# Fraction of broad absorption line quasars in different radio morphologies

A. Nair,1 M. Vivek,2
1University of Mumbai, Kalina, Mumbai 400 098, India
2Indian Institute of Astrophysics, Koramangala, Bengaluru 560 034, India
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

In this study, we investigated the orientation model of Broad Absorption Line
(BAL) quasars using a sample of sources that are common in Sloan Digital Sky
Survey (SDSS) Data Release (DR)-16 quasar catalog and Very Large Array
(VLA)-Faint Images of the Radio Sky at Twenty Centimeters (FIRST) survey.
Using the radio cut-out images from the FIRST survey, we first designed a deep
learning model using convolutional neural networks (CNN) to classify the
quasar radio morphologies into the core-only, young jet, single lobe, or
triples. These radio morphologies are further sub-classified into core-
dominated and lobe-dominated sources. The CNN models can classify the sources
with a high precision of >98$\%$ for all the morphological sub-classes. The
average BAL fraction in the resolved core, core-dominated, and lobe-dominated
quasars are consistent with the BAL fraction inferred from radio and infra-red
surveys. We also present the distribution of BAL quasars as a function of
quasar orientation by using the radio core-dominance as an orientation
indicator. A similar analysis is performed for HiBALs, LoBALs, and FeLoBALs.
All the radio morphological sub-classes and BAL sub-classes show an increase
in BAL fraction at high orientation angles of the jets with respect to the
line of sight. Our analysis suggests that BAL quasars are more likely to be
found in viewing angles close to the equatorial plane of the quasar. However,
a pure orientation model is inadequate, and a combination of orientation and
evolution is probably the best way to explain the complete BAL phenomena.

###### keywords:

quasars: absorption lines – quasars: general – galaxies: jets – methods: data
analysis

††pubyear: 2021††pagerange: Fraction of broad absorption line quasars in
different radio morphologies–A

##  1 Introduction

Quasars are highly luminous radio sources powered by accretion onto
supermassive black holes located at the center of their host galaxies. These
sources consist of non-thermal and polarized radio emissions, which can be
seen as jets arising from the central region of the quasar. Such quasars can
have different morphologies in the radio wavelengths depending on the
orientation of the radio jets with respect to the line of sight. In quasars
with extended radio emissions, sometimes only a single lobe is visible,
whereas double lobes along with a core at the center are seen in many other
cases. These radio lobes can extend from a few kiloparsecs to megaparsec
scales on each side of the central core. Fanaroff & Riley (FR) classification,
based on the brightness of the extended radio sources, consists of low-
luminosity FR I and high luminosity FR II sources (Fanaroff & Riley, 1974). In
FR I sources, radio luminosity becomes fainter as one moves away from the
core. Conversely, the end of the radio lobes, also known as ’hot spots’, are
brighter in FR II sources. As of now, multiple sub-classifications have been
defined to describe the morphological structure of these quasars, a few of
which include core/lobe-dominated quasars (Kimball et al., 2011); X-shaped
radio galaxies (Cheung, 2007; Leahy & Parma, 1992); narrow/wide-angle tail
sources (Rudnick & Owen, 1976); ring-like radio galaxies (Proctor, 2011).

Outflows from the central regions of active galactic nuclei (AGN) are thought
to be the main agents that regulate the evolution of both the central
supermassive black holes as well as the host galaxies (Silk & Rees, 1998; Di
Matteo et al., 2005). The presence of high-velocity outflows from AGN can be
established from the evidence provided by the blue-shifted broad absorption
lines (BALs) seen in the spectra of 10–20% of quasi-stellar objects
(QSOs)111In this work, we use ’QSO’ to refer optically selected AGN and
’quasar’ to denote AGN with radio emission. (Weymann et al., 1991). BALQSOs
are classified into three sub-classes based on the ionization state of the
absorbing gas:(a) high-ionization BALQSOs (HiBALs) consists of absorption from
high-ionization lines such as C iv, Si iv, and N v (Gibson et al., 2008; Filiz
Ak et al., 2013; Vivek et al., 2016; Vivek, 2019; Mishra et al., 2021) (b)
low-ionization BALQSOs (LoBALs) show absorption from low-ionization lines such
as Mg ii and Al iii along with the high-ionization lines (Voit et al., 1993;
Vivek et al., 2014; Vivek et al., 2018; Yi et al., 2019), and (c) iron-LoBALs
(FeLoBALs) are LoBALs with excited fine-structure Fe ii and/or Fe iii
absorption lines (Vivek et al., 2012; McGraw et al., 2015). The observed
BALQSO fraction is explained either by an orientation model, where the line of
sight intersects with the BAL absorbing clouds in 10–20% QSOs (Weymann et al.,
1991; Elvis, 2000), or an evolutionary model, where the QSO spends 10–20% of
its lifetime in the BALQSO phase (Farrah et al., 2007; Lipari et al., 2009).
Although the similarity in the optical/NIR properties of BAL and non-BALQSOs,
higher reddening and polarization features in BALQSOs support the orientation
model, the observed radio spectral indices of BALQSOs and the discovery of
polar winds in BALQSOs challenge this scenario (Reichard et al., 2003; Wang et
al., 2007; Montenegro-Montes et al., 2008; Zhou et al., 2006). On the other
hand, the anti-correlation between the radio loudness parameter and balnicity
index, Compact Steep Spectrum (CSS) nature of BALQSOs, and the redshift
dependence of BALQSO fraction favour the evolutionary model (Gregg et al.,
2006; Farrah et al., 2007; Allen et al., 2011).

The exact nature of BALQSOs is yet unsettled mainly due to the lack of a
reliable orientation indicator in quasars. The current approach uses
statistical indicators of orientation for large data samples that involve
properties from the radio, UV, and optical domains. The indicators in the
UV/optical region are based on the properties of emission lines. A strong
correlation is found between the velocity offsets and line width ratio of the
high-ionization C iv and the low-ionization Mg ii lines in the ultraviolet
region. Simulations carried out by Yong et al. (2020) show that an increase in
the line width ratio of C iv and Mg ii line is observed for face-on viewing
angles as compared to the edge-on viewing angles. Properties of emission lines
such as the full width at half maximum (FWHM) of H$\beta$ and the equivalent
width of O iii have also been studied as an orientation indicator for low
redshift quasars (Shen & Ho, 2014; Risaliti et al., 2011).

In the standard AGN unification theory, the anisotropic radio emission
produced by relativistic jets points to a description where properties like
radio morphology and radio spectral index depend on orientation. Two widely
used orientation indicators in the radio regime are the (a) core-to-lobe flux
density ratio (R), which is the ratio of the flux densities of the core and
lobe in radio wavelengths, and (b) radio-to-optical ratio of the quasar core
(RI), which is the ratio of flux densities of the core in radio and optical
wavelengths (See Eqn. 5&6 for the exact definition of R and RI parameters). A
high R-value suggests a small viewing angle to the jet axis, while a low
R-value indicates more of an edge-on view to the quasar (Orr & Browne, 1982;
Kapahi & Saikia, 1982; Morisawa & Takahara, 1987; Morganti et al., 1997).
Studies have shown that R correlates with core radio luminosity (Hardcastle &
Worrall, 2000) as well with the core optical luminosity (Kharb & Shastri,
2004). Factors like age and environment are believed to introduce the scatter
in the correlation involving the R parameter suggesting that R might not be
the best measure for orientation. The R parameter depends on both the core’s
radio flux as well as the radio flux of the lobes arising from the quasar
jets. These jets are suggested to be affected by environmental factors. Wills
& Brotherton (1995), and Kharb et al. (2010) showed that the radio-to-optical
ratio (RI) of the quasar core might be a better measure of studying the
orientation. The RI parameter measures the core-boosting factor by normalizing
the core’s radio flux by the core’s optical flux. Although with some scatter
in the correlation, Kimball et al. (2011) demonstrated a strong correlation
between R and RI parameter suggesting that the two parameters are good
indicators of quasar orientation. The scatter in the correlation supports the
idea that other factors like age, size, environment, and luminosity also
influence these two measurements.

