# The Energetics of the Central Engine in the Powerful Quasar, 3C298

Brian Punsly  1415 Granvia Altamira, Palos Verdes Estates CA, USA 90274
ICRANet, Piazza della Repubblica 10 Pescara 65100, Italy  ICRA, Physics
Department, University La Sapienza, Roma, Italy  Christian Groeneveld  Leiden
Observatory, Niels Bohrweg 2, 2333 CA Leiden  Gary J. Hill McDonald
Observatory, University of Texas at Austin, 2515 Speedway, Austin, TX 78712,
USA  Department of Astronomy, University of Texas at Austin, 2515 Speedway,
Austin, TX 78712, USA  Paola Marziani  INAF, Osservatorio Astronomico di
Padova, Italy  Gregory R. Zeimann  Hobby-Eberly Telescope, 32 Mt. Locke Rd.,
McDonald Observatory, TX 79734, USA  McDonald Observatory, University of Texas
at Austin, 2515 Speedway, Austin, TX 78712 USA  Donald P. Schneider
Department of Astronomy, Pennsylvania State University, 525 Davey Lab,
University Park, PA 16802, USA  Institute for Gravitation and the Cosmos,
Pennsylvania State University, University Park, PA 16802, USA

(Received …; Revised …; Accepted …)

###### Abstract

The compact steep spectrum radio source, 3C 298, (redshift of 1.44) has the
largest 178 MHz luminosity in the 3CR (revised Third Cambridge Catalogue)
catalog; its radio lobes are among the most luminous in the Universe. The
plasma state of the radio lobes is modeled with the aid of interferometric
radio observations (in particular, the new Low Frequency Array observation and
archival MERLIN data) and archival single-station data. It is estimated that
the long-term time-averaged jet power required to fill these lobes with
leptonic plasma is $\overline{Q}\approx 1.28\pm 0.51\times
10^{47}\rm{erg}\,\rm{s}^{-1}$, rivaling the largest time averaged jet powers
from any quasar. Supporting this notion of extraordinary jet power is a 0.5
keV -10 keV luminosity of $\approx 5.2\times 10^{46}\rm{erg}\,\rm{s}^{-1}$,
comparable to luminous blazars, yet there is no other indication of strong
relativistic beaming. We combine two new high signal to noise optical
spectroscopic observations from the Hobby-Eberly Telescope with archival
Hubble Space Telescope, Two Micron Survey and Galaxy Evolutionary Explorer
data to compute a bolometric luminosity from the accretion flow of
$L_{\rm{bol}}\approx 1.55\pm 0.15\times 10^{47}\rm{erg}\,\rm{s}^{-1}$. The
ratio, $\overline{Q}/L_{\rm{bol}}\approx 1$, is the approximate upper limit
for quasars. Characteristic of a large $\overline{Q}/L_{\rm{bol}}$, we find an
extreme ultraviolet (EUV) spectrum that is very steep (the “EUV deficit” of
powerful radio quasars relative to radio quiet quasars) and this weak ionizing
continuum is likely a contributing factor to the relatively small equivalent
widths of the broad emission lines in this quasar.

black hole physics — galaxies: jets—galaxies: active — accretion, accretion
disks

††journal: ApJ

##  1 Introduction

The quasar 3C 298, at a redshift of z = 1.44, has the highest 178 MHz
luminosity, $L_{178}$, of any source in the 3CR (revised Third Cambridge)
catalog (Bennett, 1962; Salvati et al., 2008). The small angular size of
2$\farcs$5 estimated in Spencer et al. (1989) makes this a member of a
subclass of radio sources known as a compact steep spectrum radio source
(CSS). The CSS sources are a particular class of small extragalactic radio
sources with a size less than the galactic dimension and this can be taken as
a working definition (O’Dea, 1998). They typically have synchrotron self-
absorbed spectra, in which the spectral peak frequencies, $\nu_{\rm{peak}}\sim
100$ MHz, before turning over to the characteristic steep spectrum. This low
frequency value of $\nu_{\rm{peak}}$ distinguishes them for other peaked radio
sources, gigahertz peaked sources (GPS) and high frequency peaked sources
(HFP) (O’Dea, 1998; Orienti and Dallacasa, 2008). They could be frustrated by
the denser galactic environment, but in general, it is believed that most are
in the early stages of an evolutionary sequence in which the CSS sources are
younger versions of the larger radio sources, $>50\rm{kpc}$ (O’Dea, 1998).
Traditional estimates of long term time average jet power, $\overline{Q}$, are
based on radio sources that are much larger than the host galaxy (Willott et
al., 1999; Birzan et al., 2008; Cavagnolo et al., 2010). Thus, these estimates
of $\overline{Q}$ are not valid in general for CSS sources (Barthel and
Arnaud, 1996; Willott et al., 1999). One of our primary goals is to determine
if the large value of $L_{178}$ for 3C 298 is indicative of one of the most
powerful jets in the Universe or if it is amplified by the dissipative
interaction of the expanding radio source with the host galaxy.

3C 298 is also known for having very strong star-burst regions and a conical
ionized wind along the jet direction (Podigachoski et al., 2015; Vayner et
al., 2017). Since the bulge luminosity is extremely low for the virial
estimated central black hole mass, $M_{bh}$, it was concluded that strong
negative feedback is occurring in a conical outflow early in the gas-rich
merger phase (Vayner et al., 2017). This highly dynamical system motivates a
detailed analysis of the central engine of this quasar with an extraordinarily
powerful jet. In particular, we explore the UV continuum and emission lines
with the aid of the upgraded Hobby-Eberly Telescope111The Hobby-Eberly
Telescope is operated by McDonald Observatory on behalf of the University of
Texas at Austin, Pennsylvania State University, Ludwig-Maximillians-
Universität München, and Georg-August-Universität, Göttingen. The HET is named
in honor of its principal benefactors, William P. Hobby and Robert E. Eberly.
(HET, Ramsey et al. 1994; Hill et al. 2021) and archival Hubble Space
Telescope (HST) observations in order to characterize the nuclear environment.

The paper is organized as follows. Section 2 compiles the radio data with a
particular emphasis on the new Low Frequency Array (LOFAR) photometry and the
International LOFAR Telescope (ILT) images at frequencies below 100 MHz.
Sections 3 and 4 fit the radio data with parametric models of the radio lobes
and the nucleus. Section 5 finds an infinite set of physical models that
correspond to this fit. The solution that has equal internal energy in the two
lobes, bilateral symmetry, is one in which both lobes are near minimum
internal energy. For this solution, we compute the jet power. Section 6
describes the new optical observations and provides a detailed discussion of
the broad emission lines (BELs). The optical spectra are combined with
archival data in Section 7 in order to find the continuum spectral energy
distribution (SED) of the thermal emission from the accretion flow and its
bolometric luminosity. $L_{\rm{bol}}$. In Section 8, we make a connection
between the weak BELs (relative to the UV continuum) found in Section 6 and
the steep extreme ultraviolet spectrum found in Section 7. Finally, in Section
9, we have the insight gained in the previous sections to address how to best
approach the virial mass estimate of $M_{bh}$ for the particular continuum SED
of 3C 298. Throughout this paper, we adopt the following cosmological
parameters: $H_{0}$=69.6 km s-1Mpc-1, $\Omega_{\Lambda}=0.714$ and
$\Omega_{m}=0.286$ and use Ned Wright’s Javascript Cosmology Calculator
222http://www.astro.ucla.edu/ wright/CosmoCalc.html (Wright, 2006).

##  2 Radio Observations

3C 298 is a famous bright radio source that has been extensively observed. We
have collected radio data in Table 1. Most of the data are archival integrated
flux density measurements from 26.3 MHz to 15 GHz. We also include archival
interferometric component data at 327 MHz, 5 GHz, 8.4 GHz and 15 GHz that have
insufficient u-v coverage and sensitivity to detect all of the lobe flux
density, rendering their value as merely lower bounds (Fanti et al., 2002;
Dallacasa et al., 2021; Ludke et al., 1998; Akujor and Garrington, 1995; van
Breugel et al., 1992). The source is very small with a projected size on the
sky plane of 1$\farcs$5 typically claimed (Akujor and Garrington, 1995).
However full track 1.66 GHz MERLIN observations detected diffuse lobe flux and
found that the overall size is actually 2”.5 (Spencer et al., 1989). The small
size and steep spectrum requires extremely challenging interferometric
observations in order to characterize the lobes. Until recently the MERLIN
observation was the only interferometric observation that had sufficient
sensitivity and resolution to characterize the lobes. We review the archival
low frequency integrated flux density observations and discuss a new LOFAR
image in detail in this section. The low frequency emission is the most
difficult to observe, yet the most crucial data for this analysis.

Most of the data in Table 1 are survey results and we apply a 10% uncertainty
in spite of much more optimistic estimates in their original published form.
In our experience, this approach is consistent with the repeatability of such
measurements with different telescopes. There are two exceptions. For the GMRT
150 MHz survey data in the TIFR GMRT Sky Survey Alternative Data Release (TGSS
ADR), the 10% uncertainty used in TGSS ADR does not appear to be vetted well
on a case by case basis and can be considerably larger for individual sources;
15% uncertainty is a more prudent choice (Hurley-Walker, 2017). The best case
is a low resolution Very Large Array (VLA) observation that does not resolve
out the diffuse lobe flux density (such as L-band observations). For this best
case, the uncertainty in the flux density measurements is 5% based on the VLA
manual333located at
https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/fdscale,
see also (Perley and Butler, 2013). High frequency measurements are difficult
to find because both ATCA and VLA will resolve out lobe flux density.

