Fabio Iocco

ICTP-SAIFR / IFT-UNESP

Miguel Pato

Wenner-Gren FellowThe Oskar Klein Centre for Cosmoparticle Physics, Stockholm University

School on Dark Matter, ICTP/UNESP, Sao Paulo, 08 Jul 2016

big bangnucleosynthesis

[PDG ’14]

cosmic microwavebackground

[PDG ’14]

large scalestructure

[Springel+ ’06]

dwarfs

[ESO]

galaxies

[Begeman+ ’91]

galaxy clusters

[Clowe+ ’06]

-time

�redshift

[Lectures: Serpico, Sheth]

[– this Lecture –]

big bangnucleosynthesis

[PDG ’14]

cosmic microwavebackground

[PDG ’14]

large scalestructure

[Springel+ ’06]

dwarfs

[ESO]

Milky Way

[Begeman+ ’91]

galaxy clusters

[Clowe+ ’06]

-time

�redshift

[Lectures: Serpico, Sheth]

[– this Lecture –]

dark matter in astrophysical structures

Part I. Clusters

Virial estimatesHot gas emissionSunyaev-Zeldovich e↵ectGravitational lensingMerging clusters

Part II. Galaxies

Hubble sequenceEllipticalsSpiralsDwarfs

Part III. Milky Way

Tour of the GalaxyKinematicsDark matter contentState of the art and future

It was Hubble that set in 1936 the main scheme for the classification of galaxies in theuniverse.

[in Baudis ’12]

The (revised) Hubble sequence contains:

ellipticals: smooth and spheroidal

spirals: disk-like with spiral arms

lenticulars: smooth and disk-like

irregular: lack of symmetry

Our Galaxy is an SBb.

[Credit: Brunier / NASA]

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

[Gillessen+ ’09]

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

Galactic centre

[Gillessen+ ’09]

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

bulge/bar

Galactic centre

[Binney+ ’97]

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

stellar disk

bulge/bar

Galactic centre

[Reid+ ’09]

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

stellar diskgas disk

bulge/bar

Galactic centre

[Ferriere+ ’12]

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

stellar diskgas disk

bulge/bar

Galactic centre

Sun

[Binney & Tremaine+ ’87]

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

dark halo

stellar diskgas disk

bulge/bar

Galactic centre

Sun

= + + +

how can we constrain the parameters of agalactic mass model?

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

The Sun is located slightly above the Galactic planeat R0 8 kpc from the Galactic centre, in betweentwo major spiral arms, and travels together with thelocal standard of rest at about 220 km/s in a roughlycircular orbit.

[Brunier]The Milky Way is a complex bound system of stars, gas, dust and dark matter.

not to scale!

edge!on

Milky Way

dark halo

stellar diskgas disk

bulge/bar

Galactic centre

Sun

= + + +

how can we constrain the parameters of agalactic mass model?

We can identify the following main components:

supermassive black hole, with mass 4 106 ;

stellar bulge, with barred shape of scale length2 3 kpc and mass 1010 ;

stellar disc, decomposed into thin and thickcomponents of scale length 10 kpc and total mass1010 with a marked spiral structure;

gas, in molecular, atomic and ionised phases(mainly H) with a patchy distribution towards thecentre and a disc-like structure otherwise; and

dark matter halo, extending hundreds of kpc.

Problem 4: Convince yourself that the gravitationalinfluence of the central supermassive black hole isirrelevant for R 1 kpc.

Look at the board!

