Post on 25-Nov-2021
Type Ia Supernovaeas
Distance IndicatorsPhilip A. Pinto
Steward Observatory
University of Arizona
Type Ia SupernovaeasDistance Indicators – p.1/45
Cosmic Connections
In an FRW universe, luminosity distance is
��� ��
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� � � � � � � �� �� � � � � � � �� � ��
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#
with curvature parameter �
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%%&�
' (*) ��$ � � + ,.-
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Type Ia SupernovaeasDistance Indicators – p.2/45
Comparing expansion velocity (� ) with luminosity distance (
��� )type Ia supernovae (SNe Ia)
have provided best measurement of current expansion rate
�� �� �
��������
today
gave the first hard evidence for an additional component (darkenergy)
� � �
� �
� �� �� �
allow measurement of the EOS of dark energy, and perhapseven �� �
� � � � � � �
Type Ia SupernovaeasDistance Indicators – p.3/45
Measuring redshift is easyby spectroscopy of known atomic transitionswith laboratory wavelength calibration.
Measuring distance is hardthere is no easily-determined standard of length for calibration.
This has always been a central problem in astronomy
Type Ia SupernovaeasDistance Indicators – p.4/45
Standard Candles
Favorite astronomical technique:
Discover a class of bright objects
Assert they all have the same luminosity – a “standard candle”
Measure the flux from the object and assign a distance
When possible, try to reduce dispersion in distance bycorrelating luminosity with an easily-measured surrogateparameter.
Type Ia SupernovaeasDistance Indicators – p.5/45
The problems with this process have been understood for a longtime...
The distance to a light cannot beestimated from its apparent brightness.There are too many factors which canchange the perceived intensity.
(Bowditch, American Practical Navigator, 1802)
Type Ia SupernovaeasDistance Indicators – p.6/45
How good are SNe Ia as standardcandles?
What systematic effects may be lurking in cosmologicalmeasurements made with them?
measurement problems, e.g. K-corrections
statistical problems, e.g. sample biases
Intervening material: extinction, gravitational lensing
Evolution of sample properties:are SNe Ia the same at� � as in the local sample at� � ,
?
Type Ia SupernovaeasDistance Indicators – p.7/45
Type Ia Supernovae: observed
� �� �� � � ���
(w/ � �
mag)
Peak phase lasts � ,
days (in co-moving frame!)
Unique lightcurve shape and colors.
Unique spectrum:early: Si, S, Ca, He, (C?), Fe, no H
late: Fe, Co, Ni, (Si?) after 100
�or so
Seen in all types of galaxies.
Rate:
,�� � ,�� , �
SNU (Hamuy & Pinto 1999)(1 SNU � �� � , � � � �� ��� �� ��� �� )
Type Ia SupernovaeasDistance Indicators – p.8/45
SNe Ia as Standard Candles
A good standard candle has the smallest possible range in luminositySNe Ia exhibit
� � �� �� � �
( � �
in L)� too large for precision cosmology
Phillips (’93) discovered that the width of the lightcurve peak iscorrelated with the peak luminosity:Brighter � Broader
time20
15 d
MB
15M∆
Larger
��� smaller
���
Can use the� � ��
relation to
“standardize” the candle
to �� ��� �
mag
Type Ia SupernovaeasDistance Indicators – p.9/45
Three Techniques (same sample!)� �� : initerpolate in �� among a set of fiducial lightcurvesfrom nearby sample. (Hamuy et al.1996)
MCLS: fit to one-parameter family of lightcurves derived fromthe same fiducial sample (Riess et al.1998)
Stretch Factor: use a relation beween��� � � ��� � and ��� �
derived from the nearby sample (Perlmutter et al.1998)
All three methods have similar statistical properties and all usevirtually the same “training set” of nearby supernovae.
