# The spatially offset quasar E1821+643: New evidence for gravitational recoil

Yashashree Jadhav,1 Andrew Robinson,2 Triana Almeyda3 Rachel Curran2 and
Alessandro Marconi4
1Astronomy Program, Department of Physics and Astronomy, Seoul National
University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
2School of Physics and Astronomy, Rochester Institute of Technology, 1 Lomb
Memorial Drive, Rochester, NY 14623, USA
3Department of Biological and Physical Sciences, South Carolina State
University, Orangeburg, SC 29117,USA
4University of Florence, Firenze, Florence E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

A galaxy merger is expected to cause the formation of a supermassive black
hole (SMBH) binary, which itself eventually coalesces through the anisotropic
emission of gravitational waves. This may result in the merged SMBH receiving
a recoil kick velocity $\sim 100-1000$ kms-1, causing it to oscillate in the
gravitational potential of the host galaxy. The luminous quasar E1821+643,
identified as an SMBH recoil candidate via spectropolarimetry observations,
shows Doppler shifting of the broad emission lines in direct and scattered
light, consistent with a relative velocity of 2100 km s-1 between the quasar
nucleus and host galaxy. In this paper, we attempt to detect the expected
spatial displacement using a combination of optical spectroastrometry and
Hubble Space Telescope (HST) narrow band images. The spectroastrometry reveals
a relative spatial displacement between the quasar nucleus and the gas
emitting the [OIII]$\lambda\lambda 4959,5007$ lines of $\sim 130$mas ($\sim
580$ pc) to the North-West. Our HST images resolve the [OIII] emission on sub-
arcsecond scales, showing that it is asymmetrically distributed, extending to
radial distances $\sim 0.5-0.6$″from the nucleus in a wide arc running from
the North-East around to the West. A simulated spectroastrometry observation
based on the HST [OIII] image indicates that only a small fraction of the
measured displacement can be attributed to the asymmetric [OIII] emission.
This displacement therefore appears to be a real spatial offset of the quasar
nucleus with respect to the narrow-line region, presumed to be located at the
host galaxy center, further supporting the interpretation that a post-merger
gravitational recoil of the SMBH has occurred in E1821+643.

###### keywords:

quasars: supermassive black holes – gravitational waves – quasars: emission
lines

††pubyear: 2020††pagerange: The spatially offset quasar E1821+643: New
evidence for gravitational recoil–The spatially offset quasar E1821+643: New
evidence for gravitational recoil

##  1 Introduction

There is compelling evidence that a supermassive blackhole (SMBH) resides at
the center of every large galaxy in the universe. In active phases, when
accreting gas at a sufficient rate, SMBHs can be identified as active galactic
nuclei (AGN).

Galaxy mergers are thought to play a major role in galaxy and SMBH evolution.
Following a major merger (two relatively similar sized large galaxies
merging), the two SMBHs are expected to form a binary at the center of the
merged galaxy (Begelman et al., 1980). The resulting SMBH binary tightens
through dynamical processes and then eventually coalesces through anisotropic
emission of gravitational waves (e.g., Merritt & Milosavljević (2005)). In
general, the gravitational radiation is emitted anisotropically, causing the
merged SMBH to receive a recoil kick (Favata et al., 2004). Detailed
simulations following the coalescence of spinning black holes (Baker et al.,
2006; Campanelli et al., 2007) have shown that kick velocities up to several
$\times 10^{3}$ kms-1 are possible for certain binary black hole (BBH) spin
configurations (Campanelli et al., 2007; Lousto et al., 2012).

The post recoil oscillations are affected by several different initial
conditions including the kick velocity as well as the gas content of the
galaxy (Blecha et al., 2016). During the initial harmonic oscillations that
are quickly damped due to dynamical friction, the recoiling SMBH can have
oscillation amplitudes greater than the radius of the core of the galaxy
(Gualandris & Merritt, 2008). These are followed by shorter amplitude, longer
lived oscillations which eventually turn to Brownian motion as the SMBH
settles down in the center of the merged galaxy.

The kicked SMBH retains some of the surrounding gas depending on the kick
velocity. The radius ($R_{out}$) within which the material remains bound to
the recoiling SMBH is given by,

$R_{out}\sim\left(\frac{GM}{v^{2}_{rec}}\right)\sim
0.43\left(\frac{M}{10^{8}\mbox{M}_{\odot}}\right)\left(\frac{v_{rec}}{10^{3}\mbox{km\,s}^{-1}}\right)^{-2}\,\mbox{pc}$
(1)

where $M$ is the mass and $v_{rec}$ the kick (recoil) velocity of the SMBH
(Loeb, 2007). This is the radius at which the Keplerian velocity is equal to
the recoil velocity. Depending on the recoil velocity, typically the broad
line region (BLR) remains bound to the SMBH while the narrow line region (NLR)
is left behind.

As long as the SMBH continues to accrete gas, it can be identified as an AGN.
Recoiling SMBH can then be identified through spatial offsets between the
position of the AGN and the center of the galaxy using imaging (e.g, offset
optical, IR, Radio, X-ray point sources; (e.g., Batcheldor et al., 2010; Lena
et al., 2014)). A second method of detecting the recoiling SMBH is by
analyzing the Doppler shifts of emission lines from the retained gas, showing
a relative velocity between the SMBH and the host galaxy. For example, if part
of the BLR is retained, the broad Balmer lines will be shifted with respect to
the narrow lines (e.g., Bonning et al., 2007).

Offset AGN are signposts of binary SMBH coalescence, which in turn are strong
sources of gravitational waves. Even though the frequencies of these waves are
too low to be detected by the Laser Interferometer Gravitational-Wave
Observatory (LIGO), identifying these events can help build the base sample
for Laser Interferometer Space Antenna (LISA) and Pulsar Timing Arrays. We can
also use instances of recoiling SMBH in the nearby universe to further
understand the rate of galaxy mergers which allows us to study galaxy
evolution.

The quasar E1821$+$643 has been identified as an SMBH recoil candidate by
Robinson et al. (2010) (hereafter R10) using spectropolarimetry. E1821$+$643
is a radio-quiet quasi stellar object (RQQ) at a redshift of $z\approx 0.3$,
and with an absolute magnitude of MV = -27.1 (Pravdo & Marshall, 1984;
Hutchings & Neff, 1991), it is one of the most luminous quasars in the local
universe. Although classified as an RQQ, it exhibits many similarities to
radio-loud quasars (RLQs) and is associated with an FR-1 radio source
(Blundell & Rawlings, 2001). Hutchings & Neff (1991) have found that the host
galaxy is red, featureless and very large, with an estimated diameter of 75
kpc ($\sim$ 24″ ), which suggests an elliptical galaxy – however most RQQs are
located in spiral galaxies. It has a huge extended emission line region
(Fried, 1998), and is located at the center of a cooling flow (Russell et al.,
2010), in a cluster of galaxies with an Abell richness class $\geq$ 2 (Lacy et
al., 1992) – which again, is usually typical of RLQs. Russell et al. (2010)
trace the Intra-Cluster Medium (ICM) gas down to $\sim$ 15 kpc from the
nucleus – about the extent of the emission line nebula, and calculate that the
QSO is currently accreting at 50% of the Eddington rate.