= + + +

kinematics traces total potential

R 0 1 30 kpc rotation curve tracers

R 8 60 kpc star population tracers

R 100 300 kpc satellite kinematics

R 300+kpc timing in Local Group

photometry traces individual baryonic components

bulge star counts, luminosity, microlensing

disc star counts, luminosity, stellar dynamics

gas emission lines, dispersion measure

⇣⇣⇣⇣⇣⇣⇣)��

���

��

����

= + + +

kinematics traces total potential

R 0 1 30 kpc rotation curve tracers

R 8 60 kpc star population tracers

R 100 300 kpc satellite kinematics

R 300+kpc timing in Local Group

photometry traces individual baryonic components

bulge star counts, luminosity, microlensing

disc star counts, luminosity, stellar dynamics

gas emission lines, dispersion measure

⇣⇣⇣⇣⇣⇣⇣)��

���

��

����

= + + +

kinematics traces total potential

R 0 1 30 kpc rotation curve tracers

R 8 60 kpc star population tracers

R 100 300 kpc satellite kinematics

R 300+kpc timing in Local Group

photometry traces individual baryonic components

bulge star counts, luminosity, microlensing

disc star counts, luminosity, stellar dynamics

gas emission lines, dispersion measure

⇣⇣⇣⇣⇣⇣⇣)��

���

��

����

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

[Credit: HST] [Credit: Brunier / NASA]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

[Begeman+ ’91] [Credit: Brunier / NASA]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

[Begeman+ ’91] [Sofue+ ’09]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

v =v

c

(R )

R R0v0 cos b sin

Doppler shift1. gas (21cm, H , CO)2. stars (H, He, O, ...)3. masers (H2O, CH3OH, ...)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

v =v

c

(R )

R R0v0 cos b sin

distance Doppler shift1. terminal velocities (gas)2. photo-spectroscopy (stars)3. parallax (masers)

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

There are three important kinematic tracers used to constrain the rotation curveacross our Galaxy:

1. gas kinematics, for the inner Galaxy;2. local stars, for the solar neighbourhood; and3. halo stars, for the outer Galaxy.

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

There are three important kinematic tracers used to constrain the rotation curveacross our Galaxy:

1. gas kinematics, for the inner Galaxy;2. local stars, for the solar neighbourhood; and3. halo stars, for the outer Galaxy.

Let us start by considering a circular ring of gas of radius R rotating at velocity v(R)about the centre of the Galaxy.

R0

Galactic Centre

v0

Sun

Problem 5: Find the line-of-sight velocity of the gas asobserved from the local standard of rest.

Look at the board!

Rings of di↵erent radii leave a specific trace in a ( v ) plot.

[Binney & Merrifield ’98] [Rodriguez-Fernandez & Combes ’08]

These patterns are observed in the HI and CO line maps of the gas in our Galaxy.

Let us start by considering a circular ring of gas of radius R rotating at velocity v(R)about the centre of the Galaxy.

Rt

R

R0

Galactic Centre

v0

Sun

l.o.s.

l

a Problem 5: Find the line-of-sight velocity of the gas asobserved from the local standard of rest.

Look at the board!

Rings of di↵erent radii leave a specific trace in a ( v ) plot.

[Binney & Merrifield ’98] [Rodriguez-Fernandez & Combes ’08]

These patterns are observed in the HI and CO line maps of the gas in our Galaxy.

Now say we measure the Doppler shift along a given line of sight. Then, each ringcontributes with a di↵erent v

los

.

Rt

R0

Galactic Centre

v0

Sun

l.o.s.

l

[Rodriguez-Fernandez & Combes ’08]

However, the highest vlos

detected, the so-called terminal velocity v

t

, corresponds tothe innermost ring, which is tangent to the line of sight.

Problem 6: Express the circular velocity at the tangent point as a function of vt

.

Look at the board!

Therefore, measuring the terminal velocity at di↵erent longitudes we can construct therotation curve of our Galaxy at R R0.

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

There are three important kinematic tracers used to constrain the rotation curveacross our Galaxy:

1. gas kinematics, for the inner Galaxy;2. local stars, for the solar neighbourhood; and3. halo stars, for the outer Galaxy.

The terminal velocity method is very powerful, but it is only applicable in the innerGalaxy at R R0. In the solar neighbourhood alternative tracers are needed.

We could for instance measure the line-of-sight velocities of local stars. We have thenthe same expression as before,

v = v(R)R0

R

v0 sin

but now we are interested in the regime R R0.

