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Keith Horne

Publications and source records attributed to Keith Horne.

At least 37 records · Page 2Linked to original sources

A Phenomenological Study of the Accretion Disk in the Super-Eddington AGN I Zw 1

The structure of the accretion disk in AGN is still an unsolved question, especially how it may change with Eddington ratio. Here we examine the accretion disk in the super-Eddington AGN I Zw 1 using reverberation mapping of the optical continuum. We use three years of optical monitoring with Las Cumbres Observatory at sub-day cadence in $uBgVriz_s$. The lag-wavelength spectrum, calculated using the cross correlation method and PyROA, shows a $u$-band excess. PyROA lags are equally well fitted with a thin and slim disk profile. The UV/optical AGN spectral energy distribution is consistent with a thin disk. The disk size at 4495 Å for a thin disk model is $4.23\pm0.24\:\mathrm{ld}$ and for a slim disk model is $1.71\pm0.09\:\mathrm{ld}$, larger by a factor of $2-4$ than the fiducial disk size of $1.07\pm0.15\:\mathrm{ld}$ as determined using the Eddington ratio. We find evidence of different size scales probed with different variability timescales. Lags evaluated at longer variability timescales increase as do frequency-resolved lags at low frequencies, which we interpret as an additional secondary reprocessor at large radii consistent with the broad-line region (BLR) in I Zw 1. The high frequency lags, predicted well with just a disk, are fit with a thin disk profile and a size of $0.61\pm0.37\:\mathrm{ld}$. This indicates that the actual disk size may be on the order of the fiducial size. We also collate the most extensive set of directly measured internal sizes of an AGN, from optical to mid-infrared with reverberation mapping and optical interferometry. Assuming that the disk is indeed the fiducial size, these show little evidence that the accretion disk extends into the BLR significantly, tentatively disfavouring the failed radiatively accelerated dust driven outflow BLR formation model.

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Charged black holes in Weyl conformal gravity

We present a parametric study of the spacetime structures obtainable in Weyl conformal gravity's dyonic Reissner-Nordström solution. We derive expressions for photon sphere radii and horizons for this metric in terms of the conformal gravity parameters, from which we then determine analytic formulae for extremal limits and Hawking temperatures. Due to the surprising lack of the inverse quadratic $1/r^2$ term in this fourth-order metric, there is no guarantee for the innermost horizon of a black hole spacetime to be a Cauchy horizon, which is in direct contrast to the corresponding metric in general relativity. For example, for certain parameter values, a ``nested black hole'' is seen to exist; in such a spacetime, we find a Cauchy horizon trapped between two event horizons, which is not a structure known to be obtainable in standard general relativity. In addition to such exotic spacetimes, we also find a critical value for the electric and magnetic charges, at which the stable and unstable photon spheres of the metric merge, and we obtain extremal limits where three horizons collide.

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From Earths to Super-Earths: Five New Small Planets Transiting M Dwarf Stars

Earth-sized planets transiting M dwarf stars present one of the best opportunities with current facilities for studying the atmospheric and bulk compositions of terrestrial worlds. Here, we statistically validate five new transiting Earth and super-Earth sized planets orbiting M dwarf stars using a combination of light curves from the Transiting Exoplanet Survey Satellite, multi-color observations from Palomar and Las Cumbres Observatory, high-resolution imaging, and stellar spectroscopy. The sample includes: TOI-5716 b, an Earth-sized planet (R_p = 0.96 $\pm$ 0.05 Rearth) with a 6.766-day orbit around a metal-poor thin-disk star ([Fe/H] = -0.54 $\pm$ 0.10); TOI-5728 b, a super-Earth (R_p = 1.31 $\pm$ 0.05 Rearth) on an 11.497-day orbit; and TOI-5736 b, a larger planet (R_p = 1.56 $\pm$ 0.07 Rearth) with an ultra-short period of just 0.649 days. We also statistically validate a multi-planet system, TOI-5489, hosting two similarly-sized super-Earths: TOI-5489 b (R_p = 1.40 $\pm$ 0.05 R_earth) and TOI-5489 c (R_p = 1.28 $\pm$ 0.07 R_earth) with orbital periods of 3.152 and 4.921 days, respectively. Due to their longer orbital periods, TOI-5716 b and TOI-5728 b both have equilibrium temperatures $\leq$ 400 K, making them useful test cases for studies of atmospheric mass loss. If TOI-5728 b is confirmed to have an Earth-like bulk composition, it would join the very small sample of rocky planets orbiting mid- to late-M dwarfs that lie below the cosmic shoreline and therefore may have retained high mean molecular weight atmospheres.

