# Efficient Analysis Routines for Single and Double Peaked Type 2 AGN Spectra

M. Selwood,1 G. Calderone,2 S. Fotopoulou,1 M. N. Bremer1
1H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK
2INAF – Osservatorio Astronomico di Trieste, Via G.B. Tiepolo 11, 34143
Trieste, Italy
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Driven by the imminent need to rapidly process and classify millions of AGN
spectra drawn from next generation astronomical facilities, we present a
spectral fitting routine for Type 2 AGN spectra optimised for high volume
processing, using the Quasar Spectral Fitting library (QSFit). We analyse an
optically selected sample of 813 luminous Type 2 AGN spectra at $z<0.83$ from
the Sloan Digital Sky Survey (SDSS) to qualify its performance. We report a
median narrow line H$\alpha$/H$\beta$ Balmer decrement of 4.5$\pm$0.8,
alluding to the presence of dust in the narrow line region (NLR). We publish a
specialised QSFit fitting routine for high signal to noise ratio spectra and
general fitting routine for double peaked Type 2 AGN spectra applied on a sub-
sample of 45 spectra from our parent sample. We report a median red and blue
peak velocity separation of 390$\pm$60 kms-1. No trend is found for red or
blue peaks to exhibit systematically different luminosity or ionization
properties. Emission line diagnostics show that the double peaks in all
sources are illuminated by an AGN-powered ionizing continuum. Finally, we
examine the morphology of host galaxies of our double peaked sample. We find
double peaked Type 2 AGN reside in merging systems at a comparable frequency
to single peaked AGN. This suggests that the double peaked AGN phenomenon is
likely to have a bi-conical outflow origin in the majority of cases. We
publicly release the code used for spectral analysis and produced catalogues
used in this work.

###### keywords:

methods: data analysis – galaxies: active – quasars: emission lines

††pubyear: 2022††pagerange: Efficient Analysis Routines for Single and Double
Peaked Type 2 AGN Spectra–A.2

##  1 Introduction

Active galactic nuclei (AGN) are a phase of luminous accretion of matter onto
a central supermassive black hole (SMBH) in a galaxy, signifying the growth of
the massive compact object. A significant fraction of the accreted matter
rest-mass energy is converted to electromagnetic radiation that, through a
number of mechanisms, is observed from radio to gamma ray bands. Observational
and cosmological simulation-based works suggest that the properties and
evolution of SMBH and AGN host galaxies are closely related (Alexander &
Hickox, 2012, and references therein). Accurate determination of AGN emission
line and energetic properties, which are encoded in the spectra of the objects
is therefore essential for the study of this co-evolution.

AGN are classified optically as Type 1 (unobscured) and Type 2 (obscured)
based on the presence or lack of broad ($\gtrsim 10^{3}$ km s-1) emission
lines in their spectra. The unification model of AGN postulates that all AGN
have an ubiquitous central structure comprising of several distinct components
(Antonucci, 1993; Urry & Padovani, 1995; Netzer, 2015). In this formalism,
many of the discrepancies in spectral appearance between different AGN species
arise from the orientation of a standard AGN structure with respect to the
observer (see Netzer, 2015, for a review). Type 2 AGN are therefore proposed
to have their central engine, i.e. accretion disk and broad line region (BLR),
obscured from the observer by an axisymmetric dusty molecular torus located
0.1 - $10\text{\,}\mathrm{p}\mathrm{c}$ from the central SMBH.

Complete extinction of optical emission from the BLR requires a dust obscuring
screen of $A_{V}$ = 5 - 10 mags (Schnorr-Müller et al., 2016), which
corresponds to an X-ray absorbing hydrogen column density of $N_{H}>10^{22}$
cm-2 using typical dust-to-gas ratios (e.g. Predehl & Schmitt, 1995). Hence,
Type 2 AGN have severely diminished optical, ultraviolet (UV) and soft X-ray
emission, which originate from the central few parsecs of the AGN, compared to
their Type 1 counterparts. This obscuration introduces difficulty into the
identification of Type 2 AGN in these bands, particularly as host-galaxy
dilution can compete with and in extreme cases overwhelm AGN emission in lower
luminosity sources (Hickox & Alexander, 2018).

Type 2 AGN nevertheless exhibit strong narrow optical emission lines with
velocity full-width at half-maximum (FWHM) values of a few $\sim$ 100 - 1000
kms-1. These emission lines originate from forbidden transitions in the low
density narrow-line region (NLR) of AGN. The NLR extends beyond the influence
of the obscuring medium, up to a few kiloparsecs from the central SMBH.

Despite successfully reconciling many features of Type 1 and Type 2 AGN, there
is significant evidence to suggest that the standard unified orientation model
does not fully explain the properties observed between the optical subtypes.
The host-galaxy properties between the two classes have been found to deviate,
with Zou et al. (2019) finding hints that Type 2 AGN have higher host-galaxy
stellar masses than Type 1 AGN. The works of Bornancini & García Lambas (2020)
and Villarroel & Korn (2014) proposed that Type 1 and Type 2 AGN are found in
different environments with distinct neighbours, favouring an evolutionary
scenario between Type 1 and Type 2 AGN. Similarly, the mid-IR luminosity
function study of Lacy et al. (2015) shows that Type 1 and Type 2 AGN
populations follow significantly different evolutionary trends through cosmic
time, with an earlier peak in space density for Type 2 AGN. It is therefore of
importance to characterise the spectroscopic and physical properties of
samples of Type 2 AGN in order to understand their standing in relation to
their Type 1 counterparts.

While early work concentrated on single AGN spectra or a handful of sources,
the introduction of large scale spectroscopic surveys such as the Sloan
Digital Sky Survey (SDSS, Blanton et al., 2017) and in years ahead Euclid
(Laureijs et al., 2011), DESI (DESI Collaboration et al., 2016), 4MOST (de
Jong et al., 2019) and MOONS (Cirasuolo et al., 2020) have shifted the field
towards the analysis of large samples of thousands to millions of spectra
(Selwood et al., in prep; Merloni et al., 2019; Dey et al., 2019). The volume
of data from such large scale surveys has borne a plethora of codes, software
distributions and recipes to analyse and decompose the properties of optical
AGN spectra. Each of these routines serve a different purpose, with some codes
focussing on fitting the spectra of particular types of AGN. Others are
written for the extraction of specific spectral properties (eg. SFR, velocity
dispersion) and some with the aim of providing precise decompositions of a
given feature or conversely for high performance on large spectroscopic
samples. This software ecosystem has obvious shortcomings such as the lack of
transparency and reproducibility stemming from analysis codes being kept
private or being close source. Many available codes are unable to treat both
Type 1 and Type 2 AGN spectral fitting. As different fitting routines use
varied models and algorithms systematic differences in their measurements can
appear, which are often overlooked.

Quasar Spectral Fitting library (QSFit, Calderone et al., 2017)) is a software
package aiming to perform high volume automatic analysis of Type 1 AGN and QSO
optical spectra. Originally implemented in IDL, it has recently been
ported111https://github.com/gcalderone/QSFit.jl/ in Julia language (Bezanson
et al., 2012) to simplify analysis customization and allowing easier sharing
of the recipes and of the results (Calderone et al., in prep.). The software
provides a scalable means to consistently analyse large spectroscopic samples
of spectra, by adopting a flexible fitting recipe which incorporates several,
physically motivated, AGN spectral components to model the data. The package
aims to be as general as possible providing acceptable fits in the vast
majority of cases, and being customisable enough to deal with the more exotic
ones.

The QSFit recipe iteratively add the model components while performing a fit
following a Levenberg–Marquardt least-squares minimization algorithm
(Markwardt, 2009), until all component are simultaneously fit to the data,
providing an overall coherent picture of the spectral quantities. It is
agnostic to the instrument used to collect the spectra, allowing the user to
define an instrumental resolution.

In this work, we developed a new spectral fitting recipe specifically targeted
to Type 2 AGN. We have applied our procedure to the Reyes et al. (2008) sample
(Sect. 3) of high luminosity Type 2 AGN SDSS spectra (Sect. 2) in order to
demonstrate the software’s utility and explore specific issues around the
interpretation of such spectra. We discuss self-consistency checks,
consistency with the literature and initial scientific results of our sample
in Sect. 4. As a consequence of our analysis we also develop specialised
approaches to analysing Type 2 AGN spectra with high signal to noise ratios
(S/N, Sect. 5) and double peaked emission lines (Sect. 6)222All codes and
recipes used for spectral analysis in this work are publicly available at
https://github.com/MattSelwood/Type2AGN with instructions to reproduce our
analysis..

Throughout this paper we assume a $\Lambda$CDM cosmology with $H_{0}$ = 70
kms-1Mpc-1, $\Omega_{m}$ = 0.3 and $\Omega_{\Lambda}$ = 0.7.

##  2 Type 2 AGN Sample

Reyes et al. (2008) presented a catalogue of 887 optically selected high
luminosity Type 2 AGN with $z<$ 0.83, selected from the SDSS Data Release 6
(DR6; Adelman-McCarthy et al., 2008). The sample is selected using the
following criteria; a redshift cut of $z<0.83$ is applied so that [O
iii]$\lambda$5007 is present in all spectra. A requirement for [O
iii]$\lambda$5007 rest-frame equivalent width (EW) to be greater than 4 Å is
then employed to select objects with clear emission lines. A signal-to-noise
ratio (S/N) cut of S/N $\geq$ 7.5 is performed with a metric that neglects
continuum dominated sources with low S/N (see Zakamska et al., 2003). An [O
iii]$\lambda$5007 line luminosity cut of $L_{[\mathrm{O}\textsc{iii}]\lambda
5007}$ $\geq 10^{41.9}\ $ergs-1, which corresponds to an approximate
bolometric luminosity cut of $L_{bol}\gtrsim 10^{44}\ $ergs-1 (Lamastra et
al., 2009), is then applied to ensure completeness in emission line ratio
selection. This procedure is followed by applying emission line ratio criteria
to distinguish between a stellar and AGN ionizing continuum (see section 4.3),
constraining the sample to sources which satisfy either

$\log{\left(\frac{[\mathrm{O}\textsc{iii}]\lambda
5007}{\mathrm{H}\beta}\right)}>\frac{0.61}{\log{([\mathrm{N}\textsc{ii}]\lambda
6583/\mathrm{H}\alpha)}-0.47}+1.19$ (1)

or

$\log{\left(\frac{[\mathrm{O}\textsc{iii}]\lambda
5007}{\mathrm{H}\beta}\right)}>\frac{0.72}{\log{([\mathrm{S}\textsc{ii}]\lambda\lambda
6716,6731/\mathrm{H}\alpha)}-0.32}+1.30$ (2)

for objects with $z<0.36$. In the redshift range $0.36\leq z<0.83$ objects
with a H$\beta$ detection with S/N > 3 are identified as an AGN candidate
using the criterion

$\log{\left(\frac{[\mathrm{O}\textsc{iii}]\lambda
5007}{\mathrm{H}\beta}\right)}>0.3.$ (3)

Alternatively in this redshift range, if H$\beta$ is undetected while [O
iii]$\lambda$5007 is detected a source is accepted as an AGN candidate.
Finally each spectrum is visually inspected to reject objects exhibiting broad
permitted emission lines and star-forming galaxies from the sample.

