Cosmology with Supernovae: Lecture 1 Josh Frieman I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil July 2010
Download ReportTranscript Cosmology with Supernovae: Lecture 1 Josh Frieman I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil July 2010
Cosmology with Supernovae: Lecture 1 Josh Frieman
I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil July 2010 1
Hoje
• I. Cosmology Review • II. Observables: Age, Distances • III. Type Ia Supernovae as Standardizable Candles • IV. Discovery Evidence for Cosmic Acceleration • V. Current Constraints on Dark Energy 2
Coming Attractions
• VI. Fitting SN Ia Light Curves & Cosmology in detail (MLCS, SALT, rise vs. fall times) • VII. Systematic Errors in SN Ia Distances • VIII. Host-galaxy correlations • IX. SN Ia Theoretical Modeling • X. SN IIp Distances • XI. Models for Cosmic Acceleration • XII. Testing models with Future Surveys: Photometric classification, SN Photo-z’s, & cosmology 3
References
• Reviews: Frieman, Turner, Huterer, Ann. Rev. of Astron. Astrophys., 46, 385 (2008) Copeland, Sami, Tsujikawa, Int. Jour. Mod. Phys., D15, 1753 (2006) Caldwell & Kamionkowski, Ann. Rev. Nucl. Part. Phys. (2009) Silvestri & Trodden, Rep. Prog. Phys. 72:096901 (2009) Kirshner, astro-ph/0910.0257
4
The only mode which preserves homogeneity and isotropy is overall expansion or contraction: Cosmic scale factor
a
(
t
)
On average, galaxies are at rest in these expanding (comoving) coordinates, and they are not expanding--they are gravitationally bound.
Wavelength of radiation scales with scale factor: ~
a
(
t
) Redshift of light: 1
z
(
t
2 ) (
t
1 )
a
(
t
2 )
a
(
t
1 ) emitted at
t 1
, observed at
t 2
a
(
t
1 )
a
(
t
2 ) 6
Distance between galaxies:
d
(
t
)
a
(
t
)
r
where
r
fixed comoving distance Recession speed:
d
(
t
2 )
t
2
d
(
t
1 )
t
1
r
[
a
(
t
2 )
t
2
t
1
a
(
t
1 )]
d da
dH
(
t
)
a dt
dH
0 for `small'
t
2
t
1 Hubble’s Law (1929)
d
(
t
2 )
a
(
t
1 )
a
(
t
2 ) 7
Modern Hubble Diagram Hubble Space Telescope Key Project Freedman etal Hubble parameter
Recent Measurement of H
0 Riess, etal 2009 HST Distances to 240 Cepheid variable stars in 6 SN Ia host galaxies
H
0 74.2
3.6 km/sec/Mpc 9
How does the expansion of the Universe change over time?
Gravity: everything in the Universe attracts everything else expect the expansion of the Universe should slow down over time
Cosmological Dynamics
H
2 (
t
)
a a
2 Ý
a
Spatial curvature:
k
=0,+1,-1 8
G
i
(
t
) 3
i k a
2 (
t
) Friedmann Equations 4
G
3
i
i
3
p i c
2 Density Pressure Equation of state parameter :
w i
Non - relativistic matter :
p m
~
p i
m
/
i c
2 v 2 ,
w
Relativistic particles :
p r
r c
2 / 3,
w
0 1/ 3
Size of the Universe In these cases, decreases with time, Ý 0 : , expansion
decelerates
Empty Today Cosmic Time
Cosmological Dynamics
H
2 (
t
)
a a
2 8
G
i
(
t
) 3
i k a
2 (
t
) Friedmann Equations Ý
a
4
G
3
i
i
3
p i c
2 Equation of state parameter :
w i
Non - relativistic matter :
p m
~
p i
m
/
i c
2 v 2 ,
w
0 :
p r
r c
2 / 3,
w
1/ 3 Dark Energy : component with negative pressure :
w DE
1/ 3
Size of the Universe Ý 0 p = (w = 1) Accelerating Empty Today Cosmic Time
``Supernova Data” 15
Discovery of Cosmic Acceleration from High-redshift Supernovae Log(distance) Accelerating Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Not accelerating redshift = 0.7
= 0.
m = 1.
16
Cosmic Acceleration Ý
0
Ý
Ha
increases with time
Hd
we could watch the same galaxy over cosmic time, we would see its recession speed increase.
B. For a galaxy at
d
=100 Mpc, if
H 0
=70 km/sec/Mpc =constant, what is the increase in its recession speed over a 10-year period? How feasible is it to measure that change?
