Turning Quasar Microlensing From A Curiosity Into a Tool

1
Turning Quasar Microlensing From A Curiosity Into
a Tool

• C.S. Kochanek, X. Dai, N. Morgan, C. Morgan, S.
  Poindexter (OSU)
  
• G. Chartas (PSU)

• Introduction to gravitational lenses
• The nature of the data
• Results
• Physical, computational, statistical and
  observational challenges

2
The Gravitational Lens RXJ1131-1231
Quasar image D
Quasar image B
Einstein Ring image of quasar host galaxy
Quasar image A
Quasar image C
lens galaxy
3
Monitor Quasar Image Brightness

• Two sources of time variability
• Intrinsic quasar variations, which appear with a
  time delay between each image
  
• Uncorrelated variations due to microlensing by
  the stars in the lens galaxy

(For non-astronomers, magnitudes are
2.5log(flux)constant)
4
First Determine Time Delays

• For RXJ1131-1231 they are 12, 10 and 87 days
  for images B, C and D relative to A (B leads, D
  trails)
  
• The delays can be used to study the mass
  distribution of the lens or to estimate the
  Hubble constant, but this is not our present topic

5
Whats left is the microlensing Variations in
the flux ratios of the images after correcting
for the time delays
6
What Determines an Images Flux?

• The local magnification is determined by the
  local derivatives of the potential, ?
  
• What contributes to these derivatives?
• Overall smooth potential the macro model
• Satellites/CDM substructure millilensing
• Stars microlensing
• Finite source sizes ? smoothing of the small
  scale structures in the magnifications, in
  particular, smoothing of the caustics on which
  the magnification diverges

7
Length Scales Set by the mass of the lenses and t
he distances

• Lens galaxy M1010M ???E1arcsec
• Satellite galaxy M106M ???E10
  milliarcsec
  
• Star MM ???E10
  microarcsec

The stars produce complex magnification patterns
with different structures near each image
8
Source plane scale40 2h-11/2pc3351/2?as
B
C
D
A
For a 109M black hole RBH0.0001pc 0.01?
as
0.l-1/2pixels
9
What can we study using microlensing?

• Quasar Structure microlensing resolves quasar
  accretion disks, allowing us to measure their
  structure as a function of wavelength
  
• Dark matter microlensing depends on the
  fraction of the mass near the lensed images
  comprised of stars
  
• Stellar populations microlensing can estimate
  the mean stellar mass the halos of cosmologically
  distant galaxies

10
Quasar Accretion Disks Have A Very Similar Size
Scale
Should be able to study structure of quasar
accretion disks because variability amplitude ?
source size
11
Minima Saddle Points
Depends on the fraction of the surface density in
stars
High optical depth
Low optical depth
Or in the statistics (Schechter Wambsganss 2002)
12
Mean Stellar Mass

• All observable properties of the microlensing
  are in Einstein units of 1/2cm.
  Converting to just cm requires a prior on
  
• The mean microlens mass
• The true physical velocities
• The true source size
• We have good physical priors for the physical
  velocities, which means we can sensibly estimate
  in cosmological distant galaxies

13
But how do you go from light curves to physics?
One of the two basic problems in using quasar
microlensing for astrophysics.
The other is the sociological difficulty of doing
the observations.
OGLE (Wozniak et al. 2000ab) microlensing light
curves of Q22370305
14
For Galactic microlensing events you just fit the
light curves.
Binary microlensing event MACHO 98-SMC-1 In th
is case solutions must include binary orbital
motion..
Afonso et al. 2000
15
We will just do the same, using computer power
and the Reverend Bayes

• Given the local properties (?, ?, ?) and the
  stellar mass function
  
• Generate random realizations of the magnification
  patterns
  
• Given a model for the quasar accretion disk
• Randomly choose disk parameters, convolve with
  patterns
  
• Given a random selection of a source velocity
• Randomly pick nuisance parameters (direction,
  starting point)
  
• Fit the resulting light curve to data to estimate
  a ?2 statistic
  
• Combine all the trials using Bayesian methods to
  estimate probability distributions for the values
  of interesting parameters

16
We Obtain Statistically Acceptable Fits To The
Data Good fits mean fitting all 6 difference ligh
t curves between the 4 images (the average light
curve gives the intrinsic source variability)
17
Are Galaxies Composed of Stars?
Q22370305
RXJ1131-1231
Most lenses, like RXJ1131-1231, should only have
a small fraction of the surface density near the
quasar images comprised of stars (?/?0.1 to
0.2), but one lens, Q22370305, where we see the
images through the bulge of a low redshift spiral
galaxy, should be almost all stars (?/?1)
18
The Microlensing Knows.. (although for most lens
es it has yet to converge significantly)
RXJ1131-1231 should be mostly dark matter
Q2237030 should be mostly stars
19
What is Mean Mass of the Microlenses?
All directly measured quantities are in Einstein
units 1/2cm Best physical priors are for the
true velocities P(ve)
Q2237030

• For any one lens, the uncertainties will be
  large
  
• Mass goes as (velocity)2
• Physical prior for any one less has a velocity
  uncertainty of order a factor of two from the
  unknown peculiar velocity

Best single case Q22370305 0.61 M? 0.12 M
? ? ?2.85 M?
20
Ensembles of Lens Should Provide An Accurate
Estimate

• Dominant uncertainty in priors is a random
  variable (peculiar velocities) whose dispersion
  is known, but not the value for a particular
  system
• Multiply P() for each system to get a joint
  estimate for ensemble of lenses
  
