Connection between the Accretion Disk and Jet in the Radio Galaxy 3C 111

Abstract

We present the results of extensive multi-frequency monitoring of the radio
galaxy 3C 111 between 2004 and 2010 at X-ray (2.4--10 keV), optical (R band),
and radio (14.5, 37, and 230 GHz) wave bands, as well as multi-epoch imaging
with the Very Long Baseline Array (VLBA) at 43 GHz. Over the six years of
observation, significant dips in the X-ray light curve are followed by
ejections of bright superluminal knots in the VLBA images. This shows a clear
connection between the radiative state near the black hole, where the X-rays
are produced, and events in the jet. The X-ray continuum flux and Fe line
intensity are strongly correlated, with a time lag shorter than 90 days and
consistent with zero. This implies that the Fe line is generated within 90
light-days of the source of the X-ray continuum. The power spectral density
function of X-ray variations contains a break, with steeper slope at shorter
timescales. The break timescale of 13 (+12,-6) days is commensurate with
scaling according to the mass of the central black hole based on observations
of Seyfert galaxies and black hole X-ray binaries (BHXRBs). The data are
consistent with the standard paradigm, in which the X-rays are predominantly
produced by inverse Compton scattering of thermal optical/UV seed photons from
the accretion disk by a distribution of hot electrons --- the corona ---
situated near the disk. Most of the optical emission is generated in the
accretion disk due to reprocessing of the X-ray emission. The relationships
that we have uncovered between the accretion disk and the jet in 3C 111, as
well as in the FR I radio galaxy 3C 120 in a previous paper, support the
paradigm that active galactic nuclei and Galactic BHXRBs are fundamentally
similar, with characteristic time and size scales proportional to the mass of
the central black hole

Full text

Page 1

arXiv:1104.0663v1 [astro-ph.HE] 4 Apr 2011
Draft version April 5, 2011
Preprint typeset using LATEX style emulateapj v. 8/13/10
CONNECTION BETWEEN THE ACCRETION DISK AND JET IN THE RADIO GALAXY 3C 111
Ritaban Chatterjee1, Alan P. Marscher2, Svetlana G. Jorstad2,3, Alex Markowitz4, Elizabeth Rivers4,
Richard E. Rothschild4, Ian M. McHardy5, Margo F. Aller6, Hugh D. Aller6, Anne L¨ ahteenm¨ aki7, Merja
Tornikoski7, Brandon Harrison2, Iv´ an Agudo2,8, Jos´ e L. G´ omez8, Brian W. Taylor2,9, Mark Gurwell10
Draft version April 5, 2011
ABSTRACT
We present the results of extensive multi-frequency monitoring of the radio galaxy 3C 111 between
2004 and 2010 at X-ray (2.4–10 keV), optical (R band), and radio (14.5, 37, and 230 GHz) wave
bands, as well as multi-epoch imaging with the Very Long Baseline Array (VLBA) at 43 GHz.
Over the six years of observation, significant dips in the X-ray light curve are followed by ejections
of bright superluminal knots in the VLBA images.
radiative state near the black hole, where the X-rays are produced, and events in the jet. The X-ray
continuum flux and Fe line intensity are strongly correlated, with a time lag shorter than 90 days
and consistent with zero. This implies that the Fe line is generated within 90 light-days of the source
of the X-ray continuum. The power spectral density function of X-ray variations contains a break,
with steeper slope at shorter timescales. The break timescale of 13+12
scaling according to the mass of the central black hole based on observations of Seyfert galaxies and
black hole X-ray binaries (BHXRBs). The data are consistent with the standard paradigm, in which
the X-rays are predominantly produced by inverse Compton scattering of thermal optical/UV seed
photons from the accretion disk by a distribution of hot electrons — the corona — situated near the
disk. Most of the optical emission is generated in the accretion disk due to reprocessing of the X-ray
emission. The relationships that we have uncovered between the accretion disk and the jet in 3C 111,
as well as in the FR I radio galaxy 3C 120 in a previous paper, support the paradigm that active
galactic nuclei and Galactic BHXRBs are fundamentally similar, with characteristic time and size
scales proportional to the mass of the central black hole.
This shows a clear connection between the
−6 days is commensurate with
Subject headings: galaxies: active — X-rays: galaxies — X-rays: binaries — Galaxies: individual (3C
111) — quasars: general — Black hole physics
1. INTRODUCTION
In many cosmic systems containing jets, e.g., ac-
tive galactic nuclei (AGNs), stellar mass black hole X-
ray binaries (BHXRBs), and young stellar objects, the
presence of an accretion disk is inferred from observa-
tions.One of the prominent theories of jet produc-
tion asserts that the jet plasma is propelled by mag-
netic field lines that thread the accretion disk (and
perhaps, in AGNs and BHXRBs, the black hole) and
1Department of Astronomy, Yale University, PO Box 208101,
New Haven, CT 06520-8101; ritaban.chatterjee@yale.edu
2Institute for Astrophysical Research, Boston University, 725
Commonwealth Avenue, Boston, MA 02215
3Astronomical Institute of St. Petersburg State University,
Universitetskij Pr.28, Petrodvorets, 198504 St.
Russia
4Center for Astrophysics and Space Sciences, University of
California, San Diego, M.C. 0424, La Jolla, CA, 92093-0424,
USA
5Department of Physics and Astronomy,
Southampton, Southampton, SO17 1BJ, United Kingdom
6AstronomyDepartment,
Dennison, 501 East University Street, Ann Arbor, Michigan
48109-1042
7Aalto University,Mets¨ ahovi
Mets¨ ahovintie 114, FIN-02540, Kylm¨ al¨ a, Finland
8Instituto de Astrofisica de Andalucia, CSIC, Apartado 3004,
18080 Granada, Spain
9Lowell Observatory, 1400 West Mars Hill Road, Flagstaff,
AZ., USA
10Harvard-Smithsonian Center for Astrophysics, MS 42, 60
Garden Street, Cambridge, MA 02138, USA
Petersburg,
University of
Universityof Michigan,830
Radio Observatory,
are twisted by differential rotation (Blandford & Payne
1982; Lovelace, Berk & Contopoulos 1991; Begelman
1995; Meier, Koide & Uchida 2001; Vlahakis & K¨ onigl
2004). This suggests that any relations observed between
events in the accretion disk and those in the jet can be
used to characterize the disk-jet connection and there-
fore to constrain models of jet formation. In BHXRBs,
the connection between accretion state and events in
the jet is well-established. In these objects, transitions
to high-soft X-ray states are associated with the emer-
gence of very bright features that proceed to propa-
gate down the radio jet (Fender, Belloni & Gallo 2004;
Fender, Homan & Belloni 2009).
Observations related to the disk-jet connection in
AGNs are complicated, since a single AGN usually does
not show the entire range of properties that we wish
to analyze. For example, in Seyfert galaxies, most of
the observed X-ray (and optical) emission is generated
in the accretion disk-corona region, but their radio jets
tend to be weak and non-relativistic (e.g., Ulvestad et al.
1999). On the other hand, in radio-loud AGNs with
strong, highly variable nonthermal radiation (blazars),
the Doppler beamed emission from the jet at most wave-
lengths masks the thermal emission from the accretion
disk and its nearby regions. The radio galaxies 3C 120
and 3C 111 provide an excellent opportunity to study
the relationship between events in the accretion disk and
those in the jet. At optical and X-ray frequencies, their
properties are similar to Seyfert galaxies, e.g., the pres-