The selection criteria and visual inspection of each spectrum ensures that the
sample contains the brightest Type 2 AGN with visible [O iii]$\lambda$5007
emission lines, with the authors estimating that 90$\%$ of luminous Type 2 AGN
in the SDSS DR6 database are successfully selected.

We use our QSFit Type 2 AGN recipe to analyse the Reyes et al. (2008) sample
of 887 Type 2 AGN. In a few cases we discarded spectra since the number of
reliable spectral channels (SDSS quality mask = 0) amount to less than 50$\%$
of the total. We neglected 39 spectra due to this. We remove a further 34
spectra which have insufficient ‘good’ spectral channels to successfully
constrain the continuum components of our model. In addition to these
omissions we were unable to locate one spectrum included in the Reyes et al.
(2008) sample, spec-0190-51457-0198, on the SDSS archive servers. We therefore
have 813 sources in our sample appropriate to be analysed with QSFit. Fig. 1
shows the distribution of redshifts for the sources in our sample, which has a
median redshift of z = 0.28.

All spectra are corrected for reddening using E(B-V) values derived using
Schlegel, Finkbeiner and David galactic dust maps (Schlegel et al., 1998) with
a Milky Way extinction curve (O’Donnell, 1994) prior to fitting. We account
for instrumental broadening assuming a Gaussian line spread function and using
the SDSS spectral resolving power R$\sim$2000 to derive
FWHM${}_{instr}\sim$150 kms-1.

Figure 1: Distribution of redshifts for our sample of 813 sources derived from
Reyes et al. (2008) sample of optically selected luminous Type 2 AGN from SDSS
DR6.

##  3 QSFit: Type 2 AGN Fitting Recipe

In this section, we describe the models utilized for the primary spectral
components used in our QSFit Type 2 AGN recipe. The primary difference between
optical Type 1 and Type 2 AGN is the presence of a dusty obscuring medium
between the observer and the AGN central engine. In the optical spectra of AGN
the obscuring medium manifests as a lack of components that physically
originate within a few parsecs of the central engine. Table 1 provides a
summary of the components considered for Type 2 AGN as a comparison to those
used in the default QSFit recipe for Type 1 AGN (Calderone et al., in prep.).
The Type 2 recipe does not include Balmer continuum and pseudo-continuum
modelling or UV and optical iron complex templates. Fig. 2 provides an example
of an SDSS Type 2 AGN spectrum fit with our QSFit Type 2 AGN recipe.

Table 1: Main components included in the QSFit Type 1 AGN (Calderone et al., in prep.) and Type 2 AGN fitting recipes. Model Component | Type 1 | Type 2
---|---|---
AGN Continuum | Single PL | Single PL
Balmer Continuum (+ Pseudo-Continuum) | Yes | -
Host-Galaxy Template | Optional | Yes
UV and Optical Iron Templates | Yes | -
Known Emission Lines | Yes | Yes
Known Emission Line Profiles | Gaussian | Gaussian
Unknown Lines | 10 | 2

###  3.1 AGN Continuum

The majority of the AGN continuum emission emanating from the central
accretion disk is obscured in Type 2 AGN. Many sources, however, still require
the presence of a detectable base continuum that becomes increasingly
subdominant to host-galaxy contributions as the AGN luminosity decreases.

QSFit’s Type 2 AGN recipe employs a single power-law to model the continuum of
the form:

$L_{\lambda}=A\left(\frac{\lambda}{\lambda_{\rm 0}}\right)^{\alpha_{\rm 0}}$
(4)

where $\lambda_{0}$ is a reference wavelength, $A$ is the luminosity density
at $\lambda=\lambda_{0}$ and $\alpha_{\rm 0}$ is the spectral slope. We fix
$\lambda_{0}$ at the median value of the available spectral sample
wavelengths, $A$ is constrained to be positive and $\alpha_{\rm 0}$ is
constrained to be in the range [-5, 5].

###  3.2 Host-Galaxy Template

The obscured nature of Type 2 AGN results in non-negligible host-galaxy
contributions to their optical spectra being commonplace, particularly in the
regime of low luminosity AGN. This factor necessitates effective modelling of
host-galaxy light for the analysis of Type 2 AGN spectra.

QSFit incorporates a library of host-galaxy SEDs, consisting of the SWIRE
templates collated by Polletta et al. (2007) supplemented with twelve BC03
(Bruzual & Charlot, 2003) stellar population synthesis model generated
templates used to model COSMOS galaxies by Ilbert et al. (2009). The SWIRE
library contains 25 SEDs, generated using the GRASIL code (Silva et al.,
1998), ranging from quiescent Elliptical galaxies through to Starbursts and
Type 1 AGN. The supplementing Ilbert et al. (2009) library of 12 BC03
templates consists of starburst templates with ages ranging from 0 to 11 Gyr.
For the purpose of modelling AGN hosts, templates including AGN emission are
disregarded from consideration as QSFit deals with the AGN component itself,
leaving a total of 27 elliptical, spiral and starburst templates from the
parent library.

Despite this wide range of available host-galaxy templates, we have found that
the 5 Gyr elliptical template from the SWIRE library is appropriate and
effective when modelling the continuum emission of the Type 2 AGN in our
sample. Consequently, we adopt this as our default host-galaxy in the
following analysis of Type 2 AGN spectra. The only free parameter in the model
associated to the host-galaxy component is its normalization (luminosity) at
5500Å.

###  3.3 Known Emission Lines

QSFit incorporates a spectral transition database of common permitted,
forbidden and intercombination AGN atomic transitions collected from The
Atomic Line List333https://www.pa.uky.edu/~peter/atomic/. All emission lines
in QSFit are considered using their vacuum wavelengths. Known emission lines
represent a subset of these spectral transitions that are considered in a
given fitting recipe. The known emission lines considered for our Type 2 AGN
recipe and their wavelengths are given in Table 2. Each line considered by a
recipe can be configured as "Broad", "Narrow", "VeryBroad", or a combination
of these (see Calderone et al., in prep. for detailed definitions). Each line
can also be assigned to have a Gaussian, Lorentzian or Voigt line profile. In
this work all emission lines are modelled with a Gaussian line profile unless
explicitly specified as otherwise.

For Type 2 AGN the Narrow line profile is solely utilised and is modified with
respect to the Type 1 AGN recipe to have FWHM constrained in the range [10 -
2,000] km s-1. A reduced lower limit on the FWHM of narrow lines is required
to appropriately fit the intrinsically narrower lines of Type 2 AGN when
compared with Type 1. The lower limit to the FWHM is set by the expected scale
of thermal broadening (i.e. ignoring bulk kinematics of any line), so any
observed line will have a FWHM larger than this. This theoretical limit should
never be met however, as the SDSS spectral resolution of 150 kms-1 limits the
narrowest measurable line FWHM to this value.

A subset of the lines considered are members of emission line doublets (eg. [O
ii]$\lambda$3727). In cases where the individual emission lines of a doublet
cannot be distinguished in a typical SDSS spectrum, the line complex is fit
with a single narrow line component placed at the wavelength of the midpoint
between the two line locations (a velocity offset term is used in the fit to
allow varying this value to best fit the data).

Table 2: List of emission lines considered in the Type 2 AGN QSFit recipe and their rest-frame vacuum and air wavelengths. Line | Vacuum Wavelength (Å) | Air Wavelength (Å)
---|---|---
Mg ii | 2796.35 | 2795.53
[Ne v] | 3426.50 | 3425.88
[O ii] | 3728.48 | 3727.42
[Ne iii] | 3870.16 | 3868.76
H$\gamma$ | 4341.68 | 4340.47
H$\beta$ | 4862.68 | 4861.33
[O iii] | 4960.30 | 4958.91
[O iii]bw | 4960.30 | 4958.91
[O iii] | 5008.24 | 5006.84
[O iii]bw | 5008.24 | 5006.84
[O i] | 6302.05 | 6300.30
[O i] | 6365.54 | 6363.78
[N ii] | 6549.85 | 6548.05
H$\alpha$ | 6564.61 | 6562.82
[N ii] | 6585.28 | 6583.46
[S ii] | 6718.29 | 6716.44
[S ii] | 6732.67 | 6730.81

The [O iii]$\lambda$5007 emission line is among the most ubiquitous and
brightest emission lines observed in AGN and Star-forming Galaxy (SFG) optical
spectra. Due to its prevalence and high luminosity, the measured properties of
the [O iii]$\lambda$5007 line are often significantly affected by the
kinematics of the NLR. Bulk motions produce distortions such as blue wings
when a portion of NLR gas is moving radially towards the observer, which are
often used as tracers for outflows in AGN (eg. Zakamska & Greene, 2014). Our
Type 2 AGN recipe includes an [O iii]$\lambda$5007 asymmetric tail component
to model the line asymmetries of [O iii]$\lambda$5007 lines where it is
required ([O iii]bw in Table 2). This emission line feature is modelled with a
Gaussian narrow line component constrained to have a velocity offset on the
blue (shorter wavelength) side of its parent line as well as FWHM larger than
its parent line to ensure it is used to model asymmetries at the base of the
emission line as intended.

Due to quantum mechanical transition probabilities the [O iii]$\lambda$4959
line profile exhibits an identical form to that of [O iii]$\lambda$5007 with a
third of the luminosity (see Sect. 4.4). We therefore include a blue wing
component for the [O iii]$\lambda$4959\. QSFit allows for two parameters to be
fit using a single free parameter value, reducing the number of free
parameters in the model. In these cases the two parameters are “patched" to
one another. We use the patching feature of QSFit to provide a simultaneous
fit for the [O iii]$\lambda$5007 and [O iii]$\lambda$4959 components where we
constrain the luminosity of the [O iii]$\lambda$4959 blue wing to be one third
times the luminosity of the [O iii]$\lambda$5007 blue wing component and to
share the same FWHM and velocity offsets. This system allows the correct
asymmetric profile component of [O iii]$\lambda$4959 to be modelled even in
spectra where the asymmetry is poorly constrained due to the S/N of the
spectrum.

###  3.4 Unknown Lines

In the final stages of QSFit’s spectral fitting analysis, Gaussian-profile
“unknown” lines are placed at areas of highest residuals with the aim to model
emission lines that are present in the spectrum but have not been included in
the known spectral lines library of the current recipe.

