The field of atomic hydrogen in the Milky Way is once again poised for an
observational revolution. The new SKA Pathfinders, ASKAP and MeerKAT, are
providing highly sensitive interferometric data over wide-fields, helping to
bridge the gap between the limited area, low sensititivity interferometric
surveys with $\sim$ arcminute resolution and the large area, high sensitivity
single dish surveys with $3-16$ arcminute resolution. MeerKAT has a one degree
field-of-view with outstanding surface brightness sensitivity at sub-arcminute
angular resolution. With its surface brightness sensitivity, MeerKAT will make
excellent contributions to highly sensitive imaging over areas of 10’s of
degrees. We can envisage that MeerKAT will lead the way with deep, 10′′
imaging of high-latitude H i, with applications towards phase decomposition of
H i emission and studies of turbulence.

ASKAP makes use of phased-array technology to extend its field-of-view to
$\sim 25~{}{\rm deg^{-2}}$ with a surface brightness sensitivity at 30′′ that
is similar to previous interferometric H i surveys but 300 times faster (Hotan
et al., 2021). The GASKAP-HI survey is specifically targeting H i in the Milky
Way at high angular ($\sim 30\mbox{${}^{\prime\prime}$}$) and spectral
resolution ($\sim 0.4~{}{\rm km~{}s^{-1}}$) with an order of magnitude
improvement in sensitivity and angular resolution on the Galactic Plane,
Galactic Center and a large swathe of high latitude sky covering the
Magellanic Clouds and Stream plus Milky Way foreground. GASKAP-HI will jointly
deliver H i emission images and catalogs of H i absorption. These data will be
outstanding for joint studies of the CNM and WNM distribution with
galactocentric radius and in $z$ height.

H i absorption surveys at high Galactic latitudes have been slow to carry out
and almost exclusively targeted. For example, the MACH survey measured H i
absorption in the direction of just 42 background sources in 50 hrs of
observation to trace the latitude dependence of absorption properties. The
GASKAP-HI high latitude survey GASKAP-HI will obtain $\sim 150$ absorption
spectra of similar quality to MACH in every $25~{}{\rm deg^{2}}$ field after
30 hours of integration. In the Galactic foreground of the Magellanic Stream,
GASKAP-HI should yield over 7000 new H i absorption measurements over a range
of Galactic latitudes. The spatial sampling of this “H i absorption grid” will
help trace variations in spin temperature and column density over scales of a
parsec or less.

The next major advance in H i studies of the Milky Way will come when the
spatial sampling of an all-sky irregular grid of H i absorption finally
reaches the effective angular resolution that we currently have with HI4PI in
emission. The full SKA, when operational in $\sim$ 2028, will extend Milky Way
H i studies further in both emission and absorption. Together the pathfinders
and ultimately the SKA, will be able to provide a catalog several orders of
magnitude larger than bighicat, with values of optical depth, spin temperature
and column density determined from a dense grid of absorption measurements,
finally allowing us to realize the goal of having all (Southern)-sky cubes of
the CNM with an effective resolution of $\lesssim 0.25$ deg.

Two other telescopes that will enormously improve the sensitivity of H i
surveys are: FAST for H i emission and ngVLA for H i absorption. By virtue of
its 500 m collecting area, FAST can reach brightness temperature sensitivity
limits better than any other telescope in the world at a few arcminutes
angular resolution. The ngVLA, which if designed to specification, will be
superb for measuring H i absorption to deduce the properties of the WNM. ngVLA
should produce absorption spectra with about 60 times lower noise for a given
observation time than 21-SPONGE, which is the most sensitive comprehensive
survey of H i absorption. If the spectral baselines are stable the ngVLA
should produce observations at $\sigma_{\tau}<10^{-5}$ towards bright ($\sim
1-10$ Jy) sources with minimal telescope time.

As we move into the realm of “big data” for H i it is no longer possible to
look at each cube and fit each spectrum by hand. It will be essential to bring
new techniques to bear for extracting physical properties from the data as
well as characterizing the morphological interpretation of multi-dimensional
data. Some of these new techniques have recently been tested and applied to
new surveys (e.g. Gausspy, ROHSA, AstroHOG, RHT, CNN Lindner et al., 2015,
Marchal et al., 2019, Soler et al., 2019, Clark et al., 2015, Murray et al.,
2021). The requirements for new tools and techniques to analyze the spectrally
and spatially complex H i datasets will be essential to further our
understanding of H i in the Milky Way. Applying these techniques to synthetic
observations of simulations will help us to infer astrophysical quantities
from the observational H i data.

###  7.1 Future complementary data

New H i data will be complemented by other datasets capable of tracing the
dust, molecular gas and magnetic field structure of the ISM with better
resolution in all dimensions. We already starting to see the power of linking
H i datasets with the 3-D dust distribution within a few hundred parsecs of
the Sun (e.g. Lallement et al., 2019, Green et al., 2019, Leike et al., 2020,
Vergely et al., 2022). For example, Panopoulou & Lenz (2020) used the
association with dust to show that there are 2 to 3 kinematically distinct H i
components along most high Galactic latitudes lines-of-sight. Tchernyshyov &
Peek (2017) and Tchernyshyov et al. (2018) used the 3-D dust together with H i
for 4-D (3 spatial plus 1 velocity) information about the gas distribution.
While these dust maps are currently limited to local gas, future infrared
surveys with the Nancy Grace Roman Space Telescope could be used to extend the
3-D dust distribution within the Galactic plane to much further distances.
Associating H i with dust to derive distances and trace 4-D H i information
will open new opportunities to use H i for spiral structure, physical gas
properties and many other areas.

Essential to interpretation of future observational data will be future
simulations at sub-parsec resolution over the full disk of a galaxy to trace
the micro-physics visible through our new observational datasets. Simulations
have a particular advantage as they can turn on and off individual heating and
cooling processes and introduce different feedback channels. By comparing the
simulated mass fractions across different phases with observations we can gain
insight into the importance of various feedback channels. From this point of
view, a database of simulations made consistently while varying different
input parameters would be very useful for future investigations. With
thousands of H i absorption spectra to be provided by future surveys, we
envision that both observations and simulations can start to focus on
individual regions (e.g. Galactic center vs. outer regions, the H i warp, off-
plane, etc.), instead of the entire Milky Way, to investigate the mass flow of
H i across different phases and how this changes with local conditions.

[SUMMARY POINTS]

  1. 1.

The CNM is ubiquitous in the Milky Way. The CNM temperature distribution peaks
at 50-200 K and is broad, likely due to the sampling of both dense and diffuse
environments. Some evidence exists that only colder and denser CNM goes on to
form H2. The CNM temperature decreases with $A_{V}$: higher-$A_{V}$ regions
have a lower $T_{s}$, while lower-$A_{V}$ regions have a higher $T_{s}$.

  2. 2.

The average CNM mass fraction in the Milky Way is $\sim 40$%. The CNM fraction
increases with Av due to the increase of the mean density. Local density plays
a strong role in constraining the CNM fraction and spin temperature. The
morphology of the CNM, as observed in emission, is highly filamentary and is
correlated with the orientation of the magnetic fields.

  3. 3.

The UNM remains difficult to constrain observationally because it requires
highly sensitive absorption measurements. The most robust estimate to date for
the average UNM mass fraction is $\sim 20$%, in agreement with predictions
from recent numerical simulations. The morphology, spatial distribution, and
other properties of the UNM still remain as open questions.

  4. 4.

The WNM peak of the H i temperature distribution remains observationally
unconstrained from H i absorption observations due to its very low optical
depth. The likely reason is that the WNM has a higher excitation temperature
than what has been assumed over the last few decades. The spatial distribution
of the WNM in relation to the CNM and UNM needs better constraints. The
average WNM mass fraction is $\sim 40$%, even the densest ISM regions have
some WNM. Shells and superbubbles are important for setting the H i emission
morphology and create H i structures as broken remnants of shells and
supershells driven away from the disk.

  5. 5.

The interpretation of the spatial power spectrum of H i emission depends on
many effects. Large areas of the Milky Way appear to have a relatively uniform
SPS slope.

  6. 6.

The cold disk of the Milky Way extends to at least three times the solar
radius. Throughout the disk, the CNM has a scale height that is intermediate
between that of the WNM and the molecular gas.

[FUTURE ISSUES]

Throughout the compilation of this review we encountered countless questions
for future work. It is impossible to describe them all here, but we have
chosen to list below some of the biggest questions that we might reasonably
hope to answer within the next decade through savvy combination of multi-
wavelength observational and simulated datasets and new techniques.

  1. 1.

New surveys of H i absorption will expand the number of H i absorption
detections by a factor more than 100 to help us to answer questions about how
the spin temperature changes with location around the Galaxy, hopefully
revealing what fraction of the observed H i is in the UNM and how this varies
with environment. These extensive databases of H i absorption should show how
the H i excitation processes and the heating and cooling rates change with
environment, e.g. within the star-forming disk versus the halo, and inner
versus outer disk regions.

  2. 2.

Projects combining stellar and dust distances to produce a complex model of
the 3-D structure of the Milky Way’s ISM are currently underway. Coupling a
3-D ISM model with H i spectra will help to break some of the current distance
velocity degeneracies that trouble H i. With this we might hope to be able to
answer: How do the H i properties correlate with large-scale Galactic
structure? Are there opacity or scale height variations with $R$ and azimuth?
Can H i be routinely linked to dust to provide 3-D spatial information
together with the velocity information? The 3-D dust and stellar distribution
models will also help researchers to create a 3-D UV radiation field to
understand how the H i properties change with local UV radiation field or
column density.

  3. 3.

By combining new high spatial and spectral resolution H i surveys with machine
learning and other spectral decomposition techniques, future work may be able
to investigate the CNM and WNM separately everywhere in the Galaxy. Combining
fully decomposed atlases of the CNM and WNM with ever improving statistical
descriptors of morphology (e.g. Rayleigh statistics Soler et al. (2020)) we
hope that researchers will be able to understand the differences in structure
between the phases and whether magnetic fields are a dominant contributor to
the structure of the H i in both or in just the CNM.

  4. 4.

With the revolution of large-area, high-resolution H i observations, H i will
remain a unique tracer for observationally determining the relative importance
of various turbulent driving modes in diverse ISM environments. As numerical
simulations become increasingly complex and move beyond prescribed turbulence
driving to directly include various channels of stellar feedback they will
require the detailed understanding of the effects these modes have on the
surrounding ISM that will be provided by future statistical studies of H i.

Perhaps the most important question is: What lessons can we take from the
Milky Way to help us understand other galaxies?  Over the next five years
extragalactic H i surveys with the Jansky VLA, ASKAP and MeerKAT will start to
reveal nearby galaxies with the spatial resolution and number of H i
absorption spectra that we have for the Milky Way in this review. Through
comparison of Milky Way H i with the properties of H i measured in nearby
galaxies we will start to probe how the H i phases responds to metallicity and
vastly different UV radiation fields. We started this review noting that it is
only in the Milky Way that we can resolve the sub-parsec scales needed to
understand the transition from the WNM to the CNM and its role as a throttle
in star formation. It is not obvious that we yet understand the full details
of that transition, but it it is clear that the physics is rich and by
extending detailed H i studies from the Milky Way to other galactic
environments we might just reach an answer.

## DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or
financial holdings that might be perceived as affecting the objectivity of
this review.

## ACKNOWLEDGMENTS

We have benefited enormously from conversations with S. Bialy, J. M. Dickey,
M. Gong, P. Hennebelle, C.-G. Kim, A. S. Hill, A. Marchal, M.-A. Miville-
Deschênes, C. Murray, & H. Nguyen. We are very grateful to Eve Ostriker for
many suggestions that have improved the early version of the manuscript. We
are grateful to Amit Mittal for providing Figure 8. The authors acknowledge
the Interstellar Institute’s program “With Two Eyes” and the Paris-Saclay
University’s Institut Pascal for hosting discussions that nourished the
development of the ideas behind this work. The authors are grateful to D.
McConnell for significant comments on drafts of this review. NMMc-G
acknowledges funding support through an Australian Research Council Laureate
Fellowship (project number FL210100039) funded by the Australian Government.
SS and DRR acknowledge support provided by the University of Wisconsin -
Madison Office of the Vice Chancellor for Research and Graduate Education with
funding from the Wisconsin Alumni Research Foundation. This work was supported
by the NSF Award AST-2108370 and the National Aeronautics and Space
Administration under Grant No. 4200766703.

