AGN Accretion Disks Under the Micro-Lens Xinyu Dai (OSU) C.S. Kochanek, C. Morgan, N. Morgan, S. Poindexter, S. Kozlowski (OSU) G. Chartas, G. Garmire (PSU), E. Agol (UW) December 4, 2018 Opening Symposium of KIAA-PKU

Basic Observables “Einstein Ring” image of quasar host galaxy Quasar image B Quasar image D Quasar image A Lens galaxy Quasar image C Hubble Image of Gravitational Lens RXJ1131-1231 (Morgan, Kochanek, Falco, and Dai 2006) December 4, 2018 Opening Symposium of KIAA-PKU

Intrinsic Variability = Time delays  halo structure and distances AB = 12.0, AC = 9.6, AD = 87 days December 4, 2018 Opening Symposium of KIAA-PKU

Shift To Determine These Delays December 4, 2018 Opening Symposium of KIAA-PKU

We observe this in almost all the systems we monitor But after shifting and removing the intrinsic source variability, there is still time variability in the flux ratios – Microlensing We observe this in almost all the systems we monitor December 4, 2018 Opening Symposium of KIAA-PKU

Time Delay in PG1115+080 Measured in X-rays A1-A2=0.16 days Chartas, Dai, Garmire 2004 December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU Applications Cosmology Estimates of H0 CDM Halos Structure Lensing Statistics Lens Galaxy Estimates of Surface Density c Fraction in stars * Average stellar mass <M> ISM Properties Quasar Accretion disk structure Spectral properties using the lensing magnification December 4, 2018 Opening Symposium of KIAA-PKU

Schematic Plot of a Gravitational Lens Dos Dls Dol Image  Source ξ η December 4, 2018 Opening Symposium of KIAA-PKU

Deflection Potential Analogy to Gravitational Potential December 4, 2018 Opening Symposium of KIAA-PKU

Relate to Observables (Blandford & Narayan 1986) Geometric Time Delay Gravitational Time Delay (u,v) source position (x,y) image position Time Delay Image Position Magnification (flux) December 4, 2018 Opening Symposium of KIAA-PKU

Time Delay: Hubble Constant and CDM Halo Structure Time delays measure a combination of H0 and the surface density t 2tisothermal(1<>)/H0 to lowest order Current Direction: Fix H0 and constrain the CDM Halo Structure Kochanek & Schechter 2004 December 4, 2018 Opening Symposium of KIAA-PKU

What Determines an Image’s Flux? Beyond Source Variability What contributes to these derivatives? All scales are equally important! Overall smooth potential – the “macro” model Satellites/CDM substructure – millilensing Stars – microlensing The source size matters because it can average out the smaller scale structures in the magnification pattern Differential extinction between the images December 4, 2018 Opening Symposium of KIAA-PKU

Anomalous Flux Ratios: Gravity, ISM or Bad Models? minimum The close pair images should have similar flux saddle saddle Hubble Image of SDSS0924+0219 minimum December 4, 2018 Opening Symposium of KIAA-PKU

Dust Extinction Is Observed And you can use it to study dust to z~1 A roughly Galactic extinction curve at z=0.83 (Motta et al 2002) 2175 A feature December 4, 2018 Opening Symposium of KIAA-PKU

Soft X-ray Absorption is Correlated With Dust and you can use it to study the evolution of the dust to gas ratio Galactic Stars (Bohlin et al 1978) Dai et al. (2006, 2008) December 4, 2018 Opening Symposium of KIAA-PKU

Anomalies Exist Even for Big Radio Sources  “CDM Substructure” Dalal & Kochanek (2002) See also Mao & Schneider (1998); Mao et al. (2004) Springel, White & Tormen (1999) December 4, 2018 Opening Symposium of KIAA-PKU

But What About Small Substructures (Stars)? Source plane scale=40<E> 2h-1<M/M•>1/2pc=335<M/M•>1/2as B C D A For a 109M• black hole RBH=0.0001pc =0.01as =0.l<M/M•>-1/2pixels December 4, 2018 Opening Symposium of KIAA-PKU

Length Scales Set by the mass of the lenses and the distances Lens galaxy M~1010M• E~1arcsec CDM sub-halo M~106M• E~10 milliarcsec Star M~M• E~10 microarcsec Microlensing is not sensitive to large source size, but millilensing do. December 4, 2018 Opening Symposium of KIAA-PKU

Time Scales set by the crossing time of the Einstein radius Milli-lensing (by CDM sub-halos) has longer time scale than microlensing (by stars) ISM in the lens galaxy does not vary on short time scales December 4, 2018 Opening Symposium of KIAA-PKU