As Type 1 AGN optical spectra contain broader BLR components, some of which
are not seen in the NLR, Type 2 AGN inherently require fewer components to
model. Due to the reduced degrees of freedom it is important that QSFit’s
unknown lines are not relied upon to fill large areas of residuals in Type 2
AGN spectra, which occurs when there are more unknown lines considered than
there are genuine unaccounted-for emission lines in the spectrum. To this end,
in our Type 2 AGN recipe the number of unknown lines is reduced from the
default value of ten to two. This value may need to be adjusted according to
the spectral coverage and redshift of a given spectrum or sample of spectra
and is easily done so through QSFit’s `source.options` dictionary. Using two
unknown lines is found to give qualitatively good fits for SDSS Type 2 AGN
spectra analysed in this work (z $\leq$ 0.83).

We constrain the FWHM of unknown lines to lie in the range [10 - 2,000] kms-1
reducing both the maximum and minimum values from the default constraints in
the range [500 - 1$\times$104] kms-1. This further prevents unknown lines from
being used to fill large areas of residuals, which cause the host-galaxy
template to have an incorrect normalisation in some cases, and forces them
into their intended role of being placed at locations of lines not considered
in the current set of known spectral lines. We do not fix the FWHM of unknown
lines to those of known emission lines because they may be from kinematically
or spatially different components.

Figure 2: Example spectral decomposition of an SDSS Type 2 AGN spectrum (SDSS
J085205.38+024310.9) using QSFit Type 2 AGN fitting routine developed in this
work. The top panel shows the decomposition of the entire spectrum, while the
bottom left and right panels present zoomed-in views of the [O iii]+H$\beta$
and H$\alpha$+[N ii] complex fits, respectively. In all three figures the
solid black line represents the overall model attained by our fitting, the
host-galaxy template is shown in solid green and the power-law AGN continuum
in solid dark orange. The dashed red line presents the overall continuum level
given by the sum of the host-galaxy and AGN continuum, while the solid orange
lines represent the known narrow emission lines considered in the fitting
recipe. The solid blue lines depict the [O iii] blue wing asymmetry components
and the solid purple lines show the unknown lines.

##  4 Baseline Type 2 Recipe Results

In this section we present the results of the baseline fitting recipe
described in Sect. 3. We discuss spectral properties derived from our sample
of 813 luminous Type 2 AGN spectra analysed with our Type 2 AGN QSFit recipe.
Using multiple emission line diagnostics we check the self-consistency and
consistency with the literature of our results. We publish a catalogue of our
luminous Type 2 AGN sample spectral measurements alongside this paper (see
App. A.1 for a description and download instructions).

###  4.1 Line Profiles

Gaussian and Lorentzian emission line profiles are the most widely accepted
for the modelling of AGN emission lines. The literature is undecided on which
profile is most effective to use; some works employ Gaussian profiles (eg.
Sexton et al., 2021; Sarzi et al., 2006; Kuraszkiewicz et al., 2004) and
others Lorentzian profiles, particularly for narrow line Seyfert 1 (NLS1) and
highly accreting AGN (eg. Marziani et al., 2013; Sulentic et al., 2002; Véron-
Cetty et al., 2001). Alternatively, some works opt to use both profiles and
keep the result with the best fit statistic (eg. Dias dos Santos et al., 2022;
Shen et al., 2011; Liu et al., 2010). For the majority of spectral resolutions
and S/N the two line profiles are largely interchangeable. Some works explore
the underlying line profile of AGN emission lines with both Kollatschny &
Zetzl (2013) and Naddaf & Czerny (2021) reporting that broad AGN emission
lines intrinsically tend towards a Lorentzian profile. Naddaf & Czerny (2021)
also highlight the non-triviality of emission line profile generation with the
overall profiles depending on a host of parameters from viewing angle to dust-
to-gas mass ratio. Berton (2019) report that some NLS1 galaxies from the SDSS
have narrow emission lines best modelled using Gaussian profiles while others
with Lorentzian profiles. They show the two samples present different physical
and energetic properties, suggesting that line profiles may evolve with the
AGN over time.

We perform QSFit analysis of our sample using both Gaussian and Lorentzian
line profiles for all emission lines considered in our recipe. Gaussian line
profiles give a median $\chi^{2}_{red}$ value of 1.39$\pm$0.36 across the
sample, while Lorentzian line profiles give a median of 1.45$\pm$0.38. Given
the insignificant change in $\chi^{2}_{red}$ between the two line profiles,
there is no clear evidence to choose one over the other. We therefore opt to
use Gaussian profiles for this work. This is not to say that the underlying
profile is Gaussian, but that this provides the best results for the
instrumental resolution and S/N of low-z SDSS spectra. Indeed, we explore in
Sect. 5 with high S/N emission lines that the underlying profiles are non-
Gaussian and require multiple components to be correctly modelled.

###  4.2 Continuum Slope

The distribution of power-law continua spectral slopes ($\alpha_{\rm 0}$, in
equation 4) for our sample along with representative error bars for different
measured $\alpha_{\rm 0}$ values is shown in Fig. 3. The distribution shows
that in cases where a continuum component is required an approximately even
spread of blue continua ($\alpha_{\rm 0}$ < 0) and red continua ($\alpha_{\rm
0}$ > 0) are utilized. Outliers beyond $\alpha_{\rm 0}$ = $\pm$2 have large
statistical and un-quantified systematic uncertainties with a median 1$\sigma$
statistical uncertainty of 0.3 for these values of $\alpha_{\rm 0}$.
Measurements of $\alpha_{\rm 0}$ within this range have much lower statistical
uncertainties with a median 1$\sigma$ uncertainty of 0.07. This indicates that
the true distribution is likely to lie within the $\alpha_{\rm 0}$ = $\pm$2
range in continuum slope values and is broadened by the associated
uncertainties.

In works analysing the power-law continuum slopes of Type 1 AGN steeper
negative values are found. Calderone et al. (2017) report an average slope of
$\alpha_{\rm 0}$ = -1.7 for Type 1 AGN with z $\sim$ 0.7. The median continuum
slope value of our Type 2 AGN sample is $\alpha_{\rm 0}$ = -0.2$\pm$0.7. The
difference between our median value for Type 2 AGN and that found by Calderone
et al. (2017) for Type 1 AGN may well indicate the effect of reddening and
obscuration on the underlying continuum on Type 2 sources. However, some
caution should be exercised with this interpretation as it is also possible
that the result is in part due to the power-law filling residuals that that
arise from modelling the stellar population with a single host-galaxy
template.

Figure 3: Distribution of power-law continuum spectral slopes ($\alpha_{\rm
0}$) for 743 luminous Type 2 AGN. The red line is drawn at a continuum slope
value of 0, which corresponds to a flat continuum. Grey bars depict
representative $\pm$1$\sigma$ statistical uncertainties.

###  4.3 BPT Diagrams

Named after their pioneers Baldwin, Phillips and Terlevich (Baldwin et al.,
1981), BPT diagrams are a set of emission line diagnostic plots used to
separate AGN (referred to as Seyfert in the diagrams) from pure star forming
galaxies (also referred to as HII galaxies) and LINERs (Low-Ionization Nebula
Emission Regions). These non-Seyfert classes possess similar spectroscopic
properties and are more numerous than AGN. By comparing line flux ratios of
narrow emission lines which have varying degrees of ionization, the parameter
space of the BPT diagrams can be divided into regions that discern the nature
of the ionizing continuum in the object (ie. from OB type stars; star
formation, power-law AGN continua or interstellar medium shocks).

The most prominent of these diagnostic diagrams compare the ratio of [O
iii]$\lambda$5007/H$\beta$ lines with the corresponding ratios of other pairs
of neighbouring lines, such as [N ii]$\lambda$6583/H$\alpha$, [O
i]$\lambda$6300/H$\alpha$ and [S ii]$\lambda$6716$,\lambda$6731/H$\alpha$.
Each of these diagrams is supplemented with a theoretical maximum starburst
line, introduced by Kewley et al. (2001) who used stellar population synthesis
and photoionization models to determine the emission line ratio upper limits
for pure stellar photoionization models. The [N ii]$\lambda$6583/H$\alpha$
diagram makes use of a modification of the Kewley et al. (2001) starburst
line, defined by Kauffmann et al. (2003), which empirically divides pure star-
forming galaxies from AGN-HII composite sources. Kewley et al. (2006) derive
an empirical boundary used to cleanly separate AGN (Seyferts) and LINER
sources in the [O i]$\lambda$6300/H$\alpha$ and [S
ii]$\lambda$6716$\lambda$6731/H$\alpha$ diagrams.

Figure 4: BPT line diagnostic diagrams plotted for QSFit emission line
measurements of Type 2 AGN, for which the four emission lines required for
each diagram are considered in the fit and well constrained. The solid black
curve in all three diagrams shows the theoretical maximum starburst line
dividing AGN from HII regions (star-forming galaxies) (Kewley et al., 2001).
(left) [O iii]$\lambda$5007/ H$\beta$ vs [N ii]$\lambda$6583/H$\alpha$
diagram. The black dashed curve defines the empirical AGN-HII region
demarcation (Kauffmann et al., 2003). (centre) [O iii]$\lambda$5007/H$\beta$
vs [O i]$\lambda$6300/H$\alpha$ diagram. The dashed black line represents the
empirical separation between Seyfert (AGN) and LINER driven sources (Kewley et
al., 2006). (right) [O iii]$\lambda$5007/H$\beta$ vs [S
ii]$\lambda\lambda$6716,6731/H$\alpha$ diagram. The dashed black line holds
the same meaning as the center plot.

Narrow emission line ratios as measured in our analysis are plotted on BPT
diagrams as a self-consistency check of the measurements. The three BPT
diagrams discussed above are plotted in Fig. 4 for the sources in our analysed
sample where all four emission lines needed for each diagram are available in
the spectrum. As expected from the Reyes et al. (2008) [O iii]$\lambda$5007
line luminosity selection criteria, all the sources exhibit large values of [O
iii]$\lambda$5007/H$\beta$ which to first order traces ionization parameter in
the Seyfert/LINER branch. This places them in the top portion of each diagram.
Every source analysed with QSFit falls into the AGN region of the [N
ii]$\lambda$6583/H$\alpha$ diagram (fig. 4a). This is the expected result as
Reyes et al. (2008) makes use of emission line ratio cuts based on the Kewley
et al. (2001) maximum starburst line in [N ii]$\lambda$6583/H$\alpha$ space
for their sample selection. Thus, emission line measurements derived with our
QSFit Type 2 AGN recipe are compatible with expectations.

Sources that stray from the central bulk of points in the [N
ii]$\lambda$6583/H$\alpha$ diagram consist of spectra that exhibit strong
asymmetries in the [O iii]+H$\beta$ complex and spectra with double peaked
emission lines, for which additional components are required to model in both
cases. Figure 5 presents an example of such an [O iii]+H$\beta$ complex.
Double peaked Type 2 AGN spectra are treated in section 6.

Figure 5: Example case (SDSS J084314.55+285059.9) where a poor fit is achieved
using our Type 2 AGN QSFit recipe due to a heavily asymmetric [O iii] complex.
Component colour scheme identical to Fig. 2.

