COUPP Project Internship

Using Bubble Chambers for Dark Matter Detection

Summer 2007

Overview

• Introduction to Dark Matter Detection

• Introduction to COUPP• Chicagoland Observatory for Underground Particle Physics (COUPP)

• Data Analysis Review Project

Introduction to Dark Matter

DetectionWhat is dark matter?Why do we think it

exists?How can we “see” dark

matter?What are the current leading experiments?

What is Dark Matter?

About 95% of the Universe’s mass and energy is invisible to us

DM ≈ one third

Dark Matter is matter that does not emit or reflect electromagnetic radiation

Therefore, except for gravitational effects, it is functionally invisible

Dark Matter is one hypothesis explaining several cosmological challenges

Why do we think DM exists?

Galactic Dynamics:For stars to move with velocities they have, there must be far more mass (to keep in orbits)[Vera Rubin, Fritz Zwicky]

Weak Lensing:Photons are deflected by a gravitational field, so clumps of matter will cause distortions in the appearance of galaxies

Cosmological Structure:Slow-moving dark matter appears necessary to generate galaxies and large-scale structures (need fluctuations)

Universe’s Expansion:Inflation demands Universe have critical density, but visible mass accounts for considerably less than this

Why do we think DM exists?

The Bullet Cluster:One idea is simply to modify gravity at large scale

Why not just modify gravity?

Collision between two galaxy clusters with hot gas

Hot gas (red) slowed by drag force, while dark matter (blue) not slowed by impact

If hot gas most massive component (per alternative gravity theory), this would not occur

*

*

*

*Separation of dark matter

and the gas

How can we detect dark matter?

Direct DetectionIndirect DetectionWe know WIMPs can collide with each other, producing neutrinos or gamma rays

Gamma rays produced as a factor of density squared -- look for high density of DM (center of galaxy)

So look for neutrinos and gamma rays -- because WIMPs really high energy, look for GeV energy gamma rays and neutrinos

WIMPs can also collide with target nuclei

Set up experiment to watch for WIMP collisions with target nuclei

What are the current leading experiments?

CDMS Xenon 10

(Direct Detection)

Cryogenic Dark Matter SearchTo reduce noise :

Very coldBottom of Soudan Mine(neutrons produced from atmospheric muons)

Phonons -- tiny increase in heat in single cold Germanium crystal

Phototubes in liquid Xenon

Surpassed CDMS early 2007

Ionization

Look for ratio of:

Look for ratio of ionization to scintillation signal

Introduction to COUPPMethods of Detection

DesignAdvantages over

Competitors

Methods of Detection

Heavy

heavy target nucleus

Dark matter particle from galatic halo

nuclear recoilEnergy 1-100 keV

Design

Liquid, temperature and pressure tuned so

that WIMP must provide majority of

energy to form bubble

Advantages of Bubble Chambers

• Low cost• Easily reaches large sizes

• Low energy thresholds for nuclear recoils

• Backgrounds ( and ) easily suppressed [run at low pressure]

fairly convention pressure vesselcommercial partsprimary cost associated with maintaining cleanness

Heat is tuned (low enough) to not allow bubble formation by gamma or beta particlesAlso why runs for extended period of time

Because sufficient degree of superheat

Advantages of Bubble Chambers

•Variety of target nuclei

• CF3Br• CF3I• C3F8• Xe• etc.

•Neutron backgrounds can be measured by multiple bubble events

Neutrons bounce Some fraction produce more than one bubbleSource of neutrons included to simulate neutron Important b/c lack of muon shielding (except eriks)

Different kinds of dark matter interact differently with different target atoms/nuclei

Data Analysis Review Project

ProblemMethod of Assessment

Results

Problem

With what accuracy does the current method of data analysis report the radon levels in the bubble

chamber?

Method of Assessment1) Develop Monte Carlo to simulate the real data2) Analyze MC data using the project’s data analysis

methods (Maximum Likelihood method of fit)3) Determine the fraction of bubble counts that data

analysis would attribute to Radon4) Compare the data analysis fraction to the fraction

actually input into the Monte Carlo

The bubble chamber is contaminated with Radon. This results in a significant background count.