## References

  * Audit & Hennebelle (2005) Audit E, Hennebelle P. 2005. A&A 433:1
  * Baker & Burton (1979) Baker PL, Burton WB. 1979. A&AS 35:129–152
  * Beaumont et al. (2013) Beaumont CN, Offner SSR, Shetty R, Glover SCO, Goodman AA. 2013. ApJ 777(2):173
  * Begum et al. (2010) Begum A, Stanimirović S, Goss WM, Heiles C, Pavkovich AS, Hennebelle P. 2010\. ApJ 725(2):1779–1785
  * Belfort & Crovisier (1984) Belfort P, Crovisier J. 1984. A&A 136:368–370
  * Beuther et al. (2016) Beuther H, Bihr S, Rugel M, et al. 2016. A&A 595:A32
  * Beuther et al. (2020) Beuther H, Wang Y, Soler J, et al. 2020. A&A 638:A44
  * Bialy (2020) Bialy S. 2020. ApJ 903(1):62
  * Bialy & Sternberg (2019) Bialy S, Sternberg A. 2019. ApJ 881(2):160
  * Bihr et al. (2015) Bihr S, Beuther H, Ott J, et al. 2015. A&A 580:A112
  * Blagrave et al. (2017) Blagrave K, Martin PG, Joncas G, et al. 2017. ApJ 834(2):126
  * Bland-Hawthorn et al. (2017) Bland-Hawthorn J, Maloney PR, Stephens A, Zovaro A, Popping A. 2017. ApJ 849(1):51
  * Bournaud et al. (2010) Bournaud F, Elmegreen BG, Teyssier R, Block DL, Puerari I. 2010. MNRAS 409(3):1088–1099
  * Bracco et al. (2020) Bracco A, Jelić V, Marchal A, et al. 2020. A&A 644:L3
  * Braun & Walterbos (1992) Braun R, Walterbos RAM. 1992. ApJ 386:120
  * Burton (1971) Burton WB. 1971. A&A 10:76–+
  * Burton (1988) Burton WB. 1988. Galactic and Extragalactic Radio Astronomy, chap. The Structure of Our Galaxy Dervived from Observations of Neutral Hydrogen. Springer, 2nd ed., 295
  * Campbell et al. (2022) Campbell JL, Clark SE, Gaensler BM, et al. 2022. ApJ 927(1):49
  * Carilli et al. (1998) Carilli CL, Dwarakanath KS, Goss WM. 1998. ApJ 502(1):L79–L83
  * Carilli & Walter (2013) Carilli CL, Walter F. 2013. ARA&A 51(1):105–161
  * Chengalur et al. (2013) Chengalur JN, Kanekar N, Roy N. 2013. MNRAS 432(4):3074–3079
  * Chepurnov et al. (2010) Chepurnov A, Lazarian A, Stanimirović S, Heiles C, Peek JEG. 2010\. ApJ 714:1398–1406
  * Choudhuri & Roy (2019) Choudhuri S, Roy N. 2019. MNRAS 483(3):3437–3443
  * Clark (1965) Clark BG. 1965. ApJ 142:1398
  * Clark et al. (2012) Clark PC, Glover SCO, Klessen RS, Bonnell IA. 2012. MNRAS 424(4):2599–2613
  * Clark & Hensley (2019) Clark SE, Hensley BS. 2019. ApJ 887(2):136
  * Clark et al. (2015) Clark SE, Hill JC, Peek JEG, Putman ME, Babler BL. 2015. Phys. Rev. Letters 115(24):241302
  * Clark et al. (2019) Clark SE, Peek JEG, Miville-Deschênes MA. 2019. ApJ 874(2):171
  * Clark et al. (2014) Clark SE, Peek JEG, Putman ME. 2014. ApJ 789(1):82
  * Cortese et al. (2021) Cortese L, Catinella B, Smith R. 2021. PASA 38:e035
  * Cox (2005) Cox DP. 2005. ARA&A 43(1):337–385
  * Cox & Smith (1974) Cox DP, Smith BW. 1974. ApJ 189:L105
  * Crovisier (1978) Crovisier J. 1978. A&A 70:43
  * Crovisier (1981) Crovisier J. 1981. A&A 94:162
  * Crovisier & Dickey (1983) Crovisier J, Dickey JM. 1983. A&A 122:282–296
  * Crovisier et al. (1978) Crovisier J, Kazes I, Aubry D. 1978. A&AS 32:205–282
  * Crutcher (1999) Crutcher RM. 1999. ApJ 520:706–713
  * Dawson et al. (2011) Dawson JR, McClure-Griffiths NM, Kawamura A, et al. 2011. ApJ 728:127
  * Dawson et al. (2008) Dawson JR, Mizuno N, Ohnishi T, McClure-Griffiths NM, Fukui Y. 2008. MNRAS 0802:4463
  * De Cia et al. (2021) De Cia A, Jenkins EB, Fox AJ, et al. 2021. Nature 597(7875):206–208
  * Deguchi & Watson (1985) Deguchi S, Watson WD. 1985. ApJ 290:578–586
  * Dénes et al. (2018) Dénes H, McClure-Griffiths NM, Dickey JM, Dawson JR, Murray CE. 2018\. MNRAS 479(2):1465–1490
  * Dickey & Benson (1982) Dickey JM, Benson JM. 1982. AJ 87:278–305
  * Dickey et al. (2022) Dickey JM, Dempsey JM, Pingel NM, et al. 2022. ApJ 926(2):186
  * Dickey & Lockman (1990) Dickey JM, Lockman FJ. 1990. ARA&A 28:215–261
  * Dickey et al. (2003) Dickey JM, McClure-Griffiths NM, Gaensler BM, Green AJ. 2003. ApJ 585:801
  * Dickey et al. (2001) Dickey JM, McClure-Griffiths NM, Stanimirović S, Gaensler BM, Green AJ. 2001\. ApJ 561:264
  * Dickey et al. (1977) Dickey JM, Salpeter EE, Terzian Y. 1977. ApJ 211:L77
  * Dickey et al. (1978) Dickey JM, Salpeter EE, Terzian Y. 1978. ApJS 36:77–114
  * Dickey et al. (2009) Dickey JM, Strasser S, Gaensler BM, et al. 2009. ApJ 693:1250
  * Dobbs et al. (2012) Dobbs CL, Pringle JE, Burkert A. 2012. MNRAS 425:2157–2168
  * D’Onghia & Fox (2016) D’Onghia E, Fox AJ. 2016. ARA&A 54:363–400
  * Dove & Shull (1994) Dove JB, Shull JM. 1994. ApJ 423:196
  * Dwarakanath et al. (2002) Dwarakanath KS, Carilli CL, Goss WM. 2002. ApJ 567:940–946
  * Ehlerová & Palouš (2005) Ehlerová S, Palouš J. 2005. A&A 437:101–112
  * Ehlerová & Palouš (2013) Ehlerová S, Palouš J. 2013. A&A 550:A23
  * Ekers & Rots (1979) Ekers RD, Rots AH. 1979. Short Spacing synthesis from a primary beam scanned interferometer. In IAU Coll. 49: Image Formation from Coherence Functions in Astronomy, eds. C van Schooneveld, D Reidel, vol. 49
  * Elmegreen et al. (2003) Elmegreen BG, Elmegreen DM, Leitner SN. 2003. ApJ 590(1):271–283
  * Elmegreen & Parravano (1994) Elmegreen BG, Parravano A. 1994. ApJ 435:L121
  * Elmegreen & Scalo (2004) Elmegreen BG, Scalo J. 2004. ARA&A 42:211–273
  * Ewen & Purcell (1951) Ewen HI, Purcell EM. 1951. Nature 168:356
  * Field (1958) Field GB. 1958. Proceedings of the IRE 46:240–250
  * Field et al. (1969) Field GB, Goldsmith DW, Habing HJ. 1969. ApJ 155:L149
  * Ford et al. (2010) Ford HA, Lockman FJ, McClure-Griffiths NM. 2010. ApJ 722:367
  * Ford et al. (2008) Ford HA, McClure-Griffiths NM, Lockman FJ, et al. 2008. ApJ 688:290
  * Fukui et al. (2014) Fukui Y, Okamoto R, Kaji R, et al. 2014. ApJ 796:59
  * Fukui et al. (1999) Fukui Y, Onishi T, Abe R, et al. 1999. PASJ 51(6):751–764
  * Fukui et al. (2015) Fukui Y, Torii K, Onishi T, et al. 2015. ApJ 798(1):6
  * Gibson et al. (2005) Gibson SJ, Taylor AR, Higgs LA, Brunt CM, Dewdney PE. 2005. ApJ 626:195–213
  * Gibson et al. (2005) Gibson SJ, Taylor AR, Higgs LA, Brunt CM, Dewdney PE. 2005. ApJ 626:214
  * Gibson et al. (2000) Gibson SJ, Taylor AR, Higgs LA, Dewdney PE. 2000. ApJ 540:851–862
  * Glover & Clark (2012) Glover SCO, Clark PC. 2012. MNRAS 421(1):9–19
  * Glover et al. (2010) Glover SCO, Federrath C, Mac Low MM, Klessen RS. 2010. MNRAS 404(1):2–29
  * Goldbaum et al. (2011) Goldbaum NJ, Krumholz MR, Matzner CD, McKee CF. 2011. ApJ 738(1):101
  * Gong et al. (2017) Gong M, Ostriker EC, Wolfire MG. 2017. ApJ 843(1):38
  * González-Casanova & Lazarian (2017) González-Casanova DF, Lazarian A. 2017. ApJ 835(1):41
  * Green (1993) Green DA. 1993. MNRAS 262:327–342
  * Green et al. (2019) Green GM, Schlafly E, Zucker C, Speagle JS, Finkbeiner D. 2019. ApJ 887(1):93
  * Grenier et al. (2005) Grenier IA, Casandjian JM, Terrier R. 2005. Science 307:1292–1295
  * Grisdale et al. (2018) Grisdale K, Agertz O, Renaud F, Romeo AB. 2018. MNRAS 479(3):3167–3180
  * Grisdale et al. (2017) Grisdale K, Agertz O, Romeo AB, Renaud F, Read JI. 2017. MNRAS 466(1):1093–1110
  * Hagen et al. (1955) Hagen JP, Lilley AE, McClain EF. 1955. ApJ 122:361
  * Haud & Kalberla (2007) Haud U, Kalberla PMW. 2007. A&A 466:555
  * Haworth et al. (2018) Haworth TJ, Glover SCO, Koepferl CM, Bisbas TG, Dale JE. 2018. New A Rev. 82:1–58
  * Hayashi et al. (2019) Hayashi K, Okamoto R, Yamamoto H, Hayakawa T, Tachihara K, Fukui Y. 2019\. ApJ 878(2):131
  * Heeschen (1955) Heeschen DS. 1955. ApJ 121:569
  * Heiles (1979) Heiles C. 1979. ApJ 229:533–537
  * Heiles (1984) Heiles C. 1984. ApJS 55:585–595
  * Heiles (1989) Heiles C. 1989. ApJ 336:808–821
  * Heiles (1997) Heiles C. 1997. ApJ 481:193–+
  * Heiles (1998) Heiles C. 1998. ApJ 498:689
  * Heiles (2000) Heiles C. 2000. AJ 119:923–927
  * Heiles & Troland (2003a) Heiles C, Troland TH. 2003a. ApJS 145:329
  * Heiles & Troland (2003b) Heiles C, Troland TH. 2003b. ApJ 586:1067
  * Heiles & Troland (2004) Heiles C, Troland TH. 2004. ApJS 151:271
  * Heiles & Troland (2005) Heiles C, Troland TH. 2005. ApJ 624:773
  * Hennebelle & Audit (2007) Hennebelle P, Audit E. 2007. A&A 465:431
  * Hennebelle & Falgarone (2012) Hennebelle P, Falgarone E. 2012. Astronomy & Astrophysics Reviews 20:55
  * Hennebelle & Inutsuka (2006) Hennebelle P, Inutsuka Si. 2006. ApJ 647(1):404–411
  * Heyer & Dame (2015) Heyer M, Dame TM. 2015. ARA&A 53:583–629
  * HI4PI Collaboration et al. (2016) HI4PI Collaboration, Ben Bekhti N, Flöer L, et al. 2016. A&A 594:A116
  * Hill et al. (2018) Hill AS, Mac Low MM, Gatto A, Ibáñez-Mejía JC. 2018. ApJ 862(1):55
  * Hopkins et al. (2020) Hopkins PF, Grudić MY, Wetzel A, et al. 2020. MNRAS 491(3):3702–3729
  * Hopkins et al. (2012) Hopkins PF, Quataert E, Murray N. 2012. MNRAS 421(4):3522–3537
  * Hopkins et al. (2018) Hopkins PF, Wetzel A, Kereš D, et al. 2018. MNRAS 477(2):1578–1603
  * Hotan et al. (2021) Hotan AW, Bunton JD, Chippendale AP, et al. 2021. PASA 38:e009
  * Hu (1981) Hu EM. 1981. ApJ 248:119–127
  * Hu et al. (2021) Hu Y, Lazarian A, Xu S. 2021. arXiv e-prints :arXiv:2104.02842
  * Hughes et al. (1971) Hughes MP, Thompson AR, Colvin RS. 1971. ApJS 23:323
  * Iffrig & Hennebelle (2017) Iffrig O, Hennebelle P. 2017. A&A 604:A70
  * Iwasaki & Inutsuka (2014) Iwasaki K, Inutsuka Si. 2014. ApJ 784(2):115
  * Kalberla et al. (2005) Kalberla PMW, Burton WB, Hartmann D, et al. 2005. A&A 440:775–+
  * Kalberla & Dedes (2008) Kalberla PMW, Dedes L. 2008. A&A 487:951
  * Kalberla et al. (2007) Kalberla PMW, Dedes L, Kerp J, Haud U. 2007. A&A 469:511
  * Kalberla & Haud (2015) Kalberla PMW, Haud U. 2015. A&A 578:A78
  * Kalberla & Haud (2018) Kalberla PMW, Haud U. 2018. A&A 619:A58
  * Kalberla & Haud (2019) Kalberla PMW, Haud U. 2019. A&A 627:A112
  * Kalberla & Kerp (2009) Kalberla PMW, Kerp J. 2009. ARA&A 47:27
  * Kalberla et al. (2020) Kalberla PMW, Kerp J, Haud U. 2020. A&A 639:A26
  * Kalberla et al. (2021) Kalberla PMW, Kerp J, Haud U. 2021. A&A 654:A91
  * Kalberla et al. (2016) Kalberla PMW, Kerp J, Haud U, et al. 2016. ApJ 821(2):117
  * Kalberla et al. (2010) Kalberla PMW, McClure-Griffiths NM, Pisano DJ, et al. 2010. A&A 521:17
  * Kanekar et al. (2011) Kanekar N, Braun R, Roy N. 2011. ApJ 737(2):L33
  * Kanekar et al. (2003) Kanekar N, Subrahmanyan R, Chengalur JN, Safouris V. 2003. MNRAS 346(4):L57–L61
  * Kang & Koo (2007) Kang Jh, Koo BC. 2007. ApJS 173(1):85–103
  * Khalil et al. (2006) Khalil A, Joncas G, Nekka F, Kestener P, Arneodo A. 2006. ApJS 165(2):512–550
  * Kim et al. (2022) Kim CG, Kim JG, Gong M, Ostriker EC. 2022. arXiv e-prints :arXiv:2211.13293
  * Kim & Ostriker (2017) Kim CG, Ostriker EC. 2017. ApJ 846(2):133
  * Kim & Ostriker (2018) Kim CG, Ostriker EC. 2018. ApJ 853(2):173
  * Kim et al. (2013) Kim CG, Ostriker EC, Kim WT. 2013. ApJ 776:1
  * Kim et al. (2014) Kim CG, Ostriker EC, Kim WT. 2014. ApJ 786:64
  * Kim & Kim (2013) Kim JG, Kim WT. 2013. ApJ 779(1):48
  * Knapp (1974) Knapp GR. 1974. ApJ 79:527
  * Knapp & Verschuur (1972) Knapp GR, Verschuur GL. 1972. AJ 77:717–725
  * Knee & Brunt (2001) Knee LBG, Brunt CM. 2001. Nature 412:308–310
  * Koch et al. (2019) Koch EW, Rosolowsky EW, Schruba A, et al. 2019. MNRAS 485(2):2324–2342
  * Körtgen et al. (2021) Körtgen B, Pingel N, Killerby-Smith N. 2021. MNRAS 505(2):1972–1986
  * Koyama & ichiro Inutsuka (2000) Koyama H, ichiro Inutsuka S. 2000. ApJ 532:980
  * Koyama & Inutsuka (2002) Koyama H, Inutsuka S. 2002. ApJ 564:L97–L100
  * Kritsuk et al. (2007) Kritsuk AG, Norman ML, Padoan P, Wagner R. 2007. ApJ 665:416–431
  * Krumholz & Burkhart (2016) Krumholz MR, Burkhart B. 2016. MNRAS 458(2):1671–1677
  * Krumholz et al. (2011) Krumholz MR, Leroy AK, McKee CF. 2011. ApJ 731:25
  * Krumholz et al. (2009) Krumholz MR, McKee CF, Tumlinson J. 2009. ApJ 693:216–235
  * Kulkarni & Fich (1985) Kulkarni SR, Fich M. 1985. ApJ 289:792–802
