# SDSS-IV MaNGA: The Radial Profile of Enhanced Star Formation in Close Galaxy
Pairs

Joshua L. Steffen11affiliation: Department of Physics & Astronomy, University
of Iowa, Iowa City, IA 52242 , Hai Fu11affiliation: Department of Physics &
Astronomy, University of Iowa, Iowa City, IA 52242 22affiliation: Insititute
for Astronomy, University of Hawaii, Honolulu, HI 96822 , J. M.
Comerford33affiliation: Department of Astrophysical and Planetary Sciences,
University of Colorado, Boulder, CO 80309 , Y. Sophia Dai (戴昱)44affiliation:
Chinese Academy of Sciences South America Center for Astronomy
(CASSACA)/National Astronomical Observatories of China (NAOC), 20A Datun Road,
Beijing 100012, China , Shuai Feng55affiliation: Department of Physics, Hebei
Normal University, 20 South Erhuan Road, Shijiazhuang, 050024, China
66affiliation: Key Laboratory for Research in Galaxies and Cosmology, Shanghai
Astronomical Observatory, Chinese Academy of Sciences, 80 Nandan Road,
Shanghai 200030, China 77affiliation: University of the Chinese Academy of
Sciences, No.19A Yuquan Road, Beijing 100049, China , Arran C.
Gross11affiliation: Department of Physics & Astronomy, University of Iowa,
Iowa City, IA 52242 , and Rui Xue11affiliation: Department of Physics &
Astronomy, University of Iowa, Iowa City, IA 52242

###### Abstract

We compare the radial profiles of the specific star formation rate (sSFR) in a
sample of 169 star-forming galaxies in close pairs with those of mass-matched
control galaxies in the SDSS-IV MaNGA survey. We find that the sSFR is
centrally enhanced (within one effective radius) in interacting galaxies by
$\sim$0.3 dex and that there is a weak sSFR suppression in the outskirts of
the galaxies of $\sim$0.1 dex. We stack the differences profiles for galaxies
in five stellar mass bins between log($M/M_{\odot}$) $=$ 9.0$-$11.5 and find
that the sSFR enhancement has no dependence on the stellar mass. The same
result is obtained when the comparison galaxies are matched to each paired
galaxy in both stellar mass and redshift. In addition, we find that that the
sSFR enhancement is elevated in pairs with nearly equal masses and closer
projected separations, in agreement with previous work based on single-fiber
spectroscopy. We also find that the sSFR offsets in the outskirts of the
paired galaxies are dependent on whether the galaxy is the more massive or
less massive companion in the pair. The more massive companion experiences
zero to a positive sSFR enhancement while the less massive companion
experiences sSFR suppression in their outskirts. Our results illustrate the
complex tidal effects on star formation in closely paired galaxies.

###### Subject headings:

galaxies: star formation — galaxies: nuclei — galaxies: interactions —
galaxies: mass evolution

##  1\. Introduction

In the $\Lambda$CDM model, galaxy evolution is a hierarchical process. In this
model, massive galaxies are the product of several past merger events of
smaller galaxies. In fact, cosmological hydrodynamical simulations have shown
that repeated merger events may be responsible for as much as $\sim$60% of
stellar mass in massive galaxies like M87 (e.g., Rodriguez-Gomez et al., 2016;
Pillepich et al., 2018). As the galaxies undergo the merging process, the gas
within the galaxies are subjected to gravitational torques which perturb the
morphology of the galaxies.

The internal dynamics of these interacting galaxies were first modeled in the
seminal work, Toomre & Toomre (1972). Since then, hydrodynamical simulations
have expanded upon the N-body simulations of Toomre & Toomre (1972) by
modeling gas-dynamics within the galaxies. These simulations show the process
by which barred structures develop within the disks of the interacting
galaxies due to the tidal torques between them (Barnes & Hernquist, 1991). As
the bars form, the gases within the galaxy’s disk lose angular momentum and
get funneled into the centers of the galaxies.

When the gas-inflows impact upon the gases in the nucleus of the galaxy, a
burst of new star formation is triggered (Barnes & Hernquist, 1996; Mihos &
Hernquist, 1996). These gas inflows will also bring metal-poor gases from the
disk into the center of the galaxy which can dilute the central metallicity
(Rupke et al., 2010; Perez et al., 2011; Scudder et al., 2012). The gas-
inflows may also be able to reach into the very center of the galaxy and
trigger an episode of supermassive black hole (SMBH) accretion (Capelo et al.,
2017).

Interaction induced star formation was first seen observationally in the bluer
colors of peculiar galaxies in Larson & Tinsley (1978). Similar observations
have has also been shown in more recent works using the single-fiber
spectroscopic survey, SDSS (Sloan Digital Sky Survey) (Ellison et al., 2008;
Li et al., 2008; Scudder et al., 2012; Patton et al., 2013; Bustamante et al.,
2020). From these previous works it has been shown that the strength of the
star formation enhancement in the centers of paired galaxies is dependent on
the stellar mass of the pairs (Li et al., 2008), the projected separation
between the pairs (Ellison et al., 2008; Li et al., 2008; Scudder et al.,
2012), and the mass ratio between the pairs (Ellison et al., 2008).