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2
ence of strong broad emission lines in the optical band
(Sargent 1977), and an iron emission line in the X-ray
spectrum (Lewis et al. 2005), while at centimeter and
millimeter wavelengths their emission is dominated by
a bright relativistic jet. Nevertheless, the source of the
optical continuum emission in radio galaxies is not well-
known. For example, it may be blackbody emission from
the accretion disk (Malkan 1983) or synchrotron radia-
tion from the jet.
An accretion disk-jet connection in AGNs has been
suggested by Marscher et al. (2002). During ∼3 yr of
monitoring of the radio galaxy 3C 120 (1997 to 2000),
each of four dips in the X-ray flux, accompanied by
spectral hardening, preceded the appearance of a bright
knot moving down the radio jet at a superluminal ap-
parent speed. Using similar, but more extensive, multi-
frequency monitoring observations of this object between
2002 and 2007 at X-ray (2.4–10 keV) and radio (37
GHz) wave bands as well as VLBA images at 43 GHz,
Chatterjee et al. (2009) established an unambiguous con-
nection between events in the accretion disk and jet.
They showed that, during this interval, the X-ray and
37 GHz variations are anti-correlated, with the X-ray
variations leading those in the radio by ∼120 days. Fur-
thermore, nearly every X-ray dip is followed by the ejec-
tion of a new knot in the VLBA images. These findings
imply that a decrease in the X-ray production is linked
with increased speed in the jet flow, causing a shock wave
to form and propagate downstream, appearing as a knot
of bright emission in the jet. In 3C 120, the presence
of an X-ray Fe emission line implies that most of the
X-rays are produced in the accretion disk region. There-
fore, the above pattern is strong evidence for a disk-jet
connection.
In this work, we present the results of extensive multi-
frequency monitoring of 3C 111 between 2004 and 2009
at X-ray energies (2.4–10 keV), optical R band, and ra-
dio frequencies 14.5, 37, and 230 GHz, as well as imag-
ing with the Very Long Baseline Array (VLBA) at 43
GHz. We use these data to investigate the presence of a
disk-jet connection similar to that in 3C 120. 3C 111 is
a relatively nearby (z = 0.049) broad-line radio galaxy
(BLRG) (Sargent 1977; Lewis et al. 2005).
sified as a Fanaroff-Riley class II (FR II) radio galaxy
(Fanaroff & Riley 1974) containing two radio lobes with
hot spots and a single-sided jet (Linfield & Perley 1984).
At radio frequencies, 3C 111 has blazar-like behav-
ior, although the jet lies at an angle ∼18◦to our
line of sight (Jorstad et al. 2005), significantly greater
than is the case for typical blazars.
is too faint to detect, presumably because of Doppler
de-boosting.3C 111 exhibits the brightest compact
radio core at cm/mm wavelengths of all FR II radio
galaxies and a blazar-like spectral energy distribution
(Kadler et al. 2008; Sguera et al. 2005). It was one of
the first radio galaxies in which superluminal motion was
detected (G¨ otz et al. 1987; Preuss, Alef, & Kellermann
1987); knots are ejected 1-2 times per year with typi-
cal apparent speeds of 3-5c (Jorstad et al. 2005). Re-
cently, Hartman, Kadler & Tueller (2008) showed that
part of the γ-ray emission from the EGRET source
3EG J0416+3650 is associated with 3C 111, and inte-
gration over the first 11 months of observations with
the Large Area Telescope of the Fermi Space Tele-
It is clas-
The counter-jet
scope detected 3C 111 at a rather low flux level, 1.5 ±
0.5 × 10−9phot cm−2s−1at energies exceeding 1 GeV
(Abdo et al. 2010). At optical and X-ray frequencies,
3C 111 possesses properties similar to Seyfert galaxies
and BHXRBs. It has a prominent iron emission line
at a rest energy of 6.4 keV (e.g., Reynolds et al. 1998;
Eracleous, Sambruna & Mushotzsky 2000). This implies
that most of the X-rays are produced in the immediate
environs of the accretion disk: the corona, a hot wind, or
the base of the jet (Haardt, Maraschi & Ghisellini 1994;
Markoff, Nowak, & Wilms 2005; Nayakshin 2000).
Power spectral density (PSD) analysis is a common
technique to characterize time variability, which in turn
is a powerful diagnostic of the geometry and physics of
the accretion disk, corona, and jet. The PSD corresponds
to the power in the variability of emission as a function
of timescale. Marshall et al. (2009) and Chatterjee et al.
(2009) found that the X-ray PSD of 3C 120 can be fit
by a piece-wise power law, with a slope that steepens
above a break frequency.This property of 3C 120 is
similar to Seyfert galaxies and BHXRBs, although in
many cases the PSDs of the latter have more than one
break, as well as sharp peaks representing quasi-periodic
oscillations.The PSD break frequency in BHXRBs
and Seyfert galaxies scales inversely with the mass of
the black hole (Edelson & Nandra 1999; Nowak et al.
1999; Pounds et al. 2001; Uttley, McHardy & Papadakis
2002; Markowitz et al. 2003; McHardy et al. 2004).
McHardy et al. (2006) showed that the break frequency
and BH mass are inversely related over a range of BH
masses from 10 to 108M⊙, and that, for a given black
hole mass, the break frequency also increases with higher
accretion rate ( ˙ m).
Here, we use our data set to verify that the X-ray
PSD of 3C 111 also has a break. Measuring the PSD
of 3C111 gives us an opportunity to test whether an-
other radio-loud AGN (in addition to 3C 120) has a
broadband X-ray PSD similar to those of other Seyfert
galaxies and BHXRBs. We can investigate whether the
break timescale (TB) is consistent with the empirical re-
lation between TB, black hole mass (MBH), and bolomet-
ric luminosity (Lbol) proposed by McHardy et al. (2006),
based on a sample of mainly radio-quiet Seyfert galaxies.
We analyze the X-ray and radio light curves as well as
the sequence of VLBA images to test whether the X-ray
dips and ejection of new radio knots in the pc scale jet
are temporally related, as is the case in 3C 120. In order
to investigate the source of optical emission in 3C 111,
we cross-correlate the optical flux variations with those
at X-ray energies. Uneven sampling, as invariably oc-
curs, can cause the correlation coefficients to be artifi-
cially low. In addition, the time lags can vary across
the years owing to physical changes in the source. In
light of these issues, we estimate the significance of the
derived correlation coefficients by repeating the analy-
sis with simulated light curves, based on the underlying
PSD. We also follow the variation in the degree of po-
larization of the optical emission in order to discriminate
between nonthermal and thermal emission.
In §2 we present the observations and data reduction
procedures, while in §3 we describe the correlated vari-
ations in the X-ray continuum and Fe Kα emission line.
In §4 we carry out the power spectral analysis and dis-
cuss its results and implications. In §5 we investigate

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3
Table 1
Parameters of the Light Curves.
Data set StartEndT(days)a
∆T (days)b
Npointsc
Monitor
Medium
Longlook
Monitor
Medium
Monitor
Monitor
Monitor
2004 March
2006 November
2009 February 16
2004 November
2005 July
2004 February
2005 January
2004 January
2010 April
2007 January
2009 February 17
2010 August
2006 January
2010 February
2008 December
2010 April
2246.0
56.0
1.2
2080.0
160.0
2216.0
1458.0
2288.0
15.0
0.25
0.01
15.0
5.0
-
-
-
822
224
120
336
37
398
98
161
X-ray
Optical
14.5 GHz
37 GHz
230 GHz
aTotal length of light curves.
bBin size.
cNumber of data points in the unbinned light curve.
1
2
3
4
5
6
7
8
2005 2006 2007 2008 2009 2010
Flux (10-11 erg cm-2 s-1)
Monitor
2
3
4
5
6
2006.9 2006.94 2006.98 2007.02
Flux (10-11 erg cm-2 s-1)
Medium
3.5
3.7
3.9
4.1
4.3
4.5
2009.138 2009.139
YEAR
2009.140
counts sec-1
Longlook
Figure 1.
rates. The dotted and dashed vertical lines at the top panel denote
the intervals shown in the middle and bottom panel, respectively.
X-ray light curves of 3C 111 with different sampling
the relation between the X-ray dips and ejections of su-
perluminal radio knots, as well as the X-ray/radio flux
correlation. In §6 we cross-correlate the X-ray and opti-
cal variations and discuss the possible sources of optical
emission. In §7 we compare the properties of 3C 111 with
those of the radio galaxy 3C 120, while §8 contains the
summary and conclusions.
2. OBSERVATIONS AND DATA ANALYSIS
Table 1 summarizes the intervals of monitoring at dif-
ferent frequencies for each of the three wave bands in
our data set. We term the entire light curve “monitor
data”; shorter segments of more intense monitoring are
described below.
2.1. X-Ray Monitoring
The X-ray light curves are based on observations of
3C 111 with the PCA detector of the Rossi X-ray Tim-
ing Explorer (RXTE) from 2004 March to 2010 April,
with typical exposure times of 1-2 ks.
posure, we used routines from the X-ray data analy-
sis software FTOOLS and the program XSPEC ver-
sion 11.6 to calculate and subtract the standard X-
ray background model for the faint sources from the
data and to fit the X-ray spectrum from 2.4 to 10 keV
as a power law with low-energy photoelectric absorp-
tion by intervening gas in our Galaxy.
ter, we used a hydrogen column density of 9.0 × 1021
atoms cm−2. This value of the absorbing column
was determined by Sambruna, Eracleous & Mushotzky
(1999) by analyzing the X-ray spectrum of 3C 111
with data from the Advanced Satellite for Cosmol-
ogy and Astrophysics (ASCA). Using observations from
XMM-Newton, Lewis et al. (2005) have also obtained
a value close to this. It should be noted that a gi-
ant molecular cloud is present in the foreground of 3C
111 (Marscher, Moore & Bania 1993; Moore & Marscher
1995) and it contributes significantly to the optical to X-
ray extinction of emission received from 3C 111.
The sampling of the X-ray flux varied. Normally, ob-
servations were made 2-3 times per week except during
8-week intervals each year when the radio galaxy is too
close to the Sun’s celestial position to observe safely. In
order to sample shorter-term variations, between 2006
November and 2007 January we obtained, on average,
four measurements per day for almost two months. We
refer to these observations as the “medium” data. Our
monitoring program also contains an interval from 2008
September to 2008 December when we obtained roughly
one data point per day. In order to sample variations
on as short timescales as possible, we observed 3C 111
with the European Photon Imaging Camera (EPIC) on
board XMM-Newton continuously for about 130 ks on
2009 February 16-17. The EPIC-pn and EPIC-MOS
data were obtained in the Small Window and Partial
Window mode, respectively, using the thin filter. The
data were processed with the the Science Analysis Soft-
ware version 8.0.0. We filtered the pn data to include
only single and double-pixel events (i.e., PATTERN ≤
4). A pn light curve was extracted in the 2.4–10 keV
energy band, similar to that of our RXTE data, and was
For each ex-
For the lat-