  * Kulkarni & Heiles (1987) Kulkarni SR, Heiles C. 1987. The Atomic Component. In Interstellar Processes, eds. DJ Hollenbach, J Thronson Harley A., vol. 134
  * Kulkarni & Heiles (1988) Kulkarni SR, Heiles C. 1988. Galactic and Extragalactic Radio Astronomy, chap. Neutral hydrogen and the diffuse interstellar medium. Springer-Verlag, 95–153
  * Lallement et al. (2019) Lallement R, Babusiaux C, Vergely JL, et al. 2019. A&A 625:A135
  * Lazareff (1975) Lazareff B. 1975. A&A 42:25
  * Lazarian & Pogosyan (2000) Lazarian A, Pogosyan D. 2000. ApJ 537:720–748
  * Lee et al. (2015) Lee MY, Stanimirovic S, Murray CE, Heiles C, Miller J. 2015. ApJ 809:56
  * Leike et al. (2020) Leike RH, Glatzle M, Enßlin TA. 2020. A&A 639:A138
  * Leroy et al. (2008) Leroy AK, Walter F, Brinks E, et al. 2008. AJ 136:2782–2845
  * Levine et al. (2006) Levine ES, Blitz L, Heiles C. 2006. ApJ 643:881–896
  * Li & Goldsmith (2003) Li D, Goldsmith PF. 2003. ApJ 585:823–839
  * Li & Goldsmith (2012) Li D, Goldsmith PF. 2012. ApJ 756:12
  * Lindner et al. (2015) Lindner RR, Vera-Ciro C, Murray CE, et al. 2015. AJ 149:138
  * Liszt (2001) Liszt H. 2001. A&A 371:698–707
  * Liszt et al. (2018) Liszt H, Gerin M, Grenier I. 2018. A&A 617:A54
  * Lockman (1984) Lockman FJ. 1984. ApJ 283:90–97
  * Lockman (2002) Lockman FJ. 2002. ApJ 580:L47–L50
  * Lockman et al. (1986) Lockman FJ, Hobbs LM, Shull JM. 1986. ApJ 301:380–394
  * Lockman & McClure-Griffiths (2016) Lockman FJ, McClure-Griffiths NM. 2016. ApJ 826(2):215
  * Mac Low et al. (2005) Mac Low MM, Balsara DS, Kim J, de Avillez MA. 2005. ApJ 626(2):864–876
  * Maloney (1993) Maloney P. 1993. ApJ 414:41
  * Marchal et al. (2021) Marchal A, Martin PG, Gong M. 2021. ApJ 921(1):11
  * Marchal & Miville-Deschênes (2021) Marchal A, Miville-Deschênes MA. 2021. ApJ 908(2):186
  * Marchal et al. (2019) Marchal A, Miville-Deschênes MA, Orieux F, et al. 2019. A&A 626:A101
  * Martin et al. (2015) Martin PG, Blagrave KPM, Lockman FJ, et al. 2015. ApJ 809(2):153
  * McClure-Griffiths & Dickey (2016) McClure-Griffiths NM, Dickey JM. 2016. ApJ 831(2):124
  * McClure-Griffiths et al. (2001) McClure-Griffiths NM, Dickey JM, Gaensler BM, Green AJ. 2001. ApJ 562:424
  * McClure-Griffiths et al. (2002) McClure-Griffiths NM, Dickey JM, Gaensler BM, Green AJ. 2002. ApJ 578:176–193
  * McClure-Griffiths et al. (2003) McClure-Griffiths NM, Dickey JM, Gaensler BM, Green AJ. 2003. ApJ 594:833
  * McClure-Griffiths et al. (2004) McClure-Griffiths NM, Dickey JM, Gaensler BM, Green AJ. 2004. ApJ 607:L127–L130
  * McClure-Griffiths et al. (2006) McClure-Griffiths NM, Dickey JM, Gaensler BM, Green AJ, Haverkorn M. 2006\. ApJ 652:1339–1347
  * McClure-Griffiths et al. (2005) McClure-Griffiths NM, Dickey JM, Gaensler BM, Green AJ, Haverkorn M, Strasser S. 2005. ApJS 158:178–
  * McClure-Griffiths et al. (2006) McClure-Griffiths NM, Ford A, Pisano DJ, et al. 2006. ApJ 638:196
  * McClure-Griffiths et al. (2009) McClure-Griffiths NM, Pisano DJ, Calabretta MR, et al. 2009. ApJS 181:398
  * McKee & Ostriker (1977) McKee CF, Ostriker JP. 1977. ApJ 218:148–169
  * Mebold et al. (1997) Mebold U, Düsterberg C, Dickey JM, Staveley-Smith L, Kalberla P. 1997\. ApJ 490(1):L65–L68
  * Mebold et al. (1982) Mebold U, Winnberg A, Kalberla PMW, Goss WM. 1982. A&A 115(2):223–241
  * Meyer et al. (2006) Meyer DM, Lauroesch JT, Heiles C, Peek JEG, Engelhorn K. 2006. ApJ 650(1):L67–L70
  * Meyer et al. (2012) Meyer DM, Lauroesch JT, Peek JEG, Heiles C. 2012. ApJ 752(2):119
  * Miville-Deschênes et al. (2003) Miville-Deschênes MA, Joncas G, Falgarone E, Boulanger F. 2003. A&A 411:109–121
  * Moss et al. (2013) Moss VA, McClure-Griffiths NM, Murphy T, Pisano DJ, Kummerfeld JK, Curran JR. 2013\. ApJS 209(1):12
  * Muller & Oort (1951) Muller CA, Oort JH. 1951. Nature 168(4270):357–358
  * Murray et al. (2014) Murray CE, Lindner RR, Stanimirović S, et al. 2014. ApJ 781(2):L41
  * Murray et al. (2020) Murray CE, Peek JEG, Kim CG. 2020. ApJ 899(1):15
  * Murray et al. (2015) Murray CE, Stanimirović S, Goss WM, et al. 2015. ApJ 804(2):89
  * Murray et al. (2018) Murray CE, Stanimirović S, Goss WM, et al. 2018. ApJS 238(2):14
  * Murray et al. (2021) Murray CE, Stanimirović S, Heiles C, et al. 2021. ApJS 256(2):37
  * Murray et al. (2017) Murray CE, Stanimirović S, Kim CG, et al. 2017. ApJ 837(1):55
  * Nguyen et al. (2019) Nguyen H, Dawson JR, Lee MY, et al. 2019. ApJ 880(2):141
  * Nguyen et al. (2018) Nguyen H, Dawson JR, Miville-Deschênes MA, et al. 2018. ApJ 862(1):49
  * Nidever et al. (2019) Nidever DL, Price-Whelan AM, Choi Y, et al. 2019. ApJ 887(2):115
  * Normandeau et al. (1996) Normandeau M, Taylor AR, Dewdney PE. 1996. Nature 380:687–689
  * Ntormousi et al. (2011) Ntormousi E, Burkert A, Fierlinger K, Heitsch F. 2011. ApJ 731(1):13
  * Offner & Arce (2014) Offner SSR, Arce HG. 2014. ApJ 784(1):61
  * Panopoulou & Lenz (2020) Panopoulou GV, Lenz D. 2020. ApJ 902(2):120
  * Payne et al. (1978) Payne HE, Dickey JM, Salpeter EE, Terzian Y. 1978. ApJ 221:L95–L98
  * Peek et al. (2018) Peek JEG, Babler BL, Zheng Y, et al. 2018. ApJS 234(1):2
  * Peek & Clark (2019) Peek JEG, Clark SE. 2019. ApJ 886(1):L13
  * Peek et al. (2011) Peek JEG, Heiles C, Peek KMG, Meyer DM, Lauroesch JT. 2011. ApJ 735(2):129
  * Peek et al. (2022) Peek JEG, Tchernyshyov K, Miville-Deschenes MA. 2022. ApJ 925(2):201
  * Pidopryhora et al. (2015) Pidopryhora Y, Lockman FJ, Dickey JM, Rupen MP. 2015. ApJS 219(2):16
  * Pidopryhora et al. (2007) Pidopryhora Y, Lockman FJ, Shields JC. 2007. ApJ 656:928
  * Pingel et al. (2018) Pingel NM, Lee MY, Burkhart B, Stanimirović S. 2018. ApJ 856(2):136
  * Pingel et al. (2013) Pingel NM, Stanimirović S, Peek JEG, et al. 2013. ApJ 779(1):36
  * Piontek & Ostriker (2004) Piontek RA, Ostriker EC. 2004. ApJ 601(2):905–920
  * Piontek & Ostriker (2005) Piontek RA, Ostriker EC. 2005. ApJ 629(2):849–864
  * Piontek & Ostriker (2007) Piontek RA, Ostriker EC. 2007. ApJ 663(1):183–203
  * Pisano (2014) Pisano DJ. 2014. AJ 147(3):48
  * Planck Collaboration et al. (2011) Planck Collaboration, Ade PAR, Aghanim N, et al. 2011. A&A 536:A19
  * Price-Whelan et al. (2019) Price-Whelan AM, Nidever DL, Choi Y, et al. 2019. ApJ 887(1):19
  * Pritchard & Loeb (2012) Pritchard JR, Loeb A. 2012. Reports on Progress in Physics 75(8):086901
  * Putman et al. (2012) Putman ME, Peek JEG, Joung MR. 2012. ARA&A 50(1):491–529
  * Radhakrishnan & Goss (1972) Radhakrishnan V, Goss WM. 1972. ApJS 24:161
  * Rathjen et al. (2021) Rathjen TE, Naab T, Girichidis P, et al. 2021. MNRAS 504(1):1039–1061
  * Roy et al. (2013a) Roy N, Kanekar N, Braun R, Chengalur JN. 2013a. MNRAS 436(3):2352–2365
  * Roy et al. (2013b) Roy N, Kanekar N, Chengalur JN. 2013b. MNRAS 436(3):2366–2385
  * Rybarczyk et al. (2022) Rybarczyk DR, Stanimirović S, Gong M, et al. 2022. ApJ 928(1):79
  * Saintonge & Catinella (2022) Saintonge A, Catinella B. 2022. ARA&A :arXiv:2202.00690
  * Sault (1994) Sault RJ. 1994. A&AS 107:55–69
  * Savage & Wakker (2009) Savage BD, Wakker BP. 2009. ApJ 702(2):1472–1489
  * Scalo & Elmegreen (2004) Scalo J, Elmegreen BG. 2004. ARA&A 42(1):275–316
  * Scalo (1987) Scalo JM. 1987. Theoretical Approaches to Interstellar Turbulence. In Interstellar Processes, eds. DJ Hollenbach, J Thronson Harley A., vol. 134
  * Schaye (2004) Schaye J. 2004. ApJ 609(2):667–682
  * Schruba et al. (2011) Schruba A, Leroy AK, Walter F, et al. 2011. AJ 142(2):37
  * Seifried et al. (2022) Seifried D, Beuther H, Walch S, et al. 2022. MNRAS 512(4):4765–4784
  * Seon & Kim (2020) Seon Ki, Kim CG. 2020. ApJS 250(1):9
  * Shaver et al. (1983) Shaver PA, McGee RX, Newton LM, Danks AC, Pottasch SR. 1983. MNRAS 204:53–112
  * Shull et al. (2021) Shull JM, Danforth CW, Anderson KL. 2021. ApJ 911(1):55
  * Sidorin et al. (2014) Sidorin V, Douglas KA, Palouš J, Wünsch R, Ehlerová S. 2014\. A&A 565:A6
  * Snow & McCall (2006) Snow TP, McCall BJ. 2006. ARA&A 44(1):367–414
  * Sofue (2018) Sofue Y. 2018. PASJ 70(3):50
  * Soler et al. (2019) Soler JD, Beuther H, Rugel M, et al. 2019. A&A 622:A166
  * Soler et al. (2020) Soler JD, Beuther H, Syed J, et al. 2020. A&A 642:A163
  * Soler et al. (2022) Soler JD, Miville-Deschênes MA, Molinari S, et al. 2022. A&A 662:A96
  * Spitzer Jr (1978) Spitzer Jr L. 1978. Physical Processes in the Interstellar Medium. John Wiley & Sons, Inc.
  * Stanimirović (2002) Stanimirović S. 2002. Short-Spacings Correction from the Single-Dish Perspective. In ASP Conf. Ser. 278, eds. S. Stanimirovic, D. Altschuler, P. Goldsmith, C. Salter, vol. Single-Dish Radio Astronomy: Techniques and Applications. San Francisco, CA: ASP
  * Stanimirović et al. (2014) Stanimirović S, Murray CE, Lee MY, Heiles C, Miller J. 2014. ApJ 793(2):132
  * Stanimirović et al. (2006) Stanimirović S, Putman M, Heiles C, et al. 2006. ApJ 653:1210
  * Stanimirović et al. (1999) Stanimirović S, Staveley-Smith L, Dickey JM, Sault RJ, Snowden SL. 1999. MNRAS 302:417–436
  * Stanimirović & Zweibel (2018) Stanimirović S, Zweibel EG. 2018. ARA&A 56:489–540
  * Staveley-Smith et al. (1997) Staveley-Smith L, Sault RJ, Hatzidimitriou D, Kesteven MJ, McConnell D. 1997. MNRAS 289:225–252
  * Stevens et al. (2019) Stevens ARH, Diemer B, Lagos CdP, et al. 2019. MNRAS 483(4):5334–5354
  * Stil et al. (2006) Stil JM, Lockman FJ, Taylor AR, et al. 2006. ApJ 637:366
  * Stil et al. (2006) Stil JM, Taylor AR, Dickey JM, et al. 2006. AJ 132:1158–1176
  * Strasser et al. (2007) Strasser ST, Dickey JM, Taylor AR, et al. 2007. AJ 134:2252
  * Syed et al. (2020) Syed J, Wang Y, Beuther H, et al. 2020. A&A 642:A68
  * Szotkowski et al. (2019) Szotkowski S, Yoder D, Stanimirović S, et al. 2019. ApJ 887(2):111
  * Taylor et al. (2003) Taylor AR, Gibson SJ, Peracaula M, et al. 2003. AJ 125:3145–3164
  * Tchernyshyov & Peek (2017) Tchernyshyov K, Peek JEG. 2017. AJ 153(1):8
  * Tchernyshyov et al. (2018) Tchernyshyov K, Peek JEG, Zasowski G. 2018. AJ 156(6):248
  * Turić et al. (2021) Turić L, Jelić V, Jaspers R, et al. 2021. A&A 654:A5
  * Valdivia et al. (2016) Valdivia V, Hennebelle P, Gérin M, Lesaffre P. 2016. A&A 587:A76
  * Van Eck et al. (2019) Van Eck CL, Haverkorn M, Alves MIR, et al. 2019. A&A 623:A71
  * Vázquez-Semadeni et al. (2010) Vázquez-Semadeni E, Colín P, Gómez GC, Ballesteros-Paredes J, Watson AW. 2010. ApJ 715(2):1302–1317
  * Vergely et al. (2022) Vergely JL, Lallement R, Cox NLJ. 2022. arXiv e-prints :arXiv:2205.09087
  * Verschuur (1995) Verschuur GL. 1995. ApJ 451:645
  * Wada et al. (2002) Wada K, Meurer G, Norman CA. 2002. ApJ 577(1):197–205
  * Walch et al. (2015) Walch S, Girichidis P, Naab T, et al. 2015. MNRAS 454(1):238–268
  * Wang et al. (2020a) Wang Y, Beuther H, Rugel MR, et al. 2020a. A&A 634:A83
  * Wang et al. (2020b) Wang Y, Bihr S, Beuther H, et al. 2020b. A&A 634:A139
  * Wang et al. (2020c) Wang Y, Bihr S, Beuther H, et al. 2020c. A&A 634:A139
  * Wenger et al. (2019) Wenger TV, Balser DS, Anderson LD, Bania TM. 2019. ApJ 887(2):114
  * Winkel et al. (2010) Winkel B, Kalberla PMW, Kerp J, Flöer L. 2010. ApJS 188:488
  * Wolfire (2015) Wolfire MG. 2015. Highlights of Astronomy 16:600–602
  * Wolfire et al. (1995) Wolfire MG, Hollenbach D, McKee CF, Tielens AGGM, Bakes ELO. 1995. ApJ 443:152–168
  * Wolfire et al. (1995) Wolfire MG, McKee CF, Hollenbach D, Tielens AGGM. 1995. ApJ 453:673–+
  * Wolfire et al. (2003) Wolfire MG, McKee CF, Hollenbach D, Tielens AGGM. 2003. ApJ 587:278–311
  * Wouthuysen (1952) Wouthuysen SA. 1952. AJ 57:31–32
  * Yoo & Cho (2014) Yoo H, Cho J. 2014. ApJ 780(1):99
  * Yuen et al. (2021) Yuen KH, Ho KW, Lazarian A. 2021. ApJ 910(2):161
  * Yuen & Lazarian (2017) Yuen KH, Lazarian A. 2017. ApJ 837(2):L24


