Supernova Cosmology and Cosmic Rays: Developing Methods to Understand the Universe

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Supernova Cosmology and Cosmic Rays Developing
Methods to Understand the Universe

• Brian Connolly
• Columbia University
• 3/29/07

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National Research Councils Committee on Physics
of the Universe 11 Physics Questions of the New
Century

• What is dark matter?
• What is dark energy?
• How were the heavy elements from iron to uranium
  made?
• Do neutrinos have mass?
• Where do ultrahigh energy particles come from?
• Is a new theory of light and matter needed to
  explain what happens at very high energies and
  temperatures?
• Are there new states of matter at ultrahigh
  temperatures and densities?
• Are protons unstable?
• What is gravity?
• Are there additional dimensions?
• How did the Universe begin?

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Outline

• Dark Energy
• Studying Dark Energy with Standard Candles
• Why Type Ias Are Standard Candles
• almost
• Classifying Supernovae
• New Technique
• Extensions of this technique
• Ultrahigh Energy Cosmic Ray Spectrum Controversy
• Conclusions

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A Startling Discovery

• In 1998, the Supernova Cosmology Project and
  High-Z Supernova team construct Hubble diagrams
  using Type Ia supernovae
• Both found the expansion of the universe is
  accelerating!

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What Is Dark Energy?

• What we know about it
• Constitutes 70 of the Universe
• Accelerates the Universes expansion
• Determines the fate of the Universe
• What we dont know about it
• What is it? Einsteins cosmological constant,
  some kind of dynamic scalar field?

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Understanding Dark Energy

• A Dark Energy Task Force has been set up to
  address this question
• It includes 13 members from 12 institutions, as
  well as representatives from 3 funding agencies
  (DOE, NASA, NSF)
• One of their recommendation is to make use of the
  following four techniques for understanding dark
  energy
• Standard candles (type Ia supernovae)
• Weak gravitational lensing
• Baryon acoustic oscillations
• Galaxy cluster surveys

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Standard Candles and Dark Energy

• Suppose we have a source whose intrinsic
  luminosity Lsource is known (standard candle).
  The measured flux will be
• where dL is the luminosity distance related
  to redshift (z) and cosmology
• By measuring dL and z, can extract behavior of
  dark energy

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Outline

• Dark Energy
• Studying Dark Energy with Standard Candles
• Why Type Ias Are Standard Candles
• almost
• Classifying Supernovae
• New Technique
• Extensions of this technique
• Ultrahigh Energy Cosmic Ray Spectrum Controversy
• Conclusions

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Type Ia Supernovae

• Best objects that can be used as standard candles
• A type Ia supernova is a thermonuclear detonation
  of a progenitor C/O white dwarf, accreting from a
  companion.
• Since they all detonate at the Chandrasekhar
  Limit, standard candles

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Type Ia Supernovae as Standardized Candles
The Stretch Parameter
Luminous SNe Ia have slower light curves!
supernovae have peak magnitude dispersion
of 0.25 0.30 mags
Brightness
Brightness
Time after explosion
Time after explosion
0.15 mags dispersion
now the peak magnitude dispersion is 0.15 mag
STRETCH
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So Compelling Need to Find Type Ias

• Usually trying to pick Type Ias out of a heap of
  junk (lots of transients)
• AGNs
• Bad Images
• Other Types of Supernovae
• This will be difficult for large upcoming
  ground-based surveys with thousands of supernovae

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Next Generation Large Ground-based Supernova
Surveys

• The next-generation ground-based wide-field
  imaging surveys (DES, Pan-STARRS, LSST) will have
  a large impact on supernova cosmology
• They are naturally suited for the study of
  low-redshift supernovae, which are important
  because they provide
• a strong anchor for cosmology
• detailed SN heterogeneity studies
• peculiar velocity maps
• Galactic extinction maps

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Outline

• Dark Energy
• Studying Dark Energy with Standard Candles
• Why Type Ias Are Standard Candles
• almost
• Classifying Supernovae
• New Technique
• Extensions of this technique
• Ultrahigh Energy Cosmic Ray Spectrum Controversy
• Conclusions

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Typing Ground-based Supernovae

• Supernovae are most reliably classified as Ias
  or non-Ias through their spectrum
• The restframe 6150Å SiII feature is the strongest
  indicator that the candidate is a type Ia
• However, for very large ground-based surveys it
  will be impractical to try and obtain the
  spectral confirmation of each supernova
  candidates type
• It is thus crucial to develop methods of
  classifying supernova based on their photometric
  information alone

u band
b band
r band
i band
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Why is this difficult?

