Type Ia Supernovae Distance Indicators · Comparing expansion velocity ( ) with luminosity distance type Ia supernovae (SNe Ia) have provided best measurement of current expansion

Type Ia Supernovaeas

Distance IndicatorsPhilip A. Pinto

Steward Observatory

University of Arizona

Type Ia SupernovaeasDistance Indicators – p.1/45

mailto:[email protected]

Cosmic Connections

In an FRW universe, luminosity distance is

��

��

��

� � ��

��

� � � � � � � ��

� !"

#

with curvature parameter �

� ��

� � � and

� ��$ � ��

%%&�

' (*) ��$ � � + ,.-

$ � � ,.-

' (*) / ��$ � � 0 ,


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 ��

� � � � � � �


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


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.


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)


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 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 � �� , � � � �� )


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


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.


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


Reddening-Free Luminosity-Width Relation (Phillips et al.1999)


In the stretch factor methoda scaling of the time axis iscorrelated with an offset inluminosity


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


Local Hubble diagram scatter � ,

%: (Perlmutter & Schmidt 2003)


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 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


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


Current evolution/explosion scenarios are notsufficiently predictive to reliably assessevolutionary effects

Given an explosion, what can we say about theluminosity-width relation?


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


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

� �


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]


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


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


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


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



2000 4000 6000 8000

10-5

10-4

10-3

wavelength

lum

inos

ity

30000 K20000 K

10000 K

σ = 0.25ε = 0


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]


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.


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


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...


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


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


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


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


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


-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


-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


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=


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


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...)


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 ?


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.


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


Documents

Type Ia Supernovae Distance Indicators · Comparing expansion velocity ( ) with luminosity distance type Ia supernovae (SNe Ia) have provided best measurement of current expansion