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4
Figure 2. Light curves for 2.4–10 keV continuum flux F2−10 (in
erg cm−2s−1), photon index ΓX(of the continuum), intensity of
the Fe line IFeKα (in ph cm−2s−1), and the Fe line equivalent
width EQW (in eV) derived from time-resolved spectral fits to
the RXTE-PCA monitoring data. The dashed lines are the mean
values.
background-subtracted and binned to 1000 s time inter-
vals. In general, pn data are more suitable for timing
analysis and the average count rate in the pn light curve
was higher than that in the MOS light curves. Hence, we
use the pn light curve as the “longlook” data. Figure 1
presents these three data sets. The X-ray data are given
in Tables 2 and 3 of the electronic version.
We performed time-resolved spectroscopy on the
RXTE monitoring data in order to explore the vari-
ability of the Fe Kα emission line.
indeed respond to X-ray continuum variations, then
one can place constraints on the distance between the
X-ray continuum source and the bulk of the line-
emitting gas.The analysis closely followed that em-
ployed by previous studies (e.g., Vaughan & Edelson
2001; Markowitz, Edelson & Vaughan 2003).
spectra were constructed by combining the data from
the individual ∼1 ks observations within the defined
time bins.A time-averaged model was applied to all
binned spectra. The first five time bins were defined to
match the start/stop times of the RXTE campaigns in
1997 March, 1999 January–February, 2001 March, 2001
September and 2003 September. For the sustained long-
term monitoring that started on 2004 March 1, we con-
sidered all data acquired up to 2010 February 14. Bin
sizes were chosen to optimize the trade-off between min-
imizing the uncertainties in the Fe line flux and maxi-
mizing the number of bins. This yielded 31 bins each
of roughly 60 days in duration.
If the line does
Summed
The response of the
PCA and the conversion factor between count rate per
PCU and incident flux, evolve slowly. In the 2–10 keV
band, 1.0 ct/s/PCU corresponds to roughly 1.12×10−11,
1.09×10−11, and 1.04×10−11erg cm−2s−1during 1997,
2003, and 2008, respectively. Consequently, regarding
long-term PCA light curves, fluxes obtained from spec-
tral fitting are more valuable than count rates. We have
taken this long-term trend in response into account in
our analysis. The number of PCUs used during the anal-
ysis of data from various epochs are as follows: PCU 0,
1 and 2 for 1997 March, PCU 0 and 2 for 1999 Jan–Feb,
since PCU 1 had started to have thermal breakdown in
1998, and PCU 2 only for all data from 2001 to 2010,
since PCU 0 lost its propane layer in 2000. The number
of counts in a typical binned spectrum ranged from ∼105
to 106.
We summed the PCA spectra from the individual ob-
servations within each time interval to create the binned
spectra.PCA response matrices were generated for
each individual observation using pcarmf v.11.7 and
summed, weighted by exposure time, to yield a response
for each binned spectrum. We did not include HEXTE
data in the time-resolved fits, as those data yielded no
additional model constraints compared to the PCA alone
on these time scales given the flux level of 3C 111. Spec-
tra were fit over the 3–25 keV energy range in XSPEC
v.12.5.1k using a model of the same form as the best-fit
to the long-term time-averaged spectrum determined by
Rivers, Markowitz & Rothschild (2011). Those authors
performed joint RXTE PCA + HEXTE spectral fitting
over the 3–100 keV energy band to a summed spectrum
comprising all RXTE data on 3C 111 observed from 1997
March until 2008 July. The model we use thus consists of
a power law with a photon index ΓXallowed to vary after
being initially set at 1.67, plus a Gaussian component to
model the Fe Kα emission line, with photo-electric ab-
sorption in our Galaxy similar to that given above. The
intensity of the Gaussian component IFeKαwas allowed
to vary; the energy centroid and width σ were kept fixed
at 6.19 keV (rest-frame) and 0.72 keV, respectively, since
there was no significant evidence to allow these param-
eters to vary from these best-fit time-averaged values.
Rivers, Markowitz & Rothschild (2011) found no signif-
icant evidence to warrant inclusion of a Compton hump
in the model. Background level corrections were applied
using recorn within XSPEC.
Figure 2 shows the resulting light curves for the 2–10
keV continuum flux F2−10, ΓX, IFeKα, and the Fe line
equivalent width EQW. These data are given in Table 4
of the electronic version. Errors on IFeKα, ΓX, and EQW
were derived using the point-to-point variance11. We de-
termined errors on values of F2−10within a time bin from
the 2–10 keV continuum light curve, using the mean flux
error on the ∼1 ks exposures in that time bin.
2.2. Optical Monitoring
We monitored 3C 111 in the optical R band over a
portion of the time span of the X-ray observations. The
majority of the measurements in R band are from the
2 m Liverpool Telescope (LT) at La Palma, Canary Is-
11
See
§3.3ofVaughan & Edelson(2001)or
§3.3of
Markowitz et al. (2003) for further details and the definition of
the point-to-point variance.

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5
Table 2
X-ray (2.4-10 KeV; RXTE-PCA) light curve of 3C 111 from 2004 to 2010 (first 5 rows).
RJDa
exp (s)fluxb
err
αc
err counts/s/PCUerr
3065.9070
3068.8816
3072.8645
3075.8169
3080.0244
...
2080.
752.
1952.
2032.
1936.
...
2.565E-11
1.975E-11
1.503E-11
1.458E-11
1.292E-11
...
5.683E-13
8.709E-13
5.269E-13
5.173E-13
5.291E-13
...
−0.691
−0.530
−0.672
−0.657
−0.394
...
0.062
0.123
0.096
0.100
0.112
...
2.613E+00
2.035E+00
1.544E+00
1.480E+00
1.329E+00
...
5.307E-02
8.308E-02
4.893E-02
4.770E-02
4.920E-02
...
aRelative Julian Date: JD−2450000.
bUnit: ergs cm−2s−1.
cα: Energy Index.
Table 3
X-Ray Longlook light curve
of 3C 111 from
XMM-Newton in 2.4–10
keV band on 2009 Feb
16–17 (first 5 rows).
RJDa
Counts/serror
4878.50
4878.51
4878.52
4878.53
4878.55
...
4.26
4.06
3.91
3.98
3.98
...
0.12
0.11
0.12
0.13
0.13
...
a
Relative
JD−2450000.
JulianDate:
lands, Spain, supplemented by observations at the 1.8 m
Perkins Telescope of Lowell Observatory, Flagstaff, Ari-
zona. We used star A (Figure 3) located ∼50′′west of
3C 111 as a comparison star, for which we determined an
R-band magnitude R = 14.93±0.05 based on differential
photometry with standard stars from other fields of view.
Data acquisition and analysis procedures were identical
to those described by Chatterjee et al. (2009). We also
monitored the R-band linear polarization of 3C 111 from
2006 to 2009 with the PRISM camera on the Perkins
telescope at Lowell Observatory and with the 2.2 m tele-
scope at Calar Alto Observatory, Spain12. Interstellar
polarization (ISP) is significant in the field of 3C 111.
We used the polarization parameters of the comparison
star, presumed to be intrinsically unpolarized, to correct
the polarization of 3C 111 for ISP (see also Jorstad et al.
2007). We corrected the degree of linear polarization for
statistical bias using the method of Wardle & Kronberg
(1974).
2.3. Radio Monitoring
We monitored the 14.5 GHz flux of 3C 111 with the 26
m antenna of the University of Michigan Radio Astron-
omy Observatory. Details of the calibration and analysis
techniques are described in Aller et al. (1985). The flux
scale is set by observations of Cassiopeia A (Baars et al.
1977).We have compiled a 37 GHz light curve with
data from the 13.7 m telescope at Mets¨ ahovi Radio Ob-
servatory, Finland. The flux density scale is based on
observations of DR 21, with 3C 84 and 3C 274 used
as secondary calibrators. A detailed description of the
12
DataacquiredaspartoftheMAPCATprogram:
http://www.iaa.es/∼iagudo/research/MAPCAT
3C111
A
Figure 3.
star with R = 14.93 ± 0.05, located ∼50′′west of 3C 111, used
to calculate the magnitude and interstellar polarization correction
(p = 3.6 ± 0.2%, χ = 123◦± 2◦).
Finding chart for 3C 111. Star A is the comparison
data reduction and analysis is given in Ter¨ asranta et al.
(1998). We have also compiled a 230 GHz light curve of
3C 111 over a portion of the time span of the X-ray obser-
vations with calibration data from the the Submillimeter
Array (SMA; see Gurwell et al. 2007, for details).
Figure 4 presents the X-ray, optical, and radio light
curves.The variation of the total R-band flux, po-
larization percentage, and electric vector position angle
(EVPA) are shown in Fig. 5. These data are given in
Tables 5, 6, 7, 8, and 9 of the electronic version.
2.4. VLBA Imaging
Starting in 2004 May, we observed 3C 111 with the
Very Long Baseline Array (VLBA) at 43 GHz at roughly
monthly intervals, with some gaps of 2-4 months. The
sequence of images (Figure 6) from these data provide
a dynamic view of the jet at an angular resolution ∼0.1
milliarcseconds (mas) in the direction of the jet, corre-
sponding to 0.094 pc for an adopted Hubble constant of
H0= 70 km s−1Mpc−1. We processed the data in the
same manner as described in Jorstad et al. (2005). We
modeled the brightness distribution at each epoch with
multiple components with circular Gaussian brightness