The previously mentioned works using SDSS were restricted to studying the
centers of the paired galaxies through 1-1.5″-radius optical fibers. With the
recent large integral field spectroscopic (IFS) surveys, interacting galaxies
can now be studied with unprecedented spatial detail. These surveys allow us
to study the centers of merging galaxies more rigorously since apertures can
be set to the physical scale of the galaxies instead of being bound by a fixed
sky aperture. These IFS surveys will also allow us to see the extent of the
centrally induced star formation and to see how the star formation in the
disks of the galaxies are affected.

Indeed, Barrera-Ballesteros et al. (2015) used the CALIFA (Calar Alto Legacy
Integral Field Area) survey to study a sample of 103 paired galaxies by
varying the size of the aperture through which the EW(H$\alpha$) is extracted.
In this study, they found a moderate enhancement to the sSFR in the centers of
paired galaxies and a moderate suppression to the sSFR in outskirts of the
paired galaxies.

Pan et al. (2019) used the SDSS-IV MaNGA survey to study radial profiles of a
sample of 205 paired galaxies. The enhancement to the sSFR was shown to be the
strongest in the centers of the paired galaxies. This central enhancement
linearly fell with increasing galactocentric radii; however, a moderate
enhancement to the sSFR remains in the outskirts of the galaxies. Pan et al.
(2019) further studied the paired galaxies as a function of merger stage, from
well separated pairs to post-merger galaxies. Across the different merger
stages, the sSFR enhancement was greatest in close pairs with tidal features
and in post-merger galaxies. This was in agreement with previous
hydrodynamical simulations which showed that a burst of star formation is
triggered after the first pericenter and as the two galaxies begin to coalesce
(Scudder et al., 2012).

The radial profile of sSFR in post-merger galaxies has also been studied with
the MaNGA survey by Thorp et al. (2019). The post-merger galaxies were shown
to have a strong enhancement to the sSFR in their centers as well as a
moderate enhancement in their outskirts.

Where previous studies on the radial profile of the sSFR offsets in paired
galaxies have focused on studying the profiles as a function of interaction
stage, we will focus on the radial profile as a function of the stellar mass,
projected separation, and mass ratio. As mentioned previously, these
parameters have been covered by studies restricted to the nuclear region of
the paired galaxies. With the MaNGA survey, we will be able to expand upon
these previous studies in greater spatial detail. We will be able to analyze
how these three parameters affect both the level of the sSFR offsets in the
centers of the paired galaxies and the offsets in the outskirts of the
galaxies. We will also be able to study whether any of the three parameters
influence the gradient of the sSFR enhancement profiles or if the gradient is
preserved between different configurations.

In our previous work using the MaNGA data included in the 14th Public Data
Release (DR14; Abolfathi et al., 2018), we built a sample of close galaxy
pairs where both components of the pair were contained within the field of
view of a single integral field unit (Fu et al., 2018, hereafter Paper I). We
found that approximately 5.7% of the MaNGA galaxies have a companion galaxy
contained within the field-of-view of a single IFU. In this work, we update
this sample and supplement it with a sample of companion galaxies identified
outside the field-of-view of the MaNGA IFUs.

This paper is organized as follows; in § 2 we will discuss the properties of
the MaNGA survey along with the construction of our pair and control samples,
in § 3 we will discuss how we measure star formation rates and how we build
radial profiles of star formation, in § 4 we study the radial profiles as a
function of stellar mass, projected separation, and the mass ratio, in § 5 we
compare our work against previous works, and in § 6 we summarize the findings
of the work. Throughout we adopt the $\Lambda$CDM cosmology with $\Omega_{\rm
m}=0.3$, $\Omega_{\Lambda}=0.7$, and $h=0.7$.

##  2\. Data and Samples

Figure 1.— (Left) Color-magnitude diagram for MaNGA galaxies. (Center) BPT
diagram for the MaNGA galaxies. (Right) The WHAN diagram for the MaNGA
galaxies. The grey circles represent the whole MaNGA sample and the color
scale reflects the local density around each data point in this color-
magnitude plane, as indicated by the color bar on the top. The purple diamonds
represent the paired galaxies which are classified as retired (by the
EW(H$\alpha$) cut), the blue diamonds represent the star forming paired
galaxies (by the BPT diagram), the green diamonds represent the composite star
forming-AGN paired galaxies (by the BPT diagram), and the Red diamonds
represent the paired galaxies containing an AGN (by the BPT diagram).