Both the [O i]$\lambda$6300/H$\alpha$ (Fig. 4 middle panel) and [S
ii]$\lambda$6716$\lambda$6731/H$\alpha$ (Fig. 4 right panel) diagnostic
diagrams have the vast majority of Reyes et al. (2008) sources lie in the AGN
portion of their plots. The former of these plots has three sources and the
latter ten sources that stray into the HII galaxy or LINER region of the
diagrams. Visual inspection of these non-AGN classified sources shows that the
fits are acceptable and the sources genuinely lie in these portions of the
diagram.

###  4.4 [O iii]$\lambda$5007: [O iii]$\lambda$4959 Flux Ratio

In low density NLR-like environments in which collisional de-excitation is
negligible, the relative number of [O iii]$\lambda$5007 and [O
iii]$\lambda$4959 photons is governed by the ratio of the probabilities of the
quantum mechanical transitions that produce them. Hence, the ratio of the
fluxes in the [O iii]$\lambda$5007 to [O iii]$\lambda$4959 emission lines are
fixed at a 3:1 ratio (Osterbrock & Ferland, 2006). Although the asymmetric
blue wing components of these lines are fixed at a 3:1 luminosity ratio in our
recipe, we do not constrain the core components of the [O iii] emission lines
to conform to a fixed ratio in our analysis. The fixed nature of this [O iii]
emission line ratio therefore provides a self-consistency check for QSFit, as
the observed flux ratio inherent to the spectra should be recovered by the
core components in our fitting.

Fig. 6 gives a histogram of the ratio of [O iii]$\lambda$5007 to [O
iii]$\lambda$4959 emission line luminosities (sum of luminosity in core and
blue wing components) as measured by QSFit for the 767 sources in our sample
for which the two lines available. Across the sample, we measure a ratio of
3.1$\pm$0.1. This measurement is slightly larger, although compatible, with
the value of 3 used in Reyes et al. (2008) and found by Liu et al. (2010),
while smaller than those reported by Francis et al. (1991) and Vanden Berk et
al. (2001) (3.66 and 3.63, respectively). In the latter cases, however, the [O
iii] ratio has been estimated on a composite quasar spectrum of a Type 1 AGN,
while here we are providing the average of ratios as measured in individual
Type 2 AGN spectra.

Figure 6: Distribution of [O iii]$\lambda$5007 /[O iii]$\lambda$4959 line flux
ratios for QSFit measurements of Type 2 AGN for which both lines are
considered in the fit and are well constrained. The red dashed line is drawn
at a flux ratio of 3:1, the value predicted by quantum mechanical transition
probabilities (Osterbrock & Ferland, 2006).

The Type 2 spectra in our analysis which deviate from the modal value observed
in Fig. 6 are exclusively comprised of low S/N spectra. Many of these outliers
have masked spectral channels in the [O iii] complex region or features not
accounted for by our model, such as double peaked emission lines treated in
Sect. 6.

###  4.5 Balmer Decrement

Hydrogen Balmer lines are permitted Hydrogen recombination transitions from
higher orders to the $n=2$ state and are among the most prominent lines
observed in AGN spectra. The brightest of the Balmer lines in low-z AGN are
typically H$\alpha$ and H$\beta$, produced from electrons originating in the
$n=3$ and $n=4$ state, respectively. The Balmer decrement ratio
H$\alpha$/H$\beta$ exhibits a constant value over all sources with similar
line emitting gas conditions. Using optically thick recombination, an
intrinsic H$\alpha$/H$\beta$ value of 2.87 is predicted for HII regions
photoionized by a hot star, while a value of 3.1 is predicted for AGN NLRs
(Osterbrock & Ferland, 2006). The value of H$\alpha$/H$\beta$ is elevated for
NLRs of AGN due to H$\alpha$ emission being enhanced by collisional excitation
from higher density gas and the creation of a partly ionized transition region
by the AGN ionizing continuum, which is much harder than those produced by
stars (Gaskell & Ferland, 1984; Halpern & Steiner, 1983).

In Fig. 7 we show the H$\alpha$/H$\beta$ Balmer decrement measured for the 456
sources in our sample where both emission lines are available in the spectrum.
The dashed red line represents the theoretical optically thick recombination
value of the H$\alpha$/H$\beta$ decrement for HII regions, while the dashed
blue line represents the same for AGN NLRs. The median value of
H$\alpha$/H$\beta$ in our sample is 4.5$\pm$0.8 (solid cyan line in Fig. 7).
The discrepancy in expected theoretical and measured values of the Balmer
decrement is postulated to be due to intrinsic dust extinction from obscuring
dust at the redshift of the AGN, which is unaccounted for in our analysis.
Line of sight dust extinction will absorb, and therefore diminish emission
preferentially at shorter wavelengths. H$\alpha$ and H$\beta$ are separated by
a relatively large wavelength span, with H$\beta$ observed at a shorter rest-
frame wavelength of 4863Å compared to H$\alpha$ at 6564Å. Therefore intrinsic
reddening by dust at the redshift of a source will act to reduce the flux
observed from the H$\beta$ emission line, while having a much weaker effect on
the flux from the H$\alpha$ emission line. The effect of this is to skew the
H$\alpha$/H$\beta$ Balmer decrement to a higher value than would be measured
if intrinsic dust reddening was accounted for using a dust reddening curve or
not present. Through comparison of observed and theoretically predicted
values, the Balmer decrement is often utilized as a means to measure the
intrinsic obscuration towards a line emitting region (Gaskell, 2017; Domínguez
et al., 2013). Adopting this methodology implies an average NLR optical
reddening in our sample of $A_{V}\approx$ 1 mag.

Figure 7: Distribution of Balmer decrement values (H$\alpha$/H$\beta$ emission
line flux ratio) for 456 sources in which both lines are available in the
spectrum. The solid cyan line denotes the median value measured in this work.
Theoretically derived Balmer decrement values for gas photoionized by a hot
star (HII region) and gas photoionized by an AGN continuum are shown with
dashed red and blue lines, respectively (Osterbrock & Ferland, 2006; Halpern &
Steiner, 1983). Narrow line Balmer decrements derived by other works are shown
with dashed lines; Lu et al. (2019) (green), Jin et al. (2012) (orange) and
Puchnarewicz et al. (1997) (purple). Figure 8: Measured Balmer decrement
values for our sample of luminous Type 2 AGN as a function of median spectrum
S/N. The solid cyan line represents our measured median Balmer decrement value
of 4.5 for our sample of luminous Type 2 AGN spectra. Grey error bars
corresponding to the $\pm$1$\sigma$ statistical uncertainties of our
measurements are visualised.

The S/N of each spectrum in our sample is estimated by dividing the median
flux value of the spectrum by the median uncertainty. This metric provides an
estimate of the continuum S/N for each spectrum as the majority of spectral
pixels consist of continuum emission. Fig. 8 presents our Balmer decrement
measurements as a function of median S/N with their associated statistical
uncertainties visualised. The solid cyan line depicts the median Balmer
decrement value of our sample. In general, Balmer decrement values above five
have significantly larger statistical uncertainties due to the low S/N nature
of the spectra for which they are measured. The actual uncertainties are
larger than visualised as the systematic uncertainties of the fit remain un-
quantified. Sources with a measured Balmer decrement value above seven are
likely to be non-physical and highlight the limitations of the software used
in the low S/N spectra. We therefore recommend caution in the interpretation
of the high Balmer decrement value tail in the histogram of Fig. 7. The
clustering of low uncertainty measurements around our sample median suggests
that the overall sample measurement is robust.

The skewing of the H$\alpha$/H$\beta$ Balmer decrement to higher values in our
sample is not unexpected as Type 2 AGN, by definition, have a large amount of
dust present in their vicinity which obscures the central structure of the
AGN. The large Balmer decrement values observed across the sample imply that
dust in optically selected Type 2 AGN extends beyond the obscuring torus
structure and into the NLR of the AGN. The presence of extended dust in the
NLR may well be contributed to by polar dust components in the ionization cone
of the AGN. These diffuse, elongated structures are interpreted as outflowing
dusty winds, driven by radiation pressure (Ramos Almeida & Ricci, 2017). In
agreement with our result, Lu et al. (2019) report an average NLR Balmer
decrement of a sample of 554 optically selected broad line AGN to be
4.37$\pm$1.26 (dashed green line in Fig. 7). Jin et al. (2012) derive Balmer
decrements in the range 1 - 12 with a mean value of 4.85$\pm$1.81 for narrow
emission line components in a sample of X-ray selected Type 1 AGN and suggest
that variations in electron density or dust abundance in the NLR is the cause
of their higher than predicted value (dashed orange line in Fig. 7).
Similarly, Puchnarewicz et al. (1997) find a mean Balmer decrement of 5$\pm$1
for a sample of 160 AGN from RIXOS, consisting of Type 1 and Type 2 X-ray
selected AGN and attribute this result to dust present in their sources
(dashed purple line in Fig. 7). Some studies utilize the elevated Balmer
decrement observed in Type 2 AGN as a means to classify AGN as Type 2 (eg.
Lehmann et al., 2001).

###  4.6 [O iii]$\lambda$5007 Line Luminosity Measurements

Reyes et al. (2008) catalogue of optically selected Type 2 quasars provides
measurements of [O iii]$\lambda$5007 line luminosity. The measurements are
provided with two separate methods; Gaussian, where the continuum over the
wavelength range 4860 - 5060Å is modelled with a linear fit and the [O
iii]$\lambda$5007 emission line is modelled with a single Gaussian component,
and semi-parametric where the [O iii]$\lambda$5007 line detected flux density
is integrated and the linear continuum contribution is subtracted. Reyes et
al. (2008) find that their semi-parametric fits can often provide highly non-
Gaussian solutions due to asymmetries in the line profile caused by radial
outflows (eg. blue wings) and result in systematically higher line
luminosities by $\sim$5$\%$.

Fig. 9 depicts the ratio of $L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ as
measured by QSFit to that measured in Reyes et al. (2008) with a semi-
parametric fitting as a function of redshift. We find no significant trends or
correlations among the quantities beyond the redshift induced correlation that
arises when comparing pure measured values against each other. There exists a
clear scatter between our $L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$
measurements and those measured with a semi-parametric fit in Reyes et al.
(2008). This scatter is expected from measurements made independently with two
differing methods. The same scatter is observed when comparing our
$L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ measurements to the Gaussian
fitting method.

Figure 9: Ratio of [O iii]$\lambda$5007 emission line luminosity measurements
made by QSFit to those provided by Reyes et al. (2008) semi-parametric fits
for the same sample of Type 2 AGN vs redshift. The red dashed line shows the
1:1 ratio. A median systematic offset of 1.16 is explained by the differing
emission line and continuum modelling employed by the two methods.

Alongside the intrinsic scatter between the measurements there is a systematic
offset between QSFit and Reyes et al. (2008) semi-parametric measurements,
with QSFit providing larger $L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ values
by a median ratio of 1.16. When compared to Reyes et al. (2008)’s Gaussian
$L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ measurements QSFit again provides
systematically larger measurements, with an increased median ratio of 1.22,
consistent with the observation in Reyes et al. (2008) that their semi-
parametric method provides $L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$
measurements that are systematically higher than their Gaussian method by
$\sim$5$\%$.

