COSMOLOGY PHYS 30392 DENSITY OF THE UNIVERSE Part I Giampaolo Pisano - Jodrell Bank Centre for Astrophysics The University of Manchester - March 2013 http://www.jb.man.ac.uk/~gp/ giampaolo.pisano@manchester.ac.uk
DENSITY OF THE UNIVERSE Visible Matter Dark Matter in Galaxies Dark Matter in Clusters Gravitational Lensing What is Dark Matter? Search for Dark Matter References: Ryden, Introduction to Cosmology - Par. 8.1 Liddle, Introduction to Modern Cosmology - Par. 9.1
Visible Matter in the Universe: Emission from stars - We want to understand where all the matter in the universe is. - Let s first consider the matter emitting light. - Stars emit in the IR, Visible and UV parts of the spectrum. - Within few hundreds of Mpc from our galaxy, in the B band (0.4-0.49 µm): j *,B =1.2x10 8 L ʘ,B Mpc -3 - Luminosity density of stars (L ʘ,B : Sun s luminosity in B-band) - In order to convert this luminosity density into a mass density: We need to know the mass-to-light ratio for stars (M /L)
Visible Matter in the Universe: Mass-Luminosity Ratios (M/L) - Main sequence stars have a wide range of masses and luminosities: High mass - Brightest M /L B ~ 10-3 M ʘ /L ʘ,B ( Small M/L because they are very bright compared to their mass ) Low mass - Dimmest M /L B ~ 10 3 M ʘ /L ʘ,B ( Very high M/L because they fairly dim dwarf stars ) - Within 1 kpc from the Sun, the weighted average is: M /L B ~ 4 M ʘ / L ʘ,B - Local M-L ratio of stars - Assuming this average value to be valid everywhere: ρ *,0 = M /L B j *,B 5x10 8 M ʘ Mpc -3 - Mass density of stars
Visible Matter in the Universe: Density Parameter of Stars - Using the current critical density of the Universe, we have: Ω ρ 8 5 10 MΟMpc 11 1.4 10 M Mpc 3,0, 0 = 3 ρ c,0 Ο 0.004 - Density parameter of stars Stars contribution to flatten the Universe is less than 0.5% Notes - Big uncertainty in the number of low-mass low-luminosity stars: 95% luminosity from L > L ʘ stars 80% mass from M < M ʘ - Density parameter of stars can be increased (up to ~0.01) considering also : White dwarfs, neutron stars, black holes and brown dwarfs
Visible Matter in the Universe: Galaxies and Clusters of Galaxies - Galaxies contains also the Interstellar Medium (ISM): ISM mass > ~ 0.1 stars mass - Cluster of galaxies contains also the intergalactic medium Intracluster gas much more massive than stellar mass - The best current limits on the Universe barion density come from the : Primordial Nucleosynthesis ( We will study this later in more details ) Ω Bary, 0 = 10 Ω, 0 = 0.04 ± 0.01 - Barionic matter density parameter One order of magnitude higher than the density parameter fo stars SDSS/Spitzer
Visible Matter in the Universe: Cluster of Galaxies example COMA cluster - Looking at the B-band luminosity of its thousands of galaxies and using the local M/L ratio of stars: M Coma, * ~ 3 x 10 13 M ʘ Coma cluster stellar mass - Looking in the X-ray bands there is a hot, low-density emitting gas (T~10 8 K) with extimated mass: M Coma, gas 2 x 10 14 M ʘ Coma intracluster gas mass Intracluster gas mass ~ 7 times star mass
DENSITY OF THE UNIVERSE Visible Matter Dark Matter in Galaxies Dark Matter in Clusters Gravitational Lensing What is Dark Matter? Search for Dark Matter References: Ryden, Introduction to Cosmology - Par. 8.2 Liddle, Introduction to Modern Cosmology - Par. 9.1
Dark Matter in Galaxies: Introduction - Most of the matter in the Universe is: Non-Barionic Dark Matter Matter component which doesn t absorb, emit, or scatter light of any wavelength. - How can we detect dark matter? One way is to look at the gravitational influence that it has on visible matter - For example: Studying the orbital speeds of stars in Spiral Galaxies