Figure 1: The spectrum of the nucleus of E1821$+$643 extracted from the
combined 2D spectrum obtained with the Gemini Multi-Object Spectrograph.

In the radio, there is extended low-surface brightness emission well beyond
the host galaxy (Blundell & Rawlings, 2001). On arcsecond scales, there is a
$\sim$90∘ bend in the south-west jet, which may be due to precession in a
binary, as suggested by Blundell et al. (1996); Blundell & Rawlings (2001),
but could also be explained by a spin-flip during a binary supermassive black
hole (SMBH) merger (Merritt & Ekers, 2002).

R10 conducted spectropolarimetric observations of E1821+643 as a part of a
project to characterize the polarization properties of the broad lines in AGN.
They found that the broad Balmer lines are redshifted by $\approx$ 1000 km s-1
with respect to the narrow lines and have highly red asymmetric profiles. In
polarized light, however, the broad lines are found to be comparably blue
shifted with corresponding highly blue asymmetric profiles. R10 explained
these characteristics in terms of a scattering model where the BLR moves away
from the observer and towards a scattering region in the host galaxy with a
speed $\sim 2000$ kms -1. Thus, in direct light, the BLR appears to be red
shifted with respected to the NLR. However, light from the BLR that is emitted
toward the scattering region is scattered back towards the observer, becomes
polarized and blue-shifted (as the source is moving towards the scattering
screen).

At such a velocity, the accretion disk and the bulk of the BLR remain bound to
the moving SMBH. Thus, the spectropolarimetry observations can be interpreted
as evidence the SMBH is moving through the galaxy due to a recent
gravitational recoil following the coalescence of a progenitor SMBH binary. On
the assumption that the $\sim$90∘ bend in the south-west jet is due to a spin-
flip, R10 estimated that the time that has elapsed since the coalescence event
is $\sim 1000$ yr and hence that the recoiling SMBH may have moved a distance
$\sim 200$ pc.

The spectropolarimetry results provide unambiguous evidence of a large
relative velocity between the BLR and the host galaxy (as represented by the
narrow-line system). However, R10 note that, in addition to the recoil
hypothesis, such a velocity difference could also be produced if the BLR forms
part of a one-sided wind, or is associated with an active secondary in a
binary system.

In an effort to detect the expected spatial displacement and differentiate
between the various interpretations, we have obtained high signal-to-noise
spectra suitable for spectroastrometric analysis from the Gemini North
telescope in Hawaii as well as the Hubble Space Telescope (HST) narrow and
broad band imaging observations.

We describe the data reduction, analysis and results in Section 2,
spectroastrometry in Section 2.1 and HST imaging in Section 2.2. Simulated
spectroastrometry observations were performed to determine if the observed
spectroastrometric displacement can be explained by spatially extended [Oiii]
4959, 5007Å emission (Section 3). We discuss our results in Section 4 and
finally, present our conclusions in Section 5.

Figure 2: A section of the long-slit spectrum obtained at PA = 0∘, showing the
region of H$\beta$ and [Oiii] 4959, 5007Å (in order from left to right). The
extended [Oiii] can clearly be seen towards the north (bottom of the image).
The detector chip-gap can also clearly be seen to the right of the [Oiii]
lines.

At the redshift, $z=0.297$, of E1821+643, the angular scale is 4.568
kpc/arcsec, assuming $H_{0}=67.4$ km s-1 Mpc-1, and $\Omega_{m}=0.315$(Planck
Collaboration et al., 2020).

##  2 Observations and Results

###  2.1 Spectroastrometry

####  2.1.1 Observations

Figure 3:  The spatial profile of the [Oiii] 5007Å emission line (black),
extracted from the PA=0∘ spectrum at the line center wavelength ($6493.2$Å).
The red line represents a gaussian fit to the spatial profile. The fit is
restricted to the peak of the profile, between the $25^{th}$ and $75^{th}$
percentiles, to prevent any extended emission from biasing the fit.

We acquired deep optical spectroscopy of E1821$+$643 in an attempt to detect a
spatial offset between the broad and narrow emission lines by means of
spectroastrometric analysis, i.e. studying the spatial displacements between
the different emission line velocity systems (see Bailey, 1998, for a
description of the spectroastrometry technique). The observations were
obtained at the Gemini North telescope in Hawaii, using the Gemini Multi-
Object Spectrograph (GMOS) in long-slit mode, on the nights of 20100424
(science) and 20100323 (flux calibrations). The R400 grating was used in
conjunction with a 1″ slit centered on the quasar nucleus. Two exposures of
600 s each were obtained with the slit at position angles of 0∘, 90∘ and 270∘.
See figure 2 for a section of the spectra at 0∘. Due to a “seeing bubble”,
3$\times$600s spectra were taken with the slit at a position angle of 180∘,
although only one of these was deemed useful for the spectroastrometry
analysis. CuAr arcs were taken at each position angle, immediately prior to
the object spectra.

####  2.1.2 Data Reduction & Analysis

The data were reduced using the Gemini: GMOS package within IRAF. This was
used to subtract the bias, divide by a normalized flatfield, combine the data
from the three CCDs, remove the sky emission lines and, wavelength and flux
calibrate the two-dimensional spectra. The spectra were then trimmed to remove
second order contamination at the red wavelength end and cosmic rays were
removed in the standard way.

Combined 2-D spectra were formed for the North-South and East-West directions.
The two exposures at each position angle were first co-added, with the
exception of PA = 180∘, for which only one usable spectrum was obtained. The
usable spectrum taken at PA=180° was aligned and combined with the averaged PA
= 0° spectrum, to produce a single North-South spectrum with a total exposure
time of 1800 s. Similarly, the co-added PA = 270° and 90° spectra were aligned
and combined to produce a single East-West spectrum with a total exposure time
of 2400 s . One-dimensional spectra were then extracted from 1″ apertures in
1″ spatial increments along each direction.

Finally, all of the 2-D spectra were combined to form a single spectrum with a
total exposure time of 4200 s, from which a 1-D spectrum of the nucleus was
then extracted using a 1″ aperture. The resultant spectrum can be seen in
figure 1.