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TOI-7166 b: A Habitable Zone mini-Neptune planet around a nearby low-mass star

We present the discovery and validation of TOI-7166b, a 2.01+/-0.05R_Earth planet orbiting a nearby low-mass star. We validated the planet by combining TESS and multi-color high-precision photometric observations from ground-based telescopes, together with spectroscopic data, high-contrast imaging, archival images, and statistical arguments. The host star is an M4-type dwarf at a distance of ~35 pc from the Sun. It has a mass and a radius of Ms=0.190+/-0.004M_Sun and Rs=0.222+/-0.005R_Sun, respectively. TOI-7166b has an orbital period of 12.9 days, which places it close to the inner edge of the Habitable Zone of its host star, receiving an insolation flux of Sp=1.07+/-0.08S_Earth and an equilibrium temperature of Teq=249+/-5K (assuming a null Bond albedo). The brightness of the host star makes TOI-7166 a suitable target for radial velocity follow-up to measure the planetary mass and bulk density. Moreover, the physical parameters of the system including the infrared brightness (Kmag = 10.6) of the star and the planet-to-star radius ratio (0.0823+/-0.0012) make TOI-7166b an exquisite target for transmission spectroscopic observations with the JWST, to constrain the exoplanet atmospheric compositions.

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Scalable and Robust Multiband Modeling of AGN Light Curves in Rubin-LSST

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will monitor tens of millions of active galactic nuclei (AGNs) for a period of 10 years with an average cadence of 3 days in six broad photometric bands. This unprecedented dataset will enable robust characterizations of AGN UV/optical variability across a wide range of AGN physical properties. However, existing tools for modeling AGN light curves are not yet capable of fully leveraging the volume, cadence, and multiband nature of LSST data. We present EzTaoX, a scalable light curve modeling tool designed to take advantage of LSST's multiband observations to simultaneously characterize AGN UV/optical stochastic variability and measure interband time delays. EzTaoX achieves a speed increase of $\sim 10^2-10^4 \times$ on CPUs over current tools with similar capabilities, while maintaining equal or better accuracy in recovering simulated variability properties. This performance gain enables continuum time-delay measurements for all AGNs discovered by LSST -- both in the Wide Fast Deep survey and the Deep Drilling Fields -- thereby opening new opportunities to probe AGN accretion-flow geometries. In addition, EzTaoX's multiband capability allows robust characterization of AGN stochastic variability down to hourly timescales, facilitating the identification of accreting low-mass AGNs -- such as those residing in dwarf galaxies -- through their distinctive variability signatures.

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AGN STORM 2. XI. Spectroscopic reverberation mapping of the hot dust in Mrk 817

The AGN Space Telescope and Optical Reverberation Mapping 2 (STORM 2) campaign targeted Mrk 817 with intensive multi-wavelength monitoring and found its soft X-ray emission to be strongly absorbed. We present results from 157 near-IR spectra with an average cadence of a few days. Whereas the hot dust reverberation signal as tracked by the continuum flux does not have a clear response, we recover a dust reverberation radius of $\sim 90$ light-days from the blackbody dust temperature light-curve. This radius is consistent with previous photometric reverberation mapping results when Mrk 817 was in an unobscured state. The heating/cooling process we observe indicates that the inner limit of the dusty torus is set by a process other than sublimation, rendering it a luminosity-invariant `dusty wall' of a carbonaceous composition. Assuming thermal equilibrium for dust optically thick to the incident radiation, we derive a luminosity of $\sim 6 \times 10^{44}$ erg s$^{-1}$ for the source heating it. This luminosity is similar to that of the obscured spectral energy distribution, assuming a disk with an Eddington accretion rate of $\dot{m} \sim 0.2$. Alternatively, the dust is illuminated by an unobscured lower luminosity disk with $\dot{m} \sim 0.1$, which permits the UV/optical continuum lags in the high-obscuration state to be dominated by diffuse emission from the broad-line region. Finally, we find hot dust extended on scales $> 140-350$ pc, associated with the rotating disk of ionised gas we observe in spatially-resolved [SIII] $λ9531$ images. Its likely origin is in the compact bulge of the barred spiral host galaxy, where it is heated by a nuclear starburst.

