# Optically thick jet base and explanation of edge brightening in AGN jets

Mukesh Kumar Vyas  Asaf Pe’er  Bar Ilan University,
Ramat Gan, Israel, 5290002

###### Abstract

The jet cores in blazars are resolved and found to harbour an edge brightened
structure where the jet base appears extended at sides compared to its
propagation axis. This peculiar phenomenon invites various explanations. We
show that the photosphere of an optically thick jet base in Active Galactic
Nuclei (AGNs) is observed edge brightened if the jet Lorentz factor harbours
an angular dependence. The jet assumes a higher Lorentz factor along the jet
axis and decreases following a power law along its polar angle. For an
observer near the jet axis, the jet has a lower optical depth along its
propagation axis compared to off axis regions. Higher optical depths at the
outer region makes the jet photosphere appear to extend to larger radii
compared to a deeper photosphere along its propagation axis. We tackle the
problem both analytically and numerically, confirming the edge brightening
through Monte Carlo simulations. Other than the edge brightening, the outcomes
are significant as they provide a unique tool to determine the jet structure
and associated parameters by their resolved observed cores. The study paves
way to explore the spectral properties of optically thick cores with
structured Lorentz factors in the future.

High energy astrophysics; Active Galactic Nucleus; Relativistic jets;
Theoretical models

##  1 Introduction

Blazars are a class of Active Galactic Nuclei (AGNs) where the observer is
situated near the jet axis. Radio intereferomety enables a deeper view of the
jet base to reveal their structure at launching (Readhead et al., 1978; Cohen
et al., 1979; Pearson et al., 1981; Pearson & Readhead, 1981). The cores of
extragalactic AGN jets are launched from inner regions of accretion discs
within around 100 Schwarzschild radii (Junor et al., 1999; Doeleman et al.,
2012). The jet core appears to have an extended structure towards its edges
compared to its centre, a phenomenon called limb brightening (Krichbaum et
al., 2006, 2014; Kim et al., 2016; Gabuzda, 2021). Some examples include the
event horizon telescope (EHT) image of Centaurus A, (Janssen et al., 2021),
M87 core with wide opening angle (Walker et al., 2016) etc. Understanding this
peculiar shape of the jet base is an intriguing problem.

The edge brightening in AGN jets has several explanations. Clausen-Brown et
al. (2011) attributed this phenomenon to skewness in synchrotron emission. Due
to helical magnetic fields in the jet, the synchrotron emission is anisotropic
and more prominent from off axis regions compared to the jet axis. Hence the
outer boundary of the jet appears brighter when the observer is nearly along
the axis. Similar argument applies for toroidal magnetic fields. In
relativistic magnetohydrodynamic simulations, limb brightening is shown to be
caused by the toroidal magnetic fields in jets launched by Blandford–Znajek
mechanism (Kramer & MacDonald, 2021; Takahashi et al., 2018). Additionally,
the observed limb brightening at large distances from the jet base is reported
to arise due to recollimation shocks such as seen in the narrow-line Seyfert
galaxy $1H~{}0323+342$ (Doi et al., 2018).

Most common explanation to edge brightening is given by a spine sheath
structure of the jet. In this model, a fast moving jet at the centre is
surrounded by a slow moving wind like flow. Such two component jets were
predicted theoretically (Sol et al., 1989; Henri & Pelletier, 1991; Laing,
1996; Meier, 2003). Later they were seen in several numerical investigations
using general relativistic magneto-hydrodynamic (GRMHD) simulations of
extragalactic jets (Hawley & Krolik, 2006; McKinney, 2006; Hardee, 2007). It
was shown that a jet spine is formed along its propagation axis due to
magnetic fields threading the ergosphere. This beamed spine is surrounded by a
wider sheath generated and driven by the anchored magnetic fields in the
accretion discs. The spine-sheath structure is used to explain limb
brightening in AGN jets (Komissarov, 1990a, b) such as Markarian 501
(Giroletti et al., 2004), M87 (Kim et al., 2018) and some radio galaxies
(Swain et al., 1998; Giovannini et al., 2001). The phenomenon is attributed to
Doppler deboosting (Komissarov, 1990b), where the inner region of the jet
propagates faster leading to relativistic beaming of the photons along the
direction of propagation. This makes a smaller photon flux observed by an off
axis observer. The relativistic beaming is less in outer regions of the jet as
it propagates slowly leading to a brighter limb compared to the jet axis.
Hence, the spine-sheath model used to explain the limb brightening is due to
the relativistic beaming from optically thin plasma. It predicts a higher
observed intensity from the outer regions compared to inner region.

The spine-sheath model is invoked to explain several other observed phenomena
in AGNs including TeV emission from blazars (Ghisellini et al., 2005;
Tavecchio & Ghisellini, 2008; Ghisellini & Tavecchio, 2008), efficient
neutrino productions in AGNs (Tavecchio et al., 2014; Novikova et al., 2023)
and a broadband emission from PKS 1127-145 (Siemiginowska et al., 2007).

However, the conventional explanation to limb brightening by spine-sheath jet
structure is sometimes debated and considered to be a strived explanation
(Gabuzda, 2021). The explanation may not be sufficient to explain limb
brightening in general for several reasons. Jets with persistent direction
change do show limb brightening (example includes Mrk 501). When the jet
swings, limb brightening is likely to disappear following the Doppler boosting
explanation in spine sheath model (see Gabuzda, 2021, for a review).
Additionally, sometimes the limb brightening is seen at large distances from
the jet base (Doi et al., 2018) which requires an explanation beyond the
Doppler beaming due to spine sheath model.

In recent years, in the images of resolved jet cores, bright surfaces
indicating optically thick emission region is visible near the jet base
(Krichbaum et al., 2006, 2014; Kim et al., 2016). Such a surface indicates the
transition from optically thick to optically thin region, called a
photosphere. The location of this photosphere is close to the central black
hole (BH) when viewed close to the jet axis and extends to larger radii at
larger polar angles, thereby having a concave shape (Boccardi et al., 2017;
Janssen et al., 2021). Motivated by these observations of the photospheric
surface, here we provide an alternate explanation to the limb brightening with
an angle dependent Lorentz factor profile for the jet. In our explanation, it
is caused by the emission from optically thick region in an angle dependent
jet.

