# UV/Optical disk reverberation lags despite a faint X-ray corona in the AGN
Mrk 335

Erin Kara MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Aaron J.
Barth Department of Physics and Astronomy, 4129 Frederick Reines Hall,
University of California, Irvine, CA, 92697-4575, USA  Edward M. Cackett
Department of Physics and Astronomy, Wayne State University, 666 W. Hancock
St, Detroit, MI, 48201, USA  Jonathan Gelbord Spectral Sciences Inc., 4 Fourth
Ave., Burlington, MA 01803, USA  John Montano Department of Physics and
Astronomy, 4129 Frederick Reines Hall, University of California, Irvine, CA,
92697-4575, USA  Yan-Rong Li Key Laboratory for Particle Astrophysics,
Institute of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan
Road,
Beijing 100049, People’s Republic of China  Lisabeth Santana Department of
Physics and Astronomy, University of Pittsburgh, 3941 O’Hara St, Pittsburgh,
PA 15260, USA  Keith Horne SUPA School of Physics and Astronomy, North Haugh,
St. Andrews, KY16 9SS, Scotland, UK  William N. Alston European Space Agency
(ESA), European Space Astronomy Centre (ESAC), Villanueva de la Canada,
Madrid, E-28691, Spain  Douglas Buisson  Independent  Doron Chelouche
Department of Physics, Faculty of Natural Sciences, University of Haifa, Haifa
3498838, Israel  Haifa Research Center for Theoretical Physics and
Astrophysics, University of Haifa, Haifa 3498838, Israel  Pu Du  Key
Laboratory for Particle Astrophysics, Institute of High Energy Physics,
Chinese Academy of Sciences, 19B Yuquan Road,
Beijing 100049, People’s Republic of China  Andrew C. Fabian Institute of
Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
Carina Fian  School of Physics and Astronomy and Wise observatory, Tel Aviv
University, Tel Aviv 6997801, Israel  Haifa Research Center for Theoretical
Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel  Luigi
Gallo  Department of Astronomy and Physics, Saint Mary’s University, 923 Robie
Street, Halifax, NS, B3H 3C3, Canada  Michael R. Goad School of Physics and
Astronomy, University of Leicester, University Road, Leicester, LE1 7RH, UK
Dirk Grupe  Department of Physics, Geology, and Engineering Technology,
Northern Kentucky University, 1 Nunn Dr., Highland Heights, KY 41099  Diego H.
González Buitrago Instituto de Astronomía, Universidad Nacional Autónoma de
México, Km 103 Carretera Tijuana-Ensenada, 22860 Ensenada B.C., México  Juan
V. Hernández Santisteban SUPA School of Physics and Astronomy, North Haugh,
St. Andrews, KY16 9SS, Scotland, UK  Shai Kaspi School of Physics and
Astronomy and Wise observatory, Tel Aviv University, Tel Aviv 6997801, Israel
Chen Hu  Key Laboratory for Particle Astrophysics, Institute of High Energy
Physics, Chinese Academy of Sciences, 19B Yuquan Road,
Beijing 100049, People’s Republic of China  S. Komossa  Max-Planck-Institut
für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany  Gerard A. Kriss
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218,
USA  Collin Lewin MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Tiffany Lewis
NASA Postdoctoral Program Fellow, Astroparticle Physics Lab, Goddard Space
Flight Center  Astrophysics Science Division, NASA Goddard Space Flight
Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA  Michael Loewenstein
Astrophysics Science Division, NASA Goddard Space Flight Center, 8800
Greenbelt Road, Greenbelt, MD 20771, USA  Department of Astronomy, University
of Maryland, College Park, MD 20742, USA  Anne Lohfink  Department of Physics,
Montana State University, P.O. Box 173840, Bozeman, MT 59717-3840, USA  Megan
Masterson MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Ian M.
McHardy  School of Physics and Astronomy, University of Southampton,
Highfield, Southampton SO17 1BJ, UK  Missagh Mehdipour Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Jake Miller
Department of Physics and Astronomy, Wayne State University, 666 W. Hancock
St, Detroit, MI, 48201, USA  Christos Panagiotou  MIT Kavli Institute for
Astrophysics and Space Research, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Michael L. Parker  Institute of Astronomy,
University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK  Ciro Pinto
INAF - IASF Palermo, Via U. La Malfa 153, I-90146 Palermo, Italy  Ron
Remillard  MIT Kavli Institute for Astrophysics and Space Research,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  Christopher
Reynolds  Institute of Astronomy, University of Cambridge, Madingley Road,
Cambridge CB3 0HA, UK  Daniele Rogantini  MIT Kavli Institute for Astrophysics
and Space Research, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  Jian-Min Wang Key Laboratory for Particle Astrophysics, Institute
of High Energy Physics, Chinese Academy of Sciences, 19B Yuquan Road,
Beijing 100049, People’s Republic of China  School of Astronomy and Space
Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing
100049, People’s Republic of China  National Astronomical Observatories of
China, 20A Datun Road, Beijing 100020, People’s Republic of China  Jingyi Wang
MIT Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  Dan Wilkins Kavli Institute
for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall,
Stanford, CA 94305, USA

###### Abstract

We present the first results from a 100-day Swift, NICER and ground-based
X-ray/UV/optical reverberation mapping campaign of the Narrow-Line Seyfert 1
Mrk 335, when it was in an unprecedented low X-ray flux state. Despite
dramatic suppression of the X-ray variability, we still observe UV/optical
lags as expected from disk reverberation. Moreover, the UV/optical lags are
consistent with archival observations when the X-ray luminosity was $>10$
times higher. Interestingly, both low- and high-flux states reveal UV/optical
lags that are $6-11$ times longer than expected from a thin disk. These long
lags are often interpreted as due to contamination from the broad line region,
however the $u$ band excess lag (containing the Balmer jump from the diffuse
continuum) is less prevalent than in other AGN. The Swift campaign showed a
low X-ray-to-optical correlation (similar to previous campaigns), but NICER
and ground-based monitoring continued for another two weeks, during which the
optical rose to the highest level of the campaign, followed $\sim 10$ days
later by a sharp rise in X-rays. While the low X-ray countrate and relatively
large systematic uncertainties in the NICER background make this measurement
challenging, if the optical does lead X-rays in this flare, this indicates a
departure from the zeroth-order reprocessing picture. If the optical flare is
due to an increase in mass accretion rate, this occurs on much shorter than
the viscous timescale. Alternatively, the optical could be responding to an
intrinsic rise in X-rays that is initially hidden from our line-of-sight.

accretion, accretion disks — black hole physics — line: formation – X-rays,
UV, optical: individual (Mrk 335)

††facilities: XMM-Newton, NICER, Swift, LCOGT, Liverpool:2m, Wise Observatory,
Zowada, OANSPM:HJT

##  1 Introduction

The accretion of gas onto supermassive black holes is a key driver in
understanding the formation and evolution of galaxies. Most of the accretion
power is released very close to the black hole, in the form of radiation and
large-scale outflows. Understanding the inner accretion flow–at the
intersection of inflow and outflow–is essential for understanding the Active
Galactic Nucleus (AGN) feedback phenomenon. While these scales are generally
too small to be spatially resolved, reverberation light echoes offer us a way
to infer the geometry and dynamics of gas flows close to the black hole.

