Ay 127

ISM, Cosmic Web, and Gravitational Lensing

Intergalactic Medium (IGM) •  Essentially, baryons between galaxies •  Its density evolution follows the LSS formation, and the potential

wells defined by the DM, forming a web of filaments, the co-called “Cosmic Web”

•  An important distinction is that this gas unaffiliated with galaxies samples the low-density regions, which are still in a linear regime

•  Gas falls into galaxies, where it serves as a replenishment fuel for star formation

•  Likewise, enriched gas is driven from galaxies through the radiatively and SN powered galactic winds, which chemically enriches the IGM

•  Chemical evolution of galaxies and IGM thus track each other •  Star formation and AGN provide ionizing flux for the IGM

Cosmic Web: Numerical Simulations Our lines of sight towards some luminous background sources intersect a range of gas densities, condensed clouds, galaxies …

(from R. Cen)

QSO Absorption Line Systems •  An alternative to searching for galaxies by their emission

properties is to search for them by their absorption •  Quasars are very luminous objects and have very blue colours

which make them relatively easy to detect at high redshifts •  Nowadays, GRB afterglows provide a useful alternative •  Note that this has

different selection effects than the traditional imaging surveys: not by luminosity or surface brightness, but by the cross section (size) and column density

Types of QSO Absorption Lines •  Lyman alpha forest:

–  Numerous, weak lines from low-density hydrogen clouds –  Lyman alpha clouds are proto-galactic clouds, with low density,

they are not galaxies (but some may be proto-dwarfs) •  Lyman Limit Systems (LLS) and “Damped” Lyman alpha (DLA)

absorption lines: –  Rare, strong hydrogen absorption, high column densities –  Coming from intervening galaxies –  An intervening galaxies often produce both metal and damped

Lyman alpha absorptions •  Helium equivalents are seen in the far UV part of the spectrum •  “Metal” absorption lines

–  Absorption lines from heavy elements, e.g., C, Si, Mg, Al, Fe –  Most are from intervening galaxies

Types of QSO Absorption Systems

Measuring the Absorbers We measure equivalent widths of the lines, and in some cases shapes of the line profiles

They are connected to the column densities via curves of growth

The shape of the line profile is also a function of the pressure, which causes a Doppler broadening, and also the global kinematics of the absorbing cloud

Absorber Cross Sections Column density of neutral H is higher at smaller radii, so LLS and DLA absorbers are rare Metals are ejected out to galactic coronae, and their column densities and ionization states depend on the radius

Ly α Absorbers •  Ly α Forest: 1014 ≤ NHI ≤ 1016 cm-2

–  Lines are unsaturated –  Primordial metalicity < solar –  Sizes are > galaxies

•  Ly Limit Systems (LLS): NHI ≥ 1017 cm-2

–  Ly α Lines are saturated –  NHI is ufficient to absorb all ionising photons shortward of the Ly

limit at 912Å in the restframe (i.e., like the UV-drop out or Lyman-break galaxies)

•  Damped Ly α (DLA) Systems: NHI ≥ 1020 cm-2

–  Line heavily saturated –  Profile dominated by “damped” Lorentzian wings –  Almost surely proto-disks or their building blocks

Fitting the Forest:

A Damped Lyman α System

Distribution of Column Densities

Ly α Forest

LLS DLA

f (NHI) ~ NHI-1.7

Evolution of the Hydrogen Absorbers

Low redshift QSO

High redshift QSO

Evolution of Ly α Absorbers (from Rauch 1998, ARAA, 36, 267)

(NB: this is for Λ = 0 cosmology!)

Typical γ ~ 1.8 (at high z’s)

Evolution of Ly α Absorbers The numbers are higher at higher z’s, but it is not yet clear how much of the effect is due to the number density evolution, and how much to a possible cross section evoluton - nor why is there a break at z ~ 1.5

The Forest Thickens

Estimating the Evolution of Gas Density (from Wolfe et al. 2005, ARAA, 43, 861)

Evolution of Neutral Gas

The Gunn-Peterson Effect

(from Fan et al. 2006, ARAA, 44, 415)

Even a slight amount of neutral hydrogen in the early IGM can completely absorb the flux blueward of Lyα

G-P Lyβ G-P ò

“Gunn-Peterson like” troughs are now observed along all available lines-of-sight at at z ~ 6

Transmitted Lyα Flux vs. Redshift

(from Fan et al. 2006, ARAA, 44, 415)

