Transcript Standard candles

Supernova Cosmology and
Cosmic Rays:
Developing Methods to Understand the
Universe
Brian Connolly
Columbia University
3/29/07
National Research Council’s 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?
Outline
Dark Energy
Studying Dark Energy with Standard Candles
Why Type Ia’s Are Standard Candles

…almost
Classifying Supernovae
New Technique
Extensions of this technique

Ultrahigh Energy Cosmic Ray Spectrum Controversy
Conclusions
A Startling Discovery
In 1998, the
Supernova
Cosmology
Project and HighZ Supernova
team construct
Hubble diagrams
using Type Ia
supernovae
Both found the
expansion of the
universe is
accelerating!
What Is Dark Energy?
What we know about it:



Constitutes ~70% of the Universe
Accelerates the Universe’s
expansion
Determines the fate of the
Universe
What we don’t know
about it:

What is it? Einstein’s
cosmological constant, some kind
of dynamic scalar field?
Artistic view
of dark energy
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:
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Standard candles (type Ia supernovae)
Weak gravitational lensing
Baryon acoustic oscillations
Galaxy cluster surveys
6
Standard Candles and Dark Energy
Suppose we have a source whose
intrinsic luminosity Lsource is known
(standard candle). The measured
flux will be:
Lsource
f obs 
4d L2
where dL is the luminosity distance
related to redshift (z) and cosmology
By measuring dL and z, can extract
behavior of dark energy
7
Outline
Dark Energy
Studying Dark Energy with Standard Candles
Why Type Ia’s Are Standard Candles

…almost
Classifying Supernovae
New Technique
Extensions of this technique

Ultrahigh Energy Cosmic Ray Spectrum Controversy
Conclusions
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
white dwarf
9
Brightness
supernovae have peak magnitude
dispersion
of 0.25 – 0.30 mags
Brightness
Type Ia Supernovae as Standardized
Candles: The Stretch Parameter
Luminous SNe Ia
have slower light
curves!
Time after explosion
Time after explosion
~0.15 mags dispersion
now the peak magnitude
dispersion is 0.15 mag
STRETCH
10
So Compelling Need to Find Type Ia’s
Usually trying to pick
Type Ia’s out of a heap of
junk (lots of transients)



AGN’s
Bad Images
Other Types of Supernovae
This will be difficult for
large upcoming groundbased surveys with
thousands of supernovae
Next Generation Large Groundbased 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 lowredshift supernovae, which are important
because they provide:
–
–
–
–
a strong “anchor” for cosmology
detailed SN heterogeneity studies
peculiar velocity maps
Galactic extinction maps
Outline
Dark Energy
Studying Dark Energy with Standard Candles
Why Type Ia’s Are Standard Candles

…almost
Classifying Supernovae
New Technique
Extensions of this technique

Ultrahigh Energy Cosmic Ray Spectrum Controversy
Conclusions
Typing Ground-based Supernovae
r band
i band
• However, for very large groundbased surveys it will be
impractical to try and obtain the
spectral confirmation of each
supernova candidate’s type
• It is thus crucial to develop
methods of classifying
supernova based on their
photometric information alone
b band
‒ The restframe 6150Å SiII feature is
the strongest indicator that the
candidate is a type Ia
u band
• Supernovae are most reliably
classified as Ia’s or non-Ia’s
through their spectrum
14
Why is this difficult?
HST F850LP
HST F850LP
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
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
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
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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
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 don’t 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 Ia’s
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 c2’s)
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
Outline
Dark Energy
Studying Dark Energy with Standard Candles
Why Type Ia’s Are Standard Candles

…almost
Classifying Supernovae
New Technique
Extensions of this technique

Ultrahigh Energy Cosmic Ray Spectrum Controversy
Conclusions
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(T|candidate) = “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)
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
Can’t do this directly, but can make use of Bayes’ Theorem:
P(T | {Di }) 
P({Di } | T ) P(T )
 P({Di } | T ) P(T )
T
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
Marginalizing Parameters
We therefore have:
P(T | {Di })  
t diff
s
  P({D } | t
i
t d iff
s
, s, M , Av , Rv , T | {Di }) 
diff
Calculate this
You’re done!
, s, M , Av , Rv ,sT ) P(t diff , s, M , Av , Rv , T )
M Av , Rv
i
t d iff
diff
M Av , Rv
  P({D } | t
T
 P(t
s
diff
, s, M , Av , Rv , T ) P (t diff , s, M , Av , Rv , T )
M Av , Rv
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:
P(t diff , s, M , Av , Rv ; T )  P (t diff | T ) P( s | T ) P( M | T ) P ( Av , Rv | T ) P(T )
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Gory Detail (1)
P({Di } | t diff , s, M , Av , Rv , T ) P(t diff | T ) P( s | T ) P( M | T ) P( Av , Rv | T ) P(T )
Predicted Measured
Measured

