# The Event Horizon Telescope Image of the Quasar NRAO 530

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Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan
Road, Shanghai 200030, People’s Republic of China

###### Abstract

We report on the observations of the quasar NRAO 530 (catalog ) with the Event
Horizon Telescope (EHT) on 2017 April 5$-$7, when NRAO 530 (catalog ) was used
as a calibrator for the EHT observations of Sagittarius A∗. At $z=0.902$ this
is the most distant object imaged by the EHT so far. We reconstruct the first
images of the source at 230 GHz, at an unprecedented angular resolution of
$\sim 20\,\mu$as, both in total intensity and in linear polarization. We do
not detect source variability, allowing us to represent the whole data set
with static images. The images reveal a bright feature located on the southern
end of the jet, which we associate with the core. The feature is linearly
polarized, with a fractional polarization of $\sim$5-8% and has a sub-
structure consisting of two components. Their observed brightness temperature
suggests that the energy density of the jet is dominated by the magnetic
field. The jet extends over 60 $\mu$as along a position angle PA$\sim-$28∘. It
includes two features with orthogonal directions of polarization (electric
vector position angle, EVPA), parallel and perpendicular to the jet axis,
consistent with a helical structure of the magnetic field in the jet. The
outermost feature has a particularly high degree of linear polarization,
suggestive of a nearly uniform magnetic field. Future EHT observations will
probe the variability of the jet structure on ${\mu}$as scales, while
simultaneous multi-wavelength monitoring will provide insight into the high
energy emission origin.

galaxies: active — galaxies: jet — quasars: individual: NRAO 530 — techniques:
interferometric

††software:  DIFMAP (Shepherd, 1997), Matplotlib (Hunter, 2007), DiFX (Deller
et al., 2011), NumPy (van der Walt et al., 2011), eht-imaging (Chael et al.,
2016), PolConvert (Martí-Vidal et al., 2016), SMILI (Akiyama et al., 2017),
EHT-HOPS (Blackburn et al., 2019), Themis (Broderick et al., 2020b), DMC
(Pesce, 2021)

##  1 Introduction

NRAO 530 (catalog ) (1730$-$130, J1733$-$1304) is a flat-spectrum radio quasar
(FSRQ) that belongs to the class of bright $\gamma$-ray blazars and shows
significant variability across the entire electromagnetic spectrum. The source
was monitored by the University of Michigan Radio Observatory (UMRAO, USA) at
4.8, 8.4, and 14.5 GHz for several
decades111https://dept.astro.lsa.umich.edu/datasets/umrao.php until 2012. The
quasar underwent a dramatic radio outburst in 1997 (Aller et al., 2009),
during which its flux density at 14.5 GHz exceeded 10 Jy, while the average
value is $\sim$2 Jy. Since 2002 NRAO 530 (catalog ) has been monitored by the
Sub-Millimeter Array (SMA, Maunakea, Hawai’i) at 1.3 mm and 870
$\mu$m222http://sma1.sma.hawaii.edu/callist/callist.html?plot=1733-130. The
data show high amplitude variability at 1.3 mm from 1 Jy to 4 Jy, with the
brightest outburst in the end of 2010 contemporaneous with prominent
$\gamma$-ray activity (Williamson et al., 2014). Ramakrishnan et al. (2015)
have found a statistically significant correlation between the radio and
$\gamma$-ray light curves of NRAO 530 (catalog ), based on measurements at 37
GHz by the Metsähovi Radio Observatory (Aalto University, Finland) and
$\gamma$-ray fluxes measured with the Large Area Telescope (LAT) on board the
Fermi Space Gamma-Ray Telescope. The blazar is included in a sample of active
galactic nuclei (AGN) observed with the POLAMI program (Agudo et al., 2014),
which provides both the flux density and polarization measurements at 3 mm and
1.3 mm started in 2009. According to the data during the perion 2007-2021 the
degree of linear polarization at 1.3 mm changes from 1% to 15%, with circular
polarization detections at a level of 1-2% (private communication).

The quasar is known as a violently variable object at optical wavelengths.
According to the SMARTS optical/IR monitoring program of blazars (Bonning et
al., 2012), NRAO 530 (catalog ) has a fractional variability amplitude of
$\sim$68% and $\sim$35% at optical and IR wavelengths, respectively, with an
average magnitude of $\sim$14 at K band ($\lambda_{\rm eff}\sim$2.2 $\mu$m)
and $\sim$17.5 in R band ($\lambda_{\rm eff}\sim$658 nm). Foschini et al.
(2006) have reported a short hard X-ray flare detected serendipitously by the
IBIS/ISGRI detector on board INTEGRAL on 2004 February 17, although the
timescale of the flare, $<$1 hr, questions the association with the FSRQ.
However, a moderate increase of the linear polarization at 2 cm
contemporaneous with the flare was observed as well. The recent 10-yr Fermi
LAT catalog, 4FGL (Abdollahi et al., 2020), lists the average $\gamma$-ray
flux of the source at 0.1-300 GeV as (1.8$\pm$1.2)$\times$10-7 phot cm-2s-1.
During this period NRAO 530 (catalog ) underwent the highest amplitude
$\gamma$-ray outburst in 2010 October–November, when the $\gamma$-ray flux
rose to 10-6 phot cm-2s-1 (Williamson et al., 2014). This $\gamma$-ray
activity coincided with a significant brightening at optical wavelengths and
an increase of the optical linear degree of polarization up to 15%333
http://www.bu.edu/blazars/VLBA_GLAST/1730.html.

Figure 1: EHT ($u,v$)-coverage of the NRAO 530 (catalog ) observations on 2017
Apr 5, 6, 7, and all days aggregated. Each colored point corresponds to a
single VLBI scan of 3-4 min. ALMA participated in the observations on 2017 Apr
6, 7. Dashed circles indicate the fringe spacing of 50 $\mu$as and 25 $\mu$as.
"Chile" represents the stations ALMA and APEX. "Hawai’i" represents the
stations SMA and JCMT.

NRAO 530 (catalog ) possesses a highly relativistic jet. The source is
intensively monitored with the Very Long Baseline Array (VLBA) at 15 GHz
within the MOJAVE program (e.g., Lister et al., 2016) and at 43 GHz within the
VLBA-BU-BLAZAR program (Jorstad et al., 2017; Weaver et al., 2022). VLBA
images show a radio jet dominated by the core located at the southern end of
the jet. At 15 GHz the jet extends up to 10 mas to the north, with a weak
feature observed $\sim$25 mas from the core. Based on 11 moving features,
Lister et al. (2019) report a median apparent speed of 12.3$\pm 0.6~{}c$, with
a maximum apparent speed of 27.3$\pm 1.0~{}c$. At 43 GHz the jet contains a
stationary feature located $\sim$0.3 mas from the core and curves to the
northwest $\sim$0.8 mas from the core. 8 moving knots detected at 43 GHz over
2007-2018 exhibit a wide range of apparent speeds, from 2.6$\pm 0.5~{}c$ to
37.2$\pm 0.2~{}c$ (Weaver et al., 2022), with 3 knots revealing a strong
acceleration after passing the stationary feature, while knot B3 ejected in
the beginning of 2010 demonstrates both accelerations from 4.1 c to 7.7 c and
to 33.7 c and then a deceleration to 8.5 c. Using properties of the light
curves of moving knots and their apparent speeds, Jorstad et al. (2017) have
estimated the average Lorentz and Doppler factors of the jet to be
$\Gamma\sim$8 and $\delta\sim$9, respectively, with a jet viewing angle of
$\sim$3∘. These values of the Lorentz and Doppler factors are close to the
minimum values obtained by Liodakis et al. (2018) for the jet of NRAO 530
(catalog ). These authors estimated the variability of the Doppler factor by
analyzing the 15 GHz light curve provided by the Owens Valley 40 m Radio
Telescope after taking into consideration brightness temperature arguments and
the apparent speeds of knots at 15 GHz; this resulted in $\Gamma_{\rm
max}\sim$40 and $\delta_{\rm max}\sim$21.

On kiloparsec scales the quasar shows a weak two-sided jet elongated in the
east-west direction over $2.5^{\prime\prime}$, with a very diffuse eastern
part and a bright, compact knot on the western side, located about
$1^{\prime\prime}$ from the core (Kharb et al., 2010). The kiloparsec-scale
jet is almost perpendicular to the parsec scale jet and has a complex radio
morphology: the eastern part is similar to that expected for Fanaroff-Riley I
(FRI) type radio galaxies, while the western part can be classified as FRII
type.

NRAO 530 (catalog ) has a redshift of $z=0.902$ (Junkkarinen, 1984), for which
100 $\mu$as corresponds to a linear distance of 0.803 pc (Planck Collaboration
et al., 2016, $H_{0}=67.7$ km s-1 Mpc-1, $\Omega_{m}=0.307$, and
$\Omega_{\Lambda}=0.693$). The source contains a supermassive black hole
(SMBH), the mass of which is currently uncertain, with estimates ranging from
3$\times$10${}^{8}M_{\sun}$ (Keck, 2019) to 2$\times$10${}^{9}M_{\sun}$ (Liang
& Liu, 2003).

