Download Goal: To understand how we know distances to

Goal: To understand how we
know distances to various objects
(the distance scale)
2)
3)
4)
5)
Objectives:
1) To learn about Radar (the sun)
To learn about Parallax (nearby stars)
To learn about using Cepheid variables
(galaxy and nearby galaxies)
To understand the Hubble relationship
To understand how to use Supernovae
(all the way across the universe)
How do we know the closest
distance to us, the sun?
• Not as easy of a question as you think.
• Imagine you were sent back in time and
you had to explain that the earth is an
average of 93 million miles from the sun –
how would you do that?
Here is what you say
• Um, you can’t prove it…
• All you could do is give the ratio’s of the
distances (i.e. you could prove using orbits
that Jupiter was 5.2 AU from the sun –
whatever the AU actually was).
Radar!
• 50 years ago we finally COULD measure the
distance to the sun!
• We used radar.
• No, we didn’t send the radar to the sun.
• What we did was send radar to Venus, and wait
for the reflected beams to return.
• This would take several minutes, but could be
done.
• Since we knew the speed of light we could
therefore find the distance to Venus.
The AU
• Since we knew that the earth was 1 AU
away, and we could know what the
distance for Venus was for the sun in AU,
if we knew the distance from Venus to
Earth then we knew the distance from
Venus to the sun, and the distance from
the sun to Earth.
• Radar is good out to 50 AU (4.6 billion
miles).
2nd rung - parallax
• The first use of parallax was done by
Tycho Brahe 500 years ago.
• He discovered that on the same night in 2
different locations on the earth that the
moon had a slightly different position with
respect to the stars.
• This allowed Tycho to find the distance to
the moon!
• But how does this work?
What is parallax?
• Hold out your thumb as far as possible and close 1 eye.
• Then at the same time open the closed eye and close
the opened eye.
• Your thumb will appear to move compared to stuff further
away.
• The angle the thumb moves depends on the distance
between your eyes divided by the distance your thumb is
away from your eye.
• The larger the apparent movement, the shorter the
distance (and vica versa).
• Half the movement means twice the distance away.
Astronomical parallax
• When we talk about “parallax” what are we
usually referring to?
• A) the apparent difference in position with
respect to further objects for 2 positions on the
surface of the earth
• B) the apparent difference in position of a star
over the course of a year
• C) the apparent difference in the position of a
star over the course of 6 months
• D) how quickly the star appears to move across
our sky
Using our orbit around the sun!
• If we pick 2 places 6 months apart we are
on opposite sides of the sun.
• We move a distance of 2 AU.
• So, if we look 90 degrees away from the
sun at both points, we will see a slightly
different angle with respect to stars even
further away
If an object has a parallax motion of
1 arcsecond how far away from the
earth is it?
•
•
•
•
A) 1 light year
B) 1 AU
C) 1 parsec
D) 1 trillion miles
Parallax distance
• Distance = 1 parsec / parallax motion in
arcseconds
How far out does parallax work?
•
•
•
•
A) ~ 5 light year
B) ~ 50 light years
C) ~ 500 light years
D) ~ 5000 light years
Best in show!
• The Hipparcos satellite was able to take
the most accurate images ever.
• Therefore it was able to spot parallax
movement from a few hundred parsec.
• Past that the movements are too small to
be detected – yet.
Secondary Calibrators
• These are calibrators that depend on the
“primary” ones (radar + parallax).
• If there is a change to the primary one,
then all the secondary ones change too.
• What do you think the first secondary
calibrator is?
Apparent vs. absolute magnitudes
• If you compare the apparent and absolute magnitudes of
an object you get its distance.
• How to do that?
• 1) spectra – tells you what the mass of the star is by its
temperature and its spectral type (although does not
work so well for giants – works great for main sequences
stars, but this separates them.
• 2) Main sequence fitting of clusters – we have done this
one already
• This is good for about a few million light years (we are
getting better at some of this).
