11institutetext: Main Astronomical Observatory, National Academy of Sciences
of Ukraine, 27 Akademika Zabolotnoho St, 03680, Kiev, Ukraine 22institutetext:
Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679
Munich, Germany 33institutetext: Armagh Observatory and Planetarium, College
Hill, Armagh BT61 9DG, Northern Ireland, UK 44institutetext: Kazan Federal
University, 18 Kremlyovskaya St., 420008, Kazan, Russian Federation
55institutetext: Instituto de Astrofísica de Andalucía, CSIC, Apdo 3004, 18080
Granada, Spain

# Two types of distribution of the gas velocity dispersion of MaNGA galaxies

L. S. Pilyugin Two types of distribution of the gas velocity dispersion of
MaNGA galaxiesTwo types of distribution of the gas velocity dispersion of
MaNGA galaxies I. A. Zinchenko Two types of distribution of the gas velocity
dispersion of MaNGA galaxiesTwo types of distribution of the gas velocity
dispersion of MaNGA galaxiesTwo types of distribution of the gas velocity
dispersion of MaNGA galaxiesTwo types of distribution of the gas velocity
dispersion of MaNGA galaxies M. A. Lara-López Two types of distribution of the
gas velocity dispersion of MaNGA galaxiesTwo types of distribution of the gas
velocity dispersion of MaNGA galaxies Y. A. Nefedyev Two types of distribution
of the gas velocity dispersion of MaNGA galaxiesTwo types of distribution of
the gas velocity dispersion of MaNGA galaxies J. M. Vílchez Two types of
distribution of the gas velocity dispersion of MaNGA galaxiesTwo types of
distribution of the gas velocity dispersion of MaNGA galaxies

The distribution of the gas velocity dispersion $\sigma$ across the images of
1146 MaNGA galaxies is analyzed. We find that there are two types of
distribution of the gas velocity dispersion across the images of galaxies:
$(i)$ the distributions of 909 galaxies show a radial symmetry with or without
the $\sigma$ enhancement at the center (”R distribution,” radial symmetry in
the $\sigma$ distribution) and $(ii)$ distributions with a band of enhanced
$\sigma$ along the minor axis in the images of 159 galaxies with or without
the $\sigma$ enhancement at the center (”B distribution,” band in the $\sigma$
distribution). The $\sigma$ distribution across the images of 78 galaxies
cannot be reliable classified. We select 806 galaxies with the best defined
characteristics (this sample includes 687 galaxies with R distribution and 119
galaxies with B distribution) and compare the properties of galaxies with R
and B distributions. We find that the median value of the gas velocity
dispersion $\sigma_{m}$ in galaxies with B distribution is higher by around 5
km/s, on average, than that of galaxies with R distribution. The optical
radius $R_{25}$ of galaxies with B distribution is lower by around 0.1 dex, on
average, than that of galaxies with similar masses with R distribution. Thus
the properties of a galaxy are related to the type of distribution of the gas
velocity dispersion $\sigma$ across its image. This suggests that the presence
of the band of the enhanced gas velocity dispersion can be an indicator of a
specific evolution (or a specific stage in the evolution) of a galaxy.

###### Key Words.:

galaxies: ISM – galaxies: kinematics and dynamics – galaxies: structure

##  1 Introduction

In a previous study, we considered the circumnuclear regions in 161 star-
forming (SF) galaxies from the Mapping Nearby Galaxies at Apache Observatory
(MaNGA) survey (Bundy et al. 2015; Albareti et al 2017) with four radiation
distribution configurations (Pilyugin et al. 2020b). The spaxel spectra were
classified as active galactic nucleus-like (AGN-like), H ii-region-like (or
SF-like), and intermediate (INT) spectra according to their positions in the
Baldwin-Phillips-Terlevich (BPT, Baldwin, Phillips, Terlevich 1981) diagram.
We found that the AGN-like and INT radiation in the circumnuclear region is
accompanied by an enhancement in the gas velocity dispersion $\sigma$, in the
sense that the gas velocity dispersion in a galaxy decreases with
galactocentric distance up to some radius and remains approximately constant
beyond this radius. The radius of the area of the AGN-like and INT radiation
(radius of influence of the AGN on the radiation) is similar to the radius of
the area with enhanced gas velocity dispersion, and the central gas velocity
dispersion $\sigma_{c}$ correlates with the luminosity of the AGN+INT area.
This suggests that the enhancement of the gas velocity dispersion at the
center of a galaxy can be attributed to the AGN activity.

A correlation between the gas velocity dispersion and the diagnostic emission
line ratios of the BPT diagram is revealed in the ultraluminous and luminous
infrared galaxies in the absence of any contribution from an AGN. This
correlation is interpreted as a signature of shock excitation, where shocks
are driven by galaxy mergers or interactions (Monreal-Ibero et al. 2006, 2010;
Rich et al. 2014, 2015).

Here we construct the maps of the gas velocity dispersion for a large sample
of late-type MaNGA galaxies with the aim of examining the properties of the
gas velocity dispersion fields beyond the circumnuclear regions. The
parameters of emission lines in each spaxel spectrum are estimated using a
Gaussian fit to the line profiles. The sigma of the best-fit Gaussian of the
H$\alpha$ line is converted into the gas velocity dispersion.

This paper is organized as follows. The data are described in Section 2. In
Section 3, the distributions of the gas velocity dispersion of MaNGA galaxies
are discussed, and Section 4 provides a brief summary.