Cosmic Acceleration
What can make the cosmic expansion speed up? 1. The Universe is filled with weird stuff that gives rise to `gravitational repulsion’. We call this Dark Energy 2. Einstein’s theory of General Relativity is wrong on cosmic distance scales.
3. We must drop the assumption of homogeneity/isotropy.
Cosmological Constant as Dark Energy
Einstein:
G
g
8
GT
Zel’dovich and Lemaitre:
G
8
GT
8 +
g
(matter )
T
(vacuum )
T
(vac) = 8 G
g
vac
T
00 8 G ,
p
vac
T ii
8 G
w
vac 1
H
constant
a
(
t
) exp(
Ht
) 19
Cosmological Constant
as Dark Energy
Quantum zero-point fluctuations: virtual particles continuously fluctuate into and out of the vacuum (via the Uncertainty principle). Vacuum energy density in Quantum Field Theory:
vac
8
G
1
V
1 2 h 0
M
h
c
(
k
2
m
2 ) 1/ 2
d
3
k
~
M
4
w vac
p vac
vac
1,
vac
const.
Pauli Theory: Data:
M
~
M Planck
G
1/ 2 10 28 eV
vac
~ 10 112 eV 4 vac 10 10 eV 4 Cosmological Constant Problem
Components of the Universe
Dark Matter: clumps, holds galaxies and clusters together Dark Energy: smoothly distributed, causes expansion of Universe to speed up
Equation of State parameter
w
determines Cosmic Evolution
w i
(
z
)
i
p i
i
3
H
i
(1
w i
) 0 Conservation of Energy-Momentum
r
~
a
4 ~
a
3(1
w
)
m
~
a
3 =Log[a 0 /a(t)]
History of Cosmic Expansion
• Depends on constituents of the Universe:
E
2 (
z
)
m
(1
H
2 (
z
)
H
0 2
z
) 3
DE
i
(1
i
z
) 3(1
w i
)
k
(1
w
(
z
))
d
ln(1
z
) 2 for constant
z
) 1
m w i
DE
1
z
2 where
i
i
crit
(3
H
0 2
i
/8
G
) 23
Cosmological Observables
Friedmann Robertson-Walker Metric:
ds
2
c
2
dt
2
c
2
dt
2
a
2 (
t
)
d
2
a
2 (
t
)
dr
1 2
kr
2
S k
2 ( )
d
2
r
2
d
2 sin 2
d
2 sin 2
d
2 where
r
S k
( ) sinh( ), , sin( ) for
k
1,0,1 Comoving distance:
cdt
a d
cdt
a
cdt ada da
c
da a
2
H
(
a
)
a
1 1
z
da
(1
z
) 2
dz
a
2
dz c dt da da
ad
c
Ý
a
2
dz
ad
cdz
H
(
z
)
d
24
Age of the Universe
cdt
ad
t
ad
da aH
(
a
)
dz
(1
z
)
H
(
z
)
t
0 1
H
0 0 (1 where
E
(
z
)
dz z
)
E
(
z
)
H
(
z
) /
H
0 25
Exercise 2:
E
2 (
z
)
H
2 (
z
)
m
(1
z
) 3
DE
w
(
z
))
d
ln(1
z
) 1
m
DE H
0 2 A. For
w=
1
(cosmological constant ) and
k=0
: 1
z
2
E
2 (
a
)
H
2 (
a
)
m a
3
H
0 2 Derive an analytic expression for
H 0 t 0
in terms of Plot
H
0
t
0 vs.
m
B. Do the same, but for 0,
k
0 C. Suppose
H 0
=70 km/sec/Mpc and
t 0
=13.7 Gyr. Determine in the 2 cases above.
m
D. Repeat part C but with
H 0
=72.
26
m
Age of the Universe
(flat)
Luminosity Distance
• Source
S
at origin emits light at time
t 1
into solid angle
d
,
received by observer
O
at coordinate distance
r
at time
t 0
, with detector of area
A
: S r A Proper area of detector given by the metric:
A
a
0
r d
a
0
r
sin
d
a
0 2
r
2
d
Unit area detector at
O
subtends solid angle
d
1/
a
0 2
r
2 at
S.