The optically thick region in AGN jets is due to synchrotron self absorption
(Blandford & Königl, 1979; Ma et al., 2008; Gabuzda et al., 2018; Banasinski &
Bednarek, 2022), and as we show here due to high particle density for Compton
scattering as well. At parsec scale, the electron density in AGN jets is
around few hundred to few thousand particles per cm${}^{-3}.$ This value is
inferred by various observational techniques such as core shift analysis
(Lobanov, 1998), Faraday rotation (Lisakov et al., 2021) and spectral analysis
of AGN jets (Lee et al., 2016). To estimate the density near the jet base, we
can assume an inverse square variation of electron density with distances
($n\propto r^{-2}$). It is not only a natural representation of the density
with distance, it is an observational requirement as well (Konigl, 1981;
Lobanov, 1998; Lisakov et al., 2021). Thus, calculating particle density close
to the jet base (few Schwarzschild radii) we show that the jet base should be
optically thick for Compton scattering. Furthermore, the evidence of high mass
loading in jets (Qiu et al., 2021) suggests the possibility of treating the
jet core to be optically thick. As we show below, for plausible measured
densities, the photospheric radius in many AGN jets extends much beyond the
Schwarzschild radius.

For an on axis observer, a jet having a decreasing Lorentz factor with polar
angle leads to an angle dependent optical depth along its angular extent. Due
to higher Lorentz factor along the jet axis, the jet stem is optically thin
and the photosphere appears deeper compared to optically thicker region at off
axis (Abramowicz et al., 1991; Pe’er, 2008; Vyas & Pe’er, 2023). This makes
the photosphere extended at larger polar angles as compared to the jet axis,
thus creating limb brightening in jets.

We develop a semi analytic model to estimate the photosphere in this
framework. Additionally, we perform Monte Carlo simulations for photon
scattering at the jet base and conclude that a jet with a structured Lorentz
profile produces an edge brightened photosphere for all observers at small
observing angles. Alternatively, the observed images of these jets allow us to
infer the jet structure and paves way to investigate other spectral features
of these jets in light of their photospheric emission. In section 2 below, we
formulate the theoretical analysis for estimating the jet photosphere as a
function of coordinates. In section 3 we discuss the results obtained and
conclude the study in section 4.

##  2 Photosphere of a relativistic fluid with angle dependent Lorentz factor
($\Gamma$)

###  2.1 Existence of a Compton photosphere at AGN jet base

We consider the AGN jets to be optically thick for Compton scattering at the
base. The optical depth for scattering of a photon propagating a distance $dr$
by a fluid element with density $n$ is $d\tau=\sigma ndr$. Here, it is safe to
take the Thomson cross section, namely $\sigma=\sigma_{T}$. For approximately
constant outflow velocity and conical jets, one can assume an inverse square
law for the particle density, $n(r)=n_{0}(r_{0}/r)^{2}$. Integrating the
optical depth from the jet base at $\approx 2r_{s}$ (where $r_{s}$ is the
Schwarzschild radius of the central BH) to the observer at infinity, the
required condition for optically thick plasma is

$\tau_{b}=\int d\tau\sim 10^{3}\left(\frac{10^{6}}{m_{\rm
BH}}\right)\times\left(\frac{n_{0}}{100}\right)\times\left(\frac{r_{0}}{1{\rm
parsec}}\right)^{2}>1.$ (1)

Here, $m_{BH}$ is black hole mass in units of solar mass, and $n_{0}$ is given
in units of particles/cm3. Using observationally estimated values of $n_{0}$,
$r_{0}$ and $m_{\rm BH}$, one can assert the optical depth in AGN jet bases.
For example in the quasar 3C 273, having BH mass $m_{\rm BH}=6.59\times
10^{9}$ (Paltani & Türler, 2005), the estimated particle density at distance
$7\times 10^{20}$ cm is $125$ cm-3 (Lisakov et al., 2021). The optical depth
at the jet base is therefore $\tau_{b}=10^{4}$. Similar analysis for quasar 3C
207 gives $\tau_{b}=7.87$. [Density and distance are estimated by Sambruna et
al. (2004), while the black hole mass is estimated in Tang et al. (2012)]. For
3C 345 it turns out to be 5.63 [Density and distance are taken from Sambruna
et al. (2004) while the black hole mass is estimated in Uchiyama et al.
(2007)]. Core shift analysis gives particle densities at around parsec scale
to be 1500 cm-3 (Lobanov, 1998) for various sources. This leads to a typical
optical depth at the jet base in range $\tau_{b}\sim 3-3\times 10^{3}$ for
black hole masses $m_{\rm BH}=10^{6}-10^{9}$. However, it is not the case with
all the AGN jets and sometimes the core turns out to be optically thin. One
such example is PKS $(1136-135)$, the estimated optical depth at the jet base
is 0.21 [$n_{0}$ and $r_{0}$ estimated by Sambruna et al. (2004) and the black
hole mass is taken from Uchiyama et al. (2007)].

It is important to mention that the density estimates in an AGN jet has a
large uncertainty associated with the applied method. For example, the density
estimates in M87 jet using rotation measure at distance $r_{0}=156$ parsec is
$n_{0}=1.6\times 10^{-3}$ cm-3 giving $\tau_{b}=0.06$. While from X-ray energy
spectral analysis, the density estimates come out to be four orders of
magnitude greater leading to $\tau_{b}\sim 600$ (Osone, 2023). In these
estimates, the black hole mass of M87 is $6.5\times 10^{9}$ solar mass, taken
from Event Horizon Telescope Collaboration et al. (2019). In the estimates
above, the typical calculated particle densities close to the jet base, at the
distance of a few Schwarzschild radii reach up to $10^{10-12}$ cm-3 . Such
high densities in AGN atmospheres are reported by various authors. For
example, the density inside the jet in 3C 84 is estimated at $10^{3}-10^{5}$
cm-3 at $0.07-0.14$ parsec (Kino et al., 2021; Nagai et al., 2017; Kino et
al., 2018). The intermediate line regions near AGN jets have densities
$10^{5}$ cm-3 to $10^{11.5}$ cm-3 at characteristic distances of 0.1 parsec
(Adhikari et al., 2017, 2016). Particle densities in the region above AGN
accretion discs are shown to be $\approx 10^{15}$ cm-3 (Adhikari et al.,
2016). Hence we conclude that the optically thick cores in AGN jets exist in
many sources and therefore the photospheric properties of such cores need to
be explored.

###  2.2 Jet structure

The existence of a spine-sheath structure in AGN jets has both theoretical and
observational basis. Here we consider an angle-dependent jet velocity profile,
$\Gamma=\Gamma(\theta)$. In order to avoid abrupt change in Lorentz factor
between spine and sheath, we consider a smooth transition following a power
law decay with polar angle $\theta$, given as

$\Gamma(\theta)=\Gamma_{\rm min}+\frac{\Gamma_{0}-\Gamma_{\rm
min}}{\sqrt{\left(\frac{\theta}{\theta_{\rm j}}\right)^{2p}+1}}.$ (2)

Here $\Gamma_{0}$ and $\Gamma_{\rm min}$ are the maximum and minimum values of
the jet Lorentz factor assigned to the spine and sheath regions respectively.
The angle $\theta_{\rm j}$ is a constant, separating the inner, faster jet
core from the outer, slower sheath. The parameter $p$ is a jet profile index
that determines the steepness of decrease in $\Gamma$ with $\theta$. This
profile implies an inner jet region (at angles $\theta\ll\theta_{j}$) having
constant Lorentz factor $\Gamma=\Gamma_{0}$ and outer jet region, at angles
larger than $\theta=\theta_{\rm e}=\theta_{\rm j}\Gamma_{0}^{1/p}$ has
$\Gamma=\Gamma_{\rm min}$. Within the region $\theta_{\rm j}-\theta_{\rm e}$,
the Lorentz factor decays following a power law $\Gamma\propto\theta^{-p}$.
This profile is analogous to the evolution of $\Gamma$ obtained by McKinney
(2006) in their simulations [see their Figure 9, first panel]. This continuous
transition of Lorentz factor between the spine and sheath arises from mutual
interaction and mixing of particles in these regions. However, the conclusions
of our study are independent of the form of the transition and are valid for a
step function transition as well (obtained here for $p\rightarrow\infty$).