Due to its brightness, compactness, and close location on the sky to the
Galactic Center, NRAO 530 (catalog ) is frequently used as a calibrator in
very-long-baseline interferometry (VLBI) observations of the radio source
Sagittarius A∗ (Sgr A∗ (catalog )) located in the center of the Milky Way
(e.g., Lu et al., 2011). In this paper we report on the VLBI observations of
NRAO 530 (catalog ) in 2017 April, when the source was employed as a
calibrator during the Event Horizon Telescope (EHT) observation of Sgr A∗
(catalog ) at 1.3 mm (EHTC et al., 2022a). During the EHT observation NRAO 530
(catalog ) was in a moderate activity state at $\gamma$-ray energies with the
flux $\sim$1$\times$10-7phot cm-2s-1 as well as at optical (R band magnitude
$\sim$17.8)444http://www.bu.edu/blazars/VLBA_GLAST/1730.html and radio
wavelengths (the flux density at 37 GHz $\sim$3.7
Jy)555http://www.metsahovi.fi/AGN/data/. According to the VLBA monitorings at
43 GHz (Weaver et al., 2022) and 15 GHz (Lister et al., 2019) no superluminal
components were ejected in 2017. The EHT observation of NRAO 530 (catalog )
provides unique insight into the sub-parsec scale structure of the quasar with
micro-arcsecond resolution, which are important for understanding the blazar
physics in general and properties of the NRAO 530 (catalog ) jet in
particular. The outline of the paper is as follows: in Section 2 we describe
the EHT observations of NRAO 530 (catalog ), their reduction and general data
set properties, in Sections 3 and 4 we present results of total intensity and
linear polarization (LP) imaging, respectively, in Section 5 we discuss our
results, and in Section 6 we summarize our findings.

##  2 Observations and Data Calibration

Figure 2: Top: S/N of NRAO 530 (catalog ) detections. Colors follow the
convention of Figure 1. The entire data set (2017 Apr 5-7, both frequency
bands) is shown. The data were averaged coherently in 240 s intervals. The
circles denote primary baselines, while the diamonds denote redundant
baselines (i.e., obtained with APEX or JCMT, rather than with ALMA or SMA).
The cluster of S/N $>100$ circles corresponds to ALMA baselines. Middle: Same
as the top panel, but for the correlated flux densities (visibility
amplitudes) in the a priori calibrated data set. Bottom: Visibility amplitudes
as a function of baseline length projected at the jet position angle (PA) of
-25 deg (see Section 3). Dashed line represents a Gaussian component of full
width at half maximum (FWHM) 55 $\mu$as and 0.6 Jy amplitude.

The EHT observed NRAO 530 (catalog ) on three consecutive nights on April 5-7
during the 2017 campaign (MJD 57848-57850), as a calibrator of Sgr A∗ (EHTC et
al., 2022a, b). The observations were performed with the full EHT 2017 array
of eight telescopes located at six geographical sites: the Atacama Large
Millimeter/submillimeter Array (ALMA)666ALMA joined on Apr 6 and 7, operating
as a phased array of on average 37 dishes of 12 m diameter, in a compact
configuration with longest baselines not exceeding 300 m length (Goddi et al.,
2019; Wielgus et al., 2022). and the Atacama Pathfinder Experiment (APEX)
telescope in Chile; the Large Millimeter Telescope Alfonso Serrano (LMT) in
Mexico; the IRAM 30 m telescope (PV, joined only on Apr 7) in Spain; the
Submillimeter Telescope (SMT) in Arizona; the James Clerk Maxwell Telescope
(JCMT) and the Submillimeter Array (SMA) in Hawai’i; and the South Pole
Telescope (SPT) in Antarctica. Two 2 GHz wide frequency bands, centered at
227.1 GHz (LO), and 229.1 GHz (HI), were recorded. The observations were
carried out using dual feeds, right-hand and left-hand circularly polarized
(RCP ad LCP, respectively), for all stations other than ALMA and JCMT. ALMA
recorded dual linear polarization, which was subsequently converted at the
correlation stage to a circular basis by PolConvert (Martí-Vidal et al., 2016;
Goddi et al., 2019). The JCMT only observed the RCP component, which we
utilized to approximate total intensity (this approximation is correct as long
as the fractional circular polarization of the source can be neglected), and
we typically omit JCMT baselines for the polarimetric imaging. The EHT array
setup is detailed in EHTC et al. (2019a, b).

Recorded signals were correlated at the MIT Haystack Observatory and the Max-
Planck-Institut für Radioastronomie, Bonn. Subsequent data reduction
procedures are described in EHTC et al. (2019c); Blackburn et al. (2019);
Janssen et al. (2019). There were minor updates to the calibration with
respect to the EHT results published earlier (EHTC et al., 2019a; Kim et al.,
2020), particularly regarding the telescope sensitivity estimates and complex
polarimetric gains calibration. These updates are identical to those described
in the EHT Sgr A∗ (catalog ) publications (EHTC et al., 2022a, b). Flux
density on the short intra-site baselines (ALMA-APEX and SMA-JCMT) was gain-
calibrated to the simultaneous ALMA-only flux density of 1.6 Jy, reported by
Goddi et al. (2021), providing an additional constraint on the amplitude gains
for the stations with a co-located partner (network calibration; Blackburn et
al., 2019). The polarimetric leakage calibration follows procedures outlined
in EHTC et al. (2021), where D-terms of stations with an intra-site VLBI
baseline (ALMA, APEX, SMA, JCMT) were calculated through a multi-source
fitting procedure (Martí-Vidal et al., 2021), and several estimates for
D-terms of remaining stations were reported. Here we employ the fiducial
D-terms given by Issaoun, Wielgus et al. 2022 based on the analysis presented
in EHTC et al. (2021). Some imaging algorithms that we use ignore the leakage
calibration and estimate D-terms independently, providing an additional
consistency check of the calibration procedures and their impact on the
resulting images (see Section 3).

The $(u,v)$-coverage of the EHT observations of NRAO 530 (catalog ) is given
in Figure 1. We show the coverage on each individual day, as well as
aggregated over the entire observing campaign. The longest projected baseline
reaches 8.66 G$\lambda$ for SPT-PV, which determines the instrumental angular
resolution of 24 ${\rm\mu}$as, measured as the minimum fringe spacing.
Inspection of the data revealed no indication of the source structure
evolution during the observations spanning only about 52 h on 2017 Apr 5$-$7,
with the total on-source integration time of 76 minutes (see Figures 2-3). For
that reason, the entire data set was used simultaneously for static imaging
and model fitting.

The NRAO 530 (catalog ) data set self-consistency has been rigorously verified
as a validation of the EHT Sgr A∗ results, presented in EHTC et al. (2022b).
The signal-to-noise ratio (S/N) of individual NRAO 530 (catalog ) detections
(band-averaged in frequency, scan-averaged in time) typically exceeds 100 on
baselines to ALMA, and is about an order of magnitude lower on remaining
baselines; see the top panel of Figure 2. We estimated additional 2% of
complex visibility uncertainties due to variety of non-closing effects (e.g.,
residual polarimetric leakage, frequency and time smearing), see EHTC et al.
(2019c, 2022b). Inspecting the calibrated visibility amplitudes in the middle
panel of Figure 2, we notice that the shortest inter-site baseline (LMT-SMT)
provides a lower limit on the compact emission flux density corresponding to
about 0.6 Jy, which implies the presence of up to 1 Jy of mas scale flux that
is resolved out by the EHT but measured on the intra-site VLBI baselines and
by the ALMA-only observations. Additionally, in the bottom panel of Figure 2
we present the measured visibility amplitudes as a function of the baseline
length, projected at the jet PA (see Section 3). We notice that the amplitudes
on baselines shorter than about 2.5 G$\lambda$ can be approximated by a
Gaussian of FWHM 55 $\mu$as and 0.6 Jy amplitude, roughly informing us about
the size and the total flux density of the observed compact feature.
Measurements on baselines longer than 2.5 G$\lambda$ indicate a deviation from
the Gaussian model, in agreement with the resolved source consisting of more
than one component. Both EHT Sgr A∗ (catalog ) calibrators, NRAO 530 (catalog
) and J1924-2914 (Issaoun, Wielgus et al. 2022) are fairly compact and bright
sources at 230 GHz. During the week-long EHT observing run, their source
structure and flux density did not show significant variations (see Figure 3).
These properties allowed us to use both sources for quantifying the effects of
the residual errors in the characterization of the antenna gains. Mitigating
such effects was crucial for discerning between the rapid intrinsic
variability of Sgr A∗ (catalog ) and the apparent flux density variations
produced by imperfect calibration (EHTC et al., 2022c, d; Wielgus et al.,
2022). Details about the procedures and methods used to obtain the antenna
gains from the two calibrators and the subsequent transfer to the Sgr A∗
(catalog ) data sets are reported in Section 3.2 in EHTC et al. (2022b).

