arXiv subjects

Kayhan Gültekin

Publications and source records attributed to Kayhan Gültekin.

At least 37 records · Page 2Linked to original sources

arXiv2023

ALMA gas-dynamical mass measurement of the supermassive black hole in the red nugget relic galaxy PGC 11179

We present 0$.\!\!^{\prime\prime}22$-resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations of CO(2$-$1) emission from the circumnuclear gas disk in the red nugget relic galaxy PGC 11179. The disk shows regular rotation, with projected velocities near the center of 400 km s$^{-1}$. We assume the CO emission originates from a dynamically cold, thin disk and fit gas-dynamical models directly to the ALMA data. In addition, we explore systematic uncertainties by testing the impacts of various model assumptions on our results. The supermassive black hole (BH) mass ($M_\mathrm{BH}$) is measured to be $M_\mathrm{BH} = (1.91\pm0.04$ [$1σ$ statistical] $^{+0.11}_{-0.51}$ [systematic])$\times 10^9$ $M_\odot$, and the $H$-band stellar mass-to-light ratio $M/L_H=1.620\pm0.004$ [$1σ$ statistical] $^{+0.211}_{-0.107}$ [systematic] $M_\odot/L_\odot$. This $M_\mathrm{BH}$ is consistent with the BH mass$-$stellar velocity dispersion relation but over-massive compared to the BH mass$-$bulge luminosity relation by a factor of 3.7. PGC 11179 is part of a sample of local compact early-type galaxies that are plausible relics of $z\sim2$ red nuggets, and its behavior relative to the scaling relations echoes that of three relic galaxy BHs previously measured with stellar dynamics. These over-massive BHs could suggest BHs gain most of their mass before their host galaxies do. However, our results could also be explained by greater intrinsic scatter at the high-mass end of the scaling relations, or by systematic differences in gas- and stellar-dynamical methods. Additional $M_\mathrm{BH}$ measurements in the sample, including independent cross-checks between molecular gas- and stellar-dynamical methods, will advance our understanding of the co-evolution of BHs and their host galaxies.

astro-ph.GA↗

arXiv2023

The NANOGrav 12.5-year Data Set: Search for Gravitational Wave Memory

We present the results of a Bayesian search for gravitational wave (GW) memory in the NANOGrav 12.5-yr data set. We find no convincing evidence for any gravitational wave memory signals in this data set (Bayes factor = 2.8). As such, we go on to place upper limits on the strain amplitude of GW memory events as a function of sky location and event epoch. These upper limits are computed using a signal model that assumes the existence of a common, spatially uncorrelated red noise in addition to a GW memory signal. The median strain upper limit as a function of sky position is approximately $3.3 \times 10^{-14}$. We also find that there are some differences in the upper limits as a function of sky position centered around PSR J0613$-$0200. This suggests that this pulsar has some excess noise which can be confounded with GW memory. Finally, the upper limits as a function of burst epoch continue to improve at later epochs. This improvement is attributable to the continued growth of the pulsar timing array.

gr-qc↗

arXiv2023

The NANOGrav 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background

The NANOGrav 15-year data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15-year observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values, or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach sub-parsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations.

astro-ph.HE↗

arXiv2023

The Impact of Black Hole Scaling Relation Assumptions on the Mass Density of Black Holes

We examine the effect of supermassive black hole (SMBH) mass scaling relation choice on the inferred SMBH mass population since redshift $z \sim 3$. To make robust predictions for the gravitational wave background (GWB) we must have a solid understanding of the underlying SMBH demographics. Using the SDSS and 3D HST+CANDELS surveys for $0 < z < 3$ we evaluate the inferred SMBH masses from two SMBH-galaxy scaling relations: $\mathrm{M_{BH}}$-$\mathrm{M_{bulge}}$ and $\mathrm{M_{BH}}$-$σ$. Our SMBH mass functions come directly from stellar mass measurements for $\mathrm{M_{BH}}$-$\mathrm{M_{bulge}}$, and indirectly from stellar mass and galaxy radius measurements along with the galaxy mass fundamental plane for $\mathrm{M_{BH}}$-$σ$. We find that there is a substantial difference in predictions especially for $z > 1$, and this difference increases out to $z = 3$. In particular we find that using velocity dispersion predicts a greater number of SMBHs with masses greater than $10^9 \mathrm{M}_\odot$. The GWB that pulsar timing arrays find evidence for is higher in amplitude than expected from GWB predictions which rely on high redshift extrapolations of local SMBH mass-galaxy scaling relations. The difference in SMBH demographics resulting from different scaling relations may be the origin for the mismatch between the signal amplitude and predictions. Generally, our results suggest that a deeper understanding of the potential redshift evolution of these relations is needed if we are to draw significant insight from their predictions at $z > 1$

astro-ph.GA↗

arXiv2023

The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15-yr dataset, and show that this dataset has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.

