Download and galaxies

Syllabus for 2GLSS,
Galaxies and Large Scale Structures.
Dr. P.H. Regan, 29BC04, x6783
[email protected]
Spring Semester
Books
1) Discovering Astronomy, Robins, Jefferys
and Shawl, Wiley, (RJS)
2) An Introduction to Modern Astrophysics,
Carroll and Osterlie, Wiley (CO)
3) Introductory Astronomy, Haliday, Wiley
(HAL)
4) Active Galactic Nuclei, Robson, Wiley,
(ROB)
5) Large-Scale Structures in the Universe,
Fairall, Wiley (FAI)
2GLSS P.H. Regan
1

2GLSS Course Outline
Perspectives
–
–
–
–

Size scales
Nuclei and atoms
interstellar medium
Standard Model
Galaxies
– Milky Way
– Galaxy types, spirals, ellipticals...
– Colliding Galaxies

Large Scale Structure
– Hubble’s Law
– Recognition of large scale
structures

Active Galaxies
– Active Galactic Nuclei
– Gamma-ray bursters
2GLSS P.H. Regan
2
Is the Universe Infinite ?
Olber’s Paradox (RJS p534, CO p1222)
Q. Why is the sky dark at night ?
If the universe was infinitely large and old, you
would see a star in your line of sight in all
directions, the night sky should be bright!
This is evidently NOT the case, ‘Olber’s
Paradox’.
Olber’s ‘solution’, space not transparent BUT
this wouldn’t matter as any interstellar dust
would be heated to the same temp. as stellar
surface and thus glow the same colour .
Also proposed was that the recession velocity
moved the light out of visible wavelengths
(‘redshifted’), BUT the shift is not large enough.
A. Light has a finite speed (c=3x108 ms-1) and
the light from the furthest stars has not reached
the earth yet (solution proposed by Lord Kelvin
and Edgar Allen Poe!) Thus the observable
universe is finite in size (and age).
2GLSS P.H. Regan
3
Size Scales
•Nuclei approx 10-15 m, stellar fuel.
•Atoms approx 10-10m, cosmic probes
•People approx 1m, cosmic observers
•Stars approx 104m->1012m cosmic furnaces
•Galaxies approx 1019m->1021m (this course)
Units of Distance (RJS p320, CO p64)
1 astronomical unit (AU) = 1.5x1011m
(= earth - sun distance)
1 Parsec =3.1x1016m (=1 parallax second)
d (pc) = 1 Au / p (in seconds of arc)
1 light year (ly) = 9.5x1015m
(=distance light travelled in 1 year)
Ro = 7.0x108m (= solar radius)
RO = 8.0(5)kpc (= sun -> centre of galaxy)
2GLSS P.H. Regan
4
Nuclei: Stellar Fuel.
(CO p349) Elements up to Fe (Z=26) can be
formed by nuclear fusion, which keeps the
star ‘burning’. H (Z=1), burns to He (Z=2),
which burns to Carbon (Z=6). Then Carbon,
Oxygen (Z=8) and Silicon (Z=14) burning are
all allowed in large (heavy, hot and dense)
stars. For Z>26 fusion is no longer
energetically favourable, but heavier elements
can be formed by neutron capture followed by
b- decay. (via the ‘slow’ (s) or ‘rapid’-neutron
processes).
2GLSS P.H. Regan
5
See http://www.orau.gov/ria
2GLSS P.H. Regan
6
From Wiescher, Regan and Aprahamian,
Physics World, February 2002, p33
2GLSS P.H. Regan
7
Elemental Abundances
(CO p526, RJS p109, 307)
Note x-rays from solar photosphere show
evidence of elements up to U (Z=92) in the sun.
Large stars live for only around 106-7 years, very
short compared to universal time scales. After
this, large stars collapse and expel much of their
reaction products into space for future star
formation.
2GLSS P.H. Regan
8
From 2002 RIA summer school, see
http://www.orau.gov/ria
Pm (Z=61)
Tc( Z=43)
2GLSS P.H. Regan
9
Atoms, Cosmic Probes.
2GLSS P.H. Regan
10
Emission and Absorption Lines
Interstellar medium
( diffuse gas and dust)
Absorption lines
(observation)
Star light
(black body)
Emission lines
(observation)
Most (approx 70%) of the Inter-Stellar
Medium (ISM) is made up of hydrogen, in
either atomic or molecular form.
For Hydrogen ATOMS the principal lines come
from the Lyman, Balmer and Paschen Series
2GLSS P.H. Regan
11
•A hot, dense gas (or solid object) produces a
continuous spectrum with no dark spectral
lines. (Black-body spectrum)
•A hot, diffuse gas produces bright emission
lines when an electron makes a transition
from a higher excited state to a lower one.
The wavelength of the emitted photon can be
calculated from the energy difference
between the initial and final levels.
•A cool diffuse gas in front of a black-body
source produces dark, absorption lines when
an electron is raised from a low-excitation
energy orbit to a higher one.
2GLSS P.H. Regan
12
Fe emission spectrum
Fe absorption spectrum
H absorption
H emission
See http::/jersey.uoregon.edu/elements/Elements.html
2GLSS P.H. Regan
13
Where are our body parts made ?
(% of human body by weight)
See http://www.orau.gov/ria
2GLSS P.H. Regan
14
Note that the elements Tc (Z=43) and Pm
(Z=61) have no stable isotopes. Longest lived
isotopes are 145Pm (T1/2=18 yrs) and 98Tc
(4.2x106yrs).
Observation of the atomic spectra of these
elements in extra-solar stellar atmospheres is
proof of on- going elemental synthesis.
Wiescher, Regan and Aprahamian,
Physics World (2001) p33
2GLSS P.H. Regan
15
Proposed Creation Sites of Elements.
(taken from http://www.orau.gov/ria
2GLSS P.H. Regan
16
S and R process peaks due
to nuclear shell effects
2GLSS P.H. Regan
17
Metallicity
(CO p920)
The iron (Fe, Z=26) content can be used as a
good indicator of the age of the star. Newer
stars have a higher iron content than their
predecessors (more generations of reactions).
The metallicity is defined as the iron-to-hydrogen
(Fe:H) ratio in the atmosphere of a star compared
to the solar value. This is given by the expression
[Fe/H] = log10 (NFe/NH) - log10(NFe/NH)o
where log10(NFe/NH)o corresponds to the
solar value. This stars with metallicities
identical to the sun’s have [Fe/H]=0. Typical
values range from -4.5 for old, metal-poor
stars, to +1 for young, metal-rich ones.
Note that some astronomers believe Type 1a
supernovas may distort the local values of the
[Fe/H] ratio for different regions of the
inter-stellar medium (ISM) and thus prefer the
[O/H] ratio instead as an measure of stellar age.
2GLSS P.H. Regan
18
Forbidden Lines, ‘Metastable states, ‘isomers’
CO p404,
Certain transitions from excited atomic and
molecular states are hindered in their decay,
usually by some quantum mechanical decay
selection rule. This can give rise to very long
lifetimes for such states. For such atomic
states to exist in interstellar gas etc. the
density must be very small since (as on
earth) random atomic collisions would deexcite this state.
Examples of such states at the l=21cm decay
in the neutral hydrogen atom (H-I) and the
green glow associated with some nebular
arising from emissions in doubly ionised
oxygen (O-III).
2GLSS P.H. Regan
19
Hydrogen (see RJS p445)
HI = hydrogen atoms. Existence is often seen
by radiotelescopes via the observation of the
electron-proton ‘spin-flip’ transition from
hyperfine splitting. This has a wavelength of
21cm (n =1420 MHz, E =5.9x10-6eV).
Energy
Ionisation
eproton
1st excited state of HI
(spins parallel).
0
n=3
n=2
e-
proton
Ground state of HI
(spins anti-parallel).
-13.6 eV
n=1
Nb. Zeeman effect gives B-field measurement
2GLSS P.H. Regan
20
Hendrik Van de Hulst’s prediction of the
observation of the 21 cm line allowed the study
of cold, neutral hydrogen in the cosmos.
If H atoms collide with neighbouring atoms, the
atom can be raised from its anti-parallel spins
ground state to the excited, parallel-spin config.
This is a low-energy, excited metastable state
(~107 years due to non-conservation of spin, 1s>1s, but photon has intrinsic spin 1). Due to the
low density, the atom can remain in this state for
a long time before decaying back to the ground
state via the 21 cm emission.
This discovery was important because
• It’s a feature of H (most abundant element)
• It occurs only in low density regions
• It indicates the presence of neutral ( i.e.nonionised and non-molecular) HI atoms
• It is not easily absorbed by interstellar gas.
This means that 21cm radiation emission
fromalmost anywhere in the galaxy can be
measured on earth via radiotelescopes.
2GLSS P.H. Regan
21
Hydrogen Molecules (H2)
Taken from RJS p369
(RJS p445)
If the interstellar hydrogen is close to a hot star,
the H2 molecules can be ionised and form a
region of H-II. Interstellar lines often show
different component with slightly different
wavelengths. This is caused by Doppler shifts
which depend on the relative velocity of the
specific cloud. Dust absorption means that
emissions in the visible region are not useful in
determining the overall structure of the galaxy.
2GLSS P.H. Regan
22
From http://fuse.pha.jhu.edu/Figures/data
Far Ultraviolet Spectroscopic Explorer (FUSE)
data on AGN which interstellar absorption
from gas in milky way, including H2 molecules.
2GLSS P.H. Regan
23
The Interstellar Medium (ISM)
• Importance of radio-astronomy in seeing
further due to less scattering/absorption in
interstellar dust.
• Interstellar dust is heated to approx. 10-90k
by the stars in the galaxy, which then radiated
in the far infra-red region (30-300mm).
•Stars radiate strongly in the near infrared
region (1-10 mm). Very little stellar ‘extinction’
of light (as which occurs for the visible region)
occurs in this range. See e.g., COBE spectra.
•Spin-flip transition in hydrogen gives rise to a
21cm radiowave emission. Thus, radiotelescope
surveys allow the distribution if hydrogen
across the plane of the milky way and its
Doppler shift allows us to determine the speed
at which the (H) gas in the galaxy rotates.
2GLSS P.H. Regan
24
Molecular Gas Clouds (CO p446)
•Typical temperatures of around 20K (c.f. ISM
typical temp ~ 100K).
•Density in such clouds ~ 102-7 atoms /cm3
(c.f. sea level earth atmosphere ~3x1019 /cm3).
•Gas is mostly molecular hydrogen, H2…(ISM
gas is mostly H-II, i.e., ionised H2 mols).
•Note that the H2 molecule does NOT emit the
21cm line. Thus hard to identify in visible region
(use rotational decays)…also need to use
tracers with known relative abundances, such
as CO, CH, OH and C3H2.
Giant Molecular Clouds (GMC)
These are very large collections of dust and gas
with T~20K with typical densities of
~100-300cm-3. They can stretch for distances of
50 parsecs and contain up to 106 solar masses.
Inside the GMCs are more hot and dense cores
with dimensions of 0.05-1 parsec, T~100-200K
and densities of 107-109 /cm3. 1000s of GMC are
known in our galaxy, mostly in the spiral arms
(see later)
2GLSS P.H. Regan
25
Bok Globules (RJS p375, CO p446)
Names after Bart Bok, these are dark (cold, dense)
regions which are often seen projected against bright
nebulae. Bok globules are small, dense clouds, with
large visual extinctions (al~10) and low
temperatures (~10K). They are relatively dense
(~104cm-3) and have masses between 1 and 1000
solar masses, with sizes of around 1 parsec. About
one quarter of these have young, proto-stars inside.
IC-2948
Bok
Globules
Inside this emission nebula are groups of dark,
opaque clouds, i.e., Bok globules.
See http://www.aao.gov.au/images/general
2GLSS P.H. Regan
26
Some good web pages for
galaxy informantion and figs.








