MAPPING THE SMALL - SCALE STRUCTURE OF D ARK M ATTER HALOS WITH ALMA - - PowerPoint PPT Presentation

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MAPPING THE SMALL - SCALE STRUCTURE OF D ARK M ATTER HALOS WITH ALMA O BSERVATIONS OF S TRONG L ENSES Y ASHAR H EZAVEH H UBBLE F ELLOW - KIPAC - S TANFORD U NIVERSITY R ENCONTRE DU V IETNAM - Q UI N HON - 2016 N. D ALAL , D. M ARRONE , G. H OLDER ,

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SLIDE 1

YASHAR HEZAVEH

HUBBLE FELLOW - KIPAC - STANFORD UNIVERSITY RENCONTRE DU VIETNAM - QUI NHON - 2016

MAPPING THE SMALL-SCALE STRUCTURE OF DARK MATTER HALOS WITH ALMA OBSERVATIONS OF

STRONG LENSES

  • N. DALAL, D. MARRONE, G. HOLDER, Y. MAO, W. MORNINGSTAR
  • R. BLANDFORD, J. CARLSTROM, C. FASSNACHT, P. MARSHALL, N. MURRAY
  • L. PERREAULT LEVASSEUR, J. VIEIRA, R. WECHSLER

AND THE SOUTH POLE TELESCOPE DMS TEAM

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SLIDE 2

SMALL-SCALE STRUCTURE OF DARK MATTER

Large scale structure is very well constrained. Small scale distribution of dark matter is not well understood.

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SLIDE 3

COMPARING MW DWARF GALAXIES TO DM SUBHALOS

MOTIVATION

THEORY: N>> 1000 OBSERVATION N~10 NBODY SIMULATIONS OBSERVED MW SATELLITES

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SLIDE 4

THE MISSING SATELLITE PROBLEM

STRIGARI ET AL. 2007 APJ. 669, 676

LONG STANDING PROBLEM FOR CDM

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SLIDE 5

SOLUTIONS

LOVELL ET AL 2012, MNRAS 420, 3

Cold Dark Matter 2 keV Warm Dark Matter

BARYONIC GASTROPHYSICS DARK MATTER PHYSICS

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SLIDE 6

STRONG GRAVITATIONAL LENSING

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SLIDE 7

STRONG GRAVITATIONAL LENSING MULTIPLY IMAGED FISH

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SLIDE 8

STRONG GRAVITATIONAL LENSING

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SLIDE 9

SUBSTRUCTURE LENSING

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SLIDE 10

SUBSTRUCTURE LENSING

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SLIDE 11

A SENSE OF SCALE…

Cold Dark Matter

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SLIDE 12

SDP.81

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SLIDE 13

SDP.81

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SLIDE 14

LENS MODELING

DATA MODEL

GENERATE THE LENSED

IMAGE OF THE SOURCE

RAY-TRACING SIMULATION

MAXIMIZE THE LIKELIHOOD OF THE

MODEL PARAMETERS GIVEN THE DATA

POSTULATE A SOURCE MORPHOLOGY (WITH

PARAMETERS PS)

POSTULATE A MASS

DISTRIBUTION IN THE LENS

(WITH PARAMETERS PM)

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SLIDE 15

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 16

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 17

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

FOURIER SPACE POSITION SPACE (SKY) INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 18

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 19

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 20

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 21

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 22

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 23

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 24

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 25

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 26

u [Mλ] v [Mλ] −1 −0.5 0.5 1 −1 −0.5 0.5 1

NOT NOISE

INTERFEROMETRY:

(WHAT DOES ALMA MEASURE?)

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SLIDE 27

LENS MODELING FOR INTERFEROMETRIC DATA

1 - Postulate Sky Model Parameterized by Source and Lens Properties

1 arcsec

−6 −4 −2 2 4 6 x 10 5 −6 −4 −2 2 4 6 x 10 5

2 - Predict the Visibilities on the measured uv coverage 3 - Add additional parameters for antenna phases 4 - Form a χ2 likelihood and Sample the posterior using a parameter exploration method (MCMC, etc.)

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SLIDE 28

MODEL PARAMETERS

parameters describing the light distribution in the background source (Psource)

parameters describing the mass distribution in the foreground lens (Plens) sky emission

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SLIDE 29

LENS MODELING WITH PIXELATED SOURCES

psource = L(plens)× = L(plens) × psource

sky surface brightness

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SLIDE 30

LENS MODELING WITH PIXELATED SOURCES

" e−i~

k~ r ...