###  2.3 Theoretical model : Estimation of optical depths in a structured jet

Consider that the photons are emitted deep inside the jet. These photons
escape once they reach the photospheric radius $R_{\rm ph}$ where the optical
depth for scattering between $R_{\rm ph}$ and infinity equals unity. In such a
case, the shape of $R_{\rm ph}$ as a function of the polar coordinates
($\theta,\phi$) determines the appearance of the jet base in the observations.
The observed shape is sensitive to the given observer’s location, specified
here by polar coordinates $\theta_{\rm o}$ and $\phi_{\rm o}$. We calculate
here the angular dependence of $R_{\rm ph}$ for a given observer’s location.
We calculate $R_{\rm ph}$ both analytically and numerical simulations as
follows.

Define a cylindrical coordinate system centered at the plasma expansion center
(base of the jet) and assume that the observer is located at plus infinity on
the $z$-axis. Since the observer is, in general, off the jet axis, the jet
outflow is not symmetric in this coordinate system. Consider a photon that was
emitted at point $z_{\rm min}$ along the $z$ axis and at radial distance
$r_{\min}$ from it, namely at distance $r=\left(r_{\rm min}^{2}+z_{\rm
min}^{2}\right)^{1/2}$ from the center. Assume that this photon propagates
towards the observer (along the $+z$ direction). The optical depth as measured
along the ray traveling in the $+z$ direction and reaching the observer is
(Abramowicz et al., 1991; Pe’er, 2008),

$\tau(r_{\rm min},z_{\rm min})=\int_{z_{\rm
min}}^{\infty}n^{\prime}\sigma_{\rm T}\Gamma[1-\beta\cos\theta_{l}]dz.$ (3)

Here, $n^{\prime}$ is the electron number density in the local comoving frame,
$\sigma_{\rm T}$ is Thomson scattering cross section, $\beta$ is the local
fluid velocity in units of light speed $c$, and $\theta_{l}$ is the angle
between the velocity vector of the local fluid element and the observer’s
angular location.

The comoving number density of the plasma moving with outflow rate
$\dot{M}_{\rm j}$ is defined as (Lundman et al., 2013),

$n^{\prime}(r,\theta)=\frac{1}{m_{p}c\beta\Gamma r^{2}}\frac{d\dot{M}_{\rm
j}}{d\Omega}.$ (4)

Here, $m_{p}$ is proton mass and $d\dot{M}_{\rm j}/d\Omega$ is differential
mass outflow rate in the jet. This differential mass outflow rate is connected
to the (differential) jet luminosity ($dL_{\rm j}/d\Omega$) as

$\frac{d\dot{M}_{\rm j}}{d\Omega}=\frac{1}{c^{2}\Gamma}\frac{dL_{\rm
j}}{d\Omega}.$ (5)

It has been observed that the jet luminosity is not isotropic and has angle
dependence. In various observations of extragalactic jets,
$L_{j}\propto\theta^{-2}$ is found to be a typical behaviour of jet luminosity
(Lipunov et al., 2001; Zhang & Mészáros, 2002; Rossi et al., 2002; Salafia &
Ghirlanda, 2022). In the context of our jet model, we assume that the jet
luminosity is constant at small angles, $\theta\leq\theta_{\rm j}$, and it
decreases with inverse square law at larger angles. The angle-independent
luminosity at small angles, $\theta\leq\theta_{\rm j}$, can be understood,
since the jet has constant Lorentz factor and hence the flow is radial and
steady, leading to angle-independent luminosity. The luminosity can therefore
be approximated by

$\frac{dL_{\rm
j}}{d\Omega}=\frac{L_{0}}{2\pi\left[\left(\frac{\theta}{\theta_{\rm
j}}\right)^{2}+1\right]}=\frac{L_{0}}{2\pi f(\theta)}.$ (6)

Here, $f(\theta)$ is

$f(\theta)=\left(\frac{\theta}{\theta_{\rm j}}\right)^{2}+1.$ (7)

Hence the differential outflow rate in the jet is

$\frac{d\dot{M}_{\rm j}}{d\Omega}=\frac{L_{0}}{2\pi c^{2}\Gamma f(\theta)}.$
(8)

The total mass outflow rate can be obtained by integrating over the spatial
angle $d\Omega$. One can express it in terms of the accretion efficiency in
the disk, $\eta=L_{\rm a}/\dot{M}_{\rm a}c^{2}$ where $\dot{M}_{\rm a}$ is the
disk accretion rate and $L_{\rm a}$ is the accretion luminosity, using

$\dot{M}_{\rm j}=\frac{L_{0}}{2\pi c^{2}}\int\frac{d\Omega}{\Gamma
f(\theta)}=\frac{m_{0}L_{\rm a}}{\eta c^{2}}.$ (9)

Here, $m_{0}=\dot{M}_{\rm j}/\dot{M}_{\rm a}$ is the jet mass loading
parameter, typically found between 200-500 (Qiu et al., 2021). As for the
accretion efficiency $\eta$, it is found in range $0.016-0.14$ (Bian & Zhao,
2003). Theoretically, it is estimated to be 0.056 for a non rotating black
hole while it can be as high as 0.32 in the case of a maximally rotating black
hole (Laor & Netzer, 1989).