MaNGA is an IFS survey at the Apache Point Observatory (APO) which uses the
SDSS (Sloan Digital Sky Survey) 2.5-meter telescope along with two dual-
channel BOSS spectrographs (Drory et al., 2015). MaNGA captures spectra
through 17 integral field units (IFUs) with variable numbers of fibers: 19,
37, 61, 91, and 127 fibers covering 12.5″, 17.5″, 22.5″, 27.5″, and 32.5″on
the sky respectively (Law et al., 2015). MaNGA is an optical survey with a
spectral coverage of 3600$-$10,300 Å with a resolution of R $\sim$ 2000 and a
PSF of 2.5″ FWHM (Bundy et al., 2015).

The MaNGA survey targets galaxies from a subset of 41,154 galaxies in the
NASA-Sloan Atlas (NSA v1_0_1; http://www.nsatlas.org) with a redshift range of
0.01 $<z<$ 0.15 and a luminosity range of -17.7 $<$ $\mathcal{M}_{\rm i}$ $<$
-24.0, where $\mathcal{M}_{\rm i}$ is the rest frame $i$-band magnitude within
the survey’s elliptical Petrosian apertures. MaNGA plans to cover 10,000
galaxies with a flat stellar mass distribution at two spatial coverages, 1.5
$R_{\rm eff}$ and 2.5 $R_{\rm eff}$ (where $R_{\rm eff}$ is the radius which
contains 50% of the galaxy’s total light). In this work we use the data from
the 8th MaNGA Product Launch (MPL-8), which covers 6142 unique galaxies
observed by July 3, 2018.

###  2.1. Spectral Fitting

We use spfit to model the MaNGA datacubes. The IDL package is publicly
available111https://github.com/fuhaiastro/spfit and was first used in our
previous study of close galaxy pairs in MaNGA (Paper I). While data products
from the MaNGA Data Analysis Pipeline (DAP; Belfiore et al., 2019) and pipe3d
(Sánchez et al., 2016a, b) are available, spfit allows us to combine spectra
inside a given aperture before fitting the combined spectrum. The feature
alone made it better suited for this project. Additional features of spfit
include: (1) simultaneously fitting emission lines and stellar continuum, (2)
coadding spaxels with either a Voronoi tessellation or arbitrary polygons
while accounting for covariances, (3) modeling asymmetric emission lines,
broad AGN emission lines, AGN continuum, and various dust-extinction laws, and
(4) utilizing multi-threading when processing a large number of datacubes.

Here we provide a brief description of the fitting procedure of spfit. Except
for broad-line AGN, spfit models the observed spectrum as a superposition of
emission lines and simple stellar populations (SSPs). The SSP library of
miuscat (Vazdekis et al., 2012) is matched to the MaNGA spectral resolution
and is convolved with the line-of-sight velocity distribution (LOSVD). Both
the LOSVD and the profile of the emission lines are parameterized as separate
Gauss-Hermite series (van der Marel & Franx, 1993) to the fourth order.

For model optimization, we prefer a fast algorithm like the Levenberg-
Marquardt nonlinear least-squares minimization algorithm implemented in mpfit
(Markwardt, 2009). But for complex spectral models like ours, the success of
the fitting routine relies on a good initial “guess” solution, which can be
provided by the penalized pixel-fitting method (pPXF; Cappellari, 2017). The
pPXF method is robust because it solves the weights of the templates with a
linear algorithm (Lawson & Hanson, 1974) independently from solving the Gauss-
Hermite LOSVD with a nonlinear optimizer (mpfit). The spfit package implements
a three-stage fitting procedure: First, it masks out spectral regions around
emission lines from the input spectrum and use pPXF on the masked spectrum
with SSP-only templates to obtain the initial “best-fit” parameters of the
stellar continuum; Then, it subtracts the best-fit stellar continuum model
from the spectrum and use pPXF to fit the residual emission-line-only spectrum
with Gaussian emission-line templates to obtain the initial “best-fit”
parameters of the emission lines; Finally, it uses mpfit on the full input
spectrum with the two sets of “best-fit” parameters from pPXF to
simultaneously fit all of the parameters describing the emission lines and the
stellar continuum. Saved in the final FITS file are the best-fit parameters
and their uncertainties, including emission-line fluxes, equivalent widths,
and kinematics and luminosity-weighted stellar masses, ages, metallicities,
and kinematics.

###  2.2. Selecting Star Forming Galaxies

We classify galaxies in this survey as star forming galaxies by selecting
galaxies in the blue cloud on the color-magnitude diagram (CMD). We show the
CMD for the MaNGA survey and our pair sample in Figure 1 along with
demarcation lines which separate the blue cloud, red sequence, and green
valley. We established the demarcation lines by collapsing the CMD to a color
histogram for each of the three regions. We then varied the slopes between the
regions until we found the slopes which best fit the data. These demarcation
lines are;

$NUV-r=3.1682-0.16(\mathcal{M}_{\rm i}+18)$ (1)
$NUV-r=4.7866-0.04(\mathcal{M}_{\rm i}+18),$ (2)

Where $NUV-r$ is the color from SDSS’s $k$-corrected absolute magnitude and
$\mathcal{M}_{\rm i}$ is the $i$-band magnitude from the NSA catalog.