Figure 1: This wide bandwidth ILT image provides high sensitivity and is well-suited for the detection of diffuse lobe flux. The center frequency is 53.4 MHz and the bandwidth is 48.9 MHz. The red contour levels are in a linear scale of 2 Jy increments, 1.6Jy, 3.6 Jy, 5.6 Jy ,… 31.6Jy. The dashed-blue contour levels are -3$\sigma_{\rm{rms}}$, -4$\sigma_{\rm{rms}}$, -5$\sigma_{\rm{rms}}$ where $\sigma_{\rm{rms}}$ =0.22 Jy. The rms noise is driven primarily by calibration errors (Groeneveld et al., 2021). The cross is the Gaia EDR3 optical position (Gaia Collaboration et al., 2020). This is the origin of the image. The restoring beam FWHM is represented by the ellipse in the lower left hand corner. The dashed light blue line is an approximate symmetry axis used to estimate arm length asymmetry in the source in Section 5.1. Table 1: Radio Data for 3C298 $\nu_{\rm{obs}}$ | $\log{\nu}$ | Flux | Telescope | Absolute | References
---|---|---|---|---|---
Observed | Rest | Density |  | Flux Density |
Frequency | Frame |  |  | Scale |
(MHz) | (Hz) | (Jy) |  | Factor |
Integrated | Flux | Density |  |  |
26.3 | 7.81 | $54.59\pm 13.65$ | Clark Lake | 1.03 | Viner and Erickson (1975)
34.0 | 7.92 | $73.58\pm 21.00$ | Dutch Array of LOFAR | 0.98 | Groeneveld et al. (2021)
38.0 | 7.97 | $84.68\pm 21.17$ | Large Cambridge Interferometer | 1.16 | Kellermann et al. (1969)
44.0 | 8.03 | $78.58\pm 22.00$ | Dutch Array of LOFAR | 0.98 | Groeneveld et al. (2021)
53.5 | 8.12 | $98.10\pm 26.00$ | Dutch Array of LOFAR | 0.98 | Groeneveld et al. (2021)
60.0 | 8.17 | $86.30\pm 9.97$ | LOFAR (AART-FAAC) | 1.00 | Kuiack et al. (2019)
63.0 | 8.19 | $108.89\pm 28.00$ | Dutch Array of LOFAR | 0.98 | Groeneveld et al. (2021)
73.0 | 8.25 | $101.04\pm 26.00$ | Dutch Array of LOFAR | 0.98 | Groeneveld et al. (2021)
73.8 | 8.26 | $97.7\pm 9.77$ | VLA | 1.00 | Lane et al. (2014)
150 | 8.56 | $59.59\pm 8.94$ | GMRT | 1.00 | Intema et al. (2017); Hurley-Walker (2017)
160 | 8.59 | $63.20\pm 9.48$ | Culgoora Array | 1.00 | Kühr et al. (1981)
178 | 8.64 | $52.30\pm 7.85$ | Large Cambridge Interferometer | 1.00 | Kühr et al. (1981)
327 | 8.90 | $30.00\pm 3.00$ | VLA | 1.00 |  VLA Calibrator Listaahttps://science.nrao.edu/facilities/vla/observing/callist
408 | 9.00 | $23.36\pm 2.34$ | Molonglo Telescope | 1.00 | Large et al. (1981)
1400 | 9.53 | $6.10\pm 0.31$ | VLA D-array | 1.00 | Condon et al. (1998)
1500 | 9.56 | $5.80\pm 0.29$ | VLA C and D-arrays | 1.00 |  VLA Calibrator Listaahttps://science.nrao.edu/facilities/vla/observing/callist
1600 | 9.59 | $5.40\pm 0.27$ | VLA A-array | 1.00 | Akujor and Garrington (1995)
2640 | 9.81 | $2.89\pm 0.29$ | Effelsberg 100-m | 1.00 | Mantovani et al. (2009)
4850 | 10.07 | $1.57\pm 0.16$ | Parkes 64 m | 1.00 | Griffiths et al. (1995)
8350 | 10.31 | $0.79\pm 0.08$ | Effelsberg 100-m | 1.00 | Mantovani et al. (2013)
8870 | 10.34 | $1.22\pm 0.12$ | Parkes 64 m | 1.00 | Shimmins and Wall (1973)
10070 | 10.42 | $1.03\pm 0.10$ | NRAO 140-ft | 1.00 | Kellermann and Pauliny-Toth (1973)
14900 | 10.56 | $0.69\pm 0.07$ | MPIfR 100-m | 1.00 | Genzel et al. (1976)
East Lobe |  |  |  |  |
55.0 | 8.13 | $52.92\pm 13.23$ | International LOFAR | 0.98 | Groeneveld et al. (2021)
327 | 8.90 |  $>8.55$ bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | Global VLBI | 1.00 | Fanti et al. (2002); Dallacasa et al. (2021)
1660 | 9.61 | $2.23\pm 0.22$ | MERLIN | 1.00 | Spencer et al. (1989)
4993 | 10.09 |  $>0.51$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | MERLIN | 1.00 | Ludke et al. (1998)
8414 | 10.31 |  $>0.28$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | VLA A-array | 1.00 | Akujor and Garrington (1995)
14965 | 10.56 |  $>0.12$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | VLA A-array | 1.00 | van Breugel et al. (1992)
West Lobe |  |  |  |  |
55.0 | 8.13 | $22.54\pm 5.64$ | International LOFAR | 0.98 | Groeneveld et al. (2021)
327 | 8.90 |  $>10.73$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | Global VLBI | 1.00 | Fanti et al. (2002); Dallacasa et al. (2021)
1660 | 9.61 | $2.00\pm 0.20$ | MERLIN | 1.00 | Spencer et al. (1989)
4993 | 10.09 |  $>0.35$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | MERLIN | 1.00 | Ludke et al. (1998)
8414 | 10.31 |  $>0.16$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | VLA A-array | 1.00 | Akujor and Garrington (1995)
14965 | 10.56 |  $>0.05$bbA significant amount of lobe flux density is resolved out. Thus, this is a lower bound. | VLA A-array | 1.00 | van Breugel et al. (1992)
Core + Jet |  |  |  |  |
327 | 8.90 | $0.83\pm 0.12$ | Global VLBI | 1.00 | Fanti et al. (2002); Dallacasa et al. (2021)
1660 | 9.61 | $0.88\pm 0.09$ | MERLIN | 1.00 | Spencer et al. (1989)
4993 | 10.09 | $0.49\pm 0.05$ | MERLIN | 1.00 | Ludke et al. (1998)
8414 | 10.31 | $0.43\pm 0.04$ | VLA A-array | 1.00 | Akujor and Garrington (1995)
14965 | 10.56 | $0.27\pm 0.04$ | VLA A-array | 1.00 | van Breugel et al. (1992)
22500 | 10.74 | $0.24\pm 0.04$ | VLA A-array | 1.00 | van Breugel et al. (1992)

###  2.1 Low frequency Integrated Flux Densities

Low frequency observations were an important part of the early radio
observations of extragalactic radio sources, including observations at
frequencies $<100$ MHz. There are three major complicating issues, ionospheric
propagation effects, the absolute flux density scale and the blending of
sources in the low resolution telescopes. The ionospheric correction is the
most deleterious. In particular, the varying index of refraction in both
position and time creates a time varying shift and blurring of observed images
and the associated phase delays wreak havoc on radio-interferometric
observations (de Gasperin et al., 2018). The first comprehensive study of 3C
sources at low frequency was the 38 MHz data presented in (Kellermann et al.,
1969). However, the absolute flux density scale was called into question in
later studies due in large part to the drift in the brightness of the
supernova remnant, Cas A, and the lack of well characterized flux density
calibrators at low frequency (Roger et al., 1973). They determined that the
absolute flux densities in Kellermann et al. (1969) were low by 18%. A less
well known 26.3 MHz study reanalyzed the Roger et al. (1973) conclusion using
a deep survey with the Clark Lake telescope (Viner and Erickson, 1975). The
Clark Lake telescope had considerably higher resolution than the Penticon
telescope ($\approx 0.5\ \rm{deg}^{2}$ compared to $\approx 2\ \rm{deg}^{2}$)
used in (Roger et al., 1969, 1973). They found that the agreement with
Penticon was excellent if only the sources with no confusion from nearby
sources in the Penticon field were used. If the entire Penticon sample was
used (including confused fields) the Penticon flux density scale was 5%
higher. Regardless, the Penticon flux density scale has been the most
referenced calibration scale to this day and is used by the LOFAR team (Scaife
and Heald, 2012). Recently, this flux density scale was re-examined (Perley
and Butler, 2017). Examining their non-variable calibrators (neglecting 3C
380) suggests that the Roger et al. (1973) scale is 2% high, including the
case of 3C 196 which is the absolute flux density calibrator for 3C 298. The
next to last column of Table 1 transforms all the archival data and the LOFAR
data to the Perley and Butler (2017) absolute flux density scale (the scale
factor). The only reliable $\sim 20$ MHz measurement of 3C 298 is the high
resolution Clark Lake measurement (Viner and Erickson, 1975). The radio
emission from the cluster Abel 1890 gets blended into lower resolution fields
used in other studies (Roger et al., 1969).

Note that the only scale factors different from 1.00 in Table 1 are at low
frequency. The Kellermann et al. (1969) observations have the largest scale
factor correction. The other low frequency scale factors differ only by a few
percent from unity. The Large Cambridge Interferometer observations at 38 MHz
are likely more uncertain than the 5% - 15% in Kellermann et al. (1969), even
after the scale correction factor is applied. The resolution of the telescope
is insufficient to resolve 3.7 Jy of VLA Low-Frequency Sky Survey (VLSS)
background sources at 74 MHz that were not de-blended (Lane et al., 2014). The
spectral indices from 74 MHz to 38 MHz of the background sources are unknown,
so there is no robust post-processing de-blending algorithm. We incorporate
the uncertainty introduced by the inability to de-blend known background
sources by conservatively choosing a large overall uncertainty of 25%, similar
to the LOFAR uncertainties in (Groeneveld et al., 2021).

###  2.2 LOFAR Observations

To properly characterize the lobes, one requires observations at multiple low
frequencies with high resolution in order to detect all the diffuse flux and
resolve it into two distinct components. This was impossible until recently
with the development of the International LOFAR Telescope (ILT), in particular
the Low-Band Antenna, the LBA (van Haarlem, 2013). In 2020, an observation of
8 hours duration was performed in the LBA-OUTER configuration using the outer
48 of 96 antennae in each Dutch station. More details can be found in
Groeneveld et al. (2021). Figure 1 is a remarkable previously unpublished high
sensitivity LBA-OUTER image obtained at the band center of 53.4 MHz. The high
sensitivity is achieved by using the full LBA-OUTER bandwidth of 48.9 MHz. It
is this new image and the LOFAR data in Groeneveld et al. (2021) that
motivates our new detailed analysis of the radio lobes and confirms the 1.66
GHz MERLIN detection of a 2.”5 linear size.

The Amsterdam ASTRON Radio Transient Facility And Analysis Centre (AART-FAAC),
a parallel computational back-end to LOFAR, is the source of the 60 MHz data
in Table 1. It processes data from six stations of the Dutch LBA-Outer
configuration. It was concluded that the absolute flux density of these
measurements is accurate to $10\%$ (Kuiack et al., 2019). There are about 5 Jy
of VLSS (74 MHz) background sources that are not resolved by AART-FAAC (Lane
et al., 2014). Thus, the 60 MHz observation is chosen to have an uncertainty
of 5 Jy added in quadrature with the $10\%$ estimate of Kuiack et al. (2019)
in order to account for possible errors due to potential source blending. We
included the flux density of each lobe separately from the 55 MHz ILT image in
Table 1 (Groeneveld et al., 2021). More details of the ILT observations can be
found in (Groeneveld et al., 2021). The uncertainty in the estimated ILT flux
density of 3C 298 in Groeneveld et al. (2021) and Table 1 are largely
calibration errors rather than errors inherent to the flux density scale.