##  2 Data

Our current study is based on data obtained from the public spectroscopic
observations from the Sloan Digital Sky Survey Data Release 15 (SDSS DR15)
MaNGA survey (Bundy et al. 2015; Albareti et al 2017) and described in
Pilyugin et al. (2020b). In brief, the spectrum of each spaxel was reduced as
indicated in Zinchenko et al. (2016) and Sakhibov et al. (2018). The stellar
background was fitted using the public version of the STARLIGHT code (Cid
Fernandes et al. 2005; Mateus et al. 2006; Asari et al. 2007), which was
adapted for execution in the NorduGrid Advanced Resource Connector
(ARC)111http://www.nordugrid.org/ environment of the Ukrainian National Grid.
The library of synthetic simple stellar population (SSP) spectra from the
evolutionary synthesis models in Bruzual & Charlot (2003) were used. The
reddening law from Cardelli et al. (1989) with $R_{V}=3.1$ was adopted. The
obtained stellar radiation contribution was subtracted from the observed
spectrum.

The emission lines in each spaxel spectrum were estimated using a Gaussian fit
to the line profiles. The emission line parameters include the central
wavelength $\lambda_{0}$, the sigma $\sigma$, and the flux $F$. For each
spectrum, we measured the [O ii]$\lambda\lambda$3727,3729, H$\beta$, [O
iii]$\lambda$5007, H$\alpha$, and [N ii]$\lambda$6584 emission lines. Only
those spaxel spectra where all the used lines were measured with a signal-to-
noise ratio S/N $>3$ were taken into consideration. The central wavelength of
the H$\alpha$ line was converted into the line-of-sight velocity, and the
sigma of the best-fit Gaussian $\sigma_{{\rm H}\alpha}$ was converted into the
observed gas velocity dispersion $\sigma_{obs}$. Since the values of the
observed (non-corrected-for instrumental profile) gas velocity dispersion are
used throughout the paper, we will use the notation $\sigma$ instead of
$\sigma_{obs}$. The gas velocity dispersion in the galaxy will be specified by
the median value of the gas velocity dispersion $\sigma_{m}$ of the individual
spaxels.

The measured emission line fluxes were corrected for interstellar reddening
using the theoretical H$\alpha$/H$\beta$ ratio and the reddening function from
Cardelli et al. (1989) for $R_{V}$ = 3.1. We assumed $C_{{\rm
H}{\beta}}=0.47A_{V}$ (Lee et al. 2005). The excitation properties of each
spaxel spectrum (main excitation mechanism: starburst or AGN) were determined
using the diagnostic line ratio diagram proposed by Baldwin, Phillips,
Terlevich (1981) (BPT classification diagram). The spectra located to the left
(below) the demarcation line from Kauffmann et al. (2003) are referred to as
the SF-like or H ii region-like spectra, those located to the right (above)
the demarcation line from Kewley et al. (2001) are referred to as the AGN-like
spectra, and the spectra located between those demarcation lines are the
intermediate (INT) spectra. The configuration of the radiation distribution in
the circumnuclear region of each galaxy was classified according to Pilyugin
et al. (2020b): (i) the circumnuclear region of the SF or H ii type where the
central area involves the spaxels with the H ii-region-like radiation only;
(ii) the circumnuclear region of the INT type if the radiation at the center
of the galaxy is the intermediate type; (iii) and the circumnuclear region of
the AGN type where the innermost region of the AGN-like radiation is
surrounded by a ring of radiation of the intermediate type. The circumnuclear
regions of the AGN type are divided into two subtypes, the LINER circumnuclear
regions and the Seyfert circumnuclear regions, using the dividing line between
Seyfert galaxies and LINERs defined by Cid Fernandes et al. (2010).

The geometrical parameters of the galaxy were determined from the surface
brightness distribution in the same way as in our previous studies (Pilyugin
et al. 2014, 2017, 2018). The surface brightness in the SDSS $g$ and $r$ bands
for each spaxel was obtained from broadband SDSS images created from the data
cube. The measured magnitudes are converted to $B$-band magnitudes and
corrected for Galactic foreground extinction using the recalibrated $A_{V}$
values from Schlafly & Finkbeiner (2011) as reported in the NASA/IPAC
Extragalactic Database (ned)222The NASA/IPAC Extragalactic Database (ned) is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration.
http://ned.ipac.caltech.edu/. The observed surface-brightness profile within a
galaxy was fitted by a broken exponential profile for the disk and by a
general Sérsic profile for the bulge under the assumption that the position
angle of the major photometric axis and the galaxy inclination are constant
within the disk. The optical radius of the galaxy $R_{25}$ was estimated using
the obtained fit. It should be noted that the observed surface-brightness
profile in many galaxies is well fitted by a broken exponential profile with
negligible contribution from the Sérsic component. This indicates that either
there is no appreciable bulge in this galaxy or that the surface brightness of
the bulge is described by the exponential profile. If the latter is true, then
the bulge in this galaxy can be missed.

The distances to the galaxies were adopted from ned. The ned distances use
flow corrections for Virgo, the Great Attractor, and Shapley Supercluster
infall (adopting a cosmological model with $H_{0}=73$ km/s/Mpc,
$\Omega_{m}=0.27$, and $\Omega_{\Lambda}=0.73$). We have chosen the
spectroscopic $M_{sp}$ masses of the SDSS and BOSS (BOSS stands for the Baryon
Oscillation Spectroscopic Survey in SDSS-III, see Dawson et al. 2013). The
spectroscopic masses are from the table stellarMassPCAWiscBC03 and were
determined using the Wisconsin method (Chen et al. 2012) with the stellar
population synthesis models from Bruzual & Charlot (2003).