As gas funnels in towards the supermassive black hole (SMBH) at the center of
a galaxy, collisions and angular momentum conservation cause the formation of
an optically thick, geometrically thin accretion disk around the black hole
(Shakura & Sunyaev, 1973) that emits thermal radiation in the optical/near
infrared (NIR) and peaking in the ultraviolet (UV) band. Some of those UV
photons scatter off mildly relativistic electrons in a region close to the
black hole that is known as the corona (Haardt & Maraschi, 1991). This
scattering boosts the UV photons to X-ray energies. A fraction of the X-ray
photons emitted by the corona reach the observer directly, while other photons
first intercept the accretion disk, are reprocessed, and then re-emitted. The
energetic photons interact with the material in the disk via processes such as
photoelectric absorption and fluorescence, thermalization, and Compton
scattering. The resulting reprocessed emission that is produced in the X-ray
band is often referred to as the ‘reflection spectrum’, (e.g., Fabian et al.,
1989; Ross & Fabian, 2005; García & Kallman, 2010), but much emission is
reprocessed into the UV-optical-infrared (UVOIR) band, as well, due to disk
heating.

Both the X-ray reflection spectrum and the broadband UVOIR SED from
reprocessed disk emission can be used to infer the geometry and composition of
the accretion disk, from scales of $10^{2-4}$$R_{\mathrm{g}}$111
$R_{\mathrm{g}}$$=GM/c^{2}$, as probed in the UVOIR, and down to
$1-10$$R_{\mathrm{g}}$, as probed in X-rays. X-ray spectra can be particularly
powerful because atomic features in the reflection spectrum are observed to be
broadened due to Doppler motion in the accretion disk, and also by the
gravitational redshift from the strong potential well of the black hole.

Complementary to spectral information, the time dependence of photons
originating in the innermost regions of the AGN can map out the accretion
disk, and very importantly, provide insights into the physical size scales
around the black hole (e.g. in centimeters, rather than in units of
$GM/c^{2}$). In the past decade, advances in higher cadence observing
campaigns and improved analysis techniques have allowed us to measure the
light travel time delays between the continuum emission from the innermost
regions and the reprocessed emission off the disk that shines in X-ray and
UVOIR. Typical time delays in X-ray reverberation lags are tens to hundreds of
seconds (corresponding to light travel distances of tens of gravitational
radii), and in UVOIR continuum reverberation mapping time delays are on the
order of days (probing the accretion disk at larger distances of hundreds to
thousands of gravitational radii). See Cackett et al. (2021) for a recent
review of AGN reverberation mapping on all scales from the dusty torus
($>10^{5}$$R_{\mathrm{g}}$) to the broad line region (BLR;
$10^{3-5}$$R_{\mathrm{g}}$) and down to the innermost stable circular orbit
(ISCO; $\sim 1$$R_{\mathrm{g}}$).

Figure 1: The long-term Swift light curve from 2007 to 2021, showing the
0.3–1.5 keV light curve (top), and the UVW2 light curve (bottom). Our high-
cadence disk reverberation mapping campaign in 2019–2020 took place in an
unprecedentedly low X-ray flux state (blue). Later we compare the lags to a
lower-cadence campaign taken during a high flux epoch (red). The soft band
light curve is in units of counts s-1 (note log scale), and the UVW2 light
curve is in units of $10^{-14}$ erg cm-2 s-1Å-1.

High-cadence X-ray/UV/optical continuum reverberation mapping campaigns have
successfully been successfully completed for nine AGN (NGC 5548: Edelson et
al. 2015; Fausnaugh et al. 2016, NGC 4151: Edelson et al. 2017, NGC 4593:
McHardy et al. 2018; Cackett et al. 2018, Mrk 509: Edelson et al. 2019,
Fairall 9 Hernández Santisteban et al. 2020, Mrk 142: Cackett et al. 2020, Mrk
110: Vincentelli et al. 2021, Mrk 817: Kara et al. 2021a, Mrk 335: this work),
and several more campaigns have recently been completed or are currently
underway. While the sample is yet small, the campaigns have revealed
surprising results that present challenges to standard accretion theory. In
nearly all AGN that have been the subject of these high-cadence multi-
wavelength campaigns, the amplitude of the X-ray-to-UV lag does not match the
standard model (see, e.g., Edelson et al. 2019). Moreover, the correlation
between X-ray and UV is much weaker than predicted from the standard
reprocessing model. Some have suggested that this means that the observed
X-rays are not the driving light curve at all, or that the thin accretion disk
does not extend to the ISCO, but instead, truncates at some radius ($\sim
20$$R_{\mathrm{g}}$), within which, there is a hot inner flow that emits a
soft X-ray continuum (Gardner & Done, 2017; Mahmoud & Done, 2020). This is in
tension with results from X-ray reverberation, indicating that the disk is not
highly truncated (De Marco et al., 2013; Kara et al., 2016). Yet others have
suggested that by filtering out long timescale variability (that could be due
to obscuration or the inflow of matter through the accretion disk), one can
recover the expected X-ray to UV reverberation time lags (McHardy et al.,
2018; Hernández Santisteban et al., 2020).

In this paper we examine the X-ray/UVOIR disk reverberation lags in the well-
known and rapidly variable narrow-line Seyfert 1 galaxy Mrk 335 ($z=0.025785$;
Huchra et al. 1999), which has been the subject of several X-ray, UV and
optical timing campaigns. In a 120-day ground-based photometric and
spectroscopic campaign, Grier et al. (2012) found the optical continuum to
lead the H$\beta$ broad emission line by $13.9\pm 0.9$ days, inferring a
virial mass of $(2.6\pm 0.8)\times 10^{7}M_{\odot}$. In an archival analysis
of a long XMM-Newton observation, Kara et al. (2013a) found that the X-ray
continuum led the iron K and soft excess reflection features by $\sim 100$ s.
Recently, Mastroserio et al. (2020) modelled these X-ray lags with general
relativistic ray-tracing simulations. Assuming a geometry of a point-source
corona close to the black hole, they inferred a black hole mass that was ten
times smaller than that found in the optical. These authors suggest that this
inconsistency could be due to a more complex coronal geometry that is not
accounted for in the modeling.

In addition to its rapid variability, Mrk 335 has shown dramatic, long-term
changes, revealed by long-term Swift X-ray/UV monitoring (Grupe et al. 2007,
2012; Gallo et al. 2018; Komossa et al. 2020 and Fig. 1). While there do
appear to be some long-term trends between the UV/optical and X-rays (e.g.
Gallo et al. 2018; Parker et al. 2019), generally, the amplitude of the X-ray
variability is much more dramatic, and can dip into extreme low-flux states,
while the optical/UV remain persistently variable. The origin of these
dramatic X-ray dips is still not well understood, sometimes being attributed
to a collapse of the corona (e.g. Gallo et al. 2013; Parker et al. 2014;
Wilkins et al. 2015) or to absorption and partial obscuration of the disk and
corona (e.g. Grupe et al. 2008; Longinotti et al. 2013; Komossa et al. 2020).