We use the BPT diagnostic (Baldwin et al., 1981), shown in the center of
Figure 1, to remove galaxies with possible AGN in their centers. Specifically,
we use the emission line ratios, log([O iii]/H$\beta$) and log([N
ii]/H$\alpha$), extracted from a 1.3 kpc aperture along with the maximum
starburst line of Kewley et al. (2001) as the demarcation between the star-
forming branch and the AGN branch.

Based on the WHAN diagram, shown in the right panel of Figure 1, we apply an
EW(H$\alpha$) $\geq$ 6Åcut on galaxy spectra extracted from a 1.0 $R_{\rm
eff}$ aperture to ensure that all retired galaxies are removed from the sample
(Cid Fernandes et al., 2011).

On top of the star formation cuts, we require that all galaxies are in either
the Primary or Secondary MaNGA subsamples (Wake et al., 2017), and that the
stellar mass range of the galaxy sample is between log($M/M_{\odot}$) $=$
9.0$-$11.5. We use masses calculated from the elliptical Petrosian apertures
in the NSA catalog for our total stellar masses.

We build two different pair samples in this work; the inside-IFU sample which
contains paired galaxies where both galaxies are covered by a single MaNGA IFU
and the outside-IFU sample where a MaNGA target galaxy is coupled with another
galaxy found outside of its MaNGA IFU.

###  2.3. Inside-IFU Sample

Table 1Close Galaxy Pairs and Multiples in MaNGA IFUs Plate-IFU | Index | R.A. (J2000) | Decl. (J2000) | Redshift
---|---|---|---|---
|  | (deg) | (deg) |
7443-12703 | 0 | 229.5255758 | +42.7458538 | 0.04043
$\cdots$ | 1 | 229.5265348 | +42.7440666 | 0.04079
7958-3701 | 0 | 257.5338400 | +33.5989046 | 0.11015
$\cdots$ | 1 | 257.5344200 | +33.5984600 | 0.10920
$\cdots$ | 2 | 257.5326566 | +33.5979470 | 0.11031
7960-3701 | 0 | 257.0857469 | +31.7469109 | 0.10819
$\cdots$ | 1 | 257.0850100 | +31.7470300 | 0.10800
7960-3702 | 0 | 258.2893316 | +31.5820375 | 0.02961
$\cdots$ | 1 | 258.2913540 | +31.5812244 | 0.02943
7962-3702 | 0 | 259.0637432 | +28.0140065 | 0.10725
$\cdots$ | 1 | 259.0639447 | +28.0130439 | 0.10753

To identify potential paired galaxies covered by individual IFUs, we start by
overlaying SDSS photometric objects over each MaNGA fields of view. We
manually inspect each MaNGA field, removing photometric objects which are
over-deblended galaxy fragments and, very rarely, adding any objects missed in
the SDSS photometric catalog. At this stage the object catalog includes
foreground stars and foreground/background galaxies along with the potential
paired galaxies.

To select paired galaxies out of our object catalog, we inspect the spectra of
each object. The spectra of the identified objects is extracted through a 1″
circular aperture and fitted assuming the MaNGA target’s redshift and then
manually sorted into the following categories: “good” galaxy spectra, broad-
line AGN, foreground star, foreground/background galaxies, or poor S/N
objects. The “good” galaxy spectra are the objects whose spectra are well
modeled by spfit at the target galaxy’s redshift, whether it is the target
galaxy itself or a nearby companion galaxy. This means that the companion
galaxy can be within approximately $\pm$2000 km s-1 of the MaNGA target. We
found 6573 “good” objects, 57 broad-line AGN, 836 foreground stars, 319
foreground/background galaxies, and 1546 objects with poor S/N.

Broad-line AGN comprise $\sim$0.9% of MaNGA’s galaxy sample where Lacerda et
al. (2020) found a fraction of $\sim$2.8% from the CALIFA survey and Sánchez
et al. (2018) found a fraction of $\sim$1.33% from the MaNGA’s MPL-5 sample
(which observed $\sim$2700 galaxies).

Among the 6142 MaNGA IFUs considered here, 404 cover close galaxy pairs and
multiples. The sample includes 327 pairs, 67 triplets, 7 quadruplets, and 1
quintuplet. Table 1 lists the coordinates and redshifts of these galaxy
components in pairs/multiples. When a MaNGA target has multiple companions
galaxies, we chose the closest companion to define the pair’s mass ratio and
projected separation.

For this study, we further restrict the sample by setting a relative velocity
cut of $\Delta v$ $<$ 500 km s-1. Given the redshift range of the MaNGA sample
and the size of MaNGA’s IFUs, the maximum projected separation for a companion
galaxy in the IFU is $\sim$40 kpc. Again, the galaxy sample is also restricted
to galaxies with a stellar mass range of log($M/M_{\odot}$) $=$ 9.0$-$11.5 and
galaxies in the Primary or Secondary MaNGA subsamples. We also require that
the galaxies are classified as star forming as described in § 2. These
requirements reduce our sample down to 54 star forming MaNGA targets with
inside-IFU companions. While we use the identified companions to select galaxy
pairs, we only build radial profiles for the MaNGA target galaxies. We do this
because the identified companions are not included in the NSA catalog which we
use to build the radial profiles for the galaxies.