The luminosity along the jet axis $L_{0}$ can be expressed in terms of the
disk luminosity, $L_{\rm a}$ as

$L_{0}=\frac{2\pi m_{0}L_{\rm a}}{\eta{\cal{I}}},$ (10)

with $\cal{I}$ defined as ${\cal{I}}\equiv\int\frac{d\Omega}{\Gamma
f(\theta)}.$ Using the expression of $L_{0}$, Equation 8 becomes

$\frac{d\dot{M}_{\rm j}}{d\Omega}=\frac{m_{0}L_{\rm a}}{\eta
c^{2}\Gamma}\frac{1}{f(\theta)\cal{I}},$ (11)

From Equation 4, the comoving density is

$n^{\prime}=\frac{m_{0}L_{\rm a}}{\eta
m_{p}c^{3}\beta\Gamma^{2}r^{2}f(\theta)\cal{I}}.$ (12)

Using this expression in Equation 3, the optical depth can be expressed as

$\tau=\int_{z_{\rm min}}^{\infty}\frac{m_{0}L_{\rm
a}\sigma_{T}[1-\beta\cos\theta_{l}]}{\eta m_{p}c^{3}\beta\Gamma
r^{2}f(\theta){\cal{I}}}dz.$ (13)

If the density is $n^{\prime}=n_{0}^{\prime}=n_{0}/\Gamma_{0}$ given at
distance $r=r_{0}$ at $\theta=\theta_{\rm j}$, then from Equation 12,

$\frac{m_{0}L_{a}}{\eta
m_{p}c^{3}\cal{I}}=2n_{0}r_{0}^{2}\beta_{0}\Gamma_{0}.$ (14)

Here, $\beta_{0}$ is bulk jet velocity along the jet axis. Using Equation 14
in 13,

$\tau=\int_{z_{\rm
min}}^{\infty}\frac{2n_{0}r_{0}^{2}\beta_{0}\Gamma_{0}\sigma_{T}[1-\beta\cos\theta_{l}]}{\beta\Gamma
r^{2}f(\theta)}dz.$ (15)

The observer, situated at polar angle $\theta_{o}$, will see the surface of
the plasma when the optical depth along the observer’s direction equals unity.
Considering the fact that $r\sin\theta_{l}$ is constant along the ray parallel
to $\theta$, one can convert the integration from $dz$ to $d\theta_{l}$ using
$dz=-r^{2}d\theta/(r\sin\theta_{l})$, where $\theta_{l}$ is the angle between
the local propagation direction of flow and the observer’s location
$\theta_{\rm o}$. This gives

$\tau=\int_{0}^{\theta_{l}}\frac{2n_{0}r_{0}^{2}\beta_{0}\Gamma_{0}\sigma_{T}[1-\beta\cos\theta_{l}]}{\beta\Gamma
r\sin\theta_{l}f(\theta)}d\theta_{l}.$ (16)

The photons escape to infinity from surface at which $\tau=1$ and that surface
is visible to the observer. In general, $\theta_{l}$ varies along the photon
path and is thus $\theta_{l}\neq\theta_{0}+\theta_{\rm j}$. The surface of the
photosphere therefore depends on both the polar and azimuthal location of the
observer (i.e., $\theta_{\rm o}$ and $\phi_{\rm o}$). Equation 16 can be
solved to determine the photospheric radius for unit optical depth along the
direction of the observer $\theta_{\rm o}$. In general, it is a function of
the jet’s angular coordinates [i.e., $R_{\rm ph}=R_{\rm ph}(\theta,\phi)$].
The unique photospheric appearance is determined by specifying the jet
parameters according to Equation 2 and the input parameters given particle
density $n^{\prime}=n_{0}/\Gamma_{0}$ at radius $r=r_{0}$. From various
observational estimates, it is found to be in the range of one to few $\times
100$ cm-3 at around 1 parsec (Konigl, 1981; Lobanov, 1998; Lee et al., 2016;
Lisakov et al., 2021).

###  2.4 Numerical simulations

We carry Monte Carlo simulations to confirm the predictions of the above
discussed theoretical model. In the numerical code, approximately $6$ million
monoenergetic photons with energy $10^{-10}$ (in units of rest mass of
electron) are injected deep inside the jet where the matter is optically
thick. Initially the photons have random directions and they propagate while
Compton scatter with the electrons in the jet.

Given a photon’s four vector, the code computes the location of the coming
scattering event in the following way. Initially, the photon’s location is
given in Cartesian coordinate system. As a first step, the photon location is
transformed into a cylindrical coordinate system ($r_{c},\theta_{c},z_{c}$) .
This coordinate system is chosen such that the centre of the black hole is at
$r_{c}=z_{c}=0$, and the $z_{c}$ axis is along the propagation direction of
the photon. In these coordinates, the photon’s initial location is described
by ($r_{\rm min},z_{\rm min}$). 111As the photon propagates along the $z_{c}$
direction, $r_{\min}$ and $\theta_{c}$ are not changed, and we omit discussing
$\theta_{c}$ for clarity. The photon’s initial radial distance from the center
of the black hole is $r=\sqrt{r_{\rm min}^{2}+z_{\rm min}^{2}}$ (see Figure
1).

The photon propagates along the $z_{c}$ axis (dashed line in Figure 1) until
it scatters with an electron $e_{2}$ located at $z_{\max}$. The photon travel
distance $\Delta z=z_{\max}-z_{\min}$ is determined as follows. The
probability of a photon to travel a distance $\Delta z$ along which the
optical depth is $\tau$ without being scattered is $P_{sc.}(\tau)=e^{-\tau}$.
Therefore, the optical depth $\tau$ is drawn from a logarithmic distribution.
Then the code calculates $\delta\tau$ along the photon trajectory until
reaching the randomly selected optical depth. If the randomly selected optical
depth is larger than the optical depth for escaping to infinity, the photon
assumes to escape, otherwise the scattering position is calculated along the
$z_{c}$ axis such that the travel distance $\Delta z$ is such that the optical
depth along this distance is equal to $\tau$. Finally, this scattering
location is transformed back to the original Cartesian coordinate system.

For the scattering process, a cold electron that moves at bulk velocity
$\Gamma=\Gamma(\theta)$ as given by Equation 2 is considered. The scattering
occurs at a random angle in the electron’s rest frame, considering the full,
Klein-Nishina, angle-dependent cross section for the process. For a complete
description of the scattering calculations, see Pe’er (2008).

A photon scatters multiple times until it escapes the system once it reaches
the location where the local optical depth fulfills the escape criteria. The
escape direction of each photon is stored and contributes to the observed flux
as seen by an observer along the photon escape direction. The escape location
marks the position of the photospheric radius perceptible to that observer.
This implies that for a photon at the photosphere, $z_{\rm max}=\infty$ as the
photon has its last scattering there before it escapes to infinity.

Thus, a large number of photons map the entire photospheric surface for all
observers. The photospheric surface as seen by observers located in different
directions depends on the viewing angle, and is calculated by binning the data
into certain observer’s locations.

Further details of the simulation code are found in Pe’er (2008); Lundman et
al. (2013); Vyas et al. (2021).

Figure 1: Geometry of a photons scattering (dashed line) between the two
electrons $e_{1}$ and $e_{2}$. The first electron is situated at location
$z_{\rm min}$ while the second electron at $z_{\rm max}$ in cylindrical
coordinates chosen such that the z axis is along the photon path. At
photospheric radius, $z_{\rm max}=\infty$. Figure 2: $R_{\rm ph}$ as a
function of cylindrical radius $r_{c}=\sqrt{x^{2}+y^{2}}$ with
$\Gamma_{0}=20$, $\theta_{\rm j}=0.1$ rad, $p=1.2$, $\theta_{\rm o}=0.0$ rad
for both analytic calculations (blue dots) and results from Monte Carlo
simulations (Black spheres). $n_{0}=80$ cm-3 at $r_{0}=1$ parsec.

