Observations of primordial abundance of light elements

Physical Cosmology 28/4/2017

Alessandro Melchiorri

alessandro.melchiorri@roma1.infn.it slides can be found here:

oberon.roma1.infn.it/alessandro/cosmo2016

T. Padmanabhan, structure formation in the universe Most of the discussion on BBN in current lectures

can be found here:

T>0.1 MeV Protons and

Neutrons are unbounded

T <0.1 MeV Protons and neutrons

are bounded to form light elements nuclei 4He, 3He, D, Li7

Observations of primordial abundance of light elements

BBN theory predicts with high precision the amount of primordial Helium, Deuterium and Lithium.

These predictions depend on the baryon density and on the neutrino effective number.

If we could have a precise measurement of primordial abundances we could infer constraints on these

parameters of the theory.

Stellar nucleosynthesis can produce/destroy primordial abundances, how we can derive the primordial values ?

Observations of primordial Helium

Observations are made by looking at Helium lines in extragalactic HII regions (ionized hydrogen).

Stellar activity is tracked by metallicity, (O/H) for example.

The value of Yp (primordial Helium 4) can be recovered by extrapolating at “low metallicities”.

In practice one expects that going to O/H=0 the

Yp abundance should flattens to the primordial value.

Expectations vs Reality

We don’t see much (any) flattening going

to zero O/H (zero metallicity)

From this dataset (2007) we can derive the constraint:

Systematics in the recovery of Yp

Constraints during the years have improved in

precision but not in accuracy.

There is a large scatter in the measurements.

Systematics are important.

Value obtained from SBBN assuming baryon density

consistent with cosmic microwave background anisotropies.

Recent developments

Constraints on Yp have been improved by observations of the He I λ10830 line that strongly traces the electron

density of the HI region and helps in breaking degeneracies with temperature of the HI region.

Strongest dependence on ne compared

to other lines

Lower dependence on Temperature

Analysis by Izotov, Thuan and Guzeva, 2014

Following this method, observations made by Izotov and Thuan found an higher Helium abundance.

http://arxiv.org/pdf/1408.6953v1.pdf

Analysis by Izotov, Thuan, Guzeva 2014

Assuming BBN e combining with observations

of primordial D (see next slides) IT found a best

fit value for a larger than 3.046

neutrino number !

Aver et al, 2015

http://arxiv.org/pdf/1503.08146v1.pdf extrapolated value

at zero metallicity Flattening is still not really clear…

However, a more recent analysis by Aver at al., has found a lower value, consistent with Neff=3.046

Primordial Deuterium

Deuterium is destroyed by stellar nucleosynthesis.

Best measurements are again, in low metallicity regions.

The best way to probe it is in damped lyman alpha systems.

Primordial Deuterium

At rest, the Lyman-alpha line (transition from level n=1 to n=2 in neutral H)

is at wavelength of 1216 Å.

Along the line of sight we

have many clouds, each of them absorbing the Lyman-alpha at wavelenght (1+z)1216 Å

Quasars light is absorbed by neutral H clouds between us and the quasar.

Primordial Deuterium

At rest, the Lyman-alpha line (transition from level n=1 to n=2 in neutral H)

is at wavelength of 1216 Å.

Along the line of sight we

have many clouds, each of them absorbing the Lyman-alpha at wavelenght (1+z)1216 Å

Primordial Deuterium

Cloud is at z=3.572.

Lyman-alpha absorption is at (1+z)Lya = 5557 Å

It falls in the visible (4000-7000)Å !

We can measure it from earth !

1216Å is on the UV.

It would be absorbed by the atmosphere.

Primordial Deuterium

Cloud is at z=3.572.

Lyman-alpha absorption is at (1+z)Lya = 5557 Å

It falls in the visible (4000-7000)Å !

We can measure it from earth !

1216Å is on the UV.

It would be absorbed by the atmosphere.

Primordial Deuterium

We see here a “damped"

lyman-alpha system large column density N > 2*10^20 /cmˆ2

In these systems is "easier" to isolate the D line from H lines

from other systems and clouds.

In reality this was possible just in about 10 cases.