##  3 Synchrotron Self-Absorbed Homogeneous Plasmoids

A high resolution 5 GHz MERLIN (0.05 mas synthesized beam) image reveals a
detailed structure beyond the two lobes indicated in Figure 1 (Ludke et al.,
1998). There is a core that dominates with higher frequency very long baseline
interferometry (VLBI) and is also prominent in the MERLIN image (van Breugel
et al., 1992). There is a jet emerging from the core towards the eastern lobe.
The jet surface brightness vanishes as it propagates away from the core and
then reveals itself again as it enters the eastern lobe. To even partially
resolve the jet requires a resolution of $<200$ mas. Thus, observations that
are capable of detecting the diffuse lobe flux are incapable of also detecting
the jet and vice versa. We consider the source as consisting of three regions
(or components). The western lobe, the core plus easterly directed jet, and
the eastern lobe that includes the small piece of the jet as it enters the
lobe. Our primary interest in determining the energetics of the radio source
will be to estimate the energy stored in the luminous radio lobes. A simple
homogeneous spherical volume model or plasmoid has historically provided an
understanding of the spectra and the time evolution of astrophysical radio
sources (van der Laan, 1966). Single zone spherical models are a standard
technique even in blazar jet calculations out of practical necessity
(Ghisellini et al., 2010). We have used this formalism to study a panoply of
phenomena, major flares in a Galactic black hole, a $\gamma$-ray burst and
flares in a radio quiet quasar (Punsly, 2012, 2019; Reynolds et al., 2009,
2020). Most importantly, we used this method in Punsly et al. (2020a) to study
the radio lobes in the super-luminous CSS radio quasar, 3C 82 (which should be
consulted for more details of the calculational method). The synchrotron self
absorbed (SSA) turnover provides information on the size of the region that
produces the preponderance of emission. This is useful because Figure 1 is
resolution limited and provides no fine details of the emission regions.
Furthermore, these models do not need to invoke equipartition in order to
produce a solution.

These homogeneous models produce a simple to parameterize spectrum. A SSA
power law for the observed flux density, $S_{\nu_{\rm{obs}}}$, is the solution
to the radiative transfer in a homogeneous medium such as a uniform spherical
volume (Ginzburg and Syrovatskii, 1965; van der Laan, 1966):

$\displaystyle
S_{\nu_{\mathrm{obs}}}=\frac{S_{\mathrm{o}}\nu_{\mathrm{obs}}^{-\alpha}}{\tau(\nu_{\mathrm{obs}})}\times\left(1-e^{-\tau(\nu_{\mathrm{obs}})}\right)\;,\;\;\tau(\nu_{\mathrm{obs}})=\overline{\tau}\nu_{\mathrm{obs}}^{(-2.5+\alpha)}\;,$
(1)

where $\tau(\nu)$ is the SSA opacity, $S_{\mathrm{o}}$ is a normalization
factor, $\overline{\tau}$ is a constant, and $\nu_{\rm{obs}}$ designates the
observed frequency as opposed to $\nu$ which we use to designate the frequency
in the plasma rest frame. The spectral index of the power law is defined in
the optically thin region of the spectrum by
$S_{\nu_{\mathrm{obs}}}=S_{\mathrm{o}}\nu_{\mathrm{obs}}^{-\alpha}$.

Figure 2: The broad-band radio spectrum of 3C 298 is fit by three SSA power
laws in the top panel. The radio data are from Table 1. Weighted residuals, as
defined by Equation (2), are minimized for $\nu_{obs}\leq 4.85$ GHz
(log[Frequency in Quasar Rest Frame] $\leq 10.1$ Hz). There are 22 total
measurements that contribute to the sum in Equation (2). Four of these are the
fitted lobe flux densities relative to the measured component flux densities.
18 are the sum of the fits (black-dashed curve) to the lobe flux densities and
the core-jet flux density (which contributes minimally in this frequency
range) relative to the integrated flux density measurements. The bottom panel
is a magnified view of the densely sampled low frequency region. The observed
frequencies of the data points are labeled in MHz in the bottom panel. The
optically thin power law tail of the core, east lobe and west lobe have
$\alpha=$ 0.52, 1.02 and 1.27, respectively in Equation (1) and
$\nu_{\rm{peak}}$ is at 1.4 GHz, 95 MHz and 240 MHz in the quasar rest frame,
respectively.

##  4 Fitting the Data with Three SSA Power Laws

Thus motivated, we approximate the total spectrum by three SSA power laws, one
for the western lobe, one for the eastern lobe, and one for the core plus jet.
We determine the three SSA power laws that, in combination, minimize the
residuals to the overall integrated spectral energy distribution. Since the
uncertainty of the measurements in Table 1 are significant, we need to account
for these in the calculation of the residuals of the fit to the data. It makes
sense in curve fitting to assign the least amount of weight to points that are
the least reliable. This is properly accomplished statistically by weighting
each point by the inverse square of its standard error (Reed, 1989). To
incorporate this notion, we define a weighted residual,
$\sigma_{\rm{res}}^{2}$,

$\sigma_{\rm{res}}^{2}=\frac{1}{N}\sum_{i=1}^{N}\left[\frac{(S_{i}-f_{i})^{2}}{\sigma_{i}^{2}}\right]\;,$
(2)

where, “i” labels one of the $N$ measured flux densities from Table 1, $f_{i}$
is the expected value of this flux density from the fitted curve, $S_{i}$ is
the measured flux density and $\sigma_{i}$ is the uncertainty in this
measurement. This quantity compares the fractional error of the fit to the
data to that which is expected to occur just form measurement induced scatter.
The smaller the value of $\sigma_{\rm{res}}^{2}$, the better that a particular
fit agrees with the data.

We minimize the weighted residuals of the fit to the data,
$\sigma_{\rm{res}}^{2}$, for 22 points in Table 1 (the 18 total flux density
points with $\nu_{\rm{obs}}\leq 4.85$ GHz and the 4 flux densities for the
lobes, LOFAR 55 MHz and MERLIN 1.66 GHz ). Since the total flux density is
approximately the sum of the two lobe flux densities (the core-jet
contribution is small in Figure 2 at $\nu_{obs}\leq 4.85$ GHz), the 18
$\nu_{\rm{obs}}\leq 4.85$ GHz total flux densities provide significantly more
constraints on the lobe spectra than if we merely had a limited number of flux
densities measured per lobe. The lower bounds are not used in the minimization
of the residuals and are sufficiently low that they would not provide
meaningful additional constraints. The spectral index of the optically thin
power laws of the lobes fit the total flux density data tightly between 327
MHz and 1.6 GHz. The cutoff of data suitable for fitting at
$\nu_{\rm{obs}}\leq 4.85$ GHz is motivated by the large core-jet contribution
to the total flux density at higher frequencies that masks the pure lobe
contribution. Furthermore, the core-jet contribution appears to create some
scatter to a smooth monotonic fit as evidenced by Table 1 and Figure 2. This
might represent intrinsic variability (compare the integrated flux density
entry for 8350 MHz with that of 8870 MHz in Table 1), but the data is not of
sufficiently quality to make such a claim at this point in time 444The best
way to determine this might be with a few years of monitoring with JVLA in
D-array (so as not to resolve out flux) at X-band and U-band.. Our primary
scientific goal is to fit the radio lobes, so total flux density measurements
that are strongly influenced by potential core variability are of little value
to this process. In summary, there are 3 parameters for the SSA power law of
each lobe. We are using 22 observational data points to constrain 6 total
parameters by minimizing the residuals in Equation (2). The best fit is
displayed in Figure 2. Note that the SSA turnover of the east lobe is real; an
extrapolation of the power law seen at higher frequencies would grossly
grossly over produce the flux density at 26.3 MHz and 34 MHz (see the bottom
panel of Figure 2).

Figure 3: The details of the solution with $E_{min}=m_{e}c^{2}$ for the fit to
the radio spectrum in Figure 2. The curves in the panels are the graphical
manifestation of the infinite 1-D set of solutions for each lobe. The top two
panels are the dependence of $E(\mathrm{lm})$ on the plasmoid radius, $R$, for
the western lobe (left) and eastern lobe, (right). The lower two rows are the
dependence of $E(\mathrm{lm})$ on the total number of particles in the lobes
and the magnetic field strength. The minimum energy ($E(\mathrm{lm})$) in
these solutions is the same in both lobes to within 3%.

##  5 Physical Realizations of the Lobe SSA Power Laws

The spherical homogeneous plasmoid models employed here have been described
many times elsewhere as noted above. We compile the physical equations in
Appendix A for ease of reference. More details can be found in Punsly et al.
(2020a), which will be referenced as needed in this abbreviated discussion. It
has been argued that leptonic lobes are favored in the more luminous FRII
(Fanaroff Riley II) radio sources (Croston et al., 2018; Fanaroff and Riley,
1974). This model will be our starting point, but we will consider protonic
lobes as well, subsequently. From Appendix A, mathematically, the theoretical
determination of the flux density, $S_{\nu}$, of a spherical plasmoid depends
on 7 parameters: $N_{\Gamma}$ (the rest frame normalization of the lepton
number density spectrum), $B$ (rest frame magnetic field), $R$ (the radius of
the sphere in the rest frame), $\alpha$ (the spectral index of the power law),
$\delta$ (the Doppler factor), $E_{min}$ (the minimum energy of the lepton
energy spectrum) and $E_{max}$ (the maximum energy of the lepton energy
spectrum), yet there are only three constraints from the fit in Figure 2 for
each lobe, $\overline{\tau}$, $\alpha$ and $S_{o}$, it is an under-determined
system of equations. Most of the particles are at low energy, so the solutions
are insensitive to $E_{max}$. For a slow moving lobe, $\delta=1$. $E_{min}$ is
not constrained strongly by the data, so we start with an assumed $E_{min}=1$
then subsequently explore the ramifications of letting $E_{min}$ increase. One
has four remaining unknowns, $N_{\Gamma}$, $B$, $R$ and $\alpha$ in the
physical models and three constraints from observations, $\overline{\tau}$,
$\alpha$ and $S_{o}$, for each model. Thus, there are an infinite one-
dimensional set of solutions in each lobe that results in the same spectral
output.

The primary discriminant for a meaningful solution is the physical
requirement: Over long periods of time, we assume that there is an approximate
bilateral symmetry in terms of the energy ejected into each jet arm. Thus, we
require the internal energy, $E(\mathrm{lm})$ (defined in Appendix A: Equation
A(9)) to be approximately equal in both lobes in spite of the fact that the
spectral index is not.

Figure 3 describes the physical parameters of the (infinite 1-D set of) models
that produce the fit in Figure 2. The top panels show the dependence of
$E(\mathrm{lm})$, the lepto-magnetic energy (internal lepton energy and
magnetic energy), on $R$ (the lobe radius). The middle row displays the
dependence of $E(\mathrm{lm})$ on the total number of particles in the lobe,
$\mathcal{N}_{e}$. The bottom row shows the dependence on the turbulent
magnetic field strength. The two independent lobe solutions have minimum
energies ($E(\mathrm{lm})$) that agree within a few percent. Based on the lone
physical requirement of the solution above (long term bilateral energy
ejection symmetry), the minimum energy solution is significant. The minimum
energy of the western (eastern) lobe is $E(\mathrm{lm})=8.69\times
10^{59}\,\rm{ergs}$ ($E(\mathrm{lm})=8.44\times 10^{59}\,\rm{ergs}$). We
believe this agreement to be significant and not a coincidence of the
mathematics for two reasons. First, this assertion is strongly favored based
on the finding of Punsly (2012) that ejections from the X-ray binary, GRS
1915+105, evolve towards the minimum energy configuration as they expand away
from the source. Secondly, and more on point, the detailed X-ray studies of FR
II radio sources indicate that the lobes are generally near minimum energy or
perhaps slightly dominated by the particle energy (Ineson et al., 2017).