Here we report on the results of a 100-day high-cadence campaign of Mrk 335
during its most recent extreme X-ray low-flux state, using the Neil Gehrels
Swift Observatory (Swift), the Neutron Star Interior Composition ExploreR
(NICER) on the International Space Station, and several ground-based
observatories. In Section 2, we describe details of the campaign and data
reduction. We present the results of the multi-wavelength cross-correlation
analysis in Section 3, and compare these results to archival high-flux
observations taken in 2008. Both high- and low-flux state exhibit UV/optical
lags as expected from the standard X-ray reprocessing model, and we present
possible explanations in the Discussion (Section 4). Conclusions are
summarized in Section 5.

##  2 Observations and Data Reduction

###  2.1 Neil Gehrels Swift Observatory

Our campaign of Mrk 335 began on 2019 October 14 for 100 consecutive days with
a cadence of roughly 3 visits per day, until 2020 January 22
(HJD-2450000=8770–8870). There were occasional gaps due to poor visibility or
interruptions caused by Targets of Opportunity. In particular, there was a
large gap at the end of the campaign (HJD-2450000=8863–8869), due to
gravitational wave counterpart searches. Each visit is typically $\sim$1 ksec.
The Swift XRT (Burrows et al., 2005) was operated in Photon Counting mode. The
UVOT (Roming et al., 2005) was typically operated in an end-weighted filter
mode (0x224c) to get exposures in all 6 UV/optical filters with an exposure
weighting of 3:1:1:1:1:2 (for UVW2 through V). This has the effect of greatly
improving the V band signal-to-noise at the cost of slight degradation in the
UVM2 to B band signals. This is done because the UVW2/V lag covers the largest
wavelength range, and thus is the most physically constraining.

Swift X-ray light curves were generated using the Swift-XRT (Evans et al.,
2007, 2009) data product
tool222https://www.swift.ac.uk/user_objects/index.php. All archival and new
UVOT data were processed and analyzed following the procedures described by
Edelson et al. (2019) and Hernández Santisteban et al. (2020), with HEASOFT
version 6.28 and CALDB version 20210113. Fluxes are measured using the
uvotsource tool, with a circular source extraction region of 5″ radius and
with the background measured in a surrounding 40″–90″ annulus. We apply
detector masks to reject data points when the source falls on regions of the
chip with lower sensitivity. We follow the procedure laid out in Hernández
Santisteban et al. (2020), but find that the detector masks employed there are
too aggressive for the present data, eliminating many points that are
consistent with the light curves within their measurement errors. Instead, we
use a more conservative set of masks defined by applying higher thresholds to
the sensitivity maps.

The Swift X-ray count rate during the campaign was very low compared to
archival observations from 2008-2018. The mean 0.3 – 10 keV count rate between
2007 – 2018 is 0.26 c s-1, while during our 100-day campaign the mean rate is
0.038 c s-1, a factor of 7 lower. Despite the significant change in the X-ray
count rate, the mean UVW2 flux dropped only by 12% during our campaign (to
$2\times 10^{-14}$ erg s-1 cm-2 Å-1). Because the Swift X-ray count rate is
very low, we binned the X-ray light curves to a 3-day binning. This reduces
the scatter, but the resultant X-ray to UVW2 lags are the same regardless of
bin choice. Later, in Section 3, we compare the lags in our low-state
campaign, to a relatively high-cadence high-state archival year-long campaign
in 2009 (red shaded region in Fig. 1). In this archival epoch, the X-rays were
23 times higher than during our low-flux campaign, while the UVW2 was only a
factor of 1.3 times higher.

###  2.2 NICER

Figure 2: (Top:) Background-subtracted 0.3–1.5 keV NICER light curve compared to the background rate (starting 2019 October 14). The increase in background at the end of the campaign is due to increased optical light leakage towards the end of the visibility window. Despite this, one can see an increase in the source light curve before the increase in background. The Swift light curve (bottom) also shows an increase in flux at the end of the campaign. Table 1: Ground-based Imaging Observations Observatory/Telescope | Instrument | Filters | References
---|---|---|---
Las Cumbres Observatory 1m network | Sinistro | $g^{\prime}r^{\prime}i^{\prime}z_{\mathrm{s}}$ | Brown et al. (2013)
Liverpool Telescope 2m | IO:O | $g^{\prime}r^{\prime}i^{\prime}z^{\prime}$ | Steele et al. (2004)
San Pedro Mártir Observatory 1.5m | RATIR | $g^{\prime}r^{\prime}i^{\prime}$ |  Butler et al. (2012), Watson et al. (2012)
Wise Observatory 18-inch | QSI683 | $g^{\prime}r^{\prime}i^{\prime}z^{\prime}$ | Brosch et al. (2008)
Zowada Observatory 20-inch |  | $g^{\prime}r^{\prime}i^{\prime}z_{\mathrm{s}}$ | Carr et al. (2022)
Table 2: Ground-Based Photometry

Filter | HJD-2450000 | $f_{\lambda}$ | $\sigma(f_{\lambda})$ | Telescope
---|---|---|---|---
$g$ | 8700.902 | 6.551 | 0.009 | LCO-V37
$g$ | 8704.920 | 6.385 | 0.015 | LCO-V39
$g$ | 8708.755 | 6.285 | 0.009 | LCO-V37
$g$ | 8715.890 | 5.958 | 0.010 | LCO-V37
$g$ | 8722.919 | 5.686 | 0.005 | LCO-V37
$g$ | 8726.759 | 5.657 | 0.074 | LCO-W87
$g$ | 8728.451 | 5.611 | 0.037 | Zowada
$g$ | 8730.816 | 5.647 | 0.005 | LCO-V37
$g$ | 8733.901 | 5.805 | 0.006 | LCO-V37
$g$ | 8738.712 | 6.010 | 0.047 | LCO-W86

Note. — Flux densities ($f_{\lambda}$) and uncertainties $(\sigma)$ are given
in units of $10^{-15}$ erg cm-2 s-1 Å-1. For Las Cumbres Observatory (LCO),
the Minor Planet Center telescope codes are listed to denote individual
telescopes in the 1 m network. This table is published in its entirety in the
machine-readable format. A portion is shown here for guidance regarding its
form and content.

NICER was set to accompany the same 100 days of observations as Swift, with a
one-day cadence. However, due to the historic first all-female space walk on
the International Space Station on 2019 October 18, NICER had to stow, and
could not begin the daily monitoring until 2019 October 20 (HJD-2450000=8776).
This was, in some ways, fortuitous, as this initial delay led to the later
extension of NICER’s campaign until HJD 2458883, during which time the X-rays
rose to their highest flux level of the entire campaign.

The data were processed using the NICER data-analysis software version
2017-06-01_V005, allowing for undershoot rates up to 400 (standard screening
otherwise). The source and background spectra were extracted for each
observation. The background spectra were constructed with the background
estimator, 3C50 (Remillard et al., 2022). We removed data from noisy detectors
14 and 34, and for each GTI, we removed data from any detector (FPM) that
deviates more than 3-$\sigma$ from the average in the 0–0.2 keV band, as a way
to reduce the impact of optical light leak. The count rates were scaled to be
the count rates per 52-FPMs, accounting for the detectors that were excluded
or were off at a particular time. This results in 101 individual pointings.
The source flux was so low that the background dominates above 1.5 keV, and
therefore, we only examine the soft-band light curve with NICER.

