SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics Laura Ferrarese Rutgers University Lecture 4: Beyond the Resolution Limit

SIGRAV Graduate School in Contemporary SIGRAV Graduate School in Contemporary

Relativity and Gravitational PhysicsRelativity and Gravitational Physics

Laura FerrareseLaura FerrareseRutgers UniversityRutgers University

Lecture 4: Lecture 4: Beyond the Resolution Beyond the Resolution

LimitLimit

Lecture OutlineLecture OutlineLecture OutlineLecture Outline1. The Innermost Regions of Active Galactic Nuclei

2. Variability in Active Galactic Nuclei Continuum variability Emission line variability

3. Reverberation mapping: making sense of the continuum-emission line connection

4. Potential problems….

5. … and how to solve them: the Transfer Function

6. Where the Observations Stand

Schematic View of an AGNSchematic View of an AGNSchematic View of an AGNSchematic View of an AGN

Reverberation Mapping in a Reverberation Mapping in a NutshellNutshell


Measuring masses of SBHs using Reverberation Mapping is based on the assumption that the size r and velocity of the Broad Line Region (BLR) clouds are connected by a simple virial relationship:

According to the standard model, Broad Line Region (BLR) clouds are many (107-8, Arav et al. 1997, 1998,

Dietrich et al. 1999) small, dense (Ne ~ 109-11 cm-3)

cold (Te ~ 2104 K)

photoionized (Ferland et al. 1992) localized within a volume of a few to

several tens of light weeks in diameter around the central ionization source.

As such, the BLR is, and will remain, spatially unresolved at optical wavelengths even using space based instrumentation, and its size cannot be determined using conventional images.

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M =frσ 2

G



If the BLR is photoionized, the broad lines should respond to continuum variations. The line response contains a wealth of information regarding the spatial and kinematic structure of the BLR; therefore monitoring programs for AGNs started in the early ‘80s in the attempt to quantify the nature of the continuum and emission line variations (if any!)

If everything works as planned, the time delay between continuum and line variation is simply (?) related to the size of the BLR.



Advantages:

reverberation mapping probes regions very close to the central engine (103 RSch), a factor at least 1000 smaller than allowed by “traditional’ methods which relay on resolved kinematics.

This leaves little doubt that the measured mass (if correct!) is in the form of a supermassive black hole

Disadvantages:

The observations are difficult. Close time monitoring at very closely spaced intervals and multiple frequencies is necessary.

For the virial approximation to be applicable, the kinematics must be dominated by gravity. The presence of outflows or not gravitational motions (to which gas might be prone) would undermine the method entirely.

The geometry of the BLR are not known.

Observational Requirements Observational Requirements for Monitoring Programsfor Monitoring Programs

Observational Requirements Observational Requirements for Monitoring Programsfor Monitoring Programs

Temporal Sampling

observations must be closely spaced in time relative to the physical timescale of interest (generally a problem for the early monitoring programs)

difficulties in scheduling the observations

S/N of the data

S/N must be high relative to the magnitude of the flux variations (i.e. Fvar must be >> 0)

e.g. S/N=30 is necessary to detect 10% variations in continuum flux at the 3 confidence level.

Aperture effects

variations in seeing at the time of the observations, as well as pointing and guiding errors can cause variations in the amount of light entering the spectrograph, since both the NLR and the host galaxy are extended. This can cause spurious spectral variations.

Datasets must be as homogenous as possible, ideally using a single instrument in a stable configuration

Variability in AGNsVariability in AGNsVariability in AGNsVariability in AGNs AGNs are variable at all wavelengths at which they have been studied, not

only in the continuum, but also in the emission lines. Typical quasars vary at the 0.3 - 0.5 mag level over timescales of a few

months, with extreme cases varying on timescales as short as a few days.

The variability in Seyfert galaxies is less dramatic and was not discovered until the late ‘60s.

Causality arguments imply that the emitting region is less than a few light days across

Periodicity in the light curve have been searched for but never found: variations are aperiodic and have variable amplitudes

Emission Line VariabilityEmission Line VariabilityEmission Line VariabilityEmission Line Variability Broad Emission lines in AGN spectra can vary in both flux and profile.

Narrow lines fluxes do not vary! This is due to the fact that in the NLR both the light crossing time and the recombination time are large (>100 years), therefore short-term variability is smeared out.

Line-Continuum VariationsLine-Continuum VariationsLine-Continuum VariationsLine-Continuum Variations

H line flux against the continuum flux measured at the same time (left) and 15 days earlier (right), for the Seyfert 1 galaxy Mrk 335. The emission line fluxes are

better correlated with the earlier rather than current continuum fluxes (Peterson et al. 1998, ApJ 501, 82)

Observational ResultsObservational ResultsObservational ResultsObservational Results AGNs with lags for multiple lines

show that highest ionization emission lines respond most rapidly ionization stratification

The Basis of Reverberation The Basis of Reverberation MappingMapping

The Basis of Reverberation The Basis of Reverberation MappingMapping

The fact that emission lines vary in response to the optical/UV continuum variation immediately implies that:

The line emitting clouds are close to the continuum source

the line emitting clouds are optically thick

The ionizing continuum ( < 912Å) is closely related to the observable optical/UV continuum.