Figure 4: The displacement spectra derived from the Gemini long-slit
observations. The dotted lines indicate the emission lines. The top panel is
the total flux. The middle and bottom panels show the displacement spectra in
the N-S and E-W direction respectively.  Figure 5: Displacement and flux
profiles for [OIII] 4959Å. The top left and right panels show the offset of
the [Oiii] line in the E-W and N-S directions. The bottom left panel shows the
flux for the [Oiii] 4959Å line. The bottom right panel shows the N-S and E-W
offset components of the [Oiii] 4959Å line as color coded by wavelength along
with the best fit line (in black). Figure 6: As figure 5 for [Oiii] 5007Å

Spectroastrometry is a technique for measuring the relative spatial
displacements of spectral features such as emission lines. This is done by
measuring the position of the source in the long slit 2-D spectrum as a
function of wavelength. If the spatial profile is sufficiently well sampled,
the position of its centroid can be measured to a precision of the order of
milli-arcseconds. Any wavelength dependent asymmetries in the spatial profile
will appear as deviations in the resulting ‘displacement spectrum’.

Spectroastrometry was carried out on the co-added 2D spectra obtained at each
PA following the general method described by Bailey (1998). Gaussians were
fitted to the spatial profiles to determine the position of the peak of the
flux distribution for each pixel along the dispersion direction. However, as
our HST images (Section 2.2.3) show that the nucleus is surrounded by extended
[Oiii] $\lambda\lambda$4959,5007 emission, the spatial profiles were fitted
between the $25^{th}$ and 75th percentiles (see Fig. 3), to minimize any bias
in the peak position due to asymmetries in the spatial distribution of the
extended line emission. The ”spectrum” of peak positions derived from the fits
was then fit using a low-order polynomial in wavelength to remove overall
curvature in the ‘continuum’ spectra. The spatial offsets from the fitted
polynomial were then calculated at each wavelength, yielding a spectrum of the
displacement relative to continuum for each PA. Finally, the PA =180∘ data
were subtracted from the 0∘ data, and the 270∘ data were subtracted from the
90∘ data to remove any instrumental effects. The final result is a spectrum of
the spatial displacements in, respectively, the North-South and East-West
directions.

####  2.1.3 Spectroastrometry results

In this case, we are looking for a displacement between the broad and narrow
emission lines in the spectrum of E1821+643. Such spatial displacements are
expected in the recoil hypothesis if the BLR remains bound to the SMBH but the
gas emitting the narrow lines is left behind. Segments of the displacement
spectra covering H$\beta$ – [Oiii] and H$\alpha$ – [Nii] are shown in figure 4
for both the N-S and E-W directions. The redshifted wavelengths of the
emission lines that fall within these segments are indicated. The displacement
is measured relative to the continuum. As this is dominated by the quasar
nucleus, it has zero displacement by definition. Similarly, the broad
components of the H$\alpha$ and H$\beta$ lines show no displacement relative
to the continuum. This is not surprising since the BLR is expected to have an
angular size $\lesssim 1$ mas, which is not detectable in our
spectroastrometry data. The N-S and E-W displacement spectra show clear
offsets in the [Oiii] $\lambda\lambda$4959,5007 lines in the North and West
directions. Smaller, but still significant displacements are also associated
with the narrow components of H$\alpha$ and H$\beta$. The other lines do not
show any significant offset.

The amplitudes of the displacements in the [Oiii] lines were determined by
fitting gaussians to the peaks of the displacement profiles. This yields
amplitudes of $\approx 40$ and 30 mas to the West and North of the nucleus,
respectively, in [Oiii] $\lambda 5007$ (Table 1). The maximum displacements in
[Oiii] $\lambda 4959$ are about half those in [Oiii] $\lambda 5007$. The
narrow components of H$\alpha$ and H$\beta$ only show significant
displacements to the West of the nucleus, with amplitudes $\sim 5$ and 3 mas,
respectively. No significant displacements are seen in the other narrow lines,
such as [Oi] $\lambda\lambda 6300,6363$, [Nii] $\lambda\lambda 6548,6583$, and
[Sii] $\lambda\lambda 6717,6731$, which are, however, comparatively weak.

Table 1: Measured displacements for the [Oiii] lines

Line | PA | $\mu_{NS}$ | $\mu_{EW}$
---|---|---|---
| ∘ | mas | mas
[OIII] 4959 Å | -52.9 | 14.9$\pm$1.0 | 19.7$\pm$1.9
[OIII] 5007 Å | -53.0 | 29.5$\pm$2.4 | 39.2$\pm$1.2

The values $\mu_{NS}$ and $\mu_{EW}$ were derived by fitting Gaussians to the
displacements in the North-South and East-West direction. The uncertainties
are the 1-$\sigma$ errors on the best fit amplitude. The PAs are calculated
from the displacement components.

The displacements across the [Oiii] $\lambda\lambda$4959,5007 lines are shown
in more detail in figures 5 and 6, respectively. In addition to having
different amplitudes in the E-W and N-S directions, the displacement profiles
show distinct structures. The flux profiles are asymmetric, showing an
extended blue wing in the E-W direction. The corresponding displacement
profile is similarly asymmetric, showing a prominent extended wing on the blue
side of the profile, which indicates a displacement to the West. In the N-S
direction, the cores of both [Oiii] lines show large displacements to the
North, as already noted, but the wings exhibit small displacements ($\sim 5$
mas in [Oiii] $\lambda$5007) to the South on both sides of the profile. The
[Oiii] 4959Å line shows similar structure, albeit with smaller displacements.

The E-W and N-S components of the measured displacement are plotted in the
lower right panels of figures 5 and 6. The corresponding radial displacement
in [Oiii] $\lambda$5007 has a magnitude $\approx 50$ mas with a position angle
PA$\approx 305^{\circ}$. However, the measured displacements are affected by
wavelength-dependent ”dilution” due to the underlying quasar light, which has
a greater effect on the weaker lines. For example, both of the [Oiii] lines
are superposed on the very extended red wing of the broad H$\beta$ line
(Figure 1), but [Oiii] $\lambda$4959 is not only weaker than [Oiii]
$\lambda$5007 but the local quasar flux (i.e., the continuum and broad
H$\beta$ emission) is also higher and therefore its displacement signal
suffers relatively higher dilution. A simple correction for this dilution
effect is presented in Section 3.2.

The curved pattern in the displacement locus seen in the bottom right panels
in figures 5 and 6 is a result of the asymmetry in the E-W flux profile, which
is not seen in the N-S displacement profile. This asymmetry appears to be
associated with the extended blue wing in the flux profiles, suggesting that
there is an outflow present, which is predominantly to the west of the
nucleus.

