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

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 , Y. M AO , W. M ORNINGSTAR R. B LANDFORD , J. C ARLSTROM , C. F ASSNACHT , P. M ARSHALL , N. M URRAY L. P ERREAULT L EVASSEUR , J. V IEIRA , R. W ECHSLER AND THE S OUTH P OLE T ELESCOPE DMS TEAM

S MALL -S CALE S TRUCTURE OF D ARK M ATTER Small scale distribution of Large scale structure is very dark matter is not well well constrained. understood.

M OTIVATION C OMPARING MW DWARF GALAXIES TO DM SUBHALOS N BODY SIMULATIONS O BSERVED MW SATELLITES T HEORY : N>> 1000 O BSERVATION N~10

T HE M ISSING S ATELLITE P ROBLEM L ONG STANDING PROBLEM FOR CDM S TRIGARI ET AL . 2007 A P J. 669, 676

S OLUTIONS B ARYONIC G ASTROPHYSICS D ARK M ATTER P HYSICS 2 keV Warm Dark Matter Cold Dark Matter L OVELL ET AL 2012, MNRAS 420, 3

S TRONG G RAVITATIONAL L ENSING

S TRONG G RAVITATIONAL L ENSING M ULTIPLY I MAGED F ISH

S TRONG G RAVITATIONAL L ENSING

S UBSTRUCTURE L ENSING

S UBSTRUCTURE L ENSING

A SENSE OF SCALE … Cold Dark Matter

SDP.81

SDP.81

L ENS M ODELING P OSTULATE A S OURCE M ORPHOLOGY ( WITH PARAMETERS P S ) RAY - TRACING MODEL SIMULATION P OSTULATE A M ASS G ENERATE THE LENSED DISTRIBUTION IN THE LENS IMAGE OF THE SOURCE ( WITH PARAMETERS P M ) DATA M AXIMIZE THE LIKELIHOOD OF THE MODEL PARAMETERS GIVEN THE DATA

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?)

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?)

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ] F OURIER SPACE P OSITION SPACE ( SKY )

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ]

I NTERFEROMETRY : ( WHAT DOES ALMA MEASURE ?) 1 0.5 v [M λ ] 0 − 0.5 − 1 − 1 − 0.5 0 0.5 1 u [M λ ] NOT NOISE

L ENS M ODELING FOR I NTERFEROMETRIC D ATA 1 - Postulate Sky Model 2 - Predict the Visibilities on Parameterized by the measured uv coverage Source and Lens Properties 5 x 10 − 6 − 4 − 2 0 2 4 1 arcsec 6 − 6 − 4 − 2 0 2 4 6 5 x 10 4 - Form a χ2 likelihood and 3 - Add additional Sample the posterior using a parameters for antenna parameter exploration phases method (MCMC, etc.)

M ODEL P ARAMETERS parameters describing the light distribution in the background source (P source ) sky emission parameters describing the mass distribution in the foreground lens (P lens )

L ENS MODELING WITH PIXELATED SOURCES p source = L ( p lens ) × = L ( p lens ) × p source sky surface brightness

L ENS M ODELING WITH PIXELATED SOURCES matter distribution in the lens v = F L ( p lens ) × p source |{z} |{z} e − i ~ " # k ~ r ... ∼ 10 6 . . . |{z} background source ∼ 10 4

SUCCESSFULLY TESTED ON MOCKS GENERATED WITH AN INDEPENDENT CODE W ARREN M ORNINGSTAR ( GRAD @ S TANFORD )

EXAMPLE : SOURCE RECONSTRUCTION mock data (dirty image)

EXAMPLE : SOURCE RECONSTRUCTION reconstructed source

EXAMPLE : SOURCE RECONSTRUCTION true source (mock)

EXAMPLE : SOURCE RECONSTRUCTION reconstructed source true source (mock) − 1 ⇤ − 1 ⇥ − 1 ( FBL ) + C s − 1 D ⇥ ( FBL ) T C N ( FBL ) T C N ⇤ S = For realistic ALMA data, solving this requires thousands of cpu-cores.

L INEARIZING THE M ODEL ( SUBHALO FINDER ) 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.

P ROBABILITY OF THE PRESENCE OF A SUBHALO greyscale: difference in log posterior between a model which includes a subhalo and a smooth model (no subhalos) H EZAVEH ET AL . 2016

SDP 81 
 (ALMA SCIENCE VERIFICATION DATA ) B LUE : HST D UST CO 8-7 R ED : ALMA

SDP 81 
 R ECONSTRUCTED B ACKGROUND S OURCE H EZAVEH ET AL . 2016

F IRST D ETECTION OF A DM S UBHALO WITH ALMA H EZAVEH ET AL . 2016

F IRST D ETECTION OF A DM S UBHALO WITH ALMA H EZAVEH ET AL . 2016

P ROBABILITY OF A SECOND S UBHALO H EZAVEH ET AL . 2016

C ONSTRAINTS ON THE M ASS F UNCTION OF S UBHALOS IN THE H OST H ALO H EZAVEH ET AL . 2016

C ONSTRAINTS ON THE M ASS F UNCTION OF S UBHALOS IN THE H OST H ALO T HEORY : Y AO -Y UAN M AO H EZAVEH ET AL . 2016

C OMPARISON TO T HEORETICAL P REDICTIONS T HEORY : Y AO -Y UAN M AO H EZAVEH ET AL . 2016

C ONSTRAINTS ON THE M ASS F UNCTION OF S UBHALOS IN THE H OST H ALO H EZAVEH ET AL . 2016

C ONSTRAINTS ON THE M ASS F UNCTION OF S UBHALOS IN THE H OST H ALO H EZAVEH ET AL . 2016

ALMA OBSERVATIONS OF SPT- DISCOVERED SOURCES B LUE : HST ( OPTICAL ), R ED : ALMA (C YCLE 0) V IEIRA ET AL . N ATURE 2013 H EZAVEH ET AL . A P J. 2013