The $\sigma$ distributions of the images for around 3000 MaNGA galaxies from
the DR15 release were constructed. We searched for galaxies for further
consideration via visual inspection of those maps. We required that the
spaxels with measured emission lines cover an area large enough so that the
gas velocity dispersion distribution could be classified. The distribution of
the gas velocity dispersion in a galaxy with high inclination (close to the
edge-on) in particular cannot be classified. Peculiar and strongly interacting
or merging galaxies were excluded.

We selected 1146 MaNGA galaxies that fit these criteria. The circumnuclear
regions are of the H ii type in 757 galaxies, of the INT type in 141 galaxies,
of the LINER type in 202 galaxies, and of the Seyfert type in 46 galaxies.

##  3 Two types of $\sigma$ distribution in galaxies

Figure 1:  Examples of distributions of the gas velocity dispersion $\sigma$
over images of galaxies. Panel $a1$: Galaxy with R distribution of $\sigma$
without an appreciable enhancement at the center. The values of the gas
velocity dispersion are color-coded. The circle shows the photometric center
of the galaxy, the solid line indicates the position of the major photometric
axis of the galaxy, and the dashed line marks the optical radius of the
galaxy, $R_{25}$. Panel $a2$: Observed gas velocity dispersion as a function
of radius for individual spaxels. The BPT type of the spectra is color-coded.
The line indicates the median value of the gas velocity dispersions. Panel
$b1$: Galaxy with R distribution and with a significant enhancement of the
$\sigma$ at the center Panel $b2$: Radial distribution of the $\sigma$ in this
galaxy. Panels $c1$ and $d1$: Examples of galaxies with B distribution. Panels
$c2$ and $d2$: Gas velocity dispersion as a function of radius for those
galaxies.

There is a variation in the values of the gas velocity dispersion across the
image of each galaxy. The variation of $\sigma$ can be chaotic or can show a
global structure. If the amplitude of the chaotic variation of the $\sigma$ is
more or less similar over the whole image of the galaxy, then the distribution
of the $\sigma$ in this galaxy can be considered as a uniform distribution in
the first approximation. Panel a1 of Fig. 1 shows an example of the uniform
distribution of $\sigma$ over the image of the galaxy, and panel a2 shows the
$\sigma$ as a function of radius for this galaxy. The value of the gas
velocity dispersion is usually enhanced at the center of the galaxy. Panel b1
of Fig. 1 shows an example of the distribution of the $\sigma$ with a
significant enhancement at the center, and panel b2 shows the $\sigma$ as a
function of radius. The global distribution of the $\sigma$ in the galaxy
presented in panel b1 of Fig. 1 shows a radial symmetry. The distribution of
the $\sigma$ of such a type (radial symmetry in the $\sigma$ distribution)
will be denoted as ”R distribution.” The uniform distribution of the $\sigma$
is a particular case of R distribution. By visually inspecting the $\sigma$
maps in our sample of galaxies, we found that the $\sigma$ distribution in 909
of the 1146 galaxies can be classified as R distribution.

A prominent feature in the distribution of the gas velocity dispersion in some
galaxies is a band of enhanced $\sigma$ along the minor axis of the galaxy.
The band can be found both in galaxies with and without the enhancement of the
$\sigma$ at the center. Panels c1 and d1 of Fig. 1 show examples of galaxies
with bands of enhanced $\sigma$ in the distribution of the gas velocity
dispersion across the image of the galaxy. Panels c2 and d2 of Fig. 1 show the
$\sigma$ as a function of radius for those galaxies. Such a distribution of
the gas velocity dispersion in the galaxy (band in the $\sigma$ distribution)
will be denoted as ”B distribution.” We found that the $\sigma$ distribution
in 159 out the 1146 galaxies of our sample can be classified as B
distribution. It should be emphasized that the band of enhanced $\sigma$ in
all the galaxies with B distribution is close to the minor axis of the image,
with one exception. The band of enhanced $\sigma$ in MaNGA galaxy M-8554-06101
is located along the major axis of the image; this galaxy is not included in
the list of galaxies with B distribution.

We find it difficult to classify the distribution of the gas velocity
dispersion in 78 of the galaxies from our sample. In some cases, we cannot
chose whether the distribution of the $\sigma$ corresponds with R distribution
or B distribution; the visual classification of the distribution of the gas
velocity dispersion across the image of the galaxy is somewhat arbitrary. In
other cases, there is a feature in the distribution of the gas velocity
dispersion that makes the $\sigma$ distribution peculiar.

The line-of-sight velocity field serves to examine the galaxy rotation.
Accurate rotation curves cannot be determined for many galaxies from our
sample because the curves of isovelocities in the line-of-sight velocity
fields in some galaxies more resemble a set of straight lines than a set of
parabola-like curves (the hourglass-like picture for the rotation disk).
Therefore, we restricted ourselves by the qualitative analysis of the galaxy
rotation, that is, we carried out a visual inspection of the line-of-sight map
with the aim of establishing whether the galaxy is rotating. We found that all
the galaxies from our sample are rotating objects.

For the purpose of comparing the properties of the galaxies with R and B
distributions of gas velocity dispersions, we selected a sample of galaxies
with reliably determined parameters using the following four criteria. First,
galaxies with non-classified distribution were excluded. Second, galaxies with
circumnuclear regions of the Seyfert type were also excluded. The emission
line profiles of the spaxel spectra were fitted by single Gaussians. A broad
component can be expected in the emission line profiles in the spaxel spectra
of the Seyfert type. Hence the single Gaussian is not an adequate
approximation for the profile of the emission line with a broad component;
such lines should be fitted by two Gaussians. Third, galaxies with an INT-type
circumnuclear region were excluded because their contribution from the AGN and
SF to the radiation of the circumnuclear regions can significantly change from
galaxy to galaxy. Fourth, galaxies where the spaxels with available spectra
cover less than two-thirds of the optical radius were rejected because the
determination of parameters (e.g., optical radius $R_{25}$ or the median value
of the gas velocity dispersion $\sigma_{m}$) are questionable. The selected
sample includes 806 galaxies: 687 galaxies with R distribution and 119
galaxies with B distribution.