###  2.2 HST imaging

####  2.2.1 HST observations

Understanding the morphology of the narrow line region on sub-arcsecond scales
will help to determine whether the spectroastrometric displacements presented
in Section 2.1.3 are due to a spatial offset between the quasar nucleus and
the NLR or an asymmetric distribution of the [Oiii] emission caused by partial
extinction of a bi-polar outflow. In order to map the [Oiii] emission around
the quasar and the host galaxy we obtained HST ACS (Advanced Camera for
Surveys) Wide Field Camera images of E1821+643 (proposal ID 13385, PI A.
Robinson). Narrow band images centered on the [Oiii]$\lambda\lambda$4959,5007
and H$\beta$ lines were obtained using the FR656N ramp filter set to central
wavelengths of 6460Åand 6305Å, respectively. Medium band continuum images were
also obtained using the F647M ramp filter centered at 7300Å.

For the [Oiii] and continuum observations, we used a combination of short
exposures to obtain high signal-to-noise but unsaturated images of the quasar
nucleus and longer exposures to map the host galaxy and extended [Oiii]
emission on scales $\sim$ a few arcseconds. A two-point dither pattern was
used for each set of exposures.

The dithered images were processed and combined through the ACS data
calibration pipeline. After processing, the saturated pixels around the quasar
nucleus in the long exposure images were replaced with the corresponding
unsaturated pixels extracted from the the short exposure images and scaled to
the long exposure image. The resulting images are shown in figure 7.

Visual inspection shows that the quasar nucleus is the dominant source in both
the continuum and [Oiii] images. In the continuum image, only the quasar point
spread function (PSF) is visible, showing that the host galaxy contribution is
negligible. The quasar PSF is also the dominant feature in the narrow band
image. However, clumpy emission extending in an arc from North to North-East
is visible at a distance $\sim 3$ arcseconds (13.7 kpc) from the nucleus. This
is not present in the continuum image and can therefore be attributed to the
[Oiii] lines. However, in order to map the [Oiii] on smaller scales, it is
necessary to subtract the quasar PSF.

####  2.2.2 HST image analysis

PSF subtraction was performed for the FR656N image both manually and using the
Galfit image decomposition software, which models the 2D light distribution of
galaxy images (Peng et al., 2002). An ACS image of a white dwarf standard
star, GRW+70D5824 (spectral type DA3), observed with the same filter FR656N
was obtained from the HST Legacy Archive (proposal ID: 9563) and used as a
model for the PSF.

To facilitate the PSF modeling we re-sampled the image, to expand the pixel
dimensions of the image by a factor of 3. The up-sampled image has a plate
scale of 0.017″ /pixel.

For the manual subtraction, the flux of the standard star was scaled to match
that of the nuclear point source in the FR656N [Oiii] image. However, to avoid
over-subtraction of the [Oiii] emission it is necessary to account for its
contribution to the flux of the unresolved quasar nucleus. We estimated the
[Oiii] contribution by fitting the [Oiii]$\lambda\lambda$4959,5007 lines in
the Gemini spectrum of the nucleus of E1821+643 (Fig. 1). The fit was used to
generate a spectrum containing only the [Oiii] lines and both this and the
nuclear spectrum were separately convolved with the FR656N filter transmission
curve generated using the formulae provided by Bohlin & Tsvetanov (2000) in
order to estimate the fraction of the the nuclear flux within the FR656N
bandpass that is due to [Oiii] emission. We find that about $\sim$20% of the
nuclear flux in the 1″ aperture from which the spectrum was extracted is
contributed by the [Oiii] lines. In order to perform the PSF subtraction, the
integrated flux of the standard star (i.e. the PSF template) within an
aperture of 1″ was matched to that within the same sized aperture centered on
the nucleus in the FR656N [Oiii] image and then scaled by 80% to account for
the [Oiii] contribution. The star was then subtracted from the [Oiii] image to
reveal the distribution of the resolved [Oiii] emission as seen in figure 8.

Galfit was also used to fit the quasar nucleus in the FR656N [Oiii] image,
using the scaled standard star as the PSF template (middle image in figure 9).
A Sérsic component was also included in the fit to model the galaxy light.
which was then subtracted from the original to reveal the [Oiii] distribution.
However, no significant differences were found in the residuals between models
which included or excluded the Sérsic component component, suggesting that the
galaxy component is negligible in comparison with the quasar nucleus.

Figure 7: HST ACS/WFC images. Left to right, FR647M, FR656N, FR656N. Figure 8:
Manual PSF subtraction. From left, the first panel shows the FR656N ramp
filter [OIII] image, the middle panel shows the standard star used as the PSF
template and the last panel shows the asymmetric distribution of the [OIII]
emission after subtraction of the point source. The direction is the same as
in figure 7. The individual images have been scaled in brightness in order to
highlight the circum-nuclear morphology. Figure 9: PSF subtraction using
Galfit. From left, the first panel shows the FR656N ramp filter [OIII], the
middle panel shows the Galfit model and the last panel shows the Galfit
residual showing the distribution of the [OIII] emission after subtraction of
the point source. Figure 10: FR656N ramp filter [Oiii] image after manual PSF
subtraction (Fig. 8). The image is shown at three different contrast levels to
reveal the morphology of the circum-nuclear and extended [Oiii] emission
around the nucleus of E1821+643. Figure 11: Residual of the ACS/WFC F647M
continuum image of E1821+643 after point source subtraction.

Although visual inspection of the F647M (continuum) image, as well as modeling
of the FR656N [Oiii] image, suggests that the host galaxy contribution is
insignificant, we nevertheless attempted to quantify this by modeling the
continuum image with Galfit. An ACS image of a white dwarf standard star,
GD71, observed with the same filter, FR647M, was obtained from the HST Legacy
Archive (proposal ID: 9020). The unresolved quasar nucleus was fitted using
the star as a PSF model. The residual image, after subtraction of the fitted
PSF model is shown in fig 11. As can be seen, PSF structure is still present
in the residual image, showing that the quasar light has not been entirely
removed. We performed aperture photometry on the original continuum image and
on the residual image, to obtain relative fluxes within the three regions used
for the simulated spectroastrometry observation described in Section 3 (the
unresolved nucleus within a radius $0.12\arcsec$, the annulus between
0.12$\arcsec$ and 0.5$\arcsec$ and the surrounding region beyond
0.5$\arcsec$). We found that the residual image only contributes $\sim 10\%$
of the total light in the continuum image within all three regions. However,
due to the PSF mismatch, the residual contains a significant proportion of
light from the quasar, and so the flux measured from residual image only sets
an upper limit on the contribution of the galaxy component. This result is
consistent with the image decomposition analyses of Floyd et al. (2004) and
Kim et al. (2017), both of whom estimate that the entire galaxy contributes
$\sim 10\%$ of the total flux in the $I$ band.