Type Ia SupernovaeasDistance Indicators – p.10/45
The Luminosity-Width Relation
Broader is BrighterIn all three techniques, a width parameter is proportional topeak magnitude:� can “correct” all SNe Ia to a fiducial width
(
��� �� � � )
Phillips et al.(1999) show that colors converge in nebular phase� can do accurate de-reddening
Calán-Tololo survey provides a well-observed sample of � � ,
SNe Ia for calibration
� SNe Ia are very good “standard candles” once calibrated:
� � ,�� �
mag
�� � ,�� mag
dispersion in
Hubble diagram
Type Ia SupernovaeasDistance Indicators – p.11/45
Reddening-Free Luminosity-Width Relation (Phillips et al.1999)
Type Ia SupernovaeasDistance Indicators – p.12/45
In the stretch factor methoda scaling of the time axis iscorrelated with an offset inluminosity
Type Ia SupernovaeasDistance Indicators – p.13/45
Effects of reddening and
� �� corrections (Phillips et al.1999)
3.5 4 4.5log(czCMB)
33
35
37
39
Ho = 64.1 ± 2.8σ = 0.14 mag
33
35
37
39
(m−
M)
Ho = 64.3 ± 3.2σ = 0.18 mag
33
35
37
39
Calan/Tololo "Low Extinction" Sample
Ho = 57.7 ± 3.5σ = 0.24 mag
Corrected for: Galactic Reddening
Corrected for: Galactic Reddening ∆m15(B) vs. Mmax
Corrected for: Galactic Reddening Host Galaxy Reddening ∆m15(B) vs. Mmax
Type Ia SupernovaeasDistance Indicators – p.14/45
Local Hubble diagram scatter � ,
%: (Perlmutter & Schmidt 2003)
Type Ia SupernovaeasDistance Indicators – p.15/45
Questions:What are SNe Ia?
Where do they come from?How do they work?
The luminosity-width relation is the crux of the measurement.Where does it come from?How reliable is it?
What systematic effects might it exhibitas we observe SNe at ever-higher redshift
(i.e. longer look-back times)as we require ever-smaller systematic errors
(e.g. to measure �� �
Type Ia SupernovaeasDistance Indicators – p.16/45
Type Ia Supernovae
Thermonuclear incineration of a C/O white dwarfHe dwarf � too energetic an explosionNe/Mg/O dwarf collapses to NS
Mass probably near 1.35 M �
Kinetic energy � ,� �
erg 0 � + � � , , ,
km s
� �
“Burns” C/O into0.05 - 0.9 M �
� �
Ni (NSE)0.2 - 0.9 M � Si - Ca (incomplete burning)
Luminous output powered entirely by the decay chain� �
Ni � � � � �
���
� �� ��� �
Co � � � � �
� � � �� ��� �
Fe
Type Ia SupernovaeasDistance Indicators – p.17/45
Significant uncertainty surround the details of these explosions
Progenitor populationaccreting white dwarf or “double-degenerate”
Evolution to explosion
Ignition physics
Nature of combustionturbulent burninglarge-scale instabilitiesdeflagration/detonation transition
Type Ia SupernovaeasDistance Indicators – p.18/45
Current evolution/explosion scenarios are notsufficiently predictive to reliably assessevolutionary effects
Given an explosion, what can we say about theluminosity-width relation?
Type Ia SupernovaeasDistance Indicators – p.19/45
10-3
10-2
10-1
100
mas
s fr
actio
n Mg
O
C
Si
Si
Si
SiSi
SS
SS
SAr
ArAr Ar
Ca Ca
CaCa52Fe 52Fe
52Fe
54Fe 54Fe
54Fe54Fe
56Ni 56Ni 56Ni
56Ni
0 0.2 0.4 0.6 0.8 1.0 1.210-13
10-12
10-11
10-10
10-9
M/Msun
dens
ity
ρ ρρ ρ
ρ
velocity
vv
vv
v
0
109
2×109
Type Ia SupernovaeasDistance Indicators – p.20/45
Lightcurve Physics
Three timescales:
�
PdV
� �
: shortly after explosion, radiation energy is PdV’daway to kinetic energy.
