11institutetext: National Institute of Informatics, Japan 22institutetext:
SOKENDAI (The Graduate University for Advanced Studies), Japan
33institutetext: National Institute of Advanced Industrial Science and
Technology, Japan

# MTab: Matching Tabular Data to Knowledge Graph using Probability Models

Phuc Nguyen 1122 Natthawut Kertkeidkachorn 33
Ryutaro Ichise 112233 Hideaki Takeda 1122

###### Abstract

This paper presents the design of our system, namely MTab, for Semantic Web
Challenge on Tabular Data to Knowledge Graph Matching (SemTab 2019). MTab
combines the voting algorithm and the probability models to solve critical
problems of the matching tasks. Results on SemTab 2019 show that MTab obtains
promising performance for the three matching tasks.

##  1 Introduction

Tabular Data to Knowledge Graph Matching (SemTab
2019)111http://www.cs.ox.ac.uk/isg/challenges/sem-tab/ is a challenge on
matching semantic tags from table elements to knowledge graphs (KGs),
especially DBpedia. Fig. 1 depicts the three sub-tasks for SemTab 2019. Given
a table data, CTA (Fig. 1a) is the task of assigning a semantic type (e.g., a
DBpedia class) to a column. In CEA (Fig. 1b), a cell is linked to an entity in
KG. The relation between two columns is assigned to a property or predicate in
KG in CPA (Fig. 1c). ††Copyright © 2019 for this paper by its authors. Use
permitted under Creative Commons License Attribution 4.0 International (CC BY
4.0).

(a) CTA

(b) CEA

(c) CPA

Figure 1: Tabular Data Matching to Knowledge Graph (DBpedia)

###  1.1 Problem Definition

We denotes DBpedia as a knowledge graph $G=(E,T,R)$, where $E,T,R$ are the set
of entities, the set of types (or classes), and the set of relations (or
predicates) respectively. $e$ is an entity $e\in E$, $t_{e}$ is the type of an
entity $t_{e}\in T$, and $r$ is a relation of entity-entity or entity-literal
$r\in R$.

Let a table $S$ be a two-dimensional tabular structure consisting of an
ordered set of $N$ rows, and $M$ columns. $n_{i}$ is a row of table
($i=1...N$), $m_{j}$ is a column of table ($j=1...M$). The intersection
between a row $n_{i}$ and a column $m_{j}$ is $c_{i,j}$ is a value of the cell
$S_{i,j}$. In general, the tabular to KG matching problems could be formalized
the three sub-tasks as follows.

  * •

CEA: matching a cell value $c_{i,j}$ into a relevance entity $e\in E$.

  * •

CTA: matching a column $m_{j}$ into a exact relevance type and its ancestors.

  * •

CPA: matching the relation between two columns $m_{j_{1}}$ and $m_{j_{2}}$
($j_{1},j_{2}\in[1,M],j_{1}\neq j_{2}$) into a relation $r\in R$.

###  1.2 Assumption

In MTab, we adopt the following assumptions:

###### Assumption 1

MTab is built on a closed-world assumption. It means that the target KG is
completed and corrected.

###### Assumption 2

The type of input table is vertical relational table.

###### Assumption 3

Input tables are independence, it means there is no sharing information
between input tables.

###### Assumption 4

Column cell values have the same entity types and data types.

###### Assumption 5

The first row of table ($n_{1}$) is table header. The first cell of column is
header of this column, $c_{1,j}\in m_{j}$.

In practice, table headers could have more complicated structures. Headers
could available or non-available, be located at the beginning of the table or
not, have one rows or multiple rows. In this work, we omit those issues and
assume that the table header is located at the first row.

##  2 Approach

MTab is built on the joint probability distribution of many signals inspired
by the graphical probability model-based approach [1]. However, MTab improves
the matching performance by solving two major problems:

  * •

Entity lookup: We found that using only DBpedia lookup (the most popular
service) does not usually get relevance entities for non-English queries.
Therefore, we perform entity lookup on multiple services (with language
parameter) to increase the possibility of finding the relevance entities.

  * •

Literal matching: We found that mapping cell values to corresponding values in
a KG is less effective because the corresponding value in KG is rarely equal
with a query value. Therefore, with Assumption 4, we adopt literal columns
matching to find a relevance relation (property) and aggregate these signals
to enhance MTab performance.

Additionally, we also adopt more signals from table elements, introduce a
scoring function to estimate the uncertainly from ranking. Note that, the
probabilities in this paper could be interpreted as subjective confidences.

Figure 2: The design of MTab framework

###  2.1 Framework

We design our system (MTab) as 7-steps pipeline (Fig. 2). Step 1 is to pre-
process a table data $S$ by decoding textual data, predicting languages, data
type, entity type prediction, and entity lookup. Step 2 is to estimate entity
candidates for each cell. Step 3 is to estimate type candidates for columns.
Step 4 is to estimate relationship between two columns. Step 5 is to re-
estimate entity candidates with confidence aggregation from step 2, step 3,
and step 4. Step 6, and Step 7 are to re-estimate type and relation candidates
with results from Step 5, respectively.

###  2.2 Step 1: Pre-processing

We perform five processes as follows.

  * •

Text Decoding: Reading table data has a problem of textual encoding where some
characters are loaded as noisy sequences. Loading incorrect encoding might
strongly affect the lookup performance, therefore, we used the ftfy tool [2]
to fix all noisy textual data in tables.

  * •

Language Prediction: We used the pre-trained fasttext models (126 MB) [3] to
predict the languages for tables (concatenate all table cell values) and each
cell in the table. Since table data is not only written in English but also
other languages, determining the language of the input query helpful for the
lookup tasks.

  * •

Data Type Prediction:  Next, we perform data type prediction to predict 13
pre-defined data types of duckling 222Duckling, link:
https://github.com/facebook/duckling for each cell value in a table $c_{i,j}$.
Those types are about numerical tags, email, URL, or phone number. If there is
no tag assigned, we assign this cell type as a text tag.

  * •

Entity Type Prediction:  For each cell value in a table $c_{i,j}$, we also
perform entity type prediction with the pre-trained SpaCy models [4]
(OntoNotes 5 dataset) to predict 18 entity types. If there is no tag assigned,
this cell type is assigned to a text tag. We also manually map from those
textual entity types (11 entity types) OntoNotes 5 to some DBpedia classes.

  * •

Entity Lookup:  We search the relevance entity on many services including
DBpedia Lookup333DBpedia Lookup, link: https://wiki.dbpedia.org/Lookup,
DBpedia endpoint444DBpedia Endpoint, link: https://dbpedia.org/sparql. Also,
we search relevant entities on Wikipedia and Wikidata by redirected links to
DBpedia to increase the possibility of finding the relevant entities. We use
the language information of the table and cell values as the lookup
parameters. If there is any non-English lookup URL, it is redirected to the
corresponding English URL. We use $\alpha$ 555In MTab, we set $\alpha=100$ as
the limit of lookup results. The search query could be each cell value in a
table $c_{i,j}$, or other neighbor cells in the same rows $i$.

###  2.3 Step 2: Entity Candidate Estimation

In this section, we explain how we estimate the entity candidates. Given a
cell value $c_{i,j}$, we have a set of ranking result lists from lookup
services $Q_{c_{i,j}}$. $q$ is a list of ranking of entities ordered by degree
of relevance of a lookup service, where $q\in Q_{c_{i,j}}$. In MTab, we
adopted the four services as DBpedia lookup, DBpedia Endpoint, Wikidata
lookup, and Wikipedia lookup. However, we can use any services as long as
their output is a ranking list of relevance entities.

Denote $E_{Q_{c_{i,j}}}$ is a set of relevance entities in $Q_{c_{i,j}}$,
$s^{q}_{e}$ is a confidence score of an entity $e$ where $e\in
E_{Q_{c_{i,j}}}$. The confidence score of entity $e$ is calculated as
$s^{Q}_{e}=max(s^{q}_{e})$. $s^{q}_{e}$ is the confidence score of entity $e$
in $q$, $s^{q}_{e}=\alpha-rank_{e}$, where $rank_{e}$ is the ranking index of
entity in $q$. We normalize those entity confidence score to $[0,1]$, where
$Pr(E_{Q_{c_{i,j}}}|Q_{c_{i,j}})=1$,
$Pr(e|Q_{c_{i,j}})=\frac{s^{Q}_{e}}{\sum\limits_{e\in
E_{Q_{c_{i,j}}}}s^{Q}_{e}}$ and associate those scores as the potential
probability of entities given lookup results.

###  2.4 Step 3: Type Candidate Estimation

Regarding Assumption 4, we categorize table columns to entity columns and
literal columns. We aggregate the data type (Duckling Tags and SpaCy Tags)
from each cell in a column using majority voting. If the majority tag is text
or entity-related, the columns is an entity column, else a numerical column.
Regarding numerical columns, we perform semantic labeling with EmbNum method
[5] to annotate relations (DBpedia properties) for numerical columns 666We
only use EmbNum for those columns have at least 10 numerical values. Then, we
infer types (DBpedia classes) from those relations.

####  2.4.1 Numerical Column

The set of numerical columns in table $S$ is $M_{num}$. Given a numerical
column $m_{j}$, we use re-trained EmbNum model on DBpedia [5] to derive
embedding vector for the list of all numerical values of the column and then
search the corresponding relations from the database of labeled attributes
777We used all numerical attributes of DBpedia as the labeled data. The result
$q_{m_{j}}$ is a ranking of relevance numerical attributes in terms of
distribution similarity. We also use $\alpha$ as the limit for ranking result.
The confidence score of a relation $r$ is calculated as $s^{m_{j}}_{r}=\alpha-
rank_{r}$, where $rank_{r}$ is the ranking index of $r$. These scores are also
normalized to a range of [0,1] to associate the probability of potential of
relation for numerical columns $Pr(r|m_{j})$.