Page 6

6
Table 4
Variation of 2.4–10 keV continuum flux, intensity of the Fe line,
photon index, and the Fe line equivalent width derived from
time-resolved spectral fits to the RXTE-PCA monitoring data shown
in Figure 2.
Yrfconta
errflineb
errΓc
err EQWd
err
1997.22
1999.05
2001.20
2002.69
2003.67
...
4.26
2.25
7.47
5.00
5.11
...
0.03
0.09
0.07
0.04
0.03
...
6.05
2.12
9.14
7.24
10.13
...
2.39
2.39
2.39
2.39
2.39
...
1.71
1.59
1.77
1.72
1.77
...
0.06
0.06
0.06
0.06
0.06
...
104.68
67.64
90.74
106.76
148.30
...
41.40
76.44
23.76
35.29
35.03
...
a2–10 keV continuum flux F2−10 (10−11erg cm−2s−1).
bIntensity of the Fe line IFeKα(10−5ph cm−2s−1).
cphoton index ΓXof the continuum.
dFe line equivalent width EQW (eV).
Table 5
Optical (R Band) light curve of 3C 111 from 2004 to
2010 (first 5 rows).
RJDa
R MagerrFlux Densityb
err
3325.5154
3325.5171
3325.5210
3325.5247
3325.5266
...
17.033
17.090
17.047
17.055
17.030
...
0.009
0.009
0.009
0.009
0.009
...
0.474
0.450
0.468
0.465
0.475
...
0.004
0.004
0.004
0.004
0.004
...
aRelative Julian Date: JD−2450000.
bUnit: mJy.
Table 6
Radio (14.5 GHz) light curve of 3C
111 from 2004 to 2010 (first 5 rows).
RJDa
Flux Density (Jy) error
3024.5
3042.5
3050.5
3052.5
3064.5
...
2.97
3.06
3.16
3.09
3.02
...
0.10
0.04
0.04
0.04
0.03
...
aRelative Julian Date: JD−2450000.
Table 7
Radio (37 GHz) light curve of 3C
111 from 2005 to 2008 (first 5 rows).
RJDa
Flux Density (Jy)error
3371.22
3372.20
3379.52
3423.03
3447.93
...
4.61
4.35
4.19
4.23
4.17
...
0.25
0.24
0.22
0.23
0.26
...
aRelative Julian Date: JD−2450000.
distributions using the task MODELFIT of the software
package Difmap (Shepherd et al. 1997). This represents
the jet emission downstream of the core, the bright fea-
ture situated at the western end of the jet, by a sequence
Table 8
Radio (230 GHz) light curve of 3C
111 from 2004 to 2010 (first 5 rows).
RJDa
Flux Density (Jy)error
3022.48
3031.60
3266.67
3359.38
3381.64
...
1.26
1.71
2.06
2.49
3.80
...
0.09
0.35
0.13
0.13
0.20
...
aRelative Julian Date: JD−2450000.
Table 9
Variation of the R-band Polarization
Percentage and EVPA of 3C 111 from 2006
to 2010.
RJDa
p (%)b
errorEVPAc
error
3741.74
3796.65
4048.87
4049.98
4076.88
...
3.32
0.60
3.33
3.06
1.49
...
0.60
0.80
0.70
0.40
0.80
...
42.70
97.50
65.80
22.70
26.00
...
5.20
38.30
6.00
3.70
15.40
...
aRelative Julian Date: JD−2450000.
bR-band polarization percentage.
cElectric vector position angle.
of knots (also referred to as “components”), each charac-
terized by its flux density, FWHM diameter, and position
relative to the core. The ejection time T0is the extrapo-
lated time of coincidence of a moving knot with the posi-
tion of the (presumed stationary) core. Figure 7 plots the
distance vs. epoch for all moving components brighter
than 100 mJy within 2.0 mas of the core. We use the po-
sition vs. time data to determine the projected direction
on the sky of the inner jet, as well as the apparent speeds
and ejection times of new superluminal knots. Table 10
lists the values of T0and apparent speeds of new knots
determined by the above procedure. In the top panel of
Figure 4, the arrows represent the times of superluminal
ejections, while the line segments perpendicular to the
arrows show the uncertainties in the values of T0. The
apparent speeds of the components with well-determined
motions are between 2.2 and 6.4c.

Page 7

7
2
3
4
5
6
7
8
Flux (10-11 erg cm-2 s-1)
X-ray (2.4-10 keV)
0.3
0.4
0.5
0.6
Flux Density (mJy)
Optical (R Band)
1
3
5
7
9
11
13
2005 2006 2007 2008 2009 2010
Flux Density (Jy)
Year
14.5 GHz
37 GHz
230 GHz
Figure 4.
arrows indicate the times of superluminal ejections and the line segments perpendicular to the arrows represent the uncertainties in the times.
Variation of X-ray flux, optical flux density, and radio flux density of 3C 111 from 2004 to 2010. In the top panel, the
Table 10
Times of X-ray Dips, Ejection Times (T0) of Radio Knots,
and Apparent Speeds (βapp) of Radio Knots.
Dip IDTXmina
Knot IDT0
βapp
d1
d2
d3
d4
d5
d6
d7
d8
d9
2004.19
2005.02
2005.57
2006.47
2006.88
2007.32
2008.51
2008.98
2009.26
K1
K2
K3
K4
K5
K6
K7
K8
K9
2004.30± 0.14
2005.18± 0.05
2005.70± 0.04
2006.61± 0.09
2007.01± 0.04
2007.66± 0.09
2008.83± 0.07
2009.07± 0.08
2009.29± 0.04
3.99 ± 0.19
6.37 ± 0.29
3.44 ± 0.08
2.24 ± 0.44
2.71 ± 0.38
4.18 ± 0.11
4.54 ± 0.38
4.07 ± 0.43
4.33 ± 0.66
aTime of X-ray minimum.
3. CORRELATED VARIATIONS IN THE X-RAY
CONTINUUM AND FE Kα EMISSION LINE
Figure 8 shows the zero-lag correlation diagrams of
IFeKα, ΓX, and EQW, each plotted against F2−10. Best-
fit linear relations are plotted for each and are summa-
rized in Table 11 along with the Pearson correlation coef-
ficients. From this diagram, we can see that the range of
F2−10is from 2×10−11to 8×10−11(factor of ∼4), while
that of IFeKαis from 4×10−5to 12×10−5(factor of ∼3).
Hence, we conclude that at least 75% of the Fe line flux
responds to X-ray continuum variations. We searched
for lags between F2−10and IFeKαwith the interpolated
cross correlation function (ICCF; Gaskell & Peterson
1987; White & Peterson 1994), and the discrete cross-
correlation function (DCCF; Edelson & Krolik 1988),
with errors determined using the Flux-Randomization
and Random Subset Selection (FR-RSS) technique pro-
posed by Peterson et al. (1998). We omitted the first five
points (1997–2003) from this analysis due to the large
data gaps present. The ICCF peak correlation coeffi-
cient was 0.61 at a continuum-to-line delay τ = 0 days,
with a 1σ upper limit to the lag of |τ| = 88 days (Figure
9). This implies that the bulk of the line flux originates
within ∼90 light-days of the X-ray continuum source if
it lies near the plane of the accretion disk. Figure 8 also
demonstrates that ΓXincreases with F2−10, similar to the
behavior seen in many Seyfert galaxies that lack a strong
jet contribution to the X-ray spectrum (Papadakis et al.
2002; Shih, Iwasawa & Fabian 2002).
The X-ray continuum/Fe line correlation presented
here is perhaps the strongest such correlation observed
so far (cf., for example, the continuum-line correlation
observed in NGC 3227 by Markowitz et al. 2009, where
∼50% of the line flux responded to the continuum