astro-ph.HE↗

arXiv2023

The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals.

astro-ph.HE↗

arXiv2023

The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background.

astro-ph.HE↗

arXiv2023

The NANOGrav 15-year Data Set: Search for Signals from New Physics

The 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons.

astro-ph.HE↗

arXiv2023

The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems.

astro-ph.HE↗

arXiv2023

The NANOGrav 12.5-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Pulsar timing array collaborations, such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), are seeking to detect nanohertz gravitational waves emitted by supermassive black hole binaries formed in the aftermath of galaxy mergers. We have searched for continuous waves from individual circular supermassive black hole binaries using the NANOGrav's recent 12.5-year data set. We created new methods to accurately model the uncertainties on pulsar distances in our analysis, and we implemented new techniques to account for a common red noise process in pulsar timing array data sets while searching for deterministic gravitational wave signals, including continuous waves. As we found no evidence for continuous waves in our data, we placed 95\% upper limits on the strain amplitude of continuous waves emitted by these sources. At our most sensitive frequency of 7.65 nanohertz, we placed a sky-averaged limit of $h_0 < $ $(6.82 \pm 0.35) \times 10^{-15}$, and $h_0 <$ $(2.66 \pm 0.15) \times 10^{-15}$ in our most sensitive sky location. Finally, we placed a multi-messenger limit of $\mathcal{M} <$ $(1.41 \pm 0.02) \times 10^9 M_\odot$ on the chirp mass of the supermassive black hole binary candidate 3C~66B.

astro-ph.GA↗

arXiv2023

Massive black holes in galactic nuclei: Observations

Since a black hole does not emit light from its interior, nor does it have a surface on which light from nearby sources can be reflected, observational study of black hole physics requires observing the gravitational impact of the black hole on its surroundings. A massive black hole leaves a dynamical imprint on stars and gas close by. Gas in the immediate vicinity of an accreting massive black hole can, due to the presence of the black hole, shine so brightly that it outshines the light of the billions of stars in its host galaxy and be detected across the Universe. By observing the emission from stars and gas and determining their kinematics scientists can extract vital information not only on the fundamental properties of the black holes themselves but also the impact they have on their surroundings. As it turns out, supermassive black holes appear to play a vital role in shaping the Universe as we know it, as they can profoundly impact the star formation history in galaxies. As a consequence, these black holes indirectly impact the cosmic build up of chemical elements heavier than Helium and thus affect when and where life can form. For these reasons alone, observations of massive black holes constitute a very active research area of modern astrophysics. In this chapter we aim to provide a general overview -- fit for a non-expert -- of what scientists have learned, and hope to learn, from analyzing observations of massive black holes and the material around them.

astro-ph.HE↗

arXiv2022

Intermediate-mass black holes and the fundamental plane of black hole accretion

We present new 5 GHz VLA observations of a sample of 8 active intermediate-mass black holes with masses $10^{4.9} < M < 10^{6.1}\ M_{\odot}$ found in galaxies with stellar masses $M_{*} < 3 \times 10^{9}\ M_{\odot}$. We detected 5 of the 8 sources at high significance. Of the detections, 4 were consistent with a point source, and one (SDSS J095418.15+471725.1, with black hole mass $M < 10^{5}\ M_{\odot}$) clearly shows extended emission that has a jet morphology. Combining our new radio data with the black hole masses and literature X-ray measurements, we put the sources on the fundamental plane of black hole accretion. We find that the extent to which the sources agree with the fundamental plane depends on their star-forming/composite/AGN classification based on optical narrow emission line ratios. he single star-forming source is inconsistent with the fundamental plane. The three composite sources are consistent, and three of the four AGN sources are inconsistent with the fundamental plane. We argue that this inconsistency is genuine and not a result of misattributing star-formation to black hole activity. Instead, we identify the sources in our sample that have AGN-like optical emission line ratios as not following the fundamental plane and thus caution the use of the fundamental plane to estimate masses without additional constraints, such as radio spectral index, radiative efficiency, or the Eddington fraction.