Homework 5: Local stars kinematics.

The line-of-sight velocity reads

v = Ad sin 2

A similar expression holds for the transverse velocity, i.e. proper motions, of local stars:

= B + A cos 2

The bottomline is that by measuring the motion of local stars we can constrain A B

and thus the local circular velocity: v0 = R0(A B) 220 km/s.

v

2c

= r

r

=G M ( r)

r

Rotation curve tracers are young objects or regions that track galactic rotation. Inexternal galaxies the only available tracer is the gas, while in our Galaxy we can usealso some stars and star-forming regions. However, the case of our Galaxy is muchmore challenging due to our position.

R’ R

vc

R’

R0

l.o.s.

l

Galactic Centre

v0

Sun

object

[Sofue+ ’09]

There are three important kinematic tracers used to constrain the rotation curveacross our Galaxy:

1. gas kinematics, for the inner Galaxy;2. local stars, for the solar neighbourhood; and3. halo stars, for the outer Galaxy.

The outer Galaxy is perhaps the most challenging region to constrain the rotationcurve due to the lack of suitable tracers. One possibility is to use old halo stars. Sincethese do not follow circular orbits the conversion of their motion to the circularvelocity is not trivial.

We need the so-called Jeans equations (derived from the collisionless Boltzmannequation), e.g. in the spherical case:

( 2r

)

r

+2 2

r

r

=r

v

2c

r

where is the density of stars, 2r

the radial velocity dispersion and = 1 2 2r

isthe anispotropy parameter. In this way with measured 2

r

of a given population ofstars we can constrain the total gravitational potential in the outer Galaxy.

[http://astronomy.nju.edu.cn] [Xue+ ’08]

= + + +

kinematics traces total potential

R 0 1 30 kpc rotation curve tracers

R 8 60 kpc star population tracers

R 100 300 kpc satellite kinematics

R 300+kpc timing in Local Group

photometry traces individual baryonic components

bulge star counts, luminosity, microlensing

disc star counts, luminosity, stellar dynamics

gas emission lines, dispersion measure

⇣⇣⇣⇣⇣⇣⇣)��

���

��

����

local methods

aim: use data from a patch of the sky toderive dynamics there.

+ “assumption-free”low precision

vs global methods

aim: use data across the Galaxy toderive dynamics somewhere.

global assumptions+ high precision

[Kapteyn ’22, Jeans ’22, Oort ’32, Hill ’60, Oort ’60,Bahcall ’84, Bienayme+ ’87, Kuijken & Gilmore ’91,Bahcall+ ’92, Creze+ ’98, Holmberg & Flynn ’00,Holmberg & Flynn ’04, Bienayme+ ’06, Garbari+ ’11’12, Moni Bidin+ ’12, Bovy & Tremaine ’12, Smith+’12, Zhang+ ’13, Bovy & Rix ’13, Loebman+ ’14,Moni Bidin+ ’14]

[Caldwell & Ostriker ’81, Gates+ ’95, Dehnen &Binney ’98, Sakamoto+ ’03, Dehnen+ ’06, Xue+ ’08,Sofue+ ’09, Strigari & Trotta ’09, Catena & Ullio ’10,Weber & de Boer ’10, Salucci+ ’10, Iocco+ ’11,McMillan ’11, Nesti & Salucci ’13, Bhattacharjee+’14, Kafle+ ’14, MP & Iocco ’15, MP, Iocco &Bertone ’15, Sofue ’15]

In a galaxy star encounters are rare and stars feel on average the smooth gravitationalpotential. We can therefore treat a set of stars as a collisionless gas and apply thecollisionless Boltzmann equation, whose first momentum gives the Jeans equations:

s

x

j

=(

s

v

j

)

t

+

i

(s

v

i

v

j

)

x

i

j = 1 2 3

We can couple this to the Poisson equation: 4 G = 2 .

