# Evaluating a bot detection model
on git commit messages ††thanks: This research is supported by the joint FNRS
/ FWO Excellence of Science project SECO-ASSIST and FNRS PDR T.0017.18.

Mehdi Golzadeh  Software Engineering Lab
University of Mons, Belgium
<EMAIL_ADDRESS>Alexandre Decan  Software Engineering Lab
University of Mons, Belgium
<EMAIL_ADDRESS>Tom Mens  Software Engineering Lab
University of Mons, Belgium
<EMAIL_ADDRESS>
###### Abstract

Detecting the presence of bots in distributed software development activity is
very important in order to prevent bias in large-scale socio-technical
empirical analyses. In previous work, we proposed a classification model to
detect bots in GitHub repositories based on the pull request and issue
comments of GitHub accounts. The current study generalises the approach to git
contributors based on their commit messages. We train and evaluate the
classification model on a large dataset of 6,922 git contributors. The
original model based on pull request and issue comments obtained a precision
of 0.77 on this dataset. Retraining the classification model on git commit
messages increased the precision to 0.80. As a proof-of-concept, we
implemented this model in BoDeGiC, an open source command-line tool to detect
bots in git repositories.

###### Index Terms:

bot detection, distributed software development, classification model,
empirical analysis

††publicationid: pubid: Copyright 2020 for this paper by its authors. Use
permitted under Creative Commons License Attribution 4.0 International (CC BY
4.0).

##  I Introduction

Many open source software projects rely on development bots or DevBots
(hereafter referred to as bots for short) to reduce the workload of project
maintainers and contributors [1]. These bots play a prominent role in the
software development process, especially in online coding platforms. Bots
submit pull requests (PR) to update dependencies [2], merge PRs [3], submit
issues for different problems [3], help in code review [4], and commit code
directly to the codebase [5]. Some studies propose new bots [6, 7, 8, 9, 10,
11], while other studies aim to help developers analysing the adoption of
existing bots [4, 12, 13].

The presence of bots might introduce bias in large-scale socio-technical
empirical studies, especially if these bots are very active. To prevent such
bias it is important to distinguish human activity from bot activity in
software development projects. While it is fairly easy for project members to
recognise bots in their projects (since they can rely on their project-
specific knowledge and experience), this is not necessarily the case for
researchers, especially when they are carrying out large-scale ecosystem-level
studies involving hundreds of thousands of distinct projects and accounts.

Previous studies have proposed methods to automatically identify bots by
taking into account specific bot characteristics. Dey et al. [5] proposed an
ensemble technique to identify bots relying on git commit information such as
commit messages, contributors name, and commit files. In a prior study [14],
we proposed an automatic classification model to identify bots in git
repositories hosted in GitHub based on the content of PR and issue comments.

This paper aims to evaluate the generalisability of the classification model
we proposed in [14] by applying it to git commit messages. To do so, we
evaluate the model on a set of 6,922 contributors extracted from the dataset
provided by Dey et al. [5]. As will be shown, our classification model is able
to attain a good precision, even if it was trained on PR and issue comments
rather than on git commit messages. Retraining the classifier specifically on
git commit messages slightly improves its precision. To ease the use of our
model by practitioners and researchers, we propose BoDeGiC, a command-line
tool to detect bots in git repositories.

##  II Background

In our previous work [14], we developed and proposed a classification model
and associated tool, called BoDeGHa111https://github.com/mehdigolzadeh/BoDeGHa
to identify bots in GitHub repositories based on the comments they made in PRs
and issues. To train and evaluate this model, we created a ground-truth
dataset of GitHub contributors that were manually labeled as bots and humans
by three raters. The evaluation of the model on the test set achieved a very
high overall accuracy.

In parallel to our prior research, Dey et al. [5] conducted a similar study
aiming to identify bots in git repositories based on git commit data. They
created a ground-truth dataset based on the World of Code (WoC) dataset [15]
containing 73M git repositories. Their ground-truth dataset is composed of
13,150 bots and 13,150 humans that were identified using BIN (for Bot
Identification by Name), a technique relying on the presence of some keywords
(e.g., “bot”) to identify bots. Based on this ground-truth dataset, they
proposed BIMAN (for Bot Identification by commit Message, commit Association,
and contributor Name) to detect bots based on commit activities.

Although both aforementioned studies pursue the same goal, they are different
in essence. The most prominent difference is the type of data on the basis of
which bots are being identified. PR and issue comments are messages that are
being used to explain or discuss issues or PRs. Such comments are not limited
in size, in contrast to commit messages that aim to provide one-liners that
summarise the changes made in a commit. In [14] we identified bots based on PR
and issue comments, while BIMAN relies on git commit information to
distinguish bots from humans. As a consequence, the set of contributors
considered in both cases is different, since contributors active in PR or
issue comments are not necessarily active in code commits, and vice versa.
Another difference is that we restricted our dataset to contributors active in
GitHub while BIMAN works on all types of git repositories, even if they are
not hosted on GitHub. Moreover, when a contributor is active in more than one
repository, we considered each repository individually while BIMAN aggregates
the activity from multiple repositories for each contributor.

##  III Method and approach

###  III-A Initial classification model

In prior work [14], we proposed an approach to distinguish bots from humans
based on their PR and issue commenting activities in GitHub repositories. We
developed a model (and associated command-line tool) with a high precision to
predict whether a contributor is a bot or human based on the comments made in
issues and PRs. The underlying idea was that bots perform automated tasks,
therefore, they are assumed to have more repetitive comments than humans. To
capture this repetition of comments the model was trained using four features
related to the comments associated to a contributor:  (i) we measured the
number of comment patterns on the basis of a compound comment similarity
metric. We hypothesized that the less comment patterns a contributor has, the
more likely that contributor is a bot;  (ii) we computed the Gini coefficient
to capture the inequality of the number of comments in patterns;  (iii) we
counted the number of comments since it allows to distinguish between
contributors having a similar number of comment patterns;  (iv) and we counted
the number of empty comments, driven by the assumption that bots are supposed
to have meaningful non-empty messages.  We refer to [14] for the rationale
behind these features and how we computed them.

To evaluate the performance of the model, we relied on a ground-truth dataset
composed of 5,000 distinct GitHub contributors. To create such a ground-truth
dataset, we manually labeled each contributor as bot or human with high inter-
rater agreement. The final dataset contains 527 bots and 4,473 humans. We
trained and compared various classification models, and achieved the highest
results ($F1$-score = 0.98) with a random forest classifier. Not only does the
model perform well in general, it also achieves high precision and recall for
both classes: bots achieved a precision 0.94, a recall of 0.94 and $F1$ of
0.92, and humans achieved a precision of 0.99, recall of 0.99 and $F1$ of
0.99. Only 19 out of 211 bots and 13 out of 1,789 humans were misclassified by
the model.

Our previous model performed very well to identify bots based on the
repetitiveness of their comments, a text-based activity. Since git commit
messages are also text-based, and since we can expect that bots active in
commits exhibit a similar kind of behaviour, it seems promising to apply our
model on git commit messages as well.

In this paper, we will first evaluate how our model (trained on PR and issue
comments) performs when applied as-is to git commit messages. Then, we will
evaluate the approach we developed in [14] applied on git commit messages, by
training a new model. To do so, we need a labeled dataset of contributors and
their commit messages. We rely on the dataset of git commits that was used in
[5] and has been made publicly available.222https://zenodo.org/record/4042126

We transformed the dataset to conform to the input format required by our
classification model. First of all, as explained in previous section, our
model expects a set of features related to comments of a contributor in a
specific repository. Therefore, if a contributor is active in more than one
repository, we split its activity by repository. Our approach being based on
the assumption that bots exhibit more repetitive activities, it cannot be
applied for contributors that do not have enough activities. In [16], we
observed that the performance of the model decreased when the number of
comments was below 10. Similarly, in this work, we will only consider
contributors that have at least 10 commit messages. As in previous work, we
rely on 100 commit messages to compute the set of features. This upper bound
significantly reduces the computational cost, and has been shown to be more
than sufficient to achieve a very high precision in [14]. Not imposing an
upper bound would require to consider all commits for each contributor-
repository pair, and some pairs have more than 20,000 commit messages. Even
for pairs with over 1,000 commit messages the performance begins to slow down
considerably.

After having performed these steps, the resulting dataset contains 311,622
commit messages from 6,922 contributors, 3,380 whom have been labeled as bots
and 3,542 as humans. This accounts for around 25% of the original dataset. The
dataset characteristics are summarized in Table I.

TABLE I: Summary of the dataset characteristics. original commit dataset from [5] | number
---|---
# git repositories | 6,394
# commits | 311,622
# distinct contributors | 6,922
$\hookrightarrow$ # bots | 3,380
$\hookrightarrow$ # humans | 3,542

In this section, we will first evaluate how the classification model trained
on PR and issue comments performs when applied as-is to git commit messages.
Then, we will evaluate how the approach developed in [14] applies to git
commit messages, by training a new classification model.

We start by applying the existing model to see how it performs when applied on
a new kind of data (i.e., on git commit messages). For each of the 6,922
contributors in the dataset, we computed the features required by the model,
and we asked the model to predict whether the contributor is a bot or a human.
We then compared the prediction with the ground-truth, enabling us to compute
the precision $P$ of the model, its recall $R$ and its $F1$-score. The results
are reported in Table II.

