Redshift, Distances andHubble-Law

Max CamenzindIMPRS Cosmology 2009

Day 2/1

Edwin Hubble – Pioneering Expansion

Topics

• Redshift of Galaxies• Redshift of Quasars• How to measure distances to Galaxies: Cepeheids (standard) Geometric distances (exception) Supernovae as Standard Candles• The Hubble-Law (1929)• How to measure the Hubble Constant?

Galaxy-Spectra

havecharac-teristicAbsorp-

tion lines

• All these Absorption lines are shifted by the Expansion of the Cosmos towards the red, no blueshifts.

• Today: Measurements upto z ~ 7.

Redshift, Distance and the Hubble LawRedshift, Distance and the Hubble Law

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z = λ − λ0

λ0

= ∆λλ0

z - redshift

λ0 - restframe wavelength

λ - measured wavelength

Redshift of Galaxies

• Utilizing the 100-inch telescope at California's Mount Wilson Observatory (at the time the world's largest telescope) Hubble obtained spectra and measurements of the distance to a few dozen galaxies, leading to the discovery that the Universe is expanding. Hubble compared recession velocities of galaxies measured from their spectra to their apparent brightness estimated from photographic plates. In 1929 Hubble published his findings, detailing revealed that the fainter and smaller a galaxy appeared, the higher was its redshift.

Quasars have characteristic redshifted Emission-Line Spectra

z = 4,58

z = 4,96

Distance IndicatorsDistance IndicatorsDistance Indicators

• Measurement of distance is very important in cosmology• However measurement of distance is very difficult in cosmology• Use a Distance Ladder from our local neighbourhood to cosmological distances

Primary Distance Indicators ➠ direct distance measurement (in our own Galaxy) Secondary Distance Indicators ➠ Rely on primary indicators to measure more distant object.  Rely on Primary Indicators to calibrate secondary indicators!

Parallaxes - Galactic Distances

• Geometrische Distanzen: Parallaxen-methode, beschränkt auf Galaxis, p = 1“ 1 Parsek Hipparcos, GAIA (~100 kpc)

Primary Distance IndicatorsPrimary Distance IndicatorsTrigonometric Parallax• GAIA MISSION (ESA launch 2012 - lifetime ~ 5 years)• Measure positions, distances, space motions, characteristics of one billion stars in our Galaxy.• Provide detailed 3-d distributions & space motions of all stars, complete to V=20 mag to <10-6”.• Create a 6-D map of Galaxy: angles, distance and velocities

Distances for Galaxies

• Geometrical Distances (mostly impossible).• Standard-Candles: d² = L / 4π f• (i) RR-Lyrae Stars (~ 0,5 Solar mass),

Riesensterne der Spektralklasse A, F, Pulsationsveränderliche (h Bereich)

• (ii) Delta Cephei Stars ( < 20 Mpc)• (iii) brightest stars (not well defined)• (iv) Central stars in Planetary nebulae• (v) Supernovae of Typ Ia ( z < 2 )

HR Diagram of Globular Cluster M 55

High-mass stars evolved onto the

giant branch

Low-mass stars still on the main sequence

Turn-off point

Horizontalbranch

RR Lyr

Pulsating or “Variable” Stars

• Instability- strip in HRD

• “Cepheids” are very bright Stars !

radialI7-50dClassical Cepheids-L

non radialI1-20minZZ Ceti stars

radial/non radialI1-3hrδ Scuti stars

radial/non radialI3-7hrß Cephei stars

radialII1-24hrRR Lyrae

radialII2-45dW Virginis (PII Ceph)

radialI1-6Classical Cepheids-S

radialI, II100-700dLPV*

PulsationPopPeriodType

Cepheids Observed for >100 Years• A Cepheid variable is a member of a particular class of variable stars, notable for tight correlation between their period of variability and absolute luminosity.

• Namesake and prototype of these variables is the star Delta Cephei, discovered to be variable by John Goodricke in 1784.

• This correlation was discovered and stated by Henrietta Swan Leavitt in 1908 and given precise mathematical form by her in 1912.

• Period-luminosity relation can be calibrated with great precision using the nearest Cepheid stars.

• Distances found with this method are among the most accurate available.