• Must hit a systematic floor at some point, but
  almost certainly not yet

Combining the 8 systems (mostly) analyzed as of
Saturday 0.09 M? 0.04 M? ? ? 0.19 M?
Answer stable to dropping any one lens, but it
would be nice to see the outliers shift towards
the median as we accumulate longer light curves.
21
Disk Scale Lengths Well-Determined
Why? Because the mass scale uncertainties affect
the source size little
? Means that the physical source size is little
affected by the uncertainties in the mass, which
is very convenient!
22
Beginning to Test Accretion Disk Theory
Black hole masses estimated from emission
line-width/mass correlations
23
Disk Structure Best Probed As Size Versus
Wavelength First tests, surprisingly, are optical
versus X-ray sizes
CXO Spring 2004
CXO Spring 2006
Blackburne et al
OSU/PSU

• Optical and X-ray flux ratios very different, and
  change differently with time (now known for 4
  lenses)
  
• Smaller sources will show greater microlensing
  variability

24
Partial results for 3 systems now, additional
data being collected, but X-ray sources are
roughly 1/10 the size of the optical sources
As expected, size ratios are less uncertain than
absolute sizes (remember, the X-ray size is
being determined from 4 data points!)
25
Issues of Physics

• Mass function of microlenses extensive prior
  theoretical studies showing that this is very
  hard to probe and has little effect on results
  
• Disk structure at fixed wavelength extensive
  prior theoretical studies show that microlensing
  data measures typical size rather than details of
  the surface brightness distribution better to
  focus on size versus wavelength, black hole mass
  etc..
• Only time variability or also observed flux
  ratios observed flux ratios are also affected
  by substructure (satellites) and
  extinction/absorption, but they are powerful
  constraints on where you sit in the microlensing
  magnification pattern
• The stars move. Except in experiments, we have
  used fixed magnification patterns, but in real
  life they change with time as the stars move.
  Theoretical studies suggest that we are safe so
  far, but not forever.

26
Issues of Computation

• With some physically irrelevant fiddles, it is
  possible to make the image and source regions
  periodic allows use of FFTs to generate
  magnification patterns and leads to periodic
  magnification patterns that simplify the Bayesian
  analysis method
• Dynamic range of magnification patterns need to
  maintain a large enough outer scale to get a fair
  sample of stars, and a small enough inner scale
  to deal with compact sources 40962 maps
  marginally OK
• Computationally challenging to allow stars to
  move we need 3 GByte to analyze a systems at 2
  wavelengths with static patterns, but 300 GBytes
  if we allow the stars to move and need an
  animated sequence of patterns. Probably doable
  on shared memory machines (and we have
  experimented with this), but could lead to
  catastrophic time penalties on other parallel
  machines because of the need for random access to
  all the patterns (awaits a really good
  computational student).
• Fiddles to speed execution. We have incorporated
  various fiddles to make the analysis run FAST.
  The most serious of which is an inner loop that
  does a local maximum likelihood search over
  nuisance variables that is not strictly in
  accordance with the Bayesian outline of the
  calculations.
• Monte Carlo verification. We need to spend more
  effort on generating fake data sets and verifying
  that the analysis performs as expected. So far,
  so good, but.

27
Issues of Statistics

• All looks pretty good, except for
• The interaction of priors, static magnification
  maps and the reality that the stars move and we
  need to animate the maps current approach does
  not do this properly but is designed (hopefully!)
  to lead to overly broad uncertainty estimates on
  the physically interesting quantities
• The inner, hidden, maximum likelihood loops where
  we allow a local optimization of the nuisance
  variables over restricted ranges. Needs more
  study to better approximate the true Bayesian
  integrals
• Stratified/likelihood sampling of physical
  variables needs to be understood/implemented to
  minimize wasted time on low likelihood regions of
  parameter space
• Testing with simulated data needs to be massively
  expanded

28
Issues of Observation

• Obtaining the necessary observations remains our
  biggest problem
  
• We monitor 20 lenses well at at one wavelength
  (R band), with lesser coverage at J, I and B
  
• The Babylonian observer problem for ground based
  optical/near-IR remains a major problem. For
  example, all our results are for lenses visible
  from the queue-scheduled SMARTS telescope at CTIO
  we cannot do similar analyses for Northern
  lenses.
• To study how the region near the last stable
  orbit differs from regions further from the last
  stable orbit, we need UV observations with HST
  success depends on obtaining long (years) time
  baselines before HST fails. No luck so far .
• To study the X-ray emitting region at low
  resolution we need continued support for short
  (
  largely depends on having reasonable sampling
  over long temporal baselines. Good luck so
  far.
• To study the X-ray emitting region at high
  resolution, meaning the relative sizes of the
  hard, soft and X-ray line emitting regions, will
  require a major effort (100 ksec exposure
  times). Hopefully, we prove our method with the
  current observations, propose and get shot down
  next year, propose and succeed the following..
• On the plus side, this is much better than we
  achieved in the proceeding 20 years, during which
  we completely wasted the opportunity to do this
  physics because of the sociological barriers!

29
Summary

• We are achieving physical interesting results
  that no one expected from this approach. We can
  estimate
  
• The surface density of stars relative to dark
  matter
  
• The average mass of the stars
• The structure of the accretion disk as a function
  of wavelength
  
• All of which are new and unique probes of great
  astrophysical relevance
  
• We are primarily data limited at the present time
  ? given the ability to collect the necessary
  data, we can dramatically improve over our
  already completely unexpected results
• There are challenging computational and
  statistical issues if we can get that data