Next, we use DBpedia endpoint to infer the classes (types) from those
relations as Figure 3. $T_{q_{m_{j}}}$ is a set of inferred types, $t$ denotes
a type $t\in T_{q_{m_{j}}}$. Those types will be used for entity columns. The
confidence score of types is estimated as $s_{{r}_{t}}=max(s^{M_{num}}_{r})$.
Then, we normalized those scores to [0,1] so that $Pr(T_{q_{M_{num}}})=1$,
those confidence scores are associated as the probabilities of type potential
$Pr(t|M_{num})$ given $M_{num}$.

Figure 3: Property lookup with EmbNum

####  2.4.2 Entity Column

Given a set of entity columns in table $S$ is $M_{ent}$, we consider these
signals from

  1. 1.

$Pr(t|M_{num})$: the probabilities of type potential from numerical columns

  2. 2.

$Pr(t|m_{j},Q_{m_{j}})$: the probabilities of type potential aggregated from
the types of entity lookup for the all cells in column $m_{j}$ (
$Pr(t|m_{j},Q_{m_{j}})=\sum\limits_{c_{i,j}\in m_{j}}Pr(t|Q_{c_{i,j}})$ ). We
normalized these aggregated potentials and associates these as potential
probabilities.

  3. 3.

$Pr(t|m_{j},SpaCy_{m_{j}})$: the probabilities of type potential aggregated
from SpaCy entity type prediction for the all cell in column $m_{j}$. We used
majority voting and normalized these voting value to [0,1]. Then, we associate
those normalized voting value type potential probabilities.

  4. 4.

$Pr(t|c_{1,j})$: the probabilities of type potential given header value of the
column $m_{j}$. We associate the normalized Levenshtein distance as potential
probability that a type (DBpedia class) correspond with a header value.

The probabilities of type potential is derived from the four signals as
$Pr(t|m_{j})=w_{1}Pr(t|M_{num})w_{2}Pr(t|m_{j},Q_{m_{j}})w_{3}Pr(t|m_{j},SpaCy_{m_{j}})w_{4}Pr(t|c_{1,j})$,
where $w_{1},\\\ w_{2},\ w_{3},\ w_{4}$ are learnable weights. Note that, some
probabilities of signals might be 0 or too small, and aggregate those might
add too much noise to the final aggregation. Therefore, if any signal
probabilities less than $\beta$888In MTab, $\beta=0.5$, we omit those signals.
After aggregation, we also perform normalization for $Pr(t|m_{j})$ to a range
of [0,1] so that $Pr(T_{m_{j}}|m_{j})=1$.

###  2.5 Step 4: Relation Candidate Estimation

Given two columns $m_{j_{1}}$ and $m_{j_{2}}$, we estimate the probabilities
of relation potential of $Pr(r|m_{j_{1}},m_{j_{2}})$. We consider two type of
relation between two columns: Entity column to Entity column and Entity column
to non-Entity column. To be simple, we associate the first entity column is
$m_{j_{1}}$. If the second column is entity column, we denote it as
$m^{ent}_{j_{2}}$, else $m^{non-ent}_{j_{2}}$.

####  2.5.1 Entity - Entity columns $Pr(r|m_{j_{1}},m^{ent}_{j_{2}})$:

Given $c_{i,j_{1}}$ is a cell value of the column $m_{j_{1}}$ and the row
$r_{i}$, $c_{i,j_{2}}$ is a cell value of the column $m^{ent}_{j_{2}}$. We
assume that there is a relation between entity candidates of $c_{i,j_{1}}$ and
$c_{i,j_{2}}$, therefore we use DBpedia endpoint to find how many links
(relations or properties) between entity candidates of $c_{i,j_{1}}$ and
$c_{i,j_{2}}$. The confidence score of relation is calculated as
$s^{c_{i,j_{1}},c_{i,j_{2}}}_{r}=1$ if there is any relation between entity
candidates of two columns. Then, we aggregate those scores of all rows to get
the candidate score for two columns as
$s^{m_{j_{1}},m^{ent}_{j_{2}}}_{r}=\sum\limits_{i\in[1,N]}s^{c_{i,j_{1}},c_{i,j_{2}}}_{r}$.
Then, we normalize those score to a range of [0,1] so that
$Pr(R_{m_{j_{1}},m^{ent}_{j_{2}}}|m_{j_{1}},m^{ent}_{j_{2}})$ and associate it
as the probability of relation potential of Entity and Entity Columns
$Pr(r|m_{j_{1}},m^{ent}_{j_{2}})$.

####  2.5.2 Entity - Non-Entity columns $Pr(r|m_{j_{1}},m^{non-ent}_{j_{2}})$:

Given $c_{i,j_{1}}$ is a cell value of the column $m_{j_{1}}$ and the row
$r_{i}$, $c_{i,j_{2}}$ is a cell value of the column $m^{non-ent}_{j_{2}}$. We
estimate the relevance ratio between entity candidates and non-entity value
$c_{i,j_{2}}$. Given an entity candidate $e$ have pairs of
relation($r_{e}$)-values($v_{e}$), we compare the non-entity value
$c_{i,j_{2}}$ with all attribute values $v_{e}$. We select those pairs have
ratio larger than $\beta$. We only compare two values of $c_{i,j_{1}}$ and
$v_{e}$ based on there data types (textual type or numerical type).

  * •

For textual values: We use the normalized Levenshtein distance to estimate the
relevance ratio between $v_{e}$ and $c_{i,j_{2}}$ as $s(v_{e},c_{i,j_{2}})$.

  * •

For numerical values: the relevance ratio is calculated as

$s(v_{e},c_{i,j_{2}})=\begin{cases}0,&\text{if}\
max(|c_{i,j_{2}}|,|v_{e}|)=0\text{ and}\ |c_{i,j_{2}}-v_{e}|\neq 0\\\
1,&\text{if}\ max(|c_{i,j_{2}}|,|v_{e}|)=0\text{ and}\
|c_{i,j_{2}}-v_{e}|=0\\\
1-\frac{|c_{i,j_{2}}-v_{e}|}{max(|c_{i,j_{2}}|,|v_{e}|)},&\text{if}\
max(|c_{i,j_{2}}|,|v_{e}|)\neq 0\\\ \end{cases}$ (1)

We aggregate all relevance ratio with respect to relations. Then we normalize
those aggregated ratio to [0,1], and associate this as probability of relation
potential. $Pr(r|m_{j_{1}},m_{j_{2}})$. If the column of $m_{j_{2}}$ is
numerical columns, we also aggregate the re-calculated probability from
$Pr(r|m_{j_{2}})$ (step 3) as:

$Pr(r|m_{j_{1}},m_{j_{2}},m_{j_{2}}\text{is
numerical})=w_{5}Pr(r|m_{j_{1}},m_{j_{2}})w_{6}Pr(r|m_{j_{2}})$ (2)

where $w_{5},w_{6}$ are learnable parameters.

###  2.6 Step 5: Entity candidate Re-Estimation

In this step, we present a method to re-estimate the probabilities of entity
candidates $Pr(e|S)$. Given a cell $S_{i,j}$ containing a cell value $c_{i,j}$
at row $n_{i}$, and column $m_{j}$, we consider these signals from:

  * •

$Pr(e|Q_{c_{i,j}})$: The entity candidate probabilities given look up results.

  * •

$Pr(e|m_{j})$: The probabilities of entity candidates given their type’s
probabilities (Step 3). This can be estimated by
$Pr(e|m_{j})=max(Pr(t_{e}|m_{j},Q_{m_{j}}))$, where $t_{e}$ is a type of the
entity $e$.

  * •

$Pr(e|c_{i,j})$: The probabilities of entity candidates given the cell value
$c_{i,j}$. We get the mean ratio of the normalized Levenshtein distance,
heuristic abbreviation rules (first character of words, titles, dates, time).

  * •

$Pr(e|n_{i},m_{j_{1}})$: The probabilities of entity candidates given cell
values in a row $c_{i,j}\in n_{i}$. We do the same procedure as Step 4 to
compare all entity values with a cell value, and compute the mean probability
for all cell value in a row.
$Pr(e|n_{i},m_{j_{1}})=mean(Pr(e|m_{j_{1}},m_{j_{2}}))$, where $j_{1}\neq
j_{2}$.

Overall, the equation is as follows.

$Pr(e|S)=w_{7}Pr(e|Q_{c_{i,j}})w_{8}Pr(e|m_{j})w_{9}Pr(e|c_{i,j})w_{10}Pr(e|n_{i},m_{j_{1}})$
(3)

where $w_{7},w_{8},w_{9},w_{10}$ are learnable parameters.

###  2.7 Step 6, 7: Re-Estimate Types and Relations

We select the highest probabilities of entity candidates in Step 5 for each
cell $S_{i,j}$ to re-estimate types and relations with majority voting.

##  3 Results

Table 1 reports the overall results (The Primary Score) of MTab for three
matching tasks in the four rounds of SemTab 2019 [6]. Overall, these results
show that MTab achieves promising performances for the three matching tasks.

Table 1: Overall result of MTab system on the four round dataset of SemTab 2019 SemTab |  CEA (F1) |  CTA (AH) |  CPA (F1)
---|---|---|---
Round 1 |  1.000 |  1.000 (F1) |  0.987
Round 2 |  0.911 |  1.414 |  0.881
Round 3 |  0.97 |  1.956 |  0.844
Round 4 |  0.983 |  2.012 |  0.832
88footnotetext: https://github.com/phucty/MTab

##  4 Discussion

In this paper, we present MTab for the three matching tasks in SemTab 2019.

Novelty: The MTab performance might be explained in part by tackle the two
major problems of the three matching tasks. MTab is built on top of multiple
lookup services, therefore, it increases the possibility of finding the
relevant entities. Additionally, MTab adopted many new signals (literal) from
table elements and use them to enhance matching performance.

Limitation:  Since MTab is built on the top of lookup services, therefore, the
upper bound of accuracy strongly relies on the lookup results. In MTab, it is
computation-intensive because of aggregating the confidence signals from many
parts of the table. Therefore, MTab is not suitable for the real-time
application, where we need to get the result as fast as possible. MTab could
be modified to match only some parts of the table to reduce the processing
time as Table Miner+ [7]. However, we find that this is a trade-off between
effectiveness and efficiency when using Table Miner+ [7] method. A concrete
analysis of the trade-off issue is left as our future investigation.