Page 8

8
3
3.5
4
4.5
5
5.5
6
6.5
Flux Density (0.1 mJy)
R-Band Flux Density
0
1
2
3
4
5
Polarization Percentage
R-Band Polarization
-50
0
50
100
150
200
2006 2007 2008
Year
2009 2010
EVPA (Degree)
R-Band EVPA
Figure 5.
ization percentage, and electric vector position angle (EVPA) of
3C 111 during 2006 to 2010. The average polarization was only
1.6% ± 0.6%, rather low for synchrotron radiation from the jet.
This supports the notion that most of the optical emission is
thermal radiation from the accretion disk.
Variation of the optical R-band flux density, polar-
Table 11
Best-fit Linear Relations For Parameters Derived From
Time-resolved Spectroscopy.
Parameters Slopey-intercept
rP
Pr
IFeKαvs. F2−10
ΓXvs. F2−10
EQW vs. F2−10
1.27 ± 0.31
0.040 ± 0.008
−5.51 ± 4.97
1.83 ± 1.65
1.52 ± 0.04
150 ± 29
0.594
0.796
–1.92
1.3 × 10−4
5.8 × 10−8
0.26
Note. — The parameters for the best-fit linear solutions plotted in
Figure 8. rPis the Pearson correlation coefficient and Pr is the null
hypothesis probability, i.e., the probability of obtaining the observed
correlation by chance.
variations on time scales of ? 700 days). If the bulk
of the Fe line originates within 90 light-days of the
X-ray continuum source, then an origin in material com-
mensurate with the optical broad line region (located
light-days to light-weeks away from the central black
hole in Seyferts) is plausible.
inconsistent with a model wherein the bulk of the line
emission originates in a ∼parsec-scale, homogeneous
molecular torus commonly invoked in Seyfert 1/2
unification schemes.
However, this delay is
4. POWER SPECTRAL ANALYSIS
4.1. X-ray
We use a variant of the Power Spectrum Response
method (PSRESP; Uttley, McHardy & Papadakis 2002)
to determine the intrinsic PSD of the X-ray light
curve.Our realization of PSRESP is described in
Chatterjee et al. (2008). PSRESP gives both the best-
fit PSD model and a “success fraction” Fsucc (fraction
of simulated light curves that successfully represent the
observed light curve) that indicates the goodness of fit of
the model.
At first we fit a simple power-law model to the X-ray
PSD, but found that the value of Fsuccis unacceptably
low (0.1). This implies that a simple power law is not
the best model for this PSD. We therefore fit a bend-
ing power-law model (broken power law with a smooth
break) to the X-ray PSD (see
Chatterjee et al. 2009),
McHardy et al. 2004;
P(ν) = AναL[1 + (ν
νB)(αL−αH)]−1.(1)
Here, A is a normalization constant, νB is the break
frequency, and αH and αL are the slopes of the power
laws above and below the break frequency, respectively.
During the fitting, we varied the break frequency νB
from 10−9to 10−5Hz in steps of 100.05, αH (slope of
the power law above the break frequency) from −1.5
to −3.0 in steps of 0.1, and αL (slope below the break
frequency) from −1.0 to −1.5 in steps of 0.1.
ranges include the values of α found in the light curves
of BHXRBs, for which αL≈ −1 and αHis between −2
and −3 (e.g., Remillard & McClintock 2006). This pro-
cedure yields a much higher success fraction than the
simple power-law model. Based on the model with the
highest success fraction (0.85), we obtain a good fit with
the parameters αL = −1.0 ± 0.1, αH = −2.5+0.2
log10(νB) = −6.05+0.25
timescale 13+12
−6
days. Figure 10 presents this best-fit
model and the corresponding PSD. As seen in the fig-
ure, the high frequency part of the PSD is dominated by
Poisson noise. That is because i) this part of the PSD
is generated from the longlook light curve, and fluxes in
the longlook light curve have larger uncertainties owing
to shorter exposure times than those in the other light
curves and ii) due to the red noise nature of the PSD, the
intrinsic power is smaller at the higher frequencies and
hence the power generated by Poisson noise is relatively
more important. The figure shows that when the esti-
mated Poisson noise is added to the best-fit model PSD,
it matches the observed PSD quite well.
The PSD break frequency in BHXRBs and Seyfert
galaxies scales inversely with the mass of the black hole
(Uttley, McHardy & Papadakis
2004, 2006; Edelson & Nandra 1999; Markowitz et al.
2003). McHardy et al. (2006) showed that this holds over
a range of BH masses from 10 to 108M⊙, and that, for a
given black hole mass, the break frequency increases with
accretion rate ( ˙ m). The bolometric luminosity (Lbol) can
serve as a proxy for ˙ m. Since the BH mass in 3C 111 is
not well-established, we need to derive its value from
independent observations. To do this, we need to deter-
mine the optical luminosity of the central engine.
These
−0.5, and
−0.30Hz, which is equivalent to a
2002;McHardy et al.

Page 9

9
Figure 6.
FWHM size 0.32×0.16 mas at PA = −10◦. The global peak over all maps is 4.80 Jy/Beam. The contour levels are 0.25, 0.354, 0.5, 0.707,
..., 90.51 % of the global peak. Note that the time spacing of the images is not uniform, hence the lines denoting the proper motion of a
given knot do not pass through the centroid of the knot at every epoch.
Sequences of VLBA images at 7 mm during 2004 to 2009. The images are convolved with an elliptical Gaussian beam of
The optical emission received from 3C 111 is sub-
ject to substantial extinction owing to the presence of
a translucent (Av between ∼1 and 5) molecular cloud
in the foreground. The standard method for deter-
mining the extinction, star counts in the surround-
ing region on the sky, is subject to systematic uncer-
tainties because of possible gradients in dust absorp-
tion.In fact, Marscher, Moore & Bania (1993) and
Moore & Marscher (1995) have reported time variations
in radio H2CO absorption lines toward 3C 111, indicat-
ing that the column density and/or excitation conditions
may vary throughout the cloud, causing changes in ab-
sorption as our line of sight to the quasar drifts across
the cloud from relative motion between the Earth and
the cloud. Sargent (1977) gives essentially simultaneous
multi-band optical and near-infrared flux measurements
of 3C 111, which are not corrected for extinction. We an-
alyze this spectrum to calculate a value of the extinction,
Av = 2.5, that generates an extinction-corrected spec-
trum that can be fit well by a power law, the functional
form that fits the optical continuum of a typical AGN.
The spectral index of the extinction-corrected spectrum,

Page 10

10
Figure 7.
moving knots brighter than 100 mJy within 2.0 mas of the core.
The black lines indicate the motion of each knot listed in Table 10.
A knot is identified through continuity of the trajectory from one
epoch to the next. The identification of the knot across epochs
considers its position angle relative to the core and, in some cases,
its polarization. At some epochs, the model fit breaks a knot into
two pieces.
Angular separation from the core vs.epoch of the
displayed in Figure 11, is −1.38. Our value of Av is
consistent with the values E(B-V) ∼1 for translucent
clouds with total N(H) ∼9×1021cm−2(Rachford et al.
2002) and Av/E(B-V) ∼2.1 derived for the translucent
cloud HD 36982 by Larson, Whittet & Hough (1996).
We note, however, that these values have high uncer-
tainties and could differ significantly from one cloud to
another.After correcting the optical luminosity from
Sargent (1977) by this value of Av, we arrive at a de-
reddened optical luminosity of λLλ= 6.1 × 1043erg s−1
at λ = 510 nm.
In a recent paper, Decarli, Dotti & Treves (2011) used
the properties of the Hα line of a sample of blazars in ad-
dition to other parameters to determine the mass of the
central BH. Using the deprojection factor and Hα line to
continuum (510 nm) luminosity ratio from equation (3)
and (5), respectively, of that paper, as well as the width
and luminosity of the Hα line from Eracleous & Halpern
(2003), we calculate the BH mass of 3C 111, MBH =
2.4+0.6
Another method for estimating
the BH mass is to use the relationship between MBH
and the FWHM line width of the Hβ broad emission
line along with equation (2) of Vestergaard & Peterson
(2006). Unfortunately, no accurate measurement of
FWHM(Hβ) in 3C 111 has been published; instead, we
assume that FWHM(Hβ) ≈ FWHM(Hα) = 4800 km s−1
(Eracleous & Halpern 2003). From this value and the
de-reddened optical luminosity given above, we derive
MBH= 1.5+0.4
estimate of the uncertainty in the zero point value of the
scaling relation between the masses determined using re-
verberation mapping and those from single-epoch spectra
from Vestergaard & Peterson (2006), then the respective
−0.5× 108M⊙.
−0.3×108M⊙. If we use the more conservative
Figure 8. Zero-lag correlation diagrams for intensity of the Fe line
IFeKα, photon index ΓX(of the continuum), and Fe line equivalent
width EQW each plotted against 2–10 keV continuum flux F2−10
with the best-fit linear relation plotted for each as a dashed line;
units are the same as in Figure 2. The X-ray continuum/Fe line
correlation presented here is one of the strongest such correlation
observed so far. The best-fit linear relations plotted here are sum-
marized in Table 11 along with the Pearson correlation coefficients.
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-1 -0.5 0 0.5 1
Correlation Coefficient
Time Delay (Days)
Figure 9.
(DCCF), and
correlation function (ICCF) of the variation of intensity of the
Fe line IFeKαwith that of 2–10 keV continuum flux F2−10. The
two variations are strongly correlated with a time delay consistent
with zero with a 1σ upper limit of 88 days.
Points denote discrete cross-correlation function
the solid line shows the interpolatedcross-