• Because the parameters of various classes of
  supernovae vary quite a bit, supernovae of
  different types can end up with similar
  lightcurves
• Especially difficult if the data are poorly
  sampled

HST F850LP
HST F850LP
Left plot solid line Ia at z 0.9, rest frame
B-band mag -18.15 dashed line
Ibc (early spectra have no H or Si), rest frame
B-band mag -17.92 Right plot dashed line 2p
(plateau in lightcurves), rest frame B-band mag
-16.08
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Current Techniques Color/Color and
Color/Magnitude Plots

• Color/Color Plot difference in magnitudes of
  different wave bands
• Differences in magnitudes in two pairs of filters
  plotted agains one another
• Curves vary dramatically with changing extinction
• Not trivial to do in practice
• Need to insert uncertainty in redshift
• Need to insert uncertainty in time of maximum
• Need to know systematics of own experiment
  systematics in template
• Need at least 3 spectral bands
• Color/Magnitude Plot magnitude vs. difference in
  magnitude i.e. B vs. B-V

http//wise-obs.tau.ac.il/dovip/typing/newMachine
.html
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Using Light Curve Fitter to ID Type Ia
Supernovae SALT Fitter

• Many light curve fitters
• c2 used by SNLS to fit photometric templates to
  data
• Can use c2 to ID supernovae
• c2, so dont account for different supernovae
  occupying same template space
• Only use information from best fit if doing
  classification

SNLS (Ground-based survey) 73 Spectroscopically
Confirmed Type Ias
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Need For Another Method

• Photometry for different supernovae may look
  similar
• It would be convenient to have a single number
  for the probability that a candidate is a Ia
  (i.e. not 5 c2s)
• No need to rely on color/color or color/magnitude
  plots from the literature
• Existing methods don't work very well for
  sparsely measured data in few filter bands

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Outline

• Dark Energy
• Studying Dark Energy with Standard Candles
• Why Type Ias Are Standard Candles
• almost
• Classifying Supernovae
• New Technique
• Extensions of this technique
• Ultrahigh Energy Cosmic Ray Spectrum Controversy
• Conclusions

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General Idea

• Developed by N. Kuznetsova and B. Connolly, ApJ
  659, 530 (2007)
• Pull a candidate from a sample and ask, what is
  the probability that a supernova candidate is of
  a particular type
• That is P(Tcandidate) probability of a
  supernova type given a candidate
• Will assume that the candidate is one of a number
  of known types that can be modeled
• Discuss later how to purify candidate sample
  (i.e. remove anomalies)

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New Approach

• Want to calculate the probability that a given
  candidate is a type T, P(T Di), where Di
  photometric measurement in some broadband filter
• Cant do this directly, but can make use of
  Bayes Theorem
• where P( Di T) is the probability to
  obtain the data Di for supernova type T, P(T)
  contains prior information about type T
  supernovae, and the denominator is the
  normalization over all of the known supernova
  types T.
• How can we calculate P( Di T) P(T)?
• We express it as a function of observables that
  characterize a given supernova type, and then
  marginalize them. These observables are
• Stretch
• Time of maximum
• Interstellar extinction
• Restframe B-band magnitude

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Marginalizing Parameters
We therefore have
Calculate this Youre done!
s
where tdiff difference in time of maximum
between model and data s stretch M
restframe B-band magnitude Av, Rv
Cardelli-Clayton-Mathis interstellar dust
extinction parameters
We assume that all of these parameters are
independent, so that
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Gory Detail (1)
Predicted
Measured
Error in Measurement
Assume flat prior for the difference between the
dates of max light between model and data
Flux
Time
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Gory Detail (2)
Number
Stretch
s, ss - Sullivan et al. astro-ph/0605455
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Gory Detail (3)

• Difficult, as no consensus on the model for
  Cardelli-Clayton-Mathis interstellar extinction
  parameters Av, Rv (ApJ 329, L33 (1988))
• Values of Rv from 2 to 3.5 have been suggested
  in literature
• Use some reasonable assumptions no extinction,
  modest extinction Av 0.4, and two values for
  Rv, 2.1 and 3.1
• Assume all three cases equally likely
• That is,

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Gory Detail (4)
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Redshift

• For these studies assume can measure redshift
  precisely
• In general, far from the case

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Rest frame B and V shift to NIR
Z 0.8
Z 1.2
Z 1.6
Optical Bands
Rest frame B
NIR Bands
Rest frame V
space-based 2-meter class telescope
Change in redshift means change in light curve in
filter band
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Mini-Summary

• P(Tcandidate) where the candidate is defined by
  its light curves and redshift
• Weve parameterized P(Tcandidate) in terms of
  stretch, magnitude, extinction so that
• We dont know what the true values for the
  stretch, magnitude, extinction are, so we
  marginalize them or integrate them out

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How Well Does It Work?