# Drop in the Hard Pulsed Fraction and a Candidate
Cyclotron Line in IGR J16320$-$4751 seen by _NuSTAR_

A. Bodaghee Dept. of Chemistry, Physics and Astronomy, Georgia College and
State University, 231 W. Hancock St., Milledgeville, GA 31061, USA  J.-L. Chiu
National Space Organization, National Applied Research Labs, Hsinchu City 300,
Taiwan  J.A. Tomsick  Space Sciences Laboratory, University of California, 7
Gauss Way, Berkeley, CA 94720, USA  V. Bhalerao  Indian Institute of
Technology Bombay, Powai, Mumbai 400076, India  E. Bottacini  W.W. Hansen
Experimental Physics Laboratory & Kavli Institute for Particle Astrophysics
and Cosmology, Stanford University, 452 Lomita Mall, Palo Alto, CA 94305, USA
Dipartimento di Fisica e Astronomia “G. Galilei,” Università di Padova, Via
Belzoni 7, 35131 Padova, Italy  Eureka Scientific, 2452 Delmer Street, Suite
100, Oakland, CA 94602, USA  M. Clavel  Université Grenoble Alpes, CNRS, IPAG,
38000 Grenoble, France  C. Cox  Dept. of Chemistry, Physics and Astronomy,
Georgia College and State University, 231 W. Hancock St., Milledgeville, GA
31061, USA  F. Fürst  Quasar Science Resources SL for ESA, European Space
Astronomy Centre (ESAC), Science Operations Department, 28692 Villanueva de la
Cañada, Madrid, Spain  M.J. Middleton  Department of Physics and Astronomy,
University of Southampton, Highfield, Southampton SO17 1BJ, UK  F. Rahoui
European Southern Observatory, Karl Schwarzchild-Strasse 2, 85748 Garching bei
Munchen, Germany  J. Rodriguez  Université Paris-Saclay, Université Paris
Cité, CEA, CNRS, AIM, 91191, Gif-sur-Yvette, France  P. Romano  INAF,
Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, Italy  J.
Wilms  Dr. Karl-Remeis-Sternwarte and ECAP, Sternwartstrasse 7, 96049 Bamberg,
Germany

###### Abstract

We report on a timing and spectral analysis of a 50-ks NuSTAR observation of
IGR J16320$-$4751 (catalog ) ($=$ AX J1631.9$-$4752 (catalog )); a high-mass
X-ray binary hosting a slowly-rotating neutron star. In this observation from
2015, the spin period was 1,308.8$\pm$0.4 s giving a period derivative
$\dot{P}\sim 2\times 10^{-8}$ s s-1 when compared with the period measured in
2004. In addition, the pulsed fraction decreased as a function of energy, as
opposed to the constant trend that was seen previously. This suggests a change
in the accretion geometry of the system during the intervening 11 years. The
phase-averaged spectra were fit with the typical model for accreting pulsars:
a power law with an exponential cutoff. This left positive residuals at 6.4
keV attributable to the known iron K$\alpha$ line, as well as negative
residuals around 14 keV from a candidate cyclotron line detected at a
significance of 5$\sigma$. We found no significant differences in the spectral
parameters across the spin period, other than the expected changes in flux and
component normalizations. A flare lasting around 5 ks was captured during the
first half of the observation where the X-ray emission hardened and the local
column density decreased. Finally, the binary orbital period was refined to
8.9912$\pm$0.0078 d thanks to Swift/BAT monitoring data from 2005–2022.

high mass X-ray binaries: cyclotron lines: spectroscopy: stars: neutron ;
X-rays: binaries ; X-rays: individual (IGR J16320-4751)

††facilities: NuSTAR, Swift (XRT and BAT)††software: HEASoft v6.29 (Nasa High
Energy Astrophysics Science Archive Research Center (2014), Heasarc), FTOOLS
v6.29 (Blackburn et al., 1999), NuSTARDAS v2.1.1, XSpec v12.12.0 (Arnaud,
1996), Matlab R2021b (MATLAB, 2021)

,

,

##  1 Introduction

Hard X-ray monitoring of the Galactic Plane by INTEGRAL has uncovered dozens
of new High-Mass X-ray Binaries (HMXBs: Walter et al., 2015; Sidoli & Paizis,
2018; Kretschmar et al., 2019). These are systems in which a neutron star (NS)
or a black hole (BH) accretes from a massive companion star ($M\gtrsim
5\,\,M_{\odot}$). Given that INTEGRAL’s position uncertainty is a few
arcminutes, the only way to tell that these objects are HMXBs is thanks to
follow-up observations with X-ray telescopes such as Chandra, NuSTAR, Suzaku,
Swift, and XMM-Newton.

During follow-up observations, many of these HMXBs presented characteristics
that understandably hindered their detection in lower-energy X-ray surveys.
They could be extremely obscured below 5 keV with X-ray absorbing column
densities ($N_{\mathrm{H}}$) several times $10^{23}$ cm-2, or an order of
magnitude more than the cumulative Galactic absorption along the line of sight
(e.g., Matt & Guainazzi, 2003; Walter et al., 2003; Patel et al., 2004). Some
stayed at a low-level of emission for months or years ($\sim 10^{32}$ erg s-1)
and awakened with huge flares where the luminosity would increase by up to 6
orders of magnitude (i.e., supergiant fast X-ray transients or SFXTs: in’t
Zand, 2005; Negueruela et al., 2006; Romano et al., 2014; Bozzo et al., 2015;
Romano et al., 2015; Sidoli et al., 2016). Finally, they could have spin
periods lasting around 1 ks (e.g., Zurita Heras et al., 2006; Bodaghee et al.,
2006; Rodriguez et al., 2006).

Figure 1: Images of IGR J16320$-$4751 gathered with NuSTAR FPMA (_left_) and FPMB (_right_) in 3–79 keV. The images are presented in J2000.0 equatorial coordinates, they are scaled logarithmically, and extraction regions for the source (75′′-radius) and background (100′′-radius) are indicated. Table 1: Journal of observations of IGR J16320$-$4751\.  telescope | observation ID | pointing R.A. (J2000) | pointing decl. (J2000) | start date (UT) | end date (UT) | effective exposure (ks)
---|---|---|---|---|---|---
NuSTAR | 30001008002 | 248.0277 |  $-$47.904 | 2015-06-06 18:46:07 | 2015-06-07 23:36:07 | 49.845
Swift/XRT | 00081642001 | 247.9418 |  $-$47.8672 | 2015-06-06 20:07:38 | 2015-06-06 22:06:56 | 1.703

One of the obscured HMXBs detected early in the INTEGRAL mission was IGR
J16320$-$4751 (catalog ) (Tomsick et al., 2003; Rodriguez et al., 2003). This
turned out to be the high-energy counterpart of an unclassified X-ray source
named AX J1631.9$-$4752 that was discovered two years earlier by ASCA
(Sugizaki et al., 2001). A coherent pulsation of 1,309$\pm$40 s, consistent
with the spin period of an accreting NS, was measured with XMM-Newton
(Lutovinov et al., 2005), and was later refined to 1,303.8$\pm$0.9 s
(Rodriguez et al., 2006). While the source varies on short timescales, its
average, hard X-ray flux since its discovery by ASCA has stayed within a
narrow range (Krimm et al., 2013; Krivonos et al., 2022). Near-IR spectroscopy
suggests a supergiant donor star whose spectral type is BN0.5 Ia (Coleiro et
al., 2013), thereby confirming its status as an HMXB at a distance of
$\sim$3.5 kpc (Rahoui et al., 2008). Six arcminutes away from IGR
J16320$-$4751 (catalog ) is an unrelated pulsar wind nebula (Acero et al.,
2015) detected in the gamma-rays by Fermi/LAT (4FGL J1633.0$-$4746e (catalog
): Abdollahi et al., 2020) and HESS (HESS J1632$-$478 (catalog ): Aharonian et
al., 2006).

With a short orbital period of 8.99$\pm$0.01 days (Corbet et al., 2005; Levine
et al., 2011; García et al., 2018), the large absorption
($N_{\mathrm{H}}$$\gtrsim 10^{23}$ cm-2) is likely due to the NS being
shrouded in the wind of its companion star. In the case of supergiant donors,
the stellar wind is the main contributor to the photoelectric absorption and
the Fe K$\alpha$ emission (Giménez-García et al., 2015; Pradhan et al., 2018).
In the specific case of IGR J16320$-$4751 (catalog ), García et al. (2018)
demonstrated that these parameters as measured by XMM-Newton were modulated
with the orbital period of the binary as determined by Swift/BAT, i.e., they
were related to the configuration of the X-ray source and surrounding wind as
viewed by the observer.

In 2015, NuSTAR pointed at IGR J16320$-$4751 (catalog ) for 29 hours and those
results are presented for the first time in this paper. Procedures for
analysis of the NuSTAR data are described in Section 2. Results from timing
and spectral analyses are in Section 3, and they are discussed in Section 4.

##  2 OBSERVATIONS AND DATA ANALYSIS

NuSTAR observed IGR J16320$-$4751 (catalog ) for a total of 103.6 ks from
18:46:07 (UT) on 2015 June 6, until 23:36:07 (UT) on 2015 June 7. This
observation (ObsID: 30101026002) collected 49.8 ks of on-source time (Good
Time Intervals or GTIs) on each of its two focal plane modules A and B (FPMA
and FPMB) which have a 13’$\times$13’ field of view (FoV).