Page 11

11
-7
-6
-5
-4
-3
-2
-1
0
-8-7-6-5-4-3
log [Power X Frequency (rms2)]
log [Frequency (Hz)]
Figure 10.
the X-ray light curve of 3C 111.
data at high, medium, and low frequencies is given by the solid,
dashed, and dotted jagged lines, respectively, while the underlying
power-law model is given by the thicker solid bent line. Points
with error bars (open squares, filled circles, and open circles for
high, medium, and low frequency range, respectively) correspond
to the mean value of the PSD simulated from the underlying
power-law model (see text). The error bars are the standard
deviations of the distribution of simulated PSDs. The broadband
power spectral density is best described by a bending power law
with low frequency slope −1.0, high frequency slope −2.5, and
break frequency 10−6.05Hz.The high frequency part of the
PSD is dominated by Poisson noise. The figure shows that when
the estimated Poisson noise is added to the underlying bend-
ing power-law model PSD, it matches the observed PSD quite well.
Result of application of the PSRESP method to
The PSD of the observed
-26.2
-26.1
-26
-25.9
-25.8
-25.7
-25.6
-25.5
-25.4
-25.3
-25.2
14.4 14.5 14.6 14.7 14.8 14.9 15
log(Flux [erg cm-2s-1])
log(Frequency[Hz])
Av=2.5
Slope=1.38
Figure 11. The extinction corrected optical spectrum of 3C 111.
The best-fit power-law has a slope −1.38 for Av= 2.5.
uncertainty in the value of the BH mass becomes larger,
MBH= 1.5+2.5
the widths of Hα and Hβ emission lines from equation
(3) of Greene & Ho (2005), we calculate FWHM(Hβ)
of 3C 111 to be 5400 ± 400 km/s from FWHM(Hα) =
4800 km s−1(Eracleous & Halpern 2003).
value in equation (2) of Vestergaard & Peterson (2006)
and keeping other parameters same as above, we obtain
MBH= 1.8+0.5
Marchesini, Celotti & Ferrarese (2004) derived a much
higher value of MBHestimating the bolometric luminos-
ity of 3C 111 from the optical nuclear luminosity along
with the bolometric correction from Elvis et al. (1994).
The former is derived by fitting the unresolved nuclear
−1.0×108M⊙. Using the correlation between
Using this
−0.4× 108M⊙.
-2
-1
0
1
2
2.8 3 3.2
log (FWHM [kms-1])
3.4 3.6 3.8
log (TB [Days])
Figure 12.
break timescale for a sample of mainly radio-quiet AGNs from
McHardy et al. (2006) is denoted by the dashed straight line
and the solid circles. The open circle and the open square show
data points corresponding to radio galaxies 3C 120 and 3C 111,
respectively, which follow the correlation. For 3C 111, line width
of Hβ has been calculated from that of Hα using equation (3) of
Greene & Ho (2005).
The correlation of Hβ line-width with the PSD
component with the appropriate HST PSF in the re-
spective HST image. They adopted an extinction cor-
rection from Schlegel, Finkbeiner & Davis (1998) which
is higher than the extinction we calculated above by
almost 3 magnitudes.If we adjust the calculation of
Marchesini, Celotti & Ferrarese (2004) to our extinction
correction of Av=2.5, we obtain Lbol= (2.5±1.0)×1044
ergs s−1. We also calculate Lbol = (4.8 ± 3.3) × 1044
ergs s−1from Young, Elvis, & Risaliti (2010) using the
2.4–10 keV X-ray flux and 510 nm optical flux, which
is consistent with the above value within uncertainties.
Performing a similar calculation using equation (11) of
Lusso et al. (2010), we find Lbol= (1.8±1.1)×1045ergs
s−1, which is close to the above values as well.
Using the intermediate values from above, Lbol =
(4.8 ± 3.3) × 1044erg/s, and MBH= 1.8+0.5
we find Eddington ratio Lbol/Ledd = 0.02 ± 0.01. We
adopt the best-fit values and uncertainties in the TB—
MBH—Lbolrelation proposed by McHardy et al. (2006),
and the above values of MBHand Lbol. We then calcu-
late the expected break frequency to be 10−6.6±0.7Hz. If
we use the more conservative estimate of the uncertainty
in BH mass from above, we obtain 10−6.6±1.1Hz for the
same. Both of these are consistent with the value we have
obtained from the best-fit PSD, log10(νB) = −6.05+0.25
Hz, within uncertainties. This demonstrates that 3C 111
also follows the TB—MBH—Lbolrelation, the first FR II
radio galaxy for which this has been tested.
McHardy et al. (2006) also showed that FWHM(Hβ)
in AGNs is strongly correlated with the observed PSD
break timescale (TB) given by
−0.4× 108M⊙,
−0.30
log(TB) = 4.2log([FWHM(Hβ)]) − 14.43(2)
Using the results of the above analysis and that contained
in Chatterjee et al. (2009), we can now add data points
corresponding to the radio galaxies 3C 120 and 3C 111
in Figure 3 of McHardy et al. (2006), resulting in Figure
12. The plot shows that these two radio galaxies also
follow the empirical TBversus FWHM(Hβ) correlation.