TABLE II: Evaluation of the classification model of [14]. | classified | classified | P | R | F1
---|---|---|---|---|---
| as bot | as human |  |  |
Bot | 2,631 (TP) | 749 (FN) | 0.76 | 0.78 | 0.77
Human | 848 (FP) | 2,694 (TN) | 0.78 | 0.76 | 0.77
weighted avg |  |  | 0.77 | 0.77 | 0.77

The model achieved a precision of 0.77, with about 22.1% (749 out of 3,380)
false negatives (FN) of bots misclassified as humans, and about 23.9% (848 out
of 3,542) false positives (FP) of humans misclassified as bots. Most
contributors are correctly classified as bot or human by the existing model
even if it was not trained on git commit messages but on PR and issue
comments. A possible explanation for this result is that even though the model
was originally trained on issue and PR comments, it mostly captures the
repetitive nature of tasks. Therefore, it shouldn’t be that surprising that it
also works on commit messages, where we can also expect bots to have
repetitive behaviour.

To see how the approach developed in [14] behaves on git commit messages, we
trained a new model on git commit messages as opposed to the previous model
that was trained on PR and issue comments. To do so, we divided the ground-
truth dataset into two disjoint subsets. 60% of the data are used to perform
grid-search cross-validation to select the best classifier and its parameters.
A test set composed of the remaining 40% is used to evaluate the selected
classifier on unseen data. At the end of the cross-validation set, we obtained
91 different classifiers. The performance of these classifiers was measured
using traditional performance metrics of precision $P$, recall $R$, and
$F1$-score for the population of each class (i.e., for bots $B$ and human
$H$). We report the highest $F1$-score for each classifier in Table III, in
descending order. We retained the random forest (RF) classifier, as it
slightly outperforms the other classifiers. Its score was obtained with the
_entropy_ split criterion, 20 estimators (i.e., trees) and a tree depth of 8.

TABLE III: Precision, recall and $F1$ of the best-performing classifiers per classifier family (in descending order of $F1$). | bots | humans | overall
---|---|---|---
classifier family | $P(B)$ | $R(B)$ | $P(H)$ | $R(H)$ | $P(B\cup H)$ | $R(B\cup H)$ | $F1(B\cup H)$
random forest (RF) | 0.817 | 0.748 | 0.775 | 0.837 | 0.817 | 0.748 | 0.793
decision trees | 0.845 | 0.698 | 0.750 | 0.876 | 0.845 | 0.698 | 0.787
support vector machine | 0.798 | 0.735 | 0.762 | 0.819 | 0.798 | 0.735 | 0.777
logistic regression | 0.807 | 0.720 | 0.755 | 0.832 | 0.807 | 0.720 | 0.776
k-nearest neighbours | 0.831 | 0.653 | 0.722 | 0.872 | 0.831 | 0.653 | 0.761

We evaluated the selected classifier on the test set containing the remaining
40% data. This test set includes 2,769 identities, of which 1,417 correspond
to humans and 1,352 correspond to bots. The evaluation results are reported in
Table IV. With this retrained model about 24.6% of bots (333 out of 1,352) are
misclassified as humans (FN), and about 15.9% of humans (226 out of 1,417) are
misclassified as bots (FP). Compared to the previous model, the model trained
on commit messages detects humans more accurately, while the converse can be
observed for bots. With a value of $0.80$, the precision of the retrained
model is slightly higher than the previous one.

TABLE IV: Evaluation of the retrained classification model. | classified | classified | P | R | F1
---|---|---|---|---|---
| as bot | as human |  |  |
Bot | 1,019 (TP) | 226 (FP) | 0.82 | 0.75 | 0.78
Human | 333 (FN) | 1,191 (TN) | 0.78 | 0.84 | 0.81
weighted avg |  |  | 0.80 | 0.80 | 0.80

##  IV A Bot Detector Tool for git repositories

In order to enable practitioners to use the classification model, we
implemented it through BoDeGiC (Bot Detector for Git
Commits)333https://github.com/mehdigolzadeh/BoDeGiC, a command-line tool to
detect bots in given git repositories. The tool analyses the commit messages
of each contributor in the specified git repositories and predicts whether the
contributor is a bot or a human. BoDeGiC is implemented in Python 3.7 and is
easily installable through pip, the official package manager for Python.

BoDeGiC works in three steps. The first step consists of extracting all commit
information from the specified git repository using git log. This step results
in a list of commits, authors and their corresponding commit messages. The
second step consists of computing the features to feed the classification
model. Features consists of the total number of messages, the number of empty
messages, the number of message patterns and the inequality between the number
of messages within patterns. In the third step, we apply the classifier that
was trained on commit messages to the extracted data. The tool outputs the
prediction made by the model for each contributor.

Listing 1: List of command-line arguments for BoDeGiC 0.2.0.

⬇

$ bodegic -h

usage: bodegic [-h] [--include [NAME [NAME ...]]]

[--start-date START_DATE][--mapping [MAPPING]]

[--verbose] [--min-commits MIN_COMMITS][--committer]

[--max-commits MAX_COMMITS][--text | \--csv | \--json]

[REPOSITORY [REPOSITORY ...]][--only-predicted]

The command-line interface of BoDeGiC is summarized in Listing 1. The output
and the behaviour of BoDeGiC can be adapted by many optional command-line
arguments in several different ways. By default, BoDeGiC relies on the author
names in git commits, but the committer names can be used instead by
specifying \--committer. The list of names to consider can be explicitly
specified with \--include. BoDeGiC also supports identity merging (i.e., when
a contributor uses multiple names) through the \--mapping parameter. This
parameter expects a path to a CSV file specifying how to map names to
identities. This file can also be used to ignore specific names, by mapping
them to the special “IGNORE” identity. Since the model (and by extension, the
tool) requires at least 10 commits for a contributor to generate a prediction,
contributors that have commits less than this number are predicted as
“Unknown”. These cases can be excluded from the output by means of the
\--only-predicted parameter. Additionally, The minimum and maximum number of
commits to consider can be changed respectively with \--min-commits and
\--max-commits. By default, BoDeGiC outputs one line per author with the
predicted class. The set of computed features can be included in this output
by adding the \--verbose parameter. Finally, the output of BoDeGiC can be
exported in text (by default) or in JSON or as a CSV.

Fig. 1 presents the output of BoDeGiC on a randomly chosen git repository that
was analysed on 2020-10-14. The first columns shows the contributor name, the
second column the number of extracted commit messages, the third column the
number of computed message patterns, and the fourth column the statistical
dispersion of the number of comments per pattern as computed by the Gini
inequality index. The last column provides the predicted class of each
contributor.

Figure 1: Example of running BoDeGiC (version 0.2.0).

The main threats to validity and mitigation strategies mentioned in our prior
work [14] also apply to the current study.

A distinct threat to construct validity stems from the ground-truth dataset
that has been used to train and evaluate the models. The dataset was created
by other researchers and we have assumed it was correctly built and validated.
Any presence of mislabeled items in that dataset could negatively affect the
results of applying our original classification model (i.e., that was trained
on PR and issue comments) as well as the retrained model that was directly
trained on this dataset.

In order to assess to what extent this threat holds, we selected a subset of
contributors from the dataset and manually verified whether they are actually
humans or bots. We randomly selected 25 contributors from each category of
correctly and incorrectly classified contributors (i.e., from TP, TN, FP and
FN). Each of these cases was independently evaluated and labeled by the three
authors of this paper. At the end of this process, we compared the labelings
and observed agreement on all 100 cases. We then compared our own labelings
with the actual labels found in the dataset, and observed a disagreement for
19 out of 100 cases. Among these cases, 13 corresponded to bots and 6 to human
contributors. The prediction made by our classification model for these 19
cases matched our own labeling, i.e., the model was able to correctly predict
them.

While manually looking at some other contributors in the dataset, we
encountered a few cases we could not agree on because they combine both bot-
like and human-like behaviours. We already encountered such “mixed”
contributors in our previous study [14] where we found that some contributors
were occasionally relying on tools or bots to automate part of their
activities. The presence of such mixed cases in git commit messages reinforces
our belief that a better definition of “what a bot is” is required, with a
clearer boundary between humans and bots. We also believe, in view of these
mixed cases, that it might be interesting to identify bots not at the level of
a contributor but at the level of its activity. In other words, the question
“Is this contributor a bot?” would become ”Is this contributor activity
produced by a bot?”.

##  V Conclusion

In prior work [14] we proposed a classification model to predict bots based on
features extracted from the PR and issue comments of GitHub accounts. The
motivation behind the model was that bots tend to carry out repetitive tasks,
implying that they are more likely to use repetitive messages. In this paper,
we evaluated to which extent this approach performs on git commit messages,
another text-based activity for which we expect bots to exhibit a similar
repetitive behaviour.

We first evaluated how the model that we developed and trained on PR and issue
comments in GitHub repositories performs on this new type of data. We then
generalised the classification model by retraining it on a ground-truth
dataset composed of commit messages for 6,922 git contributors. We found that
the highest precision was achieved by a random forest classifier, improving
the precision of the previous model by 3% to $0.80$.

We implemented BoDeGiC, a command-line tool to enable practitioners to take
advantage of this classification model. It analyzes the commit messages of a
git repository and predicts whether the contributors are bots or humans.

Although promising, the obtained results suggest that, to achieve a precision
comparable to the one we obtained for GitHub PR and issue comments, it will be
necessary to use other data and features in complement to git commit messages.
This is reminiscent of the BIMAN approach [5] which, in addition to analysing
commit messages (the BIM part of BIMAN) combines two other independent models
based on the contributor names (BIN) and features related to files and
projects associated with the commits (BICA). Given that our model is able to
accurately capture more bots (+8%) than BIM, it would be interesting to
evaluate how the BIMAN approach would improve by substituting BIM by our
classification model.