###  5.1 Converting Stored Lobe Energy into Jet Power

There is a direct physical connection between $E(\mathrm{lm})$ and the long-
term time-averaged power delivered to the radio lobes, $\overline{Q}$. If the
time for the lobes to expand to their current separation is $T$, in the frame
of reference of the quasar, then the intrinsic jet power is approximately

$\overline{Q}\approx E(\mathrm{lm})/T$ (3)

This expression ignores the work done by the inflating radio source as it
displaces the galactic medium. For powerful sources like 3C 298 and 3C 82, the
lobes are over-pressurized relative to an elliptical galaxy environment and
the work of expansion is negligible compared to $E(\mathrm{lm})$ (Punsly et
al., 2020a; Mathews and Brighenti, 2003).

The mean lobe advance speed, $v_{\rm{adv}}$, can be found from the arm length
asymmetry in Figure 1, if one assumes intrinsic bilateral symmetry and there
is inconsequential disruption of jet propagation from interactions with the
enveloping medium. The system appears very linear in Figure 1 and in the
MERLIN observations at 1.66 GHz and 5 GHz (Spencer et al., 1989; Ludke et al.,
1998). Thus, this might be a system where arm length ratio is a valid method
of estimating $v_{\rm{adv}}$. The arm length ratio of approaching lobe,
$L_{\rm{app}}$, to receding lobe, $L_{\rm{rec}}$ (Ginzburg and Syrovatskii,
1969; Scheuer, 1995), is

$\displaystyle
R=\frac{L_{\rm{app}}}{L_{\rm{rec}}}=\frac{1+(v_{\rm{adv}}/c)\cos{\theta}}{1-(v_{\rm{adv}}/c)\cos{\theta}}\;,\rm{where}$
$\displaystyle
L_{\rm{app}}=\frac{(v_{\rm{adv}}T)\sin{\theta}}{1-(v_{\rm{adv}}/c)\cos{\theta}}\;:\;L_{\rm{rec}}=\frac{(v_{\rm{adv}}T)\sin{\theta}}{1+(v_{\rm{adv}}/c)\cos{\theta}}\;,$
(4)

where $T$ is the time measured in the quasar rest frame and projected length
on the sky plane of an earth observer (corrected for cosmological effects) is
$\mathcal{L}\equiv L_{\rm{app}}+L_{\rm{rec}}$. The arm length ratios were
computed in Scheuer (1995) using the lowest contour level in the images. We
choose the second lowest contour in Figure 1, for the reasons given below, and
find $R\approx 1.35$,

  * •

the outer contour has an exaggerated distortion not seen in the more robust
higher contour levels,

  * •

the second lowest contour is about one-half of the synthesized beam width (the
resolution limit of the image) from the lowest contour and

  * •

this method applied to the MERLIN 1.66 GHz image in Spencer et al. (1989) also
yields $R\lesssim 1.4$.

Using the second lowest contour, the linear size of the source on the sky
plane is 2$\farcs$8; using the lowest contour in Figure 1, the linear size is
3$\farcs$1\. This angle is slightly larger than the 2$\farcs$5 found by
Spencer et al. (1989); however, even with the best efforts to correct for
ionospheric scattering, we expect some blurring in the image. We assume that
the modest blurring is fairly uniform over the small image and does not
significantly affect the $R$ estimate.

For a quasar, we can eliminate the possibility of a highly oblique line of
sight (LOS) to the jet. The LOS to the jet in quasars is believed to be
$<45^{\circ}$ with an average of $\approx 30^{\circ}$ (Barthel, 1989). Since
3C 298 is very lobe dominated, one does not expect a LOS near the low end of
this quasar range (Wills and Browne, 1986). In accord with this conclusion, a
variability study consisting of thirty-eight observations at 408 MHz spread
out over 19 years found no evidence of variability, which strongly disfavors a
blazar-like LOS, $<10^{\circ}$ (Bondi et al., 1996)555Note that in Section 4,
we remarked on possible modest variability above 8 GHz. Even though this is a
tentative finding that is not verified, it does not indicate that a hidden
blazar is necessarily present (as would be the case if a factor of a few
variability were detected). In view of the thirty-eight observations at 408
MHz with the same telescope noted here, the modest variability at higher
frequency requires rigorous verification to be considered more than
tentative.. In our adopted cosmology, at the distance of 3C298 the scale is
8.58 kpc per arc-second. From Equation (4), with $R$=1.35, and assuming
$20^{\circ}<\rm{LOS}<40^{\circ}$

$v_{\rm{adv}}\approx 0.18c\pm 0.02c\;\rm{and}\;9.59\times 10^{12}\
\rm{sec}<T<2.22\times 10^{13}\ \rm{sec}\;.$ (5)

The value of $v_{\rm{adv}}$ in Equation (5) agrees with the mean value of
$v_{\rm{adv}}$ estimated for a sample of relatively straight 3C CSS quasars
(Punsly et al., 2020a). The large spread in $T$ in Equation (5) arises from
the uncertainty in the LOS. Inserting Equation (5) into Equation (3) with
$E(\mathrm{lm})=1.71\times 10^{60}\rm{ergs}$ from the minimum energy solutions
in Figure 3 yields

$7.73\times 10^{46}\rm{ergs/sec}<\overline{Q}<1.79\times 10^{47}\ \rm{erg\
sec}^{-1}\;.$ (6)

We compare our estimate with the well-known estimates of $\overline{Q}$ that
is based on the spectral luminosity at 151 MHz per steradian, $L_{151}$. This
method is more suited to a relaxed classical double radio source and might not
be applicable to CSS sources in general (Willott et al., 1999). $\overline{Q}$
is given as a function of $f$ and $L_{151}$ in Figure 7 of Willott et al.
(1999),

$\overline{Q}\approx 3.8\times 10^{45}fL_{151}^{6/7}\ \rm{erg\ s}^{-1}\;,$ (7)

The parameter $f$ was introduced to account for deviations from 100% filling
factor, minimum energy, a low frequency cut off at 10 MHz, the jet axis at
$60^{\circ}$ to the line of sight, and no protonic contribution as well as
energy lost expanding the lobe into the external medium, back flow from the
head of the lobe and kinetic turbulence (Willott et al., 1999). The exponent
on $f$ in Equation (7) is 1, not 3/2 as was previously reported (Punsly et
al., 2018). The quantity $f$ has been estimated to lie in the range of
$10<f<20$ for most FRII radio sources (Blundell and Rawlings, 2000). Using
$L_{151}$ from Table 1 and $10<f<20$

$\overline{Q}=2.18\pm 0.71\times 10^{47}\ \rm{erg\ s}^{-1}\;.$ (8)

The uncertainty in Equation (8) corresponds to the range of $10<f<20$. The
marginal agreement between Equations (6) and (8) is reasonable considering all
the unknown dynamics. De-projecting a linear size of 2$\farcs$5 with
$20^{\circ}<\rm{LOS}<40^{\circ}$ yields $\sim 30-60$ kpc. The larger value of
Equation (8) compared to Equation (6) does support the notion that compact
sources will tend to be over-luminous relative to their jet power due to
interactions with the galactic environment (Barthel and Arnaud, 1996; Willott
et al., 1999). Formally, there is an overlap in the values of $\overline{Q}$
if the uncertainty is considered which is remarkable considering that the two
methods are independent and are based on different assumptions.

The result is not strongly dependent on the choice of the second lowest
contour of Figure 1 for the computation of $R$ as opposed to the lowest
contour in (Scheuer, 1995). Using the lowest contour in Figure 1, $R=1.38$ and
Equation (5) becomes

$v_{\rm{adv}}\approx 0.19c\pm 0.02c\ \ \ \ \rm{and}\ \ \ \ 1.02\times 10^{13}\
\rm{s}\ <T<\ 2.35\times 10^{13}\ \rm{s}\;.$ (9)

###  5.2 Assessing the $E_{min}\approx m_{e}c^{2}$ Assumption and Protonic
Content

We started the analysis of the solution space with two basic assumptions:

  * •

$E_{min}(\rm{West\,Lobe})=E_{min}(\rm{East\,Lobe})=m_{e}c^{2}$ and

  * •

The plasma is predominantly positronic, not protonic.

In this section, we examine the solutions when these assumptions are violated.

We explored the possibility of altering the low energy cutoff, by arbitrarily
setting $E_{min}(\rm{West\,Lobe})=E_{min}(\rm{East\,Lobe})=5m_{e}c^{2}$. In
this case $E_{\rm{lm}}(\rm{East\,Lobe})=1.45E_{\rm{lm}}(\rm{West\,Lobe})$ in
their minimum energy states. This ratio continues to increase as one raises
$E_{min}$. For a system that requires long term bilateral energy flux
symmetry, raising $E_{min}$ arbitrarily at least the west lobe must start
deviating significantly from its minimum energy state. The solution that we
have explored in Figure 3 has
$E_{min}(\rm{West\,Lobe})=E_{min}(\rm{East\,Lobe})=m_{e}c^{2}$. The solution
has bilateral symmetry in energy content, $E_{\rm{lm}}(\rm{West\,Lobe})\approx
E_{\rm{lm}}(\rm{East\,Lobe})$ if both lobes are near their minimum energy
state in Figure 3. This is a natural state of a relaxed plasmoid and radio
lobes in particular (Punsly, 2012; Ineson et al., 2017). There are no
unexplained spectral breaks or low energy cutoffs in the lepton spectra. Thus,
we consider this the most plausible solution, but we cannot rule out other
configurations.

If we assume protonic matter instead of positronic matter, the spectral fit in
Figure 2 remains unchanged and is created by electrons in the magnetic field.
A significant thermal proton population in FR II radio lobes has been argued
to be implausible based on pressure balance with the enveloping medium
(Croston et al., 2018). These are therefore cold protons. In this case,
consider the mass stored in the lobes based on Figure 3 for the minimum
energy, minimum $E(\mathrm{lm})$, solution, $M_{\rm{lobe}}=1.38\times
10^{8}M_{\odot}$. For the average $T$ in Equation (5), this mass corresponds
to 274 $M_{\odot}$ on average that must be ejected a year in order to fill the
lobes with protonic matter. For the black hole mass $M_{bh}\approx 3\times
10^{9}M_{\odot}$ from Vayner et al. (2017), the lobes would need to be fed at
$>4$ times the Eddington rate in order to be populated with protonic matter.
In Section 9, we find a viral $M_{bh}$ even smaller than this value. As with
3C 82, the baryon ejection rate must greatly exceed the accretion rate for
protonic lobes to exist. We come to the conclusion that the protonic lobe
solutions are not highly plausible.

Figure 4: The SED of 3C 298 showing the prominent emission lines. The data are
presented in terms of frequency in the cosmological frame of reference of the
quasar. The spectral energy is computed in the quasar reference frame in terms
of the spectral luminosity, $L_{\nu}$, as $\nu L_{\nu}$. The SED was corrected
for Galactic extinction. The SED combines three spectra, the HST archival
spectrum, and the new HET LRS2 and VIRUS spectra obtained for the purposes of
this paper. The broad emission lines are presented in detail with fits in
Appendix B.