Page 12

12
1
2
3
4
5
6
7
8
-8.5-8-7.5
log [Frequency (Hz)]
-7-6.5-6-5.5
log [Power (rms2Hz-1)]
Figure 13. Result of application of the PSRESP method to the
optical light curve of 3C 111. The PSD of the observed data at
high and medium frequencies is given by the dashed and solid
jagged lines, respectively, while the underlying power-law model
is given by the solid straight line. Points with error bars (filled
circles and open squares for high and medium frequency range,
respectively) correspond to the mean value of the PSD simulated
from the underlying power-law model (see text). The error bars
are the standard deviations of the distribution of simulated PSDs.
The broadband power spectral density is best described by a
simple power law with slope −2.0. The smoothly bending dotted
line is the underlying best-fit bending power-law model of the
X-ray PSD from Fig. 10. This shows that the X-ray variability
has more power than that in the optical on shorter timescales
while on longer timescales variability at the two wave bands tend
to be similar.
4.2. Optical
We use the same method as above to calculate the
PSD of the optical variability. The optical R-band PSD
of 3C 111 (Figure 13) shows red noise behavior, i.e., there
is higher amplitude variability on longer than on shorter
timescales. Based on the model with the highest success
fraction, the optical PSD is best fit with a simple power
law of slope −2.0+0.3
−0.7, for which the success fraction is
0.52. During the fitting, we varied the slope from −1.0
to −3.0 in steps of 0.1. The rejection confidence, equal
to one minus the success fraction, is much less than 0.9,
hence the model provides an acceptable fit to the PSD.
We also fit a broken power law to the optical PSD, set-
ting the low-frequency slope at −1.0 and allowing the
break frequency and the slope above the break to vary
over a wide range of parameters (10−8to 10−6Hz and
−1.0 to −2.5, respectively) while calculating the success
fractions. This gives lower success fractions than the sim-
ple power-law model across the entire parameter space.
Since we do not have any significantly long segment of
the R-band data when the sampling frequency was more
than 2-3 days per week, we determine the optical PSD up
to the highest variational frequency that can be achieved
with the existing data. A better constraint on the ex-
istence of a break in the optical PSD could be achieved
with a broader range of sampled frequencies.
The slope of the optical PSD in the range 10−8.1to
10−5.8Hz is significantly steeper than that in X-rays over
the same range (∼1.0). Hence, the ratio of shorter to
longer timescale variability amplitude is smaller at opti-
cal than at X-ray wavelengths.
4.3. Excess Variance
We calculate the fractional root mean squared variabil-
ity amplitude, i.e., the “excess variance” normalized by
the square of the mean flux, as a measure of the variabil-
ity in the X-ray and optical data. It is defined as
Fvar=
?
S2− σ2
x2
err
,(3)
where S is the variance, σerris the observational uncer-
tainty, and x is the mean of the data (Nandra et al. 1997;
Edelson et al. 2002; Vaughan et al. 2003). We find that
the values of Fvarof the X-ray and optical variability for
the entire data set are 0.28 and 0.14, respectively. This
supports the above conclusion from the PSD analysis
that the optical is less strongly variable than the X-ray
flux at the longest timescales we probe. It also implies
that optical variations cannot be completely responsible
for driving all of the X-ray variability observed, if we
assume that most of the X-ray emission we observe is
not relativistically beamed.
5. X-RAY/RADIO CORRELATION
We can see in Fig. 4 that, from the middle of 2009 to
the present, the X-ray flux undergoes only minor fluctu-
ations about a mean value of 5 × 10−11erg cm−2s−1.
During this interval, the 230 GHz flux is at a very low
level, while the 15 GHz flux is decreasing. Therefore, the
high-state X-ray plateau coincides with a low state of the
radio jet. We can extend this X-ray/radio connection to
the observations of earlier years as well. The times of
“ejection” of new radio knots in the jet (shown by the
arrows) are related to the low X-ray states. We convolve
the X-ray light curve with a Gaussian smoothing func-
tion with a 10-dayFWHM smoothing time to identify the
major long-term trends. Figure 14 shows the smoothed
X-ray light curve and denotes the times of superluminal
ejections with arrows. Based on inspection of this light
curve, we consider an X-ray fluctuation to be a significant
dip if the smoothed X-ray flux falls by more than 30%
and remains at a low level for longer than one month.
We calculate the central time of each dip by determining
the local minimum of the X-ray flux. We note that the
minimum amplitude measured from unsmoothed data of
every dip is below the average of the X-ray flux over the
length of the light curve (4 × 10−11erg cm−2sec−1). It
can be seen that each of the ejections is preceded by a
significant dip in the X-ray flux. The prolonged low level
of X-ray flux in 2005 is associated with knot K3, which
was extended along the jet axis, as is apparent in the
images starting in late 2006 (Fig. 6). This suggests that
a prolonged disturbance near the base of the jet resulted
in an elongated superluminal knot. Hence, d3 and the
two significant dips just before and after that are consid-
ered to be one dip with multiple branches and is related
to K3. Detection of the ejection of a new knot requires
the analysis of a sequence of VLBA images of sufficient
duration to define the trajectory and speed of a knot, as
is evident from Figures 6 and 7. No new bright, mov-
ing knots after K9 appeared in subsequent imaging with
the VLBA during the first 8 months of 2010 (images not
shown here).
The time delay between the minimum of the X-ray dips
and the time of ejection of the corresponding superlumi-

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13
1
2004
2
3
4
5
6
7
2005 2006 2007 2008 2009 2010
Flux (10-11 erg cm-2 s-1)
Year
K1K2 K3K4 K5 K6
K7 K8K9
d1
d2
d3
d4
d5
d6
d7
d8
d9
Figure 14.
data, smoothed with a Gaussian function with a 10-day FWHM smoothing time.
ejections and the line segments perpendicular to the arrows represent the uncertainties in the times.
listed in Table 10 are marked with the respective ID numbers.
light curve are followed by ejections of bright superluminal knots in the VLBA images.
the radiative state near the black hole, where the X-rays are produced, and events in the jet.
just before and after that are considered to be one dip with multiple branches and is related to K3 which was also extended along the jet axis.
X-ray light curve of 3C 111 as in Figure 4, with data indicated by small circles.The curve corresponds to the same
The arrows indicate the times of superluminal
X-ray dips and VLBA knots
Over the six years of observation, significant dips in the X-ray
This shows a clear connection between
Dip d3 and the two significant dips
nal knot is distributed between 0.03 and 0.34 yr (Table
10) with a mean of 0.15 ± 0.08 yr. We plot the times
of ejection of new knots along with the corresponding
times of X-ray dips in Figure 15. A straight line fits
the data extremely well with small scatter, which indi-
cates that there is a clear association between X-ray dips
and superluminal ejections.
the points has a slope of 1 and y-intercept of 0.15, which
is identical to the mean delay of 0.15 ± 0.08 yr given
above. We have performed a numerical simulation to
calculate the significance of the dip-ejection correlation.
If we keep the times of dips fixed and choose one million
sets of nine ejections, times of which are drawn from a
uniform random distribution between 2004.3 and 2010.3
(the duration of our observations), the probability that
there is at least one ejection event following all 9 dips
by 0.03 to 0.34 yr is 0.007. In a similar simulation, we
found that the probability that all 9 dips will have ex-
actly one following ejection is 3×10−5. This shows that
the dip-ejection association in 3C 111 is highly signifi-
cant. To further investigate the relationship between the
characteristics of the X-ray dips and VLBA knots, we
calculate the average flux over all epochs of the latter.
We do this via modeling of the brightness distribution at
each epoch with multiple components characterized by
circular Gaussian brightness distributions, as described
in §2.4. This shows that the average flux of the VLBA
knots corresponding to the shallower dips (d2, d4, and d8
in Fig. 14) is significantly smaller (0.3±0.1 Jy) than that
for the larger dips (d1, d3, d5, and d7), 0.9±0.4 Jy. Dip
d6 is also shallow, but this may be due to the absence of
data during the Sun-avoidance gap, while d9 is of inter-
mediate depth. Hence K6 and K9 were not included in
The best-fit line through
2004
2005
2006
2007
2008
2009
2010
2004 2005 2006
Start Times of X-ray Dips
2007 2008 2009 2010
Times of Corresponding Ejection
x+0.15
Figure 15. Times of ejection of new VLBA knots versus times of
X-ray dips from Table 10. The dashed line is the best-fit straight
line through the points. It fits the data extremely well with small
scatter. This indicates that there is a clear association between
X-ray dips and superluminal ejections. The y-intercept of this line
minus 2004.0 indicates the value of mean time delay between the
times of dips and ejections.
the average calculation. That the brighter knots corre-
spond to more pronounced dips supports the conclusion
that the X-ray minima and the ejection of knots in the
jet are physically related.
As determined by the discrete cross-correlation func-
tion (DCCF; Edelson & Krolik 1988) shown in the top
panel of Figure 16, the X-ray flux variations are weakly
correlated with those at 15 GHz in 3C 111. The peak
X-ray versus 15 GHz DCCF is 0.35. We simulate X-
ray light curves from the underlying PSD as determined