Figure 3: NRAO 530 (catalog ) closure phases measured on a selected non-
trivial triangles. LO band data points averaged in 240 s intervals are shown.
There is no statistically significant indication of structural variation
between the 3 consecutive observing days. Predictions of the models obtained
with a variety of imaging algorithms, discussed in Section 3, are indicated
with thin black lines. The blue-shaded region indicates the range of
predictions from different reconstructions presented in this paper.

##  3 Total Intensity Imaging

For the imaging of NRAO 530 (catalog ) we have utilized data calibrated by the
EHT-HOPS pipeline (Blackburn et al., 2019), combined over all days (2017 Apr
5-7) and both frequency bands (227.1 and 229.1 GHz). Non-zero closure phases
shown in Figure 3 reveal resolved and non-trivial structure of the source. We
used three analysis methods across five different implementations. These are:
imaging via inverse modeling (the traditional CLEAN method), forward
regularized maximum likelihood (RML) modeling (eht-imaging and SMILI
algorithms), which are described in detail in EHTC et al. (2019d), as well as
two posterior exploration methods based on a Markov chain Monte Carlo (MCMC)
scheme – a D-term Modeling Code (DMC; Pesce, 2021) and a dedicated Bayesian
image reconstruction framework Themis (Broderick et al., 2020b). For each of
the method the freedom to decide resolution, field of view, or amount of data
coherent averaging was left to the expert imaging sub-teams, who made such
decisions based on the specific properties of each algorithm. As an example,
MCMC methods tend to average data more to reduce the computational complexity
of the likelihood evaluation. Below we give a short description of each
method, with some details on the particular application to the NRAO 530
(catalog ) imaging.

###  3.1 DIFMAP

For CLEAN imaging we have used the DIFMAP software package (Shepherd, 1997).
We have constructed multiple manual images prior to the final process to
obtain a set of CLEAN windows corresponding to the source structure and
agreeing best with the data. This window set includes a large circular
Gaussian with a radius of 1 mas, located in the center of the map, which
models the large-scale extended emission present in the source. The standard
process of multiple consecutive CLEAN iterations, along with self-calibration
procedures, was employed to achieve the best normalized $\chi^{2}$ values
between the data and the model for the closure phases, closure amplitudes, and
visibilities. We have used data averaged in 10 s segments, a field of view of
1024$\times$1024 pixels with a pixel size of 2 $\mu$as and uniform weighting
to optimize the image resolution.

###  3.2 eht-imaging

The eht-imaging code (Chael et al., 2016, 2018) implements the RML-based
approach to imaging. In this method, an updated image is being proposed at
every iteration, while the algorithm optimizes a cost function comprised of
the error term describing consistency with the data (predominantly through
closure phases and log closure amplitudes; Blackburn et al. 2020), and
regularization terms, similar to Bayesian priors. The latter may promote image
properties such as smoothness, sparsity, compactness, or consistency with the
imaging prior – here chosen to be a 60 $\mu$as FWHM circular Gaussian. For the
NRAO 530 (catalog ) analysis we assumed a field of view of 200 $\mu$as and a
64$\times$64 pixel grid, and used scan-averaged data. The algorithm proceeds
with an iterative sequence of gain calibration and cost function optimization.

###  3.3 SMILI

SMILI (Akiyama et al., 2017) is another RML imaging library that reconstructs
interferometric images utilizing a similar set of regularizers including
weighted-$\ell_{1}$ ($\ell_{1}^{w}$), total variation (TV), total squared
variation (TSV), and the maximum entropy regularizer (MEM). Prior to the
imaging, we rescale the intra-site baseline flux density of NRAO 530 (catalog
) to 0.9 Jy to remove the contributions from the large-scale extended
emission. During the imaging we adopt a field of view of 300 $\mu$as and a
150$\times$150 pixel grid, initializing the algorithm with a circular Gaussian
prior, and using 10 s averaged data set. Subsequently, the imaging algorithm
minimizes the regularized cost function. After 1000 iterations, self-
calibration of the stations gains is performed and the image prior is updated.
This imaging and self-calibration loop is repeated until the reconstruction
converges.

###  3.4 DMC

DMC formulates the imaging problem in terms of posterior exploration, which is
carried out using a Hamiltonian Monte Carlo sampler as implemented in the
PyMC3 Python package (Salvatier et al., 2016). The output of DMC is a
collection of samples from the joint posterior over the image structure and
calibration quantities. Rather than carrying out an iterative self-calibration
procedure, DMC fits the complex gains at every station simultaneously with the
full Stokes image structure. For NRAO 530 (catalog ) imaging, a field of view
of 300 $\mu$as and a 30$\times$30 pixel grid were used, the data were scan-
averaged, and D-terms were fixed following Issaoun, Wielgus et al. 2022. A
comprehensive description of the DMC model and implementation can be found in
Pesce (2021).

###  3.5  Themis

Themis is a framework for fitting VLBI data with a Markov chain Monte Carlo
(MCMC) posterior space exploration method (Broderick et al., 2020b). For NRAO
530 (catalog ) data analysis the image was modeled with a spline raster
defined using 6$\times$5 control points, and an adaptively selected field of
view (Broderick et al., 2020a). The data were scan-averaged. We solved for
D-terms with Themis in order to provide a consistency test for the fiducial
D-terms of EHTC et al. (2021) and Issaoun, Wielgus et al. 2022, see Section
4.1.

###  3.6 Fiducial Images of NRAO 530

Brightness Temperature ($10^{9}$ K)

Figure 4: Images of NRAO 530 (catalog ) from the 2017 April EHT observations
produced using DIFMAP, eht-imaging, SMILI, DMC and Themis, shown within the
adopted field of view of 128 $\mu$as. To simplify visual comparisons, the
models were blurred to similar effective resolutions $\sim 15\,\mu$as,
indicated in the bottom right corner of each image.

Figure 4 presents final (fiducial) total intensity images obtained by the
methods discussed in Sections 3.2-3.5. For the presentation purposes all
images are shown using the same field of view of $128\times 128\,\mu$as, more
narrow than the field of view typically used for the imaging. The contribution
of emission outside of this region is relatively small and consistent with the
image noise level, which in case of the EHT is rather high and dominated by
the systematic uncertainties related to sparse $(u,v)$-coverage. There is a
high degree of agreement between the different imaging methods in terms of the
source structure and the relative brightness of individual features. All
images show the jet to be elongated from the southeast to the northwest over
$\sim$60 $\mu$as. A visual inspection suggests that the jet consists of two
dominant features (see Figure 5), with the brightest one, C0, located at the
southeast end of the jet and itself exhibiting substructures C0a and C0b.
However, there is also a difference between the models – DIFMAP and DMC images
contain a very low-brightness extended feature that turns to the northeast,
almost by $\sim$90∘ to the main direction of the jet, the eht-imaging image
shows a hint of such a feature, while the SMILI and Themis methods do not
reveal its presence. This discrepancy is likely related to the latter two
algorithms promoting sparsity and compactness in the reconstructed images. We
have designated this ambiguous feature as C2 in Figure 5, marked by a dashed
line ellipse. Although the knot appears in the fiducial method-averaged image
if we increase the dynamic range, its brightness peak is on the level of the
image noise. In addition, DIFMAP, eht-imaging, and SMILI images correspond to
very similar peak brightness values, but the Themis and DMC images indicate
somewhat brighter and weaker brightness peaks, respectively.

Figure 3 shows consistency between closure phase measurements on selected
triangles and corresponding predictions of the fitted models. Table 1 provides
goodness of fit normalized $\chi^{2}$ statistics computed for the models shown
in Figure 4 for self-calibrated visibility amplitudes ($\chi^{2}_{\rm AMP}$),
closure phases ($\chi^{2}_{\rm CP}$), and log closure amplitudes
($\chi^{2}_{\rm logCA}$). The estimated total flux density of the compact
source model is also provided. This quantity is particularly challenging to
constrain with the EHT array, which in 2017 lacked baselines between 5
M$\lambda$ and 500 M$\lambda$ projected length, sensitive to mas-scale
emission. Based on the presented statistics, there is no strong preference for
any particular model. Therefore, we have combined the final images constructed
by the different methods, shown in Figure 4, to produce a fiducial method-
averaged total intensity image of NRAO 530 (catalog ), presented in Figure 5.
The averaging procedure involves aligning images to maximize their cross-
correlation, regridding them to a common resolution and field of view, and
taking a standard arithmetic mean on a pixel-by-pixel basis. It follows the
practice of EHTC et al. (2019d), Kim et al. (2020), EHTC et al. (2022c), and
Issaoun, Wielgus et al. 2022, and it is designed to make the resulting image
domain morphology more robust against method-specific systematics.

###  3.7 Total Intensity Component Modeling

Figure 5: Fiducial EHT total intensity image of NRAO 530 (catalog ); the color
scale corresponds to the brightness temperature; the contours represent the
total intensity, with a peak value of $1.4\times 10^{10}$ K, starting at 10%
of the peak and increasing in steps of 10%; the circle in the bottom right
corner shows the size of the nominal EHT beam with a FWHM diameter of 20
$\mu$as. The C2 contour is shown with dashed line as it is below the 10% level
of peak total intensity in the averaged image.  Table 1: Characterization of
the fits to NRAO 530 (catalog ) data.