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XRISM/Resolve Spectroscopy of the Central Engine in the Seyfert-1 AGN Mrk 279

High-resolution X-ray spectroscopy with XRISM gives an unprecedented view of the ``central engine'' in active galactic nuclei, providing unique insights into black hole accretion and feedback. We present an analysis of the first XRISM/Resolve spectrum of the Seyfert-1 galaxy Mrk 279, known for its complex line profiles and variability. The data reveal velocity components within the Fe K$_α$ emission line that can be associated with the inner face of the molecular torus ($r \geq 10^{4}~GM/c^{2})$, the broad line region (BLR; $r = 1650^{+5780}_{-1480}~GM/c^{2}$), and the inner accretion disk ($r = 81^{+280}_{-75}~GM/c^{2}$). We find evidence of low-velocity, highly ionized gas that contributes an H-like Fe XXVI emission line at 6.97 keV, confirming suggestions from prior low-resolution spectra. The data do not show slow winds in absorption, but two pairs of lines - consistent with He-like and H-like Fe shifted by $v\simeq 0.22c$ and $v\simeq 0.33c$ - improve the fit, and could represent an ultra-fast outflow (UFO). Their addition to the model only reduces the Akaike Information Criterion by 3.6 and 3.5, respectively, signaling modest support. Additional observations are needed to definitively test for the presence of fast X-ray winds in Mrk 279. We discuss these results in the context of the geometry of the central engine in AGN, emerging trends in XRISM studies of AGN, and the nature of the potential UFOs.

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The SDSS-V Black Hole Mapper Reverberation Mapping Project: Light Echoes of the Coronal Line Region in a Luminous Quasar

We present a reverberation mapping analysis of the coronal line [Ne V]$λ$3427 emitting region of the quasar COS168 (SDSS J095910.30+020732.2). [Ne V]$λ$3427 is known as one of the "coronal lines," which are a species of emission lines present in AGN spectra with high ionization potentials ($\geq$ 100 eV) that can serve as tracers for AGN activity. The spatial extent of the coronal line region has been studied with only spatial resolving techniques that are not sensitive to the innermost regions of AGN. Through our reverberation mapping analysis of [Ne V]$λ$3427, we measure a nominal `optimal emission radius' for [Ne V]$λ$3427 of $381.1^{+16}_{-22}$ light days (observed-frame). We place the coronal line region in context with other AGN regions by comparing it with the characteristic radius of H$α$, the dust-sublimation radius, and the dusty torus. The coronal line region is located at a larger radius from the black hole than the characteristic radius of the dusty torus, measured using a torus-radius luminosity relationship. The virial product ($v^2 R/G$) of both H$α$ and [Ne V]$λ$3427 is consistent within the uncertainties, implying that the coronal line region, as probed by the [Ne V]$λ$3427 line, may be in a virialized orbit that is dominated by the gravitational potential of the black hole. This plausibly suggests that coronal lines could be an effective method for estimating black hole masses.

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NGTS-11 c: a transiting Neptune-mass planet interior to the warm Saturn NGTS-11 b

We report the discovery of NGTS-11 c, a transiting warm Neptune ($P \approx 12.8$ d; $M_{p} = 1.2^{+0.3}_{-0.2} M_{\mathrm{Nep}}$; $R_{p} = 1.24 \pm 0.03 R_{\mathrm{Nep}}$), in an orbit interior to the previously reported transiting warm Saturn NGTS-11 b ($P \approx 35.5$ d). We also find evidence of a third outer companion orbiting the K-dwarf NGTS-11. We first detected transits of NGTS-11 c in TESS light curves and confirmed them with follow-up transits from NGTS and many other ground-based facilities. Radial-velocity monitoring with the HARPS and FEROS spectrographs revealed the mass of NGTS-11 c and provides evidence for a long-period companion ($P > 2300$ d; $M_{p} \sin i > 3.6 M_{\mathrm{Jup}}$). Taking into account the two additional bodies in our expanded datasets, we find that the mass of NGTS-11 b ($M_{p} = 0.63 \pm 0.09 M_{\mathrm{Sat}}$; $R_{p} = 0.97 \pm 0.02 R_{\mathrm{Sat}}$) is lower than previously reported ($M_{p} = 1.2 \pm 0.3 M_{\mathrm{Sat}}$). Given their near-circular and compact orbits, NGTS-11 c and b are unlikely to have reached their present locations via high-eccentricity migration. Instead, they probably either formed in situ or formed farther out and then underwent disk migration. A comparison of NGTS-11 with the eight other known systems hosting multiple well-characterized warm giants shows that it is most similar to Kepler-56. Finally, we find that the commonly used 10-day boundary between hot and warm Jupiters is empirically well supported.

