Tidal Streams, Dark Matter, and Volunteer Computing with

MilkyWay@home

Heidi Jo Newberg Rensselaer Polytechnic Institute

Outline of Talk

• Dark Matter and tidal streams

• MilkyWay@home

• Statistical Photometric Parallax

• Constraining dark matter with N-body simulations of tidal streams

Mercury

Venus

Earth

Mars

Jupiter

Saturn Uranus

Keplerian decline

99.9% of the mass of the solar system is in the Sun. For the case where all of the mass is at the center, the orbital speed is proportional to r-1/2.

Distance from the Sun (AU)

Re

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If the mass stops where the light stops, then we expect the rotation speed to fall off like the blue curve.

The nearly flat rotation curves of galaxies lead us to believe that the stars in galaxies are at the centers of large dark matter halos.

The nearly flat rotation curves of galaxies lead us to believe that the stars in galaxies are at the centers of large dark matter halos.

Billions of dark matter particles may be passing through each of our bodies every second.

That is, in addition to the trillions of neutrinos that are passing through our bodies every second.

Possible Dark Matter Halo Shapes

spherical oblate

prolate

triaxial lumpy

Also, the shape could change with time and radius…

V. Springer et al. (2008)

Kat

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n J

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on

Simulation of a dwarf galaxy in orbit around the Milky Way.

Determining the distribution of dark matter from tidal streams

We can in principle measure the positions and velocities of every star in the Milky Way. But the stars in tidal streams are the only ones for which we know where they were in the past (in the dwarf galaxy). This gives us information about the gravitational potential through which the stars have moved.

Sagittarius dwarf galaxy

Position of Sun (the excess of stars here are disk stars near the Sun)

Dashed line shows the position of stars pulled off the dwarf galaxy into “tidal tails”

Positions of M giant stars in the Milky Way

(1) Measure spatial density and velocity information for a dozen known tidal streams

(2) Define parameters for orbits and internal properties of dwarf galaxies (11 parameters for each tidal stream), and parameters for the spatial distribution of dark matter (any number of parameters)

(3) Run N-body simulations of the tidal disruption of the dwarf galaxies, and optimize parameters so that the results of the simulation match the measurements of actual tidal streams (30 minutes for 1 dwarf, 1 CPU).

Determining the distribution of dark matter from tidal streams

Wow – that’s a lot of parameters!

Began: November 9, 2007 Computing power: 0.5 PetaFLOPS (high over 2 PetaFLOPS) Number of volunteers (total people): 146,863 Number of computers volunteered (total): 291,944 Number of active volunteers: 25,670 Number of active computer being volunteered: 35,686 Applications: (1) Fit density structure of tidal streams, (2) fit dwarf galaxy properties with N-body simulations

Number of volunteers as of 10/4/2012

~100 people per day join MilkyWay@home.

Milkyway@Home is currently run by:

Heidi Newberg, Professor of Physics, Applied Physics, and Astronomy Travis Desell, Assistant Professor of Computer Science, University of North Dakota Malik Magdon-Ismail, Professor of Computer Science Carlos Varela, Associate Professor of Computer Science Boleslaw Szymanski, Claire and Roland Schmitt Distinguished Professor of Computer Science Matthew Newby, now Adjunct Faculty in Physics, Applied Physics, and Astronomy Jeffery Thompson, Graduate Research Assistant in Physics, Applied Physics, and Astronomy Matt Arsenault, Graduate Research Assistant in Physics (on leave at AMD) Adam Susser, Undergraduate Research Assistant in Physics, Applied Physics, and Astronomy Jake Bauer, Undergraduate Research Assistant in Physics, Applied Physics, and Astronomy Jake Weiss, Undergraduate Research Assistant in Physics, Applied Physics, and Astronomy

With previous support from: Benjamin Willett, Nathan Cole, Steve Ulin, Colin Rice, Shane Reilly, Joe Doran, Brian Chitester, Dave Przybylo, John Vickers, and Anthony Waters

Astronomy students write algorithms to measure goodness of fit between data and models with parameters.