Quantity | DIFMAP | eht-imaging | SMILI | DMC | Themis
---|---|---|---|---|---
$\chi^{2}_{\rm AMP}$ | 0.974 | 0.638 | 0.858 | 0.517 | 1.211
$\chi^{2}_{\rm CP}$ | 3.812 | 0.899 | 2.346 | 0.977 | 4.210
$\chi^{2}_{\rm logCA}$ | 1.513 | 1.137 | 2.727 | 0.943 | 2.844
Flux (Jy) | 1.030 | 0.958 | 0.899 | 1.585 | 1.120

NOTE – For the $\chi^{2}$ calculation the original thermal error budget was
inflated by a non-closing systematic error amounting to 2% of the complex
visibilities.

Table 2: Parameters of total intensity components.

Knot |  $S$ (mJy) |  $R$ ($\mu$as) |  $\Theta$ (deg) |  $a$ ($\mu$as) |  $T_{\rm b}$ (1010 K)
---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6)
DIFMAP (Gaussian modeling)
C0a | 278$\pm$29 | 1.8$\pm$4 | 85.6$\pm$71 | 16.3$\pm$4.2 | 2.3
C0b | 61$\pm$15 | 21.9$\pm$4 | 149.6$\pm$13 | 0.0 |
C1 | 124$\pm$15 | 35.1$\pm$5 | -26.9$\pm$9 | 15.0$\pm$3.8 | 1.3
C2 | 106$\pm$53 | 57.5$\pm$20 | -5.2$\pm$24 | 33$\pm$16 | 0.2
BG | 871 | 1.8 | 46.8 | 1000 |  $\cdots$
eht-imaging (Gaussian modeling)
C0a | 210 | 0.0 |  $\cdots$ | 10.6 | 4.4
C0b | 74 | 18.8 | 154.2 | 5.0 | 6.9
C1 | 108 | 28.5 | -21.2 | 15.8 | 1.0
C2 | 158 | 44.3 | -23.8 | 42.8$\times$13.6 | 0.6
BG | 1000 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
eht-imaging (image domain, no blur)
C0a | 228 | 0.0 |  $\cdots$ | 13.8$\times$12.3 | 3.1
C0b | 86 | 18.9 | 154.8 | 10.3$\times$11.5 | 1.7
C1 | 110 | 35.8 | -28.0 | 13.0$\times$12.7 | 1.6
BG | 978 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$

The columns are as follows: (1) - designation of knot; (2) - flux density in
mJy; (3) - distance from the core in $\mu$as; (4) - position angle with
respect to the core in degree; (5) - size in $\mu$as; (6) - observed
brightness temperature in 1010K.

Figure 6: A comparison between the leakage calibration D-terms estimated by
Themis from the NRAO 530 (catalog ) data set and D-terms assumed by other
imaging methods, following the procedures described in Section 2. Empty
circles correspond to LO band, crosses correspond to HI band, and error bars
represent 1$\sigma$ width of the Themis posteriors.

We have modeled the visibilities, calibrated to the fiducial image, with
circular Gaussian components using the task modelfit in DIFMAP. We also fitted
a Gaussian model to the data in the eht-imaging framework, using closure-only
data products to constrain the resolved source structure. In the latter case
the simplest model representing data properties sufficiently well consisted of
a single elliptical and 3 circular Gaussian components. Each component (knot)
is characterized by a flux density $S$ at distance $R$ from the center of the
image with the relative right ascension and declination equal to $(0,0)$,
located at the flux density peak of the image, a position angle $\Theta$ with
respect to the image center measured from north to east, and a size $a$
corresponding to the FWHM of the Gaussian brightness distribution.
Additionally, we performed modeling of the NRAO 530 (catalog ) eht-imaging
results by fitting elliptical Gaussian components to the image domain
features. Table LABEL:tab:modeling_total_intensity gives the results of these
three separate fitting procedures. To estimate uncertainties of components’
parameters we have used an approach employed in high frequency VLBI, e.g.,
Jorstad et al. (2005): the flux density uncertainties correspond to either 10%
of the flux density measurement or the noise level of the map obtained as the
result of the modelfit task in DIFMAP depending on whatever is higher, while
the position uncertainties are calculated as 1/5-th of the synthetic CLEAN
beam corresponding to the ($u,v$)-coverage for compact components, or equal to
the beam size for diffuse knots with a size larger than the size of the beam.

The source consists of two main components, C0 and C1, as indicated in Figure
5. The knots are separated by $\sim$30 $\mu$as, with C0 being a factor of
$\sim$3 brighter than C1. We associate C0 with the core of NRAO 530 (catalog )
at 1.3 mm and determine the jet direction on $\mu$as-scales to be $\sim-$28∘
east of north. All images shown in Figure 4 indicate non-trivial structure in
C0, elongated along the jet axis. The models super-resolve the substructure of
C0 into components C0a and C0b. In the case of DIFMAP the model yields the
best fit to C0b as a point source. We interpret the brighter component C0a as
the VLBI core. The weaker component C0b is located $\sim$20 $\mu$as southeast
from the C0a core, along the same jet axis as the C0a and C1 components.
Taking into account a small viewing angle of the jet, it is very unlikely that
C0b is a counter-jet component. Instead, we interpret C0b as the result of the
opacity stratification in the core, with C0b representing more optically thick
part of the jet. The Gaussian component fits show the presence of C2
component, and although uncertainties of the parameters are large, there is a
good agreement between the results of Gaussian fits of DIFMAP and eht-imaging
modeling.

We have calculated the observed brightness temperature of the knots, $T_{\rm
B}$, in the same manner as in Issaoun, Wielgus et al. 2022 (no cosmological
redshift or Doppler corrections accounted for). According to Table 2, C0 has a
higher $T_{\rm B}$ than the C1 component, which supports the interpretation
that it is a VLBI core at 1.3 mm. The observed brightness temperature of the
core is close to the equipartition value of $T_{\rm eq}\sim 5\times 10^{10}$ K
(Readhead, 1994), which implies an intrinsic (plasma frame) brightness
temperature $T^{\prime}_{\rm B}=T_{\rm B}(1+z)/\delta<<T_{\rm eq}$, if we
assume the same Doppler factor of $\delta\sim 9$ on $\mu$as scales as
estimated on mas scales (Jorstad et al., 2017). A robust comparison with
$T_{\rm eq}$ requires calculation of $T_{\rm B}$ either for an optically thin
knot or for the flux density corresponding to the turnover frequency in the
spectral energy distribution (SED) of a knot. However, the spectral index
obtained for NRAO 530 (catalog ) by Goddi et al. (2021) is steep, $\alpha\sim
0.8$ ($S_{\nu}\propto\nu^{-\alpha}$), while the source is dominated by the
core at 221 GHz, so that even for C0 we can assume that we measure $T_{\rm B}$
either near the turnover frequency or at the optically thin branch of the SED.
The brightness temperature is somewhat higher at lower frequencies, where the
core is optically thick. This will be discussed in a separate paper devoted to
multi-wavelength observations of NRAO 530 (catalog ) (Lisakov et al. in
prep.). The results shown in Table 2 also contain a large Gaussian component,
BG, with a flux density of $\sim$1 Jy, which characterizes the unconstrained
source emission on larger angular scales, overresolved on inter-site EHT
baselines.

##  4 Linear Polarization Images

We have performed linear polarization imaging of NRAO 530 (catalog ) using
four out of five algorithms described in Section 3: DIFMAP (CLEAN), eht-
imaging, DMC, and Themis. SMILI implementation does not currently have the
capability to reconstruct polarimetric images. Given the large and poorly
constrained systematic uncertainties in the polarimetric calibration of the
EHT data at times when ALMA is not participating in observations, only 2017
Apr 6 and 7 data were used, except for DMC, which allows for a very flexible
calibration of complex polarimetric gains simultaneous with the image
reconstruction (Pesce, 2021), and hence could reliably fit the entire data
set. Similarly, except for DMC and Themis, we disregarded JCMT single
polarization data for the LP analysis.

###  4.1 Consistency Test for D-terms

For all methods other than Themis, we either fixed all polarimetric leakage
D-terms following multi-source fitting procedures described in EHTC et al.
(2021) and Issaoun, Wielgus et al. 2022, or we only solved for the SPT
D-terms. The latter resulted in the SPT D-terms being no larger than 1%, with
uncertainties comparable to or larger than the values themselves, which
justifies setting SPT D-terms to zero. In the case of Themis, we performed
full fitting of D-term coefficients simultaneously with the image
reconstruction as an additional consistency test. In Figure 6 we provide a
comparison between the assumed and estimated D-terms. The results show a
generally high level of consistency, particularly when considering the
difficulty of quantifying the systematics present in a fit to a single
sparsely sampled data set. JCMT D-terms are constrained very poorly as a
consequence of the station operating with a single polarization receiver in
2017. There is a good correlation between the assumed and calculated D-terms,
corresponding to a Pearson coefficient of 0.86 for the vector of 64 D-terms
(ignoring the uncertainties) and median residual of 2% on a single complex
D-term. Altogether, the consistency test results support fixing D-terms for
the model fitting and data analysis.