- Leavitt, Henrietta S. "1777 Variables in the Magellanic Clouds". Annals of Harvard College Observatory. LX(IV) (1908) 87-110. - Miss Leavitt in Pickering, Edward C. "Periods of 25 Variable Stars in the SMC". Harvard College Observatory Circular 173 (1912) 1-3.

Stellar Evolution: Variable Stars

Einige Sterne zeigen intrinsische Helligkeitsvariationen, die nicht auf Verdunklung im Doppelsternsystem

zurückgehen.

Prominent Example:δ Cephei

Light Curve of δ Cephei

Cepheid MechanismCepheid usually a population I giant yellow star, pulsing regularly by expanding and contracting, regular oscillation of its luminosity from 103 to 104 times L☼

Cepheids, population I stars: “Type I Cepheids”, Similar (population II) W Virginis: Type II Cepheids.

Luminosity variation due to cycle of ionization of helium in the star's atmosphere, followed by expansion and deionization. Key: ionized, the atmosphere more opaque to light.

Period equal to the star's dynamical time scale: gives information on the mean density and luminosity.

Cepheids as Standard-CandlesHenrietta Leavitt 1912

Henrietta Leavitt’s Original Data

The “Period” (Duration) of Pulsation correlates with the Luminosity

• Measure Measure PeriodPeriod

• Measure Measure LuminosityLuminosity

• Measure Measure apparent apparent MagnitudeMagnitude

• Distance Distance !!

The Luminosity of observed the Star ~1500L

Cepheiden: Die Periode-Leuchtkraft Relation

Die Periode eines Cepheiden ist mit der Leuchtkraft korreliert.

Messen der Periode bestimmt die Leuchtkraft !

Relation muss geeicht werden ! (LMC)

Je heller, desto langsamer pulsiert der Stern.

The LMC PC RelationSandage et al (2004)

�

Non-Linearity of the V-Band LMC PL Relation

OGLE data MACHO data

Hubble Rocks!

Nearby Galaxy DistancesCepheids in M100

Hubble found in 1929, that more distant Galaxies show apparently bigger Redshifts.

• Measure Redshift “z”, and derive from this “Expansion Velocity”

zcv ×=

€

z ≡ ∆ λλ

Distance

velo

city

The original Hubble Diagram(Galaxies)

“Hubble Diagram”• Hubble

velocity is proportional to Distance:

• H0 is the “Hubble Constant”, Units: km/s/Mpc

DHv 0=

A modern Hubble Diagram

Rotverschiebung Distanz

€

v =H0d

zcv ×=

• Messe Rotver-schiebung z.

• V

• Hubble Gesetz Distanz d

Messe dies …

…

The History-I of H0

The History-II of H0

The Distance LadderThe Distance Ladder Virgo Cluster Distance Virgo Cluster Distance

Comparison eight main methods used to find the distance to the Virgo cluster.

19.4 ±5.0Type Ia Supernova8

16.8 ±2.4Faber Jackson7

15.8 ±1.5Tully Fisher6

15.9 ±0.9Surface Brightness5

18.8 ±3.8Globular Cluster4

15.4 ±1.1Planetary Nebula3

21.1 ±3.9Novae2

14.9±1.2Cepheids1

Distance MpcMethod

Jacoby etal 1992, PASP, 104, 599

HST Measures distance to Virgo (Nature 2002) D=17.1 ± 1.8Mpc

The Distance Ladder (old)The Distance Ladder (old)

RADAR Reflection (0-10AU)

Parallax (0.002-0.5kpc)

Spectroscopic Parallax (0.05-10kpc)

RR Lyrae (5-10kpc)

Cepheid Variables (1kpc-30Mpc)

Tully Fisher (0.5-00Mpc)

Supernova (1-1000Mpc)

1kpc

10kpc

100kpc

1Mpc

10Mpc

100Mpc

1000Mpc

Proxima Centauri (~1pc)

Pleides Cluster (~100pc)

Galactic Centre (~10kpc)

LMC (~100kpc)

M31 (~0.5Mpc)

Coma (~100Mpc)

Virgo (~10Mpc)

Hubble Sphere (~3000Mpc)

