1B11 Foundations of Astronomy Cosmic distance scale

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1B11 Foundations of AstronomyCosmic distance
scale

• Liz Puchnarewicz
• emp_at_mssl.ucl.ac.uk
• www.ucl.ac.uk/webct
• www.mssl.ucl.ac.uk/

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1B11 Cosmic distance scale
Why is it so important to establish a cosmic
distance scale? Measure basic stellar
parameters,
eg radii, luminosities, masses Explore the
distribution of stars,
eg Galactic structure Calibrate
extragalactic distance scale,
eg galaxy scales, quasar luminosities,
cosmological models
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1B11 Direct methods
1. Trigonometric parallax
star
1AU
p
Sun
d
Ground-based telescopes measure p to 0.01
(d100pc) Hipparcos measured p to 0.002
(d500pc) Gaia will measure p to 2x10-5 arcsec
(d50,000pc)
Parallax
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1B11 Sun-Earth distance
To measure parallax accurately, we must know the
distance from the Earth to the Sun.
The Earths orbit is elliptical. An Astronomical
Unit is the size of the semi-major axis.
In order to measure the length of the semi-major
axis, we need a nearby planet, a radar and
Keplers Third Law, which is
1AU
Where T is the orbital period of a planet, and a
is the semi-major axis of its orbit.
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1B11 Measuring an AU
We can measure the orbital periods of the planets
by tracking them across the sky.
So then we can calculate, in units of the
Sun-Earth distance, the distances to all of the
planets.
Wait until the Earth and a planet, eg Venus are a
known AU distance apart, eg when theyre closest
together. Then bounce a radar signal to Venus and
back, measure the time it takes, multiply by the
speed of light and you have the distance in, eg,
km.
At their closest, the Earth and Venus are 0.28AU
apart.
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1B11 Converting from AU to km
In this position, it takes 280 seconds for light
to bounce back from Venus to the Earth. So the
distance in km is
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1B11 Nova expansion
Remember that for the proper motion of a star, m,
(measured in arcsecs per year), the tangential
velocity of the star, vt4.74md (where d is in
parsecs and vt is in km/s).
nova shell
d
m
vr
vt
Instead of a star, consider a nova an explosion
from a star. We assume that the shell thrown off
is spherically-symmetric.
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1B11 Distances from nova shells
nova shell
d
m
vr
vt
Using spectroscopy and measuring the Doppler
effect
m is the proper motion of the shell due only to
its expansion
and since vt vr, then
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1B11 Indirect methods Cepheid variables
Cepheid period-luminosity relation
Dm 1mag
magnitude
average mag
time
P1-50 days
Cepheid variables are pulsating variable stars
with a characteristic lightcurve named after
dCephei. Henrietta Leavitt (1912) found that the
period of variability increased with star
brightness.
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1B11 Calibrating Cepheids
The period-luminosity of Cepheid variables must
be calibrated and this has been done by measuring
their parallax using Hipparcos.
For P in days,
The mean magnitude is typically very bright
so they can be seen at very large distances
(Henrietta Leavitt was working on a cluster of
stars in the Small Magellanic Cloud). Measuring P
provides MV, which gives distance via the
distance modulus. This is especially important
for calibrating extragalactic distance, eg the
Hubble Space Telescope Key Project.
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1B11 Spectroscopic distances H-R diagram
106
103
Luminosity (LSUN)
1
10-2
10-4
30000 20000 10000 6000 4000 2000
temperature, K
This is a Hertzsprung-Russell diagram a plot of
luminosity against temperature for stars.
colour/spectral type gt luminosity
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1B11 Distances from H-R diagrams
If an H-R diagram is well-calibrated (ie the
temperatures and spectral types are well-known),
the absolute luminosities can be derived. The
distances are then calculated by measuring their
apparent magnitudes and applying the distance
modulus equation (ie (mV-MV)5log10d-5AV)). Spec
tral distances can be calibrated using
trigonometric parallaxes.
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1B11 Cluster distances from H-R diagrams
calibrated main sequence
MV
Vertical shift gives (mV-MV)
horizontal shift gives E(B-V) gt AV
(B-V)
And the distance modulus is (mV-MV)5log10d-5AV.
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1B11 Standard candles
If there is a type of object whose intrinsic
luminosity we can reliably infer by indirect
means, then this is a standard candle. We
measure its apparent flux, calculate the
intrinsic luminosity and the inverse square law
gives us the distance. Globular
clusters Construct the H-R diagram for a globular
cluster of stars and find the spectroscopic
distance. Also look for variables in the
cluster. Integrated absolute magnitudes can be
estimated by assuming MV. Then you can estimate
the distances for globular clusters around other
galaxies.
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1B11 Novae
Novae The absolute magnitude of a nova can reach
MV -10. And novae which decline faster, are
brighter where R2 is the decline rate in
magnitudes per day, over the first two magnitudes.
Dm2m
MV
Calibrate using novae in our Galaxy.
t2
Then you can use the relationship to infer
extragalactic distances.
t
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1B11 Supernovae
Type II supernovae core collapse of massive
star Type Ia supernovae dumping of matter from
secondary star onto a primary star in binary
systems. In Type Ia SN, MV(max) reaches approx
20 with only a small variation between different
events. So as long as you catch the maximum, you
have a good standard candle out to very large
extragalactic distances.
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1B11 Tully-Fisher relationship
In 1977, Tully and Fisher found that the width of
the 21cm emission line from a galaxy, was broader
when the galaxy was brighter.
21cm x (1z)
flux
wavelength
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1B11 Tully-Fisher relationship
They suggested that this is a fundamental
physical property, because More stars gt more
mass gt higher rotation brighter The stars and
gas in the galaxy are in orbit, so
Centrifugal force gravitational force
M(star)v2/R GM(galaxy)m(star)/R2 M(galaxy)
v2R/G (GGravitational constant) And since
luminosity is (probably) proportional to
M(galaxy), Luminosity(galaxy) would be
proportional to v2
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1B11 Tully-Fisher relationship
The trouble is Its not yet clearly understood
why the relation works so well. It works really
well over at least 7 magnitudes (a factor of 600
in luminosity terms). It implies a cross-talk
between the bulge and the disk components in
galaxies we dont know how the bulge and the
disk conspire to produce the same mass to light
ratios for such a range of luminosities.
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1B11 Hubbles Law
In 1929, Edwin Hubble discovered that all
galaxies (beyond our local group) were moving
away from us, and that their recession speed was
proportional to their distance. v H0d Where v
is the recessional velocity, measured from the
redshift, d is the distance to the galaxy and H0
is Hubbles constant. This general expansion of
the Universe demonstrated to Einstein that it was
not static as he had thought. H0 is hard to
measure, Hubble thought it should be 500 km s-1,
Mpc-1 current observations indicate 50-90 km
s-1 Mpc-1. The best measurements indicate 65 km
s-1 Mpc-1
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1B11 The age of the Universe
Once the Hubble constant has been measured, if we
can assume that the rate of the expansion of the
Universe has not changed, then we can calculate
the age of the Universe, Hubbles law v
H0d And in general, d vt, so t
d/v Substituting for Hubbles law, then t
d/(H0d) So t 1/H0 And if H0 65 km s-1 Mpc-1,
then t 1.3x1010 years. Maybe expansion was
faster in the early stages of the Universe, but
there is evidence for a dark energy in the
Universe which is increasing the expansion rate
now.