users.erols.com/arendt/Galaxy/mw.html
www.whfreeman.com/universe6e
antwrp.gsfc.nasa.gov/apod/archivepix.ht
ml
adc.gsf.nasa.gov/mw/mmw_sci.htmlmaps
cdsweb.ustrasbg.fr/astroweb/survey.html
skyandtelescope.com
www.eso.org/outreach/press-rel/pr2002/pr-17-02.html
zebu.uoregon.edu/~soper/MilkyWay/sah
pley.html
2GLSS P.H. Regan
27
ISM, Composition (RJS p444)
Interstellar Dust
Early studies of UV radiation showed spectral
features at 220 nm wavelength, corresponding to
known transitions from graphite (carbon).
Infra-red astronomy then showed that some
stars were surrounded by dust shells which heat
up and subsequently re-radiate in the infra-red
region. Although these spectra are generally
continuous, for some stars, an extra continuous
peak was superimposed on the usual black body
spectrum at wavelengths of approx. 10,000 nm.
This was consistent with significant amounts of
silicates (e.g. quartz SiO2) in the dust cloud.
It has been suggested that C and Si grains are
formed in the carbon-rich atmospheres of giant
pulsating stars. At expansion, the outer layers of
such stars cool and the carbon atoms can stick
together to make ‘grains’. When this region heats
up again, the increased radiation pressure from
the star pushes these out of the star’s atmosphere
and into space.
2GLSS P.H. Regan
28
Interstellar Gas (RJS p366ff,CO p447)
The ISM also contains large amounts of gas,
which is mostly made up of hydrogen. Depending
on the density and temperature of the regions
where this hydrogen is, it can exists either in its
natural atomic form (HI), its stable molecular form
(H2) or the ionised form of the molecule (HII).
In addition to hydrogen, a number of other
molecules have been observed in the ISM, such as
CO (carbon monoxide), SO2 (sulphur dioxide),
OH (hydroxyl), H2O (water), NH3 (Ammonia),
H2CO (formaldehyde), H2S (hydrogen sulphide)
CH3CH2OH (ethyl alcohol!), HC11N (organic?).
These molecules are identified by their emissions
which occur in the UV, visible and IR regimes.
Usually decays from excited states are by photon
with wavelengths in the mm region corresponding
from the decay from a rotational state to one with
a slightly slower rotation. Such wavelengths can
penetrate the earth’s atmosphere and be observed.
2GLSS P.H. Regan
29
Interstellar Reddening.
(CO p265) Dust particles scatter short
wavelengths (blue) more effectively than long
(red) ones. (Sky is blue, setting sun is red!)
This effect can give rise to an interstellar
reddening effect of stars which are partially
obscured by dust clouds. This scattered light
also tends to be (partially) polarised.
Scattered
(blue) light
Original light
from source
Interstellar
dust cloud.
Transmitted
(red) light
Dust clouds can obscure the view of stars (and
galaxies), and the centre of the Milky Way.
The amount of interstellar extinction depends
on the wavelength, l, and the path length, s.
2GLSS P.H. Regan
30
(See CO p265, p438)
Absorption includes the scattering of light and
true absorption from e.g., electrons being to
higher energy states in atoms and molecules. It is
wavelength dependent. If dIl is the change in
intensity through distance ds, then
dI l  kI l ds
integratin g we obtain
s
I l  I l (0)e tl , where tl   kl  ds
0
tl  optical depth (dimension less)
al  interstell ar extinction  1.086tl
kl  opacity ( cm 2 .g 1 )
  density ( g.cm 3 )
ds  path increment (cm)
mean free path of photons is given by
1
1
l
(
)
kl 
n l
Opacity is the cross-section for absorbing photons
of wavelength, l, per gm of stellar material.
2GLSS P.H. Regan
31
Spectral Maps of the Galaxy
Ref
http://adc.gsfc.nasa.gov/mw/mmw_images.html
2GLSS P.H. Regan
32
Standard Model of the Universe.
•Big Bang ~2x1010 years ago, created an
expanding universe, now 2x1010 ly radius
(constant expans.)
•Primordial Abundances: ~80% Hydrogen,
~20% Helium, trace amounts of Li and Be.
•After ~105 years, regions condense,
gravitational energies leads to heating, nuclear
reactions (proton-proton chain), stars form.
•H burns to He (p-p chain). For heavy stars,
nuclear fusion reactions can burn to form
elements all the way up to Iron (Fe, Z=26).
•Small stars eject planetary nebula which
releases some material into space, but most kept
in core (to form white dwarf).
•Large stars (>10Mo) have life cycles of ~107
years followed by cataclysmic supernova. Most
of their material is expelled into the ISM.
•New stars form in the ISM which are metalsrich ( i.e., higher metalicities).
2GLSS P.H. Regan
33
•Galaxy formation….a problem. An early
period of rapid expansion is need to give
sufficient inhomogeneity.
•Inflation theory. Recent distant (> 5 billion ly)
supernova type 1A (good ‘standard candles’)
red-shifts imply that expansion rate is
increasing with time and the universe is older
than originally thought? i.e, ‘anti-gravity’ ?
Possible evidence for so-called dark energy.
(see Burrows, Nature 403 (2000) p727-733).
From SPATIUM, no7. May 2001, p11
2GLSS P.H. Regan
34
See http://physicsweb.org/article/news/2/11/3
Type 1a supernova
(see HOL p246) are
excellent standard
candles for distance
measurements using
Hubble’s law (see later).
See Perlmutter et al., Nature, 391 (1997) p51
2GLSS P.H. Regan
35
Our Galaxy, The Milky Way
(CO, chapter 22 RJS chapter 20)