NICER’s background is largely affected by optical light leakage, which
increases depending on space weather and the proximity of bright objects
(e.g., Sun, Earth, Moon, and their reflections on ISS solar panels). While we
were fortunate that NICER was able to extend observations beyond the Swift
campaign to when optical telescopes reached their peak luminosity, these NICER
observations had a lower sun angle, and so this is also when NICER’s
background level rose to the highest of the campaign (Fig. 2). The inferred
rise in source flux does not appear to be due to high background levels
because (1) the X-ray source flux rises before the background does, (2) Swift
also observed a rise in X-rays (albeit with very sparse sampling), and (3) the
NICER spectrum during the flare (see Section 3.2) clearly looks like the
spectrum of Mrk 335 (i.e. with a soft continuum and emission lines from
circumnuclear material), and not like the particle background spectrum, which
is much harder ($\Gamma\sim 1$). See Section 3.2 for more details of the NICER
spectrum during the flare state.

###  2.3 XMM-Newton

XMM-Newton observed Mrk 335 once, starting on HJD 2458845 for 105 ks during
the 100-day reverberation mapping campaign through an XMM-Newton Director’s
Discretionary Time (DDT) observation (PI: N. Schartel; Tripathi et al. 2020;
Liu et al. 2021). We reduced the data using the XMM-Newton Science Analysis
System (SAS v. 19.0.0) and the newest calibration files. We started with the
observation data files and followed standard procedures. The PN observations
were taken in Full Frame Mode. The source extraction regions are circular
regions of radius 35 arcsec centered on source position. The background
regions are also circular regions of radius 35 arcsec or greater, avoiding
other bright sources and the detector edges where the instrumental copper line
is most prominent. The observations had some distinct soft proton background
flares, which we removed by screening based on the 13–15 keV light curve count
rate, resulting in a net exposure of 70 ks. The response matrices were
produced using rmfgen and arfgen in SAS.

Figure 3: Left: Mrk 335 light curves from the high-cadence reverberation
mapping campaign (starting 2019 October 14) with Swift (blue), NICER (purple),
and ground-based telescopes (green). The portions of the ground-based light
curves before the start date of the Swift campaign are not shown. Right: Solid
black lines show the cross-correlation function with respect to the Swift UVW2
band. A positive lag indicates the band of interest is lagging behind the UVW2
reference band. Colored histograms show the ICCF centroid lag distributions
from the FR/RSS technique. See text for details.

###  2.4 Ground-based photometry

Ground-based optical imaging observations were obtained at several sites,
listed in Table 1. The ground-based campaign spanned a longer duration than
the Swift program, beginning on 2019 July 29 and continuing through 2020
February 13. Filters included the SDSS
$g^{\prime}r^{\prime}i^{\prime}z^{\prime}$, and Pan-STARRS $z_{s}$. We
combined the $z^{\prime}$ ($\lambda_{c}=9134$ Å) and $z_{s}$
($\lambda_{c}=8700$ Å) bands for the final light curve measurements, and for
simplicity we refer to the SDSS and Pan-STARRS filters as _griz_ bands
hereinafter. We also obtained some data in the SDSS $u^{\prime}$ and Johnson
_BV_ bands, but the temporal coverage of the _BV_ observations was poor
compared with the SDSS bands, and the S/N of the $u^{\prime}$ data was too low
to measure an accurate light curve. Since the Swift data includes the _UBV_
bands, we do not include the lower-quality ground-based $u^{\prime}$ and _BV_
data in this paper. Initial data processing including bias and overscan
subtraction and flat-fielding was carried out using the standard reduction
pipeline for each telescope.

Aperture photometry was carried out using an automated pipeline based on
AstroPy (Astropy Collaboration et al., 2018) routines, following the same
methods used for a recent campaign on Mrk 817 as described by Kara et al.
(2021a). The photometric aperture radius for the AGN and comparison stars was
5″, and an annulus of $r=15\arcsec-20\arcsec$ was used to measure the sky
background. For each filter, data points measured from multiple images taken
at an individual telescope during a night were averaged to produce a single
data point in the final light curve, but data points from different telescopes
were not averaged together. All light curves in a given filter from different
telescopes were intercalibrated using the code PyCALI (Li et al., 2014), which
also expands the measurement uncertainties on data points to account for the
systematic intercalibration uncertainty for each telescope’s data. The data
were flux calibrated using comparison star magnitudes from the APASS catalog
(Henden et al., 2018). The total number of data points in the final combined
light curves is 260 ($g$), 296 ($r$), 278 ($i$), and 240 ($z$). The optical
light curve data are listed in Table 2 and displayed in Figure 3.

##  3 Results

###  3.1 Continuum lag results

Figure 4: Observed continuum lags calculated with respect to the Swift/UVW2 band. The NICER soft X-ray lag is shown as a purple diamond; Swift as blue circles and ground-based $griz$ bands as green squares. The dotted and dashed lines show the best-fitting $\tau\propto\lambda^{\beta}$ relations, where $\beta$ is fixed at the canonical value of 4/3 for the dotted line, and allowed to be free for the dashed line ($\beta=1.5\pm 0.4$). While the canonical $\tau\propto\lambda^{4/3}$ relation provides a good fit, the normalization of the lag is almost 10x larger than expected given the mass and accretion rate of this object. The Swift soft X-ray point has been removed for clarity, but is consistent with the NICER lag, just with a much larger error bar; see Table 3 for exact numbers.  Table 3: Continuum lags and light curve properties. Lags are computed with respect to the UVW2 reference band, where positive indicates a lag behind UVW2. Filter/Band | Telescope | $R_{\rm max}$ | Lag centroid
---|---|---|---
|  |  | (days)
Hard X-ray (1.5–10 keV) | Swift | 0.68 | 2.4_-1.8^+2.9
Soft X-ray (0.3–1.5 keV) | Swift | 0.58 | 10.4_-4.3^+3.0
Soft X-ray (0.3–1.5 keV) | NICER | 0.62 | 11.4_-1.3^+1.4
UVW2 (1928Å) | Swift | 1.00 | 0.00±0.2
UVM2 (2246Å) | Swift | 0.95 | -0.07_-0.32^+0.37
UVW1 (2600Å) | Swift | 0.95 | 0.41_-0.32^+0.38
U (3465Å) | Swift | 0.94 | 1.77_-0.38^+0.39
B (4392Å) | Swift | 0.89 | 1.78_-0.50^+0.42
g (4770 Å) | Ground | 0.95 | 2.34_-0.36^+0.38
V (5468Å) | Swift | 0.83 | 2.02_-0.62^+0.55
r (6215Å) | Ground | 0.87 | 5.31_-1.17^+0.67
i (7545Å) | Ground | 0.88 | 6.27_-0.65^+0.49
z (8700Å) | Ground | 0.76 | 6.88_-0.83^+0.79

We calculate lags with PyCCF (Sun et al., 2018), using the standard linear
Interpolated Cross-Correlation Function (ICCF) technique, where uncertainties
are estimated with the flux randomization, random subset sampling approach (as
implemented by Peterson et al., 2004). This entails creating 1000 realizations
of the light curves, where each flux point is drawn randomly from a Gaussian
distribution with mean and standard deviation equal to the measured flux and
its 1$\sigma$ uncertainty. In addition, the light curve is randomly resampled
with repetitions, i.e., some points are selected multiple times, while others
are not selected at all. For each realization we measure the cross-correlation
function (CCF) and its centroid value. The lag is the median of the CCF
centroid distribution, and its 1$\sigma$ uncertainty from the 16% and 84%
quantiles. The time lag range considered in the CCF was $\pm 30$ days. Because
it probes closest to the thermal peak of the hot accretion disk, and for
consistency with previous results, we use the Swift/$UVW2$ band as the
reference light curve.