The Absorber - Galaxy Connection •  Metallic line absorbers are generally believed to be associated

with galaxies (after all, stars must have made the metals)

An example with multiple metallic line systems:

Galaxy Counterparts of DLA Systems •  Several examples are known with

Lyα line emission •  Properties (size, luminosity,

SFR) are typical of field galaxies at such redshifts, and consistent with being progenitors of z ~ 0 disks

Numerical Simulations of IGM

DLA systems as the densest knots in the cosmic web However, the simulations cannot resolve whether these are rotating (proto)disks (from Katz et al. 1996)

Clustering of Metallic Absorbers

Metallic absorbers are found to cluster in redshift space, even at high z’s, while Ly α clouds do not. This further strengthens their association with galaxies

Metallic absorbers

Ly α clouds

Number Density Evolution of Absorbers While the H I seems to decline in time (being burned out in stars?), the density of metals seems to be increasing, as one may expect

Abundances in DLA Systems and Disks

Chemical Enrichment Evolution of

DLA Systems

Solar g

(Wolfe et al.)

But different types of systems may be evolving in different ways …

(from M. Pettini)

IGM Summary •  Intergalactic medium (IGM) is the gas associated with the large

scale structure, rather than galaxies themselves; e.g., along the still collapsing filaments, thus the “cosmic web” –  However, large column density hydrogen systems, and strong

metallic absorbers are always associated with galaxies •  It is condensed into clouds, the smallest of which form the “Ly α

forest” •  It is ionized by the UV radiation from star forming galaxies and

quasars •  It is metal-enriched by the galactic winds, which expel the gas

already processed through stars; thus, it tracks the chemical evolution of galaxies

•  Studied through absorption spectra against background continuum sources, e.g., quasars or GRB afterglows

Gravitational Lensing:���Mapping the Distribution of the Dark Matter •  We know from general relativity that mass - whether it is

visible or not - bends light. This opens a possibility of “seeing” the distribution of dark matter

•  Chowlson (1924) and Einstein (1936) predicted that if a background object is directly aligned with a point source mass, the light rays will be deflected into an “Einstein Ring”

Walsh, Carswell & Weymann 1979

The first gravitational lens

Gravitational lensing in the strong regime������Misalignment of the line of sight and the center of the lensing mass splits the Einstein ring into multiple images

B1938+666 HST-NICMOS

zsource = ? zlens = 0.881

Full Einstein ring in the IR diameter ≅ 1”

MG 0414+0534 HST-WFPC2 diameter ≅ 2.12” zsource = 2.64 zlens = 0.96

RXJ1131-1231

Examples of Einstein

Rings

Gravitationally Lensed Galaxies - “Arcs” In 1937, Zwicky predicted that one could study the mass distribution (dark matter) in clusters by studying background galaxies that are lensed by the dark matter in the cluster. This was not observationally feasible until the mid-1990’s

Gravitational Lensing Photons are deflected by gravitational fields - hence images of background objects are distorted if there is a massive foreground object along the line of sight. Bending of light is similar to deflection of massive particles, except that GR predicts that for photons the bending is exactly twice the Newtonian value:

€

α =4GMbc 2

=2Rs

b…where Rs is the Schwarzschild radius of a body of mass M, and b is the impact parameter. This formula is valid if b >> Rs:

•  Not valid very close to a black hole or neutron star •  Valid everywhere else •  Implies that deflection angle a will be small

e.g., for the stars near the Solar limb, ~ 2 arcsec

Geometry for Gravitational Lensing Consider sources at distance dS from the observer O. A point mass lens L is at distance dL from the observer:

a

q b b

y

S L Observer

x

dLS dL dS

S’

I

Observer sees the image I of the source S’ at an angle q from line of sight to the lens. In the absence of deflection, would have deduced an angle b.

Recall that all the angles a, b, q are small, so:

€

θ =bdL

=xdS

, β =ydS

, α =x − ydLS

Substitute these angles into expression for deflection angle:

€

x − ydLS

=4GMbc 2

θdS −βdS =4GMbc 2

dLS

θ −β =1θ4GMc 2

dLSdSdL

Geometric factors

Quadratic equation for the apparent position of the image q, given the true position b and knowledge of the mass of the lens and the various distances

Simplify this equation by defining an angle θE, the Einstein radius :

€

θE =2c

GMdLSdLdS

Equation for the apparent position then becomes:

€

θ 2 −βθ −θE2 = 0

Solutions are:

€

θ± =β ± β 2 + 4θE

2

2For a source exactly behind the lens, b = 0. Source appears as an Einstein ring on the sky, with radius θE For b > 0, get two images, one inside and one outside the Einstein ring radius

Different Lensing Regimes Conceptually simplest situation for gravitational lensing is when the lens is massive enough to produce a large angle of deflection. Case where we can resolve multiple images of the background source is called strong lensing

Einstein Ring

If the lensing is not strong enough to split the images, but it does magnify and distort them, it is called weak lensing. This is the effect of the large-scale structure or the outskirts of clusters of galaxies on the background sources (galaxies). These image distortions can then be inverted to map the mass distribution.