(R z) t 0 F

R

= R F

z

= z

4 G =1

R R

(RFR

) +F

z

z

F

R

=1

s

(s

v

2R

)

R

+(

s

v

R

v

z

)

z

+v

2R

v

2

R

F

z

=1

s

(s

v

R

v

z

)

R

+(

s

v

2z

)

z

+v

R

v

z

R

4 G =z

1

s

(s

v

2z

)

z

This is the so-called Oort limit.

[Oort ’32]

In a galaxy star encounters are rare and stars feel on average the smooth gravitationalpotential. We can therefore treat a set of stars as a collisionless gas and apply thecollisionless Boltzmann equation, whose first momentum gives the Jeans equations:

s

x

j

=(

s

v

j

)

t

+

i

(s

v

i

v

j

)

x

i

j = 1 2 3

We can couple this to the Poisson equation: 4 G = 2 .

(R z) t 0 F

R

= R F

z

= z

4 G =1

R R

(RFR

) +F

z

z

F

R

=1

s

(s

v

2R

)

R

+(

s

v

R

v

z

)

z

+v

2R

v

2

R

F

z

=1

s

(s

v

R

v

z

)

R

+(

s

v

2z

)

z

+v

R

v

z

R

4 G =z

1

s

(s

v

2z

)

z

This is the so-called Oort limit.

[Oort ’32]

In a galaxy star encounters are rare and stars feel on average the smooth gravitationalpotential. We can therefore treat a set of stars as a collisionless gas and apply thecollisionless Boltzmann equation, whose first momentum gives the Jeans equations:

s

x

j

=(

s

v

j

)

t

+

i

(s

v

i

v

j

)

x

i

j = 1 2 3

We can couple this to the Poisson equation: 4 G = 2 .

(R z) t 0 F

R

= R F

z

= z

4 G =1

R R

(R⇢⇢FR

) +F

z

z

F

R

=1

s

(s⇢vR 2)

R

+(

s⇢vRvz )z

+⇢vR2 ⇢v 2

R

F

z

=1

s

(s⇢vRvz )R

+(

s

v

2z

)

z

+⇢vRvzR

4 G =z

1

s

(s

v

2z

)

z

This is the so-called Oort limit.

[Oort ’32]

In a galaxy star encounters are rare and stars feel on average the smooth gravitationalpotential. We can therefore treat a set of stars as a collisionless gas and apply thecollisionless Boltzmann equation, whose first momentum gives the Jeans equations:

s

x

j

=(

s

v

j

)

t

+

i

(s

v

i

v

j

)

x

i

j = 1 2 3

We can couple this to the Poisson equation: 4 G = 2 .

(R z) t 0 F

R

= R F

z

= z

4 G =1

R R

(RFR

) +F

z

z

F

R

=1

s

(s

v

2R

)

R

+(

s

v

R

v

z

)

z

+v

2R

v

2

R

F

z

=1

s

(s

v

R

v

z

)

R

+(

s

v

2z

)

z

+v

R

v

z

R

[Read ’14][Bienayme+ ’87, Kuijken & Gilmore ’89, Creze+ ’98, Holmberg & Flynn ’00, Garbari+ ’11 ’12, Smith+ ’12, Zhang+ ’13]

local methods

aim: use data from a patch of the sky toderive dynamics there.

+ “assumption-free”low precision

vs global methods

aim: use data across the Galaxy toderive dynamics somewhere.

global assumptions+ high precision

[Kapteyn ’22, Jeans ’22, Oort ’32, Hill ’60, Oort ’60,Bahcall ’84, Bienayme+ ’87, Kuijken & Gilmore ’91,Bahcall+ ’92, Creze+ ’98, Holmberg & Flynn ’00,Holmberg & Flynn ’04, Bienayme+ ’06, Garbari+ ’11’12, Moni Bidin+ ’12, Bovy & Tremaine ’12, Smith+’12, Zhang+ ’13, Bovy & Rix ’13, Loebman+ ’14,Moni Bidin+ ’14]