Tully-Fisher RelationTully-Fisher RelationRedshift

Blueshift

∆ν

Flux

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v R2

R= G M

R 2Centrifugal Gravitational

€

l =M /LAssume same mass/light ratio for all spirals

€

σ=L / R 2Assume same surface brightness for all spirals

€

L = v R4

σ l 2 G 2 ∝ v R4

In Magnitudes

€

M = M o −2 .5 lgL

L o

= M o −2 .5 lg

C v R4

L o

€

M = − 1 0 l g ( v R ) + C

M = − a l gW o

s i n i

− bMore practically

Wo = spread in velocitiesi = inclination to line of sight of galaxy

A sample of TF profiles - from Haynes et al. (1999, ApJ, 117, 2039)

Surface BrightnessFluctuations

• The SBF Method measures the irreducible mottling in an early-type galaxy image due to the Poisson fluctuations in the finite number of stars per pixel. It was pioneered by John Tonry and Don Schneider (1988, AJ, 96, 807). The method has important applications for both extragalactic distance and stellar population studies.

The Hubble Key ProjectThe Hubble Key Project

€

cz =H odThe Hubble Constant • Probably the most important parameter in astronomy• The Holy Grail of Cosmology • Sets the fundamental scale for all cosmological distances

The Hubble Key ProjectThe Hubble Key Project

€

cz =H od

Cepheids in nearby galaxies within 12 million light-years. Not yet reached the Hubble flow Need Cepheids in galaxies at least 30 million light-years away Hubble Space Telescope observations of Cepheids in M100. Calibrate the distance scale

Observations with HST to determine the value of the Hubble Constant to high accuracy• Use Cepheids as primary distance calibrator• Calibrate secondary indicators

• Tully Fisher•Type Ia Supernovae• Surface Brightness Fluctuations• Faber - Jackson Dn-σ relation• Comparison of Systematic errors• Hubble Constant to an accuracy of ±10%

Hubble’s Law (Hubble Key Project)

Freedman et al. (2001), The Astrophysical Journal 553, 47

HubbleKeyProject2003

AllData

H0 = 71±6 km s-1 Mpc-1 → τ0 = 1.3 × 1010 yr

Since 1997 SNe Ia as Standard Candles

• A Type Ia supernova is a sub-category of cataclysmic variable stars that results from the violent explosion of a white dwarf star. A white dwarf is the remnant of a star that has completed its normal life cycle and has ceased nuclear fusion.

Tycho supernova (1572) Type Ia

SN Iaare bright

CosmologicObjects

SNe appear asas bright asthe center ofa Galaxy

SN 1994D CO White Dwarfat Chandrasekharlimit

Krisciunas et al. (2003)

The nearby SNe Ia•excellent coverage for a few objects–fairly complete picture–allows detailed comparisons with models

SN 2003duEuropean Supernova Collaboration

© SDSSII

Supernovae in the Cosmos

Defining Properties of Supernovae

Supernova Light Curves

Typical SN Ia

Peak brightness

Lightcurve width

(stretch)

Historical Supernovaein our Galaxy

IaEU, Chi> JupiterKepler SNR12 MonOphiuchuAD 1604

n ? ---Cas A SNR ?CassiopeiAD 1670

IaEU, Chi,VenusTycho SNR18 MonCassiopeiAD 1572

npChinaSirius3C 586 MonCassiopeiAD 1181

npChina,VenusKrebsnebel

21 MonTaurusAD 1054

nChina, Japan

10 x Venus

SNR 10063 yrLupusAD 1006

?ChinaJupiter ?8 MonScorpiusAD 393

npChina ?G11.2 –0.33 MonSagittariAD 386

nChinaMarsRCW 861 yrCentaurAD 185

NSObservMagnitudRemnantVisibleConstellatDate

Cra

b N

ebul

a 10

54 (T

yp I)

Cha

ndra

(b),

HS

T (g

), S

pitz

er (r

)

PulsarNS

ThermischeFilamente

SN

R 1

006

Cha

ndra

ThermalNS

Cas

A /

Cha

ndra

ThermalNS

Suntzeff

Observat-ions

Super-nova

SN87Ain the LMC

SINS

Progenitor of SN 1987A

The Distance to SN 1987Ad = 51.2 ± 3.1 kpc… occurred at167,000 yrs ago!