Future work:  MTab could be improved by relaxing our assumptions:

  * •

Assumption 1: The closed-world assumption might not hold in practice.
Improving the completeness and correctness of knowledge graph might improve
MTab performance.

  * •

Assumption 2: Classify table types before matching could help to improve MTab
performance [8].

  * •

Assumption 3: In reality, some tables could have shared schema. For example,
tables on the Web could be divided to many web pages, therefore we can expect
improving matching performance by stitching those tables in the same web page
(or domain) [9], [10]. Therefore, performing holistic matching could help
improve MTab performance.

  * •

Assumption 5: Correctly recognize table headers could help to improve MTab
performance.

## References

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  * [2] Robyn Speer.  ftfy.  Zenodo, 2019.  Version 5.5.
  * [3] Armand Joulin, Edouard Grave, Piotr Bojanowski, and Tomas Mikolov.  Bag of tricks for efficient text classification.  In EACL 2017, pages 427–431. ACL, April 2017.
  * [4] Matthew Honnibal and Ines Montani.  spaCy 2: Natural language understanding with Bloom embeddings, convolutional neural networks and incremental parsing.  2017\.
  * [5] Phuc Nguyen, Khai Nguyen, Ryutaro Ichise, and Hideaki Takeda.  Embnum: Semantic labeling for numerical values with deep metric learning.  In Semantic Technology, pages 119–135, Cham, 2018. Springer.
  * [6] Oktie Hassanzadeh, Vasilis Efthymiou, Jiaoyan Chen, Ernesto Jiménez-Ruiz, and Kavitha Srinivas.  SemTab2019: Semantic Web Challenge on Tabular Data to Knowledge Graph Matching - 2019 Data Sets, October 2019.
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# BOSS Quasar Outflows Traced by C iv

Jarred Gillette,1 Fred Hamann1
1Department of Physics & Astronomy, University of California Riverside, 900
University Avenue, Riverside CA 92521, USA E-mail<EMAIL_ADDRESS>(JOG)

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We investigate possible factors that drive fast quasar outflows using a sample
of 39,249 quasars at median redshift $\langle z\rangle\approx$ 2.17. Unique to
this study, the quasar redshifts are re-measured based on the Mg ii emission
line, allowing for exploration of unprecedented outflow velocities (>6000 km
s-1) while maintaining statistical significance and uniformity. We measure
reliable C iv blueshifts for 1178 quasars with velocities >2500 km s-1. From
those, 255(13) quasars have blueshifts above 4000(6000) km s-1, with the
highest C iv velocity $\approx$ 7000 km s-1. Several correlations are
observed, where higher C iv blueshifts in general are in quasars with broader,
weaker C iv emission profiles, weak He ii emission, larger Eddington ratios,
and bluer UV continuum slope across the rest-frame UV to Near-IR. Analysis
reveals two primary factors contributing to faster outflows: higher Eddington
ratios, and softer far-UV continuum (h$\nu$ >24.6 eV). We find supporting
evidence that radiative line-driving may generate extreme outflow velocities,
influenced by multiple factors as suggested by the aforementioned
correlations. This evidence highlights the importance of considering a multi-
dimensional parameter space in future studies when analyzing large C iv
blueshifts to determine the fundamental causes of outflows.

###### keywords:

galaxies: active – quasars: emission lines – quasars: general – galaxies:
high-redshift

††pubyear: 2023††pagerange: BOSS Quasar Outflows Traced by C iv–BOSS Quasar
Outflows Traced by C iv

##  1 Introduction

High-z quasars are associated with formation and growth of massive galaxies,
and it is believed that the feedback from these quasars plays a crucial role
in regulating both galaxy growth and star formation processes (Hopkins et al.,
2008, 2016; Wylezalek & Zakamska, 2016; Veilleux et al., 2016; Rupke et al.,
2017; Baron et al., 2017; Vayner et al., 2021). However, the physical nature
and driving mechanism(s) of quasar outflows remain poorly understood. We need,
in particular, better empirical constraints on the quasar properties and
physical conditions that correlate with a higher incidence, greater speeds, or
more powerful outflows.

Quasar outflows are often studied via blueshifted broad absorption lines
(BALs) and their narrower cousins, mini-BALs, in rest-frame UV spectra
(Weymann et al., 1991; Hamann & Sabra, 2004; Baskin et al., 2013; Muzahid et
al., 2013; Hamann et al., 2018; Chen et al., 2019). Another approach is to use
the blueshifts in their broad emission-lines (BELs). These strategies are
complementary, but the BELs offer unique advantages. One is that the location
of BEL regions is known from reverb studies to be unambiguously near the
central engines, at radial distances of roughly 0.01 to 0.1 pc in luminous
quasars (Netzer, 2020, and references therein). Thus, emission lines provide
specific constraints on quasar outflow models. Another advantage is that
emission-line studies are less sensitive to orientation and time-dependent
effects than absorption lines, which can only measure the gas/outflow
structures that happen to lie along our line of sight to the continuum source
during the observing epoch. Specific values of emission blueshift can vary
depending on the sample and selection criteria, previous studies have found
typical blueshifts ranging from a few thousand km s-1 in BELs, to tens of
thousands of km s-1 for BALs (e.g., Richards et al., 2011; Coatman et al.,
2019; Temple et al., 2020; Rankine et al., 2020).

We do not know the geometry with certainty, but strongly blueshifted profiles
from high ionization lines suggest the emission comes from a wind that is
moving toward us, with the receding component blocked by the optically thick
accretion disk. Intermediate and lower ionization lines may be emitted by gas
in the accretion disk atmosphere, or a low-velocity base of the wind (Leighly
& Moore, 2004; Leighly, 2004; Casebeer et al., 2006; Richards et al., 2011;
Hamann et al., 2017; Rankine et al., 2020; Temple et al., 2023).

Investigating these line shifts require accurate systemic redshift of the
quasar. In many quasar blueshift studies the systemic redshift is estimated by
fitting of multiple emission lines simultaneously, which are assumed to be at
or near their rest wavelength (Richards et al., 2011; Coatman et al., 2016;
Coatman et al., 2019; Rankine et al., 2020; Temple et al., 2020; Temple et
al., 2023). Many studies estimate redshift using emission-lines or emission-
templates that may include higher ion lines. High ion lines like C iv
$\lambda$1549 can be blueshifted from systemic by several hundreds of km s-1
(Gaskell, 1982; Richards et al., 2002). The best indicators are narrow
emission lines arising from the extended host galaxies and halo environments.
Efforts have been undertaken to establish accurate redshifts for select quasar
populations in order to better constrain extreme outflow velocities (e.g.,
Gillette et al., 2023).

Low-ion BELs such as Mg ii, O i $\lambda$1304, and C ii $\lambda$1335 are also
generally good indicators of quasar redshifts, e.g., with small or negligible
offsets relative to narrow [O ii] and [O iii] emission lines. Mg ii is
estimated to be near the systemic redshift when compared to these other lines
in high redshift quasars (Richards et al., 2002), and is much more reliable
than high-ion lines like C iv. A mean shift between Mg ii \- C iv has been
shown of $\sim$920 $\pm$ 750 km s-1 (Ref. appendix in, Shen et al., 2007).

For this work, we present a sample of Mg ii emission-line measurements for
39,249 quasars from BOSS DR12. We then use these data to study the blueshifts
in the C iv BEL compared to a wide variety of other quasar properties that can
be measured or derived from this dataset. This study differs from previous
work by determining redshifts only from careful fitting of the Mg ii line,
allowing us to explore an unprecedented range of outflow velocities uniformly,
and maintain a statistically significant sample size. We can then focus more
sharply on trends in other lines and quasar properties that correlate with
blueshifts.

In this paper we analyze blueshifted emissions of C iv, and compare their
emission profiles and UV features to understand what correlates with strong
outflows. It is organized as follows. Section 2 describes criteria for
selecting quasars from catalogue spectra. Section 3 describes our methods and
measurements of blueshift, Mg ii line features, and black hole mass. Section 4
describes correlations in measured parameters of UV emission features, such as
blueshift, emission line widths, Eddington ratio, and spectral shape. Section
5 we discuss implications for quasar outflows. Section 6 concludes the paper.
Throughout this paper we adopt a $\Lambda$-CDM cosmology with $H_{0}$ = 69.6
km s-1 Mpc-1, $\Omega_{\text{M}}$ = 0.286 and $\Omega_{\Lambda}$ = 0.714, as
adopted by the online cosmology calculator developed by Wright (2006). All
magnitudes are on the AB system. Reported wavelengths are in vacuum and in the
heliocentric frame.

##  2 Quasar Samples and Data Sets

We started from a C iv emission-line sample of 173,636 quasars, measured by
(Hamann et al., 2017), from the Baryon Oscillations Survey (BOSS) from the
Sloan Digital Sky Survey Data Release 12 (hereafter DR12Q; Pâris et al., 2014,
2017). We limit our study to Type 1 sources based on the crude distinction
FWHM(C iv) $\geq$ 2000 km s-1 following previous studies by Alexandroff et al.
(2013) and Ross et al. (2015). This was done to avoid contamination by Type 2
quasars unless C iv FWHM is explicitly used for comparison to other
parameters. Sample selection criteria and quasar totals are summarized in
Table 1. Other subsamples after the “full” sample use additional constraints
as described in the sections noted. Figure 1 shows redshift and luminosity
distributions. To ensure C iv and Mg ii spectral coverage we are limited to
the redshift range 1.50 $\leq z\leq$ 2.46. By our quality standards, outlines
in Section 3.1, we have 39,249 quasars with a median redshift of $\langle
z\rangle\approx$ 2.17.