###  2.4. Outside-IFU Sample

We supplement the inside-IFU sample with a set of pairs identified outside of
the field of view of the MaNGA IFU. We select these outside-IFU pairs from the
NSA catalog. We search for these external pairs by selecting objects with a
projected separation from the MaNGA targets of $r_{\rm p}$ $<$ 50 kpc using
the MaNGA target’s redshift. We further use a relative velocity cut of $\Delta
v$ $<$ 500 km s-1 to remove projected galaxies from the selection.

From the NSA catalog’s 641,409 galaxies, we find 492 galaxies which are paired
to MaNGA targets. After restricting the sample to SFGs, we have another 115
MaNGA targets with paired galaxies outside of the IFU. MaNGA targets which
have both an inside-IFU and an outside-IFU pair are left to the inside-IFU
sample.

###  2.5. Control Sample

To show how the population of galaxy pairs differs from isolated galaxies, we
will compare our pair sample to a sample of control galaxies in the MaNGA
survey. We build this control sample from the MaNGA target galaxies which have
no spectroscopic companions within $r_{\rm p}$ $<$ 50 kpc and $\Delta v$ $<$
500 km s-1 either inside or outside of the IFU. This gives us a control sample
of 1830 star forming control galaxies.

It has been shown that the SFR in galaxies is dependent on both the stellar
mass and the redshift of the galaxies (e.g., Noeske et al., 2007). We will
compare our interacting galaxies with control galaxies of a similar stellar
mass, redshift, and radial size, to account for these other dependencies. To
do this, we will use two different methods of pair - control comparison.

In the first method, we simply control for the stellar mass between the pairs
and controls. We split both the pair and control samples into five evenly
spaced stellar mass bins over the range, log($M/M_{\odot}$) $=$ 9.0$-$11.5.
The pairs are then compared to their respective controls within each stellar
mass bins. While the redshift is not constrained in this method, we will show
in § 4.1.1 that this method is sufficient to reveal the merger induced star
formation.

In the second method, we select a “tailored” control sample for each paired
galaxy from the full sample of isolated galaxies. We select a subsample of 20
control galaxies for each paired galaxy. We first select all of the control
galaxies which are within 0.1 dex in stellar mass, 0.025 in redshift, 20% in
effective radii, and within the same MaNGA subsample (e.g. Primary or
Secondary) as the paired galaxy. With these requirements, most paired galaxies
will find between 20$-$60 control galaxies. Since we want each paired galaxy
to be treated in a similar manner, we randomly down-select the total number of
acquired control galaxies to 20. A given control galaxy may be selected for
multiple pairs by the pipeline; most of the control galaxies are used at least
once and the average number of times a given control is reused is between
2$-$4 times. In the cases where a paired galaxy does not initially acquire 20
control galaxies we iteratively expand the stellar mass limit by 0.1 dex, the
redshift by 0.025, and the $R_{\rm eff}$ by 5% until at least 20 control
galaxies are found. 39 pairs required 1 extra iteration, 15 pairs required 2
extra iterations, 5 pairs required 3 extra iterations, and 2 pairs required 4
extra iterations.

##  3\. Analysis Methods

###  3.1. Specific Star Formation Rate

We calculate the star formation rates in the pair and control galaxies with
the emission lines extracted with our spectra fitting code, spfit (described
in Section 2.1). We correct the emission lines for reddening using the
extinction curve from Cardelli et al. (1989) with updated coefficients from
O’Donnell (1994). The extinction is parameterized as $R_{V}$ $\equiv$
$A_{V}/E(B-V)$ $=$ 3.1, where we estimate the value of the $V$-band
extinction, $A_{V}$, by comparing the H$\alpha$/H$\beta$ ratio to the expected
value of 2.85 for Case-B recombination.

We measure the SFR from the extinction corrected H$\alpha$ luminosity,
$L_{{\rm H}\alpha}$. We use the SFR formula, Equation 3, from Murphy et al.
(2011) which uses a Kroupa IMF, Solar metallicity, a constant SFR at an age of
100 Myr, and Case-B recombination:

$\frac{\rm{SFR}}{M_{\odot}\,\rm{yr^{-1}}}=\frac{L_{\rm H\alpha}}{1.86\times
10^{41}\,\rm{erg\,s}^{-1}}.$ (3)

Since the stellar mass of a galaxy is not uniformly distributed within the
galaxy, we normalize the SFR by the stellar mass in the same spaxel, $M$,
giving us the specific star formation rate (sSFR):

${\rm sSFR}=\frac{\rm SFR}{M}.$ (4)

The local stellar masses used here is derived from spfit’s best-fit stellar
continuum. Utilizing sSFR, instead of SFR, allows us to compare regions of
high mass surface density to regions of low mass surface density.