Therefore, our hopes are realized: by characterizing the emission line response to continuum variations, the kinematics and geometry of the BLR can be constrained:

the time delay between continuum and emission line variations are ascribed to light travel time effects within the BLR: the emission lines ‘echo’ or ‘reverberate’ to the continuum changes (Blandford & McKee 1982, ApJ, 255, 419).

Reverberation Mapping Reverberation Mapping AssumptionsAssumptions


The continuum originates in a single central source. Typical scalelengths are: Accretion disk (for 107 – 108 M SBH): 1013–14 cm Broad Line Region: 1016 cm

To all effects, as seen from the BLR, the continuum source can be treated as point-like

The continuum is not required to be emitted isotropically (although isotropy is usually assumed)

The most important timescale is the light-travel time. the cloud response to a change in the continuum flux is instantaneous.

Light travel time:

Timescale to re-establish photoionization equilibrium:

Timescale it takes a Lyman photon to diffuse outward through the BLR:

ne = electron density; U = ionization parameter; B= recombination coefficient; Rion = depth to which the BLR is completely ionized

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τ rec = (neα B )−1 ≈ 40ne

1011 cm −3

⎛

⎝ ⎜

⎞

⎠ ⎟−1

seconds

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τdiff = 20Rion

c≈ 20

U

neα B≈ 60

ne

1011 cm −3

⎛

⎝ ⎜

⎞

⎠ ⎟−1

seconds

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τ lt =Rion

c≈

U

neα B≈ 3

ne

1011 cm −3

⎛

⎝ ⎜

⎞

⎠ ⎟−1

seconds



The structure of the BLR does not change on the variability time scale (or the timescale over which the experiment is conducted).

Dynamical (cloud-crossing) time:

There is a simple, though not necessarily linear, relationship between the observed continuum and the ionizing continuum.

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τdyn =r

V = 3 - 5 years



Once the (responsivity weighted) size r of the BLR is known, the AGN central mass can be obtained through the virial relationship:

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M =frσ 2

G

where f is a dimensionless factor of order unity that depends on the geometry and kinematics of the BLR, and is the emission line velocity dispersion.

The velocity width of the lines is measured in the rms spectrum:

the rms spectrum only contains information on the variable part of the lines; constant components do not contribute.

Potential ProblemsPotential ProblemsPotential ProblemsPotential Problems

What is f?

circular, coplanar orbits: mean-square line-of-sight velocity is GMsin2i/(2r), therefore f=2/sin2i. f could therefore take any value between 2 and .

random, isotropic circular orbits: mean-square line-of-sight velocity is GM/(3r), therefore f=3

random, isotropic parabolic orbits: mean-square line-of-sight velocity is 2GM/(3r), therefore f=3/2

These potential problems add to the systematics arising from the (generally) inadequate temporal sampling of the observations, and the (generally) short duration of the experiments.

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M =frσ 2

G

Potential Problems: the Virial Potential Problems: the Virial HypothesisHypothesis


How can we test the virial hypothesis?

If the motion of the gas is gravitational, using BLR sizes and velocity derived from different emission lines in the same AGN must produce the same estimate of the central mass.

NGC 5548: highest ionization lines have smallest lags and largest Doppler widths, such that virial product r V 2 is constant.

1989 data from IUE and ground-based telescopes. 1993 data from HST and IUE.

Virial relationship with M = 6 107 M.



There are a total four AGNs for which lag measurements for multiple emission lines exist, all supporting the virial approximation (Onken & Peterson 2002)

NGC 7469: 8.4 106 M

NGC 3783: 8.7 106 M

NGC 5548: 5.9 107 M

3C 390.3: 3.2 108 M

Potential ProblemsPotential ProblemsPotential ProblemsPotential Problems To summarize, all of our problems would be solved if the geometry and

kinematics of the broad line region were completely determined:

One of the major remaining mysteries of AGN astrophysics We need to know this to understand systematic uncertainties in AGN

masses.

Can we determine the BLR geometry and kinematics from the observations? YES!

BUT… this will require a leap in data quality.

Accurate mapping requires a number of characteristics (nominal values follow):

High time resolution ( 0.2 day) Long duration (several months) Moderate spectral resolution ( 600 km s-1) High homogeneity and signal-to-noise (~100)

Given these data, we could not just restrict ourselves to measuring time lags, but we could measure the complete transfer function.

The Transfer FunctionThe Transfer FunctionThe Transfer FunctionThe Transfer Function

Emission-lineflux at line of

sight velocity Vz

TransferFunctio

n

ContinuumLight Curve

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LVz,t ()=Ψ(Vz,τ)C(t−τ)0

∞

∫dτ

The transfer function determines the relation between continuum and emission lines variations:

The transfer function is simply the time-smeared emission-line response to a function outburst in the continuum. In other words, the transfer function can be interpreted as a ‘velocity delay map’.