Quasar orientation in BALQSOs has been studied with the help of radio spectral
indices of the sources (Montenegro-Montes et al., 2008; Fine et al., 2011;
Bruni et al., 2012). Montenegro-Montes et al. (2008) found that for a sample
of 15 BALQSOs, all sources had convex spectra typical for CSS/GPS sources
indicating young age for these sources. However, Bruni et al. (2012) found no
difference in the incidence of GPS sources amongst BALQSOs and non-BALQSOs,
inconsistent with BALQSOs as a complete class of younger objects. DiPompeo et
al. (2011) showed that BAL quasars have an over-abundance of steep spectrum
sources compared to non-BAL quasars, favoring the orientation model. Thus,
radio spectral index studies are not yet successful in completely settling the
debate between orientation and evolutionary models, most likely due to the
small number of sources in these studies. Studying the orientation of the
quasar using the R and RI parameter in large sets of quasars with different
radio morphologies is helpful to obtain a better picture of the orientation
dependence of BAL quasars. With the availability of large-sky-area high-
sensitive radio continuum surveys, such as Very Large Array (VLA)-Faint Images
of the Radio Sky at Twenty Centimeters (FIRST) survey (Becker et al., 1995),
it is now possible to carry out statistical studies of different morphological
classes of radio quasars. Upcoming radio sky surveys such as the Low-Frequency
Array (LOFAR) survey (de Gasperin et al., 2021), Very Large Array Sky Survey
(VLASS) (Lacy et al., 2020), and Square Kilometer Array (SKA) will increase
the sample of radio sources by several multitudes. As a visual classification
of these many sources is impractical, machine learning algorithms offer an
excellent solution to these big data problems. Machine learning techniques
have already been implemented in many problems such as classification of
optical transients (Mahabal et al., 2011), estimation of photometric redshifts
(Mountrichas et al., 2017), prediction of solar flares (Benvenuto et al.,
2018) and even morphological classification of active galactic nucleus (Aniyan
& Thorat, 2017; Lukic et al., 2018).

In this paper, we built Convolutional Neural Network (CNN) models to classify
the SDSS selected radio quasars from the FIRST survey into different radio
morphological classes like compact core, young jets, single lobe, and double-
lobe. The training sample in this study is derived from the Kimball et al.
(2011) catalog, which consists of spectroscopically confirmed quasars with
robust visual classifications of radio quasar morphology using FIRST images.
We use the sources with predicted labels from the CNN model as the base sample
for studying the BAL fraction’s dependence on the quasar’s orientation. Sample
of BAL quasars classified as HiBALs, LoBALs, and FeLoBALs from Trump et al.
(2006) is also used for checking the orientation dependence in these sub-
classes.

This paper is outlined as follows: The quasar sample data is explained in
section 2. In section 3 we describe the CNN model used for automatic
classification of radio morphologies adopted in our study. Section 4 discusses
the dependence of BAL quasars on orientation using multiple orientation
indicators. Discussion of the results and conclusion are given in sections 5 &
6. Throughout the paper, we adopt a cosmology with H0 = 70 kms-1 Mpc-1,
$\Omega$M = 0.3, and $\Omega$$\Lambda$ = 0.7.

Figure 1: Example cut-out images of sources with different radio morphological
classes used in this study. The 4’x4’ image cutouts from the FIRST survey are
scaled linearly.

##  2 The DATA

Our parent quasar sample is drawn from the SDSS DR16 quasar catalog (hereafter
DR16Q, Lyke et al., 2020) and the VLA FIRST survey (Becker et al., 1995). SDSS
DR16Q catalog contains the largest set of spectroscopically confirmed quasars.
The VLA FIRST survey is the largest available radio continuum survey covering
the same region of the sky as the SDSS.

We first started with the DR16Q quasar catalog, containing $\sim$750,414
quasars. This includes 225,082 quasars obtained for the extended Baryon
Acoustic Oscillation Spectroscopic Survey (eBOSS, Dawson et al., 2016) that
appear in the quasar catalog for the first time. The quasar catalog contains
around 480,000 sources in the redshift range 0.8 $<$ z $<$ 2.2 and more than
239,000 higher redshift sources observed for the Ly$\alpha$ forest studies.
Using this catalog, broad absorption line quasars and Damped Ly$\alpha$
systems (DLAs) were classified using automated algorithms by Guo & Martini
(2019) and Parks et al. (2018) respectively. The catalog includes 99,856 BALs
and 35,686 DLAs. This quasar-only catalog is estimated to be 99.8$\%$ complete
with 0.3-1.3$\%$ contamination. BAL quasars are identified using the
’BAL_PROB’ keyword in the DR16Q catalog, which is adapted from Guo & Martini
(2019) and gives the probability of the quasar to be a BAL quasar.

The VLA FIRST survey covered $\sim$9055 deg2 of the North Galactic Cap and
Equatorial Strip. It used the NRAO VLA telescope operating at a frequency of
1.4 GHz (20cm) with a beam size of 5.4," and an RMS sensitivity of about 15
mJy beam-1. The catalog contains 946,432 sources with a source detection
threshold of $\sim$1 mJy and an astrometric accuracy better than 1". The
catalog includes the integrated flux density at 20 cm (S20) and peak flux
density at 20 cm (Speak) for each source. For this study, we make use of the
"14dec17" version of the catalog.

We first obtained a set of 21,843 sources from the FIRST catalog, which fall
within 2" of the SDSS DR16Q catalog. Sources with the integrated flux density
at 20 cm (S20 Kimball et al., 2011) > 2mJy were selected to obtain a sample
with enough flux to distinguish between different morphological classes. The
threshold limit is set not to define a radio-loud population but rather to
obtain a sample similar to the training set used for our CNN model. This
threshold limit helps the CNN classifier identify and learn the morphological
features accurately. We exclude the sources with S20 $\leq$ 2 mJy from our
classification study. The remaining 16,491 "radio sources" are further
classified into different radio morphologies using CNN algorithms.

###  2.1 Radio Morphology Classes

The radio morphology classification used in this study is derived from Kimball
et al. (2011) that classified radio sources using a visual examination. The
sample provided in Kimball et al. (2011) consists of 4714 radio quasars from
the VLA FIRST survey. These sources have $S_{20}$ $>$ 2 mJy and an optical
counterpart in the SDSS DR7 quasar catalog within 2" of the radio source.
These sources are further classified according to their radio morphology into
core, doubles, triples, and jets. Following Kimball et al. (2011), we also
classify the radio quasars in our sample into the following morphological
classes:

  1. 1.

Core; a quasar core with compact radio emission

  2. 2.

Jet; a source with a quasar core and young radio jet

  3. 3.

Double; a source with radio emission from the quasar core and a single lobe.

  4. 4.

Triple; a double-lobed source with radio emission from quasar core and both
lobes

Doubles and Triples are further sub-classified as core-dominated and lobe-
dominated radio sources. The core-dominated sources are defined to have a core
brighter than its lobe, whereas the lobe-dominated sources have a lobe
brighter than its core. Kimball et al. (2011) includes another sub-
classification for the triples called "irregular triples", for triples having
one lobe brighter than the other one. We classify the "irregular triples" as
lobe-dominated triples in our classification model. For the classification
model, we use image cut-outs of dimension 4’x4’ from the VLA FIRST survey,
which has an instrumental resolution of 5". Example cut-out images of sources
with different radio morphological classes used in this study are shown in
Fig. 1.

##  3 Automatic classification of Radio morphologies

Unlike Kimball et al. (2011), we use CNN models to automatically classify the
radio quasars into different morphological classes.

###  3.1 Convolutional Neural Network

Artificial neural network is a computational framework inspired by how
biological neural networks in the human brain process information. The
building block of an artificial neural network is called a neuron, which is
responsible for accepting input data, performing calculations, and producing
output. Several neurons are stacked together to form a layer of neurons, and a
deep neural network contains many layers placed between the input and output
layers. A single neuron receives multiple inputs from all the neurons in the
previous layer. Each of these inputs is multiplied by a weight term, and their
sum is sent to neurons in the next layer after applying a bias and an
activation function. The activation function outcome then decides if a neuron
is activated or not. An activated neuron transfers information into the other
layers. The following equation gives the output of a single neuron,

$y=f\left(\sum_{i=0}^{n}\left(W_{i}*X_{i}\right)+B\right)$ (1)

where Wi, Xi, B, n, and f denote the weight vector, input vector, bias term,
number of neurons, and activation function, respectively. The process of
calibrating the values of weights and biases of the network is called training
of neural network. During the training process, known samples are passed
through the network and the network fine-tunes the weights and bias of each
neuron based on the error between the predicted responses and known responses
in a backpropagation step. Proper tuning of the weights and biases reduces
error and makes the model reliable.

A CNN is built using a series of layers which help in the classification
problem. The first layer of an image classifier CNN model is the input layer,
that can be grey-scaled or 3 channel RGB images. The second type of layer is
the convolutional layer, which contain the kernels that extract features from
different classes of images. Kernel convolution is a process in which a small
filter matrix when passed over the target image transforms the image based on
the values of the filter matrix. These filters are tensors which keep track of
information and extract features in a convolutional layer. The convolution of
the image matrix multiplied with the filter matrix gives the feature map.
Small kernel sizes help in extracting a large amount of information in cases
containing many local features from the input. Each neuron is then multiplied
with an activation function such as the Rectified Linear Unit (ReLU) that
introduces the necessary non-linearity into the model. Such non-linearity is
essential to produce non-linear decision boundaries.

