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This week at Astro 3303
• I’m teaching for the next 3 weeks
• HW#6 is due Wednesday
• If you need help, please email/visit me!
• HW#7 will be posted Wed; HW #8-10 deal with your final project!
• 2nd 30min test is Nov 11. Covers material through Wed Nov 6.
• Today:
• Relativistic Doppler formula and why we need cosmology
• Determining distances: the extragalactic distance scale
• Reading:
• Chapter 4; start looking at Chapter 5
Evidence for the Big Bang Model
• Olber’s paradox: (Heinrich Olbers: 1823)
• The sky is dark at night.
• Hubble’s Law & the expansion of the Universe (Edwin Hubble: 1927)
• If the universe is finite in space and time and is expanding, it
must have been smaller in the past.
• The Cosmic Microwave Background (CMB) Radiation (Arno Penzias
and Robert Wilson: 1965)
• Thermal spectrum with equivalent temperature of 3 degrees
=> 3 degree blackbody radiation = CMB
• Abundance of the elements via primorial nucleosynthesis
• The large scale structure of the universe: the way galaxies are seen
today to cluster into groups, clusters and superclusters.
Large Scale Structure
Our cosmological model must explain how the structure developed to
look this way (and not something else) and it has to do it in 13.7
billion years (not earlier, not later)
Smoother
earlier on
Time =>
Galaxies, clusters,
superclusters and voids
today
Early History
• Slipher (~1912) noticed that spiral nebulae showed
almost predominantly redshifts.
• By 1925 he had radial velocities for 40 galaxies
• Hubble used the 100-inch telescope on Mt. Wilson
to measure distance to 18 galaxies
• Found linear relation between increasing
redshift and increasing distance, now known as
Hubble’s law
Ho d = v ~ cz
• Of course. A major goal of HST has been to
measure Ho ~ 72 km/s/Mpc
Sometimes use Ho ~ 100 h km/s/Mpc = (1010 yrs)-1
Hubble’s Law
The dominant motion in the Universe is the smooth expansion known as
the “Hubble flow”.
Hubble’s Law: Vobs= HoD
where Ho is Hubble’s “constant” and D is distance in Mpc
Spread in velocity
for objects in a
cluster due to
their orbital
motion within the
cluster.
“redshift” z =
An object at z is receding
at velocity:
λ(obs) - λ(rest)
λ(rest)
=
(z+1)2 -1
V
= (z+1)2 +1
c

1+v/c
1-v/c
–1
Note that as
vc, z > 1
Relativistic Doppler Formula
• We observed galaxies/quasars with redshifts of ~7-10
• That does not mean that they are traveling faster than the
speed of light
This reduces to the
simple Doppler formula
for v << c.
For z= 10, this becomes
v=c
1 -(
)
1
11
2
= 0.995 c
In fact, the Cosmic Microwave Background photons have a
redshift z = 1000!
Distant galaxies
• The galaxy ON-108036
• It has a redshift of 7.2.
• That redshift corresponds
to a “look back time” of
12.9 Gyr, or an epoch of
only 749 Myr after the
Big Bang occurred.
• PE #11: What is its
recessional velocity?
(The galaxy with z~10.3 is still
unconfirmed; this one is for sure.)
Distant galaxies
• The galaxy ON-108036
• It has a redshift of 7.2.
• That redshift corresponds
to a “look back time” of
12.9 Gyr, or an epoch of
only 749 Myr after the
Big Bang occurred.
V = 0.992 c
What stars have MS lifetimes of 750 Myr?
(see PE#3)
Measuring extragalactic distances
Primary distance methods:
• Measure distance to some “standard candle” (object
whose luminosity you can infer) within the galaxy
• Works for nearest systems (where e.g. we can resolve
the individual stars) or, in very special cases, also for
distance systems.
Hubble’s Law:
• Observationally “low-cost” (but not exactly “cheap”)
• Measure the redshift => measure the distance
• Need to worry however about orbital motions in
groups/clusters (and other similar effects)
Determining distances
• Parallax
• Good for nearby stars; not for extragalactic objects… until
now/soon!
• Method of spectroscopic parallax
• Need to know position of object(s) on H-R diagram
• Can be used for nearby galaxies where we can detect the stars
individual (“resolved stellar populations”)
• “Tip of the Red Giant Branch”
• Cepheid Period-luminosity relation distances
• Can be used for relatively nearby objects (distances closer
than about 50 million light years)
• Similar method used for Supernovae Type 1a
• Hubble’s Law
• Works as long as we understand the “tricks”
Cosmic distances
• Because of the Earth's revolution around the Sun, nearby stars appear to
move with respect to very distant stars.
• The parallax of a star is the apparent angular size of the ellipse that a
nearby star appears to trace against the background stars.
• A parsec is the distance at which a star would be if its parallax where
exactly 1 second of arc.
1 A.U. = Astronomical unit = Mean Earth-Sun distance
1 parsec = 3.26 light years = 206265 A.U.
Distance from Sun to center of Milky Way ~ 8.0 kpc
Distance from Milky Way to Andromeda ~ 800 kpc (2.9 million lt yr)
Local Group Proper Motions
• 1920s van Maanen claimed to
see M33 spin!