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The Accretion Disk Size Problem in AGN Disk Reverberation Mapping is an Obscuration Effect: A Uniform AGN Sample Study with Swift

In the past decade, Swift has performed several AGN high-cadence reverberation mapping campaigns, and generally found that the UV/optical interband lags are $\sim$3 times longer than predicted for a standard thin disk, thus coined "the accretion disk size problem". Here we present a systematic sample of Swift-monitored AGN. In this analysis, we confirm the accretion disk size problem, but find that the lag excess occurs only in the subset of obscured AGN, which show a significantly elevated mean normalization of $5.21 \pm 0.47$ ($p = 0.008$), whereas the unobscured AGN exhibit a mean excess consistent with standard disk predictions ($1.00 \pm 0.31$). Correlation and regression analyses similarly reveal X-ray column density as the strongest predictor of lag excess, explaining over 80% of its variance. We interpret these results as line-of-sight obscuration being linked to the too-long lags via additional reprocessed emission from the absorbing material itself. The consistency of lags in the unobscured subgroup with standard disk predictions suggests that the accretion disk size problem is not the result of shortcomings of standard accretion disk theory nor contamination by the broad-line region (BLR). X-ray to UV lag amplitudes and correlations show more complex and variable behavior in obscured AGN, suggesting that obscuration may disrupt or complicate the connection between high- and low-energy emission potentially through reprocessing, scattering, and/or ionization changes.

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Structure of Kerr black hole spacetimes in Weyl conformal gravity

We analyze the stationary, uncharged, rotating, vacuum solution to Weyl conformal gravity. We elucidate the causal and ergoregion structure of the spacetimes found in the parameter space of the metric for positive mass. These are then compared to the analogous Kerr, Kerr-de Sitter, and Kerr-Anti-de Sitter solutions to general relativity. Additionally, we investigate and derive the extremal limits for both the horizons and ergosurfaces of the spacetimes. The horizon surface gravities and Hawking temperatures at the extremal horizon limits are then calculated to show that they vanish.

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Continuum Reverberation Mapping of Accretion Disks Surrounding Supermassive Black Hole Binaries: Observational Signatures

It has remained challenging to reliably identify sub-parsec supermassive black hole binaries (SMBHBs), despite them being expected to be ubiquitous. We propose a new method using multi-band continuum reverberation mapping to identify low-mass-ratio SMBHBs in active galactic nuclei. The basic principle is that, due to the presence of a low-density cavity between the mini-disks and the circumbinary disk, the continuum emissions show a deficit at certain wavelengths, leading to a distinguishing feature in the relation between the inter-band time lag and wavelengths $τ(λ)$. Specifically, the relation appears flat at short wavelengths because of the truncated sizes of the mini-disks and transits to a power law $λ^{4/3}$ at long wavelength stemming from the circumbinary disk. This transition feature is distinct from the uniform relation $λ^{4/3}$ of the standard accretion disk around a single black hole. Using the lamp-post scenario and assuming that only the secondary black hole is active in a low-mass-ratio SMBHB, we design a simple continuum reverberation model to calculate the transfer function of the accretion disks and the resulting $τ(λ)$ relations for various SMBHB orbital parameters. The transition wavelength typically can lie at UV/optical bands, mainly depending on the total mass and orbital separation of the SMBHB. We apply our SMBHB model to the intensive multiwavelength monitoring data of the SMBHB candidate PG1302-102 and find that the SMBHB model can reproduce the inter-band time lags. Remarkably, the inferred total mass and orbital period from the SMBHB fitting are consistent with values derived from other independent methods.