MilkyWay@home server sends out jobs to volunteers and collects results – one set of parameters to each volunteer.

Parameter optimization algorithms are adapted to run on asynchronous, heterogeneous, parallel computing environment. The code is compiled and tested on 15 platforms including CPUs and GPUs, and attached to the server. Mechanisms are created to start and end “runs.” The MySQL database is maintained.

Volunteer Computing with

150,000 volunteers:

• Let us use their CPUs for scientific calculations

• Continously upgrade their hardware

• Populate extensive forum discussions on science, technical support, and well, anything

• Monitor the health of our system (especially our volunteer moderator)

• Wrote the first GPU version of

our software

• Donate money and hardware

Volunteer Computing with

150,000 volunteers also:

• Compete with each other for BOINC “credits”

• Become angry if another person or team is getting an unfair number of credits

• Return garbage results (which require zero computations) so they can earn credit faster

• Insult each other on public

forum boards

• Link anti-Semitic websites to ours

206 countries (of which 193 are UN members)

from boincstats.com, 12/3/13

Communication with Volunteers

• News

• Message Boards

• Science Pages

• YouTube Channel

• China Publicity:

Article in current issue of “Amateur Astronomer”

Public talk at Beijing Planetarium on Saturday

Chinese language website beginning in March 2014

• Coming soon: badges for credits and donations

• Future: Allow volunteers to choose their own parameters.

The use of statistical knowledge of the absolute magnitudes of stellar populations to determine the density distributions of stars.

Statistical Photometric Parallax

Newberg (2013), IAU Syposium 289

Newberg et al. 2002

Vivas overdensity, or Virgo Stellar Stream

Sagittarius Dwarf Tidal Stream

Stellar Spheroid

Monoceros stream, Stream in the Galactic Plane, Galactic Anticenter Stellar Stream, Canis Major Stream, Argo Navis Stream, Anticenter Comples

Hercules-Aquila cloud

Ringing in the disk??

All halo density substructures have been identified by eye. Though their structure is complex, they have been characterized by very simple measurements.

Pal 5

Newby et al. (2011)

SDSS CMDs for 11 globular clusters studied Mg vs. (g-r)

Matthew Newby

All halo GCs have the same turnoff at g=4.2!

Newby et al. (2011) selected all of the stars in each cluster that were in the 0.1<(g-r)<0.3 range. We then made a histogram of the absolute magnitude distributions of these stars, and fit a double-sided Gaussian.

The shape and absolute magnitude of the peak is independent of metallicity and age of the cluster.

That is because increasing the age moves the turnoff fainter and redder, but older populations are generally more metal poor, which moves the turnoff brighter and bluer.

Increased age dimmer and redder

Decreased metallicity brighter and bluer

The maximum likelihood technique finds the model parameters Q that make the observed star positions (li,bi,gi) the most likely. The probability density function (PDF) is constructed in the following way: (1) For each stellar component, one assumes a parameterized model (for

example a double exponential, NFW, Hernquist, etc.) (2) The spatial density is transformed to (l,b,g) coordinates. (3) This density is convolved with the absolute magnitude distribution of

the tracers, so that we find the distribution that we expect to observe. (4) This expected distribution is multiplied by the fraction of stars that are

observed in a given survey, as a function of apparent magnitude. (5) The resulting distribution is normalized so that the integrated

probability of finding a star in the entire volume observed is one. (6) The final PDF is the sum of the fraction of stars in each component

times the normalized distribution, summed over the number of components in the model. The fraction of stars in each component are also parameters that are fit in the maximum likelihood optimization.

Maximum Likelihood

Cole et al. (2008), Newby et al. (2013)

Doing this integral is very time-consuming!

Automatic detection of tidal streams The original plan was to create an algorithm that would

automatically detect tidal streams and fit the parameters of each individual stream and any remaining smooth component.