Figure 2:  Median values of gas velocity dispersion $\sigma_{m}$ in galaxies
with R and B distributions. Panel $a$: $\sigma_{m}$ as a function of the
spectroscopic stellar mass $M_{sp}$ for individual galaxies with R
distribution (blue circles) and with B distribution (red squares). The solid
line shows the median value of $\sigma_{m}$ in galaxies with R distribution,
and the dashed line shows the median value of $\sigma_{m}$ for galaxies with B
distribution. Panel $b$: Median values of $\sigma_{m}$ for galaxies in bins of
0.3 dex in $M_{sp}$ for R-distribution galaxies (blue circles) and
B-distribution galaxies (red squares). The lines come from panel $a$.

Figure 3:  Relation between optical radius $R_{25}$ and stellar mass $M_{sp}$.
Panel $a$: $R_{25}$ as a function of $M_{sp}$ for individual galaxies with R
distribution (blue circles) and B distribution (red squares) of the gas
velocity dispersion. Panel $b$: Median values of $R_{25}$ for galaxies in bins
of 0.3 dex in $M_{sp}$ for galaxies with R distribution, shown with blue
circles. The solid line is the linear best fit to those data. Red squares
denote the binned median values for galaxies with B distribution. The dashed
line is the linear best fit to those data.

Figure 4:  Inclination angle $i$ as a function of stellar mass $M_{sp}$ for
galaxies with R distribution (blue circles) and B distribution (red squares)
of the gas velocity dispersion.

Panel a of Fig. 2 shows the median value of the observed gas velocity
dispersion $\sigma_{m}$ as a function of spectroscopic stellar mass $M_{sp}$
for galaxies with R distribution (blue circles) and for galaxies with B
distribution (red squares). Panel b of Fig. 2 represents the median values of
$\sigma_{m}$ for galaxies in bins of 0.3 dex in $M_{sp}$ for galaxies with R
distribution (blue circles) and for galaxies with B distribution (red
squares). The median value of the $\sigma_{m}$ for the 687 galaxies with R
distribution is equal to 72.45 $\pm$ 3.24 km/s (solid lines in panels a and b
of Fig. 2). This value agrees with the median value of the $\sigma_{m}$ (72.5
$\pm$ 2.8 km/s) obtained for the 161 galaxies in Pilyugin et al. (2020b). The
median value of the $\sigma_{m}$ for the 119 galaxies with B distribution is
equal to 77.15 $\pm$ 4.66 km/s (dashed lines in panels a and b of Fig. 2).
Thus, the median value of the gas velocity dispersion in the galaxy is related
to the type of the $\sigma$ distribution across the image of the galaxy, in
the sense that the median value of the observed gas velocity dispersion in
galaxies with B distribution is higher, on average, by around 5 km/s compared
to galaxies with R distribution.

Next, we examined whether other properties of galaxies are related to the type
of $\sigma$ distributions. Blue points in panel a of Fig. 3 indicate the
optical radius $R_{25}$ as a function of stellar mass $M_{sp}$ for individual
galaxies with R distribution. The linear least-squares fit to those data is

$\log R_{25}=0.248(\pm 0.006)\log M_{sp}-1.488(\pm 0.065)$ (1)

and is shown by the solid line in panel $a$ of Fig. 3. The correlation between
the optical radius $R_{25}$ and the stellar mass for galaxies with R
distribution is rather tight. The correlation coefficient is 0.83. The mean
value of the scatter around the $R_{25}$ – $M_{sp}$ relation is 0.117 dex.

Red squares in panel a of Fig. 3 indicate the optical radius $R_{25}$ as a
function of stellar mass $M_{sp}$ for individual galaxies with B distribution.
The linear least-squares fit to those data is

$\log R_{25}=0.273(\pm 0.016)\log M_{sp}-1.849(\pm 0.164)$ (2)

and is shown by the dashed line in panel $a$ of Fig. 3. The correlation
between the optical radius $R_{25}$ and the stellar mass for galaxies with B
distribution is also tight. The correlation coefficient is 0.84. The mean
value of the scatter around the $R_{25}$ – $M_{sp}$ relation is 0.110 dex.

Panel b of Fig. 3 represents the median values of $R_{25}$ for galaxies in
bins of 0.3 dex in $M_{sp}$ for galaxies with R distribution (blue circles)
and for galaxies with B distribution (red squares). The lines are the same as
in panel a of Fig. 3. An examination of Fig. 3 shows that the optical radius
of the galaxy $R_{25}$ is related to the type of $\sigma$ distribution across
the image of the galaxy, in the sense that the optical radius in a galaxy with
B distribution is lower, on average, by around 0.1 dex compared to a galaxy of
a similar mass with R distribution.

Thus, the median value of the gas velocity dispersion in a galaxy is related
to the type of $\sigma$ distribution across the image of the galaxy. The
optical radius of a galaxy $R_{25}$ is also related to the type of $\sigma$
distribution. This suggests that the presence of the band of enhanced gas
velocity dispersion is an indicator of a specific evolutionary stage in the
galaxy.

The band of enhanced $\sigma$ in a galaxy with B distribution is located along
the minor axis of the galaxy. This can be explained if there is an asymmetry
in the gas velocity dispersion, in other words, if the radial component of the
gas velocity dispersion is larger than the azimuthal and vertical
(perpendicular to the galaxy plane) components.