## References

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  * [3] Mairieli Wessel, Bruno Mendes De Souza, Igor Steinmacher, Igor S. Wiese, Ivanilton Polato, Ana Paula Chaves, and Marco A. Gerosa.  The power of bots: Understanding bots in OSS projects.  The ACM on Human-Computer Interaction, 2018.
  * [4] Mairieli Wessel, Alexander Serebrenik, Igor Wiese, Igor Steinmacher, and Marco Aurelio Gerosa.  Effects of Adopting Code Review Bots on Pull Requests to OSS Projects.  2020\.
  * [5] Tapajit Dey, Sara Mousavi, Eduardo Ponce, Tanner Fry, Bogdan Vasilescu, Anna Filipova, and Audris Mockus.  Detecting and characterizing bots that commit code.  In Int’l Conf. Mining Software Repositories, 2020.
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# Search for LBVs in the Local Volume galaxies: study of four stars in NGC
4449

Y. Solovyeva,1 A. Vinokurov,1 A. Sarkisyan,1 A. Kostenkov,1,2 K. Atapin,3 S.
Fabrika 1,4 D. Oparin,1 A. Valeev,1,5 D. Bizyaev,3,6 P. Nedialkov7 and O.
Spiridonova1
1Special Astrophysical Observatory, Nizhnij Arkhyz, Russia
2Mathematics&Mechanics Faculty, Saint Petersburg State University, 7/9
Universitetskaya Emb., Saint Petersburg 199034, Russia
3Sternberg Astronomical Institute, Lomonosov Moscow State University,
Universitetskij Pr. 13, Moscow 119992, Russia
4Institute of Physics, Kazan Federal University, Kremlevskaya 18, 420008
Kazan, Russia
5Crimean Astrophysical Observatory, Russian Academy of Sciences, Nauchnyi
298409, Russia
6Apache Point Observatory and New Mexico State University, Sunspot, NM 88349,
USA
7Department of astronomy, Sofia University, Sofia 1164, Bulgaria
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We continue to search for LBV stars in galaxies outside the Local Group. In
this work, we have investigated four luminous stars in NGC 4449. Multiple
spectral observations carried out for J122810.94+440540.6,
J122811.70+440550.9, and J122809.72+440514.8 revealed the emission features in
their spectra that are characteristic of LBVs. Photometry showed noticeable
brightness changes of J122809.72+440514.8 ($\Delta I=0.69\pm 0.13^{m}$) and
J122817.83+440630.8 ($\Delta R=2.15\pm 0.13^{m}$), while the variability of
J122810.94+440540.6 and J122811.70+440550.9 does not exceed $0.3^{m}$
regardless of the filter. We have obtained estimates of the interstellar
reddening, photosphere temperatures, and bolometric luminosities
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})\approx 5.24-6.42$. Using the
CMFGEN code, we have modelled the spectrum of the cold state of
J122809.72+440514.8 ($T_{\text{eff}}=9300\,$K) and have obtained possible
value of the mass loss rate $\dot{M}=5.2\times 10^{-3}\,M_{\odot}\,yr^{-1}$.
Based on the observational properties, J122809.72+440514.8 and
J122817.83+440630.8 were classified as LBVs, while the other two stars were
classified as LBV candidates or B[e]-supergiants candidates.

###### keywords:

stars: emission lines, Be – stars: variables: S Doradus – stars: massive –
galaxies: individual: NGC 4449

††pubyear: 2021††pagerange: Search for LBVs in the Local Volume galaxies:
study of four stars in NGC 4449–Search for LBVs in the Local Volume galaxies:
study of four stars in NGC 4449

##  1 Introduction

Luminous blue variables are the massive ($M\geq 25M\odot$, Humphreys et al.
2016) stars with high luminosity ($\gtrsim 10^{5}L_{\odot}$), characterized by
significant spectral and photometric variability.

A characteristic feature of many LBV stars is the S Dor-type variability (van
Genderen, 2001). During this cycle, both photometric and spectral variability
are observed. The brightness variation amplitude in the V band can reach 2.5
magnitudes, with the cold state of the star corresponding to maximum
brightness, and the hotter state to minimum. Spectra of LBVs are similar to
those of the A-F supergiants, hot B supergiants, or Of/late–WN stars depending
on the photosphere temperature (Vink, 2012; Humphreys & Davidson, 1994). A
luminous star exhibiting the described variability can be unambiguously
classified as an LBV in the S Dor cycle. In addition, some LBV stars
experience dramatic brightness changes in the form of giant eruptions of more
than $2.5^{m}$. This type of brightness change is $\eta$-Car variability
(Humphreys et al., 1999). An important feature of the spectral energy
distribution of LBVs is the absence of an IR excess associated with the
emission of hot dust (Humphreys et al., 2014b).

The evolutionary status of LBVs remains poorly known. In the accepted view
they correspond to the transitional phase from single massive O-stars to the
Wolf-Rayet stars(Groh et al., 2014). Some studies have shown that rotating
LBVs with initial masses of 20-25 M⊙ can evolve directly into the core-
collapse supernovae bypassing the Wolf-Rayet stage (Groh et al., 2013).The
possibility of the appearance of LBV as a result of the evolution of close
binaries is considered in Smith & Tombleson (2015).

The classification of high luminosity stars observed in the galaxies M 33 and
M 31 was proposed in Humphreys et al. (2014b), according to spectral and
photometric characteristics of stars: B[e]-supergiants, Of/late–WN, LBV stars,
warm hypergiants, Fe II-emission stars, hot and intermediate supergiants.
These stars have similar spectral characteristics, which complicates the
search for LBVs; however, only LBVs have significant brightness variability.
Despite their similarity, the evolutionary connections between these luminous
stars have not yet been clarified.

To date, only about 40 LBVs and about a hundred LBV candidates (cLBVs) are
known in our and other galaxies, mostly belonging to the Local Group
(Richardson & Mehner, 2018). The information about these stars in the Local
Volume are incomplete, and only a few LBVs and cLBVs are known beyond 1 Mpc
(for example, Pustilnik et al. 2017; Humphreys et al. 2019; Drissen et al.
1997; Goranskij et al. 2016; Solovyeva et al. 2019). The confirmation of the
LBV status requires a large amount of observational time for revealing
photometric and spectral variability, but the discovery of new LBVs and
candidates may clarify the origin of the LBV phenomenon and evolutionary
status of LBVs.

We search for LBVs and similar objects in the Local Volume galaxies by
selecting the point-like H$\alpha$ sources associated with blue stars. For our
purposes we use archival broadband and narrowband H$\alpha$ images obtained
with the Hubble Space Telescope (HST). The first results of our search in the
NGC 4736 and NGC 247 galaxies were published in the works Solovyeva et al.
(2019, 2020). This paper presents the results of a study of the NGC 4449
galaxy (distance D=4.27 Mpc, Tully et al. (2013)). This dwarf irregular galaxy
of Magellanic-type (Ibm type) has specific star formation rate higher than
that of the Large Magellanic Cloud (according to Catalog & Atlas of the LV
galaxies111https://serv.sao.ru/lv/lvgdb/). We have discovered 4 new cLBVs in
this galaxy: J122810.94+440540.6, J122811.70+440550.9, J122809.72+440514.8 and
J122817.83+440630.8 (Fig. 1). In this paper, we present the results of a
detailed study of the detected stars based on spectral and photometric
observations.

Figure 1: Images in HST/F550M: J122810.94+440540.6 (a), J122811.70+440550.9
(b), J122817.83+440630.8 (c), J122809.72+440514.8 (d). The 1.0 arcsec slit is
shown.

##  2 OBSERVATIONS AND DATA REDUCTION

###  2.1 Spectroscopy

The spectra of the all four LBV candidates were obtained with the 6-m
telescope of SAO RAS (BTA) using the SCORPIO or SCORPIO-2 focal reducers
(Afanasiev & Moiseev, 2005, 2011). The slit size was 0.5–1.2″. The observation
dates, seeing and used grisms are shown in Table 1. Spectral data processing
was performed with the context long of midas using the standard algorithm. The
spectra were extracted using the spextra package (Sarkisyan et al., 2017)
intended to deal with long-slit spectra in the crowded stellar fields.

###  2.2 Imaging

Photometric data were obtained with the 2.5-m telescope of Caucasian Mountain
Obseravtory of SAI MSU (2.5-m CMO), the BTA and the Zeiss-1000 of SAO RAS
(Zeiss-1000). We also used archival data of HST (ACS, WFPC2 and WFC3 cameras)
and the Bok Telescope of Kitt Peak National Observatory (Bok). Details are
given in Tables 2, 3 and 4. Primary processing of the 2.5-m CMO, BTA and
Zeiss-1000 data was carried out with midas.

To determine stellar magnitudes in the ground-based observations, we performed
point spread function (PSF) photometry since the objects are located in
crowded stellar fields, and aperture photometry leads to overestimation of the
source fluxes. The PSF photometry was performed using the daophot ii package
(Stetson, 1987). Absolute calibration for the ground-base observations were
performed using 27–32 reference stars whose fluxes were measured from the HST
images. The only exception was the U-band data (observation taken with 2.5-m
CMO, Table 3) where we used reference star fluxes from the SDSS Photometric
Catalog (Abazajian et al., 2009) in order to avoid incorrect flux estimation
for stars with deep Balmer jump caused by the fact that the U filter is
centered ($\lambda_{c}\approx 3600$Å) near the Balmer jump while the HST F336W
(or F330W) filter cover these wavelength only partly. The resulting magnitudes
are shown in Table 3 with errors include statistical errors of the flux
measurements, errors of absolute calibration and also account for background
irregularities around the objects. For the objects J122810.94+440540.6 and
J122811.70+440550.9 we did not provide result of ground-based photometry
because they have nearby stars of comparable brightness and many faint stars,
which complicates the background subtraction and makes results unstable. For
these sources we show only magnitudes obtained from the HST data.

