Classical Tests of Cosmology · 2020-04-29 · Introduction Classical Tests Luminosity Distance...
Transcript of Classical Tests of Cosmology · 2020-04-29 · Introduction Classical Tests Luminosity Distance...
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Classical Tests of Cosmology
Toni Sagristà Sellés
Universitat de BarcelonaDepartament d’Astronomia i Meteorologia
8 June 2011
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Outline
1 Introduction
2 Classical TestsLuminosity DistanceAngular Diameter distanceNumber Counts
3 Conclusions
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Outline
1 Introduction
2 Classical TestsLuminosity DistanceAngular Diameter distanceNumber Counts
3 Conclusions
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Introduction
What are classical tests of cosmology?
I Techniques to determine values of cosmological parameters
I Discover global geometry and dynamics of Universe
I Only cosmology before precision cosmology
I Most tests require some standard object
I Basically, seek value of H0, Ω0 and q0
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
IntroductionSumming up
Classical cosmology
I Identify Standard candles, Standard rods and Standardpopulations at different z
I Use their properties to gauge geometry and dynamics
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Outline
1 Introduction
2 Classical TestsLuminosity DistanceAngular Diameter distanceNumber Counts
3 Conclusions
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Luminosity Distance I
Inverse-square law to determine distance through flux
M −m = −5(log10DL − 1)
DL = 10m−M
5 +1[pc]
But usually
DL =( L4πl
)1/2
I Luminoisty distance , real distance
I Inverse-square law does not hold due to expansion, geometry
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Luminosity Distance II
Expansion and redshift effect
DL = a0r0(1 + z)
Dphy = a0r0
For small distances, DL = Dphy
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Luminosity Distance III
Figure: Luminosity distance versus redshift for various flat models. Reddots are recent HST observations
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Luminosity Distance IV
Standard candles
Pulsar stars Cepheids and RR Lyrae, period-luminosity relationknown
Red clump stars Absolute magnitude depends on age andmetallicity
SNIa ∆m15 index, luminosity decrease 15 days aftermaximum
PNLF Old stars evolved into red giant phase, use OIII(doubly ionized oxygen) line to find them. Theyseem to all have the same luminosity
X-ray bursts Mass related to burst luminosity
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Luminosity Distance V
Tully-Fisher Relation Relates rotational velocity of spiral galaxieswith their luminosity
Faber-Jakcson Relation Relates velocity dispersion of spiralgalaxies with their luminosity
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Angular Diameter Distance I
Measures how large objects appear to be
DA =d
sinθ'
dθ
DA =a0r0
1 + z
(=
DL
(1 + z)2
)z → ∞, DA → 0 - Distant objects seem larger!
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Angular Diameter Distance II
I The further objects are from us, the older they are, so theircomoving size is larger
I Inflection point position depends on q0 and Ω
Figure: Angular diameter distance vs redshift. The blue line correspondsto Ωm = 0.3,ΩΛ = 0.7, and the red line corresponds to Ωm = 1,ΩΛ = 0
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Angular Diameter Distance III
Standard rods
Cluster elliptical galaxies The fundamental plane relationcombined with a correction for luminosity evolutioncan be used
Spiral galaxies Their angular diameter can be determined throughobservation
BAO Baryonic acoustic oscillations, based on size ofacoustic waves produced in baryonic matterclustering zones in the primitive universe
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Number Counts I
I Focus on cumulative count of objects instead of their physicalproperties
I We know cumulative number, we may know integrationdistance
I Number of objects per sterad up to a distance r0
N(r0) = n(t0)a30
∫ r0
0
r2dr√
1 − kr2
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Number Counts II
Problems
I Statistical method, uses great number of objects, more proneto errors
I Limiting observable magnitudes may bias sample
I We lack info on actual redshift distribution of observedgalaxies
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Number Counts III
Figure: Number counts in models and observations by HST and others
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Outline
1 Introduction
2 Classical TestsLuminosity DistanceAngular Diameter distanceNumber Counts
3 Conclusions
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
Conclusions
I Evolution problem: Standard callibrators work at shortdistances
I Standard callibrators affected by the evolution of the Universe
I Bias problem: All observations affected by biases (due tosensitivity, angular resolution, faint luminosity. . . )
I Classical tests key to development of cosmology
I From 2000 on, precision cosmology
I Gravitational lensing can be used to accurately describegeometry of space
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
References I
T. Roy Choudhury and T. Padmanabhan.
Cosmological parameters from supernova observations: A critical comparison of three data sets.Astronomy and Astrophysics, 429(807), 2005.
L.I. Gurvits, K.I. Kellermann, and S. Frey.
The ’angular size - redshift’ relation for compact radio structures in quasars and radio galaxies.Astronomy and Astrophysics, 342:378–388, 1999.
J. A. S. Lima J. V. Cunha and N. Pires.
Deflationary λ(t) cosmology: Observational expressions.Astronomy and Astrophysics, 390:809–815, 2002.
Hannu Karttunen.Fundamental Astronomy.Springer, 2006 (5th Edition).
Andrew Liddle.
An Introduction to Modern Cosmology.Wiley, 2003.
Francesco Lucchin Peter Coles.
Cosmology - The Origin and Evolution of Cosmic Structure.Wiley, 2002.
Allan R. Sandage.
The ability of the 200-inch telescope to discriminate between selected world models.Astrophysics Journal, 133:355, 1961.
Classical Tests
Toni SagristàSellés
Introduction
Classical TestsLuminosity Distance
Angular Diameterdistance
Number Counts
Conclusions
References II
Allan R. Sandage.
Cosmology: A search for two numbers.Physics Today, 23(2):34–41, 1970.
Mihran Vardanyan.icosmos cosmology calculator - www.icosmos.co.uk.
Steven Wienberg.
Gravitation and Cosmology.Wiley, 1972.