Einstein Cross

Weak Lensing Regime Simulated examples of the appearance of a background field of galaxies, with cluster-type masses in the foreground. Strong lensing is apparent near the center. At larger radii, one has to use statistics of image elongations and orientations

The effect of a cluster lens on a hypothetical graph paper on the background sky

Galaxy number density Light

Shear map

Mass

Cluster Abell 2218

Squires et al. 1996

Cluster Masses From Gravitational Lensing Strong lensing constraints:

A370 M ~ 5x1013h-1 M� M/L ~ 270h A2390 M ~ 8x1013h-1 M�

M/L ~ 240h MS2137 M ~ 3x1013h-1 M�

M/L ~ 500h A2218 M ~ 1.4x1014h-1 M� M/L ~ 360h

Weak lensing constraints (a subset): MS1224 M/L ~ 800h A1689 M/L ~ 400h CL1455 M/L ~ 520h A2218 M/L ~ 310h CL0016 M/L ~ 180h A851 M/L ~ 200h A2163 M/L ~ 300h

Clusters of galaxies imply Ωdm ~ 0.1 – 0.3

Lots of dark matter in clusters, in a broad agreement with virial mass estimates

Visible and DM Distribution From the COSMOS Survey (Scoville, Massey et al. 2007)

3-D DM Distribution From the COSMOS Survey (Massey et al. 2007)

Sun Line of sight to a background star

MACHO crossing the line of sight

Lensing event occurs as a MAssive Compact (Halo) Object, MACHO (could be a main sequence star, white or brown dwarf, neutron star or black hole, or … ?), passes within an angular distance qE of a background star:

•  background star initially brightens •  eventually fades as the alignment is lost

Gravitational Microlensing

Since the cross section for a strong lensing is small compared to interstellar separations, such events must be exceedingly rare, Plensing ~ 10-7 /star/year. Solution: monitor ~ 107 stars simultaneously, typically in the LMC or the Galactic Bulge

Expected Gravitational Microlensing Lightcurves:

The peak magnification depends on the lens alignment (impact parameter).

The event duration depends on the lens velocity.

Microlensing Experiments Several experiments have searched for microlensing events:

•  toward the Galactic Bulge (lenses are disk or bulge stars)

•  toward the Magellanic Clouds (lenses could be stars in the LMC / SMC, or halo objects)

MACHO (Massive Compact Halo Object): •  observed 11.9 million stars in the Large Magellanic Cloud for a total of 5.7 years

OGLE (Optical Gravitational Lensing Experiment): •  monitors 33 millions stars in the LMC, plus 170 million stars in the Galactic Bulge

+ many, many others

To date, thousands of microlensing events have been detected by various groups

The First MACHO Event Seen in the LMC Experiment

The Einstein radius for a single lens of mass M, at distance dL, observer-source distance is dS, lens-source distance is dLS =dS- dL

Probability that this lens will magnify a given source is:

€

P ∝θE2 ∝

dLSdLdS

$

% &

'

( ) ×M directly proportional to

the mass of the lens

Same is obviously true for a population of lenses, with total mass Mpop - just add up the individual probabilities. Conclude: •  The fraction of stars that are being lensed at any one time measures the total mass in lenses, independent of their individual masses •  Geometric factors remain - we need to know where the lenses are to get the right mass estimate

€

θE =2c

GMdLSdLdS

€

τ =4vLc

GMdLdLSdS

Time scale is proportional to the square root of the individual lens masses

Put in numbers appropriate for disk stars lensing stars in the Galactic bulge:

•  dS = 8 kpc, dL = dLS = 4 kpc •  M = 0.3 M� •  vL = 200 km s-1

Events with τ ~ 1 day: M < Jupiter mass (~10-3 M� ) Events with τ ~ 1 year: M ~ 25 M� (e.g. stellar black holes)

Lensing time scale: equals the physical distance across the Einstein ring divided by the relative velocity of the lens:

€

τ =2dLθEvL

€

τ ≈ 40 M0.3Msun

days

For each event, there are only two observables: •  Duration τ - if we know the location of the lens along the line of sight this gives the lens mass directly

•  Peak amplification A: this is related to how close the line of sight passes to the center of the Einstein ring

b

€

Define u =b

dLθE

A =u2 + 2

u u2 + 4

Note: amplification tells us nothing useful about the lens!