P({Di } | tdiff , s, M , Av , Rv , T ) 
N Epochs

i 1
e
( d j  Di ) 2
2 i2
Predicted
d j
2  i
Error in Measurement
Flux
Assume flat prior for the difference between
the dates of max light between model and data
Time
Gory Detail (2)

P( s | Ia ) 
( s s )2
2 s2
e
s
2  s
Number
P({Di } | tdiff , s, M , Av , Rv , T ) P(tdiff | T ) P( s | T ) P( M | T ) P( Av , Rv | T ) P(T )
Stretch

P( M | T ) 
e
s, s - Sullivan et al. astro-ph/0605455
( M M )2
2
2 M
M
2  M
M - D. Richardson et al. AJ 123, 745 (2002)
M - P. Nugent,
http://supernova.lbl.gov/~nugent/nugent_templates.ht
ml
Gory Detail (3)
P({Di } | t diff , s, M , Av , Rv , T ) P(t diff | T ) P( s | T ) P( M | T ) P( Av , Rv | T ) P(T )
• Difficult, as no consensus on the model for Cardelli-ClaytonMathis 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,
P( Av , Rv | T ) 
1
3
Gory Detail (4)
P({Di } | t diff , s, M , Av , Rv , T ) P(t diff | T ) P( s | T ) P( M | T ) P( Av , Rv | T ) P(T )
Method hinges on candidate is 1 of
5 possible types of supernovae
Consider 5 types: Ia, Ibc, IIL, IIP, IIn
Assume all types equally likely
(good place to put prior information
about relative rates!)

1
P (T ) 
5
Best to parameterize as a function of z
26
Redshift
For these studies assume can measure redshift
precisely
In general, far from the case
P({Di } | t diff , s, M , Av , Rv , T , z ) P(t diff | T ) P( s | T ) P( M | T ) P( Av , Rv | T ) P( z | T ) P(T )
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
Mini-Summary
P(T|candidate) where the candidate is defined by
its light curves and redshift
We’ve parameterized P(T|candidate) in terms of
stretch, magnitude, extinction so that
P(T | candidate) 
    P(stretch, magnitude, extinction, t
diff
| candidate)
stretch magnitudeextinction t diff
We don’t know what the ‘true’ values for the
stretch, magnitude, extinction are, so we
marginalize them or integrate them out
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)
30
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(T|candidate)
Testing the Method: Monte Carlo
Testing the Method: Ground-Based
Using R-, I-, Gand Z-bands
•
G-Band not well modelled – not fit by SALT
Candidates from
the 3.6m
Canada-FranceHawaii
telescope
collected by
SNLS
collaboration
• Well-sampled
ground-based
data
•4 bands
•Lots of
epochs
P(Ia|candidate) vs. P(c2|ndf)
SALT doesn’t
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 Ia’s, so can’t compare discrimination power of
P(T|candidate) and P(c2|ndf)
Examples of Best-Matching For
Ground-Based (SNLS) Experiment
Effectively maximizing
P(candidate | t diff , s, M , Av , Rv , Ia ) P(t diff | Ia ) P( s | Ia ) P( M | Ia ) P( Av , Rv | Ia ) P( Ia )
Testing the Method: Space-Based
Using I- and
Z-Bands
Looks like a IIn
“Silver” candidate
 Works nicely even for very poorly sampled data!
Examples of Best-Matching
Effectively maximizing
P(candidate | t diff , s, M , Av , Rv , Ia ) P(t diff | Ia ) P( s | Ia ) P( M | Ia ) P( Av , Rv | Ia ) P( Ia )
Effect of Priors
Stretch – fixed stretch=1
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
Outline
Dark Energy
Studying Dark Energy with Standard Candles
Why Type Ia’s Are Standard Candles