�
escape
� ���
: as
�
increases, an increasing fraction of depositedenergy from decay diffuses out and escapes conversion tokinetic energy
�
heat
� �
decay : energy deposition drops rapidly
lightcurve peaks when �
escape
� �
Type Ia SupernovaeasDistance Indicators – p.21/45
103 104
10-18
10-17
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
bound-free
free-free
e-
lines
wavelength [A]
opac
ity [c
m-1]
Type Ia SupernovaeasDistance Indicators – p.22/45
Opacity is dominated by spectral lines below critical density� modified diffusion
Time spent rattling about with small mfp in a line « time spentbetween lines: each line acts as a single interaction.
mfp �� � �
� � �� - dist. between lines
optical depth � # of lines traversed
opacity � spectral density of lines
Type Ia SupernovaeasDistance Indicators – p.23/45
1000 2000 3000 4000 5000 6000 7000 8000
101
102
103
τ>67 τ>6.7τ>2/3
all lines
wavelength [A]
num
ber
of li
nes
with
in 1
04 km
s-1 to
red
10000 K
20000 K30000 K
Type Ia SupernovaeasDistance Indicators – p.24/45
Optical depth in blue remains very high as the # of lines doesnot change rapidly
Diffusion time would be hundreds of days, yet lightcurve peaksat � 20 days.
Optical depth in red is small, even at maximum light
Type Ia SupernovaeasDistance Indicators – p.25/45
opacity aises in nearly-neutral iron-group ions with verycomplex spectra – thousands of optical transitions
density of the supernova is low � slow electron collision ratecannot couple radiation and matter distributions
In an iron-group plasma, fluorescence most common result ofradiative absorption:
photon absorption is followed by raditive cascade, effectively“splitting” blue photons into many red photons
Type Ia SupernovaeasDistance Indicators – p.26/45
Type Ia SupernovaeasDistance Indicators – p.27/45
2000 4000 6000 8000
10-5
10-4
10-3
wavelength
lum
inos
ity
30000 K20000 K
10000 K
σ = 0.25ε = 0
Type Ia SupernovaeasDistance Indicators – p.28/45
Supernova is less than a thermalization length thick
(Lucy)
103 1041037
1038
1039
1040
1041
wavelength [A]
L λ [e
rg s
-1 c
m-2 A
-1]
Type Ia SupernovaeasDistance Indicators – p.29/45
At peak (20
�
) the interior of the SN is a radiation-dominatedgas at
� � , �
K, w/ peak
� � , ,
Å
UV opacity is very large & evolves only slowly� diffusion time in blue is �500 days
Energy escapes where it can, as optical/IR flux where
� � � � �
.
Transport in energy longward in wavelength is thus moreimportant than outward in radius.
Energy escape is mediated by fluorescence.
Type Ia SupernovaeasDistance Indicators – p.30/45
Rate at which stored UV energy can be converted to low- �
wavelengths determines the bolometric lightcurve
What transitions are available is set by the ionization state
Less-ionized species have redder lines than more-ionized ones� ionization determines the color evolution & the effectiveopacity
More
� �
Ni � higher ionization � bluer transitions � highereffective opacity � BROADER LIGHTCURVE
More heating � BRIGHTER LIGHTCURVE
M � is the “hidden parameter” inthe luminosity width relation
Type Ia SupernovaeasDistance Indicators – p.31/45
Consequences for the luminosity-width relation:
Because spatial transport is less important, how thecomposition of the explosion is distributed may not stronglyaffect the lightcurve.
Higher velocities lead to larger numbers of lines traversed, sothat explosion energy might vary the width independently ofM� � and hence luminosity
Complex physical system demands a detailed numerical simulation...
Type Ia SupernovaeasDistance Indicators – p.32/45
An Experiment
Use the time-dependent, �-ray/optical NLTE transport codeEDDINGTON (Pinto & Eastman 1993-2001) to perform a simpleexperiment.
Take a single explosion model (from Weaver & Woosley):
vary M� �
(most energy comes from C � Si)
vary radial distribution of composition, esp.
� �
Ni.
vary stable Fe/Ni ratio(effect of non-radioactive composition)
vary kinetic energy
Type Ia SupernovaeasDistance Indicators – p.33/45
10-3
10-2
10-1
100
mas
s fr
actio
n Mg
O
C
Si
Si
Si
SiSi
SS
SS
SAr
ArAr Ar
Ca Ca
CaCa52Fe 52Fe
52Fe
54Fe 54Fe
54Fe54Fe
56Ni 56Ni 56Ni
56Ni
0 0.2 0.4 0.6 0.8 1.0 1.210-13
10-12
10-11
10-10
10-9
M/Msun
dens
ity
ρ ρρ ρ
ρ
velocity
vv
vv
v
0
109
2×109
Type Ia SupernovaeasDistance Indicators – p.34/45
Result is a time series of spectra for each explosion.