Figure 3: Upper Panel: $R_{\rm ph}$ as a function of $x$ and $y$ coordinates
(in cm). Lower panel: $R_{\rm ph}$ as a function of the polar angle $\theta$.
The color gradient shows the luminosity of the photosphere decreasing from
blue to yellow shade. Chosen parameters $\Gamma_{0}=10$, $\theta_{\rm j}=0.1$
rad, $p=1.2$ for the observer’s location at $\theta_{\rm o}=0.0$ rad.
$n_{0}=80$ cm-3 at $r_{0}=1$ parsec

##  3 Results

As an example, we consider an environment characterized by a particle density
$n_{0}=80$ cm-3 at $r_{0}=1$ parsec. In Figure 2, we plot the photospheric
radius $R_{\rm ph}$ with horizontal distance from the jet axis
$r_{c}=\sqrt{x^{2}+y^{2}}$. The observer is assumed along the jet axis (polar
angle $\theta_{\rm o}=0$). The estimated values of $R_{\rm ph}$ from the
analytic calculations (Equation 16) are shown by blue curve while the inferred
values from Monte Carlo simulations are overplotted with black dots. The edge
brightening of the jet due to relativistic effects on the apparent optical
depth is perceptible as the photospheric radius extends up to larger distances
for off axis regions compared to the jet axis. Considering a black hole mass
equivalent to $10$ million solar mass, (with Schwarzschild radius $\sim
3\times 10^{12}$ cm), the photosphere is well above the horizon, extending up
to one order of magnitude above it. However, the extent of the magnitude
primarily depends upon considered value of $n_{0}$ and could extend much
further for larger densities.

Figure 4: Top panel: Analytic estimation of $R_{\rm ph}$ as a function of $x$
and $y$ coordinates for $\theta_{\rm o}=0.3$ rad; Middle panel: for
$\theta_{\rm o}=0.3$ rad, we plot the variation of $R_{\rm ph}$ along the y
axis for $x=0$ with black spheres. The colored plot is the normalized photon
flux $dN/dA$ calculated by simulations at a given location $x=0,y$. Bottom
panel: variation of the simulated photon flux along the $y$ coordinate at
$x=0$ for different observing angles $\theta_{\rm o}=0.1$ rad (black),
$\theta_{\rm o}=0.2$ rad (blue) and $\theta_{\rm o}=0.3$ rad (red) curves. For
larger viewing angles the asymmetry is larger. Chosen parameters in all the
panels are $\Gamma_{0}=10$, $\theta_{\rm j}=0.1$ rad, $p=1.2$. $n_{0}=80$ cm-3
at $r_{0}=1$ parsec.

To show the appearance of the jet to an observer, analytic results are shown
in Figure 3 (upper panel) where we project the photospheric radius $R_{\rm
ph}$ as measured in Cartesian coordinates on the $x-y$ plane. Here, the
observer is assumed on axis, namely situated along the $z$ axis (at polar
angle $\theta_{\rm o}=0$). This makes the surface symmetric around the $x$ and
$y$ coordinates. In producing this plot, we have assumed a jet profile as
given in Equation 2, with parameters $\Gamma_{0}=10$, $\theta_{\rm j}=0.1$ rad
and profile index $p=1.2$.

The important outcome is the increase of $R_{\rm ph}$ at the jet’s edges up to
several times compared to the jet axis (at $x=y=0$). The blue region at the
centre of the jet compared to yellow region at outskirts signifies a deeper
photosphere at the centre. In the lower panel, we have plotted the
photospheric radius $R_{\rm ph}$ as a function of the polar angle $\theta$
(black solid curve). In the inner regions of the jet, the photospheric radius
$R_{\rm ph}$ is well approximated as a parabolic function of the polar angle,
obeying the relation $R_{\rm ph}=a\theta^{2}+b$ where $a=5\times 10^{13}$ cm
and $b=2.55\times 10^{12}$ cm for the jet profile presented here (blue dashed
curve).

In the upper panel of figure 4, we show the photospheric radius as seen by an
off-axis observer. The photospheric radius $R_{\rm ph}$ is plotted on the
$x-y$ plane for jet parameters $\Gamma_{0}=15$, $\theta_{\rm j}=0.1$ rad,
$p=1.2$. The observer assumes $\theta_{\rm o}=0.30~{}$rad and an azimuthal
location $\phi_{\rm o}=\pi/2$, making the surface symmetric around the $x$
axis, while asymmetry appears along $y$ axis. To indicate the observed
asymmetry of the photospheric radius and observed flux for such an off-axis
observer, we plot the photospheric radius $R_{\rm ph}$ along the $y$ axis in
the middle panel of figure 4 for $x=0$ (black dots). The color bar shows the
simulated photon flux $dN/dA$, where $dA(y)=dxdy$ is the differential cross
section shown along the $y$ axis. The base of the photospheric surface
(minimum of the last scattering surface) shifts towards positive $y$ axis. The
bright spot peaks near the dip (the smallest photospheric radius, at $5\times
10^{12}$ cm). It asymmetrically extends towards both sides. The arm along the
left side (further away from the observer) appears twice as long compared to
right side, which is purely an effect of the observer’s location. Such
asymmetry of the limb brightened arms is widely observed in off axis jets
(Walker et al., 2016). The shorter arm appears brighter compared to the longer
one. In the bottom panel, we show the variation of the simulated photon flux
along $y$ coordinate at $x=0$ for different choices of the observer’s location
at $\theta_{\rm o}=0.1,0.2$ and $0.3$ rad. The asymmetry in the flux decay at
both sides increases as the observer is further away from the jet axis.
Subsequently, the peak in the flux also shifts further along $y$ axis.
Further, the implication of this asymmetry in the flux is that by looking at
the ratio of the observed signal at both sides, one can infer the viewing
angle of the jet.

##  4 Conclusions

In this letter, we have studied the photospheric appearance of a relativistic
AGN jet with polar angle dependent Lorentz factor profile. Using density
estimates of AGN jets, we argue that the jet cores near their launching sites,
and up to a few- few tens of Schwarzschild radii can generally be optically
thick for Compton scattering. Photons undergo multiple scattering with
electrons in this region, before they escape from it to infinity. The last
scattering surface represents the innermost region that can be observed.