Monitoring Leads to Microlensing Variability (OGLE light curves of Q2237+030) December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU How to use microlensing to measure the source size? — Qualitative Approach Larger sources smooth the magnification pattern and have smaller microlensing variability. December 4, 2018 Opening Symposium of KIAA-PKU

Qualitative Approach (Cont’d) Comparing microlensing variability IR size > optical size (Agol et al. 2000) Optical > X-ray > Iron K Line (Dai et al. 2003) Opitcal Narrow line > optical continuum (Mediavilla et al. 1998) December 4, 2018 Opening Symposium of KIAA-PKU

Quantitative Approach — Fitting the Microlensing Light Curve Galactic Binary microlensing event MACHO 98-SMC-1 In this case solutions must include binary orbital motion….. Afonso et al. 2000 December 4, 2018 Opening Symposium of KIAA-PKU

Let’s Just Do The Same Thing Although a Monte-Carlo Approach in needed December 4, 2018 Opening Symposium of KIAA-PKU

Let’s Just Do The Same Thing (Cont’d) We just generate those messy magnification patterns, pick a source size/structure, randomly draw light curves and fit the data We keep the acceptable solutions We then calculate the probability distributions for interesting physical variables We can get light curves that are statistically good fits to the data December 4, 2018 Opening Symposium of KIAA-PKU

Examples of Magnification Patterns in the Monte-Carlo Simulations Image A (a minimum) */=1 */=0.5 */=0.25 */=0.125 Image C (a saddle point) December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU What Matters? Velocities – sets the time scales – higher velocities give more rapid variability at fixed source size Mean stellar masses – sets the length scale – higher mean masses give longer time scales at fixed velocity and smaller variability amplitudes at fixed source size Source size – sets the smoothing – larger sizes give reduced variability amplitudes and longer time scales for fixed mean mass and velocity Surface density in stars – sets the statistics of the microlensing December 4, 2018 Opening Symposium of KIAA-PKU

Sometimes, brute force is the solution…. Fits to OGLEI data for Q2237 1 solution in 10^14 trials We used at least 10000 solutions to estimate the interesting parameters Kochanek 2004 December 4, 2018 Opening Symposium of KIAA-PKU

Finally the Accretion Disk Size We obtain probability distributions for the disk size. December 4, 2018 Opening Symposium of KIAA-PKU

Testing the Simplest Accretion Disk Theory December 4, 2018 Opening Symposium of KIAA-PKU

Beginning to Test Accretion Disk Theory – Size versus Mass Morgan et al. (2007) Black hole masses estimated from emission line-width/mass correlations December 4, 2018 Opening Symposium of KIAA-PKU

Size versus Wavelength (Temperature) From Microlensing Poindexter et al. 2007 HE1104-1805 A was bright and blue when found, now close to emission line/mid-IR flux ratio and red December 4, 2018 Opening Symposium of KIAA-PKU

Fit Models With Size Rβ Corresponding To TR-1/β In thin disk theory β=4/3 Consistent with theory but could allow a shallower slope December 4, 2018 Opening Symposium of KIAA-PKU

X-Ray Emission from AGN Inverse Compton emission However, geometric configuration is uncertain December 4, 2018 Opening Symposium of KIAA-PKU

X-ray Microlensing in Q2237+030 December 4, 2018 Opening Symposium of KIAA-PKU

Can Also Examine Thermal versus Nonthermal Emission December 4, 2018 Opening Symposium of KIAA-PKU

X-ray Emission Tracks Inner Disk Edge? X-ray: ~10-20 rg Optical: ~100-200 rg Dai et al. (2008) December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU Issues of Observation We monitor ~20 lenses well at at one wavelength (R band), with lesser coverage at J, I, V and B with the SMARTS 1.3m telescope at CTIO, much worse for Northern lenses with the MDM 2.4m – now have ~(4 years)(20 lenses)(3 images) = 2.4 image monitoring centuries UV monitoring with HST for two lenses (RXJ1131 and Q2237) – fortunately with ACS semi-death both of these lenses have flux past their Lyman limits and can be observed with the ACS/SBC! X-ray monitoring with Chandra for RXJ1131 and Q2237 sparse coverage of other lenses from archive and other programs Increase the sample size to ~10 monitored with HST and Chandra The challenge problem – microlensing of the Iron K line – hints in published data (Dai and Chartas), but quantitative results for the size of the K emission region are a Megasecond CXO project December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU Summary Microlensing is the first new probe of accretion disk structure in ~10 years Disk sizes scale with black hole mass as in thin disk theory M2/3 The absolute size is roughly consistent with theory but larger than expected for black body radiation and the TR-3/4 The scaling of disk size with wavelength is consistent with this temperature profile but could allow a flatter profile that would help to solve the size problem X-ray emission is more compact and seems to trace the scale of the inner disk edge We are primarily data limited at the present time  given the ability to collect the necessary data, we can dramatically improve over our existing results December 4, 2018 Opening Symposium of KIAA-PKU