astro-ph.HE↗

arXiv2022

Gas inflows in the polar ring of NGC 4111: the birth of an AGN

We have used Hubble Space Telescope (HST) images, SAURON Integral Field Spectroscopy (IFS) and adaptative optics assisted Gemini NIFS near-infrared K-band IFS to map the stellar and gas distribution, excitation and kinematics of the inner few kpc of the nearby edge-on S0 galaxy NGC 4111. The HST images map its $\approx$ 450 pc diameter dusty polar ring, with an estimated gas mass $\ge10^7$ M$_\odot$. The NIFS datacube maps the inner 110 pc radius at $\approx$ 7 pc spatial resolution revealing a $\approx$ 220 pc diameter polar ring in hot ($2267\pm166$ K) molecular H$_2$ 1-0 S(1) gas embedded in the polar ring. The stellar velocity field shows disk-dominated kinematics along the galaxy plane both in the SAURON large-scale and in the NIFS nuclear-scale data. The large-scale [O III] $\lambda5007$ Åvelocity field shows a superposition of two disk kinematics: one similar to that of the stars and another along the polar ring, showing non-circular motions that seem to connect with the velocity field of the nuclear H$_2$ ring, whose kinematics indicate accelerated inflow to the nucleus. The estimated mass inflow rate is enough not only to feed an Active Galactic Nucleus (AGN) but also to trigger circumnuclear star formation in the near future. We propose a scenario in which gas from the polar ring, which probably originated from the capture of a dwarf galaxy, is moving inwards and triggering an AGN, as supported by the local X-ray emission, which seems to be the source of the H$_2$ 1-0 S(1) excitation. The fact that we see neither near-UV nor Br$γ$ emission suggests that the nascent AGN is still deeply buried under the optically thick dust of the polar ring.

astro-ph.GA↗

arXiv2021

Investigating the Accretion Nature of Binary Supermassive Black Hole Candidate SDSS J025214.67-002813.7

We present results on a multi-wavelength analysis of SDSS J025214.67-002813.7, a system which has been previously classified as a binary AGN candidate based on periodic signals detected in the optical light curves. We use available radio-X-ray observations of the system to investigate the true accretion nature. Analyzing new observations from XMM-Newton and NuSTAR, we characterize the X-ray emission and search for evidence of circumbinary accretion. Although the 0.5-10 keV spectrum shows evidence of an additional soft emission component, possibly due to extended emission from hot nuclear gas, we find the spectral shape consistent with a single AGN. Compiling a full multi-wavelength SED, we also search for signs of circumbinary accretion, such as a "notch" in the continuum due to the presence of minidisks. We find that the radio-optical emission agrees with the SED of a standard, radio-quiet, AGN, however there is a large deficit in emission blueward of ~1400 A. Although this deficit in emission can plausibly be attributed to a binary AGN system, we find that the SED of SDSS J0252-0028 is better explained by emission from a reddened, single AGN. However, future studies on the expected hard X-ray emission associated with binary AGN (especially in the unequal-mass regime), will allow for more rigorous analyses of the binary AGN hypothesis.

astro-ph.HE↗

arXiv2021

H$α$ Reverberation Mapping of the Intermediate-Mass Active Galactic Nucleus in NGC 4395

We present the results of a high-cadence spectroscopic and imaging monitoring campaign of the active galactic nucleus (AGN) of NGC 4395. High signal-to-noise-ratio spectra were obtained at the Gemini-N 8 m telescope using the GMOS integral field spectrograph (IFS) on 2019 March 7, and at the Keck-I 10 m telescope using the Low-Resolution Imaging Spectrometer (LRIS) with slitmasks on 2019 March 3 and April 2. Photometric data were obtained with a number of 1 m-class telescopes during the same nights. The narrow-line region (NLR) is spatially resolved; therefore, its variable contributions to the slit spectra make the standard procedure of relative flux calibration impractical. We demonstrate that spatially-resolved data from the IFS can be effectively used to correct the slit-mask spectral light curves. While we obtained no reliable lag owing to the lack of strong variability pattern in the light curves, we constrain the broad line time lag to be less than 3 hr, consistent with the photometric lag of $\sim80$ min reported by Woo et al. (2019). By exploiting the high-quality spectra, we measure the second moment of the broad component of the H$α$ emission line to be $586\pm19$ km s$^{-1}$, superseding the lower value reported by Woo et al. (2019). Combining the revised line dispersion and the photometric time lag, we update the black hole mass as $(1.7\pm 0.3)\times10^4$ M$_{\odot}$.