For the HST/WFPC2 data, we performed PSF photometry using the hstphot 1.1
package (Dolphin, 2000) on c0f images. The data from the ACS and WFC3 cameras
were analyzed by the aperture photometry method using the APPHOT package of
iraf. The calibrated pipeline-processed drizzled images were acquired from the
MAST archive. Radii of circular apertures ($r_{\rm ap}$) for the source flux
measurements and radii of annuli ($r_{\rm in},r_{\rm out}$) for the background
were chosen depending on the camera: $r_{\rm ap}=0.15\arcsec$, 0.075″ and
0.12″, $r_{\rm in}=0.25\arcsec$, 0.25″ and 0.20″, $r_{\rm out}=0.45\arcsec$,
0.50″ and 0.44″ for ACS/WFC, ACS/HRC and WFC3/UVIS, respectively. The aperture
corrections were taken into account by photometric measurements of 20
(ACS/WFC), 35 (ACS/HRC), and 36 (WFC3/UVIS) single bright stars.

The object J122809.72+440514.8 has a saturated central pixel in the F435W,
F555W, F814W images of the HST/ACS/WFC data obtained on 2005 November 11. To
exclude damaged part of its PSF, we carried out photometry of this source in
the annular aperture with inner and outer radii of 0.1″ and 0.2″. To obtain
valid absolute magnitudes, this aperture was calibrated on $\sim 40$ reference
stars. The sky background for this source was measured from the annulus with
$r_{\rm in}=0.3$″ and $r_{\rm out}=0.5$″. Correctness of this approach is
confirmed by the fact that after the conversion to the standard (Johnson-
Cousins) system, the V magnitudes from the damaged observation (obtained from
the F555W image) and from the closest subsequent observation (the F500M
filter, November 18) appeared to be consistent within measurement errors.

The measured HST magnitudes were converted into the standard Johnson-Cousins
system using the calcphot function of the PySynphot package. For
J122810.94+440540.6 and J122817.83+440630.8, we assumed a power law as the
model spectrum, and determined spectral indices from the fluxes in adjacent
filters. Another two objects J122811.70+440550.9 and J122809.72+440514.8
(according to the 1997 data) show evidences of Balmer discontinuity (see
below). Therefore, to convert the F336W or F330W magnitudes into the U band,
we used the model spectra presented in Sec. 3. The rest magnitudes were
converted using a power law with spectral indices calculated in the manner
described above.

Resulting magnitudes are shown in Tables 3 and 4. The provided errors include,
beside the statistical error of the flux measurement, the accuracy of the
conversion between the photometric systems (Sirianni et al., 2005; Harris,
2018), the stability of zero
points222https://www.stsci.edu/hst/instrumentation/wfc3/data-
analysis/photometric-calibration,
https://www.stsci.edu/itt/review/ihb_cy15/ ACS/c03_intro_acs6.html and the
stability of the filter PSF in each particular observation. (for example,
Anderson & King 2006). Thus, since the instrumental errors have a
characteristic value of the order of 1-3%, we obtained the total photometry
errors not better than 3% even in the cases where the statistical errors were
insignificant.

Also, we analysed infrared images of three LBV candidates obtained with the
WFC3/IR camera on 2019 April 4 (Table 4). J122817.83+440630.8 was outside the
field of view of this pointing. We carried out aperture photometry using
aperture radii $r_{\rm ap}=0.26\arcsec$, $r_{in}=0.43$″ and $r_{in}=0.82$″.
The aperture correction factor was determined by measurements of $\sim$ 20
single bright stars in 0.26″ and 0.40″ apertures. The obtained magnitudes are
shown in Table 4. In this table we also present the results of photometry in
the $H\alpha$ filter (F658N) of the ACS/WFC and ACS/HRC cameras.

Table 1: Log of spectral observations on the BTA. Star | Date | Spectrograph, grism | Spectral | Spectral | Seeing | Total exp., s
---|---|---|---|---|---|---
|  |  | resolution,Å | range, Å |  |
J122810.94+440540.6 | 2014/01/02 | SCORPIO/VPHG1200R | 5.0 | 5700-7400 | 1.6″ | 2400
| 2015/01/18 | SCORPIO/VPHG1200G | 5.0 | 3900-5700 | 1.7″ | 2400
| 2020/01/18 | SCORPIO/VPHG1200B | 5.5 | 3600-5400 | 1.8″ | 1800
J122811.70+440550.9 | 2014/01/02 | SCORPIO/VPHG1200R | 5.0 | 5700-7400 | 1.6″ | 2400
| 2015/01/18 | SCORPIO/VPHG1200G | 5.0 | 3900-5700 | 1.7″ | 2400
| 2020/01/18 | SCORPIO/VPHG1200B | 5.5 | 3600-5400 | 1.8″ | 1800
J122817.83+440630.8 | 2021/02/11 | SCORPIO-2/VPHG1200@540 | 5.2 | 3650-7250 | 2.3″ | 1200
J122809.72+440514.8 | 2014/01/02 | SCORPIO/VPHG1200R | 5.0 | 5700-7400 | 1.5″ | 2400
| 2015/01/18 | SCORPIO/VPHG1200G | 5.0 | 3900-5700 | 1.7″ | 2400
| 2017/03/31 | SCORPIO/VPHG1200G | 5.0 | 3900-5700 | 1.8″ | 3000
| 2018/02/18 | SCORPIO/VPHG1200G | 5.0 | 3900-5700 | 1.1″ | 2400
| 2018/02/18 | SCORPIO/VPHG550G | 7.3 | 3100-7300 | 1.2″ | 1800
| 2020/08/18 | SCORPIO/VPHG1200B | 5.5 | 3600-5400 | 1.6″ | 2700
Table 2: Log of HST observations. Objects J122810.94+440540.6, J122811.70+440550.9, J122817.83+440630.8 and J122809.72+440514.8 are marked with 1, 2, 3 and 4. Date | Camera | Filters | Objects
---|---|---|---
1995/05/10 | WFPC2 | F606W | 1, 2, 3, 4
1997/07/28 | WFPC2 | F170W, F336W, F555W, F814W | 4
1998/01/09 | WFPC2 | F170W, F336W, F555W, F814W | 1, 2, 3
2005/11/10 | ACS/WFC | F435W, F555W, F814W | 1, 2
2005/11/11 | ACS/WFC | F435W, F555W, F658N, F814W | 1, 2, 3, 4
2005/11/17 | ACS/WFC | F814W | 1, 2, 3, 4
2005/11/18 | ACS/WFC | F550M | 1, 2, 3, 4
2006/01/26 | ACS/HRC | F330W, F550M, F658N, F814W | 1, 2
2014/07/09 | WFC3/UVIS | F275W, F336W | 1, 2, 3, 4
2019/04/04 | WFC3/IR | F110W, F160W | 1, 2, 4
Table 3: Results of the optical and UV photometry. The columns show the instruments, dates and observed stellar magnitudes (not corrected for reddening). All magnitudes are given in the VEGAMAG system. Telescope | Date | F170W, mag | F275W, mag | U, mag | B, mag | V, mag | R, mag | I, mag
---|---|---|---|---|---|---|---|---
J122810.94+440540.6
WFPC2 | 1995/05/10 | — | — | — | — | — | $19.15\pm 0.04$ | —
WFPC2 | 1998/01/09 | $>20.00$ | — | $18.91\pm 0.04$ | — | $19.34\pm 0.03$ | — | $18.60\pm 0.03$
ACS/WFC | 2005/11/10 | — | — | — | — | $19.34\pm 0.03$ | — | $18.63\pm 0.03$
ACS/WFC | 2005/11/11 | — | — | — | $19.67\pm 0.03$ | $19.33\pm 0.03$ | — | $18.64\pm 0.03$
ACS/WFC | 2005/11/17 | — | — | — | — | — | — | $18.67\pm 0.03$
ACS/WFC | 2005/11/18 | — | — | — | — | $19.45\pm 0.03$ | — | —
ACS/HRC | 2006/01/26 | — | — | $19.09\pm 0.04$ | $19.60\pm 0.03$ | $19.31\pm 0.03$ | — | $18.66\pm 0.03$
WFC3/UVIS | 2014/07/09 | — | $19.69\pm 0.05$ | $18.80\pm 0.04$ | — | — |  |
J122811.70+440550.9
WFPC2 | 1995/05/10 | — | — | — | — | — | $19.74\pm 0.04$ | —
WFPC2 | 1998/01/09 | $18.83\pm 0.11$ | — | $19.19\pm 0.04$ | — | $20.19\pm 0.03$ | — | $19.50\pm 0.03$
ACS/WFC | 2005/11/10 | — | — | — | — | $20.12\pm 0.03$ | — | $19.48\pm 0.03$
ACS/WFC | 2005/11/11 | — | — | — | $20.29\pm 0.03$ | $20.15\pm 0.03$ | — | $19.51\pm 0.03$
ACS/WFC | 2005/11/17 | — | — | — | — | — | — | $19.47\pm 0.03$
ACS/WFC | 2005/11/18 | — | — | — | — | $20.25\pm 0.03$ | — | —
ACS/HRC | 2006/01/26 | — | — | $19.33\pm 0.04$ | $20.32\pm 0.03$ | $20.28\pm 0.04$ | — | $19.60\pm 0.03$
WFC3/UVIS | 2014/07/09 | — | $18.40\pm 0.05$ | $19.12\pm 0.04$ | — | — |  |
J122817.83$+$440630.8
WFPC2 | 1995/05/10 | — | — | — | — | — | $22.03\pm 0.06$ | —
WFPC2 | 1998/01/09 | $>20.29$ | — | $21.25\pm 0.08$ | — | $22.01\pm 0.06$ | — | $21.60\pm 0.07$
BOK | 2001/03/31 | — | — | — | — | — | $19.88\pm 0.12$ | —
ACS/WFC | 2005/11/11 | — | — | — | $20.98\pm 0.03$ | $20.69\pm 0.03$ | — | $20.03\pm 0.03$
ACS/WFC | 2005/11/17 | — | — | — | — | — | — | $20.00\pm 0.03$
ACS/WFC | 2005/11/18 | — | — | — | — | $20.72\pm 0.03$ | — | —
WFC3/UVIS | 2014/07/09 | — | $21.28\pm 0.05$ | $21.79\pm 0.03$ | — | — |  |
2.5m CMO | 2020/03/07 | — | — | — | — | — | $22.04\pm 0.20$ | —
J122809.72+440514.8
WFPC2 | 1995/05/10 | — | — | — | — | — | $18.22\pm 0.04$ | —
WFPC2 | 1997/07/28 | $>20.20$ | — | $18.14\pm 0.03$ | — | $17.98\pm 0.04$ | — | $17.48\pm 0.03$
BOK | 2001/03/31 | — | — | — | — | — | $17.71\pm 0.11$ | —
ACS/WFC | 2005/11/11 | — | — | — | $18.30\pm 0.08$ | $18.05\pm 0.09$ | — | $17.56\pm 0.07$
ACS/WFC | 2005/11/17 | — | — | — | — | — | — | $17.50\pm 0.03$
ACS/WFC | 2005/11/18 | — | — | — | — | $17.94\pm 0.03$ | — | —
WFC3/UVIS | 2014/07/09 | — | $19.19\pm 0.05$ | $17.98\pm 0.03$ | — | — |  |
BTA | 2018/02/18 | — | — | — | $18.61\pm 0.15$ | $18.23\pm 0.15$ | $18.01\pm 0.11$ | $17.73\pm 0.07$
2.5m CMO | 2019/01/18 | — | — | — | $18.49\pm 0.11$ | $18.13\pm 0.10$ | $18.02\pm 0.07$ | —
Zeiss-1000 | 2019/04/09 | — | — | — | $18.53\pm 0.09$ | $18.28\pm 0.09$ | — | —
Zeiss-1000 | 2019/05/22 | — | — | — | $18.51\pm 0.11$ | $18.16\pm 0.09$ | — | —
Zeiss-1000 | 2019/11/24 | — | — | — | $18.60\pm 0.18$ | $18.28\pm 0.06$ | $18.18\pm 0.11$ | —
BTAS | 2020/01/18 | — | — | — | $18.61\pm 0.21$ | $18.38\pm 0.19$ | — | —
Zeiss-1000 | 2020/02/17 | — | — | — | — | $18.46\pm 0.14$ | $18.20\pm 0.05$ | $18.17\pm 0.13$
2.5m CMO | 2020/03/07 | — | — | $17.72\pm 0.13$ | $18.51\pm 0.09$ | $18.32\pm 0.07$ | $18.14\pm 0.06$ | $18.02\pm 0.11$
Zeiss-1000 | 2020/11/14 | — | — | — | $18.60\pm 0.16$ | $18.28\pm 0.10$ | $18.19\pm 0.07$ | $18.03\pm 0.12$
2.5m CMO | 2020/12/03 | — | — | — | $18.54\pm 0.08$ | $18.27\pm 0.12$ | $18.17\pm 0.08$ | —
2.5m CMO | 2021/03/05 | — | — | — | $18.48\pm 0.13$ | $18.23\pm 0.05$ | $18.13\pm 0.07$ | —
Table 4: Results of the photometry in H$\alpha$ and near-IR. | HST/ACS/WFC | HST/ACS/HRC | HST/WFC3/IR
---|---|---|---
| (2005/11/11) | (2006/01/26) | (2019/04/04)
Object | F658N, | F658N, | F110W, | F160W,
| mag | mag | mag | mag
J122810.94+440540.6 | – | $17.44\pm 0.05^{m}$ | $18.46\pm 0.03$ | $18.06\pm 0.04$
J122811.70+440550.9 | – | $17.41\pm 0.05^{m}$ | $19.35\pm 0.03$ | $18.87\pm 0.04$
J122817.83+440630.8 | $18.33\pm 0.05^{m}$ | – | – | –
J122809.72+440514.8 | $17.44\pm 0.05^{m}$ | – | $17.83\pm 0.02$ | $17.57\pm 0.02$