Each convolutional layer is followed by a pooling layer which helps in
decreasing the dimensionality of the neural network. Max-pooling downsamples
the feature map by retaining only the maximum value for patches of a feature
map. Hence, it contains the most prominent features from the previous feature
map. The dropout layer helps to reduce over-fitting by randomly setting the
output of neurons to zero for a certain duration of the time during training.
A flatten layer is used to convert the network into a one-dimensional vector.
The flattened vector undergoes a few more fully connected dense layers before
the output layer. The Softmax activation function used in the output layer
helps scale the CNN’s output into probabilities. It scales the output between
0 and 1. This becomes helpful in the output layer where categorical
classification is to be performed. We implemented the CNN model using the
Tensor Flow222https://www.tensorflow.org, which is an open-source software for
deep learning applications.

###  3.2 Pre-Processing of training set

To train the neural network, we make use of the classified sources from the
Kimball et al. (2011) catalog. We collect 4’x4’ linearly scaled FIRST image
cut-outs of 4517 sources for our training set.

In order to maintain homogeneity in the training set, we use multiple image-
transformations to generate additional images from the existing set. Since all
the FIRST images obtained from Kimball et al. (2011) have the quasar at the
center of the image, the transformations made to generate new images were such
that they did not change the position of the central core of the quasar. The
transformations and their ranges applied to the images are as follows:

  * •

Rotation range = 5° and 10°

  * •

Shear range = 0.2

  * •

Horizontal flip = True

  * •

Vertical flip = True

The rotation transform rotates the image by the specified angle. We also apply
a shear transform to the image by providing a shear range. The images are also
flipped horizontally and vertically to generate new sets of images.

Table 1: The number of sources in each morphological sub-class, before and
after pre-processing of the data. The first column gives the main class of the
source, and the second column gives the sub-classification within that
morphological class. The third and fourth columns give the number of sources
present before and after the pre-processing, respectively.

Class | Sub-class | Before | After
---|---|---|---
|  | pre-processing | pre-processing
Core | - | 3433 | 9786
Double† | - | 387 | 9809
Triple† | - | 619 | 9982
Jet | - | 183 | 8437
Double | Core-dominated | 232 | 9038
Double | Lobe-dominated | 150 | 7837
Triple | Core-dominated | 165 | 8171
Triple | Lobe-dominated | 354 | 8360

† 5 doubles and 100 triples are sub-classified as ’unclassified’ by Kimball et
al. (2011)

The number of sources before and after applying image-augmentation are shown
in Table 1. A sample with a large number of training data for a specific class
will cause the model to over-fit for specific cases. Image-augmentation allows
the CNN model to obtain homogeneous input data for all source sub-classes. We
observe a considerable increase in the number of sources with extended radio
emissions, which otherwise had few sources. Such an increase in the data size
helps reduce the amount of over-fitting that occurs due to a high number of
sources in one specific class.

###  3.3 CNN structure to classify radio quasar morphologies

---
Figure 2: The CNN architecture for the model used for the (a) broad
classification (top panel), (b) sub-classification of double sources (middle
panel), and (c) sub-classification of triple sources (bottom panel).

As the test accuracy for a single CNN model was not good enough, we followed
an approach to first design a CNN model that broadly classified the sources
into core, doubles, triples, and jets. We then perform the sub-classification
for ’double’ and ’triple’ sources using two separate models. The sources
classified as ’doubles’ and ’triples’ using the first broad classification are
used as inputs for the sub-classification CNN models. This approach is helpful
to reduce the misclassification caused due to the similarity between double
and triple lobe sources (for e.g., between a double and an irregular triple
with one bright and one faint lobe). It also allows us to independently design
architectures for feature-specific classification (i.e., number of extended
emissions or core/lobe dominance).

The input images are grey-scaled images of 50 x 50 pixels. The number of core,
double and triple sources included in the training set of the broad classifier
can be found in Table. 1. We experimented with varying the number of layers,
the number of neurons, and the size of convolution kernels to arrive at a
structure with three 2-D convolutional layers having 64, 128, and 128 kernels
of size 5x5, 3x3, and 3x3 pixels, respectively. The outputs from each
convolutional layer have a 2x2 max pooling layer applied to reduce
dimensionality. A couple of dropout layers are applied to reduce over-fitting.
We set the dropout rate at 0.25 and 0.2 for the first and second dropout layer
seen in Fig. 2. We used the Rectified Linear Unit (ReLU) activation function
for each of the convolutional layers. After the third convolutional layer, we
used two one-dimensional dense layers of fully connected 128 and 64 neurons,
respectively, with ReLU activation. The final layer is a dense layer with 4
neurons corresponding to 4 morphological classifications. This layer is
assigned a softmax activation function to obtain a categorical classification
of data.

For the sub-classification of the double lobes into core-dominated and lobe-
dominated doubles, we followed a CNN structure with four convolutional layers
with 64, 128, 128, 256 kernels of size 5x5, 3x3, 3x3, and 3x3 pixels,
respectively. We applied a 2x2 max pooling after each convolutional layer. A
rate of 0.2 is assigned to the first two drop-out layers, and a rate of 0.3 is
assigned to the last two drop-out layers. Three dense layers of 256, 128, and
64 neurons are placed after the fourth convolutional layer. All the layers
mentioned above are assigned with the ReLU activation function. The final
layer is a dense layer with 2 neurons corresponding to the 2 classification
labels. The architecture for the sub-classification of triple lobes into core-
dominated and lobe-dominated triples is similar to that of the doubles, except
that the first two convolutional layers are not followed with any drop-out
layers.

In all the three CNN models, we used sparse categorical cross-entropy to
determine the loss of our network and the "adam" adaptive learning rate
optimization algorithm (Kingma & Ba, 2014). The architecture of the three
models are shown in Fig. 2.

We applied a 25 % validation split on the training data for the broad
classifier and a 30 % split for the sub-classifier models. We trained the
models for 15 epochs with a batch size of 100 for the broad classifier and
double’s sub-classifier and a batch size of 80 for the triple’s sub-
classifier. Fifteen epochs were deemed good enough for the models as we saw a
rise in the validation loss afterward. The confusion matrix for the validation
set and the learning curve of these models are shown in Fig. 12 in the
appendix.

###  3.4 CNN classifier results

Table 2: Precision, Recall and F1 score for all the classes under the three CNN models discussed in section 3. Model | Class | Validation Sample (Augmented) | Precision | Recall | F1 Score
---|---|---|---|---|---
Main | Core | 2447 | 0.9908 | 0.9779 | 0.9846
| Triple | 2496 | 0.9935 | 0.9823 | 0.9878
| Double | 2452 | 0.9823 | 0.9959 | 0.9889
| Jet | 2109 | 0.9765 | 0.9826 | 0.9824
Double | Core-dominated | 2712 | 0.9987 | 0.9957 | 0.9971
| Lobe-dominated | 2351 | 0.9963 | 0.9988 | 0.9975
Triple | Core-dominated | 2452 | 0.9938 | 0.9938 | 0.9937
| Lobe-dominated | 2508 | 0.9940 | 0.9940 | 0.9939

In order the evaluate the performance of our CNN models, we make use of the F1
score. The F1 score is an evaluation metric for classification algorithms that
uses precision and recall for a specific class. It is the weighted average of
precision and recall with a high F1 score of 1 showing an ideal classification
and a low F1 score of 0 expressing a failed classification. The F1 score is
expressed as

$\text{F1}=2\left(\frac{\text{Precision $\times$ Recall}}{\text{Precision +
Recall}}\right)$ (2)

where the precision is a measure of correctly classified samples, and the
recall is a measure of the sensitivity of the classifier model. Equations 3
are used for calculating the precision and recall respectively.

$\text{Precision}=\dfrac{\text{TP}}{\text{TP + FP}};\hskip
28.45274pt\text{Recall}=\dfrac{\text{TP}}{\text{TP + FN}}$ (3)

TP and FP stand for true positives and false positives, respectively, while FN
stands for false negatives. For example, if we look at triples, true positives
are the sources for which the actual and predicted labels are the same. We
count it as a false positive for sources predicted as triples but with a
different actual label. Similarly, for the actual label of triples, predicted
otherwise sources are counted as false negatives.