[Caldwell & Ostriker ’81, Gates+ ’95, Dehnen &Binney ’98, Sakamoto+ ’03, Dehnen+ ’06, Xue+ ’08,Sofue+ ’09, Strigari & Trotta ’09, Catena & Ullio ’10,Weber & de Boer ’10, Salucci+ ’10, Iocco+ ’11,McMillan ’11, Nesti & Salucci ’13, Bhattacharjee+’14, Kafle+ ’14, MP & Iocco ’15, MP, Iocco &Bertone ’15, Sofue ’15]

= + + +

vc

r

rotation curve traces all matter

baryons

dark matter

[Dehnen & Binney ’98, Sofue+ ’09, Catena & Ullio ’10, Weber & de Boer ’10, Salucci+ ’10,McMillan ’11, Iocco+ ’11, Nesti & Salucci ’13, Sofue ’15]

v

2c

= v

2 + v

2v

2 = G M ( r) r

Homework 6: Spherical dark matter distribution.

R

R

R

[everybody et al]

[Catena & Ullio ’10] [Weber & de Boer ’10] [Salucci ’10]

[McMillan ’11] [Iocco+ ’11] [Nesti & Salucci ’13]

(r r

s

) (1 + r r

s

) 3+ [MP, Iocco & Bertone ’15, 1504.06324]

]3 [GeV/cm0ρ

0 0.2 0.4 0.6 0.8 1

γin

ner s

lope

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2=20 kpcsgen. NFW, r

σ2

σ

excluded >5

0 = 0 420+0 0210 018 (2 ) 0 025 3

0 = 0 420+0 0190 021 (2 ) 0 026 3

baryonic bracketing

R [kpc]0 5 10 15 20 25 30

[km

/s]

cv

100

200

300

400

500

600

= 8 kpc0R = 230 km/s0v

gas kinematicsstar kinematicsmasers

R [kpc]0 5 10 15 20 25 30

[km

/s]

cv

0

50

100

150

200

250

300

= 8 kpc0R

Stanek+ '97 (E2)Stanek+ '97 (G2)Zhao '96Bissantz & Gerhard '02Lopez-Corredoira+ '07Vanhollebeke '09Robin '12

bulge

Han & Gould '03Calchi-Novati & Mancini '11deJong+ '10Juric+ '08Bovy & Rix '13

disk

Ferriere '98Moskalenko+ '02

gas

bulge

disc

(r r

s

) (1 + r r

s

) 3+ [MP, Iocco & Bertone ’15, 1504.06324]

]3 [GeV/cm0ρ

0 0.2 0.4 0.6 0.8 1

γin

ner s

lope

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2=20 kpcsgen. NFW, r

σ2

σ

excluded >5

0 = 0 420+0 0210 018 (2 ) 0 025 3

0 = 0 420+0 0190 021 (2 ) 0 026 3

baryonic bracketing

bulge

disc

?

6

� -

(r r

s

) (1 + r r

s

) 3+ [MP, Iocco & Bertone ’15, 1504.06324]

]3 [GeV/cm0ρ

0 0.2 0.4 0.6 0.8 1

γin

ner s

lope

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2=20 kpcsgen. NFW, r

σ2

σ

excluded >5

0 = 0 420+0 0210 018 (2 ) 0 025 3

0 = 0 420+0 0190 021 (2 ) 0 026 3

baryonic bracketing

bulge

disc

?

6

� -

The local dark matter density is an emblematic observable where local and globalmethods are nicely complementary.

Local methods infer the dark matter density within a few hundred pc fromthe Sun, while global methods usually constrain the dark matter densitywithin a spherical shell at the Sun’s position.

local

[J. Read ’14]

global

[J. Read ’14]

Problem 7: The latest measurements indicate that withinuncertainties. If future measurements reveal that , what do welearn about the shape of the dark matter distribution? What if ?

Look at the board!