Sun located 8(1)kpc from galactic
centre.
Orbital period 2.2x108 years, orbital
speed of 790,000 km/h.
50kpc disk of 600pc thickness and a
central bulge of approx. 3kpc thick.
Total galactic mass of approx 1011-12
solar masses.
10% of mass attributed to 200-400
million stars, gas and dust with other
possible 90% ‘dark matter’.
Supermassive black hole in centre with
mass of approx. 3x106 solar masses.
2GLSS P.H. Regan
36
Distribution of Globular Clusters.
(RJS p436)
(1917) Before effects of dust were known,
Harlow Shapley studied the distribution of
globular clusters in space.
He calculated their distances using
(variable) standard candles known as RRLyrae stars located within these clusters.
Shapley found that these clusters were
further from the sun that thought and thus
the galaxy must be larger than previously
believed.
Shapley reasoned that these large globular
clusters were such large components of the
galaxy that they would be unlikely to be
distributed to one side. He thus proposed
that the centre of the globular cluster
distribution coincided with the centre of the
galaxy, and thus that the sun was actually
quite far from the centre. (Modern value is
between 25-30Kly).
2GLSS P.H. Regan
37
http://www.seds.org/messier/m/m002.html
M2 cluster (‘Messier object’).
First found by Maraldi (1746). Messier
(1760) catalogued it as nebula but without
individual stars. Hershel (~1780) resolved
individual stars within the cluster.
Approx. 150,000 stars and diameter of 140 ly
2GLSS P.H. Regan
38
http://www.astrophotographer.com/Globular_plot.html
See also great pictures and info at the following.
www.ipac.caltech.edu/2mass/gallery/Images_galaxies.html
www.astr.ua.edu/choosepic.html
www.dir.yahoo/Science/Astronomy/Pictures
2GLSS P.H. Regan
39
http://aether.lbl.gov/www/projects/cobe/cobe_pics.html
Milky Way from combined images at
near-infrared wavelengths of 1.2, 2.2 and 3.4
microns from the COBE satellite.
Note thin disk and central bulge. Redder
regions are due to light absorption from dust.
Artist’s impression
of above view of
Milky Way from
computer
simulation. See
web page given
below.
http://users.erols.com/arendt/Galaxy/mw.html
2GLSS P.H. Regan
40
Details of the Structure of the Milky Way
(see CO p927ff, RJS p439, p457)
halo
disk
nucleus
bulge
sun
~15kpc
Thin disk is metal-rich, [Fe/H]~0, star formation,
lots of young blue stars. Around 325 parsec region
of sun. Thick disk, metal-poor [Fe/H]~-0.5, older
stars. Disk thickness increases towards the inner
regions of galaxy.Gas/dust in disk absorbs visible
light, but 21cm H-I line ok. Thus, radiotelescopes
can map velocity and distribution of H-I gas.
Galactic bulge. Spheroidal region near centre of
galaxy. Only certain w.lengths observed due to
dust. Disc meets the galactic bulge at a radius of
approx. 1kpc. Vertical scale in bulge is around 400
parsecs (along the bulge’s minor axis). Major to
minor axis ratio for the bulge is thought to be a
~0.6. Wide range in metallicity, in the bulge with 1 < [Fe/H] <+1, average ~ +0.3, i.e., average Fe to
H ratio is about 2 x solar value. i.e., younger stars
dominate here. Bulge mass is ~ 1010Mo.
2GLSS P.H. Regan
41
The surface brightness of the bulge, I, in units
of Lopc-2 is given by the r1/4 law, also known as
de Vaucloulers profile (1948). Confirmed by
COBE results. Re is the reference radius, Ie is
the surface brightness at re. Formally, re is
defined as the radius at which one half of the
bulge’s light is emitted.
1