Primordial Deuterium

We see here a “damped"

lyman-alpha system large column density N > 2*10^20 /cmˆ2

In these systems is "easier" to isolate the D line from H lines

from other systems and clouds.

In reality this was possible just in about 10 cases.

ISM In the Interstellar Medium we measure low values.

Chengalur, Braun e Burton(1997) looking in a

direction opposite to the galactic center :

(^{3.9 ±1.0})^⋅10−5

H = D

Libowich (2000),

Looking towards the galactic center:

(^{1.7 ± 0.3})^⋅10−6

H =

>> D

ISM In the Interstellar Medium we measure low values.

Chengalur, Braun e Burton(1997) looking in a

direction opposite to the galactic center :

Solar System

(^{3.9 ±1.0})^⋅10−5

H = D

Libowich (2000),

Looking towards the galactic center:

(^{1.7 ± 0.3})^⋅10−6

H =

>> D

Jupiter atmosphere (Mahaffy et al. 1998) :

(^{2.6 ± 0.7})^⋅10−5

H = D

Solar wind (Gloecker, 1999) :

(^{1.94 ± 0.36})^⋅10−5

H = D

Primordial Deuterium

Measurements @2007 based on Lyman-alpha.

We see a large scatter.

No clear plateau at small metallicities but values

are higher respect to

“local" measurements.

Measurements in our solar system and

interstella medium.

We can consider them just as lower limit since we had stellar activity.

Primordial Deuterium

The best measurement comes from DLA of Pettini & Cooke

http://arxiv.org/pdf/1205.3785.pdf that gives:

Combined with other measurements we have:

Primordial Deuterium

Once we have a D

measurement we can trace a line on this

plane and considering the intersection with the BBN predictions we

can bound eta and the baryon density.

We get:

Consistency D and He4

When comparing with Helium data

we found consistency with the measurements of Aver et al, 2015

but not with

Izotov et al, 2014 but this assumes standard BBN !

Izotov et al, 2014 Aver et et al, 2015

Consistency D and He4

You can increase

Helium by increasing Neff ! You keep same Yp by

increasing eta and lowering Neff

Deuterium depends also by Neff

You have same D increasing eta and increasing Neff

Consistency D and He4

Using both Helium and D measurements we can constrain both Neff and the baryon density.

Using Cooke and Pettini and Izotov et al., we get:

Constraint from D Pettini and Cooke

Constraint from He4 Izotov 2014

Neff>3.046 ? Systematics

may be present…

Lithium 7

Primordial Lithium is measured on very old

stars with low metallicity in our galaxy or globular clusters.

When we go to lower metallicities we see a plateau….

… but the value is in

complete disagreement with the expectations from standard BBN.

Observed:

Spite Plateau

Again, we plot the Lithium abundance in

function of the metallicity.

At lower metallicities we see a plateau: «Spite

Plateau»

That should indicate The primordial

abundance.

Lithium 7

The values of the baryon

density inferred from D and Li7 are very different if we

assume SBBN !!

The problem of Lithium 7

- In old stars we see a plateau as expected but the Lithium abundance is far lower than expected !

- We don’t see old stars with higher Lithium abundance ! (Lithium desert).

- We see higher Lithium abundance in the small Magellan cloud. But this system has an high metallicity. If we have

depletion of Lithium 7 by stars, why we have more Lithium in stars with higher metallicity ?

- We may have new physics in BBN, but this would alter D abundance. It is difficult to avoid this.

Big Bang Nucleosynthesis

The consequences of BBN are (from D measurements):

Assuming h=0.67 we get:

Since SN-Ia, assuming a flat universe, gives:

About 80% of the matter in the universe should be Non Baryonic !!!

Dark Matter

This unknown matter component should not interact

electromagnetically other ways would change the CMB anisotropies. This means that it must be DARK.

Is not the neutron since free neutrons all form light nuclei during BBN. Free neutrons quickly decay because of the beta decay.

Is not the neutrino since we need

But this is

excluded by beta decay experiments !

Observational evidence for Dark Matter

- Galaxy velocity rotation curves.