. . . #

|{z}

background source matter distribution in the lens

∼ 106

∼ 104

|{z}

|{z}

v = F L(plens) × psource

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SLIDE 31

SUCCESSFULLY TESTED ON MOCKS GENERATED WITH AN INDEPENDENT CODE

WARREN MORNINGSTAR (GRAD @ STANFORD)

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SLIDE 32

EXAMPLE: SOURCE RECONSTRUCTION

mock data (dirty image)

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SLIDE 33

EXAMPLE: SOURCE RECONSTRUCTION

reconstructed source

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SLIDE 34

EXAMPLE: SOURCE RECONSTRUCTION

true source (mock)

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SLIDE 35

EXAMPLE: SOURCE RECONSTRUCTION

true source (mock) reconstructed source

S = ⇥ (FBL)TCN

−1(FBL) + Cs −1⇤−1 ⇥

(FBL)TCN

−1D

⇤

For realistic ALMA data, solving this requires thousands of cpu-cores.

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SLIDE 36

Generally, likelihood evaluation is computationally very expensive. In a small neighborhood of the maximum posterior model, all parameters could be treated linearly for small perturbation to the fiducial model. We can use this linearized model to estimate the marginalized posterior for different subhalo models.

LINEARIZING THE MODEL (SUBHALO FINDER)

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SLIDE 37

PROBABILITY OF THE PRESENCE OF A SUBHALO

HEZAVEH ET AL. 2016 greyscale: difference in log posterior between a model which includes a subhalo and a smooth model (no subhalos)

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SLIDE 38

SDP 81


(ALMA SCIENCE VERIFICATION DATA)

DUST CO 8-7

BLUE: HST RED: ALMA

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SLIDE 39

HEZAVEH ET AL. 2016

SDP 81


RECONSTRUCTED BACKGROUND SOURCE

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SLIDE 40

HEZAVEH ET AL. 2016

FIRST DETECTION OF A DM SUBHALO

WITH ALMA

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SLIDE 41

HEZAVEH ET AL. 2016

FIRST DETECTION OF A DM SUBHALO

WITH ALMA

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SLIDE 42

HEZAVEH ET AL. 2016

PROBABILITY OF A SECOND SUBHALO

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SLIDE 43

HEZAVEH ET AL. 2016

CONSTRAINTS ON THE MASS FUNCTION OF SUBHALOS IN THE HOST HALO

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SLIDE 44

HEZAVEH ET AL. 2016

CONSTRAINTS ON THE MASS FUNCTION OF SUBHALOS IN THE HOST HALO

THEORY: YAO-YUAN MAO

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SLIDE 45

COMPARISON TO THEORETICAL PREDICTIONS

HEZAVEH ET AL. 2016 THEORY: YAO-YUAN MAO

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SLIDE 46

HEZAVEH ET AL. 2016

CONSTRAINTS ON THE MASS FUNCTION OF SUBHALOS IN THE HOST HALO

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SLIDE 47

HEZAVEH ET AL. 2016

CONSTRAINTS ON THE MASS FUNCTION OF SUBHALOS IN THE HOST HALO

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SLIDE 48

ALMA OBSERVATIONS OF SPT-DISCOVERED SOURCES

VIEIRA ET AL. NATURE 2013 HEZAVEH ET AL. APJ. 2013 BLUE: HST (OPTICAL), RED: ALMA (CYCLE 0)

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SLIDE 49

SPT2134-50 (ALMA CYCLE 2) BAND 6 (RED: ALMA CONTINUUM, BLUE: HST)

MORNINGSTAR LEADING THE ANALYSIS

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SLIDE 50

SPT2134-50 (ALMA CYCLE 2) BAND 6 (CONTINUUM)

MORNINGSTAR LEADING THE ANALYSIS

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SLIDE 51

HEZAVEH ET AL. 2016

CONSTRAINTS ON THE MASS FUNCTION OF SUBHALOS IN THE HOST HALO

smooth density field lensed by a field with low-k power lensed by a field with high-k power
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SLIDE 52

EFFECT OF SOURCE SIZE:

LARGER SOURCE = LOWER SENSITIVITY

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SLIDE 53

WE NEED A SMALL SOURCE, OR

A SOURCE WITH SMALL FEATURES...

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SLIDE 54

VELOCITY STRUCTURE

ENGEL ET AL 2010, APJ

WE NEED A SMALL SOURCE, OR

A SOURCE WITH SMALL FEATURES...

