Visible Matter. References: Ryden, Introduction to Cosmology - Par. 8.1 Liddle, Introduction to Modern Cosmology - Par. 9.1

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1 COSMOLOGY PHYS DENSITY OF THE UNIVERSE Part I Giampaolo Pisano - Jodrell Bank Centre for Astrophysics The University of Manchester - March giampaolo.pisano@manchester.ac.uk

2 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

3 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 ( 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)

4 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

5 Visible Matter in the Universe: Density Parameter of Stars - Using the current critical density of the Universe, we have: Ω ρ MΟMpc M Mpc 3,0, 0 = 3 ρ c,0 Ο 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

6 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 ± Barionic matter density parameter One order of magnitude higher than the density parameter fo stars SDSS/Spitzer

Coma cluster stellar mass - Looking in the X-ray bands there is a hot, low-density emitting gas (T~10 8 K)

7 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 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 M ʘ Coma intracluster gas mass Intracluster gas mass ~ 7 times star mass

8 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

9 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

10 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

11 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

12 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

13 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

14 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/

15 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

16 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

17 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 = MΟ 220 km s kpc - Mass of a Spiral Galaxy

18 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 ~ kpc M /L B Gal ~ M ʘ / L ʘ,B - Milky-Way M-L ratio Dark halo ~10 to ~40 times more massive than stellar disc

19 Dark Matter in Spiral Galaxies: Milky-Way Simulations

20 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*, 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, > Ω, > Ω*, 0 bary Baryonic + Non-Baryonic Dark Halo Baryonic Visible

21 DENSITY OF THE UNIVERSE Visible Matter Dark Matter in Galaxies Dark Matter in Clusters Gravitational Lensing What is Dark Matter? Search for Dark Matter

Cosmologists dedicate a great deal of effort to determine the density of matter in the universe. Type Ia supernovae observations are consistent with

Notes for Cosmology course, fall 2005 Dark Matter Prelude Cosmologists dedicate a great deal of effort to determine the density of matter in the universe Type Ia supernovae observations are consistent