Sample name | Selection criteria | Number | Section ref.
---|---|---|---
DR12Q | - | 297,301 |
Hamann+17 | 2.0 $<z_{e}<$ 3.4 | 173,636 |
|  $i$ mag in DR12Q |  |
| well-measured C iv |  |
Full Sample |  C iv FWHM | 39,249 | 2
|  $\geq$2000 km s-1 |  |
| well-measured Mg ii |  |
BH Mass | well-measured | 38,966 |  3.3, 4.3
|  Mg ii wings |  |
Composite | 3.1e45 < $L_{\text{bol}}$ < 2.5e46 | 29,460 | 4.2
Sample | erg s-1 |  |
Color Sample |  $r$ & $z$ mag in DR12Q | 32,365 | 4.4
| 1.8 < $z_{e}$ < 3.4 |  |
|  $W1$-detected | 25,134 |
| cc_flags = 0000 |  |
High blueshift | > 4,000 km s-1 | 255 | 4.5
C iv | > 6,000 km s-1 | 13 |
Table 1: Selection criteria with our full sample, and total quasar subsample
numbers. Figure 1: Redshifts and computed Bolometric luminosities for our full
sample. Top: Redshift distribution as provided from DR12Q. Bottom: Bolometric
luminosities computed from monochromatic luminosities as described in Section
3.3.

For more accurate luminosity estimation from BOSS, a flux correction for
atmospheric differential refraction was applied from Margala et al. (2016)
when available, and otherwise applied a correction from Harris et al. (2016).
We computed monochromatic luminosity ($\lambda\,L_{\lambda}$) using a fitted
power law continuum local to Mg ii near $2800\text{\AA}$. This local continuum
was extrapolated for the monochromatic flux at $3000\text{\AA}$ to compute
$L(3000)=4\pi\,D_{L}^{2}\,\,\lambda\,f_{\lambda}$. Where $D_{L}$ is the
luminosity distance, and $f_{\lambda}$ is the flux at wavelength lam.
Bolometric luminosity ($L_{\text{bol}}$) was determined using a monochromatic
Bolometric correction factor $k_{\text{bol}}\times L(3000)=L_{\text{bol}}$,
where $k_{\text{bol}}=25\times\left[L(3000)\,/10^{42}\,\,\text{erg
s}^{-1}\right]^{-0.2}$. This method of correction factor makes considerations
for a luminosity-dependent spectral energy distribution over a broad range of
black hole masses, accretion rates, and spin, calibrated by Netzer (2019). We
did not do a reddening correction for luminosity, which we note in our
analysis in Section 4.4.

##  3 Measurements

In this study we use a dynamic fitting algorithm on every spectra in the
Hamann et al. (2017) set to measure line-emission features in the rest frame
UV continuum, even for low signal to noise. Specifically, we used the Mg ii
emission-line peaks for systemic redshift, after we applied several Gaussian
models for fitting the emission profile, and subtracted a broadened Fe ii
template. We assume the Mg ii doublet emission is one to one ratio, and the
emission cloud itself is optically thick ($\tau\gg$ 1). We did not use BOSS
catalogue signal to noise values during fitting, because they did not
accurately represent the quality of spectral detections near C iv and Mg ii.

###  3.1 Continuum and Line Fits

The first step is an algorithm that searches the spectrum for narrow spikes
above or below the spectra caused by cosmic rays, noise, or other anomalies.
These spikes are removed by interpolation from adjacent pixels. We applied a
spectral flux correction from Margala et al. (2016) when available, and
otherwise applied a correction from Harris et al. (2016).

Next we perform an initial preliminary fit to make a rough redshift correction
in cases where the BOSS pipeline redshift is too far offset from where we
expect Mg ii emission. We dynamically adjust the size of continuum flux
sampled from $\sim$2160 to 3120Å to avoid anomalous features in the spectra
when fitting the continuum or emission lines (e.g. fringing as Mg ii is
further redshifted to the end of the spectrograph at larger $z$). We
subtracted a modified Fe ii template to remove emission local to Mg ii
(template provided through private correspondence with Yue Shen, Shen et al.,
2016b). The template emission is from a theoretical model by Salviander et al.
(2007) scaled to match the empirical template from Vestergaard & Wilkes (2001)
but includes non-zero flux 2780-2830Å under Mg ii line emission.

After defining the preliminary continuum, we we mask sharp absorption and make
a preliminary single Gaussian fit, for a rough correction to the DR12Q
catalogue redshift. We also used the preliminary fit’s FWHM as a proxy
measurement of Fe ii emission-line broadening. Next we perform the broad
absorption checks as before. Again, the Fe ii template is scaled, but before
final subtraction the template is broadened according to our preliminary-FWHM
of the Mg ii profile.

Once we establish a continuum, we check for strong broad absorption with the
median fluxes in wavelength intervals 2310-2360Å and 2550-2580Å because broad
absorption in these windows by Fe ii is always accompanied by absorption in Mg
ii. If broad absorption was found, it was flagged for rejection.

Finally, for fitting Mg ii $\lambda$$\lambda$2796,2804 line emission we ignore
the doublet separation, instead using the mean. We found a robust iterative
procedure that begins with a two-component Gaussian model, which yield good
results with a minimum of free parameters (similar to Hamann et al., 2017). If
a two-component fit that does not yield physically reasonable profile, or were
too similar in shape, we instead fit using a single Gaussian profile. A final
peak wavelength measurement is performed with an additional Gaussian fit to
the top two thirds of the fitted Mg ii profile, to mitigate wing asymmetry in
the lower one third.

In order to ensure quality spectra measurements we chose a variety of quality
standards after fitting, with which to throw out spectra dominated by noise
and otherwise “bad” fits. We vetted the final sample with the following
quality criteria.

A minimum spectral signal-to-noise ratio is chosen as well as our own defined
quality standards, such as requiring C iv and Mg ii lines to be well measured
based on their fit signal-to-noise >4 in both REW and FWHM. After fitting, we
required quality flags for each spectra that indicate no significant problem
in the Mg ii emission-line or continuum fit occurred, and similarly good
quality flags from the C iv measurements sample. We also placed conservative
upper limits on both FWHMs to ensure the algorithm did not incorrectly fit to
the continuum instead of the emission-line with our model, and obviously
nonphysical. In order to further mitigate incorrect emission-fitting, and
allow our general findings in the full sample to be more robust, we have
chosen to ignore any spectra containing Broad Absorption Lines (BALs). Spectra
were rejected for BALs by the visual inspection flag present in DR12Q, and the
Balnicity Index (BI) must be bi_civ > 0.0 and bi_civ < 1000.0. Any masking of
absorption spikes done to properly fit an emission-line in the Mg ii emission
range must not be a significant fraction of the emission width, and the Mg ii
emission-line peak height must have a good signal to noise. We rejected fits
when emission around the fitted Mg ii profile has a standard deviation >0.75
to further limit the impact of noise when fitting the upper two-thirds of the
Mg ii emission profile. For Fe ii template subtraction quality criteria, we
rejected the spectra if the intensity of Fe ii was comparable to the peak
intensity of Mg ii line-emission. This criteria is to limit the bias
introduced by the template in our Mg ii profile fit.

Visual inspections of several thousand of the remaining spectra indicate that
the continuum and Mg ii line fits are generally excellent. We specifically
examined results at the extremes of broad and narrow FWHMs, large and small
REWs, strong BALs or other broad absorption that might overlap with the Mg ii
emission-line profiles, and spectra with low SNRs in the continuum. The most
common problem is fits that underestimate the line peak height and thus
overestimate the FWHMs for observed lines that have a strong narrow core on
top of much broader wings.

###  3.2 Measured Quantities and Blueshifts

We measured C iv blueshift by comparing the emission redshift of Mg ii from
our fitting to the emission redshift of C iv $\lambda$1548,1551 measured by
Hamann et al. (2017). We used the top two thirds fit of Mg ii emission as the
improved systemic redshift. Then we used the C iv measurement of the midpoint
at half the fitted profile height as the emission velocity shifted from rest C
iv. We use negative values to correspond to inflow away from the observer, and
positive values as blueshifts, outflowing towards the observer. We visually
inspected all $\sim$250 cases with blueshifts >4000 km s-1 to ensure their
validity.

For our full sample we obtained measurements for 39,249 quasars, eliminating
those with strong BALs and poor data. From these, we measured a multitude of
emission line properties which are supplemented by C iv measured quantities
from Hamann et al. (2017). For Mg ii we measured the rest-equivalent width
(REW), full width at half maximum (FWHM), second moment line-dispersion
($\sigma$), and centroid redshift. From the continuum fit we took the
monochromatic flux ($f_{3000}$) for computing a monochromatic luminosity to
approximate Bolometric luminosity. We measured the Mg ii emission profile with
both FWHM and $\sigma$, described in Peterson et al. (2004).

###  3.3 Black Hole Masses

We computed estimates of quasar black hole mass, assuming that the Mg ii
broad-line region (BLR) has virialized. We consider estimates using both Mg ii
FWHM and $\sigma$, because spectra quality of high-$z$ AGNs can often be
insufficient for measuring line dispersion of broad lines (Peterson et al.,
2004; Shen et al., 2008; Wang et al., 2009; Shen & Liu, 2012; Woo et al.,
2018). Using the continuum luminosity as a proxy for BLR radius and the broad
line width or line dispersion for the virial velocity we estimated virial mass
with,

$\displaystyle\centering\log\left(\frac{M_{\text{BH,vir}}}{M_{\odot}}\right)\@add@centering$
$\displaystyle=\alpha+\beta\,\log\left(\frac{\text{FWHM}}{10^{3}\text{ km/s
}}\right)+\gamma\,\log\left(\frac{\lambda L_{\lambda}}{10^{44}\text{
erg/s}}\right),$

where estimator values $\alpha_{\text{FWHM}}=7.02\pm 0.04$ or
$\alpha_{\sigma}=7.56\pm 0.03$, $\beta_{\text{FWHM},\sigma}=2.00$, and
$\gamma_{\text{FWHM},\sigma}=0.50$ are recommended from (see Table 3 in Woo et
al., 2018) for using $L_{3000}$. These values were adopted by calibrated UV
mass estimators comparing dispersion of H$\beta$ to Mg ii. There they found
continuum luminosity at 3000Å provided better calibration than the line
luminosity of Mg ii. After making quality cuts based on good Mg ii signal to
noise we have a total of 38,966 quasars (ref. Table 1). Comparison
distributions for either method are shown in Figure 4 and Figure 11. FWHM
tends to overestimate large widths, and underestimate the narrow widths. Most
of our fits use single Gaussians, and therefore driven by FWHM. In this work,
we present results for both FWHM and $\sigma$, but opt to use FWHM to
parameterize line width.