Table 2 shows the precision, recall, and F1 score for all the classes under
each of the CNN models. F1 score is the harmonic mean of precision and recall
values. The average score for each model is also mentioned in the table. We
can see that all three models show high precision, recall, and F1 scores. The
high F1 scores indicate that only a tiny fraction of the validation sample is
misclassified.

Using the CNN models mentioned before, we classified our radio quasar sample
into different morphological classes. The number of sources in each
morphological subclass is compiled in Table 3. In this effort, we have
increased the sample size of core and doubles by four times, jets by three
times, and triples by two times compared to our training set’s sample size.

The "core" type sources can be divided into two sub-classes, based on whether
they are resolved or not in the FIRST survey. The "resolved" core sources are
expected to consist of quasars with very young radio emission and/or at a high
redshift where the lobes appear as a single component. The "unresolved"
sources are expected to have boosted radio cores without any extended radio
emission, or it may be a distant quasar with an unresolved extended emission.
A dimensionless concentration parameter (Equation 4) is defined in Kimball et
al. (2011), as the ratio of integrated flux density (S20) to the peak flux
density (Speak) at 20 cm.

$\theta=\sqrt{\frac{S\textsubscript{20}}{S\textsubscript{peak}}}$ (4)

The "resolved" core sources have log($\theta^{2}$) > 0.05 and "unresolved"
core sources have log($\theta^{2}$) $\leq$ 0.05. For our further analysis of
BAL quasar orientation, we mainly focused on the resolved core quasars as the
exact morphology of unresolved core sources is unknown.

Table 3: The table lists the number of sources in each morphological class. The first column refers to the main class of the quasar source, while the second column indicates the sub-classification for the source. The number of sources in each sub-class is mentioned in the third column. Class | Sub-class | No. of Sources
---|---|---
Core | Resolved | 10441
Core | Unresolved | 2526
Double | Core-dominated | 1246
Double | Lobe-dominated | 548
Triple | Core-dominated | 254
Triple | Lobe-dominated | 926
Jet | - | 550

##  4 Orientation of BAL quasars

It is believed that the difference between the core only, core-dominated, and
lobe-dominated sources arise mainly due to the difference in the orientation
angle with respect to the line-of-sight (Orr & Browne, 1982; Kapahi & Saikia,
1982). If orientation is the main factor responsible for the BAL phenomena, we
expect a difference in the BAL fraction between these different radio
morphological classes.

###  4.1 BAL fraction in different morphological classes

Table 4: The total number of BALs and non-BALs in each morphological class is listed below. The calculated BAL fraction values are listed in the last column. The error in BAL fraction is computed using Poisonian statistics. Class | No. of BALs | No. of non-BALs | BAL fraction
---|---|---|---
Resolved Core | 286 | 976 | 0.23 $\pm$ 0.01
Core-dominated | 165 | 499 | 0.25 $\pm$ 0.02
Lobe-dominated | 107 | 356 | 0.23 $\pm$ 0.03

In order to obtain the number of BALs and non-BALs from our sample of 16491
sources, we used the BAL$\\_$PROB parameter from the DR16Q catalog. We
classified the sources with BAL probability (BAL$\\_$PROB) > 0.5 as BAL
quasars and the rest as non-BAL quasars. DR16Q also has quasars BAL$\\_$PROB =
-1 which are the low redshift sources whose spectra did not cover the C iv and
Si iv wavelengths. We did not include 7697 sources with BAL$\\_$PROB = -1 in
our analysis as the BAL nature of these sources is uncertain. The resulting
sample has 2182 BAL quasars and 6612 non-BAL quasars. From hereon, we combined
the core-dominated doubles and core-dominated triples into a single class
called core-dominated quasars (hereafter, CDQ). Similarly, the lobe-dominated
doubles and lobe-dominated triples are combined into a single class, namely
lobe-dominated quasars (hereafter, LDQ). Apart from LDQs and CDQs, we also
considered resolved core quasars (hereafter, RCQ) in this analysis. We
obtained a total of 664 CDQs(BALs: 165, non-BALs: 499), 463 LDQs(BALs: 107,
non-BALs: 356) and 1262 RCQs.

Figure 3: The figure shows the distribution of radio luminosity of the sources
in our sample as a function of redshift. The loci of the BAL quasars in our
study and from samples of previous studies have been marked. The star, square,
circle and diamond points correspond to the median values of BAL sources in
our sample, Tuccillo et al. (2017), Bruni et al. (2012), and DiPompeo et al.
(2011) samples. The error bars correspond to 1-$\sigma$ of the values for each
of the samples.

Fig 3 shows the radio luminosity vs redshift comparison of our sample with
previous BAL quasar samples (Tuccillo et al., 2017; Bruni et al., 2012;
DiPompeo et al., 2011). The sample in Tuccillo et al. (2017) consists of 22
BAL sources with 3.6 $\leq$ z $\leq$ 4.8, detected both in SDSS DR7 and VLA
FIRST surveys, and having radio loudness parameter greater than 10. Sample
provided by Bruni et al. (2012) comprises 25 BAL quasars found in the SDSS DR4
catalog with a counterpart in VLA FIRST, having S1.4 $>$ 30 mJy. DiPompeo et
al. (2011) catalog consists of 74 BAL quasars that are common in FIRST and
NVSS surveys with integrated flux density greater than 10 mJy and z $\geq$
1.5. Unlike our sample, the previous studies have mainly focused on BAL
quasars with high radio fluxes. The median radio luminosity of our BAL quasar
sample is lower than the Bruni et al. (2012) and DiPompeo et al. (2011)
samples and comparable to the Tuccillo et al. (2017) sample. Though the
Tuccillo et al. (2017) sample is at high redshift, the median redshifts of the
Bruni et al. (2012) and DiPompeo et al. (2011) samples are comparable to our
sample.

The number of BALs and non-BALs in three different morphological classes is
shown in Table 4 along with the corresponding BAL fraction values. Resolved
core, core-dominated, and lobe-dominated sources have a BAL fraction of 0.23
$\pm$ 0.01, 0.25 $\pm$ 0.02, and 0.23 $\pm$ 0.03 respectively. We do not see
any difference in the BAL fraction between the core only, core-dominated, and
lobe-dominated quasars and all the three morphological classes have a BAL
fraction close to 23%. This is consistent with the previous studies that have
found intrinsic fractions closer to 20 percent or higher from the infrared and
radio wavebands. A detailed discussion on the observed BAL fractions is given
in section. 5.

The difference in sample sizes of different morphological classes can
introduce some bias in the BAL fraction analysis. To remove any such biases,
we computed the BAL fraction in each morphological class by randomly selecting
sources with a sample size defined by the smallest sample size among the three
morphological classes. Lobe-dominated sources have the smallest sample size of
463 sources. We randomly selected a set of 463 sources from each of the other
two classes and measured the BAL fractions in that respective sets. We
repeated this procedure for 1000 iterations by randomly shuffling the sources
within a morphological class for each iteration. The median value of the BAL
fraction distribution for a morphological class is taken as the unbiased BAL
fraction for that class. This exercise resulted in BAL fractions of 0.23 $\pm$
0.02 and 0.25 $\pm$ 0.01 for the resolved core and core-dominated sources,
respectively.

We observe that the BAL fraction for all three classes is nearly the same. If
the distribution of the number of sources as a function of orientation is
different for the different classes, it may bias the BAL fraction
measurements. The average BAL fraction is mainly driven by the bins having the
most significant number of sources. If those bins in the three classes, albeit
at different orientation angles, somehow have the same BAL fractions, we will
not see any difference in the BAL fraction between the three different
morphological classes. To probe further into this, we studied the BAL fraction
as a function of some quasar orientation indicators.

###  4.2 Quasar orientation indicators

Two common parameters used to study the orientation of quasars are the core-
to-lobe flux density ratio (R) and core radio loudness parameter (RI). The
definition for the R and RI parameters in this paper have been adopted from
Kimball et al. (2011).

$R=\dfrac{S\textsubscript{core}}{S\textsubscript{lobe}}(1+z)^{(\alpha\textsubscript{lobe}-\alpha\textsubscript{core})},$
(5)

where Score and Slobe refer to the 20 cm flux densities of the core and lobes
respectively. We set the values for core spectral index $\alpha$core = 0 and
lobe spectral index $\alpha$lobe = -0.8.

$log(R_{I})=\dfrac{L\textsubscript{radio}}{L\textsubscript{optical}}=\dfrac{M\textsubscript{radio}-M\textsubscript{i}}{-2.5},$
(6)

where Mradio is the K-corrected radio absolute magnitude at 20 cm (refer Eqn.5
of Kimball et al., 2011, for the exact definition of Mradio) and Mi is the
Galactic reddening corrected and K-corrected absolute i-band magnitude. The Mi
values are taken from the DR16Q catalog. We exclude 85 sources that do not
have a valid Mi value. This results in a dataset with 659 CDQs ( BALs: 162,
non-BALs: 497), 462 LDQs ( BALs: 107, non-BALs: 355), and 1260 RCQs.