####  2.2.3 Results of HST image analysis

Both the manual subtraction as well as the Galfit modeling produced similar
spatial distributions of the [Oiii] emission after PSF subtraction as seen in
figures 8 and 9. The spatial distribution of the [Oiii] emission is shown at
three different contrast levels in Figure 10, with the left panel showing the
extended structure while the other two panels reveal the morphology of the
circum-nuclear emission. It is apparent that the emission around the nucleus
is partly resolved and forms a wide fan-shaped structure, spanning
approximately $135\degr$ of azimuth from North-East to West. This structure is
approximately 1″ (4.6 kpc) wide and 1.6″ (7.3 kpc) long. The emission extends
radially as far as $\sim 0.5$ arcsecond North of the quasar nucleus, which is
slightly off-center to the South-East. There is a second, fainter, arc-like
structure of clumpy [Oiii] emission that extends from East to North at
distances $\sim 3$″ (13-14 kpc) from the nucleus. This feature is probably
photoionized by the quasar and may be associated with a tidal tail from on
ongoing interaction with a gas rich satellite galaxy (Rosborough et al., 2021,
in preparation).

##  3 Spectroastrometry modelling

In this section, we present a simulated spectroastrometry observation, to
determine if the measured displacements can be explained by the asymmetric
distribution of the circum-nuclear extended [Oiii] emission, and describe a
simple model to correct the measured displacements in the [Oiii] lines for
dilution by the quasar continuum and broad H$\beta$ line.

###  3.1 Simulated spectroastrometry observation

Figure 12: Spectra used in the spectroastrometry modeling. The top panel shows
the spectrum extracted from a 1 arcsec aperture centered on the nucleus. The
[Oiii] and narrow H$\beta$ lines have been fitted and subtracted so that this
spectrum shows only the quasar continuum and the broad emission lines. The
middle panel shows the model fitted to the [Oiii] lines. The bottom panel
shows the spectrum extracted from a 1$\arcsec$ aperture offset 1″ from the
nucleus. All plots show the flux density normalized to the flux obtained by
convolving the spectrum with the FR656N filter response.  Figure 13:  Annuli
used for the spectroastrometric simulations superimposed on the FR656 [OIII]
image. The inner blue circle shows the unresolved nucleus enclosing the PSF
within the first Airy ring. This region is represented by a spectrum that
includes the quasar continuum and broad line emission with a 90% contribution
from the [Oiii] lines, representing the unresolved [Oiii] emission (see text
and Fig. 12, top and middle panels). The annulus between the blue and red
circles encloses the [Oiii] emission that is resolved in the HST image but not
in the Gemini spectra. This region is represented by the fitted narrow lines
extracted from the spectrum of the nucleus (Fig. 12, middle panel). Beyond the
red circle, the extended [Oiii] emission is represented by a spectrum
extracted from an aperture offset by 1$\arcsec$ from the nucleus (Fig. 12,
bottom panel). The blue and red circles have radii of 0.12$\arcsec$ and
0.5$\arcsec$, respectively.

Figure 14: Spectroastrometric modelling results: The top panel shows the
reconstructed spectrum of the quasar extracted from the spectroastrometry
modeling simulations. The middle and bottom panels show the simulation of
spectroastrometric displacement spectrum where you see the expected
displacement. Middle panel: the slit is along North-South Direction. Bottom
panel: Slit is along West - East direction

The spectroastrometry shows a significant displacement between the [Oiii]
lines and the nucleus in the North-West direction (Section 2.1.3) . However,
as discussed above (Section 2.2.3) the HST image analysis shows that the
[Oiii] emission is also asymmetrically distributed with respect to the
nucleus, in broadly the same direction as the spectroastrometric displacement.
Thus, we must consider the possibility that part or all of spectroastrometric
displacement is actually caused by the asymmetric spatial distribution of the
[Oiii] emission rather than a spatial offset of the quasar nucleus. To test
this, we constructed a simulated spectroastrometry observation by combining
the HST [Oiii] image with spectra of the nucleus and the extended [Oiii]
emission extracted from the Gemini data.

A three dimensional array was created by combining the re-sampled [Oiii] image
with the Gemini spectra, where the third dimension is wavelength. Each pixel
of the image was assigned one of the three spectra described below, depending
on its position. Each spectrum was first normalized by the flux obtained by
convolving the spectrum with the FR656N filter response and then scaled to the
pixel flux from the image. The three spectra represent, respectively, the
unresolved nucleus in the HST image, an annulus surrounding the unresolved
nucleus of outer radius 0.5$\arcsec$, which corresponds to the 1$\arcsec$
aperture from which the Gemini spectrum of the nucleus was extracted, and the
extended [Oiii] emission at distances $>0.5$$\arcsec$ from the nucleus. These
regions are indicated in figure 13 by the blue shaded circle and the red
circle, respectively. The region containing the unresolved nucleus (blue
circle in Figure 13) is defined by a circle centered on the peak of the PSF,
which has a radius of 0.12$\arcsec$ ($\sim$7 re-sampled pixels). This is
approximately the radius of the first Airy ring.

The spectrum representing the unresolved nucleus was constructed from the 1-D
nuclear spectrum that was extracted from the combined Gemini 2-D spectrum
(Section 2.1). However, as the 1 arcsec extraction aperture is $\sim 4\times$
larger than the HST PSF, the spectrum contains light from resolved (in the HST
image) [Oiii] emission as well as unresolved [Oiii] emission from the nucleus.
To estimate and remove the contribution of the resolved [Oiii] emission, the
[Oiii] and H$\beta$ narrow lines were fitted and subtracted from the nuclear
spectrum, leaving only the continuum and broad emission lines (top and middle
panels of Figure 12). Simulated spectra were then computed using the method
described below, in which the unresolved nucleus was represented by the
continuum plus broad line spectrum with varying fractions of the fitted [Oiii]
and H$\beta$ narrow line spectrum added. This process was repeated until the
intensity of the [Oiii] lines relative to that of broad H$\beta$ matched that
of the original observed spectrum. In this way, we estimate that $90\%$ of the
[Oiii] emission in the spectrum extraction aperture is unresolved in the HST
image (i.e., it comes from the inner blue circle in Figure 13).

We assume that the [Oiii] emission that is resolved in the HST image, but
within 0.5$\arcsec$ of the nuclear point source, is dominated by the narrow
line emission that is blended with the quasar nucleus emission within the
Gemini extraction aperture. We represent this by the normalized [Oiii] and
H$\beta$ spectrum obtained from the fit to the nuclear spectrum (middle panel
in Figure 12). This was applied within the annulus between 0.12$\arcsec$ and
0.5$\arcsec$, shown by the blue and red circles in Figure 13), and represents
the 1 arcsec extraction aperture from which the nuclear spectrum was obtained.
This region encompasses most of the extended [Oiii] emission around the
quasar. Finally, the [OIII] emission that extends beyond the central
arcsecond, (the region beyond the red circle in Figure 13) was represented by
a spectrum extracted from a 1 arcsec aperture offset by 1 arcsec away from the
nucleus (bottom panel in Figure 12).