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14
-0.5
0
0.5
1
Correlation Coefficient
X-rays vs. 14.5 GHz
-0.5
0
0.5
1
Correlation Coefficient
X-rays vs. 37 GHz
-0.5
0
0.5
1
-300-200-100
Time Delay (Days)
0 100 200 300
Correlation Coefficient
X-rays vs. 230 GHz
Figure 16.
X-ray and radio monitoring data of 3C 111.
is defined as positive if the X-ray variations lag those at radio
frequencies. Top panel shows the correlation function for X-ray
versus 15 GHz variations while the middle and bottom panels
show the same for X-ray versus 37 and 230 GHz, respectively. The
jagged dotted and dashed lines at the top of each panel denote 99
and 95 percent significance levels of correlation, respectively (see
text). Those at the bottom of each panel show the same for anti-
correlation. This shows that the X-ray and 37 GHz variations are
correlated while the other two pairs are not significantly correlated.
Discrete cross-correlation function (DCCF) of the
The time delay
in §3 and resample the simulated light curves with the
sampling window of the actual X-ray light curve. Then
we cross-correlate the resampled simulated X-ray light
curves with the real 15 GHz light curve. The solid and
dotted jagged lines in Figure 16 indicate 99% and 95%
extremes of the distribution of correlation coefficients as
a function of time delay.
The DCCF indicates that the X-ray flux variations are
correlated with those at 37 GHz in 3C 111, with a peak
value of 0.63 (middle panel of Figure 16). The position of
the peak of the correlation function indicates the relative
time delay between the variations at the two wavelengths.
The time lag of the peak corresponds to X-ray variations
leading those at 37 GHz by 40+70
FR-RSS technique (Peterson et al. 1998) to calculate the
mean value and the uncertainty of the cross-correlation
time lag. The bottom panel of Figure 16 shows that
the X-ray and 230 GHz variations are weakly correlated,
with a peak DCCF of 0.30.
We note that if the radio flux increases within tens of
days after an X-ray minimum and the X-ray flux recovers
from the minimum to increase as well during this time,
−65days.We use the
then a relatively weak X-ray/radio correlation will result
as seen in the data presented in this paper. The signif-
icant correlation between the dips and ejections of new
knots in the jet implies that increased activity in the ra-
dio jet of 3C 111 is related to a temporary decrease in
X-ray production. Similarly, the association between the
high-state X-ray plateau with a low state of the radio jet
after the middle of 2009 suggests that a persistently high
X-ray flux is associated with a low radio state.
It is possible that the “corona,” where the X-ray emis-
sion seen in AGN is thought to arise from Compton up-
scattering of softer accretion-disk photons, might be the
base of the jet (Markoff, Nowak, & Wilms 2005). If this
is the case, then the X-ray flux will be related to the
number of electrons residing there and available for scat-
tering to create X-rays. If the same number of electrons
is injected into the base of the jet per unit time, then
faster flow velocities will correspond to lower densities
in the scattering region. The mass loading of the jet
should also affect the asymptotic Lorentz factor of the
flow downstream if the jet is magnetically driven (e.g.,
Vlahakis & K¨ onigl 2004). The same decrease in electron
number that causes a drop in scattered X-ray emission
near the disk would lead to a time-delayed increase in
the speed of the jet downstream. The increase in flow
speed of the jet could form a shock wave, eventually
seen as a superluminal radio knot (G´ omez et al. 1997).
This would then give rise to the dip-ejection sequence
discussed above.
The highest-amplitude 37 GHz outburst, from 2007.5
to 2008.8, started at the same time as at 230 GHz, but
reached maximum level at a later time than both the
230 GHz and X-ray flares. This can be explained by
the larger optical depth at the lower frequencies prior to
the 37 GHz peak. The similar amplitudes of the 37 and
230 GHz flares follow the pattern of the synchrotron-loss
stage of the shock-in-jet model (Marscher & Gear 1985),
which predicts that, in synchrotron flares produced in
the jet, the peak amplitude should stay roughly constant
as the emission becomes optically thin at progressively
lower frequencies.
The mean time delay between the minimum of
the X-ray dips and the time of ejection of the cor-
responding superluminal knot is 0.15 ± 0.08 yr.
average apparent speed of the moving components
with well-determined motions is 3.9c ± 0.7c. Therefore,
a knot moves a distance of 0.18 ± 0.1 pc in 0.15 yr,
projected on the plane of the sky. (Here we assume that
acceleration of the flow to its terminal velocity occurs
over a sufficiently short distance that the time that a
moving feature spends in the acceleration zone is short
compared with the total transit time to the 43 GHz
core.) Since the angle of the jet axis of 3C 111 to the
line of sight ∼18◦, the actual distance traveled by the
knot, given by βcδ∆tobsΓ is 0.6 ± 0.3 pc.
derive a distance 0.6 ± 0.3 pc from the corona or the
base of the jet (where the X-rays are produced) to the
core seen on the 43 GHz VLBA images. This is one of
the few cases where, similar to 3C 120 (Chatterjee et al.
2009), we are able to specify the distance between the
central engine and mm-wave core in an AGN.
The
Hence, we

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15
-1
-0.5
0
0.5
1
-300 -200 -100
Time Delay (Days)
0 100 200 300
Correlation Coefficient
Figure 17.
optical and X-ray monitor data of 3C 111 for the entire 5 yr
interval.The time delay is defined as positive if the X-ray
variations lag those at the optical frequency.
and dotted lines at the top of the panel denote 99 and 95 percent
significance levels of correlation (see text), respectively. Those at
the bottom of the panel show the same for anti-correlation. The
peak X-ray versus optical DCCF is 0.6, which corresponds to more
than 99% significance level. The peak at −15 days indicates that
the X-ray variations lead those in the optical by 15 ± 10 days.
Discrete cross-correlation function (DCCF) of the
The jagged solid
6. X-RAY/OPTICAL CORRELATION
As determined by the DCCF (Figure 17), we find that
the X-ray variations of 3C 111 are very strongly corre-
lated with those at optical R band.
versus optical DCCF is 0.6, which corresponds to more
than 99% significance level. The jagged solid and dotted
lines at the top of the panel denote 99 and 95 percent sig-
nificance levels of correlation, respectively. Those at the
bottom of the panel show the same for anti-correlation,
as described in the previous section. The time lag of the
peak indicates that the X-ray variations lead those in
the optical by 15±10 days. The highly significant corre-
lation between the X-ray and optical variations implies
that emission at these wave bands is causally connected.
Fig. 5 shows the variation of the degree of polarization
as well as the electric vector position angle (EVPA) of
3C 111 at R band from 2006 to the present. The av-
erage polarization was only 1.6% ± 0.6%, rather low for
synchrotron radiation from the jet. This agrees with the
idea that most of the optical emission is thermal radia-
tion from the accretion disk (Malkan 1983). The strong
X-ray/optical correlation, weak optical polarization, and
smaller variance of optical compared with X-ray flux
at shorter timescales are consistent with a reprocessing
model. In this scenario, the X-rays are predominantly
produced by inverse Compton (IC) scattering of ther-
mal optical/UV seed photons from the accretion disk by
hot, but non-relativistic, electrons in the corona, while a
significant fraction of the optical-UV emission is due to
heating of the accretion disk by X-rays produced in the
above process. The slope of the optical PSD in the range
10−8.1to 10−5.8Hz is ∼−2.0, significantly steeper than
that of the X-ray PSD over the same frequency range (∼
−1.0). This implies that the optical variations on shorter
time-scales are suppressed, consistent with smoothing by
reprocessing.
Alternatively, a substantial fraction of the optical emis-
The peak X-ray
sion may be generated as synchrotron radiation in the jet,
giving rise to a degree of polarization up to 3% (Fig. 5) or
even higher (Jorstad et al. 2007) and significant variabil-
ity of the position angle of polarization (between 0◦and
150◦) at some epochs. In this case, if X-rays are indeed
generated at the base of the jet, then the highly signif-
icant correlation between the X-ray and optical varia-
tions, combined with the time delay of the latter, 15±10
days, implies that the optical emission region in the jet,
if present, is situated downstream of the base of the jet.
We can calculate the mean distance (∆z)xobetween the
X-ray and optical synchrotron emission sites in the jet
if we adopt 18◦as the angle between the jet axis and
the line of sight (Jorstad et al. 2005) and assume a value
for the average speed βc of the jet flow between the two
emission regions: (∆z)xo∼ 6, 20, and 200 light-days for
β = 0.25, 0.5, and 0.974, respectively. The last value,
β = 0.974, corresponds to the velocity obtained from
analysis of the superluminal apparent motion and time-
scale of flux decline at 43 GHz of knots observed with
the VLBA (Jorstad et al. 2005). The lower values of β
near the base of the jet are in concert with theoretical
models in which jets are accelerated to relativistic flow
velocities over extended distances from the central engine
(e.g., Vlahakis & K¨ onigl 2004).
Some of the thermal optical-UV emission could be pro-
duced in the accretion disk even without reprocessing
via X-ray heating. The temporal nature of this emis-
sion would be different from that generated as a result
of reprocessing. The X-rays may be produced mainly by
up-scattering of UV rather than optical photons. This
could occur if the flux of optical photons reaching the
corona is much smaller than that of UV photons. Such
a scenario is likely if the corona is small, such that the
UV emission region is much closer to the corona than
the region where the majority of the optical photons
are produced (see Chatterjee et al. 2009, for details).
Any disturbance propagating outward in the accretion
disk will cause a change in the UV flux (and a resul-
tant nearly immediate change in the X-ray emission)
followed by a similar change in the optical flux. This
may also give rise to the X-ray/optical time delay that
is observed. As discussed in detail by Chatterjee et al.
(2009), the variability timescale described above is con-
sistent with the model proposed by King et al. (2004)
and Livio, Pringle & King (2003), in which variability in
the disk emission is caused by large-scale alignment of
poloidal magnetic field in the inner accretion disk from
random fluctuations in field direction. Such alignment
occurs on a timescale of a few tens of days for a BH of
mass of ∼108M⊙, consistent with the results described
above.
The time delay of 15 ± 10 days of the optical with
respect to the X-ray variations is larger than expected
from a pure reprocessing model.
Chatterjee et al. (2009), the region of the accretion disk
that produces the largest amount of direct (rather than
reprocessed) optical emission is at ∼100 gravitational
radii (rg) from the center, which is equal to ∼1 light-
day for a BH mass of 1.8×108M⊙(see also the detailed
modeling of Kazanas & Nayakshin 2001). Therefore, if
the X-ray/optical time delay is solely due to light travel
time from the corona to the region in the accretion disk
As discussed in