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'Stealth' singularities from self-gravitating fermions

We present a new analytic solution to the Einstein-Dirac equations formulated by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] to describe the stationary states of a pair of gravitationally interacting neutral fermions. The fermions' wavefunction in our analytic solution, as in their numerical ones, is both exponentially localized and normalizable. However, our solution differs from theirs in two key respects: it features a naked spacetime singularity at the origin, and the gravitational (Arnowitt-Deser-Misner) mass of the localized object is zero, making it gravitationally undetectable to an external observer. This is despite the arbitrarily large mass of the constituent fermions. This unexpected result may have significant implications for astronomy and cosmology, as it gives a mechanism by which mass could become 'hidden' during the universe's evolution.

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Departures from Standard Disk Predictions in Intensive Ground-Based Monitoring of Three AGN

We present ground-based, multi-band light curves of the AGN Mrk~509, NGC\,4151, and NGC\,4593 obtained contemporaneously with \sw\, monitoring. We measure cross-correlation lags relative to \sw\, UVW2 (1928~Å) and test the standard prediction for disk reprocessing, which assumes a geometrically thin, optically thick accretion disk where continuum interband delays follow the relation \( τ(λ) \propto λ^{4/3} \). For Mrk~509 the 273-d \sw\, campaign gives well-defined lags that increase with wavelength as $τ(λ)\proptoλ^{2.17\pm0.2}$, steeper than the thin-disk prediction, and the optical lags are a factor of $\sim5$ longer than expected for a simple disk-reprocessing model. This ``disk-size discrepancy'' as well as excess lags in the $u$ and $r$ bands (which include the Balmer continuum and H$α$, respectively) suggest a mix of short lags from the disk and longer lags from nebular continuum originating in the broad-line region. The shorter \sw\, campaigns, 69~d on NGC\,4151 and 22~d on NGC\,4593, yield less well-defined, shorter lags $<2$~d. The NGC\,4593 lags are consistent with $τ(λ) \propto λ^{4/3}$ but with uncertainties too large for a strong test. For NGC\,4151 the \sw\, lags match $τ(λ) \propto λ^{4/3}$, with a small $U$-band excess, but the ground-based lags in the $r$, $i$, and $z$ bands are significantly shorter than the $B$ and $g$ lags, and also shorter than expected from the thin-disk prediction. The interpretation of this unusual lag spectrum is unclear. Overall these results indicate significant diversity in the $τ-λ$ relation across the optical/UV/NIR, which differs from the more homogeneous behavior seen in the \sw\, bands.

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The TESS Grand Unified Hot Jupiter Survey. III. Thirty More Giant Planets

We present the discovery of 30 transiting giant planets that were initially detected using data from NASA's Transiting Exoplanet Survey Satellite (TESS) mission. These new planets orbit relatively bright ($G \leq 12.5$) FGK host stars with orbital periods between 1.6 and 8.2 days, and have radii between 0.9 and 1.7 Jupiter radii. We performed follow-up ground-based photometry, high angular-resolution imaging, high-resolution spectroscopy and radial velocity monitoring for each of these objects to confirm that they are planets and determine their masses and other system parameters. The planets' masses span more than an order of magnitude ($0.17\,M_J < M_p < 3.3\,M_J$). For two planets, TOI-3593 b and TOI-4961 b, we measured significant non-zero eccentricities of $0.11^{+0.05}_{-0.03}$ and $0.18^{+0.04}_{-0.05}$ respectively, while for the other planets, the data typically provide a 1-$σ$ upper bound of 0.15 on the eccentricity. These discoveries represent a major step toward assembling a complete, magnitude-limited sample of transiting hot Jupiters around FGK stars.

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11 New Transiting Brown Dwarfs and Very Low Mass Stars from TESS