• We test the method on
• Monte Carlo Events
• Well-sampled ground-based data (candidates from
  the 3.6m Canada-France-Hawaii telescope collected
  by SNLS collaboration)
• Poorly sampled space-based data (gold and
  silver candidates from the HST GOODS sample, as
  classified by Riess et al. ApJ 607 (2004)
  665-687)

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Testing the Method Monte Carlo

• Simulate space-based observations in I- and
  Z-bands
• Same sampling as GOODS data (5 epochs separated
  by 45 days)
• Generate different types
• Probability that a candidate have a certain set
  of values for stretch, magnitude, etc. determined
  by probabilities inserted into P(Tcandidate)

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Testing the Method Monte Carlo
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Testing the Method Ground-Based
Using R-, I-, G- and Z-bands

• Candidates from the 3.6m Canada-France-Hawaii
  telescope collected by SNLS collaboration
• Well-sampled ground-based data
• 4 bands
• Lots of epochs

G-Band not well modelled not fit by SALT
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P(Iacandidate) vs. P(c2ndf)
SALT doesnt Fit G-Band

• This c2 SALT fitter used to find distance modulus
  in D.A. Howell et al. (2005) (to be published in
  ApJ)
• Maximized c2 fitter that uses Type Ia template as
  a function of magnitude, stretch, etc.
• Found corresponding P(c2 DOF)
• Only have Ias, so cant compare discrimination
  power of P(Tcandidate) and P(c2ndf)

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Examples of Best-Matching For Ground-Based (SNLS)
Experiment
Effectively maximizing
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Testing the Method Space-Based
Using I- and Z-Bands
Looks like a IIn
Silver candidate

• Works nicely even for very poorly sampled data!

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Examples of Best-Matching
Effectively maximizing
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Effect of Priors

• Stretch fixed stretch1
• Magnitude Flattened magnitude prior
• Extinction assumed none
• Effect Lowered probabilities a couple
  candidates in data samples
• In these wide range of data sets, probability
  dominated by fit to light curve
• Technicality Should use the distributions of
  magnitudes, stretches as seen in the detector
  (i.e. with detector acceptance folded in), but
  this fact enabled us to use real distributions as
  an approximation

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Outline

• Dark Energy
• Studying Dark Energy with Standard Candles
• Why Type Ias Are Standard Candles
• almost
• Classifying Supernovae
• New Technique
• Extensions of this technique
• Ultrahigh Energy Cosmic Ray Spectrum Controversy
• Conclusions

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Uses and Extensions

• Immediate Use
• Rates
• Have to deal with counting candidates with
  P(Ia,zCandidate)lt1
• Template Building
• Extensions
• Removing Anomalies
• Cosmological Parameter Fitting
• Exotic Extensions The Bayes Factor
• Are two supernovae of the same type?
• Gravitational Lensing

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Type Ia Rates
High-Z
Rates decline at higher redshifts!

• Count Type Ia supernovae with low statistics
  where each has P(Ia,zCandidate)lt1
• Two prevailing models (two-component and
  delay model)
• STAY TUNED!

T. Dahlen et al. ApJ 613 (2004) 189
SNLS
Rates increase at higher redshifts!
D. Neill et al., AJ 132 (2006), 1126
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Purging Anomalies

• Calc. P(Tcandidate) assumes candidate one of a
  handful of known types
• In practice, can have samples where 90 of
  candidates do not conform to objects that can be
  modeled
• So we do quantitatively what one would do by eye
  that is, remove anything that doesnt look like
  anything weve seen before
• It doesnt look like a supernova is probability
  that light curve from known type fluctuates to
  what is observed is ltQ

Lo
Area Q
ANOMALY
Events
MC
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Fitting Cosmological Parameters

• Suppose we have some cosmological model dependent
  on pi
• Parameterize
• Or even
• Allowing you to do cosmology with the help of
  non-Ias!
• Use Bayes Factor statistic to compare different
  models

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Exotic Extensions Gravitational Lensing Bayes
Factor

• Suppose we have two supernova originating from
  the same host galaxy and there is some time delay
  between the two of them
• Want to know if they are the same supernova (i.e.
  multiple images seen through gravitational
  lensing)
• Use Bayes Factor to evaluate relative probability
  that they are different as opposed to the same
  supernova

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Exotic Extensions Gravitational Lensing Bayes
Factor

• Bayes Factor (H.Jeffreys, 1936)
• Bayes Factor no stranger to cosmology
  (A.R.Liddle, 2004) or physics for that matter
• Here,

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A Similar Application for the Bayes Factor

• Calculation similar to another Bayes Factor
• Understand the HiRes/AGASA controversy
• Two ultrahigh energy cosmic ray experiments
• AGASA a surface detector in Akeno, Japan
• HiRes a fluorescence experiment in Dugway, Utah
• Both measure energy spectrum of cosmic rays over
  1018 eV
• One of main features of the spectrum should be
  the GZK cut-off seen Egt1019.5 eV