The NuSTAR data were reduced using nupipeline and nuproducts from the NuSTAR
Data Analysis Software (NuSTARDAS v2.1.1) as distributed with HEASoft (v6.29:
Nasa High Energy Astrophysics Science Archive Research Center (2014),
Heasarc). Response files were linked to the latest calibration database
available at the time (CALDB 20220105). We extracted source counts for FPMA
and FPMB from a circular region with a radius of 75′′ centered at the source
position listed in the 4XMM Serendipitous Source Catalog (Webb et al., 2020):
R.A. (J2000.0) $=16^{\mathrm{h}}32^{\mathrm{m}}01.76^{\mathrm{s}}$, and Decl.
= $-47^{\circ}52^{\prime}29.0^{\prime\prime}$. Background counts were
extracted from a circular region (100′′ radius) situated away from the source
region while remaining on the same detector chip.

Figure 1 presents the field of IGR J16320$-$4751 (catalog ) from FPMA and FPMB
along with the source and background extraction regions. Stray light from GX
340$+$0 (catalog ), situated 3∘ outside the FoV, affected a small portion of
one detector chip from each module. The boundary of the stray light
contamination region was far enough away from the location of IGR
J16320$-$4751 (catalog ) that it did not impact our analysis.

A concurrent Swift/XRT observation (ObsID: 00081642001) was performed on 2015
June 6 between 20:07:38 and 22:06:56 (UT) for an effective exposure time of
1,703 s. The Swift/XRT data were processed according to the standard procedure
of xrtpipeline (v0.13.6). Source counts were extracted from inside a circular
region whose radius was 20 pixels (1 pixel $\sim$2.36′′). Background events
were taken from an annular source-free region centered on the source
(inner/outer radii of 70/110 pixels). Ancillary response files were generated
with xrtmkarf (v0.6.3) to account for the different extraction regions,
vignetting, and PSF corrections, while the spectral redistribution matrix was
the most recent version available (20130101v014).

Light curve data for IGR J16320$-$4751 (catalog ) was downloaded from the
Swift/BAT Hard X-ray Transient
Monitor111https://swift.gsfc.nasa.gov/results/transients/ (Krimm et al., 2013)
where the source is listed under its alias AX J1631.9$-$4752\. These data
consist of a count rate and error in 15–50 keV collected during each orbital
pointing of the Swift satellite between 2005 February 14 and 2022 July 20.
Data of poor quality were excluded by selecting only those rows where
“DATA_FLAG==0.” The remaining 78,882 pointings have exposure times that range
from 64 s to 2.64 ks (an average of 665 s) giving a total effective exposure
time of 52.5 Ms spread over 550 Ms of calendar time (6,366 d).

Figure 2: Light curve and hardness ratio from NuSTAR (3–79 keV) for IGR
J16320$-$4751 (catalog ) with 100 s in each bin ($T_{0}=$ MJD 57179.795322).
The total (FPMA$+$FPMB) net source count rate is presented in the top panel
where the background count rate, as shown in the middle panel, has been scaled
by area and subtracted. The hardness ratio is featured in the bottom panel
where $S$ and $H$ represent count rates in 3–10 keV and 10–79 keV,
respectively. The flare corresponds to an epoch 22–27 ks into the observation
(highlighted in light yellow and bounded by dashed lines). The dotted lines
indicate the start and stop times of the contemporaneous Swift/XRT pointing.

Relying on the 4XMM position above, we performed barycentric corrections on
the NuSTAR data in nuproducts, while the Swift XRT and BAT data were
barycentered using barycorr with the orbital ephemeris parameter set to
geocenter. Timing and spectral data were analyzed in Xronos (v6.0) and XSpec
(v12.12.0: Arnaud, 1996), respectively, where the latter assumed elemental
abundances from Wilms et al. (2000) and photon-ionization cross-sections from
Verner et al. (1996). NuSTAR data were restricted to 3–79 keV, Swift/XRT data
were limited to 0.3–10 keV, and known bad channels from both telescopes were
ignored. NuSTAR spectral counts were grouped such that each bin had a minimum
significance of 5$\sigma$ (for phase-resolved analysis) and 10$\sigma$ (for
phase-averaged analysis) permitting the use of $\chi^{2}$ statistics, while
Swift/XRT spectral data were grouped at 20 counts per bin. Unless specified
otherwise, error bars in the figures indicate 1$\sigma$ confidence boundaries,
while error values cited in the text and tables are given at 90% confidence. A
journal of NuSTAR and Swift/XRT observations is provided in Table 1.

Figure 3: Spin period search ($\chi^{2}$ distribution) on the NuSTAR light
curve of IGR J16320$-$4751 with 20 bins per period and a resolution of 1.2 s
in three energy bands: 3–6 keV (top panel; red curve); 6–12 keV (middle panel;
green curve); and 12–25 keV (bottom panel; blue curve). The best-fitting spin
period ($P=$ 1,308.8 s) is denoted by a dotted line.

##  3 RESULTS

###  3.1 Timing Analysis

####  3.1.1 Light Curve

Figure 2 shows the NuSTAR background-subtracted light curve (3–79 keV) and
hardness ratio where net source counts from both modules have been summed. The
hardness ratio is defined as $(H-S)/(H+S)$ where $S$ (3–10 keV) and $H$ (10–79
keV) are net count rates. In FPMA, there were a total of 110,296$\pm$333 net
counts in 49.89 ks of effective exposure time, and in FPMB, there were
98,064$\pm$314 net counts in 49.84 ks. Summing the net counts from both
modules returned a total of 208,360$\pm$458 counts or a count rate of
4.18$\pm$0.01 counts s-1.

Figure 4: Pulse profiles ($P=$ 1,308.8 s) in three energy bands from the
NuSTAR observation. The pulse is repeated once for ease of viewing. Bins
attributed to the peak (white; phases 0.2–0.6) and to the valley (gray; phases
0.0–0.2 and 0.6–1.0) are designated for phase-resolved spectroscopy. All
panels have the same vertical scale.

A flare lasting $\sim$5 ks was noticed around 22 ks into the observation. This
time interval of 22–27 ks after the observation began was called the “flare”
epoch. During the flare, there were 14,321$\pm$120 net counts in FPMA, and
12,756$\pm$113 net counts in FPMB, with an effective exposure time of 2.26 ks
per module. When the modules were summed, the total net counts was
27,078$\pm$165 with an average count rate of 11.98$\pm$0.07 counts s-1.

The rest of the observation, i.e., excluding the flare, was referred to as the
“non-flare” epoch. This epoch contained 95,975$\pm$311 net counts in FPMA
(47.64 ks), and 85,308$\pm$293 net counts in FPMB (47.59 ks). A sum of both
modules gave 181,283$\pm$427 total net counts or 3.81$\pm$0.01 counts s-1.

In Swift/XRT, there were 112$\pm$12 net counts in 1,703 s for a count rate of
(6.6$\pm$0.7)$\times 10^{-2}$ counts s-1.

Figure 5: Energy dependence of the pulsed fraction. The pulsed fractions of
IGR J16320$-$4751 light curves are shown for this 2015 NuSTAR observation
(blue; $P=1,308.8$ s) and for the 2004 observation by Rodriguez et al. (2006)
combining XMM-Newton and INTEGRAL (magenta; $P=1,303$ s). Root mean square
(RMS) values of the NuSTAR light curves (green) are also plotted as a
reference.

####  3.1.2 Spin Period

A periodicity search was performed with efsearch on the source ($+$
background) light curve (0.1-s resolution) of the full observation in five
energy bands: 3–6 keV, 6–12 keV, 12–25 keV, 25–79 keV, and 3–79 keV. A
coherent pulsation near the known period of 1,300 s was detected in all energy
bands except 25–79 keV. The pulsation was detected most significantly at lower
energies (Fig. 3). Figure 4 presents the pulse profile with 20 bins per period
for energies up to 25 keV. In the 3–6-keV band, the best-fitting period was
1,308.8$\pm$0.4 s where the centroid was determined with the Press & Rybicki
(1989) fast algorithm for Lomb-Scargle periodograms (Lomb, 1976; Scargle,
1982) and the error from Horne & Baliunas (1986) and Leahy (1987).

Featuring a single broad peak and a mirrored valley, the shape of the pulse
profile from this 2015 NuSTAR observation is similar to the one from 2004
using XMM-Newton and INTEGRAL (Rodriguez et al., 2006). However, there was a
significant difference in the pulsed fraction between the observations. The
pulsed fraction is defined as
$(I_{\mathrm{max}}-I_{\mathrm{min}})/(I_{\mathrm{max}}+I_{\mathrm{min}})$
where $I_{\mathrm{max}}$ and $I_{\mathrm{min}}$ are the normalized count rates
in the highest (phase: 0.35–0.40) and lowest intensity bins (phase: 0.0–0.05),
respectively. Figure 5 shows that the pulsed fraction decreased significantly
as a function of energy during this NuSTAR observation. The root mean square
(RMS) of the NuSTAR light curves had a similar negative correlation with
energy. This behavior is different from what was previously seen by XMM-Newton
and INTEGRAL where the pulsed fraction was consistent with being constant as a
function of energy (Rodriguez et al., 2006).

####  3.1.3 Orbital Period

Figure 6: Light curve and orbital period search from Swift/BAT Transient
Monitor (Krimm et al., 2013) data of IGR J16320$-$4751 in 15–50 keV. The main
panel presents count rates where each bin collects 1 Ms of exposure time. The
average count rate ($3.8\times 10^{-3}$ cts cm-2 s-1), which excludes the
prominent flare (whose apex occurs on MJD 58505), is denoted as a horizontal
red line. The dotted line indicates the time of the NuSTAR observation. The
upper inset panel shows results from an orbital period search centered at
8.9912 day (dotted vertical line), with 20 bins per period and a resolution of
50 s, while the lower inset panel gives two cycles of the orbital period.

The 17-year BAT light curve of IGR J16320$-$4751 (catalog ) illustrates the
stability of the source flux on timescales of years (main panel of Fig. 6).
The figure reveals a prominent flare around MJD 58500 where, over the course
of 2–3 months, the source count rate increased up to a factor of nearly 20 to
$7.4\times 10^{-2}$ cts cm-2 s-1 from a mean value (without the flare) of
$3.8\times 10^{-3}$ cts cm-2 s-1. We used efsearch with 20 bins per period and
a resolution of 50 s to generate a periodogram (upper inset panel of Fig. 6),
and we fit its peak with a Gaussian to obtain an orbital period of
8.9912$\pm$0.0078 d with $T_{\phi_{0}}=$ MJD 59760.449555 corresponding to the
phase bin with the lowest flux in the folded light curve (lower inset panel of
Fig. 6). This means the NuSTAR observation coincided with orbital phases
0.97–1.0 and 0.0–0.11. The orbital period matches the value obtained by García
et al. (2018) at a higher significance thanks to 5 additional years of data.

###  3.2 Spectral Analysis

####  3.2.1 Phase-averaged Spectroscopy

The spectral data from FPMA and FPMB were collected so that each bin had a
signal-to-noise ratio ($S/N$) of at least 10. These spectra were initially fit
with a power law attenuated by a photoelectric absorption component at low
energies (Tbabs) and an exponential cutoff at high energies (CutoffPL). An
instrumental constant (Const) was fixed at 1 for FPMA and allowed to vary for
FPMB. This constant was 0.95$\pm$0.01 in all cases except for the flare epoch
where it was 0.96$\pm$0.02. This spectral model is called “Model 1” (M1), and
it leaves positive residuals around 6.4 keV attributable to an iron K$\alpha$
line often seen in HMXBs with supergiant donors.

A Gaussian to account for the iron line was then included as “Model 2” (M2).
The improvement in fit quality was significant with $\chi_{\nu}^{2}$/d.o.f.
dropping from 1.40/930 in M1 to 1.16/927 in M2 for the full observation. A
similar improvement was seen in the non-flare epoch with
$\chi_{\nu}^{2}$/d.o.f. decreasing from 1.35/873 in M1 to 1.13/870 in M2.

The addition of a cyclotron line (cyclabs: Mihara et al., 1990; Makishima et
al., 1990) in “Model 3” (M3) to account for negative residuals in 10–20 keV
led to a slight decrease in $\chi_{\nu}^{2}$/d.o.f. to 1.12/924 for the full
observation. For the non-flare spectrum, the inclusion of the cyclotron
component led to a significant improvement in the fit quality with
$\chi_{\nu}^{2}$/d.o.f. reduced to 1.07/867.