• From the abstract of the Panagia et al (ApJL 380, L23):• We have determined the distance to the SN 1987A by

comparing the angular size of its circumstellar ring measured from an HST (Hubble Space Telescope) image ... with its absolute size derived from an analysis of the light curves of narrow UV lines ... measured with IUE (International Ultraviolet Explorer).  Our analysis confirms that the observed elliptical structure is indeed a circular ring at an inclination of 42.8° ± 2.6°. and provides a determination of its absolute diameter (1.27 ± 0.07) x 1018 cm.  Its ratio to the angular diameter of 1.66" ± 0.03" ... gives an accurate determination of the

• distance to SN 1987A ... = 51.2 ± 3.1 kpc....  • This value agrees very well with the determinations

obtained from light-curve analysis of variable stars.

Accretion onto WD SN Ia

• Weißer Zwerg akkretiert H vom Roten Riesen• H fusioniert stetig zu He Bildung einer Heliumhülle• Massenzunahme bis Chandrasekhargrenze

Red Giant White Dwarf

The “standard model”

He (+H)from binarycompanion

• Explosion energy:

•Fusion of•C+C, C+O, O+O • ⇒ "Fe“

Density ~ 109 - 1010 g/cm

Temperature: a few 109 K

Radii: a few 1000 km

C+O,C+O,

M ≈ MM ≈ Mchch

There is a lot more to this – you need to contact your explosive theory friends

Fusion Reactions in SN IaStarting reactions

Coulomb barrieres hohe Zündtemperaturen und niedrige Reaktionsraten

T ≈ 7 x 108 K

ρ ≈ 2 x 109 g/cm³

(α,γ) – chains are more effective

No elements heavier than 56Ni created!

4 4 8 12 16 20 24 28 56He He Be C O Ne Mg Si Ni+ → → → → → → → →K

4He 4He 4He 4He 4He 4He+ + + + + +

12 12 20 4

12 12 16 4

16 12 24 4

16 16 28 4

2C C Ne HeC C O HeO C Mg HeO O Si He

+ → ++ → ++ → ++ → +

Supernova explosions

Courtesy F. Röpke

t=0.0s

Pushing simulations to the limit

t=0.6st=3.0st=10.0s

Courtesy F. Röpke

SN Light Curve Simulationss

Kasen 2006

SN 2001el

Are SNe Ia standard candles?• No!

– large variations in• light curve shapes• colours• spectral evolution• polarimetry

– some clear outliers• what is a type Ia supernova?

– differences in physical parameters• Ni mass• ejecta mass

Supernovae as ‘standard candles’

• Uniform appearance– light curves

• individual filters• bolometric

– colour curves • reddening?

– spectral evolution– peak luminosity

• correlations

Phillips et al. 1999

Jha 2005

Lichtkurven SN IaAbsolute Helligkeit: bis -19,5 mag

Radioaktiver Zerfall von 56Ni zu 56Fe verzögert Abkühlung

56Ni 56Co 56Fe + e+9 Tage 112 Tage

Ähnlicher Verlauf Standardkerze

e

10 Mrd. Le

SN Ia Standard Candle M = - 19,5

“PhillipsPhillips relationrelation”: A correction to SN Ia light-curves based on light-curve

shape drastically improves the quality of the standard candle.

Time Time

Brig

htne

ss

Brig

htne

ss

Brig

htne

ss

Brig

htne

ss

Time Time

5656Ni Ni 5656Co Co 5656Fe powers the SN Ia Fe powers the SN Ia light-curvelight-curve

Conventional Wisdom:Conventional Wisdom:

SNe are a one-parameter family SNe are a one-parameter family defined by amount of defined by amount of 5656Ni Ni

synthesized in the explosion. synthesized in the explosion.

More More 5656Ni Ni greater luminosity greater luminosity higher Temperatures higher Temperatures

higher opacity higher opacity broader LC broader LC

Making a Standard Candle1. “PhillipsPhillips relationrelation”: A correction to SN Ia light-curves based on light-

curve shape drastically improves the quality of the standard candle.