Since the band of enhanced gas velocity dispersion is located along the minor
axis of the image of the galaxy, a question arises of whether or not the band
can be an artificial effect (i.e., if the band can appear due to the high
inclination of the galaxy). Figure 4 shows the inclination angle – stellar
mass diagram for galaxies with R and B distributions. Inspection of Fig. 4
shows that there are many galaxies with high inclinations (up to and even in
excess of 70$\degr$) where the band of enhanced $\sigma$ is not revealed. At
the same time, the bands are revealed in galaxies with lower inclinations.
This indicates that the band is not an artificial effect in galaxies with high
inclination. However, the band of enhanced $\sigma$ is found more often in
galaxies with high inclination. The median value of the inclination of
galaxies with B distribution is 56.6$\degr$, with a scatter of 10.2$\degr$.
The median value of the inclination of galaxies with R distribution is
50.2($\pm$14.4)$\degr$ for our sample of galaxies.

The mass of galaxies with AGN is usually higher than 1010.5 $M_{\odot}$, while
the mass of galaxies with B distribution is often lower than 1010.5
$M_{\odot}$. This suggests that the B-distribution phenomenon is not related
to the AGN phenomenon. Indeed, the LINER circumnuclear region is revealed only
in four out of the 119 galaxies with B distribution, while the LINER is
revealed in 151 out of the 687 galaxies with R distribution. A bulge is found
in several galaxies with B distribution only. This indicates that B
distribution is not related to the bulge.

##  4 Conclusions

The parameters of emission lines in spaxel spectra of MaNGA galaxies are
estimated using a Gaussian fit to the line profiles. The sigma of the best-fit
Gaussian to the H$\alpha$ line is converted into the gas velocity dispersion
$\sigma$. The distributions of the gas velocity dispersion $\sigma$ across the
images of 1146 MaNGA galaxies are constructed. We find that there are two
types of gas velocity dispersion distributions across the images of galaxies.
The distributions of 909 of the galaxies show a radial symmetry with or
without the enhancement of the $\sigma$ at the center (R distribution). There
is a band of enhanced $\sigma$ along the minor axis in the images of 159 of
the galaxies with or without the enhancement of the $\sigma$ at the center (B
distribution). The $\sigma$ distribution across the images of 78 of the
galaxies cannot be reliable classified.

We selected 806 galaxies with the best defined characteristics and compared
the properties of galaxies with R distribution (687) to galaxies with B
distribution (119). We find that the median value of gas velocity dispersion
$\sigma_{m}$ in galaxies with B distribution is higher, on average, by around
5 km/s than that in galaxies with R distribution. At the same time, the value
of $\sigma_{m}$ is similar for galaxies of different masses for a given type
of $\sigma$ distribution.

We also find that the optical radius $R_{25}$ of galaxies with B distribution
is lower by around 0.1 dex, on average, than that of galaxies of similar
masses with R distribution. Thus the properties of galaxies are related with
the type of the distribution of the gas velocity dispersion $\sigma$ across
their image. This suggests that the presence of the band of enhanced gas
velocity dispersion is an indicator of a specific evolution (or specific stage
in the evolution) of a galaxy.

The presence of the band of enhanced gas velocity dispersion is not related to
the AGN phenomenon. The band of enhanced $\sigma$ along the minor axis of the
galaxy can be explained if there is an asymmetry in the gas velocity
dispersion, that is, if the radial component of the gas velocity dispersion is
larger than the azimuthal and vertical (perpendicular to the galaxy plane)
components.

## Acknowledgements

We are grateful to the referee for his/her constructive comments.
We thank Dr. S.G.Kravchuk for useful discussion.
L.S.P acknowledges support within the framework of the program of the NAS of
Ukraine “Support for the development of priority fields of scientific
research” (CPCEL 6541230)”
I.A.Z acknowledges support by the grant for young scientist’s research
laboratories of the National Academy of Sciences of Ukraine.
The work is performed according to the Russian Government Program of
Competitive Growth of Kazan Federal University and Russian Science Foundation,
grant no. 20-12-00105
We acknowledge the usage of the HyperLeda database (http://leda.univ-
lyon1.fr).
Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation, and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/.
Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High-Performance Computing at the University of Utah. The SDSS
web site is www.sdss.org.

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A monolithic frequency comb platform based on interband cascade lasers and
detectors

Benedikt Schwarz1∗, Johannes Hillbrand1, Maximilian Beiser1, Aaron Maxwell
Andrews2, Gottfried Strasser2, Hermann Detz2,3, Anne Schade4, Robert Weih4,5
and Sven Höfling4,6

1Institute of Solid State Electronics, TU Wien, Gußhausstraße 25, 1040 Vienna,
Austria
2Center for Micro- and Nanostructures, TU Wien, Gußhausstraße 25, 1040 Vienna,
Austria
3Central European Institute of Technology, Brno University of Technology,
Brno, Czech Republic
4Technische Physik, Physikalisches Institut, University Würzburg, Am Hubland,
97074 Würzburg, Germany
5Nanoplus Nanosystems and Technologies GmbH, 97218 Gerbrunn, Germany
6SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews,
KY16 9SS, United Kingdom
∗e-mail<EMAIL_ADDRESS>
Optical frequency combs enable all-solid-state spectrometers that will trigger
a breakthrough in miniaturization and on-chip integration of mid-infrared
sensing technology. Interband cascade lasers (ICLs) are an ideal candidate for
practical implementations due to their low power consumption and zero-bias
detection functionality. Here, we demonstrate the generation of self-starting
ICL frequency combs. We show that the gain is fast enough to respond to
beating of the intracavity field, which hinders the formation of short pulses.
Instead, the ICL operates in a comb state, where the phases of the fundamental
intermode beatings are splayed over a range of $2\pi$. This state appears to
be general to self-starting combs based on the inherent gain nonlinearity and
minimizes oscillations of the population inversion. Using the same epi-layer
material, we demonstrate efficient detector operation at room temperature up
to several GHz bandwidth and thereby provide a complete and unmatched platform
for monolithic and battery driven dual-comb spectroscopy.