4
 I (r ) 
r




log 10 


3
.
3307

1

r 


I
 e 
 e 

Baade’s window is a gap in the dust clouds in
the bulge which allows the observation of RRLyrae stars (standard candles) beyong the
galactic centre. Appears 3.9o below and within
550 parsecs of the galactic centre.
Galactic B-field: Disk field estimated to be
approx 0.4nT (~10-5 times solar B-field).
Deduced from Zeeman-splitting effect on the
two states in H-I resposible for the 21cm line).
Also from polarisation of scattered light.
2GLSS P.H. Regan
42
The Stellar Halo is the region around the disk
and bulge. It is made up of a few hundred
globular clusters and many high-velocity
(‘field’) stars. The globular clusters consist of
old, metal-poor stars, with the oldest clusters
([Fe/H] <-0.8) scattered throughout the halo.
Appear to be approx. 1.6x1010years old ( i.e. as
old as the universe, surely not possible..see RJS
p930 and chaps. 25 and 27)
(CO p930)
Two distinct regions of metallicity for globular
clusters, Generally, more metal-poor (older) in
spherical distribution around galactic centre with
more metal-rich (younger) in galactic plane.
2GLSS P.H. Regan
43
Dynamics of the MilkyWay
(CO p935, RJS p448)
• Motion of the Sun
Note that the celestial equator ( i.e. the plane
through the earth’s equator) is at 63o to the
galactic equator ( i.e., the plane through the
galaxy’s disk).
•Definition of galactic co-ordinates, b
(Galactic latitude) and l (Galactic longitude)
are relative to the motion of the sun.
star
To north
galactic
pole (NGP)
rotation
b
sun
l
galactic
centre
•NGP has co-ordinates of b=90o. By convention
•Galactic centre has (almost) l=0o and b=0o .
2GLSS P.H. Regan
44
Cylindrical Co-ordinate System (CO p941)
•Cylindrical co-ordinate have centre of galaxy at
origin.
Q
P
star
rotation
z
q
sun
R
galactic
centre
In this co-ordinate system, the corresponding
velocity components are given by,
dR
dq
dz
P
, QR
, Z
dt
dt
dt
2GLSS P.H. Regan
45
Local Standard of Rest (LSR) CO p942)
To investigate the motion of the sun and other
local stars, we must first define the Local
Standard of Rest (LSR). This is defined as a point
which is instantaneously centred on the sun and
moving in a perfect circular orbits about the
galactic centre. Thus, by definition, the velocity
components about the LSR must be
P  0, Q  Q0 , Z  0
The velocity of star relative to the LSR is known
as the peculiar velocity and is given by
V  (VR , Vq , Vz )  (u , v,  )
where
u  P  P LSR  P
v  Q  Q LSR  Q  Q 0
  Z  Z LSR  Z
2GLSS P.H. Regan
46
Motion of Sun in Galaxy
(see CO p945)
The LSR has Q0~220 km/s and a rotational
period of about 230 million years.
To a good approximation, there is no motion
relative to the LSR in the R and z directions, but
there is a significant Q effect (see CO p943).
The sun’s peculiar velocity (relative to the LSR)
is called the solar motion and has values of:
uo  9km / s (towards to the galactic centre)
v0  12km / s (overtakin g the LSR)
0  7km / s (north, out of the galactic plane
note already ~ 30pc above centre)
2GLSS P.H. Regan
47
Measuring Velocities
(CO 107, p126-127)
Proper motion.
Change over time of
stellar co-ordinates.
Note that need to know
distance (only useful
for nearby stars).
vq
dq
vq  r
dt
vr
star
r
observer
Doppler Shift
Christian Doppler (1842) found that as the sound
waves moved through air, the observed w.length,
lobs, is compressed in the forward direction and
expanded in the backward direction (compared
to a stationary observer) by the expression,
lobs  lrest l vr


lrest
lrest vs
vr and vs are the source - observer radial
velocity and the speed of sound respective ly.
2GLSS P.H. Regan
48
For light however, there is no speed of sound,
as there is medium involved and the expression
must be obtained using special relativity.
ut rest
d
2
u
1  
c
Source moving q
u
at velocity, u
q
x
1st signal
to observer
ut rest
u
1  
c
2
cos q
2nd signal
to observer
If trest is the time difference between the emission
of light crests and tobs is the difference in time
between their arrival at the observer then
tobs

trest   u 

1    cos q 

u2   c 

1 2
c
2GLSS P.H. Regan
49
Remembering that the frequencies of the light
from the source (nrest) and and the observed
frequency (nobs) are given by
 rest
1
1

, obs 
t rest
tobs
The Relativistic Doppler Shift is then given by
u2
 res 1  2
c , but v  u cos q
obs 
r
u
 