To measure the core-to-lobe flux ratio (R), we need the integrated flux
density (S20) of the core and lobe separately. To measure these flux density
values, we performed a radial search for radio emissions detected by VLA FIRST
within 4’ around the core of objects classified as ’doubles’ or ’triples’ by
our CNN model. For radio emissions found around the objects classified as
’doubles’, we set a limit of one emission value nearest to the core, and for
the objects classified as ’triples’, we set a limit of two radio emissions
nearest to the core. For ’triples’, the lobe with the highest flux is used to
get the Slobe value. It should be noted that the R value measured using this
technique might not provide the correct value for sources where multiple radio
emissions are found between the core and lobe. The number of BALs and non-BALs
with a corresponding R value include: 637 CDQs (BALs: 157, non-BALs: 480) and
456 LDQs (BALs: 106, non-BALs: 350). There are some sources included in the RI
dataset for which we could not identify the lobe component in VLA FIRST using
our procedure. In order to have a similar dataset while analyzing R and
$R_{I}$ parameters, we use the 632 CDQs (BALs: 154, non-BALs: 478) and 455
LDQs(BALs: 106, non-BALs: 349) that are common in both datasets.

As discussed in section 1, several studies have pointed out that RI is a
better statistical indicator of orientation than R. Both these indicators are
measures of the radio core boosting factor. The advantage of RI over R mainly
arises from the normalization used in the core boosting factor. R normalizes
using the extended lobe emission flux, which is subjected to aging and
environmental effects. Contrarily, RI normalizes using core optical flux,
independent of the age and environment. To better understand these effects, we
first checked for any correlation between the two quasar orientation
indicators defined above. Although with a large scatter, (Kimball et al.,
2011) has shown that there is indeed a correlation between these parameters in
their sample. They also argued that the observed correlation is not a
selection effect but is an intrinsic property. The top panel of Fig. 4 shows
the correlation between R and RI for core-dominated and lobe-dominated
sources. We see that core-dominated quasars have a moderate correlation with a
spearman-rank correlation coefficient of 0.49 and a p-value of
2.45$\times$10-40. Lobe-dominated quasars are weakly correlated with a
spearman-rank correlation coefficient of 0.20 and a p-value of
1.2$\times$10-5. Including both the samples result in a correlation
coefficient of 0.46 and a p-value of 3.7$\times$10-59. We also see a large
scatter in the correlation suggesting that other factors like age, environment
are also influencing these parameters. A weaker correlation for the LDQs may
suggest that LDQs may be more severely affected by these factors than the
CDQs.

Figure 4: Top panel: Spearman-rank correlation analysis between the two quasar
orientation indicators, log(R) and log(RI) for lobe-dominated quasars (LDQs),
core-dominated quasars (CDQs), and a combined sample of LDQs+CDQs. The
dashed/black, solid/red, and dot-dashed/blue lines represent the best fit for
the LDQs, CDQs, and the combined sample. Correlation coefficients and p-values
are given in the legend. Middle panel: The distribution of log(R) for LDQs
(solid/black) and CDQs (dashed/red). Bottom panel: The distribution of log(RI)
for LDQs (solid/black), CDQs (dashed/red), and resolved core quasars (RCQs,
dot-dashed/green). The vertical lines show the median values for the
corresponding distributions.

Middle panel of Fig. 4 shows the distribution of log(R) for CDQs and LDQs. The
definition of CDQ and LDQ itself points to a clear separation in log(R)
distribution between the two classes. Indeed, we also see that the
distributions of log(R) for CDQs and LDQs are well separated. The bottom panel
of Fig. 4 shows the log(RI) distributions of CDQs and LDQs together with the
RCQs. The vertical lines represent the median of the corresponding
distribution. Here again, although we see a progression in the median of
log(RI) distribution for LDQs, CDQs, and RCQs, there is significant overlap
between these distributions. It can be seen that the CDQs appear to have a
higher median log(RI) than the LDQs. The distribution for RCQs is shifted to
even higher log(RI) values than CDQs. Kolmogorov–Smirnov (KS) test between the
different samples results in statistically significant p-values ($<<$0.05),
indicating that the different samples are not drawn from the same
distribution.

Figure 5: BAL fraction vs. log(R) and log(RI) for core-dominated quasars
(CDQs) and lobe-dominated quasars (LDQs). The left column plots show the
variation of BAL fraction as a function of orientation indicator, log(R) for
CDQs, LDQs, and a combined sample of CDQs and LDQs. The right column plots
show the variation of BAL fraction as a function of another orientation
indicator, log(RI) for CDQs, LDQs, and a combined sample of CDQs and LDQs. The
error bars in each log(R)/log(RI) bin are one sigma bootstrap errors. The
number of sources in each bin is marked above the bin.

###  4.3 Dependence of BAL fraction on quasar orientation

Having defined two metrics for measuring the orientation of quasars, we
studied the distribution of BAL fraction as a function of the orientation
indicators. We first looked into the BAL fraction in bins of log(R) and
log(RI) for different morphological classes. Fig. 5 shows the BAL fraction in
different log(R) (left column panels) and log(RI) (right column panels) for
LDQs (top row panels), CDQs (middle row panels) and a combined LDQ+CDQ sample
(bottom row panels). The error bars represent one sigma bootstrap error where
we re-sampled 1000 times and computed the BAL fraction in each bins for each
iteration. The number of sources in each bin is also marked above the bin. The
core-boosting parameters R and RI are higher for small orientation angles of
the jet with respect to the line of sight. From Fig. 5, it is clear that the
BAL fraction almost doubles for a low value of orientation indicators (i.e.,
high orientation angles) as compared to high values. In the case of the R
parameter, the increase of BAL fraction towards high orientation angles is
evident for both CDQs and LDQs. As R is defined as the ratio of core-to-lobe
flux, it is not surprising that the log(R) distribution of LDQs is shifted to
low R values compared to the CDQs. However, such a clear separation of RI
parameter distribution is not seen between the CDQs and LDQs. In fact, some of
the CDQs have larger orientation angles than the maximum orientation angle of
LDQs. For log(RI) distribution, the increase in BAL fraction for high
orientation angles is very prominent for the CDQs. The trend is less prominent
for LDQs as the RI values are more clustered into two or three bins. The small
number of sources may heavily bias the highest orientation angle bins. To
improve the statistics, we also looked at the distribution of log(R) and
log(RI) with a combined sample of CDQs and LDQs. The bottom left and right
panels of Fig. 5 show the variation of BAL fraction as a function of log(R)
and log(RI), respectively, for the combined sample. It is clear from these
plots that the BAL fraction increases from 0.2 to 0.4 with the increase in the
orientation angle.

Figure 6: BAL fraction vs. log(RI) for resolved cores, unresolved cores, and a
combined sample of core-dominated, lobe-dominated, and resolved core quasars.
In all the panels, the error bars represent one sigma bootstrap error. The
total number of sources in each bin is marked above the bin. The top two
panels show the variation of BAL fraction with log(RI) for resolved and
unresolved core quasars. The bottom panel shows the BAL fraction vs. log(RI)
trend for a combined sample of core-dominated, lobe-dominated, and resolved
core quasars. The open/black, horizontally hatched /red, and 45 degree
hatched/blue histograms are for full sample sources, sample with sources
having FIRST flux greater than 3 mJy, and sample whose radio counterparts are
within 10” of the optical emission, respectively.

Since the RI parameter depends only on the radio and optical flux of the core,
we can use it to study the distribution of BAL fraction within the
morphological class of ’core only’ sources with no lobe emission. The top two
panels of Fig. 6 shows the distribution of log(RI) parameter for resolved
(left panel) and unresolved core (right panel) only quasars. Here again, it is
clear that the BAL fraction increases for higher orientation angles.
Unresolved core quasars may consist of either sources with boosted cores with
undetectable extended radio emissions or sources whose extended radio emission
is not resolved in the VLA FIRST survey. Hence, the behavior of the RI
distribution for unresolved cores can be a sum of distributions from different
morphologies. The open/black histogram in the bottom panel of Fig. 6 shows the
log(RI) distribution for a combined sample of RCQs, CDQs, and LDQs, which
again confirms the BAL fraction trend.