##  3 Results

###  3.1 J122810.94+440540.6

####  3.1.1 Spectra

The J122810.94+440540.6 spectra obtained with BTA are shown in Fig.2. The
spectra contain hydrogen Balmer emission lines with obvious broad components.
The presence of narrow components in these lines associated with nebula
emission makes it difficult to estimate the FWHM of the broad components. The
bright narrow emission lines [O iii] $\lambda$4959, $\lambda$5007, [N ii]
$\lambda$6548, $\lambda$6583, [S ii] $\lambda$6717, $\lambda$6731 also must
belong to the nebula, which is most likely background rather than physically
related to the object. The spectra also contain a large number of emission Fe
ii, [Fe ii] lines and weak He i lines. There is no significant change in the
flux and line shapes between the spectra obtained in 2015 and 2020. We have
estimated the interstellar reddening as $A_{V}=0.2\pm 0.2^{m}$ based on the
ratio of hydrogen lines of a nebula measured slightly away from the object
assuming case B photoionization (Osterbrock & Ferland, 2006).

Figure 2: Normalized spectra of J122810.94+440540.6, obtained on (upper panel)
2015 (bottom) and 2020 (top), and on 2014 (bottom panel). The unlabelled short
and long ticks represent Fe ii and [Fe ii]lines, respectively.

####  3.1.2 Photometry and spectral energy distribution

Photometry of J122810.94+440540.6 did not reveal a significant change in its
brightness, the maximal variation is $\Delta U=0.29\pm 0.06^{m}$, Table 3).

The photosphere temperature of J122810.94+440540.6 was estimated from the
photometric data in a wide range of wavelengths. For this purpose we fitted
the spectral energy distribution (SED) of the object constructed of the
magnitudes in original HST filters obtained from the observation of 1998 (Fig.
3a). The data of ACS/HRC (2006), IR (2019) and UV (2014) photometry are also
shown in Fig. 3a but not used during the fitting procedure. The SED
demonstrates a downturn in the range of F275W filter, probably associated with
strong absorption by metals. The SED was fitted with a blackbody model
accounted for interstellar extinction with $R_{V}=3.07$ (Fitzpatrick, 1999).
The interstellar reddening was restricted to vary within the range
$A_{V}=0.2\pm 0.2^{m}$ derived from the spectroscopy. We have obtained the
best-fitting temperature $\rm{T}_{\rm{eff}}=10000\pm 500$K at $A_{V}\approx
0.4^{m}$, and the corresponding bolometric magnitude and luminosity
$\textrm{M}_{\textrm{{Bol}}}=-9.60\pm 0.23^{m}$ and
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=5.76\pm 0.09$. It is worth
noting the presence of notable near-IR excess in F110W and F160W bands, which
is probably associated with free-free emission of the wind and/or with the
presence of warm circumstellar dust.

Figure 3: SED of the studied objects. The black solid and dashed line
represent the best-fitted blackbody model. The unfilled and filled symbols
correspond to the data at pivot lambda of HST filters and the data corrected
for the SED slope during the blackbody fit. The upward triangles represent the
IR data from HST/WFC3/IR (2019), and the downward triangles represent the UV
data from HST/WFC3/UVIS (2014) in all figures. (a) J122810.94+440540.6. The
squares represent the HST/ACS/HRC data (2006). The circles indicate the
HST/WFPC2 photometry (1998). (b) J122811.70+440550.9. The squares mark the
HST/ACS/HRC data (2006). The circles designate the HST/WFPC2 photometry
(1998). The red solid line indicates the composite model including
contribution of the blackbody radiation (red dashed line) and f–f and f–b
emissions (red dotted line; see details in the text). (c) J122817.83+440630.8.
The circles represent the HST/WFPC2 photometry (1998). The squares indicate
the HST/ACS/WFC photometry (2005). (d) J122809.72+440514.8. The circles
represent the HST/WFPC2 photometry (1997). The squares denote the HST/ACS/WFC
data (2005). Diamonds mark the data of the 2.5-m telescope of SAI MSU (2020).

###  3.2 J122811.70+440550.9

####  3.2.1 Spectra

The spectra of J122811.70+440550.9 (Fig. 4) show very broad hydrogen lines
H$\alpha$, H$\beta$, H$\gamma$ and H$\delta$, many emission lines of Fe ii,
[Fe ii], as well as the He i lines. In addition, the spectrum contains [O i]
$\lambda\lambda$ 6300,6363 lines, however, it is difficult to reveal whether
these lines belong to the object or to the surrounding nebula. We do not note
significant changes in spectral lines between the spectra of 2015 and 2020
(Fig. 4). Based on the ratio of hydrogen lines emitted by the nebula, we
estimated the interstellar reddening as $A_{V}=0.3\pm 0.2^{m}$.

Figure 4: Normalized spectra of J122811.70+440550.9, obtained in (upper panel)
2015 (bottom) and 2020 (top), and on 2014 (bottom panel). The unlabelled short
and long ticks represent Fe ii and [Fe ii] lines, respectively. Red wing of
the nebular [O iii] line was oversubtracted in the spectrum, taken in 2020.

####  3.2.2 Photometry and spectral energy distribution

The HST photometry did not reveal a noticeable brightness variability of
J122811.70+440550.9 (Table 3): the brightness of of the star is constant
within $\approx 0.2^{m}$.