We check our measurement of the specific star formation rate with the
equivalent width of the H$\alpha$ line, EW(H$\alpha$), since it is a known
proxy for the sSFR. This is useful as the sSFR is dependent on spfit’s
measurement of the stellar mass while EW(H$\alpha$) is an observable. As we
will show in Section 4, the radial profiles of EW(H$\alpha$) is consistent
with radial profiles of the sSFR.

The signal to noise ratio of the data will decrease with wide galactocentric
radii. MaNGA is designed to cover 1.5 $R_{\rm eff}$ for galaxies in the
Primary sample and 2.5 $R_{\rm eff}$ in the secondary sample. These are not
hard limits, data will exist beyond these radii, especially along the semi-
minor axis of galaxy; however, the data beyond these limits may be unreliable
due to low signal to noise. To control the quality of the used data, we only
use spaxels with S/N $\geq$ 3 for the H$\alpha$ line. We also restrict the
used spaxels to those with EW(H$\alpha$) $\geq$ 6 Å to remove retired regions
from the survey (Cid Fernandes et al., 2011), which effectively sets -10.8
yr-1 as the lower limit to the sSFR in our galaxies.

###  3.2. Radial Profiles

In order to spatially characterize the star formation in the paired galaxies
we build radial profiles of sSFR. First, the geometry of the galaxies needs to
be defined. Specifically we will need the position angle, the inclination
angle, and the effective radius of each of the MaNGA targets. We use the
$r$-band elliptical Petrosian apertures from the NSA catalog and the $r$-band
Sérsic apertures from Simard et al. (2011) to define the geometries of the
galaxies.

The NSA catalog has complete coverage over the MaNGA sample (since MaNGA
selects its targets from this catalog); however, it tends to fail to properly
fit paired galaxies with close on-sky separations. We found that the apertures
from Simard et al. (2011) work better for these close paired galaxies;
however, the catalog does not completely cover the MaNGA sample. We use the
NSA catalog for the outside-IFU pair sample because they are well separated on
the sky. The Simard et al. (2011) catalog is used for the inside-IFU sample.
If the paired galaxy is not covered by Simard et al. (2011), we use the
ellipse from the NSA catalog.

We fit the geometry with apertures from both catalogs when available. When
using the first method of pair-control comparison, where pairs and controls
are grouped into stellar mass bins, we fit the control galaxies with the NSA
apertures. When making the comparison with the second method, paired galaxies
fitted with the NSA apertures are compared against controls fitted with the
NSA apertures and paired galaxies fitted with the Simard et al. (2011)
apertures are compared against controls fitted with the Simard et al. (2011)
apertures. Further, when defining a galaxy’s geometry with the Simard et al.
(2011) apertures we also use the masses given in the catalog for the total
stellar mass of the galaxy. Note that although we carefully treat the two
catalogs separately whenever possible, we find excellent agreement in the
geometry parameters of control galaxies in both catalogs.

We calculate the inclination angle, i, of the galaxies using the major-to-
minor axis ratios from the elliptical apertures;

${\rm cos^{2}}(i)=\frac{(b/a)^{2}-q^{2}}{1-q^{2}},$ (5)

Where $b/a$ is the major-to-minor axis ratio and $q$ is the intrinsic
oblateness. We use the empirically determined oblateness of $q=0.13$, from
Giovanelli et al. (1994).

The inclination angle, along with the galaxy’s position angle, is used to
deproject the geometries of the galaxies. We use the 50% half light radius
(i.e, the effective radius, $R_{\rm eff}$) to scale the sizes of the galaxies.
Doing this will allow us to compare galaxies of different sizes against each
other.

Once the geometries of the galaxies are set, we can build azimuthally averaged
radial profiles. The spaxels are binned into radius increments of 0.2 $R_{\rm
eff}$ from 0.0$-$2.6 $R_{\rm eff}$. Within each radius bin we take the median
of the specific star formation rate. We build an azimuthally averaged radial
profile for each MaNGA star forming galaxy and later stack and differentiate
these profiles in the subsequent analysis.

The MaNGA sample does not have a uniform spatial coverage, 63% of the sample
is designed to cover 1.5 $R_{\rm eff}$ (the Primary+ subsample) and 37% of the
sample is designed to cover 2.5 $R_{\rm eff}$ (the Secondary subsample). This
means that there will be fewer selected spaxels beyond 1.5 $R_{\rm eff}$ and
the S/N of the selected spaxels will be lower than those within 1.5 $R_{\rm
eff}$. We decide to still extend our radial profiles out to 2.5 $R_{\rm eff}$
to make full use of the MaNGA data; however, we emphasize that the difference
in the sampling of the data within 1.5 $R_{\rm eff}$ and the data beyond 1.5
$R_{\rm eff}$ may create artificial slopes in the data.