Sensors are the heart of every smart technology. They allow to capture data of
environmental pollution, plant infections, or our current physiological
condition. The mid-infrared is the spectral region of choice when it comes to
sensing and spectroscopy. No other spectral region provides the same
sensitivity or selectivity for molecular fingerprinting. Established mid-
infrared spectrometers are mostly based on free space optics and moving parts.
None of these concepts can be sufficiently down-scaled to single-chip
dimensions. Dual-comb spectroscopy1, 2, 3, 4 offers the unique possibility to
directly map the optical spectrum to the electrical domain. Dual-comb
spectrometers do not require movable parts and can be miniaturized without
losing spectral resolution – there is no relation between the spectral
resolution and the spatial dimension. Its full potential for practical
applications can be unlocked, if both frequency comb generators and heterodyne
detectors are miniaturized, driven by a battery and ideally integrated on a
chip.

For a long time, frequency comb generation in the mid-infrared was limited to
table-top instruments5, 6. A first compact implementation was demonstrated
utilizing the Kerr nonlinearity in passive microresonators7, 8. While
microresonator combs recently reached the maturity to enable compact and
battery driven systems at telecom wavelengths9, frequency comb generation in
the mid-infrared is still restricted to external table-top pump lasers.

An alternative concept employs the third-order nonlinearity of the laser
itself. This per se monolithic approach is ideal for the realization of
miniaturized spectrometers and was found in quantum cascade lasers (QCLs) a
few years ago10. Due to the ultra-fast gain dynamics, the population inversion
can respond to beatings between laser modes. The resulting four-wave mixing is
responsible for coupling the modes and the formation of the frequency comb.
While QCL frequency combs are compact, their high power consumption strongly
limits their use in battery driven applications. Back in 1988, Agrawal pointed
out that the four-wave mixing process does not necessarily require ultra-fast
population inversion dynamics11. This suggests that the concept of self-
starting frequency combs based on the inherent gain nonlinearity can also be
transfered to other types of lasers that fulfill the requirements for portable
devices. ICLs are the ideal alternative12, 13, 14, because their power
consumption is 1–2 orders of magnitude smaller than that of QCLs. Also in
terms of output power and efficiency, ICLs are catching up rapidly13, 15, 16,
17.

Figure 1: ICL frequency comb. a Frequency modulation capabilities of the
optimized devices measured optically via a fast QWIP (red) and electrically
via RF rectification (blue). The black curve is corrected by the RC-cutoff of
the ICL and QWIP response to extract the portion due to the response of the
gain medium. Inset: sketch of the two-section device. b The spectral lines of
the ICL beat together leading to a modulation of the laser intensity at the
cavity roundtrip frequency. The resulting electrical beatnote can be measured
by recording the RF spectrum of the absorber current and tunes with the
absorber bias. Regions of self-starting comb operation are highlighted by the
rectangles. c Narrow electrical beatnote with a linewidth of
4$\,\mathrm{k}\mathrm{Hz}$. d&e ’Shifted Wave Intermode Beat Fourier Transform
Spectroscopy’ (SWIFTS) analysis and corresponding time domain signal of the
ICL frequency comb. The intermode difference phases cover the range from $\pi$
to $-\pi$. This and the minimum in the SWIFTS interferograms at zero-phase are
characteristic for the suppression of amplitude modulation. f Time domain
signal of a QCL frequency comb18. Irrespective of the sign, the both combs
show the same characteristic dominantly frequency modulated outout. This
suggests that the ICL frequency comb is indeed governed by the inherent gain
nonlinearity, which is connected to the suppression of amplitude modulations.

In this work, we present a new monolithic frequency comb sensing platform
based on ICLs. We demonstrate self-starting frequency comb operation of ICLs
based on the inherent gain nonlinearity. Despite the fact that the laser
transition lifetime differs by more than two orders of magnitude, ICLs can
respond to beatings between laser modes and the observed phase pattern is
strikingly similar to QCLs. Our experiments reveal that ICL frequency combs
are characterized by a strong suppression of amplitude modulation. We further
show that ICL combs can be locked to an external RF oscillator while
maintaining full intermodal coherence. This allows an all-electric control and
stabilization of the frequency comb against the harsh conditions, which are
omnipresent in real-life applications. Finally, we highlight the unique
detection functionality naturally provided by the ICL material, which can be
used to directly integrate sensitive multi-heterodyne detectors. Hence, the
ICL based monolithic platform provides all features to realize miniaturized
and battery driven dual-comb spectrometers.

Figure 2: Coherent injection locking and on-chip detection capabilities. a
Optical beatnote spectrum of the ICL depending on the injection frequency for
three different injection powers. The large locking range is due to the
optimized RF injection. b&c Intensity and SWIFTS spectral maps at 5dB
injection power as function of the injection frequency. d Spectral
responsivity and noise equivalent power of the on-chip interband cascade
detector (ICD), which was cleaved from the same chip. e Direct modulation
response of the ICL measured with the ICD. f Narrow beatnote of the ICL comb
measured with the ICD.