The observed light curves and resulting rest-frame lags (over the period
HJD=2458770–2458885) are shown in Fig. 3 and details of the lag centroid and
maximum correlation coefficient $R_{\rm max}$ are shown in Table 3. The right-
hand panels of Fig. 3 show the CCFs (solid lines) and the CCF centroid
distributions. Fig. 4 shows the lags as a function of wavelength. The UVOIR
lags increase with wavelength, approximately following
$\tau\propto\lambda^{4/3}$, as expected for a standard Shakura & Sunyaev thin
disk (Cackett et al., 2007). We fit the UVOIR lags with the function:
$\tau=\tau_{0}\left[\left(\lambda/\lambda_{0}\right)^{\beta}-y_{0}\right]$,
with $\lambda_{0}=1869$ Å (the rest-frame wavelength of the UVW2 band), and
$\beta=4/3$, and where $y_{0}$ allows the fit to cross zero lag at
$\lambda=\lambda_{0}$. This gives a best-fitting value of $\tau_{0}=1.11\pm
0.06$ days. Allowing $\beta$ to be free yields consistent results, with
$\beta=1.5\pm 0.4$. If we perform the ICCF analysis on a subset of the
campaign from HJD 2458770–2458850 (i.e., removing the flare at the end), we
find a very similarly shaped lag-wavelength relation, but the normalization is
smaller: $\tau_{0}=0.62\pm 0.08$ days. Regardless of whether we consider the
flare data or not, the normalization of the lag-wavelength relation is quite
large, and will be discussed more in Section 4.

The reprocessing model provides an adequate fit to the data, with a few
noteworthy exceptions, described in the following paragraphs. Nearly all
intensive reverberation campaigns that utilized Swift and ground-based
monitoring (Edelson et al., 2019; Cackett et al., 2018; Vincentelli et al.,
2021; Hernández Santisteban et al., 2020) have found significant excess lags
in the $u$ band and $r$ band, relative to the adjacent bands or to the model
fits. Mrk 335 is no exception. However, a systematic analysis of four AGN with
intensive Swift monitoring campaigns showed typical $u$ band excesses of a
factor of 2.2 on average (Edelson et al., 2019). Mrk 335, on the other hand,
shows an excess of the $u$ and $r$ bands of only 30% greater than expected.
See Section 4 for more details.

The other obvious outlier to the $\tau\propto\lambda^{4/3}$ relation in Fig. 4
is the soft X-ray lag. In the standard reprocessing picture, the X-rays are
the driving light curve and therefore should lead the other light curves, but
here we see that the soft X-rays are delayed with respect to the UVW2 by $\sim
10$ days. This $\sim 10$-day delay is seen both with NICER and with Swift,
though both show a low soft X-ray vs. UVW2 maximum correlation coefficient of
$R_{\rm max}\sim 0.6$. The low Swift-UVW2 correlation coefficient is likely
due to the fact that Swift did not observe the flare at high cadence. To
understand where this soft X-ray lag originates, we compare the NICER soft
X-ray light curve to the $g$-band light curve (which is the best sampled
optical light curve, and importantly, covers the flare period). The
correlation coefficient between NICER soft X-rays and the $g$-band light curve
is much higher ($R_{\rm max}=0.80$) with an X-ray lag of $3.5^{+1.1}_{-0.9}$
days.

Figure 5: Comparison of the NICER 0.3–1.5 keV soft X-ray light curve to the
$g$-band light curve, shown to highlight the late time rise of the X-rays
relative to longer wavelengths. Notice that the X-ray and optical light curve
variations are shown on different axes, with the X-ray varying more than the
optical. The gray shaded regions indicate the times from which the spectra
shown in Fig. 6 were taken.

We tested whether the 10-day soft X-ray lag is due to variability across the
entire campaign or simply driven by the large flare at the end of the campaign
seen both in X-rays and UVOIR. We performed the ICCF analysis on a subset of
the campaign from HJD 2458770–2458850 (i.e., removing the flare at the end).
While the NICER lags UVW2 slightly by $2.9\pm 2$ days, $R_{\rm max}$ value is
very low ($R_{\rm max}=0.47$), and so ought not be taken with too much
credence.

We conclude that the soft X-ray lag is mostly an artifact of the large flare
at the end of the campaign, where the X-rays rise after the UVOIR bands. This
can be seen most directly by simply overplotting the NICER soft X-ray light
curve and the $g$-band light curve (Fig. 5). We use the $g$-band light curve
simply because it is the best sampled light curve. Similar conclusions would
be drawn from comparison with the UVW2 light curve. We compare the light
curves over the same timescale (HJD 2458776-2458883), and overplot them by
dividing each light curve by its mean. One can see that the correlation from
the non-flare period is low (as discussed in the previous paragraph), but the
flare shows a distinct energy dependence. The X-rays rise $\sim 15$ days after
the rise of the $g$-band. This is counter to the canonical reprocessing
scenario where the optical rises in response to a rise in the X-ray light
curve. The standard reprocessing scenario can be salvaged if the X-ray
luminosity we observe is not the same as the X-ray luminosity ‘seen’ by the
disk. We will discuss possible interpretations for the soft X-ray delay in
Section 4.

###  3.2 Spectral evolution

Figure 6: The XMM-Newton spectrum (black) was taken during one of the lowest
points of the campaign (HJD 2458845), and the NICER (purple) and Swift (blue)
spectra are from the flare state (integrated over HJD 2458867 to HJD 2458883).
This highlights that the flare was not simply seen in soft X-rays alone, as
would be expected from a decrease in the level of obscuration.

Next we compare the X-ray spectra from the low-flux state to the flare state.
During the low-flux state of our 100-day campaign, XMM-Newton took one
observation (denoted as thin gray line at HJD=2458845 in Fig. 5). This
spectrum is shown in black in Fig. 6, and is very similar in shape and flux to
low-state observations taken one year earlier (see Parker et al. 2019 for a
detailed spectral analysis of those observations). The low energies are
dominated by narrow photoionized emission lines from circumnuclear material
(Liu et al., 2021), and a prominent neutral iron K line is present at 6.4 keV,
presumably from further out in the dusty torus.

For comparison, we overplot the NICER and Swift spectra from the flare at the
end of the campaign, from HJD 2458867 to HJD 2458883. The overall flux level
has increased by a factor of $\sim 2.3$, and most importantly, the relative
change in hard X-rays is larger than that in soft X-rays, which cannot be
explained by a change in obscurer column density alone. This larger relative
increase in hard X-rays can also be seen by comparing the Swift soft and hard
band light curves in Fig. 3. The origin of the X-ray flare is discussed in
Section 4.