A factor that is likely to contribute to the systematic offset observed
between QSFit and Reyes et al. (2008) $L_{[\mathrm{O}\textsc{iii}]\lambda
5007}$ measurements is the inclusion of an asymmetric blue wing component in
our analysis of the line. The [O iii]$\lambda$5007 blue wing component in
QSFit is a second Gaussian component constrained to be placed at a shorter
wavelength and have a larger FWHM than the main [O iii]$\lambda$5007 emission
line to model the commonly observed asymmetric blue excess in the [O
iii]$\lambda$5007 line, which is attributed to contributions to the line
emission from radially outflowing gas components in the NLR (see section 3.3).
The blue wing component accounts for more than 10$\%$ of the total [O
iii]$\lambda$5007 line flux in 707 of our spectra (88$\%$ of our sample). The
addition of the blue wing component in our [O iii]$\lambda$5007 line modelling
allows for a better fit to the profile of the line than a single Gaussian
component can offer in most cases, ensuring that the line flux in the tails of
the line profile are measured.

To test if the better fit achieved with multiple [O iii]$\lambda$5007
components is generating the systematic offset between QSFit and Reyes et al.
(2008) $L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ measurements, we repeat our
QSFit analysis of the sample with a modified procedure where the [O
iii]$\lambda$5007 emission line is modelled with a single Gaussian component,
mirroring the Gaussian method used in Reyes et al. (2008). When these
constraints are applied, the systematic offset between QSFit and Reyes et al.
(2008) $L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ measurements is reduced to a
ratio of 1.03 when compared to Reyes et al. (2008) semi-parametric method and
1.07 when compared to their Gaussian method. These results suggest that the
majority of the systematic offset between QSFit and Reyes et al. (2008)
$L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ measurements can be attributed to
the inclusion of a blue wing component to the modelling of the [O
iii]$\lambda$5007 emission line with QSFit, which allows more line flux to be
measured from the wings of the line.

Despite accounting for the [O iii]$\lambda$5007 blue wing component, there is
still a smaller systematic offset between the
$L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ measurements of QSFit and Reyes et
al. (2008). In our analysis we model the entire continuum of each spectrum
utilizing a single power-law for the AGN continuum contribution and a 5 Gyr
elliptical host-galaxy template (from SWIRE template library; Polletta et al.,
2007). These components are then summed together to generate the full
continuum. In contrast, Reyes et al. (2008) model the continuum only in the
wavelength range 4860 - 5060Å with a linear fit. We confirmed that the
remaining offset in measurements is associated with the differing continuum
modelling methods used in Reyes et al. (2008) and our work.

Figure 10: Example of spectral fits of the [O iii]+H$\beta$ complex in
outliers in our comparison between QSFit and Reyes et al. (2008) (R08)
measurements of [O iii]$\lambda$5007 emission line luminosity (see Fig 9),
despite the fit being perfectly acceptable. Left: SDSS J005813.75-001654.1,
low S/N case (QSFit/R08 ratio = 0.35). Right: SDSS J151711.48+033100.1, high
S/N case (QSFit/R08 ratio = 0.49). Component colour scheme identical to Fig.
2.

Outliers from the main locus of points in Fig 9 fall into 3 categories; (1)
low S/N spectra where we still find our modelling acceptable for the data
presented, (2) genuine acceptable fits to good quality data and (3) sources
with complex [O iii]$\lambda$5007 profiles that require additional components
to model. For the first and second cases the different fitting methods are
responsible for the discrepancies. Fig. 10 gives examples of a low S/N case
(left) and a case where our fit is good despite the disagreement in values
(right). We expect no significant differences in the spectra used between the
analyses as the SDSS spectra were downloaded using the same PLATE-MJD-FIBER
values. For the latter case, we present examples of these spectra in Fig. 5.

We derive the [O iii]$\lambda$5007 luminosity function (LF) following the
1/$V_{max}$ method (Schmidt, 1968) employed in section 3 of Reyes et al.
(2008) using our QSFit measurements of $L_{[\mathrm{O}\textsc{iii}]\lambda
5007}$. We find that our derivation of the LF is compatible within errors to
that derived using Reyes et al. (2008) $L_{[\mathrm{O}\textsc{iii}]\lambda
5007}$ measurements. Therefore the systematic offset between the two
measurement methods does not have an adverse affect on the calculated space
density of luminous optical Type 2 AGN.

##  5 SN Ratio

To investigate the effect of signal-to-noise ratio (S/N) on the measurements
attained in our analysis with QSFit, the S/N of each spectrum in the Reyes et
al. (2008) sample is estimated by dividing the median flux value of the
spectrum by the median uncertainty. Using this S/N proxy it is found that the
S/N of the SDSS spectra is a strong function of redshift, with the highest S/N
spectra at low redshift and the S/N falling non-linearly as redshift increases
as visualised in Fig. 11. The trend of falling S/N with redshift is an
expected observation as all the spectra are generated with the same
spectrograph and 3" aperture. Photon flux drops off approximately
quadratically in the redshift range considered in this work, naturally
resulting in the signal flux dropping off rapidly as redshift increases, while
the detector noise remains approximately constant.

Figure 11: Median S/N value (median flux value / median uncertainty) of each
spectrum in Reyes et al. (2008) sample of Type 2 AGN as a function of source
redshift.

In order to estimate the impact of the S/N ratio on our analysis we divide our
sample of luminous Type 2 AGN into 4 S/N groups; those with S/N $<$ 4 (298
sources), 4 $\leq$ S/N $<$ 15 (367 sources), 15 $\leq$ S/N $<$ 25 (126
sources) and those with S/N $\geq$ 25 (22 sources). Fig. 12 presents a
histogram of reduced $\chi^{2}$ fit statistics for global fits of the sample
spectra in different S/N classes. We find that higher S/N spectra result in
statistically worse fits, having a higher reduced $\chi^{2}$ than those with a
lower S/N. This observation implies that spectra with a higher S/N require a
more complex model to achieve a satisfactory fit, as weaker, often neglected
emission lines are more prominent features in the data and strong emission
line profiles are observed with increased fidelity, requiring multiple
components to properly constrain the peaks of the lines. In higher S/N cases
the above features become statistically more prominent since their spectra
exhibit lower uncertainties, contributing to a higher reduced $\chi^{2}$ and
highlighting the limitations of the model. On the contrary, for lower S/N
spectra more prominent emission lines have generally lower fluxes as they
originate from higher redshift sources and therefore have higher relative
uncertainties, so are weighted less heavily in the calculation of the reduced
$\chi^{2}$.

Figure 12: Distribution of reduced $\chi^{2}$ for global QSFit spectral fits
for our sample of 813 Type 2 AGN presented in Reyes et al. (2008), divided
into signal-to-noise ratio (S/N) classes. Black; sources with S/N $<$ 4\.
Blue; sources with 4 $\geq$ S/N $<$ 15\. Green; sources with 15 $\geq$ S/N $<$
25\. Red; sources with S/N $\geq$ 25.

###  5.1 High S/N Recipe

Motivated by statistically poor fits achieved with our QSFit Type 2 AGN recipe
for the highest S/N spectra, we develop and present a specialised recipe for
high S/N (HSNR) spectra.

Reduced $\chi^{2}$ is a statistic intended to assess the fit of a global model
to the data it attempts to describe. Therefore, to assess the performance of a
model in specific portions of our spectral fits we adopt the proxy metric
$\chi^{2}_{portion}/N_{S}$, where $\chi^{2}_{portion}$ is the total $\chi^{2}$
statistic of the samples in the portion of the fit being analysed and $N_{S}$
represents the number of spectral channels covered by the examined portion.

Via analysis of $\chi^{2}_{portion}/N_{S}$ of different components of our
spectral fits we find that in all cases, particularly so for HSNR spectra, the
most prominent lines in the spectrum are statistically the worst fit
components, suggesting that in the HSNR case a single Gaussian component is
insufficient to constrain the profile of prominent emission lines. The focus
of this specialised HSNR recipe, then, is to more flexibly model the most
prominent lines encountered in Type 2 AGN spectra.

The [O iii]$\lambda$4959, [O iii]$\lambda$5007 and H$\alpha$ emission lines
are identified as the most frequently observed prominent lines in our sample,
which prove to be insufficiently fit with a single Gaussian component in HSNR
spectra. To create a more flexible line profile we try modifying our Type 2
AGN recipe to fit these most prominent lines using; (1) two Gaussian
components, (2) a single Lorentzian component, (3) two Lorentzian components
and, for completeness, (4) a single Voigt component. In all cases the number
of unknown lines considered in the fit is increased from the two used in our
standard Type 2 recipe to six. This modification is made because for HSNR
spectra the increased protrusion of weaker emission lines above the noise
level means that unknown lines are more likely to be used as intended, at the
site of an emission line not considered in our recipe, rather than being used
to fill broad residuals.

Figure 13: Cumulative histogram of $\chi^{2}$ divided by the number of samples
for QSFit spectral fitting results around the H$\alpha$ and H$\beta$ emission
line complexes for five emission line profile variations for sources with
median S/N $\geq$ 15\. Emission line profiles of [O iii]$\lambda$4959, [O
iii]$\lambda$5007 and H$\alpha$ are varied in each case to be modelled by;
(black) single Gaussian component, (red) double Gaussian, (blue) single
Lorentzian component, (green) double Lorentzian, (purple) single Voigt
component.

We fit the spectra in our sample with S/N $\geq$ 15 (148 sources) with each
variation of our prominent line recipe modifications discussed above. Fig. 13
presents the cumulative $\chi^{2}_{portion}/N_{S}$ distributions around the
H$\beta$ and H$\alpha$ complexes for each of our recipe modifications. In each
case the $\chi^{2}_{portion}/N_{S}$ values presented are calculated for $\pm$
3 FWHM around the center of the emission lines [O iii]$\lambda$4959, [O
iii]$\lambda$5007 and H$\alpha$ in each spectrum.

Fig. 13 shows that fitting [O iii]$\lambda$4959, [O iii]$\lambda$5007 and
H$\alpha$ with a single Lorentzian line profile provides statistically worse
fits than fitting these lines with a single Gaussian component in HSNR cases,
mirroring our findings for all cases (see Sect. 4.1). We also see that
modelling [O iii]$\lambda$4959, [O iii]$\lambda$5007 and H$\alpha$ with two
Gaussian components provides a significantly improved fit in the most
prominent lines of HSNR spectra, with two Lorentzian components also showing
an improved fit compared to a single Gaussian component, yet not as successful
over the whole sample as modelling with two Gaussians. Fitting prominent lines
with a single Voigt profile is found to give marginally worse performance
compared to the fits using two Lorentzian components. Table 3 provides the
$\chi^{2}_{portion}/N_{S}$ statistic values for global model fits and
prominent line fits for the 148 spectra with S/N $\geq$ 15 analysed. The
values in Table 3 quantitatively back up our findings discussed above, showing
that modelling [O iii]$\lambda$4959, [O iii]$\lambda$5007 and H$\alpha$ with
two Gaussian components provides the statistically best fits globally and
around the most prominent line complexes of all the modelling variations
considered in this section. These results highlight the necessity to model the
most prominent emission lines in HSNR spectra with multiple components.