Figure 7: Linear polarization images of NRAO 530 produced using DIFMAP, eht-
imaging, DMC, and Themis. The total intensity is shown in grayscale with black
contours indicating 10, 25, 50 and 75% of the peak LP intensity. Black dotted
contours indicate 25, 50, and 75% of the peak polarized intensity. The ticks
show the orientation of the EVPA, their length indicates linearly polarized
intensity magnitude, and their color indicates fractional linear polarization.
Cuts were made to omit all regions in the images where Stokes $\mathcal{I}<$
10% of the peak brightness and $\mathcal{P}<$ 10% of the peak polarized
brightness. The images are all displayed with a field of view of $128\,\mu$as,
and all images are blurred to an equivalent resolution of $20\,\mu$as.

###  4.2 Linear Polarization Images

Figure 7 presents LP images of NRAO 530 (catalog ) in 2017 April, obtained
using a selection of methods. The absolute magnitude of linear polarization
($\sqrt{\mathcal{Q}^{2}+\mathcal{U}^{2}}$ for LP Stokes image domain
components $\mathcal{Q}$ and $\mathcal{U}$) is indicated with white contours
and length of the electric vector position angle (EVPA) ticks, while the EVPA
tick colors represent fractional LP magnitude. The Faraday rotation toward
NRAO 530 (catalog ) is entirely negligible at 230 GHz (Goddi et al., 2021),
hence observed EVPA can be directly interpreted as an intrinsic source
property. The grayscale background image and black contours correspond to the
total intensity. Similarly as in Section 3.6, in Figure 8 we also present the
method-averaged image, where the background image and cyan contours represent
the LP magnitude, while the white contours describe the total intensity image
map. Similarly as in case of the total intensity images, we adopted images
shown in Figures 7-8 to a common field of view of $128\,\mu$as. The
contribution of the emission outside of this region is consistent with the
image noise.

Figure 8 serves the purpose of identifying the total intensity and LP
components. As for the total intensity images, the LP images show similar
structure across all algorithms, although there are some differences in the
polarization properties of the jet features. The most consistent among the
methods is the polarized feature P0 near the core, which has a slight shift to
the north-east with respect to the total intensity peak C0 in the DIFMAP, eht-
imaging, and DMC images. In the DMC image the polarized feature in the south-
east part of the C1 knot is most prominent, compared to images produced by the
other methods. The DIFMAP and DMC images show a polarized feature, P2,
associated with the diffuse northeastern total intensity component C2, which
has the highest degree of polarization. A hint of this feature can be seen in
the eht-imaging image, while the Themis image possesses a prominent polarized
feature P1 that is rather a combination of polarization that can be associated
with knot C1 and the northeastern component. Discrepancies seen in the Themis
image may be related to the spline raster resolution limitations imposed by
the MCMC algorithm. We expect that the method-averaged LP image, shown in
Figure 8, should reveal the most reliable image domain polarization features.

Figure 8: Schematic of the total-intensity (C0, C1, and C2) and linear
polarization (P0, P1, and P2) components in the EHT fiducial image of NRAO 530
(catalog ); white contours show the total intensity levels as in Figure 5;
color scale and cyan contours represent the polarized intensity of the method-
averaged image.

###  4.3 Linear Polarization Component Modeling

Table 3: Parameters of polarized components

Knot |  $R$ ($\mu$as) |  $\Theta$ (deg) |  $a$ ($\mu$as) |  $Q$ (mJy) |  $U$ (mJy) |  $m$ (%) | EVPA (deg)
---|---|---|---|---|---|---|---
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
DIFMAP (Gaussian modeling)
P0 | 5.7$\pm$2.1 | 47$\pm$32 | 15.3$\pm$0.7 | 9.8$\pm$4.0 | 14.8$\pm$5.0 | 5.2$\pm$1.3 | 28$\pm$7
P1 | 26.6$\pm$1.8 | 1$\pm$9 | 16.8$\pm$1.1 | 3.0$\pm$4.0 |  $-$7.7$\pm$5.0 | 6.7$\pm$2.5 |  $-$34$\pm$11
P2 | 55.8$\pm$1.0 | 6$\pm$5 | 14.0$\pm$1.0 |  $-$8.4$\pm$4.0 | 13.8$\pm$5.0 | 18.1$\pm$4.2 | 61$\pm$12
Map |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $-$6.1$\pm$4.0 | 24.7$\pm$5.0 | 1.7$\pm$0.6 | 52$\pm$10
ALMA |  $\cdots$ |  $\cdots$ |  $\cdots$ | $-8.6$ | $36.8$ | 2.35$\pm$0.03 | 51.6$\pm$0.4
eht-imaging (Gaussian modeling)
P0 | 0.0 |  $\cdots$ | 10.6 | 9.5 | 10.1 | 6.6 | 24.4
P1 | 28.5 | -21 | 15.8 | 11.8 | $-8.8$ | 13.6 | $-18.4$
P2 | 44.3 | -24 | 42.8$\times$13.6 | $-6.9$ | 13.0 | 15.2 | 59.0
Map |  $\cdots$ |  $\cdots$ |  $\cdots$ | $13.6$ | 17.2 | 4.1 | 25.8
eht-imaging (image domain, blur 15 $\mu$as)
P0 | 7.3 | 68 | 11.5 | 7.6 | 0.5 | 8.0 | 2
P1 | 31.1 | 12 | 10.4 | 5.6 | $-0.5$ | 22 | $-3$
P2 | 54.5 | 7 | 20.4 | $-9.8$ | 25.2 | 58 | 56
Map |  $\cdots$ |  $\cdots$ |  $\cdots$ | $-11.2$ | 15.5 | 2.7 | 63

NOTES – 1) values presented for the Map region are obtained by integrating
modes of Stokes $\mathcal{I}$, $\mathcal{Q}$, and $\mathcal{U}$ in the entire
VLBI field of view; 2) parameters presented for ALMA are results obtained by
Goddi et al. (2021) on 2017 Apr 6. The columns are as follows: (1) -
designation of knot; (2) - distance from the core in $\mu$as; (3) - position
angle with respect to the core in degree; (4) - size in $\mu$as; (5) - Stokes
Q value in mJy; (6) - Stokes U value in mJy; (7) - degree of polarization in
percentage; (8) - position angle of polarization in degree.

The method-averaged polarized intensity image presented in Figure 8 can be
described with three polarized features designated as P0, P1, and P2.
Similarly as in Section 3.7, we have modeled Stokes $\mathcal{Q}$ and
$\mathcal{U}$ visibilities in DIFMAP using the task modelfit, in eht-imaging
Gaussian component geometric modeling framework, and we also used image-domain
feature extraction methods to characterize the eht-imaging results. Table 3
gives parameters of the polarized components, which are as follows: 1)
polarized component; 2) distance between the center of the component and the
total intensity peak; 3) position angle of the component with respect to the
center; 4) FWHM size of the component; 5) Stokes $\mathcal{Q}$ parameter; 6)
Stokes $\mathcal{U}$ parameter; 7) fractional degree of polarization; and 8)
component EVPA. Since $\mathcal{Q}$ and $\mathcal{U}$ data were modeled
separately in DIFMAP, the distance, position angle, and size of a component
are calculated as averages over the $\mathcal{Q}$ and $\mathcal{U}$ values,
and standard deviations of the averages are given as uncertainties. The
uncertainties in $\mathcal{Q}$ and $\mathcal{U}$ flux intensity are equal to
the root mean square (rms) of the $\mathcal{Q}$ and $\mathcal{U}$ map noise.
Based on the uncertainties in $R$, $\Theta$, and $a$ values given in Table 3,
there is very good agreement in the position and size of polarized components
between $\mathcal{Q}$ and $\mathcal{U}$ images, which supports the robustness
of the DIFMAP modeling. We identify polarized components P0, P1, and P2 with
the total intensity components C0, C1, and C2, respectively, with parameters
of the latter given in Table 2. The distances of the associated total and
polarized intensity knots agree within 1.5 $\sigma$ uncertainties, and their
sizes are almost identical, except the P2/C2 pair in DIFMAP modeling where the
polarized component P2 occupies only a fraction (less than a half) of knot C2.
However, the position angles of P0 and P1 show some differences relative to
those of C0 and C1, respectively, which cause the centers of the polarized
components to be placed at the eastern edge of the corresponding total
intensity components. The other EHT Sgr A∗ (catalog ) calibrator, J1924-2914,
does not exhibit similar effect (Issaoun, Wielgus et al. 2022), despite the
fact that the two sources were calibrated in the same way and the same D-terms
were employed to correct for the instrumental leakage. Hence, we conclude that
these shifts are intrinsic to NRAO 530 (catalog ) rather than caused by
instrumental effects.