The resulting data cube was convolved with a PSF modeled by a Gaussian profile
representing the typical seeing conditions for the Gemini observations and a
simulated 2-D long-slit spectrum was extracted both in the North-South and
East-West directions. Spectroastrometric measurements were then performed just
as for the original spectrum by fitting Gaussians along the spatial direction
at each wavelength. The resulting flux and displacement spectra are shown in
Figure 14. In the N-S direction The [Oiii]$\lambda 5007$ line shows a
displacement relative to the continuum of $\sim 9$ mas to the North, while in
the E-W direction, the displacement is $5.5$ mas to the East.

The simulated displacement spectra therefore yield a displacement in the N-S
direction which is in the same direction, but only 1/3 the amplitude of that
measured directly from the Gemini data. In the E-W direction, the simulated
displacement is actually in the opposite direction (East, whereas the measured
displacement is to the West) and only $\sim 1/10$ of the amplitude of the
measured value. This result shows that the measured spectroastrometric
displacement cannot be entirely explained by the asymmetric spatial
distribution of the narrow line emission.

###  3.2 Spectroastrometric continuum correction

As noted in Section 2.1.3, the measured displacements will be smaller than the
actual displacements due to dilution by the emission from the quasar itself
(by which we mean the continuum and broad emission lines) and the underlying
galaxy. In order to correct the measured displacements for dilution and find
the ‘true’ displacement, we follow the analysis in Porter et al. (2004),
approximating the QSO and the host galaxy as point sources. Assuming that the
host galaxy flux, $f_{\star}$, and the quasar flux, $f_{Q}$, vary slowly with
wavelength ($\lambda$), then $f_{\star,j}\approx f_{\star}$ and
$f_{Q,j}\approx f_{Q}$, where $j$ is the pixel index in the spectral
direction. We adapt eq. 4 in Porter et al. (2004) by adding a term
representing the narrow line flux, $f_{NL,j}$, which is assumed to be
spatially coincident with the point source representing the host galaxy. With
this modification,

$\begin{split}\frac{\mu_{j}}{d}&=\frac{f_{NL,j}+f_{\star}}{f_{NL,j}+f_{\star}+f_{Q}}-\frac{f_{\star}}{f_{Q}+f_{\star}}\end{split}$
(2)

where $\mu_{j}$ is the measured displacement, $f_{NL,j}$ is the narrow line
flux, and $d$ is the actual displacement (in the same units as $\mu_{j}$).

We define

$\begin{split}W_{NL,j}&=\frac{f_{NL,j}}{F_{C}}\end{split}$ (3)

and

$\begin{split}r_{\star}&=\frac{f_{\star}}{F_{C}}\end{split}$ (4)

where $F_{C}=f_{\star}+f_{Q}$ is the total continuum flux. By substitution in
equation 2 we get,

$\begin{split}\frac{\mu_{j}}{d}&=\frac{W_{NL,j}}{W_{NL,j}+1}(1-r_{\star})\end{split}$
(5)

In E1821+643, the host galaxy light contributes only a small fraction of
$F_{C}$ compared to the quasar nucleus, hence $r_{\star}<0.1$ (Section 2.2.2)
and

$\begin{split}\mu_{j}&\approx\frac{W_{NL,j}}{W_{NL,j}+1}d\end{split}$ (6)

This model gives us a linear relationship between the measured displacement
and the ratio of the narrow line to continuum fluxes, as given by eq. 6. The
slope, $d$, of this relationship is the corrected (”true”) displacement
between the two sources. This was determined for both [Oiii] lines in the N-S
and E-W directions from linear fits, with the values of $\mu_{j}$ and
$W_{NL,j}$ taken from the corresponding displacement and flux spectra (Figure
4), respectively. An example is shown in Figure 15. The corrected values of
the displacement for the two [Oiii] lines are given in Table 2, along with the
measured values from Table 1 for comparison. All values refer to the
displacement measured at the center of the line. The quoted uncertainties on
the $d$ values are those returned by the fit. The corrected displacements are
consistent for both lines (as is expected) and have similar magnitudes of
$\sim$80 - 90 mas, in both directions. If we assume the maximal estimated
galaxy contribution, and set $r_{\star}=0.1$, the corrected displacements
increase relative to those listed in Table 2 by approximately 10%.

The corrected displacements given in Table 2 correspond to a linear projected
distance of $\sim$400pc in each direction and hence a radial displacement
$\sim 580$ pc to the NW, where the position angles are calculated from the
corrected displacements. The results of the spectroastrometry analysis
therefore indicate that the quasar nucleus – i.e., the central continuum
source and BLR – is spatially offset by $\sim 580$ pc to the NW of the gas
producing the [Oiii] emission, i.e., the NLR. This seems consistent with the
gravitational recoil hypothesis as proposed by R10, with the accretion disk
and BLR remaining bound to the recoiling SMBH, whilst the NLR gas is left
behind. In this case, the SMBH would be recoiling away from the galaxy center
in the South - East direction.

Figure 15: Spectroastrometric continuum correction. The relationship between
the measured displacement and the ratio of the narrow line to continuum fluxes
is shown for [OIII]5007Å in the E-W direction. The slope of the relation
yields the continuum-corrected displacement, $d$, (Equation 6). The black line
shows the linear fit to the data between approximately 6473Å and 6504Å, from
which the value $d$ listed in (Table 2) was obtained. The “flat” portion of
the relation around $\mu_{j}\sim 0$ is associated with the continuum on either
side of the line. The ‘loop’ at higher displacements arises from the asymmetry
in the displacement profile (Figure 6, top left panel).  Table 2: Measured and
corrected spectroastrometric displacements for the [Oiii] lines

Line | PA | $\mu_{NS}$ | $\mu_{EW}$ | $d_{NS}$ | $d_{EW}$
---|---|---|---|---|---
| ∘ | mas | mas | mas | mas
[OIII] 4959 Å | -41.7 | 14.9$\pm$1.0 | 19.7$\pm$1.9 | 89.03 $\pm$ 6.72 | 79.22 $\pm$4.38
[OIII] 5007 Å | -44.1 | 29.5$\pm$2.4 | 39.2$\pm$1.2 | 90.64 $\pm$ 4.82 | 87.70 $\pm$ 3.87

$d_{NS}$ and $d_{EW}$ are derived from $\mu_{NS}$ and $\mu_{EW}$ respectively
by using equation 6 for the North-South and East-West direction.The PAs are
calculated from the corrected displacement.