In order to investigate frequency comb operation of ICLs, we fabricated a two
section device (fig. 1a). The short section is optimized for efficient radio-
frequency (RF) extraction and injection and its DC bias can be adjusted to
alter the locking properties19. The high frequency modulation response
provides important information about the internal gain dynamics. The extracted
frequency response is flat up to 20 GHz and reveals that the characteristic
response time of the population inversion $\tau_{\mathrm{\Delta n}}$ exceeds
at least the first two harmonics of the repetition frequency. Since the
condition $\tau_{\mathrm{\Delta n}}f_{\mathrm{rep}}\lesssim 1$ is satisfied,
four-wave mixing via population inversion oscillations is the dominant
contribution to the gain nonlinearity11 and enables self-starting frequency
comb operation.

A first indication for frequency comb operation is the observation of a narrow
beatnote. Each pair of laser lines causes a beating at their difference
frequency. In frequency combs all lines are equidistant, resulting in a narrow
beatnote. Fig. 1b shows the electrically extracted laser beatnote depending on
the short section bias. The latter can be altered to tune the ICL into the
self-locking regime. There, the beatnote appears narrow with a linewidth on
the kHz level (fig. 1c), which is more than an order of magnitude below the
Shawlow-Townes quantum limited linewidth of the unlocked laser.

In order to unequivocally proof frequency comb operation we employ SWIFTS20,
21. This technique provides a complete characterization of a comb state by
measuring the coherence and phase between each pair of comb lines. The SWIFTS
analysis of the ICL frequency comb is plotted in fig. 1d. The amplitudes of
the SWIFTS spectrum match the beating amplitudes extracted from the intensity
spectrum (blue dots), which serves as a proof for comb operation over the
entire emission spectrum. The minimum of the SWIFTS interferograms at zero
path difference is a clear sign of the suppression of amplitude modulations.
Even more exciting is additional information provided by the phases. The
intermodal phases follow a chirped pattern covering a range of $2\pi$. The
same pattern was recently observed in QCLs22. Fig. 1e&f show the direct
comparison of the time domain signals of an ICL and a QCL frequency comb.
Although the laser transition lifetimes differ by two orders of magnitude and
operate at a different wavelength, both frequency combs show the linearly
chirped instantaneous frequency accompanied by the suppression of amplitude
modulations. This remarkable similarity indicates that the comb formation is
indeed governed by the same physical mechanism. A state with a weak amplitude
modulation maximized the round-trip gain, as amplitude modulations lead to a
stronger gain saturation in fast gain media. This is the opposite of passive
mode-locking in slow gain media, where four-wave mixing occurs in the fast
saturable absorption, whereas the gain section is too slow to respond to
intermode beatings. There, the formation of pulses is advantageous, as it
minimizes the round-trip loss.

Recent findings revealed that the repetition frequency of a QCL frequency comb
can be synchronized to an external RF oscillator, while maintaining full
intermodal coherence18. This increases the range of comb operation, enables
all-electric frequency comb stabilization via control loops and increases the
stability against optical feedback. This technique can also be employed with
ICL frequency combs. Fig. 2a shows the optically measured beatnote spectrum
while sweeping the injection frequency across the beatnote for three different
injection power levels. The laser beatnote is fully controlled by the external
RF oscillator within a locking range of 1, 2 and 4 MHz, respectively. Fig. 2b
shows that full intermodal coherence is achieved within the locking range,
which serves as a proof that ICL frequency combs can be electrically injection
locked.

Integrating a complete dual-comb spectrometer on a chip requires a technology
that is capable of both frequency comb operation and high speed multi-
heterodyn detection. An elegant solution is building the laser and detector
from the very same material. This so-called bi-functional operation of the
very same material was first demonstrated using QCLs23 and trigged the
realization of a monolithic lab-on-a-chip24. However, the additional on-chip
detection feature requires large modifications of the QCL design to match the
laser and detector wavelength. Hence, bi-functional QCLs were restricted to
pulsed operation for a long time25. Fortunately the bi-functional operation of
ICLs comes naturally and does not require modifications of the design26. The
longer lifetime of the optical transition decreases the thermal noise and
increases the internal quantum efficiency. Fig. 2d shows the spectral
responsivity of the interband cascade detector (ICD) that was fabricated on
the same chip and cleaved for the characterization. A broadband spectral
responsivity of over $100\,$mA/W and an exceptional noise equivalent power of
$2.5\,\mathrm{p}\mathrm{W}\mathrm{/}\sqrt{\mathrm{Hz}}$ are achieved at room
temperature. The provided, yet not optimized, ICD performance is clearly
superior to bi-functional QCL material. In order to demonstrate the high-speed
operation, which is essential for multi-heterodyne detection, we measured the
ICD frequency response optically using the ICL (fig. 2e). The high frequency
cut-off around $5\,$GHz includes both the laser and the detector response and
is limited by parasitic capacitances. The large detection bandwidth even
enables the measurement of the beatnote of the ICL frequency comb with an SNR
of 22dB at room temperature (fig. 2f). Surprisingly, this is even higher than
the SNR obtained with a cryogenically cooled 7 GHz RF-QWIP. These results show
the remarkable detection capabilities provided by the ICL comb platform.
Integrated on the same chip, the coupling efficiencies exceed free-space
optics by at least two orders of magnitude. In principle, a monolithic sensor
chip with a few centimeters of interaction length can thus achieve the same
detector noise limited sensitivity as a setup with discrete elements and an
interaction length of a few meters.

Requirements | Microresonator | QCL | ICL
---|---|---|---
comb operation | $\circ$ | $\circ$ | $\bullet$
stabilization knobs | $\circ$ | $\circ$ | $\bullet$
compact | $\boldsymbol{-}^{*}$ | $\circ$ | $\bullet$
battery driven | $\boldsymbol{-}^{*}$ | $\boldsymbol{-}$ | $\bullet$
GHz on-chip detection | $\boldsymbol{-}$ | $\boldsymbol{-}$ | $\bullet$

(-) not demonstrated, ($\circ$) demonstrated, ($\bullet$) this work.