Figure 7: Phase-averaged NuSTAR spectra for IGR J16320$-$4751\. The column of
panels on the left presents the background-subtracted source spectrum from the
full observation, while the column of panels on the right features the
spectrum restricted to the non-flare epoch as defined in Fig. 2. Within each
column, the top panel contains the spectral data and the best-fitting model
(M3), while the lower rows of panels show residuals from fitting the three
CutoffPL-based models listed in Table 2. Each bin collects a minimum
significance of 20$\sigma$ to better highlight deviations from the model
(compared with 10$\sigma$ during fits). Table 2: Parameters from different
empirical models fit to NuSTAR spectra of IGR J16320$-$4751\.

| Flare | Non-Flare | Full | Non-Flare | Full | Non-Flare | Full
---|---|---|---|---|---|---|---
| Model 1 | Model 2 | Model 3
| photoelectric absorption (Tbabs)
$N_{\mathrm{H}}^{a}$ | 11.7${}_{-2.5}^{+2.6}$ | 19.4$\pm$0.9 | 18.0$\pm$0.9 | 13.4$\pm$1.2 | 12.2$\pm$1.1 | 10.5$\pm$1.6 | 10.4$\pm$1.4
| cutoff power law (CutoffPL)
$\Gamma$ |  $-$0.04$\pm$0.12 | 0.48$\pm$0.04 | 0.39$\pm$0.04 | 0.18$\pm$0.06 | 0.09$\pm$0.06 | $-0.08_{-0.11}^{+0.10}$ | $-0.09_{-0.10}^{+0.09}$
$E_{\mathrm{cut}}^{b}$ | 11.6${}_{-0.8}^{+1.0}$ | 15.2${}_{-0.5}^{+0.6}$ | 14.3${}_{-0.4}^{+0.5}$ | 12.7$\pm$0.5 | 12.1$\pm$0.4 | 11.0$\pm$0.6 | 10.9${}_{-0.5}^{+0.6}$
$N_{\mathrm{cut}}^{c}$ | 37.9${}_{-7.6}^{+9.5}$ | 34.4${}_{-2.7}^{+2.9}$ | 31.7${}_{-2.3}^{+2.5}$ | 18.5${}_{-2.2}^{+2.4}$ | 17.2${}_{-1.9}^{+2.0}$ | 11.9${}_{-2.1}^{+2.4}$ | 12.6${}_{-2.1}^{+2.4}$
| Fe Kα line (Gauss)
$E_{\mathrm{Fe}}^{b}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 6.34$\pm$0.06 | 6.34$\pm$0.06 | 6.28${}_{-0.07}^{+0.06}$ | 6.30${}_{-0.07}^{+0.08}$
$\sigma_{\mathrm{Fe}}^{b}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.44$\pm$0.08 | 0.46$\pm$0.08 | 0.50$\pm$0.08 | 0.48$\pm$0.09
$N_{\mathrm{Fe}}^{c}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 1.96${}_{-0.32}^{+0.34}$ | 2.12${}_{-0.33}^{+0.36}$ | 2.31${}_{-0.40}^{+0.43}$ | 2.27${}_{-0.41}^{+0.43}$
| CRSF (cyclabs)
$E_{\mathrm{cyc}}^{b}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 14.3${}_{-1.2}^{+0.9}$ | 13.4${}_{-2.0}^{+1.0}$
$\sigma_{\mathrm{cyc}}^{b}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 4.2${}_{-1.2}^{+1.4}$ | 4.3${}_{-1.4}^{+2.1}$
$\tau_{\mathrm{cyc}}^{d}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.10$\pm$0.02 | 0.08${}_{-0.02}^{+0.03}$
$\chi_{\nu}^{2}$ (d.o.f.) | 1.17 (224) | 1.35 (873) | 1.40 (930) | 1.13 (870) | 1.16 (927) | 1.07 (867) | 1.12 (924)
$F^{e}$ | 26.46${}_{-1.15}^{+0.33}$ | 8.85${}_{-0.08}^{+0.05}$ | 9.65${}_{-0.07}^{+0.06}$ | 8.91${}_{-0.11}^{+0.05}$ | 9.72${}_{-0.10}^{+0.05}$ | 8.97${}_{-0.30}^{+0.04}$ | 9.78${}_{-0.27}^{+0.04}$

Note. — (a) equivalent hydrogen column density ($\times 10^{22}$ cm-2); (b) in
keV; (c) normalization at 1 keV ($\times 10^{-4}$ ph s-1 cm-2 keV-1); (d)
optical depth; (e) model-derived flux in the 2–10 keV band ($\times 10^{-11}$
ergs s-1 cm-2)

Figure 8: Confidence regions for the cyclotron parameters from the best-
fitting spectral model (M3) during the non-flare epoch. Red, green, and blue
lines represent 68%, 90%, and 99% confidence contours, respectively, around
the optimal value shown as a cross.

Figure 7 presents the NuSTAR spectra from the full observation (left column)
and from the non-flare epoch (right column) with the best-fitting model (M3),
as well as the residuals from models that gradually include more components.
The model parameters are listed in Table 2.

During the non-flare epoch, the best-fitting spectral parameters from M3 were
a column density $N_{\mathrm{H}}$ $=$ (10.5$\pm$1.6)$\times 10^{22}$ cm-2, a
photon index $\Gamma=-0.08_{-0.11}^{+0.10}$ with a cutoff energy
$E_{\mathrm{cut}}=11.9_{-2.1}^{+2.4}$ keV. The energy and width of the iron
line were $6.28_{-0.07}^{+0.06}$ keV and 0.50$\pm$0.08 keV, respectively. The
cyclotron line had a centroid energy of $E_{\mathrm{cyc}}=14.3_{-1.2}^{+0.9}$
keV with a width of $\sigma=4.2_{-1.2}^{+1.4}$ keV and a low optical depth
$\tau=$ 0.10$\pm$0.02. Confidence contours for the continuum and CRSF
parameters are shown in Fig. 8.

Models with a high-energy cutoff (highecut: White et al., 1983), a negative
and positive power-law exponential (NPEX: Makishima et al., 1999), a
reflection component (reflect: Magdziarz & Zdziarski, 1995), thermal
Comptonization (compTT and nthComp: Titarchuk, 1994; Zdziarski et al., 1996;
Życki et al., 1999), and a Fermi-Dirac cutoff (FDcut: Tanaka, 1986) were also
attempted. None of them provided a significant improvement over M3.

There were too few counts in Swift/XRT ($\sim$100) to be useful for our
spectral analysis. Fitting the Swift 0.5–10-keV spectrum by itself with an
absorbed power law led to unconstrained parameters, whether grouping to
minimum of 20 counts per bin, or when leaving the counts unbinned and using
Cash (1979) statistics. Jointly fitting the Swift and NuSTAR spectra returned
an instrumental constant $\sim$4 for NuSTAR, even during the non-flare epoch.
Depending on the epoch, fits to the combined Swift and NuSTAR spectra in
0.5–79 keV gave a column density of (16–21)$\times 10^{22}$ cm-2. Since this
was consistent with the values we obtained when relying on NuSTAR alone, as
well as with the values cited by Rodriguez et al. (2006) and by García et al.
(2018), the Swift spectral data were no longer included in the analysis.

Figure 9: Phase-resolved NuSTAR spectra for IGR J16320$-$4751 from FPMA (blue)
and FPMB (red) during the non-flare epoch. The column of panels on the left
shows the source spectrum during the Valley phases defined in Fig. 4, while
the column of panels on the right shows data from the Peak phase. In each
column, the top row shows the spectrum and best-fitting model (M3), while the
second, third, and fourth rows present residuals from fitting the models
listed in Fig. 3. For visual clarity, the spectra were rebinned to a minimum
significance of 10$\sigma$ (compared with 5$\sigma$ during fits).

The significance of the cyclotron line was estimated using the $F$-statistic
(e.g., Orlandini et al., 2012; Sartore et al., 2015; Brumback et al., 2018).
The XSpec script fakeit was used to simulate $2\times 10^{6}$ spectra based on
the model representing the null hypothesis, i.e., an absorbed, cutoff power
law with an iron line but without a cyclabs component (“null model” or M2).
Each simulated spectrum was binned in the same way as the observed dataset,
fit with the null model and its $\chi^{2}$ was recorded. Then, each simulated
spectrum was fit with the “best-fitting model” (M3), which is the null model
plus a cyclabs component whose parameters were allowed to vary within the
90%-confidence region of the best-fitting values, and its $\chi^{2}$ was
noted. These simulations yielded a distribution of reduced (i.e., normalized
by the d.o.f.) ratios $F_{\mathrm{stat}}=\chi_{0}^{2}/\chi_{1}^{2}$, where the
subscripts 0 and 1 denote the null model (M2) and the best-fitting model (M3),
respectively. Every ratio from the simulations was less than the observed
$F_{\mathrm{stat}}=1.051$ with the largest simulated value being
$F_{\mathrm{stat}}=1.033$. From this distribution, we infer that the cyclotron
line was significant at a level of at least 5$\sigma$ after accounting for the
number of trials.

Table 3: Fitting parameters of the phase-resolved non-flare spectra of IGR
J16320$-$4751 with three empirical models.

| Valley | Peak | Valley | Peak | Valley | Peak
---|---|---|---|---|---|---
| Model 1 | Model 2 | Model 3
| photoelectric absorption (Tbabs)
$N_{\mathrm{H}}^{a}$ | 18.2$\pm$1.2 | 20.9$\pm$1.4 | 13.3${}_{-1.5}^{+1.6}$ | 13.5${}_{-1.9}^{+2.0}$ | 10.5$\pm$1.9 | 8.4${}_{-3.5}^{+3.3}$
| cutoff power law (CutoffPL)
$\Gamma$ | 0.37$\pm$0.05 | 0.60$\pm$0.06 | 0.13$\pm$0.08 | 0.22$\pm$0.11 |  $-$0.10$\pm$0.12 | $-0.25_{-0.28}^{+0.21}$
$E_{\mathrm{cut}}^{b}$ | 14.6${}_{-0.6}^{+0.7}$ | 14.9$\pm$0.8 | 12.7${}_{-0.6}^{+0.7}$ | 11.9${}_{-0.7}^{+0.8}$ | 11.2$\pm$0.7 | 9.6${}_{-1.0}^{+0.9}$
$f_{\mathrm{cut}}^{c}$ | 25.9${}_{-2.6}^{+2.9}$ | 49.5${}_{-5.6}^{+6.5}$ | 15.8${}_{-2.2}^{+2.8}$ | 22.2${}_{-4.4}^{+5.2}$ | 10.4${}_{-2.1}^{+2.6}$ | 9.8${}_{-4.0}^{+4.7}$
| Fe Kα line (Gauss)
$E_{\mathrm{Fe}}^{b}$ |  $\cdots$ |  $\cdots$ | 6.34$\pm$0.07 | 6.31$\pm$0.11 | 6.30$\pm$0.07 | 6.14${}_{-0.14}^{+0.32}$
$\sigma_{\mathrm{Fe}}^{b}$ |  $\cdots$ |  $\cdots$ | 0.34${}_{-0.14}^{+0.10}$ | 0.64${}_{-0.15}^{+0.16}$ | 0.40${}_{-0.10}^{+0.09}$ | 0.74${}_{-0.30}^{+0.18}$
$f_{\mathrm{Fe}}^{c}$ |  $\cdots$ |  $\cdots$ | 1.45${}_{-0.38}^{+0.36}$ | 3.11${}_{-0.76}^{+0.89}$ | 1.77${}_{-0.38}^{+0.39}$ | 4.17${}_{-1.87}^{+1.63}$
| CRSF (cyclabs)
$E_{\mathrm{CRSF}}$ b |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 15.1$\pm$1.0 | 13.8${}_{-3.3}^{+2.8}$
$\sigma_{\mathrm{CRSF}}^{b}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 3.9${}_{-1.4}^{+1.7}$ | 5.8${}_{-3.2}^{+3.9}$
$\tau_{\mathrm{CRSF}}^{d}$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.10$\pm$0.03 | 0.15${}_{-0.05}^{+0.11}$
$\chi_{red}^{2}$ (d.o.f.) | 1.15 (1197) | 1.25 (1029) | 1.07 (1194) | 1.16 (1026) | 1.04 (1191) | 1.13 (1023)
$F^{e}$ | 8.25${}_{-0.10}^{+0.06}$ | 9.67${}_{-0.16}^{+0.08}$ | 8.29${}_{-0.14}^{+0.06}$ | 9.75${}_{-0.31}^{+0.07}$ | 8.35${}_{-0.36}^{+0.05}$ | 9.85${}_{-0.50}^{+0.04}$

Note. — (a) equivalent hydrogen column density ($\times 10^{22}$ cm-2); (b) in
keV; (c) normalization at 1 keV ($\times 10^{-4}$ ph s-1 cm-2 keV-1); (d)
optical depth; (e) model-derived flux in the 2–10 keV band ($\times 10^{-11}$
ergs s-1 cm-2)

####  3.2.2 Phase-resolved Spectroscopy

We performed phase-resolved spectroscopy focusing only on data from the non-
flare epoch. The pulse profile was split according to phases belonging to the
“Valley” (phases: 0–0.2; 0.6–1.0) and “Peak” (phases: 0.2–0.6) as shown in
Fig. 4. This allocated a total of 105,410$\pm$325 net counts to the Valley in
28.85 ks of effective exposure time, and 75,516$\pm$557 net counts to the Peak
in 18.78 ks of effective exposure time, when summing the counts from both
modules.

Figure 9 presents the phase-resolved spectra fit with the three models
introduced earlier, and Table 3 lists the model parameters. Model 3 continued
to provide the best fit. Count rates and model-derived fluxes were between 10%
and 20% higher during the Peak than they were during the Valley, which is
consistent with the pulsed fraction. Figure 10 shows confidence regions for
the continuum and CRSF parameters during the Peak and Valley phases.

During the Valley phase, there were negative residuals in the spectral fits
for the 30–35-keV energy range. This energy is a little higher than would be
expected for the harmonic to a candidate cyclotron line at 15 keV. Introducing
a second cyclotron component did not reduce the $\chi^{2}$, and the
component’s parameters could not be constrained without holding others
constant. This dip was not observed in the spectral residuals during the Peak
phase.

Figure 10: Same as Fig. 8, with identical limits for the axes, for phases
corresponding to the Peak (dotted lines) and the Valley (solid lines).

##  4 DISCUSSION

The unusual properties of obscured, slowly-rotating pulsars such as IGR
J16320$-$4751 (catalog ) trace their origin to the interaction between the
NS’s magnetosphere and the inhomogeneous accretion stream from the stellar
wind (e.g., Grebenev & Sunyaev, 2007; Patel et al., 2007; Bozzo et al., 2008;
Oskinova et al., 2012; Manousakis et al., 2012; Hainich et al., 2020). The
magnetic field strength ($B$) of the NS can be directly measured by observing
Cyclotron Resonance Scattering Features (CRSFs) which are generally observed
as absorption lines between 10 and 100 keV. They arise through resonant
scattering of photons emitted by electrons moving perpendicular to the
$B$-field and whose energies ($E$) are discretized into integer multiples of
the fundamental Landau level: $E_{\mathrm{cyc}}\sim 12(B/10^{12}$ G) keV
(Truemper et al., 1978; Coburn et al., 2002).