The LP image in Figure 8 shows polarized component P2, which we associate with
total intensity knot C2, detected with Gaussian component models. However, due
to its diffuse nature, the surface brightness of the knot is comparable with
the noise level, so that C2 is indicated as a marginal feature in Figure 5,
yet the knot has the highest degree of polarization in the jet. As mentioned
above, in the case of the DIFMAP model polarized emission of C2, knot P2,
occupies only a part of the total intensity feature. If we fix the size and
position of a total intensity component, C2, equal to those of P2, and search
for the total flux density corresponding to the region of P2, this will yield
a low value of $\sim$27 mJy, which implies the fractional polarization in the
P2 region as high as $\sim$60%. A similarly high degree of polarization is
obtained in the case of eht-imaging image domain analysis. Therefore, the P2
region should have an almost uniform magnetic field, which implies synchrotron
emission fractional polarization of $m_{\rm max}=(\alpha+1)/(\alpha+5/3)\times
100$=75% (Pacholczyk, 1970), assuming a spectral index for P2 of $\alpha\sim
1$. One of possible explanations why the knot is prominent in polarization but
not in the total intensity is that this feature could be caused by shear,
ordering the field, but not by shocks that would make it bright in total
intensity. For the geometric modeling of $\mathcal{Q}$ and $\mathcal{U}$ in
eht-imaging we assumed that each total intensity Gaussian component
corresponds to an LP component with a constant EVPA and fractional
polarization, obtaining a lower fractional polarization of C2/P2, which is
nevertheless significantly larger than that of the core component P0.

Image domain feature extraction with eht-imaging was based on masking
disjointed image regions by LP flux density following the procedures used in
Issaoun, Wielgus et al. 2022. We obtained three components that could be
identified with P0, P1, and P2 from Figure 8. The results given in Table 3 are
mostly in qualitative, if not quantitative, agreement between the methods,
although the parameters agree within the 1.5 $\sigma$ uncertainties given for
values obtained by DIFMAP. The differences that are present can be attributed
to the low polarized intensity in the jet relative to the polarized intensity
noise and the systematic uncertainties specific to different imaging methods.

Visual inspection of Figure 7 suggests that EVPAs in the P0/C0 region lie
between 20∘ – 35∘ in all polarization images, except the eht-imaging image,
which is also consistent with the result of the $\mathcal{Q}$ and
$\mathcal{U}$ map modeling in DIFMAP and eht-imaging Gaussian modeling. The
eht-imaging image shows the EVPA to be closer to 0∘, which can be explained by
the higher level of polarization noise in the image. All images show polarized
emission in the P1 region, with the EVPA close to the jet direction, while the
EVPA of P2 is perpendicular to the inner jet position angle as seen in the
DIFMAP and DMC images in Figure 7 and determined by modeling.

We have summed all CLEAN modes within the DIFMAP total intensity image in
Stokes parameter $\mathcal{I}$ (including the flux density of the BG
component, see Table 2), and Stokes parameters $\mathcal{Q}$, and
$\mathcal{U}$. This has resulted in an integrated total intensity flux of 1.5
Jy. Polarization parameters integrated over the sub-mas EHT image field of
view are listed in Table 3 under the component name “Map”. These parameters
agree reasonably well with those obtained by Goddi et al. (2021) for NRAO 530
(catalog ) at 221 GHz using ALMA data on 2017 Apr 6 and 7. There is very
little variability of the flux density or polarization parameters between the
two days, with flux densities reported by Goddi et al. (2021) equal to
1.61$\pm$0.16 Jy (Apr 6) and 1.57$\pm$0.16 Jy (Apr 7), and polarization
parameters obtained on 2017 Apr 6 reproduced in Table 3 under the component
name “ALMA”. Including Stokes parameters $\mathcal{Q}$ and $\mathcal{U}$ of
the P2 knot in the calculation of Map values is essential for a good agreement
with the polarization measurements obtained by Goddi et al. (2021).

###  4.4 Constraints on Circular Polarization

The circular polarization of NRAO 530 (catalog ) at 230 GHz observed by ALMA
(but unresolved) is consistent with zero (Goddi et al., 2021). The high
resolution of the EHT observation can be favourable for a detection of the
circular polarization in the jet of NRAO 530 (catalog ), which is important
for determining the plasma composition (Wardle et al., 1998). To find whether
there is a statistically significant signature of spatially resolved circular
polarization in the EHT VLBI data, we employed the same procedure as Issaoun,
Wielgus et al. 2022, based on exploring the posterior distributions of the DMC
fits to the observational data. Using 1000 images drawn from the posterior
distribution, and evaluating the mean and standard deviation of circular
polarization in each reconstructed pixel, we find no pixel with a Stokes
$\mathcal{V}$ detection of significance larger than 1.4 $\sigma$. Hence, we
conclude that we did not find statistically significant circular polarization
resolved with the EHT resolution of $\sim 20\,\mu$as. For comparison, the same
procedure applied to the linear polarization maps confirms detection at the
$\sim 7\,\sigma$ level. Because of large image reconstruction uncertainties,
this statement does not translate to a robust upper limit on the fractional
circular polarization.

##  5 Discussion

The high-resolution total and polarized intensity images of the quasar NRAO
530 (catalog ) at 230 GHz obtained during the EHT campaign in 2017 April
indicate a jet direction of $\sim-$28∘ on $\mu$as scales. This jet direction
is different from those seen at 86 GHz (PA$\sim$10∘, Issaoun et al. 2019) and
43 GHz (PA$\sim-$3∘, Weaver et al. 2022), implying a wiggling of the jet with
the distance from the core. In fact, the PA of component C2/P2 (see Table 3)
agrees with that of the jet direction at 86 GHz within the uncertainties,
which can be a sign of jet curvature already at this location. If that is
indeed the case, the EVPA of the P2 component could be more aligned with the
local direction of the bending jet, which supports the origin of the emission
in the shear. The curvature could be caused by an imbalance between the
pressure inside and outside the jet resulting in the development of
instabilities in the flow, or it could be connected with jet precession. An
analysis of the jet structure from sub-parsec to kiloparsec scales using
multi-wavelength VLBI images of NRAO 530 (catalog ) contemporaneous with the
230 GHz EHT image will be presented in Lisakov et al. (in prep.).

The brightest feature in the source, C0, which we associate with the VLBI core
at 1.3 mm, is complex and consists of two components, C0a and C0b. Complex
structure in the core was also revealed in the EHT images of the quasar 3C 279
(Kim et al., 2020). Variability of such core structures can be expected on
short timescales with quasi-periodic oscillations produced by kink
instabilities in the case of a magnetically dominated jet (Dong et al., 2020).
The intrinsic brightness temperatures of both C0 components are lower than the
equipartition brightness temperature (see Table 2), even if the Doppler factor
of the jet on $\mu$as scales is lower than that found on mas scales. A
possible explanation is that the energy density of the jet on $\mu$as scales
is dominated by the magnetic field.

Homan et al. (2006) have analyzed brightness temperatures of VLBI cores at 15
GHz of a large sample of AGN. They have found that, in a quiescent state,
cores have a narrow range of intrinsic brightness temperatures close to the
value expected for equipartition, while during outbursts the characteristic
intrinsic brightness temperature significantly exceeds $T_{\rm eq}$. The
authors have estimated that in active states the energy in radiating particles
exceeds the energy in the magnetic field by a factor of $\sim$105. This
implies that somewhere between the 230 GHz and 15 GHz cores there is a region
where a magnetically dominated jet changes its state and reaches equipartition
conditions. Moreover, Jorstad et al. (2007) suggested, based on quasi-
simultaneous multi-epoch observations at 43 GHz (VLBA), 86 GHz (BIMA777The
Berkeley-Illinois-Maryland Array- Association (BIMA) operated at 3 mm and
1.3mm until 2004), and 230/345 GHz (JCMT), that this region is located between
the 86 GHz and 43 GHz VLBI cores, while Lee (2013) has found that 86 GHz VLBI
cores in a sample of compact radio sources observed with Global Millimeter
VLBI Array have a characteristic intrinsic brightness temperature lower than
the equipartition temperature. The observed low brightness temperature of C0
somewhat supports this scenario. However, analysis of the simultaneous VLBI
observations at 230 and 86 GHz is needed to draw firm conclusions.

The polarized features in the jet are shifted with respect to the total
intensity components with which they are associated. The shifts are almost
transverse to the inner jet direction – the jet direction is from southeast to
northwest, while the shifts are to the east. This feature appears robust in
the image reconstructions. One viable interpretation of this phenomenon
involves a difference in ordering of the magnetic field transverse to the jet,
with the magnetic field on the eastern part of the jet being more ordered than
that of the western part. This can be understood if the magnetic field in the
jet consists of two components – ordered and turbulent, with the turbulent
component being more pronounced on the western side of the jet, while a
helical magnetic field can represent the ordered component. Indeed, a helical
structure of the magnetic field is supported by the EVPA behavior in different
polarized components. The EVPA undergoes significant changes along $\sim$60
$\mu$as of the jet length: it goes from being oblique in the core to aligning
with the jet direction in P1 $\sim$30 $\mu$as to perpendicular to the inner
jet direction in P2 $\sim$55 $\mu$as from the core. In addition, a higher
polarization at the western side can be attributed to velocity shear between
the jet boundary and the ambient medium being stronger on the western side,
which is consistent with the explanation of the nature of component P2/C2.
However, the EVPA behavior is more aligned with a helical magnetic field,
although we do not have a sufficient resolution to resolve the EVPA structure
across the jet. Recent work by Pushkarev et al. (2022) analyzed the
polarization properties in a large sample of AGN observed with the VLBA at 15
GHz within the MOJAVE survey presented transverse fractional polarization
slices beyond the core region for 307 sources. The authors have found that the
majority of the sources (including NRAO 530 (catalog )) show a clear increase
in fractional polarization towards the jet edges, with an asymmetric profile.
They suggest that the observed patterns of polarization can be explained by
helical magnetic fields with different pitch angles and different geometric
and kinematic parameters of the jet, which is surrounded by a sheath. It
therefore appears that a helical magnetic field structure persists in the
quasar jet from sub-parsec to hundred-parsec scales.