Monte Carlo Simulation

• Must mimic Radon decay chain as well as “other” (suspected Dark Matter) component

• Bubble chamber will not detect any bubble formation within 30 seconds of a previous bubble

• Amount of “other” component relative to Radon must be easily adjusted (to be looped)

• Run quickly (very large time loops) to mimic actual week long data runs

Constraints

What occurs in the bubble chamber?

1. Radon enters, probably through “O-rings”, moves around, even through plastic, in liquids, etc.

2. Beta decays invisible, but alpha decays produce bubbles..

3. Alpha particle emission for:Radon 222 to Polonium 218

Polonium 218 to Lead 214

Polonium 214 to Lead 210

Unless tens of years, only these relevant

COUPP’s Data Analysis MethodMaximum Likelihood Method

for a sum of exponentials• We suspect that there are two

primary components to the data• Radon• Other -- (simply not Radon, may include dark matter)

• Radon has a known half life that is short enough to be highly visible in bubble chamber data

• Fit two exponentials• one is the Radon component (known exponential decay)

• the other component has decay given by the fit

• Three free parameters• two coefficients, one exponential power

Time difference in seconds

Num

ber o

f Eve

nts

Time difference in seconds

Num

ber o

f Eve

nts

Run data vs. Monte Carlo

Time difference in seconds

Num

ber o

f Eve

nts/

0.5(

min

)

Monte Carlo Simulation for COUPP Bubble Chamber data

Check Minimization of the Likelihood Function

Visual check (approximate) of minimization of likelihood function(for one free parameter)

Radon Fraction• Can determine Radon

component because of known 3.1 minute half-life

• Expect Radon to decay with known exponential curve

• To determine number of decays, integrate under curve

• For each Radon decays, two decays will later occur

• So for each bubble we label as 3-minute-Radon, we expect two additional triggers

3 x 3-minute-Radon

Total Number of Triggers

Radon Fraction =

Comparison of Data Analysis and Actual

Radon Fraction

Create a loop, inputting a variety of Radon Fraction values

• Percent error between the given Radon fraction and the calculated value

• Deviation within each fraction calculation

Goal:

Output:

alpha = 0omega = 15gap = 1for z = alpha:gap:omega Z = z+1a = Fraction_Repeat_PDM_Loop(z)% Now we fit to a Gaussianxmin = 0;xmax = 1.5;ymin = 0;ymax = 40;bingapP = .025;gauss_data = a;bin_sizeP= 0.5:bingapP:xmax;n_elementsP = histc(gauss_data,bin_sizeP);nmax = n_elementsP(n_elementsP>(n_elementsP-(.1*z)))del_TP = xmax/bingapP;mu(Z) = mean(a);sigma(Z) = std(a);j = 0:.01:1.25chi = (1/((sigma(Z))*((2*pi)^(1/2))))*…

(exp(-((j-(mu(Z))).^2)./(2*((sigma(Z))2))))%FIGURE 2figurehist(a)hold onplot(j,chi)

Results

Mean valueMean value of Radon fraction calculated by the analysis is fairly accuratefairly accurate for high Radon fractions -- for low values, problematic

VarianceVariance, however, can be quite largequite large, with values often at seven to eight percent of the actual Radon fraction (for high Rn fractions)

Analysis underestimates for lowunderestimates for low Radon fraction values and overestimates for higheroverestimates for higher Radon fraction values

Radon Fraction

Estimated Radon Fraction Estimated Radon Fraction

Estimated Radon Fraction Estimated Radon Fraction

= 0.0359 = 0.0441

= 0.0422 = 0.0349

Radon Fraction

Estimated Radon Fraction

Num

ber o

f run

s est

imat

ing

a gi

ven

Rad

on fr

actio

n

= 0.0422

Actual vs Estimated Radon Fraction

Actual Radon FractionEstimated Radon Fraction

Bias

BiasOne interesting aspect to note in the representation of the bias is that the data analysis underestimates the Radon fraction at low values and overestimates the Radon fraction at high values.

Variance

Variance

VarianceIncluding low Radon

fraction

VarianceExcluding low Radon

fraction

Conclusions

Analysis method has sufficient accuracy, but is dependent on the Radon fraction

Considerable variance in individual runs from the mean, so experiment must conduct many runs, to ensure that an accurate mean is determined

Low Rn fraction unlikely, given actual data, so accuracy good

Questions