Thanks to NuSTAR, we were able to perform a spectroscopic study of IGR
J16320$-$4751 (catalog ) with unprecedented energy resolution and sensitivity
above 10 keV. A spectral model consisting of an absorbed power law left
residuals near the known iron K$\alpha$ line energy of 6.4 keV. However, there
were also residuals around 14 keV due to a possible CRSF. The addition of a
cyclotron line to the model improved the fit quality enough that the
distribution of $F$-statistics implied a detection significance of 5$\sigma$.
The energy of the candidate cyclotron line was close to, but not statistically
compatible with, the cutoff energy. Plus, in every instance of our simulated
spectra, a model that included a cutoff and a cyclotron led to a better fit
than a model with a cutoff alone. One alternative is that the candidate
cyclotron line is an example of the “10-keV bump” noted in other accreting
X-ray pulsars (Coburn et al., 2002; Ferrigno et al., 2009). However, a model
in which the cyclotron line is replaced with with a Gaussian emission line or
a Compton hump both led to a poorer quality fit. As an additional test, we
followed the procedure in Bottacini (2022) where the cyclotron energy was
stepped in increments of 0.4 keV (NuSTAR’s energy resolution) through the full
3–79 keV band, until the best fit was obtained based on $\chi^{2}$. Once
again, the cyclotron was detected significantly around 14 keV (according to
the reduced $F$-statistic distribution) and away from the cutoff energy and
the possible bump. A cyclotron line energy of 14 keV corresponds to a
$B$-field magnitude of $1.2\times 10^{12}$ G, neglecting the gravitational
redshift of the emission region. This is the first time that the magnetic
field of this source has been measured. It is not particularly strong compared
with its peers (Staubert et al., 2019).

Cyclotron lines show variability with luminosity and pulse phase, and are
often most significantly detected during certain phases (e.g., Suchy et al.,
2012). The candidate cyclotron line in IGR J16320$-$4751 (catalog ) was easier
to detect during the non-flare epoch, and during the Valley when analyzing by
phase. We saw no evidence of an increase in the line energy with pulse phase,
as was seen in Her X-1 (e.g., Soong et al., 1990; Vasco et al., 2013), nor
were there significant negative/positive correlations with luminosity
(Staubert et al., 2019, and references therein).

The cyclotron scattering cross-section, and by extension the optical depth,
are strongly affected by the viewing angle relative to the axis defined by the
magnetic field (e.g., Schwarm et al., 2017a, b). The optical depth of
$\tau_{\mathrm{cyc}}=0.1$ in IGR J16320$-$4751 (catalog ) was lower than those
of ten other sources reported in Coburn et al. (2002), which ranged from 0.16
to 2.1. Also, the ratio of width to energy
($\sigma_{\mathrm{cyc}}$/$E_{\mathrm{cyc}}=0.3$) that we measured was more
than twice as large as expected based on the trend found in Coburn et al.
(2002) where deeper CRSFs tended to be broader (Fig. 11). On the other hand,
our values for IGR J16320$-$4751 (catalog ) occupy a region of the parameter
space that was inaccessible to the systematic study of RXTE data by Coburn et
al. (2002), but that can now be explored by NuSTAR, which we did by adding 12
more HMXBs listed in Staubert et al. (2019), and references therein. Where IGR
J16320$-$4751 (catalog ) was once an outlier compared with the HMXBs of Coburn
et al. (2002), it now has company in that it overlaps statistically with IGR
J18027$-$2016 (catalog ) and KS 1947+300 (catalog ). Both of them had many
years pass between their discoveries (Augello et al., 2003; Borozdin et al.,
1990) and the detection of weak cyclotron lines by NuSTAR (Lutovinov et al.,
2017; Fürst et al., 2014a).

Figure 11: Relative width ($\sigma/E$) versus optical depth ($\tau$) of the
CRSF feature (adapted from Coburn et al., 2002). The location of IGR
J16320$-$4751 (catalog ) in the parameter space is indicated by the red
triangle, while other HMXBs appear as black circles from Coburn et al. (2002)
and blue squares from Staubert et al. (2019), and references therein.

A coherent modulation with a period of 1,308.8$\pm$0.4 s was measured by
NuSTAR. This is known to be the spin period of the NS in IGR J16320$-$4751
(catalog ). Rodriguez et al. (2006) found an average value of 1,303 s between
two separate XMM-Newton observations from 2004, while García et al. (2018)
report a period of $\sim$1,300 s from XMM-Newton observations between 2003 and
2008. Assuming there was no torque reversal (Bildsten et al., 1997), a 5.8-s
difference between measurements from 2004 and 2015 (3,943 d) indicates a spin-
down trend with a period derivative $\dot{P}\sim 2\times 10^{-8}$ s s-1.
Attributing the slowing down of the NS to magnetic braking or propellor
effects (Illarionov & Sunyaev, 1975) would require a higher magnetic field
strength and pulsation frequency than what we measured for IGR J16320$-$4751
(catalog ). The accretion of material with negative angular momentum appears
to be the most likely explanation, and this could proceed either through an
inhomogeneous stellar wind (Shakura et al., 2012), or via a short-lived
accretion disk. In addition to provoking outbursts in the SFXT IGR
J17544$-$2619 (catalog ) (Romano et al., 2015), transient accretion disks may
explain long-term changes in the spin period of other HMXBs with supergiant
stars such as OAO 1657$-$415 (catalog ) (Jenke et al., 2012) and IGR
J16393$-$4643 (catalog ) (Bodaghee et al., 2016). The spin period derivatives
of IGR J16320$-$4751 (catalog ) and IGR J16393$-$4643 (catalog ) are equal in
magnitude, but unequal in direction: the former is slowing down while the
latter is speeding up.

The pulsation was detected in every energy band that we analyzed except for
25–79 keV where few counts remained since the spectral continuum decays
exponentially $\gtrsim$10 keV. The pulsed fraction in 3–6 keV was twice as
large as that of 12–25 keV, which is surprising given that the pulsed fraction
stayed constant with energy in 2004. It is also surprising given that in
accreting X-ray pulsars, the pulsed fraction tends to increase with energy
(Nagase, 1989; Bildsten et al., 1997; Mushtukov & Tsygankov, 2022). This
suggests a physical change in this system in the intervening 11 years which
could include, for example, a reconfiguration of the magnetic field, a change
in the energy dependence over the beam, or a change in beam pattern or size.
The low significance and low pulsed fraction of the modulation at energies
above 10 keV could explain the weakness of the candidate cyclotron line.

IGR J16320$-$4751 (catalog ) is a persistent X-ray source with a count rate
that stayed relatively constant over almost 2 decades of Swift/BAT monitoring
in 15–50 keV (Krimm et al., 2013). Still, the source underwent small flares
with the largest flare reaching a count rate a factor 20 times the average. An
orbital modulation with a refined period of 8.9912$\pm$0.0078 d was found, in
agreement with previous measurements (Corbet et al., 2005; Levine et al.,
2011; García et al., 2018). The NuSTAR observation covered orbital phases
0.97–0.11 where phase 0 ($=1$) represents the minimum point of the orbital
profile. By extension, the NuSTAR observation occurred close to superior
conjunction, i.e., when the X-ray emitting NS was furthest in its orbit with
respect to the observer. With an eccentricity of 0.2 and an inclination angle
of 62∘ (García et al., 2018), the source is not eclipsing so attenuation of
X-rays at this phase is likely due to absorption by the companion star’s wind.
The XMM-Newton observation of Rodriguez et al. (2006) coincided with phases
0.40–0.46, i.e., just before the maximum point of the orbital profile, or near
inferior conjunction.

The unabsorbed 2–10-keV flux reported by Rodriguez et al. (2006) during their
non-flare epoch was $9.2\times 10^{-11}$ erg cm-2 s-1, which is equivalent to
the absorption-corrected flux for the non-flare epoch that we found with
NuSTAR: $1.1\times 10^{-10}$ erg cm-2 s-1. This is somewhat surprising given
that the 2004 XMM-Newton and 2015 NuSTAR observations occurred, respectively,
near the highest and lowest points in the orbital profile. However, García et
al. (2018) reported on a 2008 XMM-Newton observation taken during phase 0
where the flux was $2.17\times 10^{-10}$ erg cm-2 s-1 (0.15–12 keV), so the
flux discrepancy is probably due to the stochastic variability of the source.

Based on infrared spectroscopy of the counterpart to IGR J16320$-$4751
(catalog ), Rahoui et al. (2008) estimated a source distance of 3.5 kpc. At
this distance, the intrinsic (i.e., absorption-corrected) 2–10-keV source
luminosity would be $1.7\times 10^{35}$ erg s-1 outside the flare, and
$5.1\times 10^{35}$ erg s-1 during the flare. No objects listed in the _Gaia_
DR3 (Gaia Collaboration et al., 2016, 2021) catalog of parallax-derived
distances (Bailer-Jones et al., 2021) were within 5′′ of the 4XMM position of
IGR J16320$-$4751 (catalog ). If we assume a distance of 10 kpc instead, then
the luminosities during the non-flare and flare epochs would be $1.4\times
10^{36}$ erg s-1 and $4.2\times 10^{36}$ erg s-1, respectively.

##  5 CONCLUSIONS

NuSTAR gave an exclusive look at the accreting X-ray pulsar IGR J16320$-$4751
(catalog ) in an energy band above 10 keV that has not been covered with as
fine a spectral resolution with other telescopes. The spectrum of IGR
J16320$-$4751 (catalog ) was best fit by introducing a CRSF at $\sim$14 keV in
addition to a cutoff power-law continuum and an Fe K$\alpha$ line. If
confirmed, the cyclotron line would represent the first direct measurement of
a $1.2\times 10^{12}$-G magnetic field for the neutron star in IGR
J16320$-$4751 (catalog ). In this 2015 study, the pulsed fraction showed a
significant negative correlation with energy, whereas the pulsed fraction
remained constant in 2004. This suggests that the system’s magnetically-driven
accretion geometry changed between observations.

NuSTAR provided new insights into the evolution of the line properties on long
and short time scales in HMXBs known to have CRSFs, e.g., Her X-1 (catalog )
and Vela X-1 (catalog ) (Fürst et al., 2013, 2014b). NuSTAR has also uncovered
cyclotron lines for HMXBs not previously known to have them (e.g., Fürst et
al., 2014a; Tendulkar et al., 2014; Bhalerao et al., 2015; Bodaghee et al.,
2016). With $\sim$35 known CRSF sources, including candidate cyclotron sources
of which IGR J16320$-$4751 (catalog ) is now a member, the increasing sample
size will permit studies of the relationship between the $B$-field and other
properties, such as luminosity, companion type, spin period, and orbital
period (e.g., Schönherr et al., 2014; Staubert et al., 2019; Christodoulou et
al., 2019).

The authors thank the anonymous Referee whose constructive criticism helped
improve our discussion of the cyclotron line. JAT and AC acknowledge partial
support from NASA grant NNX15AV22G under the NuSTAR Guest Observer program. MC
acknowledges financial support from the Centre National d’Etudes Spatiales
(CNES). PR acknowledges financial contribution from the agreements ASI-INAF
I/037/12/0 and ASI-INAF n. 2017-14-H.0. The scientific results reported in
this article are based on data from the NuSTAR mission, a project led by the
California Institute of Technology, managed by the Jet Propulsion Laboratory,
and funded by the National Aeronautics and Space Administration. This research
has made use of: the NuSTAR Data Analysis Software (NuSTARDAS) jointly
developed by the ASI Science Data Center (ASDC, Italy) and the California
Institute of Technology; data obtained from the High Energy Astrophysics
Science Archive Research Center (HEASARC) provided by NASA’s Goddard Space
Flight Center; NASA’s Astrophysics Data System Bibliographic Services; and the
SIMBAD database operated at CDS, Strasbourg, France.