Our sample may suffer from selection effects due to the incompleteness of the
FIRST survey. The completeness of the FIRST survey is about 93% at 3 mJy,
which falls to 53 % at 1.1 mJy (Jiang et al., 2007). To examine if our results
are affected by this incompleteness, we compared the trend of BAL fraction
increase at high orientation angles for two samples; one with the full sample
and another with a sample defined by only those radio sources with FIRST
integrated flux, fint $>$ 3 mJy (horizontally hatched/ red histogram in Fig.
6). Even with this cut, the sharp increase in the BAL fraction towards high
orientation angles remains unchanged. Another bias that can affect our results
is due to incomplete radio identifications in the DR16Q sources. We initially
adopted a search radius of 2” within the optical emission to identify the
radio counterpart. To ensure that the chosen search radius does not introduce
any bias, we generated a new radio quasar sample by cross-matching the SDSS
and FIRST with a relaxed search radius of 10” within the optical source. The
45 degree hatched/blue histogram in the bottom panel of Fig. 6) shows the BAL
fraction with the radio counterpart defined by the nearest source in FIRST
within 10”. We also tested for biases from redshift or luminosity selection
effects by repeating the analysis using sources limited to specific ranges of
redshift and luminosity. In all these checks, we see an increase in the BAL
fraction at high orientation angles which rule out any biases in our analysis.

Using radio variability arguments, several studies have shown that some BAL
quasars are viewed along the polar axis (Zhou et al., 2006; Ghosh & Punsly,
2007). As the number of these polar BAL quasars is small, it is not yet clear
if they constitute an entirely different class of outflows. There also have
been some criticisms in the literature questioning the polar nature of these
sources, i.e., whether the radio variability can be attributed to beaming
effects or not (Hall & Chajet, 2011). Borguet & Hutsemékers (2010) simulated
the two-component polar+equatorial wind model of quasar outflows and showed
that it is necessary to include both the equatorial and the polar absorption
regions to explain the C iv BAL profiles in some sources. However, the search
of Mishra et al. (2019) to find BAL blazars using intra-night optical
variability did not result in any detection. Interestingly, we find that the
BAL fraction increases for the highest log(RI) (lowest orientation angles)
bins even though the number of sources in these bins is low. If confirmed with
a larger sample, this BAL fraction increase at low orientation angles may be
due to the existence of ’polar’ BAL quasars.

Fig. 5 & 6 are also helpful to understand why the average BAL fraction for the
three morphological classes are similar (see, section 4.1). It is clear that
most sources for the CDQs, LDQs, and RCQs are distributed between the log(RI)
values 1.99 and 3.5. Incidentally, these bins have a BAL fraction $\sim$ 20 %
and these bins dominate the computation of the average BAL fraction.

###  4.4 LoBAL and FeLoBAL quasars

In the orientation model of BAL quasars, LoBALs and FeLoBALs are thought to be
arising when the line of sight is closer to the equatorial accretion disk. As
most of the true edge-on quasars would be obscured by the dusty torus, what we
mean here is that they are seen from a viewing angle farther from the
accretion disk symmetry axis compared to non-BAL quasars. In this model,
LoBALs and FeLoBALs are more reddened than HiBALs as the column density of the
absorbing material is high when the line of sight is closer to the accretion
disk. Hence, we expect an increase in the BAL fraction at high orientation
angles for LoBALs and FeLoBALs. We investigated this phenomenon using a sample
of sources classified as HiBALs, LoBALs, and FeLoBALs in the Trump et al.
(2006) catalog. We checked the distribution of the BAL fraction in different
log(RI) bins for the two BAL quasar sub-classifications.

Since the BAL quasars in Trump et al. (2006) are taken from the SDSS DR3Q
catalog, we first cross-matched the SDSS DR3Q catalog with the VLA FIRST
survey to obtain a sample of BAL and non-BAL quasars. Our sample consists of
3893 sources in total, among which 477 are BAL quasars. Using the different
BAL sub-type flag values in the Trump et al. (2006) catalog, we identified 335
HiBALs, 100 LoBALs and 42 FeLoBAL sources.

Figure 7: BAL fraction vs log(RI) distribution for All BAL, LoBAL, and FeLoBAL
quasars from the Trump et al. (2006) catalog. In all the panels, the error
bars in each log(RI) bin are one sigma bootstrap errors. The total number of
sources in each bin is marked above the bin.

The top panel in Fig. 7 shows the log$R_{I}$ distribution for total BAL
fraction (HiBALs + LoBALs + FeLoBALs) in our sample of 3893 quasars. We
observe that the distribution in the top panel is similar to the result that
we obtained for our DR16Q sample. This confirms the trend of BAL quasar
fraction increase for high orientation angles using an independent dataset.
The middle and bottom panels in Fig. 7 show the log$R_{I}$ distribution for
LoBALs and FeLoBALs respectively. LoBALs and FeLoBALs also reaffirm the
previously seen trend of BAL fraction increase at high orientation angles. To
quantify the amount of BAL fraction increase, we calculated the percentage of
BAL fraction increase between the two log($R_{I}$) bins in the upper and lower
log(RI) values, which at least have more than 50 sources. We see that the
percentage of BAL fraction increases by 53 %, 163 %, 376 %, and 113 % for the
HiBAL, LoBAL, FeLoBAL, and total samples, respectively, with the increase in
the orientation angle. Clearly, the rate of increase of BAL fraction is
maximum for FeLoBALs, intermediate for LoBALs, and minimum for HiBALs. The
progressive reduction in the rate of BAL fraction change among FeLoBALs,
LoBALs, and HiBALs adds further evidence to the orientation model of BAL
quasars where FeLoBALs and LoBALs are preferentially seen at higher
orientation angles as compared to HiBALs.

Interestingly, we also note that the BAL fractions computed for Trump et al.
(2006) catalog sources (Fig. 7) are considerably lower than the BAL fractions
computed for DR16Q catalog sources (Fig. 5 & 6). We probed the difference
between these two datasets to understand the reduction in the BAL fraction. We
first compared the radio core intensity and absolute I-mag distributions of
the sources in the Trump et al. (2006) catalog and DR16Q catalog that are
included in our analysis. We do not see any difference in the distribution of
the FIRST radio intensity between these samples. However, we see a notable
difference in the absolute I-mag distribution with the Trump et al. (2006)
catalog sources shifted towards the brighter side by two magnitudes. This is
expected as the SDSS DR3, being one of the earliest SDSS data releases,
targeted relatively brighter quasars. However, it is not clear whether this
difference in the optical luminosity affects the BAL fraction. A more
prominent and clear difference is obtained in the distribution of absorption
index (AI) between the Trump et al. (2006) and DR16Q catalog sources. The
absorption index is a metric, first proposed by Hall et al. (2002), to
characterize the presence of BAL features in quasar spectra. It is a measure
of equivalent width, measuring all absorption within the limits of every
trough when the integration limit extends from 0 to 29,000 km s-1. Fig. 8
shows the distribution of AI measured for C iv region for the Trump et al.
(2006) and DR16Q catalog sources. It is clear that the DR16Q catalog has much
more sources with small AI values as compared to the Trump et al. (2006)
catalog sources. This difference in AI can be attributed to the difference in
the continuum normalization procedure and the BAL trough definition between
the two catalogues. As DR16Q employed a PCA-based continuum normalization and
an automated BAL identification procedure using a CNN, it should be sensitive
to even low values of AI. It is possible that Trump et al. (2006) et al. have
adopted a more stringent criteria for the identification of BAL troughs in
quasars.

Figure 8: Comparison of C iv absorption index for BAL quasar sources in the
DR16Q and Trump et al. (2006) catalog. The grey histogram corresponds to the
DR16Q catalog, and the red histogram corresponds to the Trump et al. (2006)
catalog. The corresponding KDE plots are also shown as solid/black and
dashed/red lines for DR16Q and Trump et al. (2006) catalog, respectively.

##  5 Discussion

In this study, we probed the orientation of BAL quasars using a large sample
of 16491 sources that have spectra available from the SDSS DR16 as well as
radio observations available from the VLA FIRST survey. Using CNN models, we
first classified this sample into different radio morphological classes such
as core only sources, core-dominated lobe sources, and lobe-dominated lobe
sources. We found that the average BAL fraction is the same $\sim$ 23 % for
these different morphological classes. Using two quasar orientation
indicators, we investigated the BAL fraction distribution as a function of
quasar orientation. The main result from this analysis is that the BAL
fraction almost doubles at high orientation angles irrespective of the radio
morphology. We also repeated this study using samples designed to remove any
selection effects and found that the trend of BAL fraction increase at high
orientation angles is unchanged. Fig. 9 shows the variation of BAL fraction as
a function of log(RI) for the resolved core, core-dominated, and lobe-
dominated quasars. We also show the trend for a combined sample of resolved
core, core-dominated, and lobe-dominated quasars. It is clear that the BAL
fraction increases to 0.4 from 0.2 when orientation angle increases
(equivalently log(RI) decreases). A similar trend was also seen for HiBALs,
LoBALs, and FeLoBALs using a different sample taken from Trump et al. (2006)
catalog. Interestingly, among the three BAL quasar sub-classifications, the
rate of change of BAL fraction is maximum in FeLoBALs, intermediate in LoBALs,
and minimum in HiBALs.