∗ Only in the near-infrared9.

Table 1: The presented ICL frequency comb platform is the only available mid-
infrared technology that meets all requirements to build ultra-compact and
battery driven dual-comb spectrometers.

In conclusion, we presented a new mid-infrared frequency comb platform based
on ICLs. In contrast to other technologies, the ICL comb platform provides all
properties for ultra-compact and battery driven dual-comb sensors, as
summarized in table 1. We demonstrated self-starting ICL frequency combs based
on the inherent gain nonlinearity caused by the fast dynamics of the
population inversion. The resulting frequency comb state shows a dominant
frequency modulation and a linearly chirped phase signature, which is
characteristic for the suppression of amplitude modulations in fast gain
media. ICL technology reduces the power consumption by two orders of magnitude
compared to QCL to below one watt, enabling battery driven sensors.
Furthermore, ICLs provide exceptionally sensitive and high speed
photodetection capabilities that allow monolithic integration of all active
optical components. Thus, ICL technology provides all properties for all-
solid-state mid-infrared sensors and will promote dual-comb spectroscopy from
fundamental research to a broadly used sensing platform.

## Methods

### Device fabrication

The investigated ICLs were grown at the Universität Würzburg and processed at
the Center of Micro- and Nanostructures at TU Wien. The simulated
bandstructure is shown in supp. fig. 6. The laser ridges were fabricated with
standard mask photolithography, reactive ion etching to define the laser
waveguides, silicon nitride for the passivation layers and sputtered TiAu for
the contact pads. The substrate was thinned to
160$\,\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ and TiAu was sputtered on the
backside . The devices were mounted epi-side up using indium on a copper
mount. Different thickness of the passivation layer have been used to optimize
the device performance in terms of output power and modulation capability.

### Measurement setup

The devices were mounted on a copper submount, thermo-electrically stabilized
to 15 ∘C. In order to improve the noise properties of our laser driver, we
used home-built low-pass filters. The accuracy of temperature stabilization
and the noise of the laser drivers play a crucial role for the stability of
the frequency comb.

### Relevance of the spatial beatnote profile

An important aspect has to be considered for injection locking, is the spatial
patterns of the laser beatnote in standing wave lasers27. Because of the
boundary condition of the modes in the cavity, all beatings between adjacent
lines will follow a half wave cosine function along the cavity. Hence, the
modulation should be applied at the end of the cavity, where the laser is most
susceptible to injection locking.

### SWIFTS

The SWIFTS concept was realized using a fast QWIP placed at the output window
of a FTIR (sketch in supp. fig. 5). The emitted light of the ICL is shined
through the FTIR onto the QWIP. A local oscillator mixes down the the optical
beatnote of the ICL to $\approx$ 40 MHz. By recording the quadrature
components X and Y of the QWIP signal in dependence of the delay time $\tau$
using a lock-in amplifier, we obtain the two SWIFTS quadrature interferograms.
The reference signal for the lock-in amplifier is obtained by mixing another
local oscillator with the RF source used for injection into the ICL. All
interferograms were recorded by the lock-in using the Helium-Neon trigger of
the FTIR. Our FTIR (Bruker Vertex 70v) moves each arm by $\pm\tau/2$. The
complex sum of the interferograms is therefore given by

$\mathbf{F}(X+iY)(\tau)=\sum_{n}A_{n}A_{n-1}\left[\cos\left(\frac{\omega_{r}\tau}{2}\right)+\cos\left(\omega_{n-1/2}\tau\right)\right].$
(1)

By applying the fast fourier transformation, using zero-padding and peak
fitting, both amplitude and phase of all intermode beatings are obtained. The
intermode beatings describe the coherence and phases between adjacent comb
modes. The normalized intermodal coherence can be defined as 21.

$c=\frac{|<A_{n}A_{n-1}e^{(i(\phi_{n}-\phi_{n-1}))}>|}{<|A_{n}||A_{n-1}|>},$
(2)

where $A_{n}$ are the field amplitudes, $\phi_{n}$ the intermodal phases and
the brackets denote temporal averaging. The phases of the modes can be
calculated by the cumulative sum of the intermode beating phases, which
together with the intensity spectrum allows the reconstruction of the time
domain signal of a comb state.

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## Acknowledgements

This work was supported by the Austrian Science Fund (FWF) within the projects
”NanoPlas” (P28914-N27), ”Building Solids for Function” (Project W1243),
”NextLite” (F4909-N23), as well as by the Austrian Research Promotion Agency
through the ERA-Net Photonic Sensing program, project ”ATMO-SENSE” (FFG:
861581). H.D. was supported by the ESF project CZ.02.2.69/0.0/
0.0/16_027/0008371. A.M.A was supported by the projects COMTERA - FFG 849614
and AFOSR FA9550-17-1-0340. B. Schwarz thanks A. Belyanin for the fruitful
discussions at IQCLSW 2018.

## Author contributions

B.S. planned and organized this project and wrote the manuscript. J.H. and
B.S. performed the phase measurements of the combs. J.H. fabricated and tested
the RF QWIPs. M.B. designed, fabricated and tested the two-section ICLs with
guidance of B.S.. H.D., A.M.A and G.S. grew the QWIP structures. A.S., R.W.
and S.H. provided the ICL material. All authors contributed to discussions how
to interpret the results and commented on the manuscript.

## Competing financial interests

The authors declare no competing financial interests.

## Data availability statement

The data that support the plots within this paper and other findings of this
study are available from the corresponding author upon reasonable request.