For Quasar Accretion Disks We Want to Understand the Size Should be able to study structure of quasar accretion disks because variability amplitude  source size December 4, 2018 Opening Symposium of KIAA-PKU

Scales as expected with Black Hole Mass RM2/3 The implied efficiency is somewhat low or the MBH are systematically high December 4, 2018 Opening Symposium of KIAA-PKU

Amplitude Does Depend on Wavelength December 4, 2018 Opening Symposium of KIAA-PKU

Radio Data Shows No Absorption Despite seeing some scatter broadened images No sign of the frequency dependence we would expect for a propagation effect – consider an optical depth =5(/5GHz) December 4, 2018 Opening Symposium of KIAA-PKU

Problems In the Mass Models? (Kochanek & Dalal, Yoo et al., Congdon & Keeton) Lens models for 2/4 image lenses are underconstrained if you allow arbitrary angular structure Lenses with additional images or Einstein rings require models that are consistent with ellipsoids B1933+503 December 4, 2018 Opening Symposium of KIAA-PKU

Oversimplified Disk Model? Why are the microlensing sizes large – use fancier disk models to try to simultaneously fit flux, spectrum and microlensing sizes based on more realistic Hubeny et al disk models – basic problem remains – disks too big for their flux (also a problem for Galactic systems like CVs). December 4, 2018 Opening Symposium of KIAA-PKU

Contamination of the Continuum? We are “assuming” that we are monitoring continuum emission from the quasar accretion disk – what if the “continuum” emission is not? Contamination from obvious broad lines – line emission is really on much bigger (and less microlensed, but not unmicrolensed – e.g. Richards et al) scales Contamination from the pseudo-continuum – Iron lines and Balmer continuum emission Testing for this, but so far, the answer is that this does not change the results… December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU Issues of Observation Given an infinitely long light curve, you should be able to reconstruct all lens properties aside from the Einstein units conversion – but how close to “infinite”? Very crudely, you have to monitor an image for an Einstein time to start getting a “fair” sample of the microlensing for that image (~15 years) – at this point you will start sampling the pattern – for a single lens (2 or 4 images) you need 15/(2 or 4)  4-7 years The metric for a microlensing program is “image monitoring years” and you want to get to several image monitoring centuries December 4, 2018 Opening Symposium of KIAA-PKU

The Flux Size Problem (Pooley et al originally) These “flux sizes” are systematically smaller than either the microlensing or the thin disk theory sizes – not thermally radiating or flatter temperature profiles December 4, 2018 Opening Symposium of KIAA-PKU

Opening Symposium of KIAA-PKU Issues of Computation This is a tough problem – picking light curves at random from these patterns and fitting them to actual data is not easy – it probably becomes exponentially harder as the light curve length increases… But, that’s not the big problem – the exponential is still small (except for Q2237). The big problem is that the stars move – the patterns are animated, not static! Probably matters most for mass estimates Broadens errors for other variables, but who wants exaggerated error bars? Huge computational challenge – we have to use 81922 magnification patterns for many/most problems at a cost of 256 MByte/image and source size and for many problems we should be using 162842 patterns. Animating a pattern requires ~100 such patterns  25 GBytes/image and source size even for the 81922 patterns December 4, 2018 Opening Symposium of KIAA-PKU

Are Galaxies Composed of Stars? RXJ1131-1231 Q2237+0305 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, Q2237+0305, where we see the images through the bulge of a low redshift spiral galaxy, should be almost all stars (/*~1) December 4, 2018 Opening Symposium of KIAA-PKU

The Microlensing Knows Q2237+030 should be mostly stars RXJ1131-1231 should be mostly dark matter December 4, 2018 Opening Symposium of KIAA-PKU

What is the Mean Mass of the Microlenses? Mean Mass and Effective velocity are degenerate Q2237+030 If we have a statistical model for the true physical velocities, P(ve), then we can estimate the average mass of the lenses Best single case Q2237+0305 <M> = 0.61 M 0.12 M  <M> 2.85 M December 4, 2018 Opening Symposium of KIAA-PKU