Power emitted into
d
is
dP
L d
/4 Energy flux received by
O
per unit area is
f
L d
L
4
a
0 2
r
2
Include Expansion
f
• Expansion reduces received flux due to 2 effects: 1. Photon energy redshifts:
E
(
t
0 )
E
(
t
1 ) /(1
z
) 2. Photons emitted at time intervals
t 1
arrive at time intervals
t 0
:
t
0
dt t
1
a
(
t
)
t
0
t
1
t
0
t
1
dt a
(
t
)
t
1
t
1
t
1
t
1
a
(
t
1 )
dt a
(
t
)
t
0
t
1
a
(
t
0 )
t
0
t
1
dt a
(
t
)
t
0
t
1
t
1
t
0
t
1
a
(
t
)
a
(
t
0 )
a
(
t
1 )
dt
1
t
0
z t
0
t
0
dt a
(
t
)
L d
4 4
a
2 0
L r
2 (1
z
) 2 4
L d
2
L
Convention: choose
a 0 =1
d L
a
0
r
(1
z
) (1
z
) 2
d A
Luminosity Distance
Worked Example I
E
2 (
z
)
H
2 (
z
)
H
0 2
m
(1
z
) 3
DE
w
(
z
))
d
ln(1
z
) 1
m
For
w=
1
(cosmological constant ):
DE
1
z
2
E
2 (
a
)
H
2 (
a
)
H
0 2
m a
3 1
m
a
2 Luminosity distance:
d L
(
z
;
m
, )
r
(1
z
)
c
(1
z
)
S k
c
(1
z
)
S k
da H
0
a
2
E
(
a
)
H
0
a
2 [
m a
3
da
(1
m
)
a
2 ] 1/ 2 30
Worked Example II
E
2 (
z
)
H
2 (
z
)
H
0 2
m
(1
z
) 3
DE
w
(
z
))
d
ln(1
z
) 1
m
DE
1
z
2 For a flat Universe (
k=0
) and constant Dark Energy equation of state
w: E
2 (
z
)
H
2 (
z
) (1
DE
)(1
H
0 2 Luminosity distance:
z
) 3
DE
(1
z
) 3(1
w
)
d L
(
z
;
DE
,
w
)
r
(1
c
(1
z
)
H
0
z
) (1
z
)
c
(1
z H
0 1
DE
[(1 (1
z
) 3
z
) 3 / 2
w
)
a
2
da E
(
a
1] 1/ 2
dz
) Note:
H 0 d L
is independent of
H 0
31
Dark Energy Equation of State
Curves of constant
d L
at fixed
z
Flat Universe
z
= 32
Exercise 3
• Make the same plot for Worked Example I: plot curves of constant luminosity distance (for several choices of redshift between 0.1 and 1.0) in the plane of , choosing the distance for the model = 0.7,
m
• In the same plane, plot the boundary of the region between
present
acceleration and deceleration.
• Extra credit: in the same plane, plot the boundary of the region that expands forever vs. recollapses. 33
Bolometric Distance Modulus
• Logarithmic measures of luminosity and flux:
M
2.5log(
L
)
c
1 ,
m
2.5log(
f
)
c
2 • Define distance modulus: flux measure redshift from spectra
m
M
2.5log(
L
/
f
)
c
3 2.5log( 4
d L
2 ) 5log[
H
0
d L
(
z
;
m
,
DE
,
w
(
z
))] 5log
H
0
c
4
c
3 • For a population of
standard candles
(fixed
M
), measurements of vs.
z
, the Hubble diagram , constrain cosmological parameters.
34
Exercise 4
• Plot distance modulus vs redshift (
z
=0-1) for: • Flat model with • Flat model with • Open model with
m
m
1 0.7,
m
0.3
0.3
– Plot first linear in
z
, then log
z
. • Plot the residual of the first two models with respect to the third model 35
Discovery of Cosmic Acceleration from High-redshift Supernovae Log(distance) Accelerating Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Not accelerating redshift = 0.7
= 0.
m = 1.
36
Distance Modulus
• Recall logarithmic measures of luminosity and flux:
M i
2.5log(
L i
)
c
1 ,
m i
2.5log(
f i
)
c
2 • Define distance modulus: denotes passband
m i
M j
2.5log(
L
/
f
)
K ij
(
z
)
c
3 2.5log( 4
d L
2 )
K
c
3 5log[
H
0
d L
(
z
;
m
,
DE
,
w
(
z
))] 5log
H
0
K ij
(
z
)
A i
c
4 • For a population of
standard candles
(fixed
M
) with known spectra (
K
) and known extinction (
A
), measurements of vs.
z
, the Hubble diagram , constrain cosmological parameters.