Here we considered an angle dependent Lorentz factor profile, with jet
propagating faster in the middle compared to larger polar angles. We have
further considered a cold plasma. However, the last scattering surface, or the
structure of photosphere obtained in this work remains unaffected if the
plasma were hot and relativistic. Furthermore, as discussed in section 2.1,
the optical depths at the jet base are around $10$ and hence the photons
decouple from the plasma after encountering only a few scatterings before
escaping. Thus, complete thermalization does not have time to occur and most
of the photon population remains at low energies, enabling the resolved cores
to be observed at radio frequencies.

We show that for an observer situated near the jet axis, the jet core appears
relatively empty in the middle with a deeper photosphere while it appears
extended at the edges. The reason of this appearance is that the optical depth
for scattering is smaller for photons emitted along the jet axis, compared to
photons emitted from larger angles. As a result, the last scattering location
of the photons is closer to the jet base along the jet axis.

Such an appearance is consistent with various observations of the resolved jet
cores. Hence, we provide a natural explanation to the observed edge
brightening feature of the AGN jet cores. As the appearance of a jet base
depends upon jet parameters, the analysis hands over a tool to infer the jet
structure in AGNs directly from their observations.

The conventional explanation of the limb brightening due to Doppler deboosting
model is criticized based on the fact that it cannot explain persisting limb
brightening in a swinging jet. Thus, when the jet points towards the observer,
the limb brightening should vanish which is in contrast with observations of
Mrk 501 (Gabuzda, 2021). From Figure 3 we show that our model predicts a limb
brightening for an on axis jet as well. Thus it is a viable mechanism that
explains different aspects of the limb brightening phenomenon, that are
difficult to explain otherwise.

The relative flux variation at both sides of the jet depends upon the
observer’s location as shown in the bottom panel of Figure 4. This enables the
determination of the observer’s location from the observed asymmetry in the
flux variation. Additionally, the flux decays by two to three orders of
magnitude between the centre of the jet and the off axis regions or the limb.
This is consistent with the typically observed flux variation in the resolved
cores of AGN jets (See Figure 1 of Hada et al., 2013).

The analysis presented here paves a way for considering the presence of a
photospheric component in blazars. The existence of an observed photospheric
component may have additional, exciting implications on the observed AGN
properties, such as the spectra and polarization. These will be explored in
future works.

## Acknowledgments

For this project, we acknowledge the support by European Union (EU) via ERC
consolidator grant 773062 (O.M.J.).

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# Facilitating Terminology Translation with Target Lemma Annotations

Toms Bergmanis†‡ Mārcis Pinnis†‡

†Tilde / Vienības gatve 75A, Riga, Latvia
‡Faculty of Computing, University of Latvia / Raiņa bulv. 19, Riga, Latvia
<EMAIL_ADDRESS>
###### Abstract

Most of the recent work on terminology integration in machine translation has
assumed that terminology translations are given already inflected in forms
that are suitable for the target language sentence. In day-to-day work of
professional translators, however, it is seldom the case as translators work
with bilingual glossaries where terms are given in their dictionary forms;
finding the right target language form is part of the translation process. We
argue that the requirement for apriori specified target language forms is
unrealistic and impedes the practical applicability of previous work. In this
work, we propose to train machine translation systems using a source-side data
augmentation method111Relevant materials and code: https://github.com/tilde-
nlp/terminology_translation that annotates randomly selected source language
words with their target language lemmas. We show that systems trained on such
augmented data are readily usable for terminology integration in real-life
translation scenarios. Our experiments on terminology translation into the
morphologically complex Baltic and Uralic languages show an improvement of up
to 7 BLEU points over baseline systems with no means for terminology
integration and an average improvement of 4 BLEU points over the previous
work. Results of the human evaluation indicate a 47.7% absolute improvement
over the previous work in term translation accuracy when translating into
Latvian.

##  1 Introduction

Translation into morphologically complex languages involves 1) making a
lexical choice for a word in the target language and 2) finding its
morphological form that is suitable for the morpho-syntactic context of the
target sentence. Most of the recent work on terminology translation, however,
has assumed that the correct morphological forms are apriori known Hokamp and
Liu (2017); Post and Vilar (2018); Hasler et al. (2018); Dinu et al. (2019);
Song et al. (2020); Susanto et al. (2020); Dougal and Lonsdale (2020). Thus
previous work has approached terminology translation predominantly as a
problem of making sure that the decoder’s output contains lexically and
morphologically pre-specified target language terms. While useful in some
cases and some languages, such approaches come short of addressing terminology
translation into morphologically complex languages where each word can have
many morphological surface forms.

For terminology translation to be viable for translation into morphologically
complex languages, terminology constraints have to be soft. That is,
terminology translation has to account for various natural language phenomena,
which cause words to have more than one manifestation of their root morphemes.
Multiple root morphemes complicate the application of hard constraint methods,
such as constrained-decoding Hokamp and Liu (2017). That is because even after
the terminology constraint is striped from the morphemes that encode all
grammatical information, the remaining root morphemes still can be too
restrictive to be used as hard constraints because, for many words, there can
be more than one root morpheme possible. An illustrative example is the
consonant mutation in the Latvian noun vācietis (“the German”) which undergoes
the mutation t$\rightarrow$š, thus yielding two variants of its root morpheme
vācieš- and vāciet- Bergmanis (2020). If either of the forms is used as a hard
constraint for constrained decoding, the other one is excluded from appearing
in the sentence’s translation.

We propose a necessary modification for the method introduced by Dinu et al.
(2019), which allows training neural machine translation (NMT) systems that
are capable of applying terminology constraints: instead of annotating source-
side terminology with their exact target language translations, we annotate
randomly selected source language words with their target language lemmas.
First of all, preparing training data in such a way relaxes the requirement
for access to bilingual terminology resources at the training time. Second, we
show that the model trained on such data does not learn to simply copy inline
annotations as in the case of Dinu et al. (2019), but learns copy-and-inflect
behaviour instead, thus addressing the need for soft terminology constraints.

Our results show that the proposed approach not only relaxes the requirement
for apriori specified target language forms but also yields substantial
improvements over the previous work Dinu et al. (2019) when tested on the
morphologically complex Baltic and Uralic languages.

EN Src.: |  | faulty engine or in transmission[..]
---
LV Trg.: | atteice dzinējā vai transmisijas [..]
ETA: |  | faulty|w engine|s dzinējā|t or|w
---
transmission|s transmisijas|t [..]
TLA: |  | faulty|w engine|s dzinējs|t or|w
---
transmission|s transmisija|t [..]
Table 1: Examples of differences in input data in ETA Dinu et al. (2019) and
TLA (this work). Differences of inline annotations are marked in bold. |w, |s,
|t denote the values of the additional input stream and stand for regular
words, source language annotated words, target language annotations
respectively.