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SLIDE 55

3D LENS MODELING (3RD DIMENSION=WAVELENGTH)

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SLIDE 56

SENSITIVITY ANALYSIS OF DETECTING DM SUBHALOS

0.25 0.3 0.35

ϵ

106 107 108 109 110

angle [degree]

7 7.5 8 8.5 9

log Ms [M⊙]

0.4 0.6 0.8 1

x s[arcsec]

11.598 11.6 11.60211.60411.606 0.9 1 1.1 1.2 1.3

logM [M⊙] y s[arcsec]

0.25 0.3 0.35

ϵ

106 108 110

angle [degree]

7 8 9

log Ms [M⊙]

0.4 0.6 0.8 1

x s[arcsec]

0.9 1 1.1 1.2 1.3

y s[arcsec]

]

7 8 9

log Ms [M⊙]

AFTER MARGINALIZING OVER ~60 SOURCE PARAMETERS

HEZAVEH, DALAL ET AL 2013, APJ. 767, 9

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SLIDE 57

SPT2134-50 (ALMA CYCLE 2) BAND 6 (CO 7-6)

MORNINGSTAR LEADING THE ANALYSIS

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SLIDE 58

HEZAVEH ET AL. 2016

CONSTRAINTS ON THE MASS FUNCTION OF SUBHALOS IN THE HOST HALO

smooth density field lensed by a field with low-k power lensed by a field with high-k power
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SLIDE 59

WHAT ABOUT THE THOUSANDS OF LOWER MASS ONES? CAN WE DETECT THEM AS A WHOLE?

5 6 7 8 9 10 10 10

1

10

2

10

3

10

4

10

5

M [M⊙ ] N(>M)

WE CAN DETECT AND MODEL MASSIVE SUBHALOS

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SLIDE 60
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SLIDE 61
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SLIDE 62
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SLIDE 63

smooth density field lensed by a field with low-k power lensed by a field with high-k power

RESIDUALS FROM MODELING WITH A SMOOTH LENS:

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SLIDE 64

COVARIANCE OF

DEFLECTIONS

DENSITY POWER SPECTRUM

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SLIDE 65

DM SUBHALO DENSITY POWER SPECTRUM

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

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SLIDE 66

DM SUBHALO DENSITY POWER SPECTRUM

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SLIDE 67

DM SUBHALO DENSITY POWER SPECTRUM

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

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SLIDE 68

DM SUBHALO DENSITY POWER SPECTRUM

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

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SLIDE 69

DM SUBHALO DENSITY POWER SPECTRUM

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

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SLIDE 70

DM SUBHALO DENSITY POWER SPECTRUM

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

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SLIDE 71

DM SUBHALO DENSITY POWER SPECTRUM

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

10

−4

10

−3

10

−2

10

−1

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

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SLIDE 72

DM SUBHALO DENSITY POWER SPECTRUM

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SLIDE 73

DM SUBHALO DENSITY POWER SPECTRUM

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SLIDE 74

DM SUBHALO DENSITY POWER SPECTRUM

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SLIDE 75

DM SUBHALO DENSITY POWER SPECTRUM

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SLIDE 76

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

10

2

k [pc−1] P (k) [pc2]

M < 5 × 106M⊙ M < 5 × 107M⊙ 10−4 10−3 10−2 10−1

NFW Rs = Rti d a l/4 NFW Rti d a l → Rti d a l/4 point masses NFW Rs = Rti d a l/8 ∆α = 0.5

POWER SPECTRUM OF SUBHALO DENSITY FIELD

HEZAVEH, DALAL ET AL 2014

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SLIDE 77

10

−2

10

−1

10 10

1

k [pc−1] P (k) [pc2]

10−4 10−3

FORECAST FOR MEASURING THE DM SUBHALO POWER SPECTRUM WITH ALMA

HEZAVEH, DALAL ET AL 2014

BLACK: ~10 HR INTEGRATION RED: ~40 HR INTEGRATION

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SLIDE 78

FIRST DETECTION OF DM SUBHALO WITH ALMA (IN THE FIRST SOURCE STUDIED). FIRST MEASUREMENT OF THE SUBHALO MASS

FUNCTION WITH ALMA.

THE POWER OF ALMA AND THE

ABUNDANCE OF TARGETS PROMISES A BRIGHT FUTURE FOR DM STUDIES.

SUMMARY

smooth density field lensed by a field with low-k power lensed by a field with high-k power
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SLIDE 79

SIMULATIONS INDICATE THAT WITH ALMA,

WE CAN DETECT DM SUBHALOS IN THESE SYSTEMS

Msubhalo [M⊙] Probability

2 4 6 8 10 x 10

8

0.2 0.4 0.6 0.8 1

NBODY + RAY TRACING

SIMULATION

MOCK ALMA OBSERVATION DETECTED

SUBHALO

RECOVERED

SUBHALO MASS