Table 3: Performance of different line profile combinations to model [O iii]$\lambda$4959, [O iii]$\lambda$5007 and H$\alpha$ emission lines in high S/N sources (median S/N $\geq$ 15). We use $\chi^{2}$ or the total $\chi^{2}$ of a portion of the fit ($\chi^{2}_{portion}$) divided by the number of samples the considered range covers ($N_{S}$) as a proxy metric for the reduced $\chi^{2}$. Prominent line $\chi^{2}_{portion}/N_{S}$ refers to our proxy metric as calculated for a portion of the fit $\pm$3 line FWHM around the emission line centroids of [O iii]$\lambda$4959, [O iii]$\lambda$5007 and H$\alpha$ in each spectrum. Recipe | Median Global Fit $\chi^{2}/N_{S}$ | Median Prominent Line $\chi^{2}_{portion}/N_{S}$
---|---|---
Default Type 2 | 2.55$\pm$0.82 | 6.46$\pm$3.76
Double Gaussian | 2.17$\pm$0.58 | 3.60$\pm$1.89
Single Lorentzian | 2.95$\pm$1.04 | 12.90$\pm$7.96
Double Lorentzian | 3.03$\pm$1.05 | 7.43$\pm$3.99
Single Voigt | 2.46$\pm$0.78 | 6.87$\pm$3.86

##  6 Double Peaked Sources

AGN spectra hosting double peaked narrow emission lines are rare, with
$\sim$1$\%$ of low-z Type 2 AGN spectra exhibiting such features in optically
selected samples (Shen et al., 2011). The double-peaked emission line features
can be generated by kinematically disturbed NLRs induced by bi-conical
outflows and disk-like rotation of the NLR or alternatively by a merging pair
of AGNs where there is relative motion between the two NLRs. The latter of
these scenarios is of central interest in the context of studying galaxy
mergers and AGN fuelling, however the lack of unambigiously detected objects
of this kind ($\leq$0.1$\%$ of SDSS quasars) is in tension with observed and
simulation-based galaxy merger rates. Literature in the field is conflicted on
the favoured origin for the double peaked narrow emission line phenomenon in
AGN; some works favour disturbed NLR situations (eg. Wang et al., 2019; Shen
et al., 2011) while other authors favour AGN binaries (eg. Wang et al., 2009)
and some works stress ambiguity with no clear evidence for either scenario
(eg. Smith et al., 2010; Liu et al., 2010).

Throughout the testing of our Type 2 AGN fitting procedure a significant
portion of the outliers in the self-consistency checks presented in Sect. 4
have been from spectra that result in a poor fit due to the presence of double
peaked narrow emission lines. These features are not accounted for with our
default QSFit recipe. Motivated by the interesting physics found in such
sources and the lack of a publicly available, generalised fitting routine for
double peaked sources we present a specialised QSFit recipe for fitting Type 2
AGN spectra that host double peaked emission lines.

Liu et al. (2010) presented a sample of 167 Type 2 AGN with double peaked [O
iii]$\lambda$4959 and [O iii]$\lambda$5007 lines selected from SDSS DR7. The
sample is derived from a parent MPA-JHU SDSS DR7 emission line galaxy sample
with z $<$ 0.7, selecting candidates based on [O iii] emission line equivalent
width, BPT emission line ratio cuts and a S/N constraint of median S/N $>$ 5
pixel-1. The emission line galaxy sample is then supplemented with $\sim$400
Type 2 AGN from the Reyes et al. (2008) sample, creating a total parent sample
of 14,756 spectra. Each spectrum has then been visually inspected to identify
the 167 objects with unambiguously detected double peaked [O iii] lines,
requiring two components to fit.

We matched the Liu et al. (2010) double peaked source catalogue of 167 double
peaked emission line objects to the Reyes et al. (2008) Type 2 AGN sample
analysed in this work. We found an intersection of 51 objects. This
intersection constitutes 6.7$\%$ of our Type 2 AGN sample, which is a
significantly higher fraction than expected from the prevalence of double
peaked sources in the overall SDSS. This discrepancy may suggest that the
double peaked emission line phenomenon is more common in the high luminosity
Type 2 AGN ($L_{bol}\gtrsim$ 1044 ergs-1) examined in this work. In the case
of the bi-conical outflow origin of double peaked emission lines this is
consistent as higher luminosity AGN distribute more energy into their
surroundings, producing more powerful radiatively driven outflows at a greater
rate than their lower luminosity counterparts. Six of these spectra have a
significant fraction ($>50\%$) of their spectral channel flagged as possibly
affected by issues (see Section 2), hence we neglected them. We therefore have
45 double peaked Type 2 AGN spectra which are adequate for fitting with QSFit.
This sample is henceforth used as our sample of double peaked Type 2 AGN
sources.

###  6.1 Double Peaked Type 2 AGN Recipe

Our double peaked Type 2 AGN recipe aims to provide a general routine to
produce acceptable fits to the majority of sources in our sample, allowing the
characteristics of the sample to be quickly examined.

We model the [O ii]$\lambda$3727 doublet, H$\beta$, [O iii]$\lambda$4959, [O
iii]$\lambda$5007, H$\alpha$ and [N ii]$\lambda$6583 emission lines using two
narrow line Gaussian components. These are the highest luminosity lines
apparent in our sample of double peaked Type 2 AGN optical spectra for which
the red and blue components can be de-blended. Narrow lines used to model red
and blue peaks in double peaked emission lines have FWHM constrained to the
range [100 - 500] km s-1. This constraint ensures that the components model
the peaks of the line profile as intended, rather than one Gaussian dominating
the whole structure and the second being used to account for asymmetries. In
each case the second narrow component which is newly added to the QSFit recipe
has velocity offset constrained to be greater than its counterpart, placing it
on the shorter wavelength (blue) side.

An additional ‘core’ narrow line component is utilised in the modelling of [O
iii]$\lambda$4959 and [O iii]$\lambda$5007 double peaked emission lines. The
core component is constrained to have FWHM in the range [100 - 1000] kms-1.
This component accounts for asymmetries in the base of the luminous [O iii]
lines, allowing the red and blue narrow line components to model the double
peaked features as intended, rather than filling the base of the line which
contributes more strongly to the overall $\chi^{2}$ statistic of the fit.

During fitting, we patch the velocity offset and FWHM of each separate
component (red peak, blue peak and core, for [O iii] lines) of [O
ii]$\lambda$3727, [O iii]$\lambda$4959 and [N ii]$\lambda$6583 to those of [O
iii]$\lambda$5007\. The velocity offset and FWHM parameters of H$\alpha$ are
also patched to those of H$\beta$. From a physical standpoint, the red, blue
and core components of each double peaked forbidden or permitted transition is
emitted from the same gas under identical dynamical conditions, meaning that a
simultaneous fit is achievable for each of these parameters. Applying the same
velocity offsets and FWHM to red and blue double peaked components is
particularly important for H$\alpha$ and [N ii]$\lambda$6583, which are often
blended together in the H$\alpha$ complex for double peaked sources. Patching
their velocity offsets from the systematic velocity and FWHM to lines outside
of the complex allows their decomposition to be estimated where they would
otherwise become degenerate parameters.

Fig. 14 gives an example spectral fit of the H$\beta$ and H$\alpha$ complexes
of a double peaked source using our QSFitdouble peaked Type 2 AGN recipe.

Figure 14: Example spectral decomposition of the [O iii]+H$\beta$ (left) and
H$\alpha$+[N ii] (right) complexes in a double peaked Type 2 AGN SDSS spectrum
(SDSS J080218.64+304622.7) using our specialised double peaked Type 2 AGN
QSFit fitting procedure. The velocity separation of the red and blue peaks in
[O iii]$\lambda$5007 is 346 kms-1. The solid black line represents the overall
fit model, the solid red and blue lines show the red and blue components of
double peaked lines, while the magenta lines depict the core components of
these lines. The host-galaxy template is shown in solid green and the power-
law AGN continuum in solid dark orange. The dashed orange line presents the
overall continuum level given by the sum of the host-galaxy and AGN continuum,
while the solid orange lines represent the single component known narrow
emission lines considered in this fitting recipe.

###  6.2 Double Peaked Results

Figure 15: Histogram showing the distribution of separation velocities between
the red and blue peaks of the [O iii]$\lambda$5007 line in double peaked Type
2 AGN spectra analysed with QSFit in this work.

Fig. 15 presents a histogram of the separations between red and blue peaks of
[O iii]$\lambda$5007 in our sample of double peaked Type 2 AGN spectra. We
find a median separation of 390$\pm$60 kms-1. The shape of the distribution
shows that sources with a peak separation larger than the median become
progressively more rare to observe as the separation becomes larger. This
large value decline could be due to the scarcity of bi-conical outflows with
high enough velocities to produce this separation observed at orientation
angles for which the double-peaked lines are apparent in the data. We also
note a sharp decline in the number of sources observed as the separation
decreases from the median. The small separation decline is likely explained by
the visual sample selection method employed in Liu et al. (2010), which is
biased against smaller peak separations due to the lines become blended.
Indeed, no separation is observed for values lower than 150 kms-1 which is the
instrumental resolution FWHM of SDSS spectra; double peaked lines cannot
possibly be de-blended with separations lower than this value. Fig. 16 shows
examples of the [O iii] complex fits of double peaked spectra with small (278
kms-1), median (364 kms-1) and large (623 kms-1) [O iii]$\lambda$5007 peak
separations.

Figure 16: Three example QSFit spectral decompositions of double peaked Type 2
AGN SDSS spectra with varying red and blue component separations ($\Delta$v).
(Top) SDSS J095005.82+481338.5, $\Delta$v = 278 kms-1. (Center) SDSS
J153944.12+343503.9, $\Delta$v = 364 kms-1. (Bottom) SDSS J122709.83+124854.5,
$\Delta$v = 623 kms-1. Component colour scheme identical to Fig. 14.  Figure
17: Histogram showing the distribution of luminosity ratios (Lblue/Lred)
between the blue and red peaks of the [O iii]$\lambda$4959, [O
iii]$\lambda$5007 and H$\alpha$ emission lines (shown in red, blue and green,
respectively) in double peaked Type 2 AGN spectra analysed with QSFit in this
work. The black dashed line shows the 1:1 ratio for which the red and blue
peaks have equal luminosity.