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GZK Suppression

• Greisen-Zatsepin-Kuzmin Suppression
• Cosmic rays interact with the 2.7 K microwave
  background
• Protons above 71019 eV suffer severe energy
  loss from photopion production
• Proton (or neutron) emerges with reduced energy,
  and further interaction occurs until the energy
  is below the cutoff energy

11 events with energies above the GZK
suppression (1.3 - 2.6 expected)
M. Takeda et al., PRL 81 (1998) 1163
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HiRes/AGASA Energy Spectrum Controversy

• HiRes and AGASA claimed to see different spectra
• HiRes claimed to be consistent with GZK cut-off
  (suppression of energy spectrum at Egt1019 eV)
• AGASA claimed not to be consistent with GZK
  cut-off

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Uncertainties to Consider

• Plot it correctly
• Statistical Uncertainties (Poisson Statistics)
• Energy Scale
• Can shift spectra relative to one another by
  roughly 1 bin (100.1 eV) CONSIDERING THE PROB.
  OF THAT SHIFT
• Need to consider changing aperature as we shift
  spectrum
• Bayesian Formalism MARGINALIZE

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Model-Independent Method to Test the Consistency
of Two Experiments
Bayes Factor (BF) Interpretation
BFgt1 Support for H1
10-1/2ltBFlt1 Minimal evidence against H1
10-1ltBFlt10-1/2 Substantial evidence against H1
10-2ltBFlt10-1 Strong evidence against H1
BFlt10-2 Decisive evidence against H1

• Bayes Factor (cousin of Likelihood Ratio)
• Method drawn from Harold Jeffreys (1936)

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Results

• Use Bayes Factor statistic to evaluate agreement
  of experiments Egt1019.6 eV
• D. De Marco, P. Blasi and A.V. Olinto,
  Astropart.Phys. 20 (2003) 53
• AGASA, HiRes 1, HiRes 2, Auger (preliminary)
• Evidence against 2 source hypothesis for Egt1019.6
  eV
• Room for models that agree with both spectra
• In principle, a theory that is in agreement with
  one spectrum does not imply agreement the second

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Comparison of AGASA, HiRes and Auger Spectra

• Minimal to substantial evidence against
  separate-parent hypothesis
• For 30 energy uncertainties
• BF(HiRes I,AGASA) 0.71 (minimal evidence)
• BF(HiRes II,AGASA) 0.04 (substantial evidence)
• BF(HiRes I,Auger) 0.54 (minimal evidence)
• BF(HiRes II,Auger) 0.85 (minimal evidence)
• BF(Auger, AGASA) 0.74 (minimal evidence)

B.M. Connolly et al., Phys.Rev. D74 (2006) 043001
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BF versus Fractional Energy Scale Uncertainty

• Variation of Energy Scale Uncertainties

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2. (For Completeness) Is There Evidence
Anywhere of GZK Cutoff? HiRes Energy Spectrum

• (Broken) power law fits
• No break ?2/dof
  154/39

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HiRes Energy Spectrum

• (Broken) power law fits
• No break ?2/dof
  154/39
• One break allowed ?2/dof
  67/37 (4 EeV)

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HiRes Energy Spectrum

• (Broken) power law fits
• No break ?2/dof
  154/39
• One break allowed ?2/dof
  67/37 (4 EeV)
• Two breaks allowed ?2/dof 40/35
• High energy break at 60 EeV
• Difference in ?2 corresponds to 5? significance
  
• HiRes Sees Something, but is it GZK? NO NULL
  HYPOTHESIS

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HiRes/AGASA Controversy

• Needed to ask the right questions
• Bayes Factor enabled us to determine whether or
  not HiRes/AGASA were measuring same spectrum
• Then can ask whether or not they are consistent
  with something
• Conclusion Storm in a bottle
• Agreement between two experiments
• HiRes seems to be consistent with suppression at
  high energies that may be GZK cut-off

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Conclusions

• Understanding dark energy is a high priority task
  for the physics community
• Type Ia supernovae crucial for the purpose.
• Large upcoming ground-based surveys will have to
  rely on photometry to identify Ia's
• We have developed a novel method for typing
  photometrically measured supernovae using a
  Bayesian probabilistic approach
• Can easily add to the method once new information
  becomes available
• e.g., much better supernova templates from the
  Nearby Supernova Factory - to measure the spectra
  of 300 nearby supernovae
• Current applications
• Type Ia Rates
• Template building
• Lots of work in progress on extensions of the
  method!
• Cosmology
• Anomalies
• Using the Bayes factor to rule out (or confirm)
  gravitational lensing of supernovae
• Bayes factor to do model comparisons!
• Novel statistical techniques such as the Bayes
  factor have a wide range of applications
• In particular, we have used it to resolve a long
  standing controversy in the energy spectra of
  cosmic rays

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