astro-ph.GA↗

arXiv2021

Properties of cold molecular gas in four type-1 active galaxies hosting outflows

Feedback from active galactic nuclei (AGN) has proven to be a critical ingredient in the current picture of galaxy assembly and growth. However, observational constraints on AGN-driven outflows face technical challenges and as a result, the cold molecular gas outflow properties of type-1 AGN are not well known. We present new IRAM NOrthern Extended Milimeter Array (NOEMA) observations of CO (1-0) in F07599+6508, Z11598$-$0112, F13342+3932, and PG1440+356, all nearby type-1 AGN and ultraluminous infrared galaxies (ULIRGs). We achieve spatial resolution of 1-3 arcsec corresponding to physical scales of 2--8~kpc and spectral resolution of 15-60 km s$^{-1}$ which enables updated CO (1-0) redshifts and a detailed morphological view of the cold molecular gas in these sources. The CO (1-0) luminosities, $L_{CO}^{\prime}$, are in the range 2-12$\times 10^9$ K km s$^{-1}$ pc$^{2}$ and inferred molecular gas masses, $M$(H$_2$), are in the range 2-9$\times 10^9$ M$_{\odot}$. The velocity fields and gas distributions do not unambiguously identify any of these sources as having outflows. However, Z11598$-$0112 has signs of infalling material and after the subtraction of a rotating disk model PG 1440+356 shows complex kinematics in the residuals that may indicate an outflow or warped disk.

astro-ph.GA↗

arXiv2021

An ALMA Gas-dynamical Mass Measurement of the Supermassive Black Hole in the Local Compact Galaxy UGC 2698

We present 0\farcs{14}-resolution Atacama Large Millimeter/submillimeter Array (ALMA) CO(2$-$1) observations of the circumnuclear gas disk in UGC 2698, a local compact galaxy. The disk exhibits regular rotation with projected velocities rising to 450 km s$^{-1}$ near the galaxy center. We fit gas-dynamical models to the ALMA data cube, assuming the CO emission originates from a dynamically cold, thin disk, and measured the mass of the supermassive black hole (BH) in UGC 2698 to be $M_{\mathrm{BH}} = (2.46 \pm{0.07}$ [$1σ$ stat] $^{+0.70}_{-0.78}$ [sys])$\times 10^9$ $M_\odot$. UGC 2698 is part of a sample of nearby early-type galaxies that are plausible $z\sim2$ red nugget relics. Previous stellar-dynamical modeling for three galaxies in the sample found BH masses consistent with the BH mass$-$stellar velocity dispersion ($M_{\mathrm{BH}}-σ_\star$) relation but over-massive relative to the BH mass$-$bulge luminosity ($M_{\mathrm{BH}}-L_{\mathrm{bul}}$) correlation, suggesting that BHs may gain the majority of their mass before their host galaxies. However, UGC 2698 is consistent with both $M_{\mathrm{BH}}-σ_\star$ and $M_{\mathrm{BH}}-L_{\mathrm{bul}}$. As UGC 2698 has the largest stellar mass and effective radius in the local compact galaxy sample, it may have undergone more recent mergers that brought it in line with the BH scaling relations. Alternatively, given that the three previously-measured compact galaxies are outliers from $M_{\mathrm{BH}}-L_{\mathrm{bul}}$, while UGC 2698 is not, there may be significant scatter at the poorly sampled high-mass end of the relation. Additional gas-dynamical $M_{\mathrm{BH}}$ measurements for the compact galaxy sample will improve our understanding of BH$-$galaxy co-evolution.

astro-ph.GA↗

arXiv2020

Evidence for variability timescale dependent UV/X-ray delay in Seyfert 1 AGN NGC 7469

Using a month-long X-ray lightcurve from ${\it RXTE}$/PCA and 1.5 month long UV continuum lightcurves from ${\it IUE}$ spectra in 1220$-$1970 $Å$, we performed a detailed time-lag study of the Seyfert 1 galaxy NGC 7469. Our cross-correlation analysis confirms previous results showing that the X-rays are delayed relative to the UV continuum at 1315 $Å$ by 3.49 $\pm$ 0.22 days which is possibly caused by either propagating fluctuation or variable comptonisation. However, if variations slower than 5 days are removed from the X-ray lightcurve, the UV variations then lag behind the X-rays variations by 0.37$\pm$0.14 day, consistent with reprocessing of the X-rays by a surrounding accretion disc. A very similar reverberation delay is observed between ${\it Swift}$/XRT X-ray and ${\it Swift}$/UVOT UVW2, U lightcurves. Continuum lightcurves extracted from the ${\it Swift}$/GRISM spectra show delays with respect to X-rays consistent with reverberation. Separating the UV continuum variations faster and slower than 5 days, the slow variations at 1825 $Å$ lag those at 1315 $Å$ by $0.29\pm0.06$ day, while the fast variations are coincident ($0.04\pm0.12$ day). The UV/optical continuum reverberation lag from ${\it IUE}$, ${\it Swift}$ and other optical telescopes at different wavelengths are consistent with the relationship: $τ\propto λ^{4/3}$, predicted for the standard accretion disc theory while the best-fit X-ray delay from ${\it RXTE}$ and ${\it Swift}$/XRT shows a negative X-ray offset of $\sim$0.38 days from the standard disc delay prediction.

astro-ph.HE↗