1    cos q
c
if movement is (i) directly t owards
or (ii) away from observer,
(i) q  0, vr  u and (ii) q  180, vr  u , then
obs
2
 vr  vr 
vr

1  
 res 1  2
res 1 
c 
c

c 

v 
v 
1  r 
1  r 
c
c
Note
v =vel.
n = freq
obs   rest
vr
1
c
vr
1
c
2GLSS P.H. Regan
For RADIAL
MOTION
ONLY
50
For objects moving away from the observer,
there is a shift down in frequency ( i.e. up in
wavelength) towards to RED end of the
spectrum ( i.e. lobs>lrest and vr>0).
For movement towards the direction of the
observer, the shift is to the BLUE (i.e. lobs<lrest
and vr<0)
Since most astronomical objects are moving
away from the earth, a redshift parameter, z,
is used to describe the change in observed
wavelength (and thus the radial velocity), where
lobs  lrest l
z

,
lrest
lrest
lobs  lrest
since c  l ,
vr
vr
1
1
c and thus z 
c 1
vr
vr
1
1
c
c
vr z  1  1
rearrangin g gives,

c z  12  1
2
2GLSS P.H. Regan
51
Galaxy Rotation (CO p955-8, RJS p477)
Can use the circular orbits of stars and Newton’s
laws for objects far from the galaxy’s interior,
equating the centripetal and grav. forces
GmM r mv2
v2r
F (r ) 

 Mr 
,
2
r
r
G
1
v 
BUT at large r, v  const!
r
In a spherically symmetric system, the condition
for mass conservation is given by (=density)
2
dM r
v
2
 4r  ,  (r) 
dr
4Gr 2
This predicted density dependence (~1/r2) is
much slower than deduced from the star counts
beyond the centre of the galaxy. The density of
luminous (i.e., visible) stars in the stellar halo
appears to fall off as (~1/r3.5)…..
This has been put forward as an argument that the
majority of mass in the galaxy is actually in the
form of Dark Matter.
2GLSS P.H. Regan
52
Measuring Galactic Rotation Curves
//astrosun.tn.cornell.edu/courses/astro201/rotcurve.htm
//www.owlnet.rice.edu/~spac250/elio/space.html
//www.astro.ruhr_uni_bochum.de/geiers/GAL/gal_rot.htm
The rotation curves for galaxies are the
measured velocities (via the Doppler shift) of
H-I and carbon mononxide (CO) gases. The zvalue observed in these lines can be used to
calculate the radial velocity of the gas. Note
that CO emits spectral lines which are easier
detect through the region of the bright centre
of a galaxy (unlike the visible H lines).
Note, max Doppler shift (solid line above) is when
motion is directly towards or away from observer.
2GLSS P.H. Regan
53
CO p960)
(RJS p477) From Kepler’s 3rd law as modified
by Newton, for a star travelling about a galaxy
with a Rotational Period, P in years, Mstar and
Mgalaxy are in solar masses and R is the distance
to the galaxy’s centre in AU, then
M
 M galaxy P  R
2
star
3
This can be used to estimate mass of galaxies.
2GLSS P.H. Regan
54
(1) measure l for
specific spectral line
(3) Subtract vrecession
from galactic centre.
(2) measure z(v) for each
point along galaxy disk
(4) residual is
rotation curve
2GLSS P.H. Regan
55
Measuring the
Doppler at each
end of the galaxy
gives the radial
velocity as a function
of distance from the
galaxy centre
This allows the rotation
curve to be measured
(Radial velocity, vr as a
function of distance from
galaxy centre, r)
2GLSS P.H. Regan
56
Examples of galaxy rotation curves, see
Y. Sofue, PASJ 49 (1997) p17
www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig2.htm
2GLSS P.H. Regan
57
The Galaxy (cont).

21cm radiowaves from neutral H gas can
penetrate the ISM. Large hydrogen clouds can
be found in the spiral arms of galaxies (see
e.g., M31). Looking across the galactic plane,
one can observe a series of emission peaks, all
slightly shifted with respect to each other. This
can be explained by each spiral arm of the
Milky Way moving with its own specific
rotational velocity (and Doppler shift). It is
thus possible to produce maps of the number
and orientation of arms in the Milky Way.

Other molecules (as well as H2) such as OH,
CH and CO can also be detected via radio
frequency emissions. Giant Molecular Clouds
(GMC), which represent stellar formation
sites. CO which emits radiation at l=2.6mm
and regions of this molecule suggest that our
galaxy has four major spiral arms (Perscus,
Sagitarius, Centaurus and Cygnus). The Sun is
situated on a smaller branched arm spiral
known as Orion.
2GLSS P.H. Regan
58
From Astronomy by Zeilikk
(John Wiley and Sons)
Note, artists impression…not data!
2GLSS P.H. Regan
59
•There is optical evidence for the spiral
structure of the Milky Way, using socalled SPIRAL TRACERS (see RJS
p203). These include the presences of
young, (Population I) blue (O and Btype) stars, high-metallicity stars.
• Hot, ionised hydrogen (H-II) regions
are also associated with stellar
formation and might be expected to be
found in the spiral arms.
• Other spiral tracers include (i)
Emission Nebula illuminated by hot O
and B stars, (ii) Giant Molecular
Clouds (GMCs) and (iii) Supernova
Remnants
2GLSS P.H. Regan
60
Andromeda galaxy (M31) at various wavelengths
See http://sirtf.caltech.edu/Education/Messier/m31.html
2GLSS P.H. Regan
61
Rotation Curve for the Milky
Way (dark matter)






Optical and radioastronomy seem to
indicate that all stars in the galaxy travel
at the approx. the same rotational speed.
Thus stars closer to the centre complete
their orbits faster than the ones at the
edge. This results in spiral shapes.
But as we know the approx. age of the
galaxy and the rate at which the sun
rotates around the galactic centre, the
Milky Way should be more tightly wound
than it is.
Failure of Kepler’s third law…more
matter in middle maybe ? Dark matter ?
Why don’t the arms wind up ?
Supernovae may stretch new groups of
stars into arms. Also spiral density waves
and self-propogating star formation, the
‘ice-skater’ model.
Freeman’s Law (see CO p999, all spirals
have ~equal surface brightnesses)
2GLSS P.H. Regan
62
Supermassive Black Hole ?
(CO p970, HOL p263)

Our galaxy is probably a ‘barred-spiral’.

The strongest infra-red emission line is found
in a region at the centre of the galaxy called
Sagittarius A (SgrA), which is also a strong
source of synchrotron radiation (I.e. a point
radio-source, Sgr A*.