##  4 Discussion

R10 proposed the quasar E1821+643 as an SMBH gravitational recoil candidate
based on spectropolarimetric observations showing a velocity shift $\sim 2000$
km s-1 between the broad and narrow emission lines. If this interpretation is
correct, one would expect the quasar nucleus to be spatially displaced from
the centre of its host galaxy. R10 estimated that the SMBH could have moved a
distance $\gtrsim 200$ pc since the progenitor SMBH binary coalesced. This
corresponds to an angular distance $\sim 40$ mas, which is too small to be
measured directly from HST images. The isophotal analysis technique employed
by Batcheldor et al. (2010) and Lena et al. (2014) cannot be used since the
quasar point source dominates the light from the host galaxy.

However, our spectroastrometry observations reveal spatial displacements in
the [Oiii] lines of $\sim 80-90$ mas (after continuum correction) to both the
North and West, relative to the optical continuum and broad emission lines
(i.e., the quasar nucleus). The implied radial displacement of $\sim 130$ mas
corresponds to a projected distance $\sim$ 580 pc in the North-West direction
(Figure 4). Given that the optical continuum is dominated by the quasar
nucleus and that the NLR is located at the center of the host galaxy, this
implies that the SMBH is spatially offset to the South-East relative to the
galaxy center.

Our HST/ACS narrow band image resolves the [Oiii] emission around the quasar
and shows that it is asymmetrically distributed with respect to the unresolved
nucleus. After subtracting the quasar point source, it can be seen that the
[Oiii] emission spans a wide arc in azimuth from the North-East around to the
West and extends radially $\sim 0.5$″($\sim 2.3$ kpc) to the North-West of the
nucleus.

The quasar is slightly off-center to the South-East with respect to the
surrounding [Oiii] emission, as would be expected if the measured
spectroastrometric displacement represents a real spatial offset. However, the
morphology of the [Oiii] emission is itself asymmetric, and this could also
cause the spectropolarimetric displacement.

We tested this possibility by constructing simulated spectroastrometry
observations using the spatial distribution of the [Oiii] emission as mapped
by the HST image. The displacements obtained in the simulations are much
smaller in magnitude than the measured values (about 30% and $\lesssim 15$% of
the measured displacements along the North-South and East-West axes,
respectively) and furthermore the displacement along the East-West axis is in
the opposite direction to that observed (i.e., East rather than West). This
indicates that the asymmetric structure of the [Oiii] emission can account for
only a small fraction of the measured spectroastrometric displacement, which
must therefore largely represent a real spatial offset.

At the inferred recoil velocity, the SMBH would retain its accretion disk and
the bulk of the BLR, but the NLR (and the more extended [Oiii] emission) would
be left behind R10. The observed spectroastrometric displacement spectrum can
therefore be explained in terms of gravitational recoil of the SMBH: there is
no displacement between the broad H$\alpha$ and H$\beta$ lines and the
continuum, as the accretion disk and BLR remain bound to the SMBH, but the
displacement in the [Oiii] lines can be attributed to the SMBH recoiling in
the opposite direction (i.e., to the South-East). The size of the offset is a
factor $\sim 3$ larger than the lower limit estimated by R10, but that is
based on a jet advance speed of $0.1c$ and the actual speed could well be
slower. R10 also argued that the recoil velocity vector should be roughly
aligned with the radio axis, which is oriented NW-SE, consistent with the
direction of the spectroastrometric displacement.

E1821+643 has been the subject of a long-term optical photometric and
spectroscopic monitoring campaign (Shapovalova et al., 2016; Kovačević et al.,
2017, 2018). Shapovalova et al. (2016) measured reverberation lags between the
optical continuum and broad H$\beta$ and H$\gamma$ lines of 120 d and 60 d,
respectively, and estimate that the SMBH has a mass $\sim 3\times 10^{9}$ M⊙.
For this mass and the inferred recoil velocity, material orbiting within
$R_{out}\sim 3$ pc would remain bound to the recoiling SMBH (Equation 1).
Thus, $R_{out}$ easily encompasses the radius of the BLR implied by the
reverberation lags.

Shapovalova et al. (2016) also found evidence for periodic variations in the
optical continuum photometry with periods of $\sim 4000$, 1850, and 1200 days
and in the spectroscopic data (broad H$\beta$ and H$\gamma$ lines and 5100Å
continuum) of $\sim 4500$ days. Further analysis by (Kovačević et al., 2017,
2018) yields broadly consistent results but also suggests that the same three
periods ($\sim 12$, $\sim$ 6 and $\sim 5$ yrs) are present in both the
continuum and emission line light curves. The origin of these periodicities is
unclear. Shapovalova et al. (2016) (hereafter referred to as S16) suggest that
the longer periodic variations might be due to dense gas clouds orbiting a
recoiling SMBH. On the other hand, Kovačević et al. (2017) argue that the
longer periods may be associated with precession and orbital motion,
respectively, in a binary SMBH, which they estimate would have a radius $\sim
6\times 10^{-2}$ pc. This is $5\times$ smaller than the BLR radius as inferred
from the H$\beta$ reverberation lag, implying that the BLR is circumbinary,
rather than associated with one or both of the SMBH. This configuration does
not offer a direct explanation for either the strongly asymmetric shapes of
the broad line profiles, or the velocity shift relative to the narrow lines,
or indeed the spatial displacement between the broad and narrow lines inferred
from spectroastrometry.

Alternatively, setting aside the question of the periodicities, the broad line
velocity shift could conceivably be due to orbital motion in a binary SMBH, if
the secondary is active and hosts a BLR. In this case, if the orbital angular
momentum is inclined at an angle $i$ to the line of sight, the circular
velocity would be $v_{k}\sim 2100/\sin i$ km s-1 and the binary separation
would be $a\sim 3\sin^{2}i$ pc (using the SMBH mass inferred by Shapovalova et
al. (2016)), corresponding to a period $P\sim 1.1\times 10^{4}\sin^{3}i$ yr.
We would not, therefore, expect to see significant changes in the broad line
velocity shift over observable timescales. However, a “hard binary” such as
this cannot explain the spectroastrometric displacement, and also seems
inconsistent with the observed optical polarization (R10).

Overall, therefore, we consider that gravitational recoil of a post-merger
SMBH provides a more complete explanation for the unusual properties of this
object than a pre-merger binary SMBH.

