distant stars or small galaxies are good
for reference.
Limitations to parallax method
• Swing around sun: Going to Pluto would
get us a much larger swing, but the period is
over 200 years!
• Image quality; Rule of thumb is we can
measure a center to about 1/10 of an object’s
width. The best we could do on the ground a
few years ago was 0.5 arc second images =>
about 20 pc distance. If can go into space can
get a factor of 100 improvement without the
blurring effects of the Earth’s atmosphere.
Limitations to parallax method
•Swing around sun: Going to Pluto would
get us a much larger swing, but the period is
over 200 years!
• Image quality; Rule of thumb is we can
measure a center to about 1/10 of an object’s
width. The best we could do on the ground a
few years ago was 0.5 arc second images =>
about 20 pc distance. If can go into space can
get a factor of 100 improvement without the
blurring effects of the Earth’s atmosphere.
Hipparcos, the “ultimate solution”
Hipparcos is an acronym for HIgh Precision PARallax COllecting Satellite.
Appropriately the proununciation is also very close to Hipparchus,
the name of a Greek astronomer who lived from 190 to 120 BCE.
By measuring the position of the Moon against the stars,
Hipparchus was able to determine the Moon's parallax and thus its
distance from the Earth. He also made the first accurate star map
which lead to the discovery, when compared with other data from his
predecessors, that the Earth's poles rotate in the sky, a phenomenon
referred to as the precession of the equinoxes.
The concept of using the data recorded by the star mappers for
astrometric and photometric observations was conceived by Erik Høg, a
Danish astronomer involved with the Hipparcos mission. It was fitting that
the catalogue which resulted from the star mappers should then be named
after Tycho Brahe, a 16th century Danish astronomer, who produced the
first 'modern' star catalogue (1602).
Hipparcos Instrument
Main optic a mirror only 29 cm wide! For
comparison, HST is over 200 cm wide.
Being above atmosphere and having clever
designs of a mask (think if knife edge test)
to overcome the small mirror size so as to
yield 100 times better star positions than
could be done from the ground.
Hipparcos, the “ultimate solution”
Scientists now possess, for the first time, a good
three-dimensional picture of the bright stars in our
neighbourhood. Hipparcos measured the distances of
many stars, which were previously a matter of
guesswork. For example Polaris, the Pole Star, is 430
light-years away.
Hipparcos hit the headlines in 1997 when it showed
that the chief measuring rod for the Universe was
wrongly marked. Bright blue stars called Cepheids, of
which Polaris is one, vary in luminosity in predictable
ways. Astronomers use them to gauge distances of
galaxies and the scale of the cosmos. But Hipparcos
revealed them to be farther away than previously
supposed. This made the Universe about 10 percent
older. Also farther away than expected are the oldest
known stars, the so- called halo stars. The change in
distances cut their ages by a few billion years.
Combined with the change in the cosmic scale, this
solved a riddle in astronomy. Before Hipparcos the
old stars seemed to predate the Universe. That was as
nonsensical as mountains older than the Earth!
Bottom line we now have (1) a ruler measurement
to the sun and astrometry to give us accurate
positions to the (2) A satellite dedicated to the
[boring, tedious] task of accurately measuring star
positions to yield accurate (to the few percent
level) the distances to “Cepheid Variables.” And
Cepheid Variables are our closest standard candles
and they are bright enough to be seen out to nearly
20 Mpc = where we can overlap with other things!
What are Cepheid Variables
• Cepheids are unstable (on human time scales) stars
with cycles of 1-50 days. And the longer the period
the intrinsically more luminous they are =>
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Fun animation on how standard
candle works
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