As in the case of the previous object, we fitted the HST data of 1998 with a
black body model with $A_{V}$ restricted within uncertainties $0.3\pm 0.2^{m}$
obtained from the nebular hydrogen lines. As a result, we have got the best-
fitting temperature $\textrm{T}_{\textrm{eff}}=17000\pm 7000K$ for
$A_{V}\approx 0.5$, and the bolometric magnitude and luminosity estimates
$\textrm{M}_{\textrm{{Bol}}}=-10.00\pm 2.00^{m}$ and
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=5.92\pm 0.80$.

The black body model alone gave poor agreement with the observed fluxes (black
solid line in Fig. 3b) showing a strong discrepancy in ranges of the Balmer
and Paschen series limits. This situations is similar to that of the
B[e]-supergiant J004415.00 in the galaxy M31 studied by Sarkisyan et al.
(2020). Examining the SED of that object, the authors found a powerful
contribution of free–free (f–f) and free–bound (f–b) radiation. This is
consistent with the presence of an ionized circumstellar envelope typical for
B[e]-supergiants (Zickgraf et al., 1985, 1986). Following the methods
described by Sarkisyan et al. (2020), we approximate the observed SED by the
black body model with extra spectral components accounting for both f-f and
f-b radiation333When fitting with this more complicated model, additionally to
the simultaneous data points of 1998, we utilized the WFC3/UVIS/F275W and
ACS/HRC/F435W observations. The choice of these data is explained by the
desire to obtain a more detailed SED in order to reach higher accuracy of the
model parameters. Taking into account low photometric variability of the
object, this choice have to not distort the observed SED. using chianti
package (Dere et al., 1997; Landi et al., 2013). We consider the case of
isothermal pure hydrogen plasma at a temperature of $\textrm{T}_{e}=10000$ K
(Lamers et al., 1998). The reddening was restricted within the uncertainties
as above. As a result, we received the best-fitting temperature
$\textrm{T}_{\textrm{eff}}=20800\pm 4500K$, emission measure of $EM=1.47\times
10^{39}\pm 4.37\times 10^{38}$ cm-5, $A_{V}\approx 0.5$, and the bolometric
magnitude and luminosity estimates $\textrm{M}_{\textrm{{Bol}}}=-9.90\pm
1.09^{m}$ and $\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=5.88\pm
0.44$444including only the blackbody component.

The result of the SED fitting with the composite model is shown in Fig. 3b in
red lines: the dashed line shows the black body radiation, the dotted line
designates f–f and f–b emissions, and the solid red line indicates the total
model spectrum. The black solid line represent results of the black body model
alone. The IR data (WFC3/IR/F110W,F160W, 2019) and optical data
(ACS/HRC/F330W,F550M,F658N,F814W, 2006; WFC3/UVIS/F336W, 2014) are also
plotted, but not used in the fit.

###  3.3 J122817.83+440630.8

####  3.3.1 Spectra

The spectrum of the region with J122817.83+440630.8 was obtained with
SCORPIO-2 of BTA on 2021 February 11, when the magnitude of the object was
$\approx 22^{m}$. During this observations the seeing was about 2.3″. Thus,
the object was too faint for this conditions, and we took only a spectrum of a
nearby H II complex in order to measure the interstellar extinction. Using the
ratio of hydrogen lines, we obtained $A_{V}=0.4\pm 0.2^{m}$.

####  3.3.2 Photometry and spectral energy distribution

The most dramatic changes in brightness of this star occurred in the R band
(Table 3). From the table it is seen that the source brightness increased by
$\Delta R=2.15\pm 0.13^{m}$ from the 1995 (HST) to 2001 (Bok) observations,
and a return to its previous state to 2020 (2.5-m CMO). The light curves in
different filters are shown in Figure 5.

Figure 5: Light curves of J122817.83+440630.8 in V (diamonds), U (triangles)
and R (squares) bands.

The shape of the object SEDs also dramatically changed (compare the data of
1998 and 2005 in Fig. 3c). To measure the photosphere temperatures, we carried
out a joint approximation of these SEDs with a black body model taking into
account that the interstellar extinction and the bolometric luminosity of the
two data sets have to be the same if the observed variability is of the S Dor-
type. As before, $A_{V}$ was limited to the range measured from the
spectroscopy. As a result, we obtained the temperatures
$\textrm{T}_{\textrm{eff}}=19000\pm 1200$K (1998) and
$\textrm{T}_{\textrm{eff}}=9000\pm 600$K (2005) for the interstellar
extinction $A_{V}\approx 0.6^{m}$, which gives estimates of the bolometric
magnitude $\textrm{M}_{\textrm{{Bol}}}=-8.30\pm 0.38^{m}$ and the
corresponding bolometric luminosity
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=5.24\pm 0.15$.

###  3.4 J122809.72+440514.8

####  3.4.1 Spectra

The spectra of J122809.72+440514.8 are shown in Fig. 6. The spectrum obtained
in 2015 contains emission lines He i $\lambda\lambda$4472,4922 and Fe ii
$\lambda\lambda$4400-4700, $\lambda\lambda$5100-5400 with P Cyg profiles which
became less noticeable in 2017 and 2018, and then completely disappeared by
2020. The wings of the hydrogen lines H$\beta$ and H$\gamma$ broadened
noticeably from 2015 to 2020; the [Fe ii] $\lambda$5157 and Fe ii
$\lambda$5169 lines become brighter. At the same time, there is a notable
weakening of other emission lines of Fe ii and [Fe ii]
$\lambda\lambda$4500-4700 and $\lambda\lambda$5200-5400. In addtition, the
spectra show a few Cr ii and Ti ii lines. The emission lines He i $\lambda$
5876, $\lambda$6678 are also seen but their FWHM correspond to the spectral
resolution, so these lines are probably emitted by the surrounding nebula. The
study of the hydrogen lines of the surrounding nebula allowed us to estimate
the interstellar extinction $A_{V}=0.8\pm 0.2^{m}$.

Figure 6: Normalized spectra of J122809.72+440514.8. The spectra were obtained
in 2015, 2017, 2018 and 2020 (from bottom to top; upper panel), in 2014
(bottom panel).

####  3.4.2 Photometry and spectral energy distribution

The brightness variations of J122809.72+440514.8 are $\Delta U=0.28\pm
0.24^{m}$, $\Delta V=0.48\pm 0.14^{m}$, $\Delta I=0.69\pm 0.13^{m}$ from 1997
(HST) to 2020 (Zeiss-1000, 2.5-m CMO). The light curve is shown in Fig. 7.

Monitoring of the star with ground-based telescopes carried out over the past
three years, has revealed the strongest changes in the star colour and
brightness. The earlier data (HST) show weaker variability, and, at the same
time, demonstrate (up to 2014 inclusively) a clear downturn in the range
3000-4000Å (Fig. 8), which we identify as a quite deep Balmer jump. The
observations of 2020 in a wide range of wavelengths (from the U to I band)
show a significantly hotter SED without clear Balmer jump.

In the case of J122809.72+440514.8, the joint approximation of two extreme
states of the star (we used the data of 1997 from HST and of 2020 from 2.5-m
CMO) with a black body model and tied $A_{V}$ and $\text{L}_{\text{Bol}}$
values of the two data set, as we carried out for the previous object, did not
give satisfactory results. The reason for this could be variations either in
the absorption value or in the bolometric luminosity. The change of $A_{V}$
was observed in $\eta$ Car, associated with condensation of dust in the shell
ejected during the Great Eruption (Davidson & Humphreys, 1997). However, we
did not find in the literature any examples of absorption changes in the
environment around LBVs undergoing the S Dor cycle. The bolometric luminosity
changes, nevertheless, have been observed in several confirmed LBVs during
their S Dor-type variability cycle. The example is AG Car, whose bolometric
luminosity decreased by a factor of 1.5 when the source was at the brightness
maximum in the V band (Groh et al., 2009). A similar behaviour of S Dor was
noted by Lamers (1995). They also has shown that the bolometric luminosity of
LBVs can vary within 0.2 dex. This may occur due to the loss of energy for the
expansion of the envelope during transitions of the star brightness from
minimum to maximum.

In accordance to the above, we repeated the fit with the bolometric luminosity
being free but the extinctions for the two SEDs were still tied and restricted
within uncertainties. The best-fitting models gave
$\textrm{T}_{\textrm{eff}}=7600\pm 300$ K,
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=6.20\pm 0.11$
($\textrm{M}_{\textrm{Bol}}=-10.70\pm 0.27^{m}$) for the ‘cold’ state (1997),
and $\textrm{T}_{\textrm{eff}}=13500\pm 4300$,
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=6.44\pm 0.64$
($\textrm{M}_{\textrm{Bol}}=-11.30\pm 1.60^{m}$) for the ‘hot’ state (2020),
with $A_{V}=0.6^{m}$. Both SEDs together with corresponding models are shown
in Fig. 3d.

The difference between the two obtained values of $\text{L}_{\text{Bol}}$ lies
within the 0.2 dex limit discussed above. However, it is still possible that
this variation of $\text{L}_{\text{Bol}}$ is an artefact associated with
underestimation of the photosphere temperature in the cold state due to the
presence of the Balmer jump. To test this assumption, we decided to use the
CMFGEN non-LTE models (Hillier & Miller, 1998), which are capable to give more
accurate estimates of the fundamental stellar parameters under conditions of a
strong gas outflow in the form of a wind.

Figure 7: Light curves of J122809.72+440514.8 in V (triangles), R (squares)
and I (diamonds) bands. To better visualisation light curves in R and I band
shifted on -1 and -2 mag respectively.

####  3.4.3 CMFGEN model

The photometric data taken in 2014 in the F275W and F336W filters of the
HST/WFC3/UVIS are in a good agreement with the UV-range data of 1997, which
indicates the absence of significant difference in the states of the star
between these observation dates. The spectral features in the first spectrum
of the star, which we obtained in 2015, are consistent with relatively low
temperatures of the outflowing gas. Therefore, we assumed that this spectrum
also corresponds to the cold state of the star, observed at least in 1997 and
2014, and we decided to use it for modelling with the cmfgen code. Beside the
spectrum, we involved the photometric data of these years to obtain estimates
of the star luminosity.