## References

  * Abdollahi et al. (2020) Abdollahi, S., Acero, F., Ackermann, M., et al. 2020, ApJS, 247, 33, doi: 10.3847/1538-4365/ab6bcb
  * Acero et al. (2015) Acero, F., Ackermann, M., Ajello, M., et al. 2015, ApJS, 218, 23, doi: 10.1088/0067-0049/218/2/23
  * Aharonian et al. (2006) Aharonian, F., Akhperjanian, A. G., Bazer-Bachi, A. R., et al. 2006, ApJ, 636, 777, doi: 10.1086/498013
  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Augello et al. (2003) Augello, G., Iaria, R., Robba, N. R., et al. 2003, ApJ, 596, L63, doi: 10.1086/379092
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806
  * Ballhausen et al. (2017) Ballhausen, R., Pottschmidt, K., Fürst, F., et al. 2017, A&A, 608, A105, doi: 10.1051/0004-6361/201730845
  * Bellm et al. (2014) Bellm, E. C., Fürst, F., Pottschmidt, K., et al. 2014, ApJ, 792, 108, doi: 10.1088/0004-637X/792/2/108
  * Bhalerao et al. (2015) Bhalerao, V., Romano, P., Tomsick, J., et al. 2015, MNRAS, 447, 2274, doi: 10.1093/mnras/stu2495
  * Bildsten et al. (1997) Bildsten, L., Chakrabarty, D., Chiu, J., et al. 1997, ApJS, 113, 367, doi: 10.1086/313060
  * Blackburn et al. (1999) Blackburn, J. K., Shaw, R. A., Payne, H. E., Hayes, J. J. E., & Heasarc. 1999, FTOOLS: A general package of software to manipulate FITS files, Astrophysics Source Code Library, record ascl:9912.002.  http://ascl.net/9912.002
  * Bodaghee et al. (2006) Bodaghee, A., Walter, R., Zurita Heras, J. A., et al. 2006, A&A, 447, 1027, doi: 10.1051/0004-6361:20053809
  * Bodaghee et al. (2016) Bodaghee, A., Tomsick, J. A., Fornasini, F. M., et al. 2016, ApJ, 823, 146, doi: 10.3847/0004-637X/823/2/146
  * Borozdin et al. (1990) Borozdin, K., Gilfanov, M., Sunyaev, R., et al. 1990, Soviet Astronomy Letters, 16, 345
  * Bottacini (2022) Bottacini, E. 2022, MNRAS, 515, 3174, doi: 10.1093/mnras/stac1890
  * Bozzo et al. (2008) Bozzo, E., Falanga, M., & Stella, L. 2008, ApJ, 683, 1031, doi: 10.1086/589990
  * Bozzo et al. (2015) Bozzo, E., Romano, P., Ducci, L., Bernardini, F., & Falanga, M. 2015, Advances in Space Research, 55, 1255, doi: 10.1016/j.asr.2014.11.012
  * Brumback et al. (2018) Brumback, M. C., Hickox, R. C., Fürst, F. S., et al. 2018, ApJ, 852, 132, doi: 10.3847/1538-4357/aa9e91
  * Cash (1979) Cash, W. 1979, ApJ, 228, 939, doi: 10.1086/156922
  * Christodoulou et al. (2019) Christodoulou, D. M., Laycock, S. G. T., & Kazanas, D. 2019, Research in Astronomy and Astrophysics, 19, 146, doi: 10.1088/1674-4527/19/10/146
  * Coburn et al. (2002) Coburn, W., Heindl, W. A., Rothschild, R. E., et al. 2002, ApJ, 580, 394, doi: 10.1086/343033
  * Coleiro et al. (2013) Coleiro, A., Chaty, S., Zurita Heras, J. A., Rahoui, F., & Tomsick, J. A. 2013, A&A, 560, A108, doi: 10.1051/0004-6361/201322382
  * Corbet et al. (2005) Corbet, R., Barbier, L., Barthelmy, S., et al. 2005, The Astronomer’s Telegram, 649, 1
  * Ferrigno et al. (2009) Ferrigno, C., Becker, P. A., Segreto, A., Mineo, T., & Santangelo, A. 2009, A&A, 498, 825, doi: 10.1051/0004-6361/200809373
  * Fürst et al. (2013) Fürst, F., Grefenstette, B. W., Staubert, R., et al. 2013, ApJ, 779, 69, doi: 10.1088/0004-637X/779/1/69
  * Fürst et al. (2014a) Fürst, F., Pottschmidt, K., Wilms, J., et al. 2014a, ApJ, 784, L40, doi: 10.1088/2041-8205/784/2/L40
  * Fürst et al. (2014b) —. 2014b, ApJ, 780, 133, doi: 10.1088/0004-637X/780/2/133
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1, doi: 10.1051/0004-6361/201629272
  * Gaia Collaboration et al. (2021) Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1, doi: 10.1051/0004-6361/202039657
  * García et al. (2018) García, F., Fogantini, F. A., Chaty, S., & Combi, J. A. 2018, A&A, 618, A61, doi: 10.1051/0004-6361/201833365
  * Giménez-García et al. (2015) Giménez-García, A., Torrejón, J. M., Eikmann, W., et al. 2015, A&A, 576, A108, doi: 10.1051/0004-6361/201425004
  * Grebenev & Sunyaev (2007) Grebenev, S. A., & Sunyaev, R. A. 2007, Astronomy Letters, 33, 149, doi: 10.1134/S1063773707030024
  * Hainich et al. (2020) Hainich, R., Oskinova, L. M., Torrejón, J. M., et al. 2020, A&A, 634, A49, doi: 10.1051/0004-6361/201935498
  * Horne & Baliunas (1986) Horne, J. H., & Baliunas, S. L. 1986, ApJ, 302, 757, doi: 10.1086/164037
  * Illarionov & Sunyaev (1975) Illarionov, A. F., & Sunyaev, R. A. 1975, A&A, 39, 185
  * in’t Zand (2005) in’t Zand, J. J. M. 2005, A&A, 441, L1, doi: 10.1051/0004-6361:200500162
  * Jenke et al. (2012) Jenke, P. A., Finger, M. H., Wilson-Hodge, C. A., & Camero-Arranz, A. 2012, ApJ, 759, 124, doi: 10.1088/0004-637X/759/2/124
  * Kretschmar et al. (2019) Kretschmar, P., Fürst, F., Sidoli, L., et al. 2019, New A Rev., 86, 101546, doi: 10.1016/j.newar.2020.101546
  * Krimm et al. (2013) Krimm, H. A., Holland, S. T., Corbet, R. H. D., et al. 2013, ApJS, 209, 14, doi: 10.1088/0067-0049/209/1/14
  * Krivonos et al. (2022) Krivonos, R. A., Sazonov, S. Y., Kuznetsova, E. A., et al. 2022, MNRAS, 510, 4796, doi: 10.1093/mnras/stab3751
  * Leahy (1987) Leahy, D. A. 1987, A&A, 180, 275
  * Levine et al. (2011) Levine, A. M., Bradt, H. V., Chakrabarty, D., Corbet, R. H. D., & Harris, R. J. 2011, ApJS, 196, 6, doi: 10.1088/0067-0049/196/1/6
  * Lomb (1976) Lomb, N. R. 1976, Ap&SS, 39, 447, doi: 10.1007/BF00648343
  * Lutovinov et al. (2005) Lutovinov, A., Rodriguez, J., Revnivtsev, M., & Shtykovskiy, P. 2005, A&A, 433, L41, doi: 10.1051/0004-6361:200500092
  * Lutovinov et al. (2017) Lutovinov, A. A., Tsygankov, S. S., Postnov, K. A., et al. 2017, MNRAS, 466, 593, doi: 10.1093/mnras/stw3058
  * Magdziarz & Zdziarski (1995) Magdziarz, P., & Zdziarski, A. A. 1995, MNRAS, 273, 837, doi: 10.1093/mnras/273.3.837
  * Makishima et al. (1999) Makishima, K., Mihara, T., Nagase, F., & Tanaka, Y. 1999, ApJ, 525, 978, doi: 10.1086/307912
  * Makishima et al. (1990) Makishima, K., Mihara, T., Ishida, M., et al. 1990, ApJ, 365, L59, doi: 10.1086/185888
  * Manousakis et al. (2012) Manousakis, A., Walter, R., & Blondin, J. M. 2012, A&A, 547, A20, doi: 10.1051/0004-6361/201219717
  * MATLAB (2021) MATLAB. 2021, version 9.11.0 (R2021b) (Natick, Massachusetts: The MathWorks Inc.)
  * Matt & Guainazzi (2003) Matt, G., & Guainazzi, M. 2003, MNRAS, 341, L13, doi: 10.1046/j.1365-8711.2003.06658.x
  * Mihara et al. (1990) Mihara, T., Makishima, K., Ohashi, T., Sakao, T., & Tashiro, M. 1990, Nature, 346, 250, doi: 10.1038/346250a0
  * Mushtukov & Tsygankov (2022) Mushtukov, A., & Tsygankov, S. 2022, arXiv e-prints, arXiv:2204.14185.  https://arxiv.org/abs/2204.14185
  * Nagase (1989) Nagase, F. 1989, PASJ, 41, 1
  * Nasa High Energy Astrophysics Science Archive Research Center (2014) (Heasarc) Nasa High Energy Astrophysics Science Archive Research Center (Heasarc). 2014, HEAsoft: Unified Release of FTOOLS and XANADU, Astrophysics Source Code Library, record ascl:1408.004.  http://ascl.net/1408.004
  * Negueruela et al. (2006) Negueruela, I., Smith, D. M., Reig, P., Chaty, S., & Torrejón, J. M. 2006, in ESA Special Publication, Vol. 604, The X-ray Universe 2005, ed. A. Wilson, 165.  https://arxiv.org/abs/astro-ph/0511088
  * Orlandini et al. (2012) Orlandini, M., Frontera, F., Masetti, N., Sguera, V., & Sidoli, L. 2012, ApJ, 748, 86, doi: 10.1088/0004-637X/748/2/86
  * Oskinova et al. (2012) Oskinova, L. M., Feldmeier, A., & Kretschmar, P. 2012, MNRAS, 421, 2820, doi: 10.1111/j.1365-2966.2012.20507.x
  * Patel et al. (2004) Patel, S. K., Kouveliotou, C., Tennant, A., et al. 2004, ApJ, 602, L45, doi: 10.1086/382210
  * Patel et al. (2007) Patel, S. K., Zurita, J., Del Santo, M., et al. 2007, ApJ, 657, 994, doi: 10.1086/510374
  * Pradhan et al. (2018) Pradhan, P., Bozzo, E., & Paul, B. 2018, A&A, 610, A50, doi: 10.1051/0004-6361/201731487
  * Press & Rybicki (1989) Press, W. H., & Rybicki, G. B. 1989, ApJ, 338, 277, doi: 10.1086/167197
  * Protassov et al. (2002) Protassov, R., van Dyk, D. A., Connors, A., Kashyap, V. L., & Siemiginowska, A. 2002, ApJ, 571, 545, doi: 10.1086/339856
  * Rahoui et al. (2008) Rahoui, F., Chaty, S., Lagage, P. O., & Pantin, E. 2008, A&A, 484, 801, doi: 10.1051/0004-6361:20078774
  * Rodriguez et al. (2003) Rodriguez, J., Tomsick, J. A., Foschini, L., et al. 2003, A&A, 407, L41, doi: 10.1051/0004-6361:20031093
  * Rodriguez et al. (2006) Rodriguez, J., Bodaghee, A., Kaaret, P., et al. 2006, MNRAS, 366, 274, doi: 10.1111/j.1365-2966.2005.09855.x
  * Romano et al. (2014) Romano, P., Krimm, H. A., Palmer, D. M., et al. 2014, A&A, 562, A2, doi: 10.1051/0004-6361/201322516
  * Romano et al. (2015) Romano, P., Bozzo, E., Mangano, V., et al. 2015, A&A, 576, L4, doi: 10.1051/0004-6361/201525749
  * Sartore et al. (2015) Sartore, N., Jourdain, E., & Roques, J. P. 2015, ApJ, 806, 193, doi: 10.1088/0004-637X/806/2/193
  * Scargle (1982) Scargle, J. D. 1982, ApJ, 263, 835, doi: 10.1086/160554
  * Schönherr et al. (2014) Schönherr, G., Schwarm, F. W., Falkner, S., et al. 2014, A&A, 564, L8, doi: 10.1051/0004-6361/201322448
  * Schwarm et al. (2017a) Schwarm, F. W., Schönherr, G., Falkner, S., et al. 2017a, A&A, 597, A3, doi: 10.1051/0004-6361/201629352
  * Schwarm et al. (2017b) Schwarm, F. W., Ballhausen, R., Falkner, S., et al. 2017b, A&A, 601, A99, doi: 10.1051/0004-6361/201630250
  * Shakura et al. (2012) Shakura, N., Postnov, K., Kochetkova, A., & Hjalmarsdotter, L. 2012, MNRAS, 420, 216, doi: 10.1111/j.1365-2966.2011.20026.x
  * Sidoli & Paizis (2018) Sidoli, L., & Paizis, A. 2018, MNRAS, 481, 2779, doi: 10.1093/mnras/sty2428
  * Sidoli et al. (2016) Sidoli, L., Paizis, A., & Postnov, K. 2016, MNRAS, 457, 3693, doi: 10.1093/mnras/stw237
  * Soong et al. (1990) Soong, Y., Gruber, D. E., Peterson, L. E., & Rothschild, R. E. 1990, ApJ, 348, 641, doi: 10.1086/168272
  * Staubert et al. (2019) Staubert, R., Trümper, J., Kendziorra, E., et al. 2019, A&A, 622, A61, doi: 10.1051/0004-6361/201834479
  * Suchy et al. (2012) Suchy, S., Fürst, F., Pottschmidt, K., et al. 2012, ApJ, 745, 124, doi: 10.1088/0004-637X/745/2/124
  * Sugizaki et al. (2001) Sugizaki, M., Mitsuda, K., Kaneda, H., et al. 2001, ApJS, 134, 77, doi: 10.1086/320358
  * Tanaka (1986) Tanaka, Y. 1986, in IAU Colloq. 89: Radiation Hydrodynamics in Stars and Compact Objects, ed. D. Mihalas & K.-H. A. Winkler, Vol. 255, 198, doi: 10.1007/3-540-16764-1_12
  * Tendulkar et al. (2014) Tendulkar, S. P., Fürst, F., Pottschmidt, K., et al. 2014, ApJ, 795, 154, doi: 10.1088/0004-637X/795/2/154
  * Titarchuk (1994) Titarchuk, L. 1994, ApJ, 434, 570, doi: 10.1086/174760
  * Tomsick et al. (2003) Tomsick, J. A., Lingenfelter, R., Walter, R., et al. 2003, IAU Circ., 8076, 1
  * Truemper et al. (1978) Truemper, J., Pietsch, W., Reppin, C., et al. 1978, ApJ, 219, L105, doi: 10.1086/182617
  * Vasco et al. (2013) Vasco, D., Staubert, R., Klochkov, D., et al. 2013, A&A, 550, A111, doi: 10.1051/0004-6361/201220181
  * Verner et al. (1996) Verner, D. A., Ferland, G. J., Korista, K. T., & Yakovlev, D. G. 1996, ApJ, 465, 487, doi: 10.1086/177435
  * Walter et al. (2015) Walter, R., Lutovinov, A. A., Bozzo, E., & Tsygankov, S. S. 2015, A&A Rev., 23, 2, doi: 10.1007/s00159-015-0082-6
  * Walter et al. (2003) Walter, R., Rodriguez, J., Foschini, L., et al. 2003, A&A, 411, L427, doi: 10.1051/0004-6361:20031369
  * Webb et al. (2020) Webb, N. A., Coriat, M., Traulsen, I., et al. 2020, A&A, 641, A136, doi: 10.1051/0004-6361/201937353
  * White et al. (1983) White, N. E., Swank, J. H., & Holt, S. S. 1983, ApJ, 270, 711, doi: 10.1086/161162
  * Wilms et al. (2000) Wilms, J., Allen, A., & McCray, R. 2000, ApJ, 542, 914, doi: 10.1086/317016
  * Zdziarski et al. (1996) Zdziarski, A. A., Johnson, W. N., & Magdziarz, P. 1996, MNRAS, 283, 193, doi: 10.1093/mnras/283.1.193
  * Zurita Heras et al. (2006) Zurita Heras, J. A., De Cesare, G., Walter, R., et al. 2006, A&A, 448, 261, doi: 10.1051/0004-6361:20053876
  * Życki et al. (1999) Życki, P. T., Done, C., & Smith, D. A. 1999, MNRAS, 309, 561, doi: 10.1046/j.1365-8711.1999.02885.x