Additionally, observing many events gives an estimate of the probability that a given source star will be lenses at any one time (often called the optical depth to microlensing). This measures the total mass of all the lenses, if their location is known.

From the number and duration of MACHO events, if the lenses are in the Galactic Halo:

•  Typical mass is between 0.15 M� and 0.9 M�

If the halo contains a much larger population of white dwarfs than suspected, there are other problems: requires a major epoch of early star formation to generate these white dwarfs – and the corresponding metals that are not observed. Ambiguity in the distance to the lenses is the main problem!

MACHO Results

•  All the mass in the halo is MACHOs is definitely ruled out

(Alcock et al. 1997)

Distance ambiguity can be resolved in a few special cases:

a)  If distortions to the light curve caused by the motion of the Earth around the Sun can be detected (parallax events)

b) If the lens is part of a binary system. Light curves produced by binary lenses are much more complicated, but often contain sharp spikes (caustic crossings) and multiple maxima.

This provides more information

about the event. (This one was close to the SMC)

Supplementary Slides

Image

Lens

Source

Observer DL

DS

DLS

The lens equation and the Einstein radius

€

θE =4GMc 2

DLS

DLDS

€

β = θ −αEinstein radius: (dimensionless)

Lens equation:

A galaxy acting as a lens: Isothermal sphere with central singularity (SIS)

Stars considered as the particles of a perfect gas, con- fined by their own mean gravitational potential, with a spherical symmetry : equation of state thermal equilibrium hydrostatic equilibrium

2

2

)(rdrrMGgdp

kTmmTkp

v

=

=

=

ρ

σ

ρ

A galaxy acting as a lens: Isothermal sphere with central singularity (SIS)

A simple solution : SIS surface density deflection angle Multiple images only if the source verifies : β < θE

Solutions of the lens equation : θ± = β ± θE

2

2 12

)(rG

r v

πσ

ρ =

ξσ

ξ1

2)(

2

Gv=Σ

212

2

)220(4.14 −""==

kmscvv σσ

πα

A galaxy acting as a lens: Isothermal sphere with central core (CIS)

A simple solution : CIS surface density

22

2 12

)(c

v

rrGr

+=

πσ

ρ

22

2 12

)(c

v

rG +=Σ

ξ

σξ

sc

dsdv

DrDD

cD 2

2

4 σπ≡

0

20

0011

θ

θβθ

−++= D

defines the number of images

lens equation

A galaxy acting as a lens: Isothermal sphere with central core (CIS)

0

2/12000 /]1)1[( θθθβ −+−= D

multiple images if D > 2

critical lines and positions of the images (lens plane)

caustics and position of the source (source plane)

The local properties of the mapping source plane – lens plane are described by its Jacobian matrix : A ≡ ∂β /∂θ The locus of the points θ in the lens plane where strongly disturbed images are created is the set of points where the matrix A cannot be locally inver- ted, i.e., where its Jacobian is null ⇒ critical lines or caustics.

Magnification pattern due to stars in the lensing galaxy

Surface brightness preserved : photons neither created nor destroyed

The magnification µ is the ratio of the solid angles of the images and of the sources, with A ≡ ∂β /∂θ

€

µ =dω I

dωS

= det(∂ β

∂ θ )−1

Adet1

=µ

dωI+

dωI- dωS

Convergence and shear The local properties of the application source plane ↔ lens plane are

described by its jacobian matrix: A ≡ ∂β /∂θ

With the convergence κ and the shear γ :

The convergence κ has a magnification action on the light rays: the image conserve the shape of the source, but with a different size. The shear induces an anisotropy with intensity γ and orientation ϕ.

!!"

#$$%

&

−−!!"

#$$%

&−=

φφ

φφγκ

2cos2sin2sin2cos

1001

)1(A

⇒

Shear γ as a function of the convergence κ Seitz & Schneider, 1997, A&A, 318, 687

Reconstruction of the mass distribution via the gravitational distortions