Fig. 17 depicts the luminosity ratio between blue and red components
(Lblue/Lred) of double peaked [O iii]$\lambda$4959 (red), [O iii]$\lambda$5007
(blue) and H$\alpha$ (green) emission lines. Median luminosity ratios of
1.1$\pm$0.6, 1.0$\pm$0.5 and 0.8$\pm$0.4 are observed for [O
iii]$\lambda$4959, [O iii]$\lambda$5007 and H$\alpha$ respectively. All values
are consistent with unity within uncertainty across the sample, showing that
there is no preference for the red or blue peaks to be systematically more
luminous in double peaked Type 2 AGN. The similarity in distribution across
all three lines suggests that the luminosity ratio for forbidden and permitted
lines are consistent in double peaked sources.

####  6.2.1 Emission Line Origin

The measured velocity offsets of 200 - 600 kms-1 are compatible with both
galactic winds driven by AGN feedback and winds driven by stellar processes
(see Veilleux et al., 2005, for a review). Our median value of 390$\pm$60
kms-1 is a relatively low velocity for an AGN driven outflow. This is expected
from the fact we are examining Type 2 AGN which are generally less luminous
than their Type 1 counterparts. Indeed, using the
$L_{[\mathrm{O}\textsc{iii}]\lambda 5007}$ bolometric correction of Lamastra
et al. (2009) we find a median bolometric luminosity of our main sample to be
$L_{bol}\sim$1045 ergs-1. Only 2.6$\%$ of our sources have $L_{bol}\geq$ 1046
ergs-1, holding the potential to drive the strongest outflows.

Figure 18: [O iii]$\lambda$5007/H$\beta$ vs [N ii]$\lambda$6583/H$\alpha$ BPT
diagram. Double peaked Type 2 AGN red components are plotted with red diamonds
and blue components are represented by blue triangles for the 23 sources for
which QSFit measurements of all 8 lines are available. Green dashed lines
connect the red and blue component positions for each individual Type 2 AGN
spectrum. The BPT positions of our main sample of Type 2 AGN spectra are
plotted in grey. The solid curve depicts the theoretical maximum starburst
line dividing AGN from HII regions (star-forming galaxies) derived by Kewley
et al. (2001), the dashed curve defines the empirical AGN-HII region
demarcation introduced by Kauffmann et al. (2003).

We plot the red and blue double peaked components for which the [O
iii]$\lambda$5007 and H$\alpha$ complexes are present in the spectrum on the
[O iii]$\lambda$5007/H$\beta$ vs [N ii]$\lambda$6583/H$\alpha$ BPT diagram.
This is shown in Fig. 18 for which the blue component positions are given as
blue triangles and the red component positions are given as red diamonds. The
green dashed lines link the blue and red component positions for individual
double peaked sources and the grey points show the positions of all the
single-peak treated sources in our Reyes et al. (2008) sample. The positions
of red and blue double peaked components are consistent with the overall
single peaked sample positions and none of the sources change classification.
The consistency shows that both the red and blue peaks of all our double
peaked sources are ionized by AGN continuum emission. There appears to be no
preference for red or blue components to have systematically higher or lower
[O iii]$\lambda$5007/H$\beta$ or [N ii]$\lambda$6583/H$\alpha$ ratios. The
lack of trend suggests that there is no preference for red or blue components
to have higher ionization parameter, as traced to first order by [O
iii]$\lambda$5007/H$\beta$, or metallicity as traced to first order by [N
ii]$\lambda$6583/H$\alpha$ in the Seyfert/LINER branch (Agostino et al.,
2021).

From the properties explored in this section we find our double peaked sample
results to be consistent with either bi-conical outflow or dual AGN origins.

####  6.2.2 Host-Galaxy Morphology

To provide a basic insight into the origins of double peaked emission lines in
our sample we visually inspect 15" $grz$ Pan-STARRS1 (Chambers et al., 2016)
cutout morphology for the prevalence of galaxy merger evidence in our sample.
Alongside cutouts of our sample of 45 successfully fit double peaked Type 2
AGN, we create three additional samples comprised of 45 cutouts of single
peaked Type 2 AGN from our main sample. Each of these additional samples are
matched in [O iii]$\lambda$5007 luminosity and redshift with our double peaked
sample and contain a unique selection of sources. We perform identical
inspection analyses on all four samples, inspecting for several morphological
features related to major and minor galaxy mergers; tidal features, rings,
close companions at the redshift of the AGN host and multiple distinct stellar
populations within the galaxy traced by colour gradients. Fig. 19 gives
examples of positive results for each of these inspection categories.

Figure 19: Four example 15" Pan-STARRS1 images used to assess host-galaxy
morphology for merger signatures. Each example exhibits one of the features
visually inspected for in our analysis. Merger signature presented (from left
to right); tidal features, ring, close companion, colour gradient.

Table 4 presents the results of this exercise. We find in all inspection
categories our double peaked sample presents merger feature rates consistent
with those derived from the parent sample of single peaked sources. In the
case of close companions in the frame of the 15" image our double peaked
sample has the least occurrences with 16% (7 sources) displaying such a
feature compared to an average of 27% among the three single peaked samples.
To the resolution available (64 kpc at the median redshift of our sample,
$z$=0.28), a minority of double peaked AGN host galaxies show evidence of
merger activity. This suggests that the phenomenon is not directly related to
galaxy mergers and is likely largely caused by bi-conical outflows or NLR
kinematics, rather than dual AGN. This is not to say that there are no dual
AGN present in the sample, however higher resolution and multi-wavelength data
would be needed to draw conclusions on the nature of individual objects, which
is beyond the scope of this paper. Thus, to the resolution available in Pan-
STARRS1 imaging our double peaked Type 2 AGN are found to reside in galaxies
with similar rates of morphological merger signatures as their single peaked
counterparts. This suggests that the majority of double peaked sources in our
sample have a bi-conical outflow origin rather than a dual AGN origin.

Table 4: Visual inspection of 15" Pan-STARRS1 images for four categories of merger activity. Inspection is completed for our fitted sample of 45 double peaked Type 2 AGN and three unique samples of 45 single peaked Type 2 AGN from our parent sample matched in [O iii]$\lambda$5007 luminosity and redshift. Absolute counts are given the table with the percentage of the inspection sample this constitutes to given in brackets for each value. Sample (each with 45 sources) | Tidal | Ring | Companion | Colour Gradient
---|---|---|---|---
Double Peaked | 7 (16%) | 2 (4%) | 7 (16%) | 9 (20%)
Single Peaked 1 | 6 (13%) | 5 (11%) | 14 (31%) | 11 (24%)
Single Peaked 2 | 5 (11%) | 3 (7%) | 12 (27%) | 7 (16%)
Single Peaked 3 | 5 (11%) | 4 (9%) | 11 (24%) | 7 (16%)

A similar analysis was performed in Comerford et al. (2013) where visual
inspection of morphology in SDSS $gri$ imaging of dual AGN candidates that
exhibit double peaks or emission line offsets from the system redshift
selected from the AGES survey (Kochanek et al., 2012). They found that dual
AGN candidates are found to have close (within 5") companions in 29% of
sources compared to 9% in their parent sample of Type 2 AGN. This appears to
be at odds with our analysis, however the frequency of merger features in
their dual AGN candidates may be affected by their small sample size of seven
sources. We use a sample six times larger in our analysis and therefore argue
that our results give a more complete picture of the merger rates in double
peaked AGN. A 29% fraction of mergers is consistent with the value we find for
our single-peaked AGN inspection sub-samples. As our parent sample is selected
to consist of high luminosity Type 2 AGN this could suggest that high
luminosity AGN are found more frequently in galaxies with merger signatures
when compared with the overall Type 2 AGN population.

##  7 Summary

Motivated by the need to rapidly process and classify large volumes of AGN
spectra from upcoming astronomical facilities we developed an optical Type 2
AGN spectral fitting routine optimised for large volume analysis using the
scalable and automatic spectral fitting software QSFit. The development of
this recipe allows Type 2 AGN spectra to be analysed in a consistent fashion
to Type 1 AGN spectra within the same software package, eliminating systematic
biases when comparing the values derived from the fits. To qualify its
performance and carry out some initial scientific studies our presented
fitting routine is applied to a sample of 813 optically selected luminous Type
2 AGN spectra from the SDSS drawn from the sample collated in Reyes et al.
(2008). The median time taken to analyse a low-z SDSS Type 2 AGN spectrum with
our code is 1.6$\pm$0.9 s.

We find no significant statistical preference to use Gaussian or Lorentzian
emission line profiles for low-z Type 2 AGN SDSS spectra. Gaussian and
Lorentzian profiles give median sample reduced $\chi^{2}$ values of
1.39$\pm$0.36 and 1.45$\pm$0.38, respectively, which are consistent with one
another within uncertainty.

To confirm the reliability of the measurements made using our fitting routine
we plot the measured positions of our sources on the BPT emission line
diagnostic diagrams. We observe that the bulk of our measurements lie in the
expected AGN/Seyfert portion of these diagrams confirming that the ionizing
continuum generating the emission lines are of AGN origin. Outliers from the
main locus of sources are well explained by spectra exhibiting low S/N ratios
or double peaked emission lines, for which our default Type 2 AGN model is
incomplete. Alongside this test we leave the known 3:1 ratio of [O
iii]$\lambda$5007 to [Oiii]$\lambda$4959 emission line flux as a free
parameter in our fit (for the core components of the lines) to check if the
correct value is recovered. We find a median [Oiii] ratio of 3.1$\pm$0.1
across our sample, compatible with expectations and the literature.

The Balmer decrement (H$\alpha$/H$\beta$ emission line flux ratio) is
calculated for a subset of 456 sources in our sample for which both associated
Balmer emission lines are available. We find a median value of 4.5$\pm$0.8
across our sample of luminous Type 2 AGN. This value is consistent with other
works that calculate the NLR Balmer decrement for samples of Type 1 and Type 2
AGN, however is above the predicted AGN optically thick recombination value of
3.1. This discrepancy is attributed to unaccounted dust extinction at the
redshift of our sources diminishing the shorter wavelength H$\beta$ emission.
This result provides evidence that it is commonplace for dust to be present in
the NLR of Type 2 AGN.

We compare our [O iii]$\lambda$5007 emission line luminosity measurements to
those derived in Reyes et al. (2008) of the same sample of spectra to check
for consistency. We find a scatter and systematic offset between the
measurement methods. Our measurements using the QSFit Type 2 AGN routine
presented in this paper are on average 1.16 times larger than those using
Reyes et al. (2008) semi-parametric method and 1.22 times larger than their
Gaussian method. This discrepancy is largely owed to the differing models used
for measurements, as we employ a blue wing component when fitting [O
iii]$\lambda$5007 in our method. We show that modifying our routine to use a
single Gaussian component for [O iii]$\lambda$5007 reduces the observed offset
to 1.03 and 1.07 for the semi-parametric and Gaussian methods, respectively.
The remaining smaller offset is likely explained by the choice of continuum
estimation. We employ a 5 Gyr Elliptical host-galaxy template summed with a
power-law continuum, whereas a linear fit around the [Oiii] complex is adopted
in Reyes et al. (2008) which is free from absorption features in the region.