From around 1995 onwards, infra-red
(2.2mm) enabled the velocities of ~90 stars
close to to SgrA* to be measured.

Implication from Newtonian mechanics,
radio-source and x-ray flares is a
supermassive black hole with approx 2.6x106
solar masses at centre of Milky Way (see
Ghez et al,. Nature 407 (2000) p349, see also
http://physicsweb.org/article/news/6/10/12

Distance of galactic centre is approx 26,000 ly
from earth
63
2GLSS P.H. Regan
Intense radio-source in centre of Galaxy,
Sagittarius A*
http://www.aoc.nrao.edu/pr/sgr.bhole.html,
radio-frequencies between 0.7-6 cm)
2GLSS P.H. Regan
64
Baganoff et al.,f rom the CHANDRA X-ray observatory,
http://chandra.harvard.edu/press/
01_releases/press_09050/flare.html
False colour image of x-ray flare from
supermassive black hole at centre of galaxy,
associated with the compact radio source,
Sagittarius A*. It is suggested that the flare is
evidence for local matter falling into the black
hole, which fuels energetic activity in the centre
65
of the Milky Way. 2GLSS P.H. Regan
Galaxies in General: A Brief History

Messier (1730-1817) recorded 103 fuzzy
objects (nebulae) in the Messier catalogue
(M@).

Dreyer (1852-1926) published the New
General Catalogue (NGC) of almost 8,000
nebulae (NGC@), but not known at this
point whether they were galactic or extragalactic phenomena.

1923, Hubble detected Cephied variables
in M31 (Andromeda galaxy, NGC224),
showed extra-galactic nature.
2GLSS P.H. Regan
66
Morphology of Galaxies: Galaxy Types.
(RJS p468, CO p990, HOL p257) Galaxies are
broadly classified into three types by a scheme
known as the Hubble Sequence. This divides
galaxies into (i)Ellipticals (E), (ii) Spirals (S) &
(iii) Irregulars (Ir). The spirals are further
subdivided into two sequences, namely (iia)
Normal Spirals (S or SA) and (iib) Barred
Spirals (SB). There are also a class of galaxies
which are transitional between ellipticals and
spirals, known as Lenticulars, which can be
either ‘normal’ (SO) or barred (SBO). These are
arranged by Hubble’s Tuning Fork Diagram.
normal spirals
ellipticals
barred spirals
Hubble thought
(wrongly!) this was
an evolution of type
2GLSS P.H. Regan
67
(RJS p468, CO p997, HOL p258)
•ELLIPTICAL (E) galaxies are ellipsoidal in
shape and contain no spiral arms. They contain
little interstellar dust and gas and are found
mostly in rich clusters of galaxies. Elliptical
galaxies typically appear yellow-red in colour.
There are few blue, young, recycling stars (in
contrast to spiral galaxies, whose spiral arms
are full of young stars and appear quite blue).
Supergiant Ellipticals have radii up to 106 pc.
http://www.antwrp.gsfc.nasa.gov/apod/lib/ellipticals
M87 elliptical
galaxy
NGC4881 Giant
Elliptical galaxy)
2GLSS P.H. Regan
68
•SPIRAL (Sa, Sb, etc.) galaxies consist of a
large, dominant central bulge and tightly
wound spiral arms. Star formation in the bulge
region is thought to have taken place long ago
and thus light from this region is blue-deficient
(since massive, blue stars are relatively short
lived), but rather reddish (from red-giants).
This contrasts with the spiral arms, where new,
blue, stars are formed. Spirals have (i) a flat
disk, which usually contains a lot of interstellar
matter and (ii) hot, massive, young (blue. O
and B type) star clusters, which are usually
arranged in spiral patterns structures. Some
spirals have a large ‘bar’ through their central
region and are known as ‘barred spirals’. (The
milky way is thought to be a barred-spiral
galaxy). Hubble subdivided spiral galaxies into
Sa, Sab, Sb, Sbc, Sc and Sba, Sbab, SBb, SBbc
and SBc. Those galaxies with the largest bulgeto-disk luminosity ratios, the most tightly
wound spiral arms and the smoothest
distribution of stars are classified as Sa or Sba.
Conversely, Sc and SBc galaxies have loosely
wound arms etc.
2GLSS P.H. Regan
69
http://www.antwrp.gsfc.nasa.gov/apod/lib/spirals
Andromeda galaxy (M31)
closest galaxy
~ 2million ly
companion
galaxy
(NGC 5195)
Whirlpool Galaxy (M51)
2GLSS P.H. Regan
70
The ‘Sombrero’sprial galaxy (M104),
clearly showing the dust in the disk, the
central bulge and globular clusters within the
stellar halo.
See http://www.noao.edu/image_gallery
2GLSS P.H. Regan
71
NGC7479 barred spiral
galaxy
http://licha.de/AtroWeb
NGC3992, M109 barred spiral galaxy
http://www.smv.org/hastings
2GLSS P.H. Regan
72
•LENTICULAR (SO, SBO) galaxies consist of
flat disk with a central bulge but do not show
any spiral arms (unlike spiral galaxies).
Depending on the orientation relative to the
earth, such galaxies can appear circular (if
seen face on), elliptical, or thin and elongated.
NGC 4546 (SB0) Lenticular galaxy from
http://www.sunspot.noao.edu/sunspot/pr/tree
NGC 3384 (SO) lenticular galaxy
2GLSS P.H. Regan
73
•IRREGULAR (Irr) galaxies have a chaotic
appearance which does not resemble either
spiral or elliptical galaxies. Many of the smallest
galaxies are irregular (including the Magellanic
clouds which accompany the Milky Way).
M82 Irregular galaxy
http://www.sunspot.noao.edu/sunspor/pr/tree
2GLSS P.H. Regan
74
Size of Galaxies (CO p998)
By mapping contours of constant brightness,
(ISOPHOTES), one can infer the matter
radius of galaxies.
BUT, galaxies do not have have sharp edges,
thus radii are not well defined.
The effective radius (re ) , is defined as
the radius within which half of the galaxies
light is emitted.
For the bulges of spirals and large ellipticals,
this looks like (from equn, on page 42)
1


