KRONOS simulations for Dwarf Novae and Active Galactic Nuclei

KRONOS monitors variable sources for long periods of time simultaneously at X-ray, EUV, ultraviolet, and optical wavelengths. A major goal is to map the broad emission line regions of Seyfert galaxies using reverberation effects arising from the compact variable source of ionizing radiation and the finite light travel times from this source out to the surrounding sites of photo-ionized line emission.

DWARF NOVA SIMULATIONS illustrate KRONOS's ability to record the evolving structure of eclipse and orbital lightcurves of a dwarf nova during an outburst of its accretion disk. From each binary orbit of data, eclipse mapping and Doppler tomography will be performed for many continuum wavelengths and emission lines, yielding a 'snapshot' of the accretion disk at that stage of the outburst. KRONOS's high orbit avoids earth occultations to deliver nearly complete coverage of every binary cycle throughtout the outburst. Assembling the series of snapshot disk maps from Kronos data will produce detailed observational 'movies' of the evolving structure of outbursting accretion disks.

Simulated lightcurve of eclipsing dwarf nova Z Cha:, zclc.dat.

Folded lightcurve displayed as a greyscale image showing how the lightcurve shape evolves through the outburst. Comparison of Kronos, HST, Chandra, and Ground visibilities: .

The dwarf nova simulation code: cvlc.for. The simulation includes disk brightness changes, flickering of the disk and bright spot, eclipses of the disk, bright spot, and white dwarf, orbital humps from anisotropic brightspot radiation. Superhumps with period a few percent longer than the orbital period are included in a crude way, but the associated eclipse changes are not modelled. Also not modelled are disk radius and radial structure changes.

Echo Mapping of AGN Emission-Line Regions.

COLOUR MAP of an AGN disk with spiral waves. This simulation shows both the sky view and the corresponding velocity-delay map for an accretion disk orbiting around a 3e7 solar mass black hole. The disk has a 2-armed spiral density wave. The red, blue, and green colours are meaningfully set by the intensity of emission in 3 different lines, Ly-alpha 1215 , HeII 1640, and CIV 1550 respectively.

Spiral waves such as these arise from tidal effects in accretion disks in binary star systems, and are revealed by Doppler tomography. While they are not yet known to exist in AGN accretion disks, they might arise as a result of a recent galaxy merger. When the black hole from a small galaxy finds its way to the vicinity of a larger black hole in the nucleus of the other, the tidal stresses on the disk give rise to spiral waves.

At St.Andrews we have pioneered and continue to develop echo mapping techniques capable of producing such maps from observations. The method works by recording small time-delayed reverberations in the velocity profiles of photo-ionized emission lines. The emission line changes are driven by ionizing radiation from a compact and erratically varying source located near the central black hole -- i.e. the hot inner regions of the accretion disk. Time delays arising from light travel time within the system give us the information we need to map the delay structure of the emission at each velocity in each line. All we need is a suitably long record of the variations, and a good bit of computer processing to extract the velocity-delay structure.

Observational material for echo mapping is currently obtained using major campaigns with HST's ultraviolet spectrographs in conjunction with various X-ray satellites and ground-based optical telescopes. The multi-wavelength monitoring satellite KRONOS (proposed NASA Midex mission) is designed to deliver a revolutionary improvement in the quality of the spectrophotometric monitoring data, sharpening the resolving power of echo maps to measure accurate black hole masses and to reveal structures like those illustrated in the spiral disk simulation.

SPIRAL DISK SIMULATIONS illustrate KRONOS's ability to recover the velocity-delay structure of an AGN accretion disk with spiral density waves in several emission lines. The synthetic datasets assume 1-hour Kronos exposures at intervals of dt days sustained for T days. Results are available for sampling patterns (T,dt) = (400,1) , (400,0.5) , (200,0.2) , and (200,0.5) . Including systematic errors (T,dt,syserr): (200,0.2,1%) , (200,0.2,2%) , (200,0.2,3%) . These tests were undertaken in Aug 2001 by Keith Horne at St.Andrews. The intention is to make these simulations as realistic as possible given current knowledge and time constraints. Synthetic KRONOS spectra were generated using an AGN spectrum synthesis code developed in Spring 2001 while on a sabbatical visit to the University of Texas Austin. The MEMECHO code was then used to translate the reverberating emission line profiles recorded in the synthetic KRONOS data into velocity-delay maps for several strong emission lines, revealing detailed kinematic structure of an accretion disk with 2 spiral density waves. As physical conditions affect reprocessing efficiencies, the structure is different in each emission line, providing information on physical conditions in different parts of the flow.