As a first approximation of the J122809.72+440514.8 spectrum, we utilised the
models from our previously calculated CMFGEN grids of extended atmosphere
models (Kostenkov et al. 2021, in prep.). A detailed description of the
modelling method and algorithm is given in the works Kostenkov et al. (2020a,
b). The velocity distribution in the stellar wind was assumed to obey a simple
velocity law with $\beta=1$ (Lamers et al., 1996). This value of $\beta$
provides a very rapid increase of the gas velocity near the star surface,
which leads to the compact photosphere that follows from the presence of the
absorption Balmer jump observed in the star SED. The absence of forbidden
lines formed in distant wind regions (for example, [N ii] $\lambda 5755$) does
not allow us to accurately estimate the terminal wind speed. Therefore, we
have accepted its value equal to 300 km s-1, which made it possible to
reproduce the P Cyg profiles of iron lines quite accurately at the given
velocity law. Since we can not observe the electron-scattering wings of the
hydrogen lines due to the low signal-to-noise ratio, we assume homogeneity of
the wind structure (filling factor $f=1$). The metals abundance is assumed to
be equal to the metallicity of NGC 4449 $Z=0.5Z_{\odot}$ (Annibali et al.,
2017), with the exception of the nitrogen and carbon abundance that was
changed to be consistent with the values observed in detailed studied LBVs
(Table 5). The hydrogen abundance was determined iteratively based on the
ratio [O iii]$\lambda$5007/H$\beta$: we subtracted from the H$\beta$ its
stellar component obtained from the model of current iteration, and sought to
make the ratio of [O iii]$\lambda$5007 and the ‘H$\beta$ remnant‘ the same as
observed in the pure nebula spectrum extracted from nearby region.

Table 5: The main model parameters and chemical abundances ($X$) for
J122809.72+440514.8.

$L_{*}$, $L_{\odot}$ | 2.58 $\times$ $10^{6}$
---|---
$\dot{M}$, $M_{\odot}$ yr-1 | 5.2 $\times$ $10^{-3}$
$R_{2/3}$ ∗, $R_{\odot}$ | 620
$R_{*}$ ∗, $R_{\odot}$ | 410
$T_{\text{eff}}$ ∗, K | 9300
$T_{*}$ ∗, K | 11360
$\beta$ | 1.0
$V_{\infty}$, km s-1 | 300
$f$ | 1
H, % | 20
$X_{\text{C}}/X_{\odot}$ | 0.2
$X_{\text{N}}/X_{\odot}$ | 5.4
$X_{\text{Si}}/X_{\odot}$ | 0.5
$X_{\text{Fe}}/X_{\odot}$ | 0.5

Notes. ∗ $R_{2/3}$ and $T_{\text{eff}}$ are the radius and temperature at
$\tau=2/3$, $T_{*}$ is the temperature at hydrostatic radius $R_{*}$
($\tau\gtrsim 20$)

A relatively good agreement between the observed spectra and the model was
reached at $\dot{M}=5.2\times 10^{-3}\,M_{\odot}\,yr^{-1}$ and the temperature
$T_{*}=11360$ K at the hydrostatic radius of the star $R_{*}\approx
410\,R_{\odot}$ (Fig. 9). The main model parameters are presented in Table 5.
The extremely powerful outflow appearing in this model, increases opacities at
large distances from $R_{*}$ and significantly decreases the temperature at
the photosphere radius, $T_{\text{eff}}=9300$ K. However, this estimate of the
effective temperature still significantly exceeds the value obtained from the
black body approximation of the SED ($\textrm{T}_{\textrm{eff}}=7600\pm
300$K), which indicates underestimation of the temperature by the simple
model.

The accuracy of the the mass loss rate estimates is limited by the uncertainty
of the nebula contribution to the hydrogen lines observed in the object
spectrum. This uncertainty could be reduced by further observations with a
higher spectral resolution. The accuracy of the temperature estimates is
determined by several factors. First of all, it is the absence of Si ii lines
in the spectrum, which are sufficiently sensitive to changes in the ionization
state of the wind matter. Therefore, the upper limit of the photosphere
temperature in the model was limited to $\sim 11000\,$K. The lower limit for
the effective temperature ($\sim 9000\,$K) was estimated based on the strength
of the absorption components of the H$\beta$ and Fe ii lines. A decrease in
temperature leads to an increase in the amount of neutral hydrogen, and hence
to an increase in the absorption component of the H$\beta$ line. Another
consequence of a decrease in temperature below $\approx 9000\,$K is a strong
weakening of the Fe ii lines. In principle, an increase in the mass loss rate
can compensate weakening of ionized iron lines; however, the resulting
increase in the wind density also strengthens the absorption components of
these lines. Taking into account that strong absorption lines are not observed
in the object spectrum, we assume that the lower estimate of the photosphere
temperature is $9000\,$K.

The bolometric luminosity was determined by fitting of the obtained model
spectrum accounted for the interstellar extinction to the observed SED (1997).
In this case, the extinction $A_{V}$ was a free parameter. The best agreement
between the observed energy distribution and the model was obtained at
$A_{V}=1.05\pm 0.07^{m}$, which corresponds to the value obtained from
observations, but is much higher than the estimate based on the black body fit
($0.6^{m}$). The luminosity estimate is
$\log(\text{L}_{\text{Bol}}/\text{L}_{\odot})=6.41\pm 0.03$. The model
together with the observed SEDs are given in Fig. 8, where the observational
data are shown in black and the model fluxes in grey. The figure shows the
observed fluxes from the ACS/WFC data (2005) and the WFC3/UVIS data (2014).
Obvious agreement between all the observed and calculated fluxes confirms the
initial assumption that the star was in approximately the same state in 1997,
2005 and 2014-2015.

Figure 8: The best-fetting model to J122809.72+440514.8 spectrum, obtained on
2015 (grey solid line). Fluxes in the F170W, F336W, F555W and F814W of the
best-fitting model are marked by grey triangles. The black circles designate
photometric data from HST/WFPC2 (1997), black downward triangles - data from
HST/ACS/WFC (2005), black upward triangle - WFC3/UVIS data (2014). Figure 9:
Normalized spectrum of J122809.72+440514.8, obtained in 2015 (grey solid line)
and the best-fitting cmfgen model (black solid line). Long black ticks
designate He i lines, Fe ii and [Fe ii] are marked with short black and thick
grey ticks, respectively

То summarize, we carried out a modeling of the optical spectrum of the cold
state of J122809.72+440514.8. However, the poor quality of the available data,
its contamination by the nebula lines as well as the absence of IR- and UV-
spectra did not allow us to properly constrain such important parameters as
$\beta$, the terminal velocity, the hydrogen abundance, etc., which, in turn,
made less accurate the estimates of the mass loss rate and photosphere
temperature. Nevertheless, our modeling is able to reproduce many observed
features both in the spectrum and in the SED.

##  4 Discussion

###  4.1 Spectral classification

As is noted in Sec. 3.1.1, the spectrum of J122810.94+440540.6 contains Fe ii,
[Fe ii] lines, but has no [O i] $\lambda\lambda$ 6300,6363 and [Ca ii]
$\lambda\lambda$ 7291,7323 lines, which are indicators of circumstellar gas
(Aret et al., 2012) and can be observed in spectra of B[e]-supergiants and
warm hypergiants (Humphreys et al., 2013; Humphreys et al., 2014b). At the
same time, the Fe ii and [Fe ii] lines can be observed in stars of various
types, including LBVs. The SED of this object shows a noticeable IR excess in
the region of 1-2 $\mu$m (Fig. 3a). However, the excess is not large (less
than 2 times higher than the black body model in the F160W band, approximately
corresponding to the H band), therefore, it is not possible to unambiguously
establish the source of this excess without mid- and far-IR data: the possible
origin of the observed excess can be both a free-free wind radiation and a
warm dust circumstellar envelope. Also, J122810.94+440540.6 did not show any
noticeable brightness variability (it is less than 0.3m in all the studied
bands). Considering all of the above facts, we cannot clearly classify the
star, but we suppose that J122810.94+440540.6 could be either a LBV or
B[e]-supergiant.

According to the spectral features, the star J122811.70+440550.9 is similar to
J122810.94+440540.6, however, its spectrum contains the [O i] $\lambda\lambda$
6300,6363 lines, but there are no obvious [Ca ii] lines. Lines of neutral
oxygen can be excited both in the envelope of the star itself and in the gas
of the surrounding nebula. The SED of this object is found to be similar to
those of B[e]-supergiant J004415.00 (Sarkisyan et al., 2020). Applying the
same model as was proposed for that B[e]-supergiant, which takes into account
f-f and f-b radiation, to the SED of J122810.94+440540.6, we obtained a good
agreement of the model with the observed data and have demonstrated the
presence of an ionized envelope around the star. Thus, J122811.70+440550.9
shows characteristics typical of B[e]-supergiants. However the fragmentariness
of the available data do not allow us to draw definitive conclusions.

The star J122817.83+440630.8 demonstrated significant brightness ($\Delta
R=2.15\pm 0.13^{m}$) and SED shape variability. The lack of spectral data does
not allow to make unambiguous conclusion concerning the object type.
Nevertheless, we have to note that such brightness changes are characteristic
only for LBVs, since only they are highly variable objects among the entire
set of high luminosity stars (Humphreys et al., 2017). Various transient X-ray
binaries are another type of objects with a large amplitude of optical
variability and a hot photosphere. However, we examined images of Chandra and
found no X-ray sources at the J122817.83+440630.8 position. So it is unlikely
that the object is one of them. Thus, this object can probably be attributed
to LBV stars.