##  4 Results & Analysis

For a basis in presenting numbers of quasars, etc., we present distributions
of our measured parameters. Figures 2 & 3 present distributions in redshift,
Bolometric Luminosity ($L_{\text{bol}}$), REW, FWHM, and $\sigma$ for both C
iv and Mg ii.

Figure 2 shows the distributions of line strengths and widths. C iv has
slightly larger REW than Mg ii, but have similar distributions. In the general
population with broad C iv emission FWHM has similar distributions for C iv
and Mg ii. There are many examples of quasars with FWHM of C iv and Mg ii both
being large or small but there may be extreme cases where differences in width
are exacerbated, and may correlate with other quasar characteristics. The last
panel shows our integrated line dispersion for C iv and Mg ii. The
distributions appear similar, but there is a clear offset between the two
emission lines.

Figure 3 displays distributions of line strength and width of C iv and Mg ii.
Emission line strengths generally appear to correlate in REW of C iv and Mg
ii, but flatter than one to one. However, spectra showing strong C iv emission
generally have weaker Mg ii by at least 0.2dex. Emission line widths between C
iv and Mg ii FWHM are generally uncorrelated. Plotting Mg ii FWHM against
$\sigma$, we impose additional quality cuts to fits with linked-gaussian fits
to omit large wing profiles of low signal to noise ratio (see Table 1). We
compare the general distribution to robustly measured quasars at lower
redshifts by Woo et al. (2018), and show overlap in line widths. We can see in
the distribution of our sample that profiles fit with a double-Gaussian (25
percent) extend to larger values of $\sigma$ than those fit with a single-
Gaussian.

Our broad goal is to understand what physical or evolutionary properties of
quasars lead to large BEL blueshifts, and fast powerful outflows capable of
feedback. We first quantify the C iv blueshifts, and then investigate other
quasar properties and physical conditions for empirical relationships with
blueshift.

###  4.1 Blueshifts Across the Sample

Figure 5 shows distributions of Mg ii REW, C iv REW and FWHM vs blueshift.
There are several quasars that appear to show redshifted C iv. These redshifts
may be due to the uncertainties and relative motions of C iv and Mg ii, and
not high velocity inflow. We visually inspected all 255 cases with measured
blueshifts greater than 4000 km s-1. We were concerned that these extreme
cases have broad and weak C iv lines (see Section 5.2 below) that might be
poorly or incorrectly measured. However, the vast majority of these high
blueshift cases were found to have good fits. Most of the sample resides
between blueshifts of 0 and 1500 km s-1, with a median C iv blueshift of about
530 km s-1. We measure reliable blueshifts for 1178 quasars with velocities
>2500 km s-1. From those, 255 quasars with blueshifts above 4000 km s-1, 13
above 6000 km s-1, and the highest well-measured C iv velocity $\sim$ 7000 km
s-1. Figures of C iv REW vs its blueshift has become common in the literature
(e.g., Richards et al., 2011; Coatman et al., 2016; Coatman et al., 2019;
Rankine et al., 2020; Temple et al., 2020; Temple et al., 2023). This work
differs in that we exclusively use the Mg ii emission line as the proxy
measurement for systemic redshift, where others use catalogue redshifts from
template fitting or a combination of low-ionization lines, which may include
Mg ii. Our distribution is in broad agreement with other studies, and have
comparable sample sizes, but we extend to further extremes in the C iv
parameter space of line strength/weakness and blueshift. The top two panels of
Figure 5 show not only that C iv REWs are small at large blueshifts, but they
are small relative to the low-ion line Mg ii. The bottom panel shows that C iv
lines can be broad at any velocity shift, but at large blueshifts they are
almost exclusively broad.

Figure 6 is identical to Figure 5, with subdivisions in to boxes to further
inspect local median quantities across the parameter space. This partitioning
allows us to vary C iv REW and blueshift independently, and show how medians
of other measured quasar properties correlate. Figure 7 displays median values
of Bolometric luminosity, and several median properties for quasars in each
box. This figure more quantitatively shows the blueshift trends with C iv line
strength and width. The vertical trend of larger C iv REW with smaller
$L_{\text{bol}}$ is the Baldwin Effect (Baldwin, 1977), but there also appears
to be a weak trend for larger $L_{\text{bol}}$ with larger blueshifts (see
Section 4.3). Median C iv FWHM of each box is uniform in weak blueshifts, and
dramatically increases for large blueshift quasars. At high blueshifts (>3000
km s-1), C iv rarely exhibits line strength REW above 40 Å. In this high
blueshift regime C iv becomes almost always broad, with median FWHM > 7000 km
s-1, and is broad relative to Mg ii (median FWHM about 3700 km s-1). Median
Eddington ratio in each box also appears to increase with C iv blueshift.
Median strengths of Fe ii relative to the continuum, which is used to subtract
the Fe ii complex, appear stronger for large blueshift.

We further inspect other color-coded versions of this figure, and discuss
extinction effects on luminosity due to quasar reddening, in Section 4.4. We
inspect median composite spectre to confirm trends in median quantities with
blueshift in Section 4.2.

Figure 2: Distributions of measured quantities for our sample. Top: REW
distributions the full sample of quasars for both C iv (blue histogram) and Mg
ii (red histogram) emission lines. Middle: FWHM distributions for all quasars
for both C iv (red histograms) and Mg ii (blue histograms) emission lines.
Distinction between broad and narrow line quasars is made by C iv emission
FWHM, where broad emission are defined by C iv FWHM $\geq$2000 km s-1 (solid
red histogram), and narrow as C iv FWHM $<$2000 km s-1 (outlined red
histogram). The solid blue histogram shows Mg ii FWHM for quasars with C iv
FWHM $\geq$ 2000 km s-1, and the outlined cyan histogram shows Mg ii FWHM for
quasars with C iv FWHM < 2000 km s-1. Bottom: $\sigma$ distribution for single
and linked-Gaussian profiles used in our full sample.

Figure 3: Measured emission line property comparisons. Top: REW of C iv vs Mg
ii for the full sample of quasars. Middle: The ratio of FWHM C iv vs Mg ii for
the full sample. The yellow dashed line is our cutoff for broad C iv emission
quasars. Bottom: Log FWHM vs log $\sigma$ of Mg ii, for all broad C iv
emission quasars in the BH Mass sample (see Table 1). Black points are our
linked-Gaussian profile fits, blue points are from single-Gaussian fits, and
the yellow dashed line highlights the relationship of FWHM to $\sigma$ for a
Gaussian emission-profile. About 75 percent of the full sample have Mg ii
measured with a single-Gaussian, yielding FWHM /$\sigma$ = 2.355. There is
some overlap between our sample and that of Woo et al. (2018), despite their
sample redshifts $z$ $\approx$ 0.3$-$0.6. All panels show one to one as a grey
dashed line. Figure 4: Quasar black hole masses and Eddington ratios for our
sample. Top: Black hole masses computed from Mg ii FWHM, or $\sigma$, computed
from the fitted emission profile. Bottom: Eddington ratios computed from our
Bolometric luminosity and black hole mass estimates. To ensure good
measurements, we omit linked-Guassian profiles with wing component peak SNR
$<$ 0.8, or that have wing FWHM $<$11,000 km s-1 and FWHM
$\frac{\text{wing}}{\text{core}}$ ratio $>$ 5.5. Based on our repeated
experiments, the M${}_{\text{BH}}$ results are not sensitive to these
particular values. Figure 5: Measured quantities from our sample where all
distributions exclude FWHM(C iv) <2000 km s-1, unless otherwise stated. Top:
REW(C iv) vs C iv velocity shift, exhibiting the characteristic distribution
that has emerged in the literature as quasar redshift measurements have been
constrained. Middle: The ratio of REW(C iv) to REW(Mg ii) vs C iv velocity
shift, showing that for higher blueshifts the REW(C iv) /REW(Mg ii)
$\leq\sim$1\. Bottom: FWHM(C iv) vs C iv velocity shift of all quasars in our
full sample, with a yellow dashed line indicating quasar cutoff for broad C iv
line quasars for our sample. Most quasars appear to follow a trend for broader
C iv emission profiles with higher C iv blueshift. Figure 6: REW(C iv) vs C iv
velocity shift, identical to the top panel of Figure 5, but with partitions
labelled for further analysis (see Sections 4.2, 4.3, and 4.4. We choose box
sizes which can resolve overall trends, but not so few spectra to have poor
statistics for each box. Cells are 0.2dex in height and and 500 km s-1 in
width, except for column L, which needed to be 1000 km s-1 in width to include
a sufficient number of quasars. Every partitioned cell contains at minimum
$\sim$100 objects. Figure 7: REW(C iv) vs C iv velocity shift of our sample
with regions color coded for median $L_{\text{bol}}$. Within each boxed region
we present median values from the quasar spectra. The white box at the top
right gives a legend to where the values are located. These values include,
FWHM of C iv and Mg ii REW ratio of C iv to Mg ii $L_{\text{bol}}$, the
relative strength of Fe ii to continuum, and the number of quasars in the
boxed region. The color of the region indicates the median $i$–$W3$ color
within the box.  Figure 8: Bolometric luminosity vs blueshift, with boundaries
defined in luminosity to isolate trends in blueshift without biasing composite
spectra to have both high blueshift and high luminosity.

###  4.2 Composite Spectra

Here we generate composite spectra to see overall trends in quasar properties
with varying C iv line strength and blueshift. We use medians of selected rows
and columns across our partitioned boxes in Figure 6, to show variation of
spectral features across a wide range of C iv REW and blueshifts. Implications
of found correlations will be discussed in Section 5.