##  2 Method: Target Lemma Annotations

To train NMT systems that allow applying terminology constraints Dinu et al.
(2019) prepare training data by amending source language terms with their
exact target annotations (ETA). To inform the NMT model about the nature of
each token (i.e., whether it is a source language term, its target language
translation or a regular source language word), the authors use an additional
input stream—source-side factors Sennrich and Haddow (2016). Their method,
however, is limited to cases in which the provided annotation matches the
required target form and can be copied verbatim, thus performing poorly in
cases where the surface forms of terms in the target language differ from
those used to annotate source language sentences Dinu et al. (2019). This
constitutes a problem for the method’s practical applicability in real-life
scenarios. In this work, we propose two changes to the approach of Dinu et al.
(2019). First, when preparing training data, instead of using terms found in
either IATE222https://iate.europa.eu or Wiktionary as done by Dinu et al.
(2019), we annotate random source language words. This relaxes the requirement
for curated bilingual dictionaries for training data preparation. Second,
rather than providing exactly those target language forms that are used in the
target sentence, we use target lemma annotations (TLA) instead (see Table 1
for examples). We hypothesise that in order to benefit from such annotations,
the NMT model will have to learn copy-and-inflect behaviour instead of simple
copying as proposed by Dinu et al. (2019).

Our work is similar to work by Exel et al. (2020) in which authors also aim to
achieve copy-and-inflect behaviour. However, authors limit their annotations
to only those terms for which their base forms differ by no more than two
characters from the forms required in the target language sentence. Thus
wordforms undergoing longer affix change or inflections accompanied by such
linguistic phenomena as consonant mutation, consonant gradation or other stem
change are never included in training data.

Figure 1: Example of forms used in human evaluation. | Train | Test
---|---|---
|  |  | ATS
---
| WMT17+IATE
---
EN-DE | 27.6M | 768 | 581
EN-ET | 2.4M | 768 | -
EN-LV | 22.6M | 768 | -
EN-LT | 22.1M | 768 | -
Table 2: Training and evaluation data sizes in numbers of sentences. WMT2017 +
IATE stands for the English-German test set from the news translation task of
WMT2017 which is annotated with terminology from the IATE terminology
database.

##  3 Experimental Setup

### Languages and Data.

As our focus is on morphologically complex languages, in our experiments we
translate from English into Latvian and Lithuanian (Baltic branch of the Indo-
European language family) as well as Estonian (Finnic branch of the Uralic
language family). For comparability with the previous work, we also use
English-German (Germanic branch of the Indo-European language family). For all
language pairs, we use all data that is available in the Tilde Data Libarary
with an exception for English-Estonian for which we use data from WMT 2018.
The size of the parallel corpora after pre-processing using the Tilde MT
platform Pinnis et al. (2018) and filtering tools Pinnis (2018) is given in
Table 2.

To prepare data with TLA, we first lemmatise and part-of-speech (POS) tag the
target language side of parallel corpora. For lemmatisation and POS tagging,
we use pre-trained Stanza333https://github.com/stanfordnlp/stanza Qi et al.
(2020) models. We then use fast_align444https://github.com/clab/fast_align
Dyer et al. (2013) to learn word alignments between the target language lemmas
and source language inflected words. We only annotate verbs or nouns. To
generate sentences with varying proportions of annotated and unannotated
words, we first generate a sentence level annotation threshold uniformly at
random from the interval $[0.6,1.0)$. Similarly, for each word in the source
language sentence, we generate another number uniformly at random from the
interval $[0.0,1.0)$. If the latter is larger than the sentence level
annotation threshold, we annotate the respective word with its target language
lemma. We use the original training data and annotated data with a proportion
of 1:1. We follow Dinu et al. (2019) to prepare ETA and replicate their
results.

For validation during training, we use development sets from the WMT news
translation shared tasks. For EN-ET and EN-DE, we used the data from WMT 2018,
for EN-LV – WMT 2017, and for EN-LT – WMT 2019.

### MT Model and Training.

For the most part, we use the default configuration of the Transformer Vaswani
et al. (2017) NMT model implementation of the Sockeye NMT toolkit Hieber et
al. . The exception is the use of source-side factors Sennrich and Haddow
(2016) with the dimensionality of 8 for systems using inline target lemma
annotations. We train all models using early stopping with the patience of 10
based on their development set perplexity Prechelt (1998).

| IATE | Automotive Test Suite
---|---|---
| EN-DE | EN-DE | EN-ET | EN-LV | EN-LT
| BLEU | Acc. | BLEU | Acc. | BLEU | Acc. | BLEU | Acc. | BLEU | Acc.
Baseline | 29.7 | 81.7 | 26.5 | 46.2 | 19.6 | 46.7 | 30.6 | 62.2 | 25.3 | 51.2
CD | 28.5 | 99.7 | 22.9 | 99.7 | 14.9 | 98.0 | 23.5 | 99.3 | 18.1 | 98.9
ETA | 29.9 | 96.2 | $33.2^{\dagger}$ | 94.0 | 17.8 | 92.4 | 27.4 | 93.4 | 28.8† | 89.7
TLA | 29.5 | 96.5 | 33.5† | 94.0 | 21.0†‡ | 87.2 | 35.0†‡ | 92.0 | 30.1†‡ | 90.3
Table 3: Results of automatic evaluation metrics BLEU and term translation accuracy (Acc.). The numerically highest score in each column is given in bold; † and ‡ indicate statistically significant improvements of BLEU over Baseline and ETA respectively (all $p<0.05$) . |  | Correct | Wrong lexeme | Wrong inflect. | Other | $\kappa_{\mathsf{free}}$
---|---|---|---|---|---
Basel. | 55.1 | 42.9 | 1.4 | 0.7 | 0.95
ETA | 45.2 | 7.9 | 44.9 | 2.0 | 0.87
TLA | 92.9 | 5.1 | 1.4 | 0.7 | 0.98
| Baseline | Equal | TLA | $\kappa_{\mathsf{free}}$
---|---|---|---
3.0 | 58.0 | 39.0 | 0.65
ETA | Equal | TLA | $\kappa_{\mathsf{free}}$
3.0 | 36.0 | 61.0 | 0.81
Table 4: Results of human evaluation: term (on the left) and sentence (on the
right) translation quality judgements in %. Sentence comparison is pairwise
contrasting TLA vs Baseline and TLA vs ETA. $\kappa$-free: inter-annotator
agreement according to free marginal kappa Randolph (2005).

### Evaluation Methods and Data.

In previous work, methods were tested on general domain
data555https://github.com/mtresearcher/terminology_dataset annotated with
exact surface forms of general-domain words from IATE and Wiktionary. Although
data constructed in such a way is not only artificial but also gives an
oversimplified view on terminology translation, we do use the data from IATE
to validate our re-implementation of the method from Dinu et al. (2019). Other
than that, we test on the Automotive Test Suite666https://github.com/tilde-
nlp/terminology_translation (ATS): a data set containing translations of the
same 768 sentences in English, Estonian, German, Latvian, and Lithuanian. ATS
contains about 1.1k term occurrences from a glossary prepared by professional
translators. When annotating terms in the source text, we use only the
dictionary forms of term translations, since in practical applications having
access to the correct inflections (surface forms) is unrealistic.