The spectrum of J122809.72+440514.8 contains many lines characteristic of
LBVs. This star also demonstrated spectral and photometric variability, the
maximum of which is in the red range $\Delta I=0.69\pm 0.13^{m}$. The SED of
this object shows no clear IR excess, which indicates the absence of a hot gas
and dust envelope around the star. Based on the observed features,
J122809.72+440514.8 can be classified as an LBV star.

The spectrum of J122809.72+440514.8, obtained in 2015, shows similarity with
the spectra of many confirmed LBVs in the cold state (e.g. HR Car, Szeifert et
al. 2003; AG Car, Stahl et al. 2001; Var C Humphreys et al. 2014a) but it is
especially similar to the spectrum of $\eta$ Car of 2001 (Fig. 7 in Groh et
al. 2012). The authors performed a quantitative analysis of $\eta$ Car
spectrum and its modeling using the CMFGEN code.

The results of modelling of the J122809.72+440514.8 spectrum gave extremely
high values of the mass loss rate $\dot{M}=5.2\times
10^{-3}\,M_{\odot}\text{/yr}$, which is higher but still comparable to that of
$\eta$ Car ($\dot{M}=2.4\times 10^{-3}\,M_{\odot}\text{/yr}$, Groh et al.
2012). Nevertheless, we should note that it is difficult to assess the
reliability of the obtained value because there is a degeneracy between the
mass loss and the ratio of helium and hydrogen abundances at low temperatures:
an increase in the hydrogen content can be compensated for by a corresponding
increase in $\dot{M}$. The same difficulty arose when modeling the $\eta$ Car
spectrum (Hillier et al., 2001). Moreover, the use of other spectral lines can
not help to avoid the degeneracy. For example, a decrease in $\dot{M}$ can
lead to a decrease in the model intensities of the Fe ii lines but, at the
same time, the decrease in the intensities of these lines can be compensated
for by an increase in the Fe ii abundance, which is not known precisely due to
the uncertainty in the metallicity of the star. Nevertheless, despite all the
difficulties, we can assert that both stars have very powerful winds with a
large mass loss in them.

$\eta$ Car has a significantly larger photosphere ($\approx 860\,R_{\odot}$)
than J122809.72+440514.8 ($\approx 620\,R_{\odot}$) with almost the same
temperature and with lower mass loss rate. We suppose that this is due to the
following factors: firstly, to the significantly different selected values of
the clamping, and secondly, due to the use in Groh et al. (2012) of a more
complex velocity law, derived from the available spectral data in a very wide
wavelength range (far UV to IR range). In the case of J122809.72+440514.8,
there were not enough spectral lines in the optical range, so we applied the
simplest model of the $\beta$-law. The less pronounced Balmer jump indicates a
more extended photosphere of $\eta$ Car compared to J122809.72+440514.8.

###  4.2 Age of the environment stars

Figure 10: HST/ACS/WFC image in F814W band of J122810.94+440540.6 and
J122811.70+440550.9 (left), J122817.83+440630.8 (middle), J122809.72+440514.8
(right). The rectangles represent the star-forming regions that were used to
construct the colour-magnitude diagrams. The arrows indicate the objects under
study.

All the stars we study are located near the stellar associations in which
these stars were probably formed. To estimate the age of the stellar
environment, we have performed PSF photometry and have constructed «colour-
magnitude» diagrams (CMD). For J122810.94+440540.6, J122817.83+440630.8 and
J122809.72+440514.8, we have selected two regions: the small one, which
corresponds to the size of the nearest stellar groups, and the large one,
which covers all star-forming region near the star (Fig. 10). In the case of
J122811.70+440550.9, we have selected two neighbouring large stellar groups.
The choice of different regions is due to the uncertainty of the region where
the stars were formed.

Figure 11: Color-magnitude diagrams for stellar environments of four stars.
The green triangles mark stars of large star-forming regions, the black
circles denote stars in small areas around the studied objects, which are
shown by black star symbols. Theoretical isochrones of 5, 10, 30 and 100 Myr
are shown (from top to bottom).

Photometry for the selected region was performed using archival data obtained
in the F550M (2005/11/18) and F814W (2005/11/17) filters of the HST/ACS/WFC
using the dolphot package (Dolphin, 2016). Fig. 11 shows colour-magnitude
diagrams for the studied associations. The theoretical isochrones555obtained
from http://stev.oapd.inaf.it/cgi-bin/cmd from Marigo et al. (2017) for the
metallicity $Z=0.5Z_{\odot}$ and the positions of the studied objects are also
plotted on the diagram. When calculating the tracks, the canonical two-part-
power law corrected for unresolved binaries was chosen as the initial mass
function (Kroupa, 2001, 2002). The isochrones were reddened, and extinction
was varied from the Galactic value to the maximum value that we measured from
the spectral data. The optimal values of reddening were determined
individually for each region, by a comparison of the reddened isochrone with
the observed main sequence of the stars from selected regions. As a result, we
obtained reddening estimates $A_{V}\approx 0.5^{m}$ for the stellar
environment of J122810.94+440540.6 and J122817.83+440630.8, which is quite
consistent with the average internal reddening in NGC 4449 (Hill et al.,
1998), and $A_{V}\approx 0.1^{m}$ for stellar groups near the
J122811.70+440550.9 and J122809.72+440514.8, which turned out to be below the
average internal reddening.

The positions of stars in the selected regions on the CMD correspond either to
continuous star formation within the studied regions for at least the last 100
Myr, or to several episodes of star formation during the same period of time.
At the same time, the age of the youngest stars is approximately 5-10 Myr. We
suppose that they (like the objects under study) were formed in one of the
last bursts of star formation. Moreover, we did not find a difference between
the positions of the stars from the small and large regions on the CMD. More
accurate age estimates require information on the values of many parameters
such as rotation speed of stars, local metallicity (which may vary even inside
one region), initial mass function, etc. Another factors that can lead to both
underestimation and overestimation of the age of the surrounding population
are related with the relatively small number of stars in the studied
associations. Thus the upper part of the diagram is poorly populated.
Therefore, we can overestimate the age of the last starburst, as in the case
of J122809.72+440514.8, which is located well above the brightest stars in the
diagram. At the same time, there may be unresolved groups of stars among
bright stars, which can lead to underestimation of the age of the youngest
objects.

###  4.3 Masses and luminosities

Figure 12: Temperature-luminosity diagram with evolutionary tracks of massive
stars for the metallicity of $Z=0.5Z_{\odot}$ (Tang et al., 2014). The
positions of objects are shown by circle (J122810.94+440540.6), triangle
(J122811.70+440550.9), squares (J122809.72+440514.8) and diamonds
(J122817.83+440630.8) respectively. Thick grey line indicates the Humphreys-
Davidson limit. We also have shown transitions of J122817.83+440630.8 and
J122809.72+440514.8 between states by thin grey dash lines.

To estimate the mass of studied objects, we have constructed a temperature-
luminosity diagram (Fig. 12) and have compared the positions of objects with
evolutionary tracks of massive stars of different initial masses (Tang et al.,
2014). We assumed the metallicity value $Z\approx 0.5Z_{\odot}$ (Annibali et
al., 2017) when choosing evolutionary tracks of stars. An estimates of the
photosphere temperatures and luminosities of our stars (in the case of
J122809.72+440514.8 for the hot state) are obtained from the SED fitting. The
temperature and luminosity of the cold state of J122809.72+440514.8 were taken
from the results of modeling with the CMFGEN code.

Object J122817.83+440630 has an initial mass of about 20 $M\odot$. Stars with
such masses can pass the red supergiant stage during their evolution
(Humphreys et al., 2016). J122809.72+440514.8 has the largest initial mass
(more than 100 $M\odot$). The mass loss rate characteristic for stars of such
large masses does not allow them to become red supergiants (Humphreys &
Davidson, 1979) and they evolve into WR stars. The mass values of
J122810.94+440540.6 and J122811.70+440550.9 are between the indicated extreme
values. Thus, the masses of all four stars are quite typical of LBV stars or
massive supergiants.

##  5 Conclusions

In this work, we have studied four massive (from 20 to $\lesssim 100\,M\odot$)
stars in the NGC 4449 galaxy. Two stars have shown strong photometric
variability for several years, which allows us to classify them as LBVs.
Modeling the cold state ($T_{\text{eff}}=9300\,$К) of the brightest one using
the CMFGEN code showed a significantly high mass loss rate $\dot{M}=5.2\times
10^{-3}\,M_{\odot}\,yr^{-1}$. This star is a close analogue of $\eta$ Car in
its state.

The classification of the remaining two stars is complicated by their small
photometric variability and low signal-to-noise ratio in their spectra, which
do not allow us to reliably confirm or exclude their own emission in such
characteristic lines as [O i]6300 and/or [Ca ii]. The presence of a
significant contribution of both f-f and f-b radiation to the SED of one of
them indicates the presence of an ionized shell, characteristic of
B[e]-supergiants. However, a more precise classification of both stars
requires further observations.

## Acknowledgements

This research was supported by the Russian Foundation for Basic Research
19-52-18007. Observations with the SAO RAS telescopes are supported by the
Ministry of Science and Higher Education of the Russian Federation (including
agreement No05.619.21.0016, project ID RFMEFI61919X0016). The renovation of
telescope equipment is currently provided within the national project
’’Science’’. The modelling spectra was performed as part of the government
contract of the SAO RAS approved by the Ministry of Science and Higher
Education of the Russian Federation. The research made use of equipment
purchased with funds from the Program of Development of M. V. Lomonosov Moscow
State University.

## Data Availability

The data underlying this article will be shared on reasonable request to the
corresponding author.

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