Gaia

[Credit: ESA]

fact sheet

2013-2018space-based= 320 1000 nm

109 stars G 20magparallax 10 asproper motion 10 as/yrradial velocity 1 km/s

wish list

disc modellingOort’s constantslocal density

APOGEE-2 (SDSS-IV)

[Credit: SDSS]

fact sheet

2014-2020south+north hemispheres= 1510 1700 nm

300 000 starsradial velocity 0 1 km/s

wish list

bulge modellingdisc modellingkinematics all across

WFIRST

[Credit: NASA]

fact sheet

20??-20??+6space-based= 760 2000 nm

radial velocity ?

wish list

(dark energy)(exoplanets)bulge modelling??

WEAVE

[Credit: WEAVE]

fact sheet

20??-20??northern hemisphere= 370 1000 nm

1000 million starsradial velocity 5 km/s

wish list

(cosmology)kinematics all across?

4MOST

[Credit: ESO]

fact sheet

20??-20??+5southern hemisphere= 390 950 nm

30 million starsradial velocity 2 km/s

wish list

bulge kinematicsdisc kinematicsstellar halo kinematics?

(see also PanSTARRS, HERMES, MSE, MOONS)

big bangnucleosynthesis

[PDG ’14]

cosmic microwavebackground

[PDG ’14]

large scalestructure

[Springel+ ’06]

dwarfs

[ESO]

galaxies

[Begeman+ ’91]

galaxy clusters

[Clowe+ ’06]

-time

�redshift

[Lectures: Serpico, Sheth]

[– this Lecture –]

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

1970

Rub

in &

For

d

1922

Kap

teyn

1933

Zw

icky

1927

Oor

t

1937

Zw

icky

1936

Sm

ith

1939

Bab

cock

1978

Bos

ma

1972

Sho

stak

& R

ogst

ad

1973

Rob

erts

& R

ots

1960

Lim

ber

& M

athe

ws

1959

Kah

n &

Wol

tjer

1980

Rub

in+

1992

Sm

oot+

2005

Eis

enst

ein+

1998

Per

lmut

ter+

/Rie

ss+

1986

Lyn

ds &

Pet

rosi

an

1985

Rub

in+

1982

Rub

in+

2006

Clo

we+

We have come a long way since Zwicky inferred the need for dark matter from acouple of Doppler velocities in the Coma cluster of galaxies (and a lot of intuition).

We now know dark matter is present from the scale of the smallest galaxies tocosmological scales.

But we have no clue what it is. This should be enough motivation for us (read you) tokeep on looking for it.

The field of dark matter research is simply huge. Some topics I just touched upon,other I did not even mention. There are excellent books and reviews covering thedi↵erent topics at all levels of detail. Here is a good list to start with.

A: astro-oriented P: particle-oriented C: cosmology-oriented : advancedBooksA Binney & Merrifield, Galactic Astronomy (1998).A Binney & Tremaine, Galactic Dynamics (2008).A Longair, High-energy astrophysics, Vol I (1992).A Longair, High-energy astrophysics, Vol II (1994).AC Longair, Galaxy Formation (1998).C Kolb & Turner, The Early Universe (1990).C Peebles, Principles of Physical Cosmology (1993).C Padmanabhan, Structure Formation in the Universe (1993).C Dodelson, Modern Cosmology (2003).C Weinberg, Cosmology (2008).APC Bergstrom & Goobar, Cosmology and Particle Astrophysics (2004).APC Bertone (ed.), Particle Dark Matter: Observations, Models and Searches (2010).

ReviewsP Jungman, Kamionkowski & Griest, arXiv:hep-ph/9506380.A Lewin & Smith, APh, Vol 6, 87 (1996).PC Bergstrom, arXiv:hep-ph/0002126.P Munoz, arXiv:hep-ph/0309346.APC Bertone, Hooper & Silk, arXiv:hep-ph/0404175.A Schnee, arXiv:1101.5205.PC Bergstrom, arXiv:1205.4882.PC Profumo, arXiv:1301.0952.A Conrad, arXiv:1411.1925.