SPT2134-50 (ALMA C YCLE 2) B AND 6 ( RED : ALMA CONTINUUM , BLUE : HST) M ORNINGSTAR LEADING THE ANALYSIS

SPT2134-50 (ALMA C YCLE 2) B AND 6 ( CONTINUUM ) M ORNINGSTAR LEADING THE ANALYSIS

C ONSTRAINTS ON THE M ASS F UNCTION OF S UBHALOS IN THE H OST H ALO lensed by a fi eld lensed by a fi eld smooth density fi eld with low-k power with high-k power H EZAVEH ET AL . 2016

E FFECT OF S OURCE S IZE : L ARGER S OURCE = L OWER S ENSITIVITY

W E NEED A SMALL SOURCE , OR A SOURCE WITH SMALL FEATURES ...

W E NEED A SMALL SOURCE , OR A SOURCE WITH SMALL FEATURES ... VELOCITY STRUCTURE E NGEL ET AL 2010, A P J

3D LENS MODELING (3 RD DIMENSION = WAVELENGTH )

S ENSITIVITY A NALYSIS OF D ETECTING DM S UBHALOS 0.35 0.3 ϵ 0.25 angle [degree] 110 109 108 107 106 9 log M s [M ⊙ ] 8.5 8 7.5 7 1 x s [ arcsec ] 0.8 0.6 0.4 1.3 y s [ arcsec ] 1.2 1.1 1 0.9 11.598 11.6 11.60211.60411.606 0.25 0.3 0.35 106 108 110 7 8 9 0.4 0.6 0.8 1 0.9 1 1.1 1.2 1.3 7 8 9 log M [M ⊙ ] ϵ angle [degree] log M s [M ⊙ ] x s [ arcsec ] y s [ arcsec ] ] log M s [M ⊙ ] A FTER MARGINALIZING OVER ~60 SOURCE PARAMETERS H EZAVEH , D ALAL ET AL 2013, A P J. 767, 9

SPT2134-50 (ALMA C YCLE 2) B AND 6 (CO 7-6) M ORNINGSTAR LEADING THE ANALYSIS

C ONSTRAINTS ON THE M ASS F UNCTION OF S UBHALOS IN THE H OST H ALO lensed by a fi eld lensed by a fi eld smooth density fi eld with low-k power with high-k power H EZAVEH ET AL . 2016

W E CAN DETECT AND MODEL MASSIVE SUBHALOS W HAT ABOUT THE THOUSANDS OF LOWER MASS ONES ? C AN WE DETECT THEM AS A WHOLE ? 5 10 4 10 3 10 N( > M) 2 10 1 10 0 10 5 6 7 8 9 10 M [ M ⊙ ]

R ESIDUALS FROM M ODELING WITH A S MOOTH L ENS : lensed by a fi eld lensed by a fi eld smooth density fi eld with low-k power with high-k power

C OVARIANCE OF D ENSITY P OWER SPECTRUM DEFLECTIONS

DM SUBHALO DENSITY P OWER S PECTRUM 2 10 1 10 0 10 P ( k ) [pc 2 ] − 1 10 − 2 10 − 3 10 − 4 10 − 5 10 − 6 10 − 4 − 3 − 2 − 1 10 10 10 10 k [pc − 1 ]

DM SUBHALO DENSITY P OWER S PECTRUM

DM SUBHALO DENSITY P OWER S PECTRUM 2 2 10 10 1 1 10 10 0 0 10 10 P ( k ) [pc 2 ] P ( k ) [pc 2 ] − 1 − 1 10 10 − 2 − 2 10 10 − 3 − 3 10 10 − 4 − 4 10 10 − 5 − 5 10 10 − 6 − 6 10 10 − 4 − 4 − 3 − 3 − 2 − 2 − 1 − 1 10 10 10 10 10 10 10 10 k [pc − 1 ] k [pc − 1 ]

DM SUBHALO DENSITY P OWER S PECTRUM 2 2 2 10 10 10 1 1 1 10 10 10 0 0 0 10 10 10 P ( k ) [pc 2 ] P ( k ) [pc 2 ] P ( k ) [pc 2 ] − 1 − 1 − 1 10 10 10 − 2 − 2 − 2 10 10 10 − 3 − 3 − 3 10 10 10 − 4 − 4 − 4 10 10 10 − 5 − 5 − 5 10 10 10 − 6 − 6 − 6 10 10 10 − 4 − 4 − 4 − 3 − 3 − 3 − 2 − 2 − 2 − 1 − 1 − 1 10 10 10 10 10 10 10 10 10 10 10 10 k [pc − 1 ] k [pc − 1 ] k [pc − 1 ]