In these simulations the adopted broad-line region model is a population of 1E5 discrete gas clouds on elliptical Keplerian orbits with semi-major axes uniformly distributed in log(R) from 3 to 50 light days from a black hole of mass 3E7 solar masses. The orbits all lie in a plane inclined at 45 degrees to the line of sight. The eccentricity of the orbits is 0.3, and the azimuth of their major axes advances with the logarithm of their semi-major axes, thus producing a 2-armed spiral density wave pattern in the surface density of clouds on the face of the disk.

Physical conditions in the clouds vary with radius as described by a power-law model similar to the model that Kaspi+Netzer fitted to the NGC 5548 data from the 1989 AGN Watch campaign. The hydrogen number density n scales as 1/r with log(n) increasing outward from 10.92 to 9.4. Column density N scales as R^(-2/3) with log(N) decreasing outward from 23.68 to 22.67. This roughly reproduces line ratios observed in NGC 5548. In addition to their orbital Doppler shift, each cloud has a velocity dispersion 0.1 times the local Kepler velocity.

Hagai Netzer provided a grid of inward and outward emission-line fluxes as functions of hydrogen number density n, column density N, and ionization parameter U=Q/(4piR^2cn). Interpolation in the grid provided the apparent brightness of each cloud at each place along its orbit in 5 emission lines, Lyman-alpha, NV 1249, CIV 1550, HeII 1640, and H-beta.

Synthetic AGN spectra were generated using the proposed spectral range, resolution, and Aeff(lambda) for the KRONOS UV and Visible spectrographs. Gaussian noise was added with standard deviations reflecting photon-counting statistics. The adopted observing sequence assumes that a 1 hour KRONOS exposure is taken every day for 400 days.

The ionizing spectral energy distribution is normalized to Q=1E54 photons/s at the mean level, and is allowed to vary in time as a random walk with P(f)~1/f and an rms of 0.3 mag. The uv-optical continuum is represented by a single power-law spectrum with correlated flux and spectral index changes to match the observed mean and rms spectrum of NGC 5548 during the 1989 AGN Watch campaign. In addition to the non-linear and anisotropic responses of each cloud to the ionizing radiation, Doppler shifts and time delays were taken into account when adding to the spectrum at each time the line emission contributions from each gas cloud.

The synthetic spectra were measured with the same code we use to measure real spectra. A power-law continuum was fitted and subtracted from each synthetic spectrum. MEMECHO was then used to fit the measured UV continuum lightcurve and the continuum-subtracted lightcurve for typically 100 wavelength bins across the profile of each emission line. This fit reproduces the observed continuum variations and the variously time-delayed line flux and profile variations by recovering a velocity-delay map for each line. The spiral patterns seen in the true maps are clearly recovered for the stronger lines Ly-alpha, CIV, and H-beta.

BLIND SIMULATIONS were performed to evaluate KRONOS capabilities. The fake datasets consist of a set of lightcurves. The "continuum" lightcurve C(t) is characterized by a power-law power density spectrum. C(t) is convolved with a 2-dimensional transfer function, Psi(v,tau), which represents the strength of CIV emission-line response to changes in the ionizing continuum radiation as a function of velocity v and time delay tau. The result is a set of lightcurves for the emission line, one for each velocity,

L(t,v) = int Psi(v,tau) C(t-tau) dtau.

The steps above were performed by Brad Peterson at Ohio State, and the steps below were performed by Keith Horne at St.Andrews. Noise is added to the lightcurves to simulate the expected Poisson noise for observations of a bright Seyfert 1 galaxy with the instrumentation planned for the KRONOS satellite.

The fake lightcurve data are then analyzed by the MEMECHO software, which tries to recover the velocity-delay map Psi(v,tau). The model that MEMECHO fits to the data is

L(t,v) = L0(v) + int Psi(v,tau) [ C(t-tau) - C0 ] dtau.

The background continuum level C0 is fixed at the mean value of C(t). The background spectrum L0(v) and the velocity-delay map Psi(v,tau) are parameters of the fit. The fit forces Chi^2/N = 1, to ensure consistent fit to the N data points, and maximizes the entropies of the functions L0(v) and Psi(v,tau), to make these the "smoothest positive functions" that fit the data.

Results for several blind simulations:

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