Figure 7: Lag vs. wavelength, comparing our recent intensive reverberation
mapping campaign in the X-ray low state (blue points) to a high-state campaign
in 2008 (red points). The marker shape indicates the facility (diamond for
NICER, circle for Swift and square for ground based). The error bars from the
high state are much larger because of the lower cadence observations, but
despite this, one can see that the UVOT lags behave the same in the high X-ray
state compared to the low-state. There is no evidence for an X-ray lag in the
high state.

###  3.3 Continuum lags in an archival high-flux state

Mrk 335 is one of the best studied AGN in the sky, which allows us to compare
the results of our campaign to previous observations. As highlighted in Fig.
1, Swift has monitored Mrk 335 in X-rays and UVW2 at a roughly weekly cadence
since 2008. From 2008–2009, there was a particularly high-cadence campaign of
monitoring every 1–3 days in X-rays and all UVOT filters (Grupe et al. 2012,
and see red shaded region in Fig. 1). This campaign took place at a
particularly high-flux state, when the X-rays were $>10$ times brighter and
the UVW2 $\sim 1.5$ times brighter than during our campaign. While not as
high-cadence as our recent campaign, it does provide an interesting comparison
to our low-flux campaign.

We perform the same ICCF analysis described above on the archival dataset.
Similar to Gallo et al. (2018), we find marginal evidence that the X-rays lead
the UVOIR bands. Fig. 7 shows a comparison of the lag vs. wavelength for the
high-cadence campaign (low-flux) and archival campaigns (high-flux). While the
error bars are much larger in the high-flux state, the UVOIR lags do appear
consistent with the low-flux campaign. The $\sim 10$ day soft lag is not
present in the archival high-state data, and in fact, both soft and hard
X-rays are consistent with expectations from the simple reprocessing picture
where lags scale as $\tau\propto\lambda^{4/3}$ (dashed line, Fig. 7). Komossa
et al. (2020) also report a 1.5 day UV/optical lag (consistent with these
results) after the X-rays began to rise again in late 2020. These results
suggest that the UV/optical lags do not depend strongly on mass accretion
rate.

##  4 Discussion

The inflow of gas through a geometrically thin accretion disk is driven by
local disk instabilities that result in variability of the optical and then UV
emission as the fluctuations propagate inwards on a viscous timescale (tens to
thousands of years at $\sim 1000~{}R_{\mathrm{g}}{}$). Our months-to-year
monitoring campaigns commonly observe inter-day variability where the UV leads
the optical by a few days or less. This rapid variability and short lags can
be explained in a reprocessing scenario where emission from the central
regions irradiates and heats up the accretion disk at larger radii. The X-rays
are the natural choice for the driving light curve as X-rays are known to
originate in the central regions and vary rapidly. However, in several
sources, the observed X-ray/UV correlation is lower than predicted ($R_{\rm
max}<0.75$), and much weaker than the cross-correlations between UVOIR bands
($R_{\rm max}>0.8$).

It has been suggested that the low X-ray/UV correlation means that the X-rays
are not the driving light curve at all (Gardner & Done, 2017; Mahmoud & Done,
2020). Moreover, in some cases, it is clear that absorption along our line of
sight due to obscuring disk winds or the AGN torus can complicate our
inference of the intrinsic continuum and its echoes, as in the recent AGN
STORM 2 campaign of Mrk 817 (Kara et al., 2021b). The origin of the driving
light curve (and its implications for the inferred geometry and energetics of
the corona and inner accretion flow) remains one of the biggest outstanding
problems in accretion disk reverberation mapping.

Despite the campaign taking place in a low X-ray flux state, Mrk 335 shows a
relatively high correlation between X-ray and UV (especially between hard
X-rays and UV). Moreover, the UVOIR lags appear to show the same signatures of
disk reverberation in both high- and low-X-ray flux states. Similar to Mrk
817, in its X-ray low-flux state, Mrk 335 did display broad blueshifted UV
absorption troughs from an outflow at the inner BLR (Longinotti et al., 2019;
Parker et al., 2019) that is likely also responsible for some obscuration in
X-rays (Parker et al., 2019). But our 100-day campaign still reveals rapid
X-ray variability (even in hard X-rays), which indicates that there is still
some intrinsic variability from the corona. Therefore, while obscuration is
likely important in understanding the long-term evolution of the X-ray light
curve (e.g. see Komossa et al. 2020), we still see rapid variability from the
central source that can explain the UVOIR rapid variability and subsequent
reverberation lags.

In the following sub-sections, we discuss two observational puzzles arising
from this campaign that may provide important clues on the nature of the X-ray
corona: (1) How do we explain the late-time multi-wavelength flare at the end
of the campaign, and (2) Why are the observed disk lags exceptionally long in
this source? See Fig. 8 for a schematic to aid the discussion.

###  4.1 On the origin of the broadband flare

High amplitude flares are to be expected in a stochastic noise process, and so
while a flare itself is perhaps not unusual, it does provide us with a unique
opportunity to probe the impulse-response function of the disk in a new way
(i.e. without a cross-correlation analysis). In our case, the flare begins in
the optical/UV bands, but no increase is seen in either NICER or Swift. Then
in the final 2 weeks of the campaign (unfortunately, just as the NICER
background also increased due to optical loading), the NICER and Swift light
curves indicate that the X-rays also rise (with a soft X-ray spectrum similar
to that seen in low-state XMM-Newton spectra, and therefore not likely to be
associated with the background). This apparent X-ray rise occurs $\sim 15$
days after the UV rise (Fig. 6). Swift indicates that the flare in X-rays is
stronger in hard X-rays than in soft, suggesting that the flare is intrinsic
to the corona, and not due to a lower covering fraction or column density of
an obscurer (Fig. 6). Moreover, after our 100-day low-state campaign (once the
source became visible again $\sim 6$ months later), the X-rays had clearly
risen from their deep low-state (Komossa et al., 2020). Here, we explore
potential scenarios to explain the re-emergence of the X-rays after the low-
flux state, and the initial rise in UV/optical.

The initial rise in UVOIR is a much gentler and lower amplitude than that in
X-rays, which means that formally, there can be no linear response function
that can be convolved with the UVOIR light curve to produce the delayed X-ray
light curve. This may corroborate the idea that the stochastic nature of AGN
light curves could lead to coincidental flares in multiple bands, or could
indicate a non-linear response is at play. Such effects could arise, for
instance, from the inflow of mass accretion rate fluctuations that initially
start far out in the accretion disk, propagate inwards, and eventually build
up to the innermost regions. This may trigger rapid magnetic reconnection
events close to the black hole that result in a sudden flash of X-rays.

Such scenarios have been proposed to explain the long timescale ($\sim$year)
X-ray/optical correlation, which deviates from expectations from reverberation
observed on short timescales on days–weeks. For instance, Uttley et al. (2003)
found that the X-ray variability amplitude is smaller than the optical on long
timescales, and Arévalo & Uttley (2006) found the opposite was true on short
timescales. This could be explained if the optical drives the variability on
long timescales (through propagation affects), but reverberation dominates on
short timescales (where X-rays are the driving light curve). Most recently,
Hernández Santisteban et al. (2020) showed that the long timescale variability
shows the optical leading the UV (again, as expected from propagation lags),
but on short timescales, the lags scale as $\tau\propto\lambda^{4/3}$, as
expected for reverberation. A similar model is described in the recent
analysis of Neustadt & Kochanek (2022).