We present the discovery of 11 new transiting brown dwarfs and low-mass M-dwarfs from NASA's TESS mission: TOI-2844, TOI-3122, TOI-3577, TOI-3755, TOI-4462, TOI-4635, TOI-4737, TOI-4759, TOI-5240, TOI-5467, and TOI-5882. They consist of 5 brown dwarf companions and 6 very low mass stellar companions ranging in mass from $25 M_{\rm J}$ to $128 M_{\rm J}$. We used a combination of photometric time-series, spectroscopic, and high resolution imaging follow-up as a part of the TESS Follow-up Observing Program (TFOP) in order to characterize each system. With over 50 transiting brown dwarfs confirmed, we now have a large enough sample to directly test different formation and evolutionary scenarios. We provide a renewed perspective on the transiting brown dwarf desert and its role in differentiating between planetary and stellar formation mechanisms. Our analysis of the eccentricity distribution for the transiting brown dwarf sample does not support previous claims of a transition between planetary and stellar formation at $\sim42$ $M_{\rm J}$. We also contribute a first look into the metallicity distribution of transiting companions in the range $7 - 150$ $M_{\rm J}$, showing that this too does not support a $\sim42$ $M_{\rm J}$ transition. Finally, we also detect a significant lithium absorption feature in one of the brown dwarf hosts (TOI-5882) but determine that the host star is likely old based on rotation, kinematic, and photometric measurements. We therefore claim that TOI-5882 may be a candidate for planetary engulfment.

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A 16 Myr super-Neptune in Upper-Centaurus Lupus and a preliminary survey of transiting planets in Sco-Cen with TESS

Measuring the properties of planets younger than about 50 Myr helps to test different planetary formation and evolution models. NASA's Transiting Exoplanet Survey Satellite (TESS) has observed nearly the entire sky, including a wide range of star-forming regions and young stellar clusters, expanding our census of the newborn planet population. In this work, we present the discovery of the TIC 88785435 planetary system located in the Upper-Centaurus Lupus (UCL) region of the Scorpius-Centaurus OB association (Sco-Cen) and a preliminary survey of the planet population within Sco-Cen. TIC 88785435 is a pre-main sequence, K7V dwarf ($M_\star = 0.72M_\odot$, $R_\star = 0.91R_\odot$, $T_\mathrm{eff}$ = 3998K, V = 11.7 mag) located within the bounds of UCL. We investigate the distribution of rotation periods measured from the TESS long-cadence data and the Halpha and Li abundances from the spectra of TIC 88785435. TESS long-candence data reveal that TIC 88785435 hosts a transiting super-Neptune ($R_b = 5.03R_\oplus$, P = 10.51 days), TIC 88785435 b. Ground-based follow-up validates the planetary nature of TIC 88785435 b. Using the TESS data, we perform a preliminary survey to investigate how TIC 88785435 b compares to the population of newly born planets located within Sco-Cen.

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Echo mapping of the black hole accretion flow in NGC 7469

Reverberation mapping (RM) can measure black hole accretion disc sizes and radial structure through observed time lags that should increase with wavelength as $τ\proptoλ^{4/3}$. Our 250-day RM campaign on NGC 7469 combines sub-day cadence 7-band photometry from the Las Cumbres Observatory robotic telescopes and weekly X-ray and UVOT data from Swift. By fitting these light curves, we measure the spectral energy distribution of the variable accretion disc and inter-band lags of just 1.5 days across the UV to the optical range. The disc SED is close to the expected $f_ν\proptoν^{1/3}$, and the lags are consistent with $τ\propto λ^{4/3}$, but three times larger than expected. We consider several possible modifications to standard disc assumptions. First, for a $9\times10^6$ M$_\odot$ black hole and 2 possible spins $a^\star=(0,1)$, we fit the X-ray-UV-optical SED with a compact relativistic corona at height $H_x=(46,27)R_g$ irradiating a flat disc with accretion rate $\dot{m}_{Edd}\sim(0.23,0.24)$ inclined to the line of sight by $i<20^\circ$. To fit the lags as well as the SED, this model requires a low spin $a^\star=0$ and boosts disc color temperatures by a factor $f_{col}=1.8$, which shifts reprocessed light to shorter wavelengths. Our Bowl model with $f_{col}=1$ neglects relativity near the black hole but fits the UV-optical lags and SEDs using a flat disc with $\dot{m}_{Edd}<0.06$ and a steep outer rim at $R_{out}/c\sim5-10$ days with H/R<1%. This rim occurs near the $10^3$K dust sublimation temperature in the disc atmosphere, supporting models that invoke dust opacity to thicken the disc and launch failed radiatively-driven dusty outflows at the inner edge of the broad line region (BLR). Finally, the disc lags and SEDs exhibit a significant excess in the $u$ and $r$ bands, suggesting the Balmer continuum and H$α$ emission, respectively, from the BLR.

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