##  6 The Ultraviolet Spectrum

Our motivating interest in the UV spectrum is to characterize the possibility
of a strong blue wing in CIV that might be indicative of a high ionization
wind. An exaggerated blue wing in CIV is evident in the high signal-to-noise
ratio spectrum of Anderson et al. (1987). Unfortunately, these data are not
flux calibrated. Two spectrographs were employed on the upgraded 10 m Hobby-
Eberly Telescope (HET, Hill et al. 2021) in order to capture a spectrum from
the blue wing of CIV (at 3500 Å) to [OII] (at 9100 Å). The short wavelength
portion of the spectrum is covered by Visible Integral-Field Replicable Unit
Spectrograph (VIRUS, Hill et al. 2021). The long wavelength portion of the
spectrum is covered by an observation with the new Low Resolution Spectrograph
2 (LRS2, Chonis et al. 2016, Hill et al. 2022 in prep.) to obtain spectra on
April 28, UT. We used both units of the integral field spectrograph, LRS2-B
and LRS2-R with the target switched between them on consecutive exposures.
Each unit is fed by an integral field unit with 6x12 square arcsec field of
view, 0.6′′ spatial elements, and full fill-factor, and has two spectral
channels. LRS2-B has two channels, UV (3700 Å - 4700 Å) and Orange (4600 Å -
7000 Å), observed simultaneously. LRS2-R also has two channels, Red (6500 Å -
8470 Å) and Far-red (8230 Å - 10500 Å). The observations were split into two
1200 second exposures, one for LRS2-B and one for LRS2-R. The image size was
1$\farcs$38 full-width half-maximum (FWHM). The spectra from each of the four
channels were processed independently using the HET LRS2 pipeline,
Panacea666https://github.com/grzeimann/Panacea (Zeimann et al. 2022, in
prep.). The LRS2 data processing followed that for 3C82 and details can be
found in Punsly et al. (2020a).

VIRUS is a highly replicated, fiber-fed integral field spectrograph. The
entire VIRUS instrument consists of 156 integral field low-resolution
(resolving power, $R\sim$800) spectrographs, arrayed in 78 pairs. Each of the
78 VIRUS units is fed by an integral field unit (IFU) with 448 $1\farcs 5$
fibers covering 51${}^{\prime\prime}\times$51′′ area. The spectrographs have a
fixed wavelength coverage of 3500 $<\lambda<$ 5500 Å. The IFUs are arrayed in
a grid pattern in the 18′ field of view of HET with a $\sim$1$/$4.5 fill-
factor and VIRUS captures 34,944 spectra for each exposure at full compliment.
An observation consists of three dithered exposures with small position
offsets to fill in the gaps between the fibers in the IFUs. 3C298 was observed
on one of the VIRUS IFUs on June 21, 2019 UT for 3x360 seconds total exposure
time. Image quality was 1.55$\arcsec$ FWHM. The VIRUS data were reduced with
the pipeline Remedy777https://github.com/grzeimann/Remedy (Zeiman et al. 2022,
in prep.). There are multiple field stars in the VIRUS field of view with
g-band calibrations from Pan-STARRS (Chambers et al., 2019) Data Release 2
Stacked Object Catalog (PS-1 DR2, Flewelling et al. 2020) that provide direct
flux calibration of the VIRUS data; since there is overlap between the spectra
from the two spectrographs, the VIRUS observation anchors the flux density
calibration for the long wavelength portion of the spectrum from LRS2. With a
10% adjustment in the flux density of the LRS2 spectra, the independently
calibrated spectra from VIRUS and LRS2-B agree to 1% in the overlap region
(3700 $<\lambda<$ 5500 Å).

The spectrum is presented in the form of a spectral energy distribution in
Figure 4, which is corrected for Galactic extinction. The extinction values in
the NASA Extragalactic Database (NED) were used in a Cardelli et al. (1989)
model; $A_{V}=0.08$ and $R_{V}=3.1$. Figure 4 also includes the Hubble Space
Telescope (HST) Faint Object Spectrograph, G270H spectral data (from August
15, 1996) downloaded from NED (Becthold et al., 2002).

Table 2: Ultraviolet Broad Emission Line Fits Line | VBC | VBC | VBC | BLUE | BLUE | BLUE | BC | BC | Total BEL
---|---|---|---|---|---|---|---|---|---
|  PeakaaPeak of the fitted Gaussian component in km sec-1 relative to the quasar rest frame. A positive value is a redshift. | FWHM | Luminosity |  PeakaaPeak of the fitted Gaussian component in km sec-1 relative to the quasar rest frame. A positive value is a redshift. | FWHM | Luminosity | FWHM | Luminosity | Luminosity
|  km s-1 |  km s-1 |  ergs s-1 |  km s-1 |  km s-1 |  ergs s-1 |  km s-1 |  ergs s-1 |  ergs s-1
Ly$\alpha$ $\lambda 1216$ | 5246 | 9897 | $6.25\times 10^{44}$ | -3381 | 8208 | $8.18\times 10^{44}$ | 4380 | $9.57\times 10^{44}$ | $2.40\times 10^{45}$
NV$\lambda 1240$ | 5212 | 9897 | $7.70\times 10^{43}$ | -5075 | 3425 | $1.11\times 10^{44}$ | 4800 | $1.09\times 10^{44}$ | $2.97\times 10^{44}$
CIV$\lambda 1549$ | 2130 | 15000 | $3.25\times 10^{44}$ | -2460 | 5907 | $2.75\times 10^{44}$ | 3890 | $3.19\times 10^{44}$ | $9.20\times 10^{44}$
HeII$\lambda 1640$ | 2202 | 15000 | $1.77\times 10^{44}$ | -1573 | 6376 | $2.63\times 10^{43}$ | 3890 | $3.67\times 10^{43}$ | $2.12\times 10^{44}$
AlIII$\lambda 1854$ | … | … | … | … | … | … | 2810 | $1.13\times 10^{43}$ | $1.13\times 10^{43}$
AlIII$\lambda 1863$ | … | … | … | … | … | … | 2810 | $8.97\times 10^{42}$ | $8.97\times 10^{42}$
SiIII]$\lambda 1892$ | … | … | … | … | … | … | 4014 | $7.88\times 10^{43}$ | $7.88\times 10^{43}$
CIII]$\lambda 1909$ | -157 | 6000 | $1.08\times 10^{44}$ | … | … | … | 4000 | $7.95\times 10^{43}$ | $1.87\times 10^{44}$
MgII$\lambda 2799$ | 182 | 10556 | $2.83\times 10^{44}$ | … | … | … | 2795 | $1.78\times 10^{44}$ | $4.60\times 10^{44}$

Table 2 provides standard three Gaussian component decompositions of the broad
emission lines (BELs): a broad component, “BC”, (also called the intermediate
broad line or IBL; Brotherton et al, 1994), an often redshifted, “VBC” (very
broad component following Sulentic et al., 2000) and “BLUE” a blueshifted
excess (Brotherton, 1996; Marziani et al., 1996; Sulentic et al., 2000). The
table is organized as follows. The line designation is defined in the first
column. The next three columns define the properties of the Gaussian fit to
the VBC, the shift of the Gaussian peak relative to the vacuum wavelength in
km sec-1, followed by the FWHM and line luminosity. Columns (5)-(7) are the
same for the BLUE. The BC FWHM and luminosity are columns (8) and (9). The
last column is the total luminosity of the BEL.

The decompositions are shown in Appendix B, after continuum subtraction. The
line fitting is challenged by various issues.

  * •

The Ly$\alpha$, NV blend has very strong narrow absorption features
throughout. As in Becthold et al. (2002), we incorporated significant spectral
smoothing to accentuate the line profiles. The strong absorption near zero
velocity makes segregating the narrow line component impossible. Thus, the
line decomposition is not exact, but we do not require precise knowledge of
the flux associated with each component.

  * •

The CIV, HeII blend also has strong zero velocity absorption. Again, no narrow
CIV line can be decomposed from the complex. However, there are mitigating
factors. The absorption is relatively narrow (FWHM $\sim$ 1000 km/s) so that
only the central part of the profile is affected. Most of the CIV core and of
the wings are free from contaminants, so that the broad component profile
appears well-defined. To take into account the deep absorption and the
blending of HeII, we resort to the above-mentioned, multi-component fitting
that has proven to be appropriate in case of prominent CIV without strong
absorption. This permits us to extrapolate the observed profile across the
absorption seen in 3C 298. The line flux uncertainty is also well-constrained,
since the narrow component of CIV is weak, accounting for 2-20% of the total
CIV flux in quasars (Marziani et al., 1996; Sulentic and Marziani, 1999).

  * •

The MgII background is highly complex and determining the continuum level is
not trivial. There is a rather typical, strong FeII$\lambda$2235-2670 feature
and a strong Balmer continuum. The high spectral resolution, high signal-to-
noise ratio, LRS2 spectrum was used for fitting these features that mask the
continuum level.

In spite of these limitations to the fitting process, a few general conditions
are evident. There is a significant blue excess in the Ly$\alpha$, NV, CIV,
and HeII BELs; no such excess appears in SiIII], CIII], and MgII. In radio
loud quasars, even though BLUE of CIV is often detectable, it is usually
significantly weaker than the red VBC (Punsly, 2010). Yet, the BLUE of the CIV
broad line in 3C298 is nearly as luminous as the red VBC, which is extreme for
a radio loud quasar.

Table 3: Emission Line Strengths Line | Total | Total |  HST CompositeaaTelfer et al. (2002) | EW |  HST CompositeaaTelfer et al. (2002) | EW
---|---|---|---|---|---|---
| Luminosity | Luminosity | Luminosity |  | EW | Ratio
|  ergs s-1 |  Relative to Ly$\alpha$ |  Relative to Ly$\alpha$ | Å | Å |
Ly$\alpha$ $\lambda 1216$ | $2.40\times 10^{45}$ | 1 | 1 | 59.3 | 91.8 | 0.65
NV$\lambda 1240$ | $2.97\times 10^{44}$ | 0.12 | 0.20 | 7.3 | 18.5 | 0.39
CIV$\lambda 1549$ | $9.20\times 10^{44}$ | 0.38 | 0.48 | 29.0 | 58.0 | 0.50
HeII$\lambda 1640$ | $2.57\times 10^{44}$ | 0.11 | 0.01 | 7.9 |  1.5eeTelfer et al. (2002) did not deblend the red wing of CIV and the HeII profile, attributing a large fraction of the flux between the two lines to a $\lambda$ 1600 Å feature. The resulting HeII equivalent width is therefore most likely severely underestimated. |  5.7eeTelfer et al. (2002) did not deblend the red wing of CIV and the HeII profile, attributing a large fraction of the flux between the two lines to a $\lambda$ 1600 Å feature. The resulting HeII equivalent width is therefore most likely severely underestimated.
AlIII | $2.03\times 10^{43}$ | 0.009 | 0.015 | 0.8 | 2.2 | 0.36
SiIII]+CIII] | $3.00\times 10^{44}$ | 0.13 | 0.13 | 12.1 | 19.7 | 0.62
FeII$\lambda$2235-2670 | $8.58\times 10^{44}$ | 0.36 | bbNot computed in Telfer et al. (2002) | $\sim 43$ | bbNot computed in Telfer et al. (2002) | bbNot computed in Telfer et al. (2002)
MgII$\lambda 2799$ | $4.86\times 10^{44}$ | 0.20 | 0.23 | 25.6 | 51.7 | 0.49
H$\alpha$+NII |  $1.86\times 10^{45}$ ccHirst et al. (2003) | 0.78 |  0.77ddNot an HST composite result. Value used in Celotti et al. (1997) for reference purposes. | … | … |
Sum | $7.40\times 10^{45}$ | 3.10 | N/A | N/A | N/A | N/A

Table 3 lists the emission line strengths. We compare these results to the
line strengths from an HST composite based on 184 quasars (Telfer et al.,
2002). In the second column, the line luminosity is slightly larger for some
lines (SiIII]+CIII], MgII and HeII) than in Table 2 because narrow line
contributions were added (since the Telfer et al. (2002) fits were total line
luminosity and we want to compare similar quantities) . Also some lines are
blended (Telfer et al., 2002). These changes are for comparison purposes to
Table 2 of (Telfer et al., 2002). A comparison of the line luminosity ratios
in columns (3) and (4) reveals that the line strength ratios are similar to
the HST composite values, which have estimated uncertainties in Table 2 of
Telfer et al. (2002) of less than $10\%$. The last three columns compare the
rest frame equivalent widths, EW, of 3C 298 and the HST composite, no
uncertainties were given in Telfer et al. (2002). The last column indicates
that most of the EWs are 40%-60% of the HST composite EWs. The broad line
region is much smaller than can be resolved with existing telescopes, so this
is an intrinsic difference between 3C 298 and most other quasars. The physical
origin of the weak BELs are discussed in Section 8. FeII$\lambda$2235-2670 is
quite prominent in the SED of Figure 3. From Table 3, the line strength ratio
L(FeII$\lambda$2235-2670)/L(MgII)$\approx 1.8$, close to the value of 2.2
determined from a Large bright Quasar Survey Composite (Baldwin et al., 2004).