4
r

m (r )  me  8.33    1
 re 



where m( r) is the surface brightness in units of
magnitude/arcsec2 and me is the surface
brightness at the effective radius, re.
(Note, that galaxial disks are usually modelled
with an exponential , rather than r1/4 decay).
2GLSS P.H. Regan
75
The Tully-Fisher Relation
(CO p1001, RJS p476)
It is reasonable to assume that the greater
the mass in a given galaxy, the larger its
luminosity. It then follows, the greater the mass,
the larger the gravitational force at each point
in the galaxy would be. Since it is the size of this
gravitation force which determines the rotation
velocity of the galaxy (see equn. P52), there will
be a relationship between the rotational velocity
and luminosity of galaxies.
The rotational velocity of galaxy can be deduced
from the Doppler broadening of the 21 cm line.
This will be both red and blue shifted. A value
for the absolute luminosity for the galaxy can
be estimated and compared with the observed
brightness. The inverse square law of light can
be used to make an estimate of galaxy’s distance.
The relationship between the luminosity and
rotational velocity of galaxies is known as the
Tully-Fisher relation (1977).
2GLSS P.H. Regan
76
Tully-Fisher Relations at large (0.2<z<1.1) redshift see
http://www.nmsu.edu/~nicole/research/VogtNP_fig03.html
The exact form of the Tully-Fisher relation
depends on the galaxial mass distribution, and
thus the type of galaxy. But to first order, the
relationship between the absolute magnitude (M),
the luminosity (L) and the maximum rotational
velocity, (Vmax) can be given by
 L 
M  M sun  2.5 log 10    10 log 10 Vmax  c
 L 
c=constant
2GLSS P.H. Regan
77
Stellar Distributions and Metallicities
•H-I gas in our galaxy is distributed in spiral
arms, connected to the bulge.
•Most young (blue) stars are in these arms, i.e.,
these are regions of on-going star formation.
• Since stars form from gas clouds, and massive
(blue) stars form and die relatively quickly, one
expects (all) massive, main sequence stars to be
found in the spiral arms.
•Older stars are red in colour (further down
main sequence, red giants..) These are found in
the disk, not in the spiral arms. Red stars can
are also found in the bulge and halo.
• Observations indicate that the metallicity of a
galaxy correlates with its absolute magnitude and
thus luminosity. This implies that chemical
enrichment is more efficient in luminous,
massive galaxies. Possibly due to them having
more massive stars in which subsequently go to
type II supernova ?
2GLSS P.H. Regan
78
Metallicity-Magnitude Relation
(CO p1006)
From Pagel and Edwards, Annu. Rev. Astron.
Astrophysics 19 (1981) 77-113
2GLSS P.H. Regan
79
Galaxy Clusters and Colliding Galaxies
(CO p1053-10073, p1119ff)
Most galaxies belong to clusters, which can
contain 1000s of individual galaxies. Groups of
galaxies usually have less than 50 members,
with clusters containing between 50 and several
thousand individual galaxies. Galaxy clusters
are classified as either regular (spherical and
centrally condensed) or irregular.
The Milky Way belongs to the LOCAL GROUP,
which consists of approx. 30 galaxies, including
the Andromeda Galaxy (M31), M32, M33, M110
and the Small and Large Magellanic Clouds
(LMC, SMC). The Milky Way and Andromeda
galaxies are by far the largest and most
dominant members of the local group.
There are also around 20 small groups of
galaxies within approx 14Mpc of the local
group, including the Maffei-1, the South Polar
or ‘Sculptor’, the M81 and the M83 groups.
Out group of galaxies is in gravitational
interaction with these galaxy groups.
2GLSS P.H. Regan
80
http://www.seds.org/messier
M81 group
M82
M82
2 dwarf
galaxies
M81
M81
NGC3077
visible
NGC 3077
The M81 Group is one of
the closest galaxy groups
radio
to our own (~ 12Mly). The
group has two large
galaxies, M81 (‘Bodes
galaxy’) and M82 plus
NGC 3077 which all have
a mutual gravitational
interaction. Note the two
dwarf galaxies close to
M81 and the common
gaseous envelope which are
clearly apparent on on the
radiowave image.
2GLSS P.H. Regan
radio
81
M82
M81
It is thought that a few 10s of million years ago
a ‘close encounter’ occurred between M81 and
M82, with the result that M82 was dramatically
deformed by the gravitational attraction of the
larger and more massive M81. This encounter
also left traces in the spiral pattern of M81,
firstly making the overall pattern more
pronounced. Note that the M81 and M82 are
still relatively close at around 150kly apart.
2GLSS P.H. Regan
82
•Gravitational attraction between nearby
galaxies means they can interact and even
collide with each other.
•Colliding galaxies does not imply colliding stars
(size between individual stars too large).
• There can be dynamical friction between
galaxies due to the gravity (see CO p1055).
This dynamical friction force (‘drag’), fd, can
be estimated assuming fd ~ ( / v2) where v
is the relative speed of the colliding galaxies
and  is the density of the colliding material.
• Energy will also be converted from potential
and self-energy into kinetic energy of
individually scattered stars.
•Kinetic energy from the galaxies’ motions of
can be transferred into internal KE of the
gravitationally interacting galaxies.
• Gravitationally bound galaxies willeventually
merge (e.g. Milky Way and LMC & SMC,
also some evidence double nucleus in
Andromeda, M31 galaxy).
• The mergers and tidal interactions ‘tidal
stripping’ between colliding galaxies may be
responsible for matter transfer and creating
new active star-forming regions.
83
2GLSS P.H. Regan
CO p1066
2GLSS P.H. Regan
84
Recalling from basic Newtonian gravitatio n,
Mm
F  G 2  gravitatio nal force between 2 masses
r
Mm
U  G
 potential energy,
r
defined U  0 at r  
Self - energy for a uniform sphere is
3 GM 2
U 
5 R
For a system in
Hydrostatic Equilibr ium ,
(i.e. gravitatio nal attraction balanced
by random kinetic motion, ' gas pressure' )
E  U  K
and
U  2 K  E   K
2GLSS P.H. Regan
85
Calculating Galaxy Collisions (CO p1088)
Realistic ‘N-body’ computer simulations can
be carried out using Newton’s gravitational
equations. Such calculations suggest that
many large elliptical galaxies are actually the
result of mergers between two spiral galaxies.
It is thus thought that over time, spiral
galaxies are destroyed by mergers, resulting in
the creation of very large elliptical galaxies.
Evidence for this includes
• Computer based N-body simulations
• The observation that elliptical galaxies
appear to dominate in the more dense,
centres of galaxy clusters
• Observations also suggest that the more
distant (and thus younger) galaxies
appear to have (had?) a greater fraction
of spiral galaxies compared to ellipticals.
2GLSS P.H. Regan