We need to fit 20 parameters (2 smooth component, 6 for each stream) to each of eighteen 2.5°-wide stripe.

The number of iterations to compute the likelihood increases with the number of stars, and the required accuracy of the calculation.

At four hours per evaluation and 50 likelihood calculations per iteration in a conjugate gradient descent method and 50 iterations, 10,000 hours are required to optimize one stripe. This would take more than 400 days on a single processor. So it is a good thing we have MilkyWay@home!!

Newby et al. (2013)

The detections of the Sgr stream are shown in Galactic Coordinates. We also were able to fit a plane to each arm, and measure the angle of precession between them.

Galactic Z vs. X

Galacic Y vs. X

Data from one stripe Stream 1 (6 parameters) Stream 2 (6 parameters)

Stream 3 (6 parameters) Smooth (3 parameters) We can separate the data in an individual stripe into sets of stars with the density profile of the smooth background, and the density profile of each of the stripes. Newby et al. 2013

2

1.9 million F turnoff stars

160,000 stars with Sgr density 1.7 million non-Sgr stars

Polar plots of SDSS F turnoff stars in the north Galactic Cap (top). Using our density model, we place each star in either the Sgr (lower left) or non-Sgr panel (lower right), with the probability given by the model. The stars in the Sgr panel are not guaranteed to be from the stream, but they collectively have the spatial properties of the Sgr stream.

Results – Mapping the Sgr Tidal Stream

Newby et al. (2013)

In Progress: N-body fits to tidal streams

We are running n-body simulations of dwarf galaxy tidal disruption (100,000 particles per dwarf and analytical Galaxy potential). We will compare the measured positions & velocities of stars in the tidal stream with the final positions and velocities of bodies in an n-body simulation.

Eventually will fit fit: multiple dwarf galaxy parameters, orbit parameters, Galactic potential parameters, rotation curve.

Degeneracy of parameters currently being explored.

Newberg et al. 2010

Density of stars at the correct distance to be members of the Orphan Stream (left). Density of stars along the Orphan Stream (above).

The density of stars along the Orphan Stream 星流的恒星密度分布

Newberg et al. 2010

Sample 100,000 particle (sub-sampled above) semi-analytic N-body simulations of the tidal disruption of the Orphan Stream. We fit only the evolution time and the two-component Plummer sphere parameters for the dwarf galaxy, by comparing a histogram of the stellar density along the stream in the “data” and the model.

Variable Search Range Simulated

Value

Particle

Swarm

Differential

Evoluion

Evolution Time (Gyr) 1-3 2 2.1 2.1

Forward Time/Backward Time 0.5 – 1.5 1 1.0 1.0

Total Mass (simulated units) 1 – 100 10 11.0 9.6

Stellar Mass / Total Mass 0 – 1 0.5 0.8 0.46

Stellar Scale Radius (kpc) 0.15 – 2 1 1.0 1.2

Stellar Radius / Dark Radius 0 – 1 0.5 0.64 0.85

Determining the dark matter content of the

progenitor dwarf galaxy

These results are promising for being able to measure the dark matter content of the progenitor dwarf galaxies. The evolution time, total mass, and stellar scale radius are well fit. If we can fit the total mass, the stellar to total mass ratio should be easy; the problem is likely a bug. It may not be possible to fit the dark matter scale radius, since we only observe the positions of stars in the stream.

Jake Bau

er

Conclusions • MilkyWay@home is a powerful resource (0.5

PetaFLOPS) for optimizing model parameters. • We have used statistical photometric parallax to

measure the density distribution of turnoff stars in the Sagittarius dwarf tidal stream, and we are working towards a model of the halo volume, including the major tidal streams, observed by the Sloan Digital Sky Survey.

• We believe we can constrain the distribution of dark matter in dwarf galaxies and in the Milky Way with N-body simulations of tidal streams. We are in the process of building a system that will be capable of doing this. Currently, we are working on constraining the dark matter content of the progenitor dwarf galaxy.