…almost
Classifying Supernovae
New Technique
Extensions of this technique

Ultrahigh Energy Cosmic Ray Spectrum Controversy
Conclusions
Uses and Extensions
Immediate Use

Rates
Have to deal with counting candidates with
P(Ia,z|Candidate)<1
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Template Building
Extensions:
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Removing Anomalies
Cosmological Parameter Fitting
Exotic Extensions: The Bayes Factor
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Are two supernovae of the same type?
Gravitational Lensing
High-Z
Type Ia Rates
Rates decline at
higher redshifts!
Count Type Ia
supernovae with low
statistics where each
has
P(Ia,z|Candidate)<1
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
Purging Anomalies
Calc. P(T|candidate) 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 doesn’t look like anything we’ve seen before
It doesn’t look like a supernova is probability that light curve from
known type fluctuates to what is observed is <Q
l (T | candidate) 
 P(candidate | t
M
Av
, s, M , Av , Rv , T ) P(t diff | T ) P( s | T ) P( M | T ) P( Av , Rv | T ) P(T )
Rv
Lo
ANOMALY
s
Events
t diff
diff
Area = Q
MC
l (T | candidate)
Fitting Cosmological Parameters
Suppose we have some cosmological model dependent on {pi}
Parameterize
P({ pi }, Ia | Data)
Or even
P({ pi } | Data) 
 P({ p },T | Data)
i
All Types
Allowing you to do cosmology with the help of non-Ia’s!
Use Bayes Factor statistic to compare different models
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
Exotic Extensions: Gravitational
Lensing – Bayes Factor
Bayes Factor (H.Jeffreys, 1936)
P( D | H 0 )
BF 
P( D | H1 )
Bayes Factor no stranger to cosmology
(A.R.Liddle, 2004) or physics for that matter
Here,
P(Candidate 1, Candidate 2 | Same Supernova)
BF 
P (Candidate 1, Candidate 2 | Different Supernova)
A Similar Application for the Bayes
Factor
Calculation similar to another Bayes Factor
Understand the HiRes/AGASA controversy
Two ultrahigh energy cosmic ray experiments
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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 E>1019.5 eV
GZK Suppression
Greisen-Zatsepin-Kuz’min
Suppression
Cosmic rays interact with the 2.7
K microwave background
Protons above ~ 7×1019 eV suffer
severe energy loss from
photopion production
p 3K  e e p
 n
 0p

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
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 E>1019 eV)
AGASA claimed not to be consistent
with GZK cut-off
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
Model-Independent Method to Test
the Consistency of Two
Experiments
Bayes Factor (cousin of
Likelihood Ratio)

Method drawn from Harold
Jeffreys (1936)
P( D | H1 )
BF 
P( D | H 0 )
P ( D | Separate Parents Distributi on)

P ( D | Single Parent Distributi on)
Bayes Factor
(BF)
Interpretation
BF>1
Support for H1
10-1/2<BF<1
Minimal
evidence
against H1
10-1<BF<10-1/2
Substantial
evidence
against H1
10-2<BF<10-1
Strong evidence
against H1
BF<10-2
Decisive
evidence
against H1
Results
Use Bayes Factor statistic
to evaluate agreement of
experiments E>1019.6 eV

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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 E>1019.6 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
Comparison of AGASA, HiRes and
Auger Spectra
Minimal to substantial evidence against
separate-parent hypothesis
For 30% energy uncertainties

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
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
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
BF versus Fractional Energy Scale
Uncertainty
Variation of
Energy Scale
Uncertainties
2. (For Completeness) Is There Evidence
Anywhere of GZK Cutoff?: HiRes Energy
Spectrum
(Broken) power law fits

No break:
c2/dof = 154/39
HiRes Energy Spectrum
(Broken) power law fits


No break:
c2/dof = 154/39
One break allowed:
c2/dof = 67/37 (4 EeV)
HiRes Energy Spectrum
(Broken) power law fits

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No break:
c2/dof = 154/39
One break allowed:
c2/dof = 67/37 (4 EeV)
Two breaks allowed:
c2/dof = 40/35
High energy break at 60
EeV
Difference in c2
corresponds to ~ 5
significance
HiRes Sees Something,
but is it GZK? NO NULL
HYPOTHESIS
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

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Agreement between two experiments
HiRes seems to be consistent with suppression at
high energies that may be GZK cut-off
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

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Type Ia Rates
Template building
Lots of work in progress on extensions of the method!

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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