A number of other recoil candidates have also been reported in the literature,
identified either through velocity shifts between emission lines (e.g.,
Shields et al., 2009; Steinhardt et al., 2012), or spatial offsets (e.g.,
Batcheldor et al., 2010; Lena et al., 2014), but only a handful have been
found that exhibit both. One of the best studied is CID$-$42 (Blecha et al.,
2013; Novak et al., 2015; Civano et al., 2010, 2012) , a galaxy merger that
contains two optical nuclei separated by $\sim 2.5$ kpc, one of which is
associated with an X-ray point source and a compact, flat spectrum radio
source, indicating the presence of an AGN. The spectrum exhibits a weak broad
H$\beta$ line which has a velocity offset $\sim 1360$ km s-1 relative to the
narrow lines. In the radio galaxy 3C 186 Chiaberge et al. (2017), the AGN is
spatially offset by $\sim$ 11 kpc relative to the center of the host galaxy
and the broad lines have a velocity offset $\sim-2100$ km s-1 relative to the
narrow lines. The quasar SDSS J0927+2943 exhibits a velocity shift of
$\sim-2600$ km s-1 between the broad and narrow lines (Komossa et al., 2008)
with the quasar nucleus being offset by $\sim 1$ kpc from the centroid of the
[Oiii] emission (Vivek et al., 2009). Another possible candidate is the triple
merger system SDSS J1056+5516 (Kalfountzou et al., 2017), which contains three
emission-line nuclei, two of which have broad emission lines. The nuclei are
separated by $15-18$ kpc in projection, and are offset by $\sim 100$ km s-1 in
velocity. Kalfountzou et al. (2017) suggest that, among other possibilities,
one of the broad-line systems could be a recoiling SMBH.

Our results add E1821+643 to the short list of SMBH gravitational recoil
candidates that exhibit evidence for both spatial displacements and large
velocity offsets. Most of these, including E1821+643, have line of sight
velocity shifts $\sim 1000$ km s-1, implying large kick velocities of several
1000 km s-1, perhaps in excess of the escape velocity of their host galaxies.
Such large kicks are expected to be relatively rare events (Lousto et al.,
2012) but tend to produce larger spatial offsets as marginally bound SMBH will
spend most time near their large apocenters (Blecha et al., 2016). In
E1821+643, which has a relatively small spatial offset $(<1)$ kpc compared to
several other recoil candidates, the SMBH must be in an early stage of its
recoil, or approaching the pericenter on a return trajectory before the large
amplitude initial oscillations become damped by dynamical friction (Gualandris
& Merritt, 2008).

The displacement $\sim 100$ mas that we measured in E1821+643 is too small to
be detected by direct imaging with any existing telescope. It would only be
marginally detectable even with the forthcoming James Webb Space Telescope
(spatial resolution $\sim 0.1\arcsec)$. The offset in E1821+643 could, in
principle, be detected with the proposed GRAVITY+ interferometer (Eisenhauer,
2019) at the ESO Very Large Telescope (VLT), which will be capable of
achieving milli-arcsec resolutions at magnitudes down to $K=22$.
Unfortunately, E1821+643 is too far north to be observed with the VLT. It will
be necessary to await the completion of the Thirty Meter Telescope before
there is a Northern Hemisphere facility that has the capability to probe
angular scales $\sim 10$ mas, sufficient to confirm the spatial displacement
of the SMBH in E1821+643.

The HST image also reveals a fainter region of extended [Oiii] emission in the
form of a string of clumps spanning an arc from East to North, $\sim 3$″ from
the the nucleus (Figures 8 and 9). Aravena et al. (2011) detected CO emission
centered $\sim 3$″ South-East of the optical nucleus, which they suggest is a
gas-rich companion galaxy that is merging with the giant elliptical hosting
the quasar, or a remnant of a previous interaction. The arc-like [Oiii]
structure may be part of a tidal tail, which is also a product of the
interaction between the source of the CO emission and the quasar host.

##  5 Conclusions

Spectropolarimetry of the luminous quasar E1821+643 by R10 shows that the
broad Balmer lines are redshifted with respect to the narrow lines and red-
asymmetric in direct light but are conversely blueshifted and blue-asymmetric
in polarized light. They propose that these unusual characteristics can be
explained if the SMBH, with its retained accretion disk and BLR, is moving
through the host galaxy at a speed $\sim 2000$ km s-1 due to gravitational
recoil following coalescence of a progenitor binary SMBH.

In this paper, we have used a combination of optical spectroastrometry and HST
narrow-band imaging to look for the corresponding spatial offset between the
quasar nucleus and the [Oiii] emission “left behind” by the recoiling SMBH.

Our spectroastrometric analysis reveals spatial displacements in the [Oiii]
lines of $\sim$80 - 90mas to both the North and West, relative to the optical
continuum and broad lines. Assuming that the NLR is located at the center of
the host galaxy, this is consistent with the quasar nucleus being offset by a
projected distance $\sim 580$ pc approximately to the South-East.

The HST/ACS images show that the nucleus is located within a region of
extended [Oiii] emission which has a fan-like morphology spanning a wide arc
from North-East to West. Another, clumpier, arc-like feature is seen in [Oiii]
at $\sim 3$″in the North to North-East direction and may be a tidal tail
resulting from a currently ongoing merger, or a previous interaction.

The quasar appears to be located slightly to the South-East of the center of
the main [Oiii] structure, consistent with the spectroastrometric
displacement. The asymmetric morphology of the [Oiii] emission could itself
produce a spectroastrometric displacement, but a simulated spectroastrometric
observation based on the [Oiii] surface brightness distribution mapped by the
HST narrow band image shows that it cannot account for the measured
displacement in [Oiii], which we therefore attribute to a real spatial offset
between the quasar nucleus and the surrounding [Oiii] emission region.

The combination of spectroastrometry and HST imaging thus provides evidence
that the SMBH in E1821+643 is spatially offset from the center of its host
galaxy by a projected distance $\sim 580$ pc. E1821+643 can be added to the
short list of SMBH gravitational recoil candidates that exhibit both large
broad-line velocity shifts and spatial displacements.

## Acknowledgements

This research is based partly on observations made with the NASA/ESA Hubble
Space Telescope obtained from the Space Telescope Science Institute, which is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-26555. These observations are associated with
program G0-13385.

The work also made use of observations obtained at the international Gemini
Observatory, a program of NSF’s NOIRLab, which is managed by the Association
of Universities for Research in Astronomy (AURA) under a cooperative agreement
with the National Science Foundation. on behalf of the Gemini Observatory
partnership: the National Science Foundation (United States), National
Research Council (Canada), Agencia Nacional de Investigación y Desarrollo
(Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina),
Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and
Korea Astronomy and Space Science Institute (Republic of Korea).

##  6 Data availability

The HST data can be accessed from the Mikulski Archive for Space Telescopes
(MAST) using the program ID 13385 at https://archive.stsci.edu/. The
spectroscopy data can be accessed at the Gemini Observatory archive using the
proposal ID GN-2010A-Q-103 at https://archive.gemini.edu/. The derived data
generated in this research will be shared on reasonable request to the
corresponding author.

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