Table 3 indicates that the line ratios of 3C 298 are typical of most quasars,
but the line strengths are weak compared to the strength of the UV continuum
(the big blue bump) (Telfer et al., 2002; Zheng et al., 1997). This result is
consistent with a disproportionately weak ionizing continuum relative to the
UV continuum. We explore this issue in Section 8.

Finally, in spite of the small EWs for most BELs, HeII is quite strong
compared to a typical quasar. A similar powerful CSS quasar, 3C82, also has
over-luminous HeII emission (Punsly et al., 2020a).

##  7 The Bolometric Luminosity of the Accretion Flow

We have sufficient information to construct an accurate SED for the accretion
flow, and we have numerous broad line estimates, so we directly compute the
bolometric luminosity of the accretion flow, $L_{\rm{bol}}$. We do not include
reprocessed radiation in the infrared from molecular clouds located far from
the active nucleus since doing so would be double counting the thermal
accretion emission that is reprocessed at mid-latitudes (Davis and Laor,
2011). There are three major contributors to $L_{\rm{bol}}$:

  1. 1.

The thermal emission from the accretion flow which has a broad peak in the
optical and UV

  2. 2.

The broad emission lines

  3. 3.

The X-ray power law (corona) produced by the accretion flow.

Figure 5: The continuum SED of 3C 298 obtained from the SED in Figure 4, after
the emission lines (fits given in Tables 2 and 3) were removed. We also
include archival 2MASS and GALEX data. The SED contains a well-defined thermal
component with steep declines in the IR and EUV. These steep declines are
extrapolated by the dashed red lines. The _Chandra_ luminosity is much higher
than that expected from an accretion disk corona. This favors a powerful jet
as the primary source of the emission.

###  7.1 The Thermal Continuum

Figure 5 includes data from the continuum of the SED in Figure 4. To construct
the BEL fits in Table 2, we determined the continuum levels at 1300 Å, 1700Å,
1970 Å, and 3000 Å. These SED points, plus two others estimated from Figure 4
at 1100 Å and 3700 Å appear in the continuum SED in Figure 5. These six points
accurately define the peak of the SED. To estimate the red end of the thermal
SED, we added three photometric measurements from the Two Micron Survey
(2MASS) that clearly delineate the 1 micron dip that is characteristic of
quasar spectra (Skrutskie et al., 2006). The J and H band points are a perfect
extrapolation of the power law from the UV found from our HET observations. We
extrapolate the power law plunge into the 1 micron dip with a dashed red line.

There are two Galaxy Evolutionary Explorer (GALEX) far UV (FUV) photometry
points at 1539 Å (631 Å, in the quasar rest frame) in the GALEX GR6/7 Data
Release888https://galex.stsci.edu/GR6. The All Sky Imaging Survey reported a
far UV AB magnitude of $m_{\rm{AB}}(FUV)=19.39\pm 0.12$ and the Medium Imaging
Survey found $m_{\rm{AB}}(FUV)=19.17\pm 0.04$ (Morrissey et al., 2007). There
are no flags on these data, the object is detected at high signal-to-noise
ratio in both images (as reflected in the uncertainties in the magnitudes),
there is no source confusion in the images and the source is not near the edge
of the field of view. These $m_{\rm{AB}}(FUV)$ values are converted to flux
densities with the formula from the GALEX Guest Investigator Web Site
999https://asd.gsfc.nasa.gov/archive/galex

$m_{\rm{AB}}(FUV)=-2.5\log_{10}\left[\frac{F_{\lambda}(1539\
{\rm\AA})}{1.40\times 10^{-15}\ \rm{erg\ s}^{-1}\ \rm{cm}^{-2}\
\AA^{-1}}\right]+18.82\;.$ (10)

We take the average of the two flux densities from Equation (10),
corresponding to the two GALEX measurements to find (after correcting for
Galactic extinction),

$F_{\lambda}(1539\ {\rm\AA})=1.12\pm 0.11\times 10^{-15}\ \rm{erg\ s}^{-1}\
\rm{cm}^{-2}\ \AA^{-1}\;.$ (11)

We corrected this value for Ly$\alpha$ forest absorption and the broad
emission lines in the wide photometric window. The FWHM of the FUV band is 228
Å according to the GALEX Guest Investigator Web Site. In the quasar rest frame
the half-maxima points are at $631\pm 47$ Å. In a study of HST quasar spectra,
Stevans et al. (2014) reported the presence of strong OIV and OV BELs in this
region. In their composite spectra, these BELs comprise about 12% of the flux
in this band. This effect is much larger than absorption by the Ly$\alpha$
forest, since an observed wavelength of 1539 Å corresponds to a Ly$\alpha$
photon at a redshift of only, $z\sim 0.25$. The absorption is estimated to
typically be $<2\%$ at $z=0.25$ (Zheng et al., 1997). Combining the two
effects, we estimate that the GALEX FUV photometry will overestimate the flux
in the pass-band by $\approx 10\%$. After applying this correction to Equation
(11), we estimate a luminosity (in terms of the spectral luminosity
$L_{\lambda}(\lambda)$),

$\lambda L_{\lambda}(631\ {\rm\AA})=2.05\pm 0.21\times 10^{46}\ \rm{erg\
s}^{-1}\;.$ (12)

This point was added to the SED in Figure 5. The extreme ultraviolet (EUV)
spectral index from 1100 Å, (HST) to 631 Å (GALEX), $\alpha_{\rm{EUV}}$, is
defined in frequency space, $F_{\nu}\propto\nu^{-\alpha_{\rm{EUV}}}$ (from
frequency ($2.73\times 10^{15}$ Hz to $4.75\times 10^{15}$ Hz). In Figure 5,

$\alpha_{\rm{EUV}}=2.64\pm 0.18\;.$ (13)

The red dashed line in Figure 5 extrapolates this power law to higher
frequency.

###  7.2 The X-ray Data

The SED in Figure 5 includes the _Chandra_ X-ray data (Siemiginowska et al.,
2008). The X-ray power law can arise from either a jet or the corona of an
accretion disk in a powerful radio loud quasar. For perspective, if the jet
were weak (a radio quiet quasar), based on the 1100 Å edge of the big blue
bump, one expects a corona level approximately where the light blue line is
plotted in the lower right (Shang et al., 2011; Laor et al., 1997), i.e., the
_Chandra_ flux levels are far in excess of what is expected of a corona. The
X-ray luminosity in 3C 298 is large even compared to 3CR quasars with the
largest 178 MHz luminosity Salvati et al. (2008). The total _Chandra_
luminosity from 0.5 keV to 10 keV (1.2 keV to 24 keV in the cosmological rest
frame of the quasar) is $5.17\times 10^{46}$ erg s-1 (Siemiginowska et al.,
2008). This high-energy component is not only clearly X-ray emission of jetted
origin, but is extremely large for a quasar, even most blazars; it is
comparable to that of the brightest gamma-ray blazars (Ghisellini et al.,
2010). Based on the light blue line in Figure 5, we conclude that the corona
emission is masked by a much brighter jet. Due to this circumstance we need to
estimate this undetected portion of the SED using composite information from
other quasars. We estimate that $10\%$ of the big blue bump continuum
luminosity is a reasonable composite X-ray luminosity of the accretion flow
corona (Shang et al., 2011; Laor et al., 1997).

The jet X-ray luminosity is too large to be created by shocks from a
frustrated jet in the CSS quasar (O’Dea, 2017). The X-ray emission is stronger
in 3CR quasars than 3CR radio galaxies of similar radio power; this behavior
has been attributed to modest Doppler beaming (Salvati et al., 2008). This
model appears plausible for 3C 298 based on the asymmetry of the inner jet in
the VLBI images at 1.66 GHz and 5 GHz (Fanti et al., 2002).

###  7.3 Calculation of $L_{\mathrm{bol}}$

As discussed in the introduction to this section $L_{\rm{bol}}$ has three
components. The first, $L(\rm{thermal\;from\;accretion})$ is computed from
direct integration of the broken power-law approximation to the continuum in
the optical, UV and EUV in Figure 5. The second component is the broad
emission luminosity. The broad line luminosity was estimated for quasars by
$L(\rm{BELs})\approx 5.6L(\rm{Ly}\alpha)$ in (Celotti et al., 1997). From the
value of $L(\rm{Ly}\alpha)$ in Table 3, $L(\rm{BELs})\approx 1.34\times
10^{46}\rm{ergs/sec}$. This seems reasonable based on the sum of the BEL
luminosities in the last row of Table 3. The third component is the energy
radiated by high energy electrons in a corona above the disk. In radio loud
quasars this is not necessarily detected because it is likely masked by the
X-ray emission from the radio jet. Thus, we invoked a crude approximation of
10% of $L(\rm{thermal\;from\;accretion})$ from the observations of radio quiet
quasars (we assume similar coronae to first order) where it is detected. Thus,
we have

$\displaystyle
L_{\rm{bol}}=L(\rm{thermal\;from\;accretion})+L(\rm{BELs})+L(\rm{corona})$
$\displaystyle\approx 1.29\times 10^{47}\rm{ergs/sec}+1.34\times
10^{46}\rm{ergs/sec}+1.29\times 10^{46}\rm{ergs/sec}=1.55\times
10^{47}\rm{ergs/sec}\;.$ (14)

One can try to model the accretion disk SED with a mixture of thin disks and
winds. For example, Laor and Davis (2014) was able to find an explanation of
the SED turnover at $1100\AA$ in quasars. There are numerical attempts to
model quasar disks with slim disk models (Sadowski et al., 2011). All of these
models can be used to estimate accretion rates and central black hole masses.
However, none of them can explain the steep EUV continuum in powerful radio
loud quasars (Punsly, 2015). Thus, we are motivated to explore this in Section
8.