Brig

htne

ss

Brig

htne

ss

Brig

htne

ss

Brig

htne

ss

Time Time

20%20%

7%!7%!

Many methods:

• Stretch – Perlmutter 97, 99

• (M)LCS(2k2) – Riess, 95,96, Jha 07

• SALT(2) – Guy 05, 07

• SiFTO – Sullivan 07

• CMAGIC – Wang et al.; Conley 06

• Δm15 – Phillips 93; Hamuy 95; Prieto 06

2. SN colour: A correction to the SN luminosity based on the SN colour

Absolute Magnitudes SNe IaSN Galaxy m-M MB MV MI ∆ m15

1937C IC 4182 28.36 (12) -19.56 (15) -19.54 (17) 0.87 (10)1960F NGC 4496A 31.03 (10) -19.56 (18) -19.62 (22) 1.06 (12)1972E NGC 5253 28.00 (07) -19.64 (16) -19.61 (17) -19.27 (20) 0.87 (10)1974G NGC 4414 31.46 (17) -19.67 (34) -19.69 (27) 1.11 (06)1981B NGC 4536 31.10 (12) -19.50 (18) -19.50 (16) 1.10 (07)1989B NGC 3627 30.22 (12) -19.47 (18) -19.42 (16) -19.21 (14) 1.31 (07)1990N NGC 4639 32.03 (22) -19.39 (26) -19.41 (24) -19.14 (23) 1.05 (05)1998bu NGC 3368 30.37 (16) -19.76 (31) -19.69 (26) -19.43 (21) 1.08 (05)1998aq NGC 3982 31.72 (14) -19.56 (21) -19.48 (20) 1.12 (03)Straight mean -19.57 (04) -19.55 (04) -19.26 (06)Weighted mean -19.56 (07) -19.53 (06) -19.25 (09)

Saha et al. 1999

Distances in locale Universe

• Expansion is linear, i.e. use theHubble-Law

• v = cz = H0·D• Use Distance-Modulus

• µ = m - M = 5 log(D/10pc) • Distances for ‘Standard Candles’

(M=const.)• m = 5 log(cz) + b

• b = M + 25 – 5 log(H0)

Hubble-Diagram of Local SN Ia

m = 5 log10(cz) + b

MpcskmH

⋅±= 10700

Type Ia Supernovae

(Knop et al. 2003)

Redshift (amount universe “stretched” since the object’s light was emitted)

How

fai

nt e

ach

obje

ct a

ppea

rs (

whe

n vi

ewed

fro

m E

arth

)

≈ Velocity

≈ D

ista

nce

The currently most complete SN Ia sample

(Riess et al. 2007)

• Collected all available distant SNe Ia– Riess et al. (2004)– Astier et al. (2006)– Wood-Vasey et al. (2007)

23 SNe Ia with z>1 total of 182 SNe Ia with z>0.0233

(v=7000 km/s)lower redshift limit to avoid any local effects

SN Ia Hubble Diagram

Riess et al. 2007

• Luminosity distance in an isotropic, homogeneous universe as a Taylor expansion (see Lecture Friedman model)

+

±+−−−−+= )(31

61)1(

211 32

220

2

02000

0

zOzRH

cjqqzqHczDL

aaH

=02

00−−= H

aaq 3

00−= H

aaj

Corrections to the Hubble-Law

SupernovaeProjects

ESSENCECFHT Legacy Survey

Higher-z SN Search(GOODS)

SN FactoryCarnegie SN ProjectSDSSII

SNAP/DUNE/SPACE/LSST Future

Plus the local searches:LOTOSS, CfA, ESC

Summary• The Universe of galaxies is expanding.• Hubble found in 1929: cz = H0 d

(today: valid for z < 0.1); H0 = 72 km/s/Mpc.• This has been confirmed in later observsations.• The expansion is isotropic only 1 Hubble

constant and not 3 of them !• Also confirmed by CMB measurments.• Isotropy is fundamental assumpt of Cosmol.• With Supernovae Ia, distance measurements

can be extended to redshift ~2.• Quasars are not suitable distance indicators (?).

Schematic of Sunyaev-Zeldovich Effect

Quantitative SZ Effect