We isolate trends with respect to C iv blueshift from luminosity by
constraining $L_{\text{bol}}$, by setting an upper and lower bound for
inclusion, when generating medians. Figure 8 shows the distribution of
computed $L_{\text{bol}}$ across C iv blueshifts for our sample. We construct
these median composite spectra from quasars within the luminosity range
3$\times$1045 erg s-1 < $L_{\text{bol}}$ < 2.5$\times$1046 erg s-1. Imposing
this constraint ensures that median luminosities of our composite quasars
remain nearly constant across the full range of C iv blueshifts, and still
retains a large sample of $\sim$30,000 quasars (see Table 1).

Table 2 presents quasar parameter medians from the Composite Sample in Table
1, grouped by C iv velocity from $-$1500 to 6000 km s-1, and in bins of 500 km
s-1. We chose this bin size to include a significant, minimum number of
quasars at large blueshift bins ($\sim$100 quasars), without obscuring trends
by broadening the composite emission profile. We made luminosity cuts to
isolate trends that are independent of $L_{\text{bol}}$ and the Baldwin Effect
(see Table 1 and Figure 8). Our median $\lambda L_{\lambda}$ luminosities are
are roughly constant across the wide range in velocity (within about 12 per
cent of the overall median), confirming our luminosity criteria is effective,
and shows that any other trends seen are not explained by significant
variations in luminosity.

Figure 9 shows median spectra from the Composite Sample in Table 1, from
$-$1500 to 6000 km s-1, and associated with the medians in Table 2. Most
notable, is C iv FWHM and REW correlation with blueshift. The line strength of
C iv weakens, indicated by the median REW decreasing from $\sim$50 to 10 Å, as
blueshift increases. Conversely, the line broadens with increasing blueshift.
From median C iv velocity $\sim$260 to 5260 km s-1, the FWHM more than doubles
from $\sim$4300 to 9400 km s-1. Mg ii profile width as measured by FWHM, or
$\sigma$, does not display dramatic broadening or narrowing with large changes
in C iv blueshift.

Although we describe the blueshifts in terms of a parameter similar to the
line centroid (Section 5.8 in Hamann et al., 2017), the blue wings in the
highest blueshift cases extend beyond 11,000 km s-1. In addition, the changing
appearance of the C iv line profiles as we look from low to high blueshifts
suggests there is a decrease in the emission from material at low velocities,
rather an increase in emission from high-velocity gas.

Overall the spectra show changes in many line strengths, including He ii, with
increasing C iv blueshift. Near to C iv, we can see He ii also gradually
weakening until there is no line emission when C iv is at the its most extreme
blueshift. It is important to note that while He ii and C iv are getting
weaker at large blueshifts, other lines from lower-ion species (C ii], Mg ii,
etc.) stay the same or get slightly stronger. Some lines become weaker
relative to others, such as weaker C iii] $\lambda$1909 relative to Al iii and
Si iii]. Some low ionization lines appear stronger, such as C ii] and Fe
complexes, with increasing C iv blueshift. REW for Mg ii only varies slightly
in comparison to C iv line strength across blueshift velocities, which is also
visible in other low-ionization line strengths.

Low-ionization lines, such as O i and C ii, do not shift in velocity relative
to Mg ii, and appear to agree with the Mg ii emission centroid for systemic
redshift. Any velocity shifts in these lines relative to a true quasar
systemic would not be evident in our data.

Finally, C iv’s asymmetric broadening and weakening is also present in high-
ionization lines, such as Si iv and N v, but less apparent. However, the
magnitude of all of these changes is less than what appears in C iv,
consistent with less participation in a BLR outflow by lower-ionization lines.

Figure 10’s top two panels show the median composite spectra from a single
column from Figure 7, at C iv blueshifts 0 to 500 km s-1and REW 16 to 251 Å.
Both emission profiles of C iv and Mg ii remain symmetric and gradually weaken
along with C iv. All other lines in the spectrum likewise decrease in
strength. Low-ionization lines, and Fe complex, also decrease in strength with
C iv REW, which is not the case when C iv is weak and strongly blueshifted.

Figure 10’s bottom two panels display the same spectral range, but using
composites from specific partitioned boxes in Figure 6, following diagonally
along the bulk of the distribution. This composite shows the same trends seen
in Figure 9 more cleanly. Again, we see the low ionization lines remaining
strong (e.g., Mg ii, C ii, and Fe complex), while other lines weaken with C
iv. Some high ionization lines, like Si iv and N v, blueshift in a similar
asymmetric pattern as C iv’s profile.

###  4.3 Eddington Ratio Dependencies

Eddington ratio shows a nearly uniform correlation with increasing C iv
blueshift. Table 2 shows Eddington ratio in the Composite Sample increases
from 0.08 to 0.14, with larger C iv blueshift.

Figure 11 shows the distribution of Eddington ratios against blueshift for our
BH Mass sample in Table 1, with black hole mass computed using both FWHM and
dispersion methods described in Section 3.3. Using either Mg ii FWHM or
$\sigma_{\text{\mbox{Mg\,{\sc ii}}}}$ to compute $L_{\text{Edd}}$ yields a
similar distribution. We note that the $\sigma_{\text{\mbox{Mg\,{\sc ii}}}}$
has less scatter than the FWHM method. However, most Mg ii profiles were fit
using a single Gaussian, which conversion from FWHM to $\sigma$ is a constant,
and so we choose to use FWHM for our distribution comparisons. Figure 11
illustrates that the method used to measure black hole mass does not have
significant effect on Eddington ratio trends.

Figure 12’s top panel shows log Eddington ratio color-coded across the
distribution of C iv REW versus blueshift. The trend in Eddington Ratio is
stronger, and more coherent, than with Bolometric luminosity seen in Figure 7.
It is evident that the trend in Eddington ratio is not a simple correlation
with C iv blueshift, and that REW is an important third parameter, because the
trend does not strictly follow left to right across the REW and blueshift
distribution.

###  4.4 Color Dependencies & Reddening Corrections

We show distributions of the Color Sample in Table 1, requiring quasar colors
using r and z filters from the SDSS (York et al. 2000; Alam et al. 2015),
and/or $W1$ band from WISE (Wright et al. 2010, Yan et al. 2013), as provided
in the BOSS DR12Q quasar catalogue (see Pâris et al. 2014 and Pâris et al.
2017). r, z, and $W1$ filters fall approximately in the rest wavelengths 1960
Å, 2880 Å, and 1 $\mu$m at our Full Sample median redshift. These colors were
chosen to avoid contamination by the wings of the C iv profile (specifically
in r), especially if it is blueshifted, but still a wide enough sampling of
emission determine a slope of the UV continuum.

Figure 12’s bottom two panels show the Color Sample with C iv REW versus
blueshift, except color coded to $r$–$W1$ and $r$–$z$. These quasar color
panels show the same trend as Eddington ratio, although $W1$ limits the sample
more due to lower sensitivity. These panels show that the color trend is not
simply 2-dimentional with color vs blueshift, seen in Figure 13. Figure 13
presents the distribution of $r$–$z$ and $r$–$W1$ colors compared to
blueshift. $r$–$z$ shows a distribution similar to figures including C iv REW,
with $r$–$z$ decreasing with increasing blueshift. This trend is less strong
in the $r$–$W1$ distribution.

Quasars with smaller $L_{\text{bol}}$ and Eddington ratios are also redder. A
reddening correction could therefore weaken trends we find with
$L_{\text{bol}}$ and Eddington ratio. However, it’s not clear that a
correction is appropriate given that there might be real difference in the SED
unrelated to dust reddening. If we assume these quasars have the same
intrinsic SED, reddening corrections indicated by the color differences would
be quite small. We confirm this within the range of $r$–$z$ values from Figure
12, and the median redshift. Using a typical dust reddening formula (similar
to those used in Richards et al., 2003), we get E(B-V) = 0.105 and extinction
A3000 = 0.57 magnitudes, or a factor of 1.69 flux suppression.

###  4.5 Individual Spectra

Here we present spectra of individual quasars to demonstrate the reality of
the highest blueshift cases and illustrate some of the range in the emission
line properties not evident from the median spectra. Figures 14 \- 16 are sets
of individual spectra of high C iv blueshift quasars for illustration, or
spectra with extreme properties for further discussion, chosen from regions in
the top and bottom panels of Figure 5.

Figure 14 presents individual spectra with a wide range of C iv emission
strengths, and blueshifts >2000 km s-1. Quasars with strong C iv REW and high
blueshift are rare in our sample (see Figure 5). Most quasars with extremely
weak C iv lines have a more uniform distribution of blueshifts, from
$\sim$2000 - 6000 km s-1.

Figure 15 presents spectra with high signal to noise and extreme blueshifts
>4000 km s-1. J094748.06+193920.0, has narrow absorption redshifted near C iv,
and indicates Mg ii is a possible lower limit. J110018.52+314122.5 shows a C
iv mini-BAL, at approximately 1355Å (corresponding to a gas velocity of
$\sim$0.13$c$). J111800.50+195853.4 has a Mg ii profile exhibiting an unusual
blue wing, similar to the other high-ionization lines. J111800.50+195853.4 is
also an example with blue asymmetry in the Mg ii profile. J164250.45+263122.7
is a good SNR spectra with secure C iv blueshifts, and is somewhat “typical”
from these highest blueshifts.

Figure 16 presents all 13 individual spectra with blueshifts >6000 km s-1.
J012505.27+063829.5 is the highest blueshifted case, and in spite of weak C iv
it has a good Mg ii profile measurement, with possible blueshifted S iv as
additional confirmation. J084842.64+540808.2 and J140701.59+190417.9 are 2nd
largest blueshifts, confirmed by multiple weak low-ion lines, and have very
broad and flat C iv profiles. J01410.94+043210.7 has strong line measurements
despite the lack of Si ii/Si iv coverage, and coincidentally is one of the top
ten highest in C iv blueshift. It also has an absorption spike red-ward of C
iv, which could indicate C iv is more blueshifted, and Mg ii may have a blue
wing.

Analysis of these individual quasars confirms the reality of trends in the
extremes of Figure 5, and highlight unique features that could otherwise be
lost by median composite spectra.