86
CO p1088
2GLSS P.H. Regan
87
In hydrotstatic equilibrium, from the VIRIAL
THEOREM (CO p56) the Total (E), Potential
(U) and Kinetic (K) energies of a galaxies are
related by the expression 2K= -U = -2E
For a head-on galaxy collision, we can use the
impulse approximation (CO p1061) to assume
the encounter between the galaxies occurs so
quickly that the individual stars do not have
time to move much from their positions.
The gravitational potential energy, U, of the
galaxy is virtually unaltered by the collision.
If a galaxy increases its internal kinetic energy,
from K to K+K as a result of the gravitational
‘work’ each galaxy has done on the other one,
the total energy will also increase from K to
K+K, but the potential energy, U remains
unchanged (=K). The galaxy would thus no
longer be in hydrostatic equilibrium. To regain
equilibrium, the extra 2K of kinetic energy
obtained just after collision, must be ‘lost’. One
way this can be done is for this excess energy to
be converted in to increased (i.e., less negative)
gravitational potential energy, by expansion.
2GLSS P.H. Regan
88
Colliding Galaxies
http://www.seds.org/hst/Cartwheel.html
The Cartwheel galaxy (approx 500 Mly away),
is an example of a ‘ring galaxy’ (see CO
p1062) which followed from a nearly head-on
collision between galaxies. This figure, from
the Hubble Space Telescope, shows the effect
of a collision by an intruder galaxy (it is not
clear which one of the two objects to the
right), which smashed through the core of the
host galaxy. Note blue, new stars in the ring.
The ring is expanding at approx, 90km/s.
2GLSS P.H. Regan
89
Sleeping Beauty Galaxy(M64)
http://antwrp.gsfc.nasa.gov/apod
There is a central region where the stars
rotate in a different direction to the dust
and gas. This effect is thought to be result of
collision between a large and small galaxy
which has yet to equilibrate out.
2GLSS P.H. Regan
90
http://www.noao.edu/image_gallery/html/im0011.html
Interacting galaxies
Arp 273
‘Interacting Galaxies, Arp 273’ distance
approx 200Mly, false colour image from the
Anglo-Australian telescope.
Note the strong tidal distortion of the larger of
the two galaxies and the notable ‘extra’ red
nucleus in the smaller, side on galaxy in the
botton right of the picture. The lower galaxy
has a very active nucleus (see later).
2GLSS P.H. Regan
91
Superclusters
A supercluster is a group of galaxy clusters
which appear to be associated (gravitationally)
with each other. Unfortunately, this
information is not usually known for most
galaxy clusters and thus definitions of
members of superclusters are made on the
basis of how far different galaxy clusters are
separated from each other.
This definition has some problems, as the
distances between galaxies is much more
difficult to determine that the distance to them
(since we can use the doppler shift to give us
more accurate measures of the distance
perpendicular to the radial direction, than the
radial direction specifically.)
2GLSS P.H. Regan
92
Perseus galaxy cluster, see
http://antwrp.gasfc.nasa.gov/apod
The Perseus cluster of galaxies, approx. 300Mly.
This is part of the Pisces-Perseus supercluster.
Note that the confinement of gas in the large
galaxial gravitational field (purple in figure).
This extra
gravity’ which
ROSAT is sufficient to
False colour hold the gas in
x-ray image place, has
been proposed
as further
potential
evidence for
Abell 426
Dark Matter
2GLSS P.H. Regan
93
The Coma cluster contains >1,000 galaxies,
is around 6 Mpc across and lies ~360 Mly
away. Centre of galaxy is hot (T~100x106K) gas
cloud (see X-ray image) held in by gravity.
Coma cluster, see
http://www.astra.au.edu/gifimages/coma.html
visible
X ray
http://chandra.harvard.edu/x-ray_sources/coma
2GLSS P.H. Regan
94
The Virgo cluster of galaxies which is over
3Mpc across and consists of more than 2000
individual galaxies lies around 16 Mpc (~60
Mly) away. It represents the centre of the
local supercluster which includes the local
group.
http://www.seds.org/messier
‘Makarian’s
chain’
M90
M84
M86
M89
M87
NGC4371
NGC4429
Central portion of the Virgo cluster
2GLSS P.H. Regan
95
Expansion of the Universe, Hubble’s Law
(CO p1110)
Using luminosity of Cephied variable stars, Edwin
Hubble plotted the recessional velocity of such
standard candles in extra-galactic objects against
their induced distance (deduced using the inverse
square law of light). The resulting (nearly?) linear
relationship is known as Hubble’s Law, which
has the form,
V  Hr
Where V is the recessional velocity and r is the
distance from the earth. H is known as the
Hubble constant.
2GLSS P.H. Regan
96
From Hubble’s original paper, published in
Proceedings of the National Academy of Sciences
Volume 15 March 15, (1929), number 3.
‘Distances of extra-galactic nebulae depend
ultimately on the application of absolute
luminosity criteria to involved stars whose types
can be recognised. These include….Cepheid
variables, novae and blue stars involved in
nebulae emission.
……The apparent luminosities of the brightest
stars in such nebulae are thus criteria which,
although rough and to be applied with caution,
furnish reasonable estimates of the distances of
‘
extra-galactic systems’.
2GLSS P.H. Regan
97
Value of the Hubble Constant,
Scale Factors and Hubble Time
Hubble’s orginal value for H=530kms-1Mpc-1.
But subsequent measurements showed that he
underestimated the distances involved as what
he thought were the brightest stars were actually
groups of stars.
The value of H appears to have varied over time,
thus while it is still a constant of proportionality
between V and r, H=H(t).
By convention, we the present day value of the
Hubble constant is given the symbol, H0 .
There is still much debate and measurement on
the value of the Hubble constant. Currently,
it is standard to define constant using the
dimensionless quantity, h,
H0
h
1
100kms Mpc
and h has a value between 0.5 and 0.8.
2GLSS P.H. Regan
98
Hubble’s law implies a universal expansion. In
this context, the recessional velocity (due to the
expansion of space) is distinct from the
peculiar velocity (which is due to the motion
through space).
i.e
v = Hod + vpec
The recessional velocity arises because space
itself is expanding, this is the realm of
COSMOLOGY.
The cosmological redshift needs to take into
account the curvature of space-time (beyond
the scope of this course). However, it is
common practice to use the redshift equation to
obtain the effective radial velocity.
cz
d
: good for z  1 (non - relativist ic)
H0
c 1  z   1
d
: good (with 5%) for Z  2
2
H 0 1  z   1
2
Thus, by measuring redshift, the distance can
be determined. H0 is poorly known, use
H0=75(20)kms-1Mpc-1 (h=0.75(0.2))
2GLSS P.H. Regan
99