Solving for the transfer function is a classical inversion problem. In practice, it requires extremely well sampled, high quality data.

The Transfer FunctionThe Transfer FunctionThe Transfer FunctionThe Transfer Function

€

L(t)=Ψ(τ)C(t−τ)dτ0

∞

∫

In the best case, the data so far only allows us to solve for the velocity independent (or 1-d) transfer equation where both (τ) and L(t) represent integrals over the emission line width:

Integrate over time delay to get the

line profile

Integrate overvelocity to getthe delay map

Transfer Function: Keplerian Transfer Function: Keplerian DiskDisk

Transfer Function: Keplerian Transfer Function: Keplerian DiskDisk

Transfer function for a thin keplerian disk at a 45 degree inclination.

Transfer Function: BLR Transfer Function: BLR OutflowsOutflows

Transfer Function: BLR Transfer Function: BLR OutflowsOutflows

Transfer functions in the case of a BLR in spherical (left) and biconical (right) outflow.

Complex Transfer FunctionsComplex Transfer FunctionsComplex Transfer FunctionsComplex Transfer Functions Recovering complex transfer functions requires mapping at multiple

emission lines.

Transfer function recovered from the CIV emission in NGC 5548. The data has been interpreted as 1) evidence of no outflows; 2) evidence of radial outflows; 3) evidence of radial inflow

(!).

Recovering Velocity-Delay Maps from Recovering Velocity-Delay Maps from Real DataReal Data

Recovering Velocity-Delay Maps from Recovering Velocity-Delay Maps from Real DataReal Data

Transfer function recovered from the H emission in NGC 5548. Caution should be exercised since the data spans a period longer than the BLR

dynamical timescale.

Notice little response from material along our line of sight to the continuum source

Observational ResultsObservational ResultsObservational ResultsObservational Results Although no experiment yet has recovered a reliable velocity-delay map,

emission-line lags have been measured in 37 AGNs, in some cases for multiple emission lines.

The H response in NGC 5548 has been measured for 14 individual observing seasons. Measured lags range from 6 to 26 days.

Reverberation Mapped AGNsReverberation Mapped AGNsReverberation Mapped AGNsReverberation Mapped AGNs

From Kaspi et al. 2000, ApJ, 533, 631

Mass-Luminosity RelationshipMass-Luminosity RelationshipMass-Luminosity RelationshipMass-Luminosity Relationship

M L0.3±0.1

QSOs (Kaspi et al. 2000)

Seyfert 1s (Wandel, Peterson, Malkan 1999) Narrow-line AGNs NGC 4051 (NLS1)

The measured masses correlate, although with very large scatter, with the continuum luminosity, in the sense that brighter AGNs have larger SBHs.

““Secondary” Mass EstimatorsSecondary” Mass Estimators““Secondary” Mass EstimatorsSecondary” Mass Estimators Reverberation mapping opens the way to calibrate a “secondary” mass

estimators since, to first order, we expect the broad line region size to correlate with the ionizing continuum luminosity: Photoionization equilibrium models are parameterized by the shape of

the ionizing continuum, the elemental abundances, and the ionization parameter U:

where Q(H) is the number of hydrogen ionizing photons (=13.6 eV) emitted per

second by the central source:

U characterizes the ionization balance within the cloud, since Q(H)/r2 is proportional to the number of ionizations occurring per unit area, while ne is proportional to the recombination rate.

To first order, AGN spectra all look alike, i.e. they have the same ionization parameter and electron density (typical values are: Q(H) ~ 1054 h0

-

2 photons s-1; ne ~ 1011 cm-3; U ~ 0.1). Therefore, we expect

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Q(H)=Lν

hνν 1

∞

∫ dν€

U =Q(H)

4π r2ne c

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U=Q(H)

4πr2nHc

∝L

nHr2⇒r∝L

1/2⇒τ∝L

1/2

BLR Scaling with LuminosityBLR Scaling with LuminosityBLR Scaling with LuminosityBLR Scaling with Luminosity

QSOs (Kaspi et al. 2000)

Seyfert 1s (Wandel, Peterson, Malkan 1999) Narrow-line AGNs NGC 4051 (NLS1)

r(H) L0.6±0.1

This is close to what we observe! For the 37 AGNs which have been reverberation mapped, the BLR radius, measured from the H time lag, correlates (although with large scatter) with the continuum luminosity.

Suggested ReadingsSuggested ReadingsSuggested ReadingsSuggested Readings

Review: Peterson, B.M. 2001, “Variability of Active Galactic Nuclei”, in The Starburst- AGN Connection, World Scientific (astro-ph/0109495).

Criticism: Krolik 2001, ApJ, 551, 72

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SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics Laura Ferrarese Rutgers University Lecture 4: Beyond the Resolution Limit