- Cluster of galaxies I (velocity of galaxies vs virial theorem)

- Cluster of galaxies I (gas)

- Gravitational lensing (Bullet Cluster)

- Gravitational lensing (Cosmic Shear)

- Gravitational lensing (CMB lensing)

- Linear structure formation (Galaxies spectra)

- Linear structure formation (CMB angular spectra)

- Linear structure formation (BAO)

A lot of astrophysical/ cosmological evidence !

Visible Matter

Let us first give an estimate of the energy content in visible matter. i.e. the matter we see in the optical, at wavelengths:

The luminosity density in few Mpc around our galaxy is:

where

is the luminosity of the Sun in the B band.

Visible Matter

We now need to convert this luminosity density in a mass.

If we consider just stars in the main sequence we have:

This translates in a energy density of

i.e.

The energy density in baryonic matter due to stars is only 8% of the baryonic matter !!!

Visible Matter

Where are the baryons ?

http://arxiv.org/pdf/astro-ph/0406095v2.pdf Most of the baryons are thought to be distributed in a warm intergalactic plasma a T=10^{5-7} K with low numerical

density (10^{-5}-10^{-6} 1/cm^3). Not detected, yet.

Galaxy Rotation Curve

If we look at a spiral galaxy with an angle i between the line of sight and a line

perpendicular to the disk, given the

two apparent semi-axis a and b of the projected galaxy, assuming the galaxy to be in reality perfectly circular,

we have:

radial velocity of the galaxy as a whole

Orbital speed at a distance R from the center of the disk

21 cm neutral H line

When the spins are parallel, the magnetic

dipole moments are antiparallel (because the electron and proton have opposite charge), thus one would naively expect this

configuration to actually have lower energy just as two magnets will align so that the

north pole of one is closest to the south pole of the other. This logic fails here because the electron is not spatially displaced from the proton, but encompasses it, and the

magnetic dipole moments are best thought of as tiny current loops. As parallel currents

attract, it is clear why the parallel magnetic dipole moments (i.e. antiparallel spins) have lower energy.The transition has an energy difference of 5.87433 µeV that when applied in the Plank equation gives:

This transition is highly forbidden with an extremely small rate of 2.9×10⁻¹⁵ s⁻¹, and a lifetime of around 10 million (10⁷) years.

Galaxy Rotation Curve

Here is a doppler image of the M33 (Pinwheel) galaxy. It

is observed with radio

telescopes receiving the 21 cm Hydrogen line. This shows the distribution of hydrogen gas throughout the

galaxy. The colour coding shows the relative radial

velocities and clearly

demonstrates the rotation of the galaxy as a whole. Blue is moving towards us and red

is moving away from us.

Keplerian motion

By Newton law of gravity an object orbiting on the disk should have a speed following:

The surface brightness of a galaxy follows a law:

With Rs of few kpc For MW R^s = 4 kpc For M31 R^s = 6 kpc

Spiral Galaxies don’t follow

Keplerian motion !!!

Rotation curves and Dark Matter

If we postulate the existence of a dark matter component, in order to have a flat velocity curve we need:

This means a mass/luminosity ratio of

And a density of:

DM in Galaxies

From:

Solving for M and deriving:

But we can also write:

Combining the two equations we get:

DM in Galaxies

At large distances, if we want v=constant we need:

Single Isothermal Sphere Profile

At smaller distances v grows as r and

This can be obtained by a Pseudo-Isothermal profile:

DM in Galaxies: NFW profile

Assuming Cold Dark Matter (matter made of non-relativistic particles practically since the Big Bang) Navarro, Frenk

and White in 1997 found the following profile from numerical simulations:

where the central density, ρ0, and the scale radius, Rs, are parameters that vary from halo to halo.

Cusp vs Core

The NFW profile, for small values of r, goes as:

i.e. it has a “cusp" when going to small values of r.

More recent CDM simulations of NFW have:

While the pseudo-isothermal model has:

i.e. you expect a "core".

In principle, then, if you see some indications for a cusp this could be an hint for CDM.

Cusp vs Core

This started a big debate in cosmology in the past 15 years, i.e. if galaxies at the center have

a “cusp” or a “core”.