Dark Matter in Spiral Galaxies: Keplerian motion - Assume a spiral galaxy to be a flattened disk of stars on nearly circular orbits - The centrifugal acceleration of a star is: a = 2 v R v: orbital speed R: distance from galactic centre - The gravitational acceleration is: - Equating the two equations: a = GM ( R) 2 R M(R): mass contained within a sphere of radius R from galactic centre 2 v R = GM ( R) 2 R v = GM ( R) R - Keplerian rotation velocity The velocity decreases as 1/ R
Dark Matter in Spiral Galaxies: Brightness vs radius - In spiral galaxies the brightness decreases exponentially with the distance from the centre: I( R) = I 0 e R / R s - Spiral Galaxies Brightness R S : Scale length R S (M31) 6 kpc R S (Milky Way) 4 kpc Example: M64 www.calvin.edu
Dark Matter in Spiral Galaxies: Expected velocity relations - Near the galactic centre the mass increases with radius as: 4 M ( R) πr 3 3 v = GM ( R) R v R R < R S Linear velocity - radius relation - At few scale lengths R S from the centre, the mass acts as if all at the centre: M ( R) const v 1 R R >> R S Keplerian velocity expected if the stars contributed to most of the galaxy mass What it is actually observed is instead very different
Dark Matter in Spiral Galaxies: Rigid vs Keplerian rotation Rigid rotation abyss.uoregon.edu v R R < R S Keplerian rotation abyss.uoregon.edu v 1 R R >> R S
Dark Matter in Spiral Galaxies: M31 Rotation Curve -Rotation curve measurements: -Starlight: up to ~ 3 R S -HII regions emission lines: up to ~ 4 R S -HI atomic hydrogen emission line (21cm): up to ~ 5 R S R S 6 kpc R S 2R S 3R S 4R S 5R S cdms.phy.queensu.ca/public_docs/
Dark Matter in Spiral Galaxies: NGC 3198 Rotation Curve Neutral hydrogen emission line (Contours) Measurement doppler shift bustard.phys.nd.edu -Note: HI acts only as an indicator It does not contribute much to the total mass
Dark Matter in Spiral Galaxies: The Dark Halo - The behaviour of M31 is not peculiar: Thousands of spiral galaxies show orbital velocities ~ const at R > R S There must be a dark halo within which the visible stellar disc is embedded that provides the gravitational pull that keeps the high-speed stars bounded to the galaxy system
Dark Matter in Spiral Galaxies: Mass of a Spiral Galaxy - The mass of a spiral galaxy, including disc and dark halo, can be found inverting the keplerian relation (R >>R S ): v = GM ( R) R const 2 v R M ( R) = - Mass of a Spiral Galaxy G Measuring the velocity as a function of R we can infer the galaxy real mass - Normalised to the Sun s location in our galaxy: M ( R) 2 10 R v = 9.6 10 MΟ 220 km s 1 8.5 kpc - Mass of a Spiral Galaxy
Dark Matter in Spiral Galaxies: Milky-Way M/L ratio Milky Way - The estimated B-band luminosity of our galaxy is: L Gal,B =2.3x10 10 L ʘ,B - Milky-Way Luminosity - The mass-to-light ratio is: M /L B Gal ~ 50 M ʘ / L ʘ,B (R halo /100kpc) - Milky-Way M-L ratio - The radius of the dark halo is poorly known; using the motion of globular clusters and satellite galaxies: R Halo ~ 75-300 kpc M /L B Gal ~ 40-150 M ʘ / L ʘ,B - Milky-Way M-L ratio Dark halo ~10 to ~40 times more massive than stellar disc
Dark Matter in Spiral Galaxies: Milky-Way Simulations www.spacetelescope.org
Dark Matter in Spiral Galaxies: Density parameter of galaxies - If our galaxy is typical, then the density parameter (including dark halo) is: Ω gal, 0 = ( 10 40) Ω*, 0 0.04 0.16 - Density parameter of galaxies - In summary: Although poorly known, the total density of galaxies is likely to be larger than the density of baryons Ω gal, 0 0.1 > Ω,0 0.04 > Ω*, 0 bary 0.004 Baryonic + Non-Baryonic Dark Halo Baryonic Visible
DENSITY OF THE UNIVERSE Visible Matter Dark Matter in Galaxies Dark Matter in Clusters Gravitational Lensing What is Dark Matter? Search for Dark Matter