Variable stars
• The other secondary is variable stars.
• The most common is Cepheid variables
(because they are the brightest).
• As has been mentioned before, the period of the
variable depends on the size.
• So, if you know the period, you know the size.
• If you know the size and temperature then you
know how bright it actually is.
• If you know its actual brightness and its apparent
brightness you know its distance!
Tertiary Calibrators
• These are calibrators that depend on the
secondary (which depend on the primary).
• These have bigger error bars than the
primary and secondary.
• Therefore these calibrators are constantly
been improved and updated.
• All of these try to relate the brightness of a
galaxy to some other value.
Tully Fisher
• The first is the Tully Fisher relationship.
• This compares the rotation of the galaxy to the
brightness (the rotation gives an indication of mass
which therefore would affect brightness).
• The rotation is found using the Doppler shifts of the 21
cm line of Hydrogen.
• You can also use bright objects such as very massive
stars, novae, and some supernova.
• There is also some who think the size of a black hole in
the core of the star might also determine brightness (or
even the brightness of the bulge).
• Overall this works somewhat for galaxies out to 150 Mpc
(500 million light years)
Galaxy size and apparent
brightness
• If you make the assumption that all
galaxies are the same size then you can
crudely (within about a factor of a few)
estimate the size and distance to a spiral
galaxy using either its apparent brightness
(and comparing to the absolute brightness
of the average spiral galaxy) or its
apparent angular size (smaller means
further away as all are about 100,000 light
years across).
Standard Candles
• Now we are starting to get across the
universe!
• Supernovae are so bright that they can be
seen across the ENTIRE UNIVERSE!
• However, can we tell the absolute
brightness of a supernova?
• To do that, they have to be the same, or
have some pattern or relation.
Type Ia
• Type Ia supernovae (which occur when
white dwarfs get too much mass by either
taking it from a companion, or more
usually spiral into another white dwarf) are
all the same brightness because they all
do the same thing.
• So, we can judge the distance by the
apparent brightness of the explosion.
Type II supernovae
• Type II (Type II just means that there is some
Hydrogen in the supernova. Type Is have none)
supernovae come from massive stars.
• However, each star is a different mass, and
therefore a different brightness of supernova.
• The trick is that the bigger stars are brighter, and
have longer peaks.
• This one is not very accurate, but gives some
idea to distances.
Hubble’s law
• It turns out that our universe is expanding.
• So, almost everything (with the exceptions of the
most nearby galaxies like Andromeda) is moving
away from us.
• Quite simply, the velocity an object moves away
from us is just proportional to distance (twice the
distance means twice the speed).
• V = Ho * d (Ho is called Hubble’s constant)
• So, if you measure the velocity away from us
(once again we use the Doppler shift) then we
know the distance.
Redshift
• This velocity causes what we call Cosmological
redshift.
• This redshift tells us the distance to the galaxy –
sort of.
• However, guess what, that galaxy is moving
away from us.
• So, does the distance we get tell us the distance
it is NOW or the distance it was THEN, or maybe
halfway between?
• So, really, what we have is not a “distance” but a
look back time.
complications
• There are a few more complications.
• First, our planet, star, and galaxy are all in motion (but
we can account for that as we will find out how later).
• The rate of expansion is not 100% known. We think we
know it to 10%, but there seem to be 2 groups who differ
by 25-50% and each claim to know it to 10%.
• As we will see later that brings up a big dilemma.
• Also, the rate of expansion does NOT seem to be
constant with time (cosmological constant).
• So, this is only fairly accurate to about 2 billion light
years.
Conclusion
• We estimate distances using a wide range of methods.
• Many of these methods are calibrated using the previous
methods.
• By doing this we can created a ladder of methods which
go from our sun to the far edges of the observable
galaxy.
• However, if you make any changes or adjustments to
one you change all of the methods which depend on
that.
• With time we have better telescopes and better ways to
use them and our methods continue to improve
(translation we can measure distances farther out with
lower error bars).