Spectra are integrated over broadband BVR filters to yieldlightcurves
Synthetic lightcurves are then “reduced” to determine� �� as in Hamuy et al.1990 (template fitting)�
as in Riess et al.1996 (one-D family of lightcurves)
This leads to a synthetic luminosity-width relation for the variedexplosion model
Type Ia SupernovaeasDistance Indicators – p.35/45
wavelength [A]
lum
inos
ity [L
sun
s-1 A
-1]
SN 1992A
DD4
10 days past peak
2000 3000 4000 5000 6000 7000 8000 9000
104
105
106
Type Ia SupernovaeasDistance Indicators – p.36/45
0 10 20 30 40 50
-17
-18
-19
-20
days past explosion
MV
M56 = 0.27
M56 = 0.90
Models vs MCLS Templates
V lightcurves are good fit within � 30 days from peakand reproduce brighter � broader behavior
Type Ia SupernovaeasDistance Indicators – p.37/45
-10 0 10 20 30
M56 = 0.55
0 10 20 30 40 50-17
-18
-19
-20
days past explosion
days from B maximum
M
B
B
B
B
B
B
V
VV
V
V
V
V
V
R
R R
R
R
R
R
Multicolor lightcurves are a tolerably good fit to the MCLS templates
Type Ia SupernovaeasDistance Indicators – p.38/45
-10 0 10 20 30
M56 = 0.90
0 10 20 30 40 50-17
-18
-19
-20
days past explosion
days from B maximum
MB
B
B
B
B
B
B
V
V VV
V
V
V
R
R R
R
R RR
for a variety of
� �
Ni masses
Type Ia SupernovaeasDistance Indicators – p.39/45
models vs Cepeid-calibrated MCLS relation
-19
-19.5
-20
peak
MV
20 days
-.5 0 .5
-19
-19.5
-20
peak
MV
40 days
∆
K.E.
K.E.
Co->Fe
Co->FeH
H
0.90 0.63 0.48 0.37 0.28M56=
Type Ia SupernovaeasDistance Indicators – p.40/45
models vs Phillips et al.1999 calibration
.8 1 1.2 1.4 1.6 1.8
-18
-19
-20
∆m15
peak
MV Co -> Fe
K.E.H
Type Ia SupernovaeasDistance Indicators – p.41/45
Result
Luminosity-width relation is remarkablyinsensitive to variations in the underlyingexplosionssystematic effects in the explosion must besevere to significantly alter the calibration
Best Bet: evolutionary effects are unimportant(but of course these are only models...)
Type Ia SupernovaeasDistance Indicators – p.42/45
Observational Tests
Spread in metallicity and age in nearby galaxies exceeds thechange in the mean out to� �
Using a well-observed nearby sampleno correlation of
� �� with population ages in early-typegalaxiesweak correlation of metallicity and
� �� in early-typegalaxiesno correlation of projected radius and lightcurve width inlate-type galaxiesstrong tendency for brighter SNe in late-type galaxies
Might this affect measurements of ?
Type Ia SupernovaeasDistance Indicators – p.43/45
Most importantly,
Residuals from the luminosity-width relation do not correlate withcolor, metallicity, or age of progenitor population
It is unlikely that evolutionary effects areimportant to interpreting the supernovacosmology results.
Type Ia SupernovaeasDistance Indicators – p.44/45
The type Ia supernova Hubble diagram is an important tool formeasuring the rate of cosmic expansion, especially incombination with other tools such as weak lensing
Current projects such as the ESSENCE survey are extendingthe sample of intermediate-redshift SNe significantly
In the next decade, projects such as SNAP and LSST willproduce highly uniform samples of thousands of well-observedSNe Ia with much finer control of observational systematics
Type Ia SupernovaeasDistance Indicators – p.45/45