37
K corrections due to redshift
SN spectrum Rest-frame
B
filter band Equivalent restframe
i
band filter at different redshifts (
i obs
=7000-8500 A)
f i
S i
( )
F obs
( )
d
(1
z
)
S i
[
rest
(1
z
)]
F rest
(
rest
)
d
rest
38
Absolute vs. Relative Distances
• Recall logarithmic measures of luminosity and flux:
M i
2.5log(
L i
)
c
1 ,
m i
2.5log(
f i
)
c
2
m i
5log[
H
0
d L
] 5log
H
0
M i
K
(
z
)
c
4 • If
M i
is known, from measurement of
m i
infer distance to object at redshift
z 1
can infer absolute distance to an object at redshift • If
M i
(and H 0 )
un z
, and thereby determine
H 0
(for
z
<<1, known but constant, from measurement of
d L m i =cz/H
can
0
)
relative
to object at distance
z 2
:
m
1
m
2 5log
d
1
d
2
K
1
K
2 independent of
H 0
• Use low-redshift SNe to vertically `anchor’ the Hubble diagram, i.e., to determine
M
5log
H
0 39
Type Ia Supernovae as Standardizable Candles SN 1994D 40
41
SN Spectra ~1 week after maximum light Filippenko 1997 Ib Ia II Ic 42
Type Ia Supernovae
Thermonuclear explosions of Carbon-Oxygen White Dwarfs White Dwarf accretes mass from or merges with a companion star, growing to a critical mass~1.4M
sun (Chandrasekhar) After ~1000 years of slow cooking, a violent explosion is triggered at or near the center, and the star is completely incinerated within seconds In the core of the star, light elements are burned in fusion reactions to form Nickel. The radioactive decay of Nickel and Cobalt makes it shine for a couple of months
Type Ia Supernovae
General properties: • Homogeneous class * of events, only small (correlated) variations • Rise time: ~ 15 – 20 days • Decay time: many months • Bright: M B ~ – 19.5 at peak No hydrogen in the spectra • • • Early spectra: Si, Ca, Mg, ...(absorption) Late spectra: Fe, Ni,…(emission) Very high velocities (~10,000 km/s) SN Ia found in all types of galaxies, including ellipticals • Progenitor systems must have long lifetimes *luminosity, color, spectra at max. light 44
SN Ia Spectral Homogeneity
(to lowest order) from SDSS Supernova Survey
Spectral Homogeneity at fixed epoch 46
SN2004ar z = 0.06 from SDSS galaxy spectrum Galaxy-subtracted Spectrum SN Ia template 47
How similar to one another?
Some real variations: absorption-line shapes at maximum Connections to luminosity?
Matheson, etal, CfA sample
Supernova Ia Spectral Evolution Late times Early times Hsiao etal 49
Layered Chemical Structure provides clues to Explosion physics 50
SDSS Filter
S
( ) 51
Model SN Ia Light Curves in SDSS filters synthesized from composite template spectral sequence SNe evolve in time from blue to red; K-corrections are time dependent
m i
2.5log
S i
( )
F
( )
d
S i
( )
d
i
52
SN1998bu Type Ia Multi-band Light curve
Extremely
few light-curves are this well sampled Suntzeff, etal Jha, etal Hernandez, etal 53
m 15 15 days Time Empirical Correlation: Brighter SNe Ia decline more slowly and are bluer Phillips 1993
SN Ia Peak Luminosity Empirically correlated with Light-Curve Decline Rate Brighter Slower Use to reduce Peak Luminosity Dispersion Phillips 1993 Garnavich, etal Rate of decline
Type Ia SN Peak Brightness as calibrated Standard Candle Peak brightness correlates with decline rate Variety of algorithms for modeling these correlations: corrected dist. modulus After correction, ~ 0.16 mag (~8% distance error) Time 56
Published Light Curves for Nearby Supernovae Low-
z
SNe: Anchor Hubble diagram Train Light curve fitters Need well sampled, well calibrated, multi-band light curves 57
Carnegie Supernova Project Nearby Optical+ NIR LCs 58
Correction for Brightness-Decline relation reduces scatter in nearby SN Ia Hubble Diagram Distance modulus for
z
<<1:
m
M
5log 5log
H
0 Corrected distance modulus is
not
a direct observable: estimated from a model for light-curve shape Riess etal 1996 59
Acceleration Discovery Data: High-z SN Team
10 of 16 shown; transformed to SN rest-frame Riess etal Schmidt etal V B+1 60
Discovery of Cosmic Acceleration from High-redshift Supernovae Apply
same
brightness-decline relation at high
z
Type Ia supernovae that exploded when the Universe was 2/3 its present size are ~25% fainter than expected Log(distance) HZT SCP Accelerating Not accelerating redshift = 0.7
= 0.
m = 1.
61
Likelihood Analysis
Data Model 2ln
L
(
i i
(
z i
;
m
, ,
H
0 ) 2 2 This assumes errors in distance modulus estimates are Gaussian. More details on this next time.
62
63
Exercise 5
High-Z Supernova Data of Riess, etal 1998: see following tables. Assume a fixed Hubble parameter for this exercise.
• Extra credit: marginalize over
H 0
with a flat prior. 64
Riess, etal High-z Data (1998)
65
Low-z Data
66