In our case, if we are observing a single mass accretion rate wave at the end
of the campaign, the timescale of $\sim 15$ days is very fast for a viscous
timescale. In fact, it is closer to the dynamical timescale, so perhaps this
flare is a pressure wave or magnetic wave moving at the timescale for the disk
to vibrate in response to some mechanical disturbance.

Alternatively, the late response of the X-rays could also be explained if the
luminosity of the corona increases with increasing spatial extent, as
suggested by some X-ray reverberation studies (e.g., Alston et al. 2020). Even
in Mrk 335, X-ray spectral modeling of the emissivity profile of the iron K
emission line (Wilkins et al., 2015) and other reflection features (Gallo et
al., 2019) suggest that some flares may be due to a vertical expansion of the
corona. If, at early times, the intrinsic X-ray luminosity is low and the
corona is more spatially compact, an equatorial wind could obscure the corona.
Then, in the final days of the campaign, as the corona luminosity increases
and it becomes more spatially extended, this will increase the amount of
irradiation of the disk (causing the upturn in UV emission), and finally we
have a less obscured sight-line to the central source. Such a scenario would
predict that the hard X-ray light curve (1.5–10 keV) would rise before the
soft, since the hard X-rays are less impacted by line-of-sight obscuration,
but unfortunately, this cannot be tested with the current campaign as NICER
did not detect hard X-rays above the background. This interpretation of an
expanding corona during the flare may also explain the large amplitude of the
lags, as discussed in the next section.

Figure 8: Schematic demonstrating potential scenarios to explain (1) the
broadband flare at the end of the campaign (Section 4.1), and (2) the
unusually long lags (Section 4.2). HST observations have indicated the
presence of an obscurer in the low-flux state (Longinotti et al., 2019; Parker
et al., 2019). Our high-cadence campaign took place at the end of this state,
and potentially caught the initial rise out of the low-flux state. The
broadband flare at the end of the campaign starts in UV/optical, followed by a
rapid rise in X-rays. This could be due to the inflow of mass accretion rate
fluctuations that trigger rapid X-ray flaring, or in a reprocessing scenario,
could result in the late-time expansion of the corona, so the disk sees the
rise in X-rays before the observer does. Such an extended corona scenario
might also explain the anomalously long UVOIR lags.

###  4.2 On the very long X-ray/UVOIR lags

In Section 3.1 we found that the shape of the UVOIR lag-wavelength relation
roughly follows the $\tau\propto\lambda^{4/3}$ relation expected for
reverberation lags echoing off a standard thin disk. Fitting this function to
the data, we find a normalization of $\tau_{0}=1.11\pm 0.06$ days in the low
X-ray flux state, and nearly identically shaped UVOIR lags in the high-flux
state. Excluding the flare from the analysis results in a lower normalization
of $\tau_{0}=0.62\pm 0.08$ days.

Following Equation 12 of Fausnaugh et al. (2016), we compare the $\tau_{0}$
normalization of the lag-wavelength relation to expectation for a standard
Shakura & Sunyaev thin disk, where the disk temperature profile scales as
$T\propto R^{-3/4}$ (Cackett et al., 2007). As in Fausnaugh et al. (2016) and
other broadband reverberation campaigns (e.g., Cackett et al. 2020), we assume
a $T$ to $\lambda$ conversion factor of $X=2.49$, radiative efficiency of
$\eta=0.1$, and $\kappa=1$ for equal heating of the disk by X-rays and viscous
affects. With these assumptions in place, the normalization of the lags is a
function of black hole mass and the bolometric luminosity. We assume a black
hole mass of $(2.6\pm 0.8)\times 10^{7}M_{\odot}$, based on previous broad
line region reverberation mapping campaigns of Mrk 335 (Grier et al.,
2012)333An important caveat here is that the optical reverberation lags, from
which this mass was derived, were measured with respect to the 5100 Å
continuum, assuming it all originates in the accretion disk. If there there is
a contribution from the diffuse continuum emission from the BLR Korista & Goad
(2001) within this band, then the inferred mass would be larger.. For
$L/L_{\mathrm{Edd}}=0.07$ (Tripathi et al., 2020), we anticipate a lag-
wavelength normalization of $\tau_{0}=0.1$ days, 11 times shorter than our
measured $\tau_{0}$ of 1.1 days (for the entire campaign, including flare).
Excluding the flare at the end of the campaign, leads to a lower $\tau_{0}$ of
0.6 days, bringing the discrepancy between observation and prediction to a
factor of 6. Even if we make the rather extreme and unlikely assumption that
Mrk 335 is actually Eddington-limited ($L/L_{\mathrm{Edd}}=1$) despite its
low-flux state, we still predict a lag normalization that is $\sim 2.4-4.3$
times smaller than what is observed. It is not unusual to find UV/optical lags
that are ‘too long’ (e.g. Fausnaugh et al. 2016; Cackett et al. 2018; Edelson
et al. 2019), but usually the measured lags are $\sim 3$ times longer than
expected. This is the largest discrepancy with standard disk theory to date.
Perhaps the fact that removing the broadband flare from the analysis puts our
observed lags more in line with previous AGN suggests that the flare is
dominated by processes other than disk reverberation.

One proposed solution to the ‘too-long-lag’ problem is that the measured lags
are not simply due to light travel times from the corona to the accretion
disk, but also there is a contribution from diffuse continuum emission (DCE)
from the BLR, due to free-free and free-bound hydrogen transitions (Korista &
Goad, 2001, 2019). The light travel time from the inner regions out to the BLR
is much longer, and therefore even a small contribution of DCE in the
UV/optical emission will produce measured lags that are longer than expected
from just a pure accretion disk. In addition to DCE contributing to all
UV/optical continuum bands, Korista & Goad (2001) predict an excess lag at the
$u$ (which contains the Balmer jump), and the $r$ band (which contains the
H$\alpha$ line). Indeed, Cackett et al. (2018), using cadenced spectroscopic
observations, showed that in NGC 4593 this $u$ band excess was, in fact, a
broad excess leading up to the Balmer jump. Moreover, recent timescale-
resolved analysis showed that by removing the long-timescale variability from
the lag analysis, the $u$ band excess disappeared, supportive of the idea that
the $u$ band has a large contribution from the DCE much further (and therefore
more slowly varying) than the disk reverberation lags (Cackett et al., 2022).