• mas/yr motions  Spiral
nebulae nearby (Galactic)
• Hubble argued more distant
(extra-galactic)
• van Maanen’s error not found
M33
Extragalactic Masers
• Seen in lines of OH, SiO, methanol and H20.
• MASER stands for Microwave/Molecular Amplification by Stimulated
Emission of Radiation. As proposed by Einstein in 1917, an electron (or
an excited molecular state) interacting with an e-m wave of a certain
freq may drop to a lower energy level, creating a new photon with the
same phase, frequency, polarization and direction of travel as the
photons of the incident wave. A “maser” occurs when atoms have been
induced into an excited energy state and amplify the radiation at the
proper frequency.
• Arise in cool molecular regions near sites of massive star formation; the
UV radiation acts to “pump” the stimulated emission.
• Individual maser components have typical sizes of 1012m (corresponding
to 0.01 arcsec at 1 kpc; unresolved in extragalactic objects), and are
arranged in clusters typically 3·1014 - 1015 m (~ a few arcsec) in
diameter. In some active galaxies, we observe “megamasers”.
Micro-arcsec Astrometry with the VLBA
Fringe spacing:
qf~l/D ~ 1 cm / 8000 km = 250 mas
Centroid Precision:
0.5 qf / SNR ~ 10 mas
Systematics:
path length errors ~ 2 cm (~2 l)
shift position by ~ 2qf ~ 500 mas
Relative positions (to QSOs):
DQ ~ 1 deg (0.02 rad)
cancel systematics: DQ*2qf ~ 10 mas
Extragalactic Proper Motions
• Parallax accuracy:
sD ~ 10% at 10 kpc
(can’t do galaxies yet)
M33
• Proper motion:
same techniques, but
sm ~ T-3/2
• M33 & IC10
1) see spin (van Maanen)
2) see galaxy’s motion
Andreas Brunthaler’s PhD
Thesis
Extragalactic Proper Motions
• M33/IC133 – M33/19 masers
VLBA: Dmx = 30 +/- 2, Dmy = 10 +/- 5 mas/yr
HI:
Dvx = 106 +/-20, Dvy = 35 +/- 20 km/s
D = 750 +/- 50 +/- 140 kpc
sm
sv
• Improvements in Rotation Model &
3rd maser source:
sD < 10% possible
Brunthaler, Reid & Falcke
The method of “spectroscopic parallax”
1. Observe the star’s
apparent brightness.
2. Observe the star’s
spectrum; determine its
spectral class and
luminosity class.
3. Place the star on the H-R
diagram; estimate its
luminosity.
4. Use luminosity and
apparent brightness to
get distance.
Good for normal stars,
clusters of stars, some very
nearly galaxies (tip of the red
giant branch)
TRGB
Tip of the Red Giant Branch
2.Observe their
apparent
brightness
Apparent brightess
1. Assume that the bright
stars at the tip
of the red giant
branch always
have the same
luminosity
faint
blue
color
red
Cepheid Variables
• Cepheid variables: Analogs of the star  Ceph
• Giant, post-main sequence stars which pulsate due to instabilities.
• As the envelope of the star expands and contracts, the star’s
brightness changes.
http://zebu.uoregon.edu/~soper/StarLife/cepheid1.gif
Cepheid Variables
• Cepheid variables: Analogs of the star  Ceph
• Giant, post-main sequence stars which pulsate due to instabilities.
Apparent brightness varies
over time in repeated
fashion
http://www.astro.lsa.umich.
edu/Course/MMSS/Intera
ctive/Ex1.4/lightcur.jpg
Cepheid Period-Luminosity Relation
• Henrietta Leavitt discovered a
relationship between the period
of pulsation and the mean
luminosity of the star.
1. Identify the star as a Cepheid
variable by studying its
spectrum (if possible) and/or
by the shape of its lightcurve.
2. Calculate its period.
3. Use the Period-Luminosity
relationship to determine the
Luminosity.
4. Use the inverse-square law to
calculate how far a star of
that luminosity would have to
be in order to appear as a star
of that observed apparent
brightness.
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit4/plrelation.gif
HST Key Project
Main goal: determine Ho to within
10% by observing Cepheids in
nearby galaxies.
PE #12: NGC 4258 as a case study
PE #12: NGC 4258 as a case study
Composite image:
• Yellow: optical
• Purple: radio
continuum
• Blue: X-ray
• Red: Spitzer IR
X-ray/radio continuum
arms (purple/blue) are
offset from the
stars/gas/dust arms.
X-ray/radio arms not
seen in optical; appear
associated with shocked
material and the SMBH
NGC 4258
• BVI survey of 2
fields using HSTACS + 1 previously
done with HSTWFPC2
• 281 Cepheids with
periods from 4 to
45 days
• Observed 12
separate epochs
12/03 to 1/04
Macri+ 2006, ApJ 652, 1133
NGC 4258
Color composite images
• Inner field (left)
• Outer field (right)
Macri+ 2006, ApJ 652, 1133
NGC 4258
• Master V-band
image of inner field.