Figure 9: BAL fraction vs. log(RI) for the resolved core quasars (blue
diamonds), core-dominated quasars (red cross marks), lobe-dominated quasars
(green squares), and a combined sample of resolved core, core-dominated, and
lobe-dominated quasars (black circles). The error bars in the BAL fraction
indicate the one sigma bootstrap errors for the combined sample.

We validated our results against different selection effects due to redshift,
luminosity, incompleteness of the FIRST survey, and incomplete radio counter-
part identifications. However, we have not explicitly checked for any bias due
to incomplete target selection in the DR16Q catalog. As quasars are chosen for
spectroscopic observations in SDSS primarily based on their photometric
properties, our analysis can be biased due to the differential target
selection completeness for BALQSOs and non-BALQSOs. As BALQSOs are
significantly dust-reddened compared to non-BALQSOs, the completeness of
BALQSOs is expected to be less. Allen et al. (2011) computed this difference
in the selection probabilities using simulated BAL and non-BALQSO magnitudes
and found that the completeness is very high for both BALQSOs and non-BALQSOs
with z $<$ 2.1 and i $<$ 19.1, drops sharply for a narrow region close to z
$\sim$ 2.6 and rises again for higher redshifts. This completeness difference
can introduce some bias for analysis involving optically selected samples. To
our rescue, eBOSS also targets all SDSS point sources that are within 1” of a
radio detection in the FIRST point source catalog (Myers et al., 2015). As our
final sample is radio-selected BAL quasars and non-BAL quasars, we do not
expect the behavior of the BAL fraction to be severely influenced by any
incompleteness effects. As with the case of dust-reddening, strong absorption
troughs can make the broad band magnitude appear fainter for a BALQSO than an
equivalent non-BALQSO. C iv BAL troughs fall in the SDSS i-band for the
redshift range 3.5 $<$ z $<$ 4.4. Our BAL quasar sample contains 82 quasars
($<$ 4 %) in the redshift range where the i-band luminosities are
underestimated due to the presence of C iv BAL absorption. Additionally, a
small fraction of quasars ($<$ 1 %) should be LoBALs and FeLoBALs where the
i-band luminosities are affected by Mg ii, Al iii, and Fe ii broad absorption.
The orientation indicator, radio-to-optical core luminosity has the i-band
optical luminosity in the denominator. Although the fraction of BALQSOs
containing strong BAL features within the i-band wavelengths is less , any
correction of the optical luminosities will further push these sources to
lower log(RI) bins, thereby increasing the BAL fraction at higher orientation
angles. Likewise, Hewett & Foltz (2003) suggests that optically bright BAL
quasars are half as likely as non-BAL quasars to be detectable as S1.4GHZ
$\geq$ 1 mJy sources. To probe this, we divided the sample into three optical
luminosity bins, (i) Log(Li-band) $\leq$ 24 W/Hz, (ii) 24 W/Hz $<$ Log(Li-
band) $\leq$ 25 W/Hz, and (iii) Log(Li-band) $>$ 25 W/Hz, and studied the
distribution of radio luminosity of BAL and non-BAL quasars. We do not see any
difference in the distribution of radio luminosity between BAL and non-BAL
quasars for the lower optical luminosity bins. But, for the highest luminosity
bin, we see that the BAL quasars have statistically lower radio luminosities
as compared to the non-BAL quasars (p-value of KS test $<$ 0.05). Thus, a
flux-limited survey like FIRST would have missed a fraction of optically-
bright BAL quasars that have radio fluxes below the FIRST sensitivity. As
these missed BAL quasars have low radio luminosities and high optical
luminosities, a correction for the missed quasars would only populate the
lower log(RI) bins. This again will amplify the already seen trend of BAL
fraction increase at high orientation angles. To ensure that the optically
bright sources are not biasing the BAL fraction trend, we excluded the
optically bright sources from our sample and then studied the variation of BAL
fraction as a function of orientation. The pruned sample also follows the
trend of high BAL fraction for high orientation angles.

The fraction of BALQSOs, especially in radio quasars, is an interesting
parameter that can constrain the orientation vs. evolution models of BALQSOs.
An important issue here is the definition of BALQSO itself. The traditional
BALs are defined to have C iv absorption troughs broader than 2000 km s-1 and
outflow velocities larger than 3000km s-1. The fraction of ’traditional’
BALQSOs in optically selected quasar samples is typically found to be $\sim$
10 percent (Weymann et al., 1991; Gibson et al., 2008). Although the
traditional definition is helpful to include absorption only from nuclear
outflows, it also removes a significant fraction of genuine BALQSOs. Trump et
al. (2006) redefined the BALQSO definition to include absorption features
having narrower widths and lower outflow velocities. With this new definition,
Trump et al. (2006) found that the BALQSO fraction significantly increases to
26 percent. Studies using infra-red or radio selection have also found the
intrinsic fraction to be closer to 20 percent (Dai et al., 2008; Ganguly &
Brotherton, 2008; Dai et al., 2012; Morabito et al., 2014). Our results for
the average BAL fraction in different morphological classes are consistent
with the BAL fraction inferred from previous studies. We want to stress here
that BALQSOs in our analysis follows the Trump et al. (2006) definition rather
than the traditional one.

The lack of availability of a reliable indicator of quasar orientation is a
major hindrance in quasar studies. Van Gorkom et al. (2015) compared the
different indicators of quasar orientation using a sample of 126 radio-loud
quasars. Their study mainly compared four indicators that measured radio core
dominance as a proxy for quasar orientation. Core dominance compares the radio
core luminosity against the intrinsic power of the central engine. Van Gorkom
et al. (2015) used four proxies for the intrinsic power of the central engine,
namely, radio lobe luminosity, optical continuum luminosity, luminosity of the
narrow-line region, and 151 MHz luminosity. The main results from their study
are : (a) the beamed optical synchrotron emission from the jets is not a
significant component of the optical continuum, (b) normalizing the radio core
luminosity by the optical continuum luminosity yields a demonstrably superior
orientation indicator. The above study warrants the use of radio core to
optical continuum luminosity ratio as a reliable proxy for quasar orientation.

Shankar et al. (2008) found an inverse correlation between the BAL fraction
and radio luminosity where BAL fraction is found to be higher for low
luminosity sources as compared to high luminosity sources. They invoked a
simple orientation model to explain the BAL fraction-radio luminosity trend.
Their model assumes that some fraction of sources is boosted to higher
luminosities due to relativistic beaming towards the observer. As BAL quasars
are preferentially viewed close to the accretion disk plane, they are less
beamed and less luminous on average. Thus, the trend of BAL fraction with
radio luminosity is very much linked to the orientation of the jet with
respect to the line of sight, and Shankar et al. (2008) essentially used this
phenomenon to define radio luminosity as a proxy for quasar orientation. The
only caveat in their approach is that the fraction of radio sources with
relativistic beaming is not well constrained. In our analysis, we alleviate
this problem by adopting radio core dominance as the quasar orientation
indicator. By normalizing the radio core luminosity with the intrinsic power
of the central engine, the amount of relativistic beaming is well constrained
for sources in our sample. The most important result from our study is that
the BAL fraction increases considerably for higher orientation angles of radio
jets with respect to the line of sight. This trend is found in all the
samples, irrespective of their morphological classes. At low orientation
angles, the BAL fraction is $\sim$ 20 percent which increases to $\sim$ 40
percent at high orientation angles. In Shankar et al. (2008) study, the BAL
fraction for classical BALs reduced from 20 percent at faint luminosities to 8
percent at high luminosities. Adopting a broader definition of BAL quasars as
given in Trump et al. (2006), they found the fraction of radio BAL quasars to
be 44 percent at low luminosities, reducing to 23 percent at high
luminosities. Therefore, our results are consistent with the findings of
Shankar et al. (2008). Interestingly, a Spearman-rank correlation analysis
between the radio luminosity and the orientation parameter RI for sources in
our sample results in a statistically significant correlation with a
correlation coefficient of 0.7.