##  8 The EUV Deficit and the Weak Emission Lines

In this section, we synthesize three findings of this paper:

  * •

the enormous $\overline{Q}$ in Equation (6),

  * •

the steep EUV continuum in Equation (13) and Figure 5,

  * •

and the small BEL EWs in Table 3.

Figure 6: 3C 298 in the context of the EUV deficit of radio loud quasars
relative to radio quiet quasars. The EUV deficit is quantified in terms of the
spectral index in frequency space, $\alpha_{\rm{EUV}}$, taken from 1100 Å to
700 Å except in the case of 3C 298 where it is from 1100 Å to 631 Å (the
center frequency of the GALEX far UV band in the quasar rest frame). The jet
power normalized to the thermal luminosity from accretion is expressed as
$\overline{Q}/L_{\rm{bol}}$.

Figure 6 reveals that the steepness of the SED in the EUV is not that
unexpected based on the ratio of $\overline{Q}/L_{\rm{bol}}$ derived from
Equations (6) and (14). We have added 3C 298 to the figure that appeared in
Punsly et al. (2020b). The correlated trend of $\alpha_{\rm{EUV}}$ with
$\overline{Q}/L_{\rm{bol}}$ is known as the “EUV deficit” of powerful radio
loud quasars relative to radio quiet quasars. In the lower left hand corner,
the objects with a “small” value of $\overline{Q}/L_{\rm{bol}}$ have EUV
continua indistinguishable from that of radio quiet quasars (Punsly, 2015).
This result is expected as for these quasars the jet output is an
insignificant fraction of the total energy output of the quasar central
engine. 3C 273 is an example of such a quasar. The other points in Figure 6
are spectral indices from 1100 Å to 700 Å (quasar rest frame) derived from
spectral data. For 3C 298 we computed $\alpha_{\rm{EUV}}$ from 1100 Å to 631 Å
(the center frequency of the GALEX far UV band in the quasar rest frame) and
we augmented the HST data with the GALEX data point after vetting its
integrity in Section 7.1. The physical origin of the trend was explained by
the quantitative consistency of the trend in Figure 6 with a scenario in which
the jet is launched by large scale vertical magnetic flux in the inner region
of the accretion flow, thereby displacing a proportionate fraction of the
highest temperature thermal gas in the innermost accretion flow, i.e., the EUV
emitting gas (Punsly, 2015).

We proceed to explore the role of the weaker EUV continuum in producing the
depressed EWs for the BELs. First consider the average
$\alpha_{\rm{EUV}}=1.76$ for the HST observed quasars in the comparison sample
of Table 3 (Telfer et al., 2002). If we compute the ionizing luminosity,
$L_{\rm{ion}}(\rm{HST})$ from 1 Rydberg to 10 Rydberg for the HST sample and
calculate the same measure of the ionizing luminosity for 3C 298 based on
Equation (13), $L_{\rm{ion}}(\rm{3C298})/L_{\rm{ion}}(\rm{HST})=0.47$. The BEL
flux, $F(\rm{BEL})$, does not necessarily scale linearly with the ionizing
continuum, but has been described by a “responsivity,” $\eta$ (Korista and
Goad, 2004).

$F(\rm{BEL})\propto\Phi_{\rm{H}}^{\eta}\;,\Phi_{\rm{H}}\approx\int^{10\,\rm{Ryd}}_{1\,\rm{Ryd}}{[F_{\nu}(\rm{EUV})/\rm{h}\nu]\,d\nu};.$
(15)

where $\Phi_{\rm{H}}$ is the flux of hydrogen ionizing photons, and
$F_{\nu}(\rm{EUV})$ is the EUV flux power law. We estimate that

$\frac{\Phi_{\rm{H}}(\rm{3C298})}{\Phi_{\rm{H}}(\rm{HST})}=0.58\;.$ (16)

However, we do not have a robust estimate for $\eta$ for each BEL in a general
circumstance. This issue is magnified in 3C 298 and other powerful radio loud
quasars due to the large uncertainty in the coronal X-ray luminosity.

##  9 Virial Black Hole Mass Estimates

We start by choosing two virial black hole mass estimators that are based on
MgII and L(3000) from the literature. The formula from Shen and Liu (2012),
using the MgII BEL, $L(3000)=5.34\times 10^{46}$ erg sec-1 and the FWHM of the
total line profile (not tabulated in Table 2) of 3595 km s-1, yields

$\displaystyle\log\left(\frac{M_{bh}}{M_{\odot}}\right)=1.815+0.584\log\left(\frac{L(3000)}{10^{44}\,\rm{erg\
s}^{-1}}\right)+1.712\log\left(\frac{\rm{FWHM}}{\rm{km\ s}^{-1}}\right)\;,$
$\displaystyle\frac{M_{bh}}{M_{\odot}}=3.13\times 10^{9}\;.$ (17)

Alternatively, the formula of Trakhtenbrot & Netzer (2012) yields a different
estimate

$\frac{M_{bh}}{M_{\odot}}=5.6\times
10^{6}\left(\frac{L(3000)}{10^{44}\,\rm{erg}\,\rm{s}^{-1}}\right)^{0.5}\left(\frac{\rm{FWHM}}{1000\,\rm{km\
s}^{-1}}\right)^{2}=3.55\times 10^{9}\;.$ (18)

These equations are predicated on the assumption that in general L(3000) is a
uniform surrogate for the ionizing continuum, $L_{\rm{ion}}$. From Figure 5
and Section 8, however, we know that L(3000) is much larger than expected by
direct comparison with the ionizing continuum and also indirectly from the EWs
of the BELs in Table 3, suggesting that Equations (17) and (18) should over
estimate $M_{bh}$. It is therefore probably more reasonable for this
particular SED to use the line luminosity L(MgII) as a surrogate for
$L_{\rm{ion}}$. We choose two estimators based on L(MgII) from the same two
references as more accurate for this circumstance The expression form Shen and
Liu (2012) is

$\displaystyle\log\left(\frac{M_{bh}}{M_{\odot}}\right)=3.979+0.698\log\left(\frac{L({\rm
MgII})}{10^{44}\,\rm{erg\
s}^{-1}}\right)+1.382\log\left(\frac{\rm{FWHM}}{\rm{km\ s}^{-1}}\right)\;,$
$\displaystyle\frac{M_{bh}}{M_{\odot}}=2.36\times 10^{9}\;.$ (19)

The analogous formula of Trakhtenbrot & Netzer (2012) yields a different
estimate

$\frac{M_{bh}}{M_{\odot}}=6.79\times 10^{6}\left(\frac{L({\rm
MgII})}{10^{42}\,\rm{erg\
s}^{-1}}\right)^{0.5}\left(\frac{\rm{FWHM}}{1000\,\rm{km\
s}^{-1}}\right)^{2}=1.93\times 10^{9}\;.$ (20)

Based on our analysis of the continuum near 3000 Å (see Appendix B), the SED
in Figure 5, and the EUV deficit described in Section 8, the best virial
estimate of the central black hole mass is $M_{bh}=2.14\times 10^{9}M_{\odot}$
based on averaging Equations (19) and (20). The Eddington luminosity of such
objects is $L_{\rm{Edd}}=2.7\times 10^{47}$ erg s-1. Using the $L_{\rm{bol}}$
that was calculated in Section 7 produces a high Eddington ratio of 0.57.
Alternatively, if we average Equations (17)-(20), $M_{bh}=2.74\times
10^{9}M_{\odot}$ and $L_{\rm{bol}}/L_{\rm{Edd}}=0.45$. Both estimates are
consistent with the rather large BLUE components found in CIV and Ly$\alpha$
in Table 2. Such components are thought to arise from radiation driven winds
(Murray et al., 1995; Fine et al., 2010).

##  10 Summary and Conclusion

In a previous study it was noted that the quasars, 3C 82 and 3C 298, both
members of the CSS class of radio sources, were candidates to have the largest
known $\overline{Q}$ for a quasar (Punsly et al., 2020a). Hence, we initiated
an equally detailed study of 3C 298 in this paper. In Section 2, we utilized
the impressive new LOFAR observations of the radio source at 29-78 MHz. In
Sections 2-5, we developed physical models of the lobe plasmas that indicate a
long-term time-averaged jet power of, $\overline{Q}\approx 1.28\pm 0.51\times
10^{47}\rm{erg}\,\rm{s}^{-1}$ in Equation (6). This result is quantitatively
similar, but smaller than the cruder standard estimate that is computed using
only the 151 MHz flux density, $\overline{Q}\approx 2.18\pm 0.71\times
10^{47}\rm{erg\ s}^{-1}$ in Equation (8), justifying the need for a more
detailed analysis for CSS sources.

Section 6 presented the rest frame SED of 3C 298 from 1100 Å to 4300 Å using
two spectra from HET and an archival HST spectrum. Three component fits to the
broad emission lines are given in Tables 2 and 3. The line strength ratios
were typical of quasars, but the lines were relatively weak compared to the
local continuum. To investigate further, we constructed an SED of just the
continuum in Section 7 that was augmented with 2MASS and GALEX photometric
points and _Chandra_ data. We deduced three extreme circumstances

  1. 1.

3C 298 potentially belongs to the rare class of kinetically dominated quasar
jets, $\overline{Q}/L_{\rm{bol}}\approx 0.87\pm 0.41$ (see Figure 6), similar
to the other potentially kinetically dominated sources tabulated in Punsly et
al. (2020a), $\overline{Q}/L_{\rm{bol}}\approx 1$.

  2. 2.

The EUV continuum was extremely steep, $\alpha_{\rm{EUV}}=2.64\pm 0.18$
compared to $\alpha_{\rm{EUV}}=1.76\pm 0.12$ for the HST observed quasars of
comparable luminosity (Telfer et al., 2002).

  3. 3.

The cosmological rest frame 1.2-24 keV, X-ray luminosity of $5.17\times
10^{46}$ erg s-1 is extremely large for a lobe-dominated steep spectrum radio
source (a non-blazar).

In Section 8, we tried to reconcile the small BEL EWs with the steep EUV
continuum. It is highly plausible that the weak ionizing EUV continuum is the
reason for the depressed lines strengths. Even though there is poor coverage
of the EUV spectrum in Figure 5, Figure 6 demonstrates that our data place
3C298 in good agreement with the EUV deficit trend that is seen in powerful
lobe dominated quasars. The interpretation of the weak BELs and the EUV
deficit seems reasonable.

Section 9 considers the relatively weak EUV in the context of virial mass
estimates that utilize near UV luminosity. We argue that in this case it is
more consistent to use the BELs themselves as a surrogate for $L_{\rm{ion}}$,
and determined that the Eddington rate of accretion is $\approx 0.5$. This
high Eddington rate is an indication of a powerful source of radiation
pressure. This large accretion is imprinted in the BELs as strong BLUE
components in Table 2 and Figure 8 (Appendix B) in Ly$\alpha$ and CIV.
Evidence of powerful baryonic outflows is commonly seen in both UV absorption
and UV emission in high Eddington rate radio quiet quasars, but is rare in
radio-loud quasars with an FRII morphology (Richards et al, 2002; Punsly,
2010; Becker et al., 2000, 2001). Other 3C CSS quasars, such as 3C82 and 3C
286, also have this unusual property, for a radio-loud quasar, of excess blue-
shifted CIV emission (Punsly et al., 2020a). We have obtained deep HET optical
spectra of 3C CSS quasars to augment the HST archives, and plan to perform a
complete spectral analysis and report our findings in a future work.