##  5 Discussion

Blueshifts observed in the broad emission lines of quasar C iv serve as
valuable indicators of outflows in moderately to highly ionized gas from the
regions emitting these broad lines (see Section 1). We present blueshift
measurements of C iv in a total of 39,249 quasars with redshifts ranging from
1.52 to 2.42, as observed in the SDSS. Our main objective is to gain insights
into the nature and origins of these outflows. This is achieved by studying
the characteristics of the C iv blueshifts and establishing connections
between the blueshifts/outflows and other spectral properties of the quasars.
Constraining outflow speeds necessitates reliable systemic redshifts. Notably,
our approach differs from prior studies as we determine the quasar’s systemic
redshifts exclusively through fitting the low-ionization Mg ii emission line,
which is considered close to systemic redshift of the quasar (e.g. Shen et
al., 2008; Shen et al., 2016b; Li et al., 2017). This method allows us to
explore a unprecedented range of outflow velocities compared to previous work,
reaching blueshifts > 6000 km s-1, and maintain a sample size that is
statistically significant. In this section we will discuss our results for the
full sample, and interesting subsamples.

Broad emission lines offer an important advantage over absorption lines when
studying outflows, because they aren’t confined to gas along the direct line
of sight to the quasar’s emission sources. However, this flexibility also
means that the gas can be moving at various angles relative to our line of
sight, which complicates the relationship between observed blueshifts and
outflow velocities, as it becomes contingent on the specific modeling used.
The blueshifts we measure by analyzing the emission-line centroids only give
us a lower threshold for the actual flow velocities. In situations where there
are exclusively radial motions, and negligible additional sources of line
broadening, the most accurate estimate of outflow velocities comes from the
most pronounced blueshifts in the blue portion of the observed line profiles
(e.g., the $v_{98}$ parameter as employed by Perrotta et al., 2019). By
utilizing the parameters provided in our study, we can approximate the actual
C iv outflow velocities based on the blueshifts of the line centers, plus half
of the measured full width at half maximum (FWHM), while also accounting for
half of the doublet separation in C iv (equivalent to 250 km s-1). For
example, in the high-blueshift quasar J100351+001502 shown in Figure 16, we
could infer that the C iv outflow speed is roughly 6009 + 5296 - 250 $\sim$
11,000 km s-1.

Our composite median spectra reveal consistent trends of weakening He ii with
increasing C iv blueshift (see Figures 9 and 10). We see that high blueshifts
correspond to both weaker C iv strength, broader emission profile, and higher
Eddington ratios (see top panel of Figure 12). We are the first to show that
these trends extend to the most extreme blueshift velocities, which indicate
radiative line-driving may be one of the mechanisms generating extreme
outflows (Leighly & Moore, 2004; Richards et al., 2011; Rankine et al., 2020;
Temple et al., 2023).

Observational evidence strongly supports both of these factors as correlating
with faster outflows. For instance, the inverse correlation between the He ii
$\lambda$1640 emission-line REW and larger C iv emission-line blueshifts
(Leighly & Moore, 2004; Richards et al., 2011; Rankine et al., 2020; Temple et
al., 2023) as well as faster C iv broad absorption-line (BAL) outflows (Baskin
et al., 2013; Hamann et al., 2018; Rankine et al., 2020) indicates the
importance of softer UV spectra in driving outflows. This inverse relation is
also observed in hyper-luminous quasars (Vietri, G. et al., 2018).
Furthermore, larger C iv blueshifts have been found to correlate with higher
Eddington ratios (Baskin & Laor, 2005; Coatman et al., 2016; Rankine et al.,
2020; Temple et al., 2023). Higher Eddington ratios can provide a stronger
radiative driving force relative to gravity. Weak He ii indicates a weaker
far-UV flux, thus a softer UV continuum, and helps maintain moderate
ionization levels and substantial opacities in the outflow to enable radiative
driving in the near-UV (Leighly, 2004).

As C iv REW decreases with blueshift, we see low-ionization lines becoming
stronger, and a trend of weaker C iii] relative to Al iii and Si iii]. There
have been possible models proposed to explain this trend, but higher densities
and/or lower degrees of ionization would decrease C iii] relative to Si iii]
and Al iii (Leighly & Moore, 2004; Leighly, 2004; Richards et al., 2011).

Figure 9: Median composite spectra from the Composite Sample. These spectra
are generated from vertical columns, from Figure 8, defined 500km s-1 in width
from $-$1500 to 6000 km s-1. Color coded in the legend are the number of
spectra used to generate each composite, and their median C iv blueshift. For
more information, see Table 2. Spectra are normalized to unity at $\sim
7000$Å, before taking the median. Spectra included with C iv velocity over
4000 km s-1 are visually confirmed to have similar blueshifted profiles as Si
iv and/or confirmed Mg ii redshift with Si ii. Something straight forward to
correlate is stronger low-ion lines and weaker He ii and C iii]/Al iii at
larger blueshifts.

Figure 10: Median composite spectra from selected regions of Figure 6. The legend presents the number of spectra used for the composite, and median values for luminosity, Eddington Ratio, and C iv REW. Top: Ranges of C iv REW between velocities 0 and 500 km s-1. Each bin is defined moving from 16 to 251Å, using $\sim 0.2$ dex increments. Bottom: Diagonal region across the population as REW decreases and C iv blueshift increases.  Velocity | Total |  $\lambda$$L_{\lambda}$ | Eddington | REW | C iv | Blueshift | FWHM | REW | FWHM | $\sigma$
---|---|---|---|---|---|---|---|---|---|---
Range | Spectra | [ergs s-1] | Ratio | (C iv) | Blueshift | Std. Dev. | (C iv) | (Mg ii) | (Mg ii) | (Mg ii)
|  |  |  | [Å] | [km s-1] | [km s-1] | [km s-1] | [Å] | [km s-1] | [km s-1]
$-$1500 - $-$1000 | 310 | 8.20$\times 10^{45}$ | 0.04 | 60 |  $-$1155 | 132 | 6479 | 38 | 6414 | 2838
$-$1000 - $-$500 | 1009 | 7.87$\times 10^{45}$ | 0.04 | 62 |  $-$680 | 136 | 5767 | 38 | 6112 | 2735
$-$500 - 0 | 4131 | 8.31$\times 10^{45}$ | 0.06 | 61 |  $-$173 | 139 | 4526 | 37 | 5254 | 2448
0 - 500 | 8591 | 8.65$\times 10^{45}$ | 0.08 | 52 | 259 | 143 | 4335 | 35 | 4776 | 2243
500 - 1000 | 7801 | 9.05$\times 10^{45}$ | 0.08 | 41 | 729 | 142 | 4927 | 33 | 4659 | 2155
1000 - 1500 | 4339 | 9.48$\times 10^{45}$ | 0.09 | 34 | 1205 | 142 | 5473 | 31 | 4425 | 2072
1500 - 2000 | 1791 | 1.00$\times 10^{46}$ | 0.10 | 30 | 1693 | 138 | 5967 | 28 | 4161 | 1970
2000 - 2500 | 719 | 9.63$\times 10^{45}$ | 0.12 | 27 | 2182 | 143 | 6257 | 26 | 3822 | 1843
2500 - 3000 | 336 | 1.04$\times 10^{46}$ | 0.13 | 23 | 2668 | 142 | 6685 | 25 | 3781 | 1789
3000 - 3500 | 179 | 1.00$\times 10^{46}$ | 0.13 | 20 | 3216 | 146 | 7447 | 24 | 3680 | 1769
3500 - 4000 | 97 | 9.34$\times 10^{45}$ | 0.14 | 18 | 3729 | 148 | 8087 | 23 | 3686 | 1725
4000 - 5000 | 121 | 9.86$\times 10^{45}$ | 0.12 | 14 | 4374 | 274 | 8951 | 24 | 3908 | 1860
5000 - 6000 | 36 | 8.86$\times 10^{45}$ | 0.11 | 10 | 5260 | 295 | 9436 | 21 | 4018 | 1942
$-$1500 - 6000 | 29460 | 8.94$\times 10^{45}$ | 0.08 | 43 | 538 | 804 | 5048 | 33 | 4682 | 2195
Table 2: Median line properties at different velocity bins of the Composite
Sample in Table 1, with a limited luminosity range. These bins correspond to
the spectra in Figure 9 & the top panel of Figure 10. Medians were taken of
the distribution of values in each bin.

###  5.1 Eddington Ratio & Color Distributions

Figure 12 displays several trends which reveal complexities to our goal of
finding what drives powerful outflows. We find larger Eddington ratios also
correlates with increasing blueshift (bottom panel of Figure 12, and also
indicated in Baskin & Laor, 2005; Coatman et al., 2016; Rankine et al., 2020;
Temple et al., 2023). When the luminosity of the quasar is near to
$L_{\text{Edd}}$, and the gravitational force from the SMBH is nearly
balanced, it becomes easier to drive an outflow. Eddington ratio may therefore
be an important factor in allowing an ensemble of conditions (e.g., high
luminosity, continuum shape) to take maximum affect.

C iv blueshift is more strongely correlated to Eddington ratio than
$L_{\text{bol}}$. This correlation is evident in comparing Figure 12 to 7, and
from our composites contributing to Figure 9, where we find a strong trend
with Eddington ratio after sorting by blueshift at roughly fixed
$L_{\text{bol}}$ (see Table 2).

Larger Eddington Ratio and softer far-UV spectra are probably the fundamental
physical drivers behind faster, more powerful BLR outflows, and both appear to
correlate with larger blueshifts in out data. While different combinations of
these factors might produce the observed blueshifts in different individual
quasars, the overall trends evident from our composite samples (Figure 9 and
Table 2) suggests that both larger Eddington ratio and softer far-UV spectra
are involved in producing the largest blueshifts.

We confirmed any reddening that could change the Eddington ratios in Figure 12
may be influenced by about A3000 = 0.57 magnitudes extinction, or a factor of
1.69 flux suppression. The effect on Eddington ratios will go as the square-
root of that, a factor of 1.30 or 0.11 in log. Comparing that to the bottom
panel in Figure 12 shows that performing a reddening correction as above would
weaken the trend but not undo it. This is a maximal correction, because the
0.3 color difference is generous. More importantly, we assumed all of the
color difference is due to dust reddening instead of intrinsic color
differences in the quasars that might be related to outflows/blueshifts. A
reddening correction, if warranted, does not undo these trends. Additional
correlations with SED shape can also influence outflow velocities (Richards et
al., 2011; Baskin et al., 2013).