Gregg et al. (2006) too found a similar anti-correlation between the radio-
loudness and strength of the BAL features. Fig. 3 in Gregg et al. (2006) shows
the anti-correlation between balnicity index and radio-loudness for BAL
quasars. The anti-correlation is stronger for the FR II–LoBAL quasars. As the
radio loudness parameter is similar to the orientation indicator RI, the
sources with higher radio-loudness could indicate low-inclination angles to
the jet axis due to core-boosting. Hence, the anti-correlation between
balnicity index and radio-loudness is consistent with our results which favors
a prominent role of orientation. However, Gregg et al. (2006) argued for the
evolutionary model of BAL quasars due to the paucity of FR-II BAL quasars in a
large sample of quasars. They argued that the emergence of radio jets to
create FR II sources is frustrated by the obscuring BAL shroud in the quasar
infancy. In our study, we note that the fraction of BAL quasars in lobe-
dominated sources is similar to core-dominated and resolved core quasars (See,
Table. 4). Among the BAL quasar sources with extended lobe-dominated
morphology, our sample contains 49 doubles and 58 triples. Hence, we do not
notice any paucity of FR-II BAL quasars in our sample. The lack of FR-II BAL
quasars in earlier studies may arise due to adopting (i) a stringent
definition of BAL quasars based on the balnicity index and (ii) radio loudness
as a criteria for sample selection.

Several studies have tried to probe the orientation of BAL quasars using radio
spectral index (Becker et al., 2000; Montenegro-Montes et al., 2008; Fine et
al., 2011; DiPompeo et al., 2011). These studies have shown that BAL quasars
have a wide range of radio spectral indices suggesting a full range of
orientations. Becker et al. (2000) identified 29 BAL quasars in the FIRST
Bright Quasar Survey where two-thirds of sources had steep radio spectra, and
the remaining third had flat spectra. Earlier studies did not find any
significant difference in the distribution of radio spectral indices for BAL
and non-BAL quasars, probably due to small sample sizes. Using a sample of 74
radio-selected BAL quasars, DiPompeo et al. (2011) showed that BAL quasars has
an over-abundance of steep spectrum sources compared to non-BAL quasars,
though both samples spanned a wide range of the spectral index. They concluded
that BAL quasars are more often observed at high orientation angles compared
to typical quasars. The abundance of steep spectrum sources among BAL quasars
is again consistent with our finding of increased BAL fraction at high
orientation angles. Additionally, the fact that we find an appreciable BAL
fraction $\sim$ 20 percent, even at low orientation angles, is congruent with
the wide range of radio spectral indices found in BAL quasars.

We argue that our analysis is superior to the previous studies of BAL quasar
orientations for the following reasons: (a) As we work with the latest release
of SDSS data, our BAL quasar sample sizes are considerably larger than the
previous studies by at least 10 times, (b) As our analysis mainly uses radio
images which are readily available from large scale surveys like FIRST, our
radio quasar sample sizes are also significantly larger than the samples used
in radio spectral index studies, (c) The automatic classification of radio
sources into different morphological classes has enabled us to study the
variation of BAL fraction with orientation in these sub-classes, (d) By
adopting the radio core to optical luminosity ratio, we have used the best
available proxy for quasar orientation, and (e) We also show that the BAL
fraction-orientation angle trend holds for different BAL quasar sub-
classifications and find a succession in the rate of BAL fraction increase
between HiBALs, LoBALs and FeLoBALs.

It is easy to explain our results using a pure geometric model where BAL
quasars are preferentially seen close to the accretion disk plane. The
progression in the rate of BAL fraction increase between HiBALs, LoBALs, and
FeLoBALs probably points to a statistical progression in the distribution of
orientation angles between these sources. However, there are several pieces of
evidence that tell that the scenario is not that simple. In this study, we
find an appreciable fraction of BAL quasars even at low orientation angles
irrespective of the radio morphology and BAL sub-classification. The discovery
of polar BAL quasars (Zhou et al., 2006), compactness of BAL quasars at high-
resolution radio images (Kunert-Bajraszewska et al., 2010), presence of BAL
quasars with convex radio spectral shapes like Giga-Hertz peaked sources
(Montenegro-Montes et al., 2008) are some of the results which challenge the
pure orientation model. Even in our analysis, we see a tentative increase in
the BAL fraction towards very low orientation angles pointing to the existence
of polar BAL quasars. These results suggest that orientation plays a role,
apparently a significant one, in the presence of BAL features but is
inadequate to explain the whole class of BAL quasars. A combination of
orientation and evolution is probably the best way to explain the observed
fraction BAL quasars.

##  6 Conclusion

The following are the point-wise conclusions of our analysis that probed the
orientation dependence of BAL quasars using a sample of sources commonly
available in SDSS and FIRST surveys.

  1. 1.

We built three CNN models for classifying radio quasars based on the
morphology of their radio emission. The first model (broad classification) is
used to classify the sources into Core, Jets, Doubles, and Triples. The other
two models (sub-classification of Doubles and Triples) are used separately to
sub-classify Doubles and Triples into core-dominated and lobe-dominated
sources. All the three CNN models (Section 3) show an F1 score >98$\%$.

  2. 2.

The average BAL fraction appears to be nearly identical for the morphological
classes of resolved core, core-dominated, and cobe-dominated quasars. This
average BAL fraction $\sim$ 23 % is consistent with BAL fractions inferred
from the infrared and radio wavebands.

  3. 3.

We used orientation indicators such as the core-to-lobe flux density ratio (R)
and core radio loudness parameter (RI) to study the distribution of BALs at
different inclination angles with respect to the symmetry axis of the
accretion disk. It is seen that for all morphologies defined in this paper,
the BAL fraction is high ($\sim$ 40 %) at higher orientation angles and low
($\sim$ 20 %) at low orientation angles. This increase in BAL quasar fraction
is independent of any bias from optical or radio selection effects.

  4. 4.

We used the sources from Trump et al. (2006) catalog to study the distribution
of orientation indicator log(RI) amongst HiBALs, LoBALs, and FeLoBALs. The
trend for BAL fraction to increase at high orientation angles is seen in Trump
et al. (2006) catalog sources. Additionally, the rate of increase of BAL
fraction is maximum for FeLoBALs, intermediate for LoBALs, and minimum for
HiBALs.

  5. 5.

The increase of BAL fraction at high orientation angles statistically favors
the geometric model of BAL quasars. However, the presence of significant
fraction of BAL quasars at all orientation angles, tentative evidence of the
presence of polar BAL quasars in our analysis may point to a scenario where a
pure geometric model is insufficient to explain the nature of BAL quasars
completely.

The present study adds to the growing evidence of a more prominent role of
orientation in explaining the BAL phenomena, but at the same time, also hints
at a significant role of evolution. We also have started a detailed study of
lobe-dominated BAL quasars in our sample. Upcoming radio sky surveys such as
the LOFAR survey, VLASS, and SKA will increase the number of radio sources by
several times. This will significantly improve the statistics for extreme RI
bins. With these datasets, it will be desirable to unambiguously establish the
existence of polar BAL quasars at low orientation angles.

## Acknowledgements

We thank the anonymous referee for the feedback which has significantly helped
to improve the paper. MV acknowledges support from DST-SERB in the form of
core research grant(CRG/2020/1657).

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions.

SDSS-IV acknowledges support and resources from the Center for High
Performance Computing at the University of Utah. The SDSS website is
www.sdss.org.

SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics | Harvard & Smithsonian, the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

## Data Availability

The CNN models and catalog of the 16491 sources with coordinates and radio
loudness parameters can be found at
https://github.com/nairakhils/QuasarMorphCNN. DR16Q and Trump et al. (2006)
catalog information are available from their respective papers. FIRST images
can be downloaded using the FIRST cutout server link
https://third.ucllnl.org/cgi-bin/firstcutout.

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##  Appendix A Examples of sources classified using CNN models

Figure 10: Examples of morphologically classified broad classes of radio AGN
using CNN model defined in section 3.

In Fig. 10, we can see five examples each of all the morphological classes
predicted by the CNN model defined in section 3.

Figure 11: Examples of morphologically classified sub-classes of radio AGN
using CNN models defined in section 3. Figure 12: The confusion matrix and
learning curves for the three CNN models (section 3): a) Broad classifier
model (top panel), b) Double sub-classifier model (middle panel) and c) Triple
sub-classifier model (bottom panel) are shown in this figure. The confusion
matrices show the number of sources for each true/predicted label and the
learning curves show the model’s learning accuracy for the training and
validation set.

We keep a track of the training and validation accuracy of the models at each
epoch. This allows us to visualize the learning curve of our model. Right
panels of Fig 12 shows the learning curve for the broad classifier (top),
double’s sub-classifier (middle) and triple’s sub-classifier (bottom),
respectively. Left panels of Fig 12 shows the corresponding confusion
matrices.