##  4\. Results

###  4.1. Star Formation Enhancement

Figure 2.— The log(sSFR) as a function of galactocentric radius for control
galaxies (Left) and galaxy pairs (Middle). The difference between the profiles
of the paired galaxies and the control galaxies are shown in the Right panel.
The dashed black profile represents the mean of the difference profiles. The
colors of the profiles represent the mass range of the selected galaxies which
is given in the legend along with the number of galaxies in that mass bin in
parantheses. The highlighted region around the profiles represent the standard
error of the mean of the data at the given radius interval. The vertical dash-
dot line marks 1.5 $R_{\rm eff}$, beyond which the radial sampling is expected
to fall. Figure 3.— Same as Figure 2 but for EW(H$\alpha$).

With the individual log(sSFR) profiles built for each MaNGA galaxy, we now use
two different methods to compare the profiles of paired galaxies against the
profiles of control galaxies. In the first method, in § 4.1.1, paired galaxies
are compared to control galaxies within evenly spaced stellar mass-bins. In
the second method, in § 4.1.2, paired galaxies are compared to a subset of 20
control galaxies which are matched in stellar mass and redshift.

####  4.1.1 Mass-Binned Difference Profiles

In the first method, paired and control galaxies are grouped into five evenly
spaced stellar mass bins between log($M/M_{\odot}$) $=$ 9.0$-$11.5. Within
each stellar mass bin, we create a median profile of log(sSFR) as a function
of $R_{\rm eff}$-scaled galactocentric distance for both paired and control
galaxies. The control profiles are constructed using all available control
galaxies within each mass bin. The error associated with the “stacked” profile
is the standard error of mean of the data at each radius bin. Here we define
the standard error of the mean, $\sigma_{\overline{x}}$, as,

$\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}},$ (6)

where $\sigma$ is the standard deviation and $n$ is the sample size.

We show these stacked profiles for control galaxies in the left hand panel of
Figure 2 and the stacked profiles for paired galaxies in the middle panel of
Figure 2. Star formation in the control galaxies are quenched in their centers
with respect to their disks and the difference between the sSFR in their
centers and their disks increases with stellar mass, consistent with
previously published results using the MaNGA survey (Belfiore et al., 2018).
In contrast, the paired galaxies show flatter sSFR profiles where the level of
the sSFR remains roughly consistent across their disks except for paired
galaxies with stellar masses above log($M/M_{\odot}$) $=$ 10.5, which still
show some central quenching.

We then take the difference between the stacked profiles of the paired
galaxies and the control galaxies, pair - control, in log space (this means
that the difference profiles really represent a ratio between the pairs and
controls in linear space). This gives us the difference profile,
$\Delta$log(sSFR), which shows us where the sSFR is enhanced or suppressed
(shown in the right hand panel of Figure 2). Across all stellar mass bins, the
sSFR of paired galaxies are centrally enhanced by $\sim$0.3$\pm$0.1 dex, which
gradually falls to zero around $\sim$1.5 $R_{\rm eff}$. In the outskirts of
the pairs beyond 1.5 $R_{\rm eff}$, the pairs feature lightly suppressed sSFR
of 0.0$-$0.1 dex. All of the mass ranges except for the highest mass range,
log($M/M_{\odot}$) $=$ 11.0$-$11.5, trend closely to the median profile. For
the most massive galaxies, log($M/M_{\odot}$) $=$ 11.0$-$11.5, the enhancement
to the sSFR within 0.5 $R_{\rm eff}$ is significantly higher than the median
profile (reaching 0.5$-$0.6 dex). As will be discussed in § 4.1.2, we believe
this elevated enhancement in the highest mass bin is driven by more compact
mergers instead of stellar mass.

In summary, Figure 2 shows that the merger process is capable of rejuvenating
star formation in the centers of these galaxies, resulting in almost flat sSFR
radial profiles. In addition, the sSFR enhancement is mass independent – star
formation proceeds at $\sim$2$\times$ (0.3 dex) greater rates in galaxies with
close companions than in more isolated galaxies, across a wide mass range
between 9.0 $\leq$ log($M/M_{\odot}$) $\leq$ 11.5.

We repeat this analysis for the EW(H$\alpha$) in Figure 3. We find that the
EW(H$\alpha$) profiles are in close agreement with the sSFR profiles, which
shows that we can be confident of spfit’s measurement of the sSFR. We do see
that the pair-control offsets are lightly suppressed using the EW(H$\alpha$)
as the $\Delta$log(EW(H$\alpha$)) is only enhanced by 0.25 dex where the
$\Delta$log(sSFR) was enhanced by 0.30 dex.

This method of stacking sSFR profiles by a single parameter (stellar mass) has
the advantage of simplicity and large statistical samples. It has revealed the
first order result of mass-independent, centrally enhanced star formation in
close galaxy pairs. To proceed with exploring the dependency of $\Delta$sSFR
on merger parameters such as separation and mass ratio, we will utilize a more
sophisticated method of selecting control samples for individual paired
galaxies based on stellar mass and redshift in the following subsections.