Current observations in dwarf galaxies

prefer a “core” over a cusp.

Is this a problem for CDM ? Baryons expelled from

the center by Supernovae could solve this.

Problems for CDM (on galactic scales)

A part from the cusp/core problem there are the following discrepancies between CDM simulations and observations:

- Missing Satellites: The simulated and observed satellite distributions around the Milky Way are inconsistent, in the sense that simulations predict many more satellites.

Problems for CDM (on galactic scales)

Models that best reproduce observed satellite luminosity function - and hence best `solves’ the missing satellite problems, predicts

that all satellites have significantly larger rotational velocities!

Solutions

1- Feedback from baryons not included in the simulations.

2- Observations not correct (many satellites too faint to be detected).

3- New physics ? warm dark matter ? self interacting dark matter ?

MOND

Modified Newtonian Dynamics (!) proposed by Milgrom in 1983. We change Newton law with:

where:

for example, we can use:

MOND

For very small accelerations (a << a⁰):

For a particle in circular motion, assuming Newton gravitational law, we have:

Flat rotation curves !!!

The best fit to galaxy curves is provided by

(???? just a coincidence ?)

Dark Matter in Clusters of Galaxies

Let us suppose that a cluster of galaxies is comprised of N

galaxies, each of which can be approximated as a point mass,

with a mass , a position , and a velocity . .

Clusters of galaxies are gravitationally bound objects, not

expanding with the Hubble flow. They are small compared to the horizon size; the radius of the Coma cluster is

The galaxies within a cluster are moving at non-relativistic speeds; the velocity dispersion within the Coma cluster is

Dark Matter in Clusters of Galaxies

Coma cluster (view in the optical)

Dark Matter in Clusters of Galaxies

The acceleration for each galaxy in the cluster is given by:

The gravitational potential energy of the system of N galaxies is

The factor of 1/2 in front of the double summation ensures that each pair of galaxies is only counted once in computing the

potential energy.

Dark Matter in Clusters of Galaxies

The potential energy of the cluster can also be written in the form

Where:

is the total mass of all the galaxies in the cluster.

is a numerical factor of order unity which depends on the density profile of the cluster. and is the half-mass radius of the cluster: the radius of a sphere centered on the cluster’s center of mass and containing a mass M/2.

Dark Matter in Clusters of Galaxies

The kinetic energy associated with the relative motion of the galaxies in the cluster is

The kinetic energy K can also be written in the form

Dark Matter in Clusters of Galaxies

The virial theorem in the case of a a system in steady state, with a constant moment of inertia (the system is neither

expanding nor contracting) gives:

Using the previous equations, we get:

We can derive the total mass of the cluster from the velocity of galaxies.

Dark Matter in Coma

From measurements of the redshifts of hundreds of galaxies in the Coma cluster, the mean redshift of the cluster is found to

be

which can be translated into a radial velocity

and a distance

The velocity dispersion of the cluster along the line of sight is found to be

If we assume that the velocity dispersion is isotropic:

Dark Matter in Coma

If we assume that the mass-to-light ratio is constant with

radius, then the sphere containing half the mass of the cluster will be the same as the sphere containing half the luminosity of the cluster. If we further assume that the cluster is

intrinsically spherical, then the observed distribution of

galaxies within the Coma cluster indicates a half-mass radius

Moreover, for observed clusters of galaxies, it is found that α ≈ 0.4 gives a good fit to the potential energy.

Dark Matter in Coma

After all these assumptions and approximations, we may estimate the mass of the Coma cluster to be

F. Zwicky

Dark Matter in Coma

In the Coma cluster 2% of the matter is in stars and about 10% is in the Intracluster Medium, visible

in the X-rays.

ICM

the intracluster medium (ICM) is the superheated plasma present at the center of a galaxy

cluster. This gas is heated to temperatures of the order of 10ˆ11-10ˆ10 K and composed mainly of ionized hydrogen and helium, containing most of the baryonic material in the cluster. The ICM

strongly emits X-ray radiation.