In addition to EHT data, we have obtained optical polarization observations of
NRAO 530 (catalog ) several days before and after the EHT campaign. Figure 9
shows polarization measurements in the optical R-band, at 221 GHz for the
arcsec resolution of ALMA (Goddi et al., 2021), and those of the EHT resolved
components at 230 GHz. The optical observations were carried out with the 1.8
m Perkins telescope (Flagstaff, AZ) using the PRISM camera. The description of
data reduction can be found in Jorstad et al. (2010). When comparing to the
optical and ALMA values, the best agreement across wavelengths is found with
the P2 component, indicating dominance of the magnetic field direction
perpendicular to the $\mu$as scale jet direction in the source. This suggests
that the magnetic field direction in the optical emission region is similar to
that of P2, which has the highest degree of polarization in the jet.

Figure 9: Top: Degree of linear polarization at optical R-band (blue), ALMA at
221 GHz (red), and EHT knots P0 (black), P1 (green), and P2 (magenta); Bottom:
Position angle of polarization with the same color coding; parameters of knots
are shown according to DIFMAP model.

##  6 Summary

Using the 2017 EHT observations we have obtained the first total and polarized
intensity images of the quasar NRAO 530 (catalog ) at 230 GHz, with an
unprecedented angular resolution of $\sim$20 ${\mu}$as. We have not detected
statistically significant variability of the source structure on a timescale
of three days, and hence we have combined the data over epochs and frequencies
to generate final images. We have used a variety of methods to construct the
total and linearly polarized intensity images and averaged the final
reconstructions produced by different methods to obtain the fiducial total and
polarized intensity maps.

On ${\mu}$as scales the quasar has a bright core of $\sim$300 mJy, with a jet
extending up to 60 ${\mu}$as along a PA${\sim}-$28∘. The core has sub-
structure consisting of two features, C0a and C0b. We associate the 1.3 mm
VLBI core with the brightest knot, C0a, while C0b, located at a PA$\sim$+155∘
and $\sim$ 3 times weaker than C0a can be a more opaque region of the core.
The core is polarized, with a degree of polarization of $\sim$5$-$8%. The
extended jet includes two features, C1/P1 and C2/P2, with mutually orthogonal
directions of polarization, parallel and perpendicular to the jet,
respectively, suggestive of a helical magnetic field structure. The centers of
the polarized knots P0 and P1 are shifted slightly transverse to the jet with
respect to the centers of the corresponding total intensity knots C0 and C1.
This can be caused either by a more ordered magnetic field on the eastern side
of the jet, connected with a helical structure of the magnetic field, or a
stronger interaction between the jet and the external medium on this side.

Feature C2 has the highest degree of polarization in the jet, $\sim 20\%$.
However, polarized knot P2, which occupies only a fraction of the total area
of C2, has a peak polarization of $\sim 60\%$. The latter implies a nearly
uniform magnetic field in the P2 region. In fact, the optical polarization
measurement nearest in time to the EHT campaign has an EVPA similar to that in
P2. NRAO 530 (catalog ) is a bright $\gamma$-ray source, and the origin of
high-energy emission in blazars continues to be highly debated. We can
speculate that the P2 region, with a very uniform magnetic field, might be a
location where non-thermal optical and high energy emission originates. Future
multi-epoch and multi-wavelength observations of the source simultaneous with
EHT campaigns can provide a significant advance toward understanding the
location of the high-energy dissipation zone in blazar jets.

## Acknowledgments

The Event Horizon Telescope Collaboration thanks the following organizations
and programs: the Academia Sinica; the Academy of Finland (projects 274477,
284495, 312496, 315721); the Agencia Nacional de Investigación y Desarrollo
(ANID), Chile via NCN$19\\_058$ (TITANs) and Fondecyt 1221421, the Alexander
von Humboldt Stiftung; an Alfred P. Sloan Research Fellowship; Allegro, the
European ALMA Regional Centre node in the Netherlands, the NL astronomy
research network NOVA and the astronomy institutes of the University of
Amsterdam, Leiden University and Radboud University; the ALMA North America
Development Fund; the Black Hole Initiative, which is funded by grants from
the John Templeton Foundation and the Gordon and Betty Moore Foundation
(although the opinions expressed in this work are those of the author(s) and
do not necessarily reflect the views of these Foundations); Chandra DD7-18089X
and TM6-17006X; the China Scholarship Council; China Postdoctoral Science
Foundation fellowship (2020M671266); Consejo Nacional de Ciencia y Tecnología
(CONACYT, Mexico, projects U0004-246083, U0004-259839, F0003-272050,
M0037-279006, F0003-281692, 104497, 275201, 263356); the Consejería de
Economía, Conocimiento, Empresas y Universidad of the Junta de Andalucía
(grant P18-FR-1769), the Consejo Superior de Investigaciones Científicas
(grant 2019AEP112); the Delaney Family via the Delaney Family John A. Wheeler
Chair at Perimeter Institute; Dirección General de Asuntos del Personal
Académico-Universidad Nacional Autónoma de México (DGAPA-UNAM, projects
IN112417 and IN112820); the Dutch Organization for Scientific Research (NWO)
VICI award (grant 639.043.513) and grant OCENW.KLEIN.113; the Dutch National
Supercomputers, Cartesius and Snellius (NWO Grant 2021.013); the EACOA
Fellowship awarded by the East Asia Core Observatories Association, which
consists of the Academia Sinica Institute of Astronomy and Astrophysics, the
National Astronomical Observatory of Japan, Center for Astronomical Mega-
Science, Chinese Academy of Sciences, and the Korea Astronomy and Space
Science Institute; the European Research Council (ERC) Synergy Grant
“BlackHoleCam: Imaging the Event Horizon of Black Holes" (grant 610058); the
European Union Horizon 2020 research and innovation programme under grant
agreements RadioNet (No 730562) and M2FINDERS (No 101018682); the Horizon ERC
Grants 2021 programme under grant agreement No. 101040021; the Generalitat
Valenciana postdoctoral grant APOSTD/2018/177 and GenT Program (project
CIDEGENT/2018/021); MICINN Research Project PID2019-108995GB-C22; the European
Research Council for advanced grant ‘JETSET: Launching, propagation and
emission of relativistic jets from binary mergers and across mass scales’
(Grant No. 884631); the Institute for Advanced Study; the Istituto Nazionale
di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEONGRAV;
the International Max Planck Research School for Astronomy and Astrophysics at
the Universities of Bonn and Cologne; DFG research grant “Jet physics on
horizon scales and beyond” (Grant No. FR 4069/2-1); Joint Columbia/Flatiron
Postdoctoral Fellowship, research at the Flatiron Institute is supported by
the Simons Foundation; the Japan Ministry of Education, Culture, Sports,
Science and Technology (MEXT; grant JPMXP1020200109); the Japanese Government
(Monbukagakusho: MEXT) Scholarship; the Japan Society for the Promotion of
Science (JSPS) Grant-in-Aid for JSPS Research Fellowship (JP17J08829); the
Joint Institute for Computational Fundamental Science, Japan; the Key Research
Program of Frontier Sciences, Chinese Academy of Sciences (CAS, grants QYZDJ-
SSW-SLH057, QYZDJSSW-SYS008, ZDBS-LY-SLH011); the Leverhulme Trust Early
Career Research Fellowship; the Max-Planck-Gesellschaft (MPG); the Max Planck
Partner Group of the MPG and the CAS; the MEXT/JSPS KAKENHI (grants 18KK0090,
JP21H01137, JP18H03721, JP18K13594, 18K03709, JP19K14761, 18H01245, 25120007);
the Malaysian Fundamental Research Grant Scheme (FRGS)
FRGS/1/2019/STG02/UM/02/6; the MIT International Science and Technology
Initiatives (MISTI) Funds; the Ministry of Science and Technology (MOST) of
Taiwan (103-2119-M-001-010-MY2, 105-2112-M-001-025-MY3, 105-2119-M-001-042,
106-2112-M-001-011, 106-2119-M-001-013, 106-2119-M-001-027,
106-2923-M-001-005, 107-2119-M-001-017, 107-2119-M-001-020,
107-2119-M-001-041, 107-2119-M-110-005, 107-2923-M-001-009,
108-2112-M-001-048, 108-2112-M-001-051, 108-2923-M-001-002,
109-2112-M-001-025, 109-2124-M-001-005, 109-2923-M-001-001,
110-2112-M-003-007-MY2, 110-2112-M-001-033, 110-2124-M-001-007, and
110-2923-M-001-001); the Ministry of Education (MoE) of Taiwan Yushan Young
Scholar Program; the Physics Division, National Center for Theoretical
Sciences of Taiwan; the National Aeronautics and Space Administration (NASA,
Fermi Guest Investigator grants 80NSSC20K1567 and 80NSSC22K1571, NASA
Astrophysics Theory Program grant 80NSSC20K0527, NASA NuSTAR award
80NSSC20K0645); NASA Hubble Fellowship grants HST-HF2-51431.001-A, HST-
HF2-51482.001-A awarded by the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
for NASA, under contract NAS5-26555; the National Institute of Natural
Sciences (NINS) of Japan; the National Key Research and Development Program of
China (grant 2016YFA0400704, 2017YFA0402703, 2016YFA0400702); the National
Science Foundation (NSF, grants AST-0096454, AST-0352953, AST-0521233,
AST-0705062, AST-0905844, AST-0922984, AST-1126433, AST-1140030, DGE-1144085,
AST-1207704, AST-1207730, AST-1207752, MRI-1228509, OPP-1248097, AST-1310896,
AST-1440254, AST-1555365, AST-1614868, AST-1615796, AST-1715061, AST-1716327,
AST-1716536, OISE-1743747, AST-1816420, AST-1935980, AST-2034306); NSF
Astronomy and Astrophysics Postdoctoral Fellowship (AST-1903847); the Natural
Science Foundation of China (grants 11650110427, 10625314, 11721303, 11725312,
11873028, 11933007, 11991052, 11991053, 12192220, 12192223); the Natural
Sciences and Engineering Research Council of Canada (NSERC, including a
Discovery Grant and the NSERC Alexander Graham Bell Canada Graduate
Scholarships-Doctoral Program); the National Youth Thousand Talents Program of
China; the National Research Foundation of Korea (the Global PhD Fellowship
Grant: grants NRF-2015H1A2A1033752, the Korea Research Fellowship Program:
NRF-2015H1D3A1066561, Brain Pool Program: 2019H1D3A1A01102564, Basic Research
Support Grant 2019R1F1A1059721, 2021R1A6A3A01086420, 2022R1C1C1005255);
Netherlands Research School for Astronomy (NOVA) Virtual Institute of
Accretion (VIA) postdoctoral fellowships; Onsala Space Observatory (OSO)
national infrastructure, for the provisioning of its facilities/observational
support (OSO receives funding through the Swedish Research Council under grant
2017-00648); the Perimeter Institute for Theoretical Physics (research at
Perimeter Institute is supported by the Government of Canada through the
Department of Innovation, Science and Economic Development and by the Province
of Ontario through the Ministry of Research, Innovation and Science); the
Princeton Gravity Initiative; the Spanish Ministerio de Ciencia e Innovación
(grants PGC2018-098915-B-C21, AYA2016-80889-P, PID2019-108995GB-C21,
PID2020-117404GB-C21); the University of Pretoria for financial aid in the
provision of the new Cluster Server nodes and SuperMicro (USA) for a SEEDING
GRANT approved towards these nodes in 2020; the Shanghai Pilot Program for
Basic Research, Chinese Academy of Science, Shanghai Branch (JCYJ-
SHFY-2021-013); the State Agency for Research of the Spanish MCIU through the
“Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de
Andalucía (SEV-2017- 0709); the Spinoza Prize SPI 78-409; the South African
Research Chairs Initiative, through the South African Radio Astronomy
Observatory (SARAO, grant ID 77948), which is a facility of the National
Research Foundation (NRF), an agency of the Department of Science and
Innovation (DSI) of South Africa; the Toray Science Foundation; the Swedish
Research Council (VR); the US Department of Energy (USDOE) through the Los
Alamos National Laboratory (operated by Triad National Security, LLC, for the
National Nuclear Security Administration of the USDOE (Contract
89233218CNA000001); and the YCAA Prize Postdoctoral Fellowship.