This work motivates further investigations of the powerful X-ray jet in this
mildly Doppler enhanced source. Figure 2 and Table 1 suggest the possibility
of some modest variability of the nuclear region above 5 GHz (as discussed in
Sections 4 and 5), so there might be some modest relativistic behavior. In
spite of point 3 above, 3C298 is not a gamma ray source. It is, however, quite
bright, and would be an excellent target for NuSTAR to determine if there is a
turnover above 100 keV in the cosmological rest frame.

CG acknowledges support from the ERC Starting Grant ClusterWeb 804208. We
thank the staff of the Hobby Eberly Telescope for support of our VIRUS and
LRS2 observations. This research was partially funded through the McDonald
Observatory. The Hobby-Eberly Telescope (HET) is a joint project of the
University of Texas at Austin, the Pennsylvania State University, Ludwig-
Maximilians-Universität München, and Georg-August-Universität Göttingen. The
HET is named in honor of its principal benefactors, William P. Hobby and
Robert E. Eberly. VIRUS is a joint project of the University of Texas at
Austin, Leibniz-Institut für Astrophysik Potsdam (AIP), Texas A&M University
(TAMU), Max-Planck-Institut für Extraterrestrische Physik (MPE), Ludwig-
Maximilians-Universität München, Pennsylvania State University, Institut für
Astrophysik Göttingen, University of Oxford, and the Max-Planck-Institut für
Astrophysik (MPA). The Low Resolution Spectrograph 2 (LRS2) was developed and
funded by the University of Texas at Austin McDonald Observatory and
Department of Astronomy and by Pennsylvania State University. We thank the
Leibniz-Institut für Astrophysik Potsdam (AIP) and the Institut für
Astrophysik Göttingen (IAG) for their contributions to the construction of the
integral field units. We acknowledge the Texas Advanced Computing Center
(TACC) at The University of Texas at Austin for providing high performance
computing, visualization, and storage resources that have contributed to the
results reported within this paper. This work makes use of the Pan-STARRS1
Surveys (PS1) and the PS1 public science archive, which have been made
possible through contributions by the Institute for Astronomy, the University
of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
participating institutes. This work makes use of data from the European Space
Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the
Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This work makes use of the
Sloan Digital Sky Survey IV, with funding provided by the Alfred P. Sloan
Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High-Performance Computing at the University of Utah. The SDSS
web site is www.sdss.org.

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##  Appendix A The Underlying Physical Equations

To allow this article to be self-contained, this brief appendix repeats the
mathematical formalism associated with spherical plasmoids previously
described in detail in Punsly et al. (2020a). First, one must differentiate
between quantities measured in the plasmoid frame of reference and those
measured in the observer’s frame of reference. The physics is evaluated in the
plasma rest frame. The results are then transformed to the observer’s frame.
The underlying power law for the flux density is defined as
$S_{\nu}(\nu_{\mathrm{obs}})=S\nu_{\mathrm{obs}}^{-\alpha}$, where $S$ is a
constant. Observed quantities will be designated with a subscript, “obs”, in
the following expressions. The observed frequency is related to the emitted
frequency, $\nu_{\mathrm{e}}$, by
$\nu_{\mathrm{obs}}=\delta\nu_{\mathrm{e}}/(1+z)$, where $\delta$ is the bulk
flow Doppler factor, $\delta\approx 1$. The SSA attenuation coefficient is
computed in the plasma rest frame (Ginzburg and Syrovatskii, 1969),

$\displaystyle\mu(\nu_{\mathrm{e}})=\overline{g(n)}\frac{e^{3}}{2\pi
m_{e}}N_{\Gamma}(m_{e}c^{2})^{2\alpha}\left(\frac{3e}{2\pi
m_{e}^{3}c^{5}}\right)^{\frac{1+2\alpha}{2}}\left(B\right)^{(1.5+\alpha)}\left(\nu_{\mathrm{e}}\right)^{-(2.5+\alpha)}\;,$
(A1)
$\displaystyle\overline{g(n)}=\frac{\sqrt{3\pi}}{8}\frac{\overline{\Gamma}[(3n+22)/12]\overline{\Gamma}[(3n+2)/12]\overline{\Gamma}[(n+6)/4]}{\overline{\Gamma}[(n+8)/4]}\;,$
(A2) $\displaystyle
N=\int_{\Gamma_{\mathrm{min}}}^{\Gamma_{\mathrm{max}}}{N_{\Gamma}\Gamma^{-n}\,d\Gamma}\;,\;n=2\alpha+1\;,$
(A3)

where $\Gamma$ is the ratio of lepton energy to rest mass energy,
$m_{e}c^{2}$, $\overline{g(n)}$ is the Gaunt factor averaged over angle,
$\overline{\Gamma}$ is the gamma function, and $B$ is the magnitude of the
total magnetic field. The low energy cutoff is
$E_{\mathrm{min}}=\Gamma_{\mathrm{min}}m_{e}c^{2}$.

A simple solution to the radiative transfer equation occurs in the homogeneous
approximation (Ginzburg and Syrovatskii, 1965; van der Laan, 1966)

$\displaystyle
S_{\nu_{\rm{obs}}}=\frac{S_{\rm{o}}\nu_{\rm{obs}}^{-\alpha}}{\tau(\nu_{\rm{obs}})}\times\left(1-e^{-\tau(\nu_{\rm{obs}})}\right)\;,\;\tau(\nu_{\rm{obs}})\equiv\mu(\nu_{\rm{obs}})L\;,\;\tau(\nu_{\rm{obs}})=\overline{\tau}\nu_{\rm{obs}}^{(-2.5+\alpha)}\;,$
(A4)

where $\tau(\nu)$ is the SSA opacity, $L$ is the path length in the rest frame
of the plasma, $S_{\rm{o}}$ is a normalization factor and $\overline{\tau}$ is
a constant.

Connecting the parametric spectrum given by Equation (A4) to a physical model
requires an expression for the synchrotron emissivity (Tucker, 1975):

$\displaystyle j_{\nu}=1.7\times 10^{-21}[4\pi
N_{\Gamma}]a(n)B^{(1+\alpha)}\left(\frac{4\times
10^{6}}{\nu_{e}}\right)^{\alpha}\;,$ (A5) $\displaystyle
a(n)=\frac{\left(2^{\frac{n-1}{2}}\sqrt{3}\right)\overline{\Gamma}\left(\frac{3n-1}{12}\right)\overline{\Gamma}\left(\frac{3n+19}{12}\right)\overline{\Gamma}\left(\frac{n+5}{4}\right)}{8\sqrt{\pi}(n+1)\overline{\Gamma}\left(\frac{n+7}{4}\right)}\;,$
(A6)

where the coefficient $a(n)$ separates the pure dependence on $n$ (Ginzburg
and Syrovatskii, 1965). One can transform this result to the observed flux
density, $S(\nu_{\rm{obs}})$, in the optically thin region of the spectrum
using the relativistic transformation relations from Lind and Blandford
(1985),

$\displaystyle S(\nu_{\rm{obs}})=\frac{\delta^{(3+\alpha)}}{4\pi
D_{L}^{2}}\int{j_{\nu}^{{}^{\prime}}dV{{}^{\prime}}}\;,$ (A7)

where $D_{L}$ is the luminosity distance and in this expression, the primed
frame is the rest frame of the plasma.

###  A.1 Mechanical Quantities that Characterize the Lobes

First define the kinetic energy of the protons, $KE(\mathrm{proton})$,

$\displaystyle KE(\mathrm{protonic})=(\gamma-1)Mc^{2}\;,$ (A8)

here $M$ is the mass of the plasmoid. Secondly define the lepto-magnetic
energy, $E(\mathrm{lm})$ which creates the synchrotron emission. It is the
volume integral of the leptonic internal energy density, $U_{e}$, and the
magnetic field energy density, $U_{B}$. $E(\mathrm{lm})$ in a uniform
spherical volume is

$\displaystyle E(\mathrm{lm})=\int{(U_{B}+U_{e})}\,dV=\frac{4}{3}\pi
R^{3}\left[\frac{B^{2}}{8\pi}+\int_{\Gamma_{min}}^{\Gamma_{max}}(m_{e}c^{2})(N_{\Gamma}E^{-n+1})\,d\,E\right]\;.$
(A9)

The leptons also have a kinetic energy analogous to Equation (11),

$\displaystyle KE(\mathrm{leptonic})=(\gamma-1)\mathcal{N}_{e}m_{e}c^{2}\;,$
(A10)

where $\mathcal{N}_{e}$ is the total number of leptons in the plasmoid.

##  Appendix B Fits to the Broad Line Profiles

The BEL components are identified in Figure 7 as follows: the BC is the black
Gaussian profiles, the VBC is red curve and BLUE is the blue curve. Only the
sum of the three components is shown for both NV$\lambda$1240 and
HeII$\lambda$1640 (in black). For more details of the fitting process see
(Punsly et al., 2020a).

Figure 7: Line fits from Table 2 for the four regions of the spectrum with
strong UV emission lines. The flux density is in relative units with a scaling
of 1 being near the continuum level. The (black) broad line in the blue wing
of CIV is NIV]$\lambda$1486\. The MgII continuum is masked by a strong Balmer
continuum, the brown curve, and FeII in green. The BLUE component in blue, the
VBC is red and the BC is black. HeII and NIV are entirely black. In the lower
right set of panels that highlight the MgII region, the FeII complex is in
green and the Balmer continuum is brown.

Modelling of the Balmer continuum in the MgII region, in the lower right hand
panel of Figure 7, is nontrivial. The model spectrum depends upon numerous
free parameters, an intensity factor, electron temperature, $T_{e}$, and the
optical depth (Grandi et al., 1982; Jin et al., 2012). Since we lack adequate
spectral coverage of the longer wavelength discrete Balmer lines (long-ward of
4000 Å), there is little information to constrain the Balmer continuum. We
simply assume an optically thin continuum and $T_{e}=17500\rm{K}$ (Kwan and
Krolik, 1981; Jin et al., 2012). Our primary interest is to derive the MgII
broad line parameters and define the SED continuum level. In order to assess
if our modeling of the small blue bump at 3000 Å is reasonable, we compare our
results to the Shen et al. (2011) fit of the SDSS spectrum. Our (their)
$L(3000\AA\,)=5.36\times 10^{46}$ ergs $\rm{s}^{-1}$ ($L(3000\AA\,)=4.60\times
10^{46}$ ergs $\rm{s}^{-1}$ ), total BEL FWHM is 3595 km s-1 (3908 km s-1) and
the broad line luminosity is $L$(MgII) is $4.60\times 10^{44}$ erg s-1
($3.72\times 10^{44}$ erg s-1). The small differences between the two fits is
likely attributable to a larger flux allocation to the UV FeII and the Balmer
continuum than our fit. There was no effort in Shen et al. (2011) in their UV
FeII excision to assign an explicit contribution to a Balmer pseudo-continuum.
Even though ours was a dedicated fit of an individual source, we cannot claim
that our fit is better; the two are similar and produce bolometric
luminosities that agree to within $\sim 1\%$.