In our sample we observe that spectra with higher S/N exhibit a higher
(statistically worse) $\chi^{2}$ fit statistic than lower S/N spectra. This
counter-intuitive trend is attributed to the fact that increased S/N reveals
complexities in the emission line profiles that cannot be observed above the
noise in lower S/N sources, rendering our modelling of the most prominent
emission lines (ie. H$\beta$, [O iii]$\lambda$5007, [Oiii]$\lambda$4959 and
H$\alpha$) insufficient. We test a number of emission line profile
combinations to better accommodate the modelling of high S/N emission lines
and find that using two Gaussians provides an effective solution. Our high S/N
ratio spectra recipe is made available as a specialised QSFit recipe for these
cases.

We present a general QSFit routine for analysing Type 2 AGN spectra with
double peaked narrow emission lines, motivated by the interesting physics in
these sources and the frequency at which they are present as outliers in our
self-consistency tests. An intersection of 45 spectra is found between Liu et
al. (2010) sample of double peaked emission line Type 2 AGN and our sample of
luminous Type 2 AGN spectra, which we analyse using our specialised double
peaked recipe. A distribution of separations between red and blue peaks of
double peaked emission lines is observed with a median velocity separation of
390$\pm$60 kms-1. The luminosity ratios of blue and red components
(Lblue/Lred) of double peaked [O iii]$\lambda$4959, [O iii]$\lambda$5007 and
H$\alpha$ emission lines are found to be consistent with unity across the
sample, showing that it is not favoured for the red or blue peak to be more
luminous. Through plotting the red and blue components of our double peaked
sample on the BPT emission line diagnostic diagram we show that all lines are
consistent with being produced by an AGN ionizing continuum and consistent
with the positions of single peaked sources. No evidence is found for the red
or blue peaks to have systematically different ionization parameter or
metallicity and no sources change classification on the diagram between the
two sets of lines, pointing to a common ionization source for each double
peaked Type 2 AGN.

We perform visual inspection for merger evidence in the host-galaxy morphology
of Pan-STARRS1 imaging of our double peaked sample and [O iii]$\lambda$5007
luminosity and redshift matched samples of single peaked AGN from our parent
sample. To the resolution available (64 kpc at the median redshift of our
sample, $z$=0.28) we find double peaked Type 2 AGN reside in merging systems
at a comparable frequency to single peaked AGN across a number of criteria.
This suggests the double peaked AGN phenomenon is likely to have a
kinematically disturbed NLR origin rather than a dual AGN origin which is
expected in late stage mergers in the majority of cases, however this does not
eliminate dual AGN as the origin of some of the sources in our sample444
https://github.com/MattSelwood/Type2AGN.

## Acknowledgements

We thank the anonymous referee for their careful reading of our manuscript and
their insightful comments which have served to improve the quality of this
work.

This work is supported by the UKRI AIMLAC CDT, funded by grant EP/S023992/1.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan
Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space
Administration, the Japanese Monbukagakusho, the Max Planck Society, and the
Higher Education Funding Council for England. The SDSS Web Site is
http://www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortium for the
Participating Institutions. The Participating Institutions are the American
Museum of Natural History, Astrophysical Institute Potsdam, University of
Basel, University of Cambridge, Case Western Reserve University, University of
Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the
Japan Participation Group, Johns Hopkins University, the Joint Institute for
Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and
Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences
(LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for
Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico
State University, Ohio State University, University of Pittsburgh, University
of Portsmouth, Princeton University, the United States Naval Observatory, and
the University of Washington.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg and the Max Planck Institute for Extraterrestrial Physics,
Garching, The Johns Hopkins University, Durham University, the University of
Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

## Data Availability

The data underlying this article are available in CDS, at
https://dx.doi.org/[doi]

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##  Appendix A Description of Catalogues

###  A.1 Luminous Type 2 AGN Catalogue

We provide a catalogue of our QSFit measurements of the spectral properties of
our sample of 813 luminous Type 2 AGN. The catalogue is deposited as a FITS
table with 200 columns and 813 rows, available on CDS.

In this section we will list the name and meaning of each column in the QSFit
catalogue. Throughout the catalogue the value `-999.0` is used as a fill value
for when there is no measurement available for a quantity in a given spectrum.
Parameters that are patched to another to provide a single free parameter fit
are provided in the catalogue with a null value for their uncertainty and
inherit the uncertainty on the parameter they are patched to.

Table 5: List of emission lines considered in our Type 2 AGN QSFit recipe, their rest-frame vacuum wavelength and their corresponding label in the QSFit catalogue provided alongside this work. Line | Wavelength (Å) | Label
---|---|---
Mg ii | 2796.35 | `MgII_2798`
[Ne v] | 3426.50 | `NeV_3426`
[O ii] | 3728.48 | `OII_3727`
[Ne iii] | 3870.16 | `NeIII_3869`
H$\gamma$ | 4341.68 | `Hg`
H$\beta$ | 4862.68 | `Hb`
[O iii] | 4960.30 | `OIII_4959`
[O iii]bw | 4960.30 | `OIII_4959_bw`
[O iii] | 5008.24 | `OIII_5007`
[O iii]bw | 5008.24 | `OIII_5007_bw`
[O i] | 6302.05 | `OI_6300`
[O i] | 6365.54 | `OI_6364`
[N ii] | 6549.85 | `NII_6549`
H$\alpha$ | 6564.61 | `Ha`
[N ii] | 6585.28 | `NII_6583`
[S ii] | 6718.29 | `SII_6716`
[S ii] | 6732.67 | `SII_6731`
Unknown 1 | - | `unk1`
Unknown 2 | - | `unk2`

The list of columns provided in our catalogue are as follows:

  1. 1.

`SOURCE_ID`: name of the SDSS spectrum given in the format ‘spec-PLATE-MJD-
FIBER’;

  2. 2.

`SDSS_ID`: SDSS object name of the source given by its right ascension and
declination co-ordinates in the format ‘SDSS JHHMMSS.ss+DDMMSS.s’;

  3. 3.

`RA`: the right ascension (J2000.0) of the source;

  4. 4.

`DEC`: the declination (J2000.0) of the source;

  5. 5.

`Z_OBS`: the redshift of the source;

  6. 6.

`SN`: the median S/N of the spectrum;

  7. 7.

`EBV`: the colour excess used to de-redden the spectrum prior to fitting;

  8. 8.

`RECIPE`: the name of the QSFit recipe used to analyse the spectrum;

  9. 9.

`model_elapsed`: time elapsed to complete fitting of the spectrum, given in
units of seconds;

  10. 10.

`model_ndata`: the number of data points in the spectrum;

  11. 11.

`model_nfree`: the number of free parameters in the fit;

  12. 12.

`model_dof`: the number of degrees of freedom in the fit;

  13. 13.

`model_fitstat`: the total $\chi^{2}$ fit statistic of the model;

  14. 14.

`qso_cont_norm`, `qso_cont_norm_unc`: the $\lambda$Lλ luminosity of the power-
law continuum at the reference wavelength of the component and its associated
statistical uncertainty, given in units of 10${}^{42}\ $erg s-1;

  15. 15.

`qso_cont_x0`: reference wavelength of the power-law continuum fixed at median
wavelength value of the spectrum, given in units of Å;

  16. 16.

`qso_cont_alpha`, `qso_cont_alpha_unc`: power-law continuum slope and
associated statistical uncertainty;

  17. 17.

`galaxy_norm`, `galaxy_norm_unc`: the $\lambda$Lλ luminosity of the host-
galaxy template at 5500 Å, given in units of 10${}^{42}\ $erg s-1;

  18. 18.

The remaining columns pertain to emission line properties. Each property holds
the same meaning for each of the lines considered in the recipe. The
properties associated with each emission line is denoted using the assigned
labels presented in Table 5 which should be inserted in the `[LINE_ID]` part
of the column name.

    1. (a)

`[LINE_ID]_norm`, `[LINE_ID]_norm_unc`: integrated luminosity of the emission
line profile and its associated statistical uncertainty, given in units of
10${}^{42}\ $erg s-1;

    2. (b)

`[LINE_ID]_center`: central rest-frame wavelength of the emission line, given
in units of Å;

    3. (c)

`[LINE_ID]_fwhm`, `[LINE_ID]_fwhm_unc`: full width at half maximum of the
fitted emission line profile and its associated statistical uncertainty, given
in units of km s-1;

    4. (d)

`[LINE_ID]_voff`, `[LINE_ID]_voff_unc`: velocity offset of the emission line
from the system velocity and its associated statistical uncertainty, given in
units of km s-1;

    5. (e)

`[LINE_ID]_ew`, `[LINE_ID]_ew_unc`: equivalent width of the emission line and
its associated statistical uncertainty, given in units of Å.

###  A.2 Double Peaked Type 2 AGN Catalogue

Alongside our catalogue of measurements for our main single peaked luminous
Type 2 AGN sample, we publish a catalogue of measurements for our double
peaked Type 2 AGN sub-sample. Our double peaked catalogue is depositied as a
FITS table with 263 columns and 45 rows, available on CDS.

All column names and meanings are identical to those described in the prior
section, however with a revised emission line list containing the components
of our double peaked Type 2 AGN recipe which is given in Table 6.

Table 6: List of emission lines considered in our double peaked Type 2 AGN QSFit recipe, their rest-frame vacuum wavelength and their corresponding label in the double peaked QSFit catalogue provided alongside this work. Line | Wavelength (Å) | Label
---|---|---
Mg ii | 2796.35 | `MgII_2798`
[Ne v] | 3426.50 | `NeV_3426`
[O ii]blue | 3728.48 | `OII_3727_2`
[O ii]red | 3728.48 | `OII_3727`
[Ne iii] | 3870.16 | `NeIII_3869`
H$\gamma$ | 4341.68 | `Hg`
H$\beta_{blue}$ | 4862.68 | `Hb_2`
H$\beta_{red}$ | 4862.68 | `Hb`
[O iii]blue | 4960.30 | `OIII_4959_2`
[O iii]red | 4960.30 | `OIII_4959`
[O iii]core | 4960.30 | `OIII_4959_core`
[O iii]blue | 5008.24 | `OIII_5007_2`
[O iii]red | 5008.24 | `OIII_5007`
[O iii]core | 5008.24 | `OIII_5007_core`
[O i] | 6302.05 | `OI_6300`
[O i] | 6365.54 | `OI_6364`
[N ii] | 6549.85 | `NII_6549`
H$\alpha_{blue}$ | 6564.61 | `Ha_2`
H$\alpha_{red}$ | 6564.61 | `Ha`
[N ii]blue | 6585.28 | `NII_6583_2`
[N ii]red | 6585.28 | `NII_6583`
[S ii] | 6718.29 | `SII_6716`
[S ii] | 6732.67 | `SII_6731`
Unknown 1 | - | `unk1`
Unknown 2 | - | `unk2`
Unknown 3 | - | `unk3`
Unknown 4 | - | `unk4`