We thank the staff at the participating observatories, correlation centers,
and institutions for their enthusiastic support. This paper makes use of the
following ALMA data: ADS/JAO.ALMA#2016.1.01154.V. ALMA is a partnership of the
European Southern Observatory (ESO; Europe, representing its member states),
NSF, and National Institutes of Natural Sciences of Japan, together with
National Research Council (Canada), Ministry of Science and Technology (MOST;
Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA;
Taiwan), and Korea Astronomy and Space Science Institute (KASI; Republic of
Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory
is operated by ESO, Associated Universities, Inc. (AUI)/NRAO, and the National
Astronomical Observatory of Japan (NAOJ). The NRAO is a facility of the NSF
operated under cooperative agreement by AUI. This research used resources of
the Oak Ridge Leadership Computing Facility at the Oak Ridge National
Laboratory, which is supported by the Office of Science of the U.S. Department
of Energy under Contract No. DE-AC05-00OR22725. We also thank the Center for
Computational Astrophysics, National Astronomical Observatory of Japan. The
computing cluster of Shanghai VLBI correlator supported by the Special Fund
for Astronomy from the Ministry of Finance in China is acknowledged. This work
was supported by FAPESP (Fundacao de Amparo a Pesquisa do Estado de Sao Paulo)
under grant 2021/01183-8.

APEX is a collaboration between the Max-Planck-Institut für Radioastronomie
(Germany), ESO, and the Onsala Space Observatory (Sweden). The SMA is a joint
project between the SAO and ASIAA and is funded by the Smithsonian Institution
and the Academia Sinica. The JCMT is operated by the East Asian Observatory on
behalf of the NAOJ, ASIAA, and KASI, as well as the Ministry of Finance of
China, Chinese Academy of Sciences, and the National Key Research and
Development Program (No. 2017YFA0402700) of China and Natural Science
Foundation of China grant 11873028. Additional funding support for the JCMT is
provided by the Science and Technologies Facility Council (UK) and
participating universities in the UK and Canada. The LMT is a project operated
by the Instituto Nacional de Astrófisica, Óptica, y Electrónica (Mexico) and
the University of Massachusetts at Amherst (USA). The IRAM 30-m telescope on
Pico Veleta, Spain is operated by IRAM and supported by CNRS (Centre National
de la Recherche Scientifique, France), MPG (Max-Planck-Gesellschaft, Germany)
and IGN (Instituto Geográfico Nacional, Spain). The SMT is operated by the
Arizona Radio Observatory, a part of the Steward Observatory of the University
of Arizona, with financial support of operations from the State of Arizona and
financial support for instrumentation development from the NSF. Support for
SPT participation in the EHT is provided by the National Science Foundation
through award OPP-1852617 to the University of Chicago. Partial support is
also provided by the Kavli Institute of Cosmological Physics at the University
of Chicago. The SPT hydrogen maser was provided on loan from the GLT, courtesy
of ASIAA.

This work used the Extreme Science and Engineering Discovery Environment
(XSEDE), supported by NSF grant ACI-1548562, and CyVerse, supported by NSF
grants DBI-0735191, DBI-1265383, and DBI-1743442. XSEDE Stampede2 resource at
TACC was allocated through TG-AST170024 and TG-AST080026N. XSEDE JetStream
resource at PTI and TACC was allocated through AST170028. This research is
part of the Frontera computing project at the Texas Advanced Computing Center
through the Frontera Large-Scale Community Partnerships allocation AST20023.
Frontera is made possible by National Science Foundation award OAC-1818253.
This research was carried out using resources provided by the Open Science
Grid, which is supported by the National Science Foundation and the U.S.
Department of Energy Office of Science. Additional work used ABACUS2.0, which
is part of the eScience center at Southern Denmark University. Simulations
were also performed on the SuperMUC cluster at the LRZ in Garching, on the
LOEWE cluster in CSC in Frankfurt, on the HazelHen cluster at the HLRS in
Stuttgart, and on the Pi2.0 and Siyuan Mark-I at Shanghai Jiao Tong
University. The computer resources of the Finnish IT Center for Science (CSC)
and the Finnish Computing Competence Infrastructure (FCCI) project are
acknowledged. This research was enabled in part by support provided by Compute
Ontario (http://computeontario.ca), Calcul Quebec (http://www.calculquebec.ca)
and Compute Canada (http://www.computecanada.ca).

The EHTC has received generous donations of FPGA chips from Xilinx Inc., under
the Xilinx University Program. The EHTC has benefited from technology shared
under open-source license by the Collaboration for Astronomy Signal Processing
and Electronics Research (CASPER). The EHT project is grateful to T4Science
and Microsemi for their assistance with Hydrogen Masers. This research has
made use of NASA’s Astrophysics Data System. We gratefully acknowledge the
support provided by the extended staff of the ALMA, both from the inception of
the ALMA Phasing Project through the observational campaigns of 2017 and 2018.
We would like to thank A. Deller and W. Brisken for EHT-specific support with
the use of DiFX. We thank Martin Shepherd for the addition of extra features
in the Difmap software that were used for the CLEAN imaging results presented
in this paper. We acknowledge the significance that Maunakea, where the SMA
and JCMT EHT stations are located, has for the indigenous Hawaiian people.

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