• Locations of
Cepheids shown
(circles)
Macri+ 2006, ApJ 652, 1133
NGC 4258
• Individual finding
charts for the
Cepheids.
• Each image is 2.5
arcsec on a side.
Macri+ 2006, ApJ 652, 1133
NGC 4258
• CMD of outer field
• Cepheids are
filled/open
• Other stars in small
dots
• Dashed/solid lines
represent spread in
LMC Cepheids
• Arrow indicates
effect of internal
selective extinction
E(B-V) = 0.2 mag
Macri+ 2006, ApJ 652, 1133
NGC 4258
• CMD of inner field
• Cepheids are
filled/open
• Other stars in small
dots
• Dashed/solid lines
represent spread in
LMC Cepheids
• Arrow indicates
effect of internal
selective extinction
E(B-V) = 0.2 mag
Macri+ 2006, ApJ 652, 1133
NGC 4258
• Representative light
curves of Cepheids
in inner field
Blue: B
Green: V
Red: I
Macri+ 2006, ApJ 652, 1133
NGC 4258
• BVI periodluminosity relations
for the brighter
Cepheids in the
inner field
• Lower right shows
period-luminosity
relation adopted
using combination of
methods and
extinction
They use the maser
distance (next) and
the P-L relation for
LMC to get Hubble
constant
Macri+ 2006, ApJ 652, 1133
H2O maser in NGC4258
• Radiospectroscopy and VLBI
of H2O molecules reveal a
thin disk in Keplerian
rotation.
• Rotation and distance yield
an enclosed mass of
Keplerian Disk
M  4 x 107 M
within 0.3 lightyears.
Miyoshi et al. (1995), Herrnstein et al.
(1997), Humphreys et al. (2008)
NGC 4258
NGC 4258
NGC 4258
H20 masers at 22 GHz
VLBA @ 22 GHz
• Angular resolution ~ 200 µas (microarcsec)
• Spectral resolution ~ 1 km/sec
• Radial velocity (l.o.s.) =
GM/R sin θ where θ is
the azimuthal angle in
the disk measured
from the BH, R is the
radial distance from
the BH, M is the mass
of the BH.
Close to l.o.s., sin θ ~ b/R, where b is
the impact parameter, so Vz ~ b GM/R3
NGC 4258
Over time, masers are
tracked as they orbit, and
eventually disappear from
sight. Their velocities
increase by about 8 km/s/yr
from 430 km/s to 530 km/s;
we only see them when their
maser emission is beamed
along the l.o.s.
Geometric distance:
• Measure their doppler shifts => km/s
• Measure the proper motions of the masers over time => “/year
• Comparison of the angular velocities in the latter measurement
with the absolute velocities in km s-1 in the former
measurements yields the distance.
Distances to far off galaxies: SNeIa
• 1998 and 1999:
Two independent teams
studying exploding stars in
very distant galaxies found
that the galaxies are
further away than
predicted!
The universe is expanding, but….
The expansion is accelerating!
Dark energy!?
SN in M51
Distant SNeIa
SNe Types
SNeIa
Using SNe to determine distances
• What measurements would you make?
• Observe the supernova suddenly brighten, then fade over
time.
• Identify it as a SN of Type Ia from its “light curve” (how it
brightens and fades) and probably from taking spectra
(which shows heavy elements like chromium, aluminum, etc)
• What assumptions would you need to invoke?
• That all SN of Type Ia have the same luminosity when they
are at their maximum apparent brightness, i.e. that SNeIa
are “standard candles”.
• So, if we observe a supernova’s light curve and apparent
brightness, we can derive its distance.
• Then we can compare that distance to the distance we expect
from its redshift and Hubble’s law => any differences tell us
about the geometry of the universe.
Determining distances from SNe
• What measurements would you make?
• Observe the supernova suddenly brighten, then fade over
time.
• Identify it as a SN of Type Ia from its “light curve” (how it
brightens and fades) and probably from taking spectra
(which shows heavy elements like chromium, aluminum, etc)
• What assumptions would you need to invoke?
• That all SN of Type Ia have the same luminosity when they
are at their maximum apparent brightness.
• That you can properly account for dust obscuration within
the galaxy in which the SN resides.
• How do you derive the distance to a galaxy with a SNeIa?
• Now we have: luminosity and apparent brightness.
• Remember that:
Luminosity
=> distance
Apparent brightness  (Distance)2
Using SNe Ia as standard candles
Velocity = c X z
Apparent
brightness
• Identify a set of objects whose
luminosity is taken to be constant:
“standard candles”
???
• Then plot their apparent
brightness versus their redshift
• => Determine “Hubble’s Law” over
large distances
Redshift z
(or velocity)
NOTE: for small z,
cz ~ recessional velocity
c X z = H(t) x Distance
“Hubble parameter” units: (km/s)/Mpc
• We assume all
SnIa reach the
same maximum
luminosity.
• Then we
observe the
maximum
apparent
brightness.
Faint
Apparent brightness
• Type Ia
supernovae as
“standard
candles”
Evidence for acceleration
• => They appear
to be too
Bright
faint/further
away! =>
Acceleration
Distant SNeIa
appear fainter than
we expect
Applies on small scales