We compare our work with an NMT system without means for terminology
integration (Baseline) and the previous work by Dinu et al. (2019) (ETA).
Although our preliminary experiments with constrained decoding Post and Vilar
(2018) (CD) confirmed the findings by Dinu et al. (2019) that strict
enforcement of constraints leads to lower-than-baseline quality, we
nevertheless include them for completeness sake.

Similarly to the previous work, we use two automatic means for evaluation:
BLEU Papineni et al. (2002) and lemmatised term exact match accuracy. We use
BLEU as an extrinsic evaluation metric as we expect that, when successful, the
methods for terminology translation should yield substantial overall
translation quality improvements due to correctly translated domain-specific
terms. For significance testing, we use pairwise bootstrap re-sampling Koehn
(2004). We use lemmatised term exact match accuracy as an intrinsic metric
because it directly measures the adequacy of terminology translation (i.e.,
whether or not the correct lexeme appears in the target sentence).

We are aware that the automatic evaluation methods are merely an approximation
of translation quality. For example, we use lemmatised term exact match
accuracy to measure term use in target language translations; however, it does
not capture whether the term is inflected correctly. Thus human evaluation is
in place. We use the EN-LV language pair to compare TLA against baseline and
ETA. We use a 100 sentences large randomly selected ATS subset that contains
147 terms of the original test suite. We employ four professional translators
and Latvian native speakers to compare each system’s translations according to
their overall translation quality and judge individual term translation
quality. Specifically, given the original sentence and its two translations
(in a randomised order), raters are asked to answer “which system’s
translation is better overall?”. Raters are also given a list of the terms
being evaluated and their reference translations (from the term collection)
and are asked to classify translations as either “Correct”, “Wrong lexeme”,
“Wrong inflection”, or “Other”. Figure 1 gives an example of the forms
presented to raters during the human evaluation of term and overall
translation quality. We report inter-annotator agreement using free marginal
kappa, $\kappa_{\mathsf{free}}$ Randolph (2005).

##  4 Results

### Automatic Evaluation.

We first validate our re-implementation of ETA by testing on the English-
German WMT 2017 test set annotated with terms from IATE as used by Dinu et al.
(2019). Results (see columns 2 and 3 of Table 3) are similar to those of the
previous work: on this data set, ETA yields minor translation quality
improvements over the baseline (+0.2 BLEU) and considerable improvement
(+14.5%) in term translation accuracy.

When evaluated on the ATS, systems using TLA always yield results that are
better than the baseline both in terms of BLEU scores (+1.4–7 BLEU) and term
translation accuracy (29.8%–47.8%) (see columns 4-11 of Table 3). Results also
show that when compared to ETA, systems integrating terminology using TLA
achieve statistically significant improvements in terms of BLEU scores for
three out of four languages-pairs. An exception is EN-DE, for which both
systems, ETA and TLA, perform similarly. Analysing reference translations of
the EN-DE language pair, we find that as many as 87% of the German terms are
used in their dictionary forms, which explains the comparable performance of
systems trained using ETA and TLA on EN-DE.

Results also confirm the finding of the previous work by Dinu et al. (2019)
and Exel et al. (2020), that the strict enforcement of constraints by
constrained decoding leads to lower-than-baseline BLEU scores on all data sets
for all languages. BLEU scores are abysmal when translating into the
morphologically complex languages as for these languages citation form seldom
happens to be the form required in the target language sentence. This result
further illustrates why terminology constraints have to be soft when
translating into morphologically complex languages.

### Human Evaluation.

Results of human evaluation of EN-LV systems are summarised in Table 4. First,
we note that on this dataset, the baseline system translates terms correctly
55% of the time, yet it makes mistakes by choosing the wrong lexeme for most
of the other cases (Table 4, left). The system using ETA, on the other hand,
has a much lower rate of correctly translated terms – 45%, which roughly
corresponds to the proportion of Latvian terms in the reference translations
that are used in their dictionary forms (47%). The remaining cases are
mistranslated by choosing the wrong inflected form. The system using TLA, in
comparison, does very well as it gets terminology translations right 93% of
the time. Examining the cases where terms had been mistranslated by choosing
the wrong lexeme, we find that most of these cases are multi-word terms with
some other word inserted between their constituent parts. The high
$\kappa$-$\mathsf{free}$ values indicate almost perfect inter-annotator
agreement suggesting that the task of term translation quality evaluation has
been easy and results are reliable.

The overall sentence translation quality judgements (Table 4, right) also
favour translations produced by the system using TLA deeming it better than or
on par with the baseline system and system using ETA 97% of the time. The
system using TLA is strictly favoured over its ETA counterpart for 61% of the
translations. Again, annotators have reached an almost perfect agreement
($\kappa_{\mathsf{free}}=0.81$) when comparing the systems using TLA and ETA,
suggesting that the task has been easy. These results clearly show that at
least for the EN-LV language pair and the test set considered here, systems
using TLA improve term translation quality by correctly choosing adequate
translations and morpho-syntactically appropriate inflections.

### Productivity of NMT models.

Terminology translation frequently involves the translation of niche lexemes
with rare or even unseen inflections. Thus the model’s ability to generate
novel wordforms is critical for high-quality translations. To verify if our
NMT models are lexically and morphologically productive, we analysed Latvian
translations of ATS produced by the system using TLA and looked for wordforms
that are not present in either source or target language side of the training
data. We found 72 such wordforms. Of those 45 or 62.5% were valid wordforms
that were not present in training data, of which 28 were novel inflections
related to ATS terminology use, while the remaining 17 where novel forms of
general words. We interpret this as some evidence that the NMT model, when
needed, generates novel wordforms. The remaining 27 or 37.5% were not valid,
albeit sometimes plausible, Latvian language words, common types of errors
being literal translations and transliterations of English words as well as
words that would have been correct, if not for errors with consonant mutation.

##  5 Conclusions

We proposed TLA—a flexible and easy-to-implement method for terminology
integration in NMT. Using TLA does not require access to bilingual terminology
resources at system training time as it annotates ordinary words with lemmas
of their target language translations. This simplifies data preparation
greatly and also relaxes the requirement for apriori specified target language
forms during the translation, making our method practically viable for
terminology translation in real-life scenarios. Results from experiments on
three morphologically complex languages demonstrated substantial and
systematic improvements over the baseline NMT systems without means for
terminology integration and the previous work both in terms of automatic and
human evaluation judging term and overall translation quality.

## Acknowledgements

This research has been supported by the ICT Competence Centre (www.itkc.lv)
within the project “2.2. Adaptive Multimodal Neural Machine Translation” of EU
Structural funds, ID no 1.2.1.1/18/A/003.

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