We see trends in UV color (see Figures 13 and 12), showing that bluer color
across the UV to Near-IR correlates with blueshift out to extreme velocities.
It has been shown that extreme reddening across UV to IR can also correlate
with extreme blueshifts/outflows Perrotta et al. (2019). The “less luminous”
quasars are redder. In fact, their luminosities are underestimated because of
reddening, and the Baldwin Effect is at least partly a reddening trend, and
luminosity. Color as measured by spectral index, or broadband color, have
indicated slight asymmetric blueshifts in C iv correlated with bluer colors
(Richards et al., 2003; Leighly & Moore, 2004; Gallagher et al., 2005;
Richards et al., 2011).

Quasars can have intrinsically red UV continuum without involving dust.
Quasars defined by a steep optical-continuum, which are intrinsically red
without dust reddening, have been seen to have stronger C iv, C iii], and He
ii emission (Richards et al., 2003). Redder colors can also be attributed to
more extinction/reddening along inclined viewing angles in (Baskin et al.,
2013), but they do not see a color trend for higher BAL speeds, which should
correlate with inclination angle. Emission line blueshifts should have weaker
dependence on viewing angle because they sample material moving in all
directions, not serendipitous absorption along line of sight. Small
differences in reddening could be small differences in viewing angle,
therefore extremely small changes in cos($\theta$) factor affecting the
measured blueshifts. A more detailed analysis would require specific models
for the dust and outflow geometries around quasars, but is beyond the scope of
this work. We note that the trends seen in Figures 13 and 12 could be due
mostly, or entirely, to intrinsic color differences in the quasar SEDs.

Trends with Eddington ratio and color both appear along the curved diagonals
(upper left to lower right) in Figure 12 illustrate how C iv blueshift, and
thus outflow speed, is a multi-dimensional problem. This complexity is not
evident from simpler 2-parameter plots like Figures 11 and 13. Blueshifts
depend simultaneously on several quasar observables, including the C iv REW
and near-UV continuum color, in addition to the more fundamental physical
drivers like Eddington ratio and far-UV spectral shape (indicated by He ii).
These parameters might be connected to each other in different ways. For
example, photoionization models of quasar BLRs have shown that softer ionizing
spectra naturally produce smaller emission-line REWs (Korista et al., 1997,
1998), and might explain why these parameters are both related to larger
blueshifts. However, more work is needed to understand if softer ionizing
spectra are sufficient, or even necessary, to explain the strong observed
trend between C iv REW and blueshift. Another possibility is that the observed
near-UV colors are tied to reddening by dust along our line of sight and
perhaps our viewing perspective of the accretion disc and outflow environment
(Richards et al., 2002).

Overall, an interesting result that is revealed by our color coded
“3-dimentional” parameter space of C iv REW vs blueshift is that they show
trends better than the 2D scatter plots. This reveals that the blueshifts are
a multi-dimensional/multi-parameter problem. Future studies may look for where
large blueshifts cluster in a multi-dimensional parameter space to determine
their fundamental causes.

Figure 11: Distribution of C iv Blueshift vs Eddington ratio using $\sigma$ or
FWHM of Mg ii for computing $L_{\text{Edd}}$. Top: Eddington ratio computed
with FWHM of Mg ii. Bottom: Eddington ratio computed with $\sigma$ Mg ii.
Eddington luminosity computed using $\sigma$ shows a narrower distribution
than with FWHM.

Figure 12: REW(C iv) vs C iv velocity shift with the same regions as in Figure
7, color coded for various parameters within the respective region. Top: color
coded for median Eddington ratio from the BH Mass sample of Table 1. Middle:
color coded with median $r$–$W1$from spectra that have $W1$ detection (see
Color Sample in Table 1). Bottom: color coded for $r$–$z$.

Figure 13: C iv velocity shift vs color cuts for quasars with $r$,$z$, and/or
$W1$ detections. Top: Blueshift vs ($r$–$z$) color in our sample with $r$ and
$z$ mag data. Bottom: Blueshift vs ($r$–$W1$) color in our $W1$-detected
quasars.

###  5.2 Individual Spectra

Broad studies of large quasar populations seldom present rare and interesting
cases such as spectra with the most extreme properties. We present individual
spectra to convey two points. i) demonstrate the reality of the most extreme
cases with blueshifts >6000 km s-1. Our composite figures only consider
blueshifts <5000 km s-1 because there are too few to construct meaningful
medians, and the wide range in blueshifts would blend the C iv profile. ii)
display well-measured and interesting spectra at large blueshift. For example,
spectra with extreme properties of C iv like large REW, and cases of a strong
blue wing in Mg ii, that may not be evident from composite spectra.

A surprising feature in many high-blueshift spectra is a peculiar narrow
absorption spike at rest wavelengths of C iv. This absorption feature is not
typical in quasars with average broad and symmetric C iv profiles, and is
smoothed out of median composite spectra. Five of our top 13 fastest-blueshift
spectra have this narrow absorption feature (e.g., J012505.7+063829.5,
J014010.94+043210.7, and J105208.27+151004.0). This absorption feature is
commonly seen in spectra with blueshifts >4000 km s-1, and also high signal to
noise spectra when C iv is broad and blueshifted (see Figure 16). An origin of
this absorption spike is not immediately clear. One hypothesized explanation
is a viewing perspective effect of the accretion disk and BLR, which forms a
narrow associated absorption-line system at systemic redshift (Richards et
al., 2021).

Another unexpected result is blueshifted wings in Mg ii profiles. Outflows
occur only, or primarily, in the high-ionization lines of the BLR. Blueshifted
wings are typically observed in these high-ionization line profiles, not low-
ions, and is a key feature in using low-ionization lines for indicating
systemic redshift. An occasional, weak blue wing in Mg ii is seen in spectra
with the most blueshifted C iv, and indicates that a component of even the
low-ion gas is involved in fast outflows. J01410.94+043210.7 has strong line
measurements that show a blue excess in the Mg ii profile, and also contains a
C iv absorption spike at a slightly redshifted wavelength, which could also
indicate our blueshift velocity is a lower limit. There is a similar scenario
in J094748.06+193920.0. It has been speculated that low-ionization broad-lines
could also be involved in outflows under extreme conditions (Hamann et al.,
2017; Gillette et al., 2023). These blueshifted wings may have consequences
for Mg ii mass estimates of the SMBH, or for other measurements that assume
the broad-lines are virialized (Shen et al., 2016a; Shen et al., 2016b;
Coatman et al., 2016; Shen et al., 2019; Rankine et al., 2020; Temple et al.,
2023). Future studies may constrain velocities for these extremely blueshifted
outflows, perhaps with non-UV emission lines.

Figure 14: Spectra with varied C iv REW, and large blueshifts (>2000 km s-1).
Black is spectral data, green is the error spectrum, the orange curves are
fitted power laws to the local continuum of C iv or Mg ii, and dark blue curve
is the broadened Fe ii template near Mg ii. Magenta are the full C iv and N v
profile fits (from Hamann et al., 2017), or the Mg ii profile fits from this
work. Cyan curves are the two Gaussian components used when necessary to fit
the Mg ii profile. Figure 15: Selected spectra with high signal to noise, and
blueshifted >4000 km s-1, using the same color scheme as the spectra above.
Figure 16: Selected spectra with highest C iv blueshifts > $\sim$6000 km s-1,
using the same color scheme as the spectra above.

Figure 17: continued

.

Figure 18: continued

.

##  6 Summary

We present a sample of 39,249 quasars with improved redshift estimates to
constrain outflows at extreme speeds, to understand the factors driving
outflows across a wide range of velocities. We focus on the blueshift
velocities of C iv emission, relative to Mg ii, and comparing them with other
spectral properties.

This study differs from previous work by determining redshifts solely from the
Mg ii line, allowing us to explore an unprecedented range of outflow
velocities and maintain a statistically significant sample size. We identify
two primary factors contributing to stronger outflows: higher Eddington
ratios, which provide a stronger radiative driving force relative to gravity,
and a softer far-UV continuum, where weaker far-UV flux helps maintain
moderate ionization levels and substantial opacities in the outflow.

Our analysis reveals consistent trends, such as the weakening of He ii
emission with increasing C iv blueshift. High blueshifts correspond to weaker
C iv strength and broader emission profiles. This study suggests that
radiative line-driving may be a mechanism generating extreme outflows. As the
C iv rest equivalent width (REW) decreases with blueshift, low-ionization
lines become stronger, and there is a trend of weaker C iii] relative to Al
iii and Si iii]. A possible explanations for this trend is higher densities,
and/or lower degrees of ionization, at farther BLR distances.

We also find a correlation between larger Eddington ratios and increasing
blueshift, and discuss the potential influence of reddening on the Eddington
ratios but note that a reddening correction would not undo the observed
trends.

Additionally, correlations with SED shape and color are explored. Asymmetric
blueshifts in C iv are correlated with bluer continuum colors in the UV,
particularly in less luminous quasars. Quasars can have intrinsically redder
SEDs without involving dust, and the trends observed in continuum shape and
reddening may be attributed to intrinsic color differences in the quasar SEDs.

Finally we look at individual spectra with extreme characteristics in their C
iv emission profiles. We confirm the reality of trends measured across the
breadth of C iv parameter space, including line strength, profile width, and
blueshift.

Our analysis suggests that the relationship between C iv REW and blueshift is
better understood in a multi-dimensional parameter space rather than through
2D scatter plots, indicating that blueshifts are influenced by multiple
factors. We propose that future studies should investigate where large
blueshifts cluster in multi-dimensional parameter space to determine the
fundamental causes.

## Acknowledgements

JG and FH acknowledge support from the USA National Science Foundation grant
AST-1911066. JG thanks G. Richards for insightful discussion, and Y. Shen for
providing emission templates in personal correspondence.

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