The ICM is heated to high temperatures by the gravitational energy released by the formation of the cluster from smaller structures. Kinetic energy gained from the gravitational field is converted to

thermal energy by shocks. The high temperature ensures that the elements present in the ICM are ionised. Light elements in the ICM have all the electrons removed from their nuclei.

Although the ICM on the whole contains the bulk of a cluster's baryons, it is not very dense, with typical values of 10⁻³ particles per cubic centimeter. The mean free path of the particles is roughly 10¹⁶ m, or about one lightyear.

Although the ICM on the whole contains the bulk of a cluster's baryons, it is not very dense, with typical values of 10⁻³ particles per cubic centimeter. The mean free path of the particles is roughly 10¹⁶ m, or about one lightyear.

ICM

Dark Matter in Coma (Gas)

If the hot intracluster gas is supported by its own pressure against gravitational infall, it must obey the equation of

hydrostatic equilibrium:

The pressure of the gas is given by the perfect gas law

where T is the temperature of the gas, and μ is its mass in units of the proton mass (m^p).

! M is the TOTAL mass

Dark Matter in Coma (Gas)

The mass of the cluster, as a function of radius, is found by combining the previous equations:

Starting from an x-ray spectrum, it is possible to fit models to the emission and thus compute the temperature, density, and chemical composition of the gas.

We can derive the mass of the cluster by using X-ray measurements.

The mass of the Coma cluster, assuming hydrostatic

equilibrium, is computed to be (3 → 4)×10ˆ14 M⊙ within 0.7 Mpc of the cluster center and (1 → 2)×10ˆ15 M⊙ within 3.6 Mpc of the center. Consistent with previous results.

MOND and Clusters of Galaxies

MOND fails on galaxy clusters !

The Mass-Temperature relation disagrees with observational data. Using the virial theorem, we need a MOND parameter a⁰ that is about 3 times larger than the one obtained from galaxy rotation curves.

Lensing

In GR relativity gravity can deflect photons by an angle:

For example, for a photon passing by the Sun we expect:

1919 telegram from Eddington to Einstein

Lensing from MACHO

The image of the star should appear as a ring (Einstein

ring) if the star, the MACHO and the observer are perfectly aligned with angular extension given by:

where M is the mass of the lensing MACHO, d is the distance from the observer to the lensed star, and xd (where 0 < x < 1)

is the distance from the observer to the lensing MACHO

Lensing from MACHO

For x=0.5 we have:

The typical time scale for a lensing event is the time it takes a MACHO to travel through an angular distance equal to θ^E as seen from Earth; for a MACHO halfway between here and the Large Magellan Cloud, is

where v is the relative transverse velocity of the MACHO and the lensed star as seen by the observer on Earth.

Results from MACHO searches

The research groups which searched for MACHOs found a scarcity of short duration lensing events, suggesting that there is not a significant population of brown dwarfs (with M < 0.08M⊙) in the dark halo of our

Galaxy. The total number of lensing events which they detected suggest that as much as 20% of the halo mass could be in the form of MACHOs.

The long time scales of the observed lensing events, which have

∆t > 35days, suggest typical MACHO masses of M > 0.15 M⊙. (Perhaps the MACHOs are old, cold white dwarfs, which would have the correct mass.) Alternatively, the observed lensing events could be due, at least in part, to lensing objects within the LMC itself.

In any case, the search for MACHOs suggests that most of the matter in the dark halo of our galaxy is due to a smoothly distributed component, instead of being congealed into MACHOs of roughly stellar mass.

Lensing from Clusters

Gravitational lensing occurs at all mass scales. Suppose, for instance, that a cluster of galaxies, with M ∼ 10ˆ14 M⊙, at a distance ∼ 500 Mpc from our Galaxy, lenses a background galaxy at d ∼ 1000Mpc. The

Einstein radius for this configuration will be

Lensing from Clusters

The Figure shows an image of the cluster Abell 2218, which has a redshift z = 0.18, and hence is at a proper distance d = 770Mpc. The elongated arcs are not oddly shaped galaxies within the cluster; instead, they are background galaxies, at redshifts z > 0.18, which are gravitationally lensed by the cluster mass.