Here, in Mrk 335, if the DCE is to remedy this extreme ‘too-long-lag’ problem,
then this would imply that there should be a larger than usual contribution
from the BLR in the UV/optical lags, and therefore, also a larger excess in
bands where the DCE contributes. In a systematic analysis of four AGN with
intensive Swift monitoring campaigns, Edelson et al. (2019) found that the $u$
band exceeds the lag expected by the $\tau\propto\lambda^{4/3}$ relation by a
factor of 2.2 on average. In Mrk 335, we also see an excess of the $u$ and $r$
bands, but both bands are only 30% greater than expected. At face-value this
appears to present a challenge for the DCE model, but it is important to
recognize that at the redshift of Mrk 335, in addition to the $u$ band
containing the Balmer jump, several other bands also contain contributions
from the BLR, namely: the $g$ band is centered on He II and also contains
$H\beta$, $r$ band contains He I 5876 and $H\alpha$ and $z$ contains the
Paschen jump. Therefore, because the DCE component may contribute to the lags
in several bands, it could reduce the contrast between the U band excess lags
and those lags at longer wavelengths. Detailed photoionization modeling and
timescale-resolved analysis will help in isolating the contributions from the
disk, the DCE and other variability processes.

Alternatively, the long lags could be attributed to the primary irradiating
source being further from the disk than initially expected. If the corona is
extended out to $\sim 100$$R_{\mathrm{g}}$, the X-ray source will
preferentially irradiate larger radii in the disk, making the response
functions wider, and thus the UV/optical time lags longer (see Eq. 1 of
Kammoun et al. 2021 for more details). Recently, these authors modeled the
X-ray/UVOIR lags of several sources and Panagiotou et al. (2022) modeled both
the time lags and power spectra in NGC 5548 with general relativistic ray
tracing simulations (Dovčiak et al., 2022), and constrained the height of the
corona to be somewhere between $\sim 7-70$ $R_{\mathrm{g}}$ for previously
studied AGN. This accounts for the factor of 2–3 longer lags than expected
(where the irradiating source is assumed to be coplanar with the disk). Mrk
335 shows lags that are 6–11 times the expected amplitude, and so may indicate
a corona that is even more extended than other AGN in the sample.
Interestingly, of all the AGN with intensive X-ray/UVOIR monitoring campaigns
thus far, Mrk 335 has the clearest indication of a relativistically broadened
iron line in the X-ray band (e.g. Parker et al. 2014; Wilkins et al. 2015) and
short X-ray reverberation lags (Kara et al., 2013b), both of which require a
corona that is close to the black hole ($\sim 10$$R_{\mathrm{g}}$). Therefore,
to reconcile such observations, the corona needs to be vertically extended,
with a base close to the black hole.

These long X-ray/UVOIR lags may be further evidence of a vertically extended
corona in Mrk 335, as suggested by earlier X-ray spectral studies (Wilkins et
al., 2015; Gallo et al., 2019). In this picture, the fact that the $\tau_{0}$
normalization is smaller if we exclude the flare from the analysis, would
suggest that the corona is more compact in the early part of the campaign
(when the X-ray flux is lowest), and increases in spatial extent during the
flare. The vertically extended corona may represent the base of the bi-polar
parsec-scale jet recently spatially resolved with Very Long Baseline Array
observations of Mrk 335 (Yao et al., 2021).

##  5 Conclusions

To summarize, our major findings of the 100-day Swift/NICER/ground based
reverberation mapping campaign of Mrk 335 are:

  * •

Despite the campaign occurring in an unprecedented low X-ray state, the UVOIR
lags appear unaffected, and the wavelength dependence of the lags is
consistent with expectations of reverberation delays off an accretion disk
(Fig. 4).

  * •

Archival observations taken in a high-flux state show very similar UVOIR lags
as those found in the low X-ray state (Fig. 7).

  * •

Given its black hole mass and accretion rate, the amplitudes of the UVOIR lags
(in both low and high state) are 6–11 times larger than expected from a
standard Shakura-Sunyaev disk (Fausnaugh et al., 2016).

  * •

The $u$ and $r$ band excess lags (commonly attributed to contamination from
the BLR; Korista & Goad 2001) are present, but are less prominent than
typically seen in other AGN (e.g. Edelson et al. 2019; Fig. 4).

  * •

The X-rays show little variability, and do not correlate highly with the UVOIR
bands. At the end of the campaign, the UVOIR bands reach their highest level,
and though lower significance (due to limited singal-to-noise and lower
cadence), the X-rays also appear to rise (Fig. 3). This X-ray rise occurs
after the UVOIR rise, contrary to the standard reprocessing picture (Fig. 5).

  * •

The overall normalization of the X-ray spectrum rises at the end of the
campaign (Fig. 6), which suggests that the flare is not simply due to lower
absorption effects, but rather, is an intrinsic increase in the luminosity of
the corona.

  * •

AGN are known to vary as a stochastic red-noise variability process, but if we
interpret the soft X-ray delay physically, it could indicate either mass
accretion rate fluctuations propagating inwards in the flow on timescales
faster than the local viscous time, and/or that the spatial extent of the
corona increases at the end of the campaign. The latter interpretation of an
extended corona may also explain the unusually long UVOIR lags (Fig. 8).

## Acknowledgements

EK thanks the XMM-Newton Science Operations Center Coordinators, Jan-Uwe Ness
and Lucia Ballo, and NuSTAR Science Operations Manager, Karl Forster, for
their patience in organizing the XMM-Newton and NuSTAR observations, as we
waited for the X-ray flux to increase. EK thanks Daniel Proga for interesting
discussions on the X-ray/UV connection, and Rick Edelson for assistance in
organizing the campaign. This work made use of data supplied by the UK Swift
Science Data Centre at the University of Leicester.

This work makes use of observations from the Las Cumbres Observatory global
telescope network. The Liverpool Telescope is operated on the island of La
Palma by Liverpool John Moores University in the Spanish Observatorio del
Roque de los Muchachos of the Instituto de Astrofisica de Canarias with
financial support from the UK Science and Technology Facilities Council.

Some of the data used in this paper were acquired with the RATIR instrument,
funded by the University of California and NASA Goddard Space Flight Center,
and the 1.5-meter Harold L. Johnson telescope at the Observatorio Astronómico
Nacional on the Sierra de San Pedro Mártir, operated and maintained by the
Observatorio Astronómico Nacional and the Instituto de Astronomía of the
Universidad Nacional Autónoma de México. Operations are partially funded by
the Universidad Nacional Autónoma de México (DGAPA/PAPIIT IG100414, IT102715,
AG100317, IN109418, IG100820, and IN105921). We acknowledge the contribution
of Leonid Georgiev and Neil Gehrels to the development of RATIR.

EK acknowledges support from NASA grants 80NSSC20K0470 and 80NSSC20K0372, and
is supported by the Sagol Weizmann-MIT Bridge Program. Research at UC Irvine
was supported by NSF grant AST-1907290. EMC gratefully acknowledges support
from the NSF through grant AST-1909199. YRL acknowledges financial support
from the NSFC through grant Nos. 11922304 and 12273041 and from the Youth
Innovation Promotion Association CAS. PD acknowledges support from NSFC grant
12022301 and 11991051. CH acknowledges support from from NSFC grants 12122305
and 11991054. CSR thanks the UK Science and Technology Facilities Council
(STFC) for support under the Consolidated Grant ST/S000623/1, as well as the
European Research Council (ERC) for support under the European Union’s Horizon
2020 research and innovation programme (grant 834203). TL acknowledges support
from the Zuckerman Postdoctoral Scholarship Program and by an appointment to
the NASA Postdoctoral Program at NASA Goddard Space Flight Center,
administered by Oak Ridge Associated Universities under contract with NASA.

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