Figure 4.— The Left panel shows the $\Delta$log(sSFR) profiles where the
difference profiles are constructed from the difference between the paired
galaxy profiles and a set of 20 control galaxies. The profiles are split into
five different stellar mass bins and the highlighted region about the profiles
represent the standard error of mean of the profile. The black dashed line
represents the mean profile between the four difference mass ranges. The
number of paired galaxies in each mass range is given in the legend in
parentheses. The Right panel shows the nuclear $\Delta$log(sSFR) extracted
from a 0.5$R_{\rm eff}$ aperture. The black squares are the mean values within
a stellar mass bin (where the size of the bins are shown the the horizontal
error bars). The vertical error bars on the black squares represent the
standard deviation within the bin. The horizontal, dashed black line
represents the median central enhancement of the pair sample. Galaxies in the
outside-IFU (Blue) and inside-IFU (Red) samples are separately depicted. The
vertical dash-dot line marks 1.5 $R_{\rm eff}$, beyond which the radial
sampling is expected to fall.  Figure 5.— The projected separation
distribution of the whole sample (blue) against the projected separation
distribution for the highest mass galaxies, log($M/M_{\odot}$) $=$ 11.0$-$11.5
(Red).

####  4.1.2 Tailored-Controls Difference Profiles

Figure 6.— Same as Figure 4 except the difference profiles are split by the
mass ratio of the pair. The top row is the absolute value of the mass ratio
and the bottom row is the mass ratio without taking the absolute value. Taking
the mass ratio without the absolute value allows us to separately study the
more massive companions of pairs from the less massive companions from pairs.
The inside-IFU sample is left out of this analysis because we do not yet have
reliable measurements of their total stellar mass ratios.

In the second method, we match each paired galaxy to a set of 20 control
galaxies of similar stellar masses and redshifts, as described in § 2.5. We
then take the median of the azimuthally averaged profiles of the tailored
control sample. Finally, we obtain the $\Delta\log$sSFR profile for each of
the 169 paired galaxies by calculating the difference between its sSFR profile
and the median profile of its control sample.

Before delving into merger parameters, we decided to stack the profiles by
stellar mass to see how this method compares to the previous mass-binning
method. We split the individual difference profiles into five evenly spaced
stellar mass bins between log($M/M_{\odot}$) $=$ 9.0$-$11.5 and stack the
difference profiles within each mass bin. This gives us five difference
profiles covering five different stellar mass ranges shown in the left hand
panel of Figure 4. The errors of the stacked profiles are the standard error
of the mean of the difference profiles within each bin.

To focus on the sSFR offsets in the centers of the galaxies, we also calculate
the sSFR difference between each paired galaxy and its control sample within
the central 0.5 $R_{\rm eff}$. The central sSFR is calculated for each galaxy
by taking spaxels within 0.5 $R_{\rm eff}$ and whose H$\alpha$ flux has S/N
$\geq$ 3 and then taking the median value of sSFR of the selected spaxels.
Once this is done we calculate the $\Delta$log(sSFR) using the same method as
the $\Delta$log(sSFR) radial profiles are made. The central sSFR of a paired
galaxy is compared against the sSFR of a set of 20 similar control galaxies,
the same set of controls which were used for the $\Delta$log(sSFR) profiles,
by taking the difference between the central sSFR of the paired galaxy and the
median sSFR of the 20 selected control galaxies. We depict the central
$\Delta$log(sSFR) as a function of stellar mass in the right hand panel of
Figure 4.

The difference profiles are shown to be centrally enhanced by
$\sim$0.20$-$0.25 $\pm$ 0.1 dex. Similar to what was seen in § 4.1.1, the
level of the enhancement is independent of galaxy mass with the exception of
the highest mass bin, log($M/M_{\odot}$) $=$ 11.0$-$11.5, which is 0.4 dex
higher than the sample average.

The central enhancement to the sSFR falls to zero around 1.2 $R_{\rm eff}$ and
the outskirts of the galaxies are lightly suppressed by 0.0$-$0.1 dex. Within
individual mass ranges, there are some mass ranges which feature large
enhancements to the sSFR at large radii while other mass ranges show a strong
suppression to the sSFR. There appears to be no dependence on the stellar mass
of the pair but, as we will show in the next section, § 4.2, these offsets at
large radii may be dependent on the mass ratio between the galaxy pairs.

To understand why the profiles of high mass galaxies behave differently from
the rest of the sample in Figures 2, 3, and 4, we compare the distribution of
the projected separation for the whole sample and for galaxies in the highest
mass bin in Figure 5. The whole sample has a v-shaped separation distribution.
This is the result of the combination of the two different samples, the
inside-IFU and outside-IFU samples. The outside-IFU sample should find more
pairs at wide projected separations due to the larger volume to find
companions in. The separation distribution of the inside-IFU sample is limited
by MaNGA’s IFU sizes and the sample’s redshift distribution; the maximum
possible projected separation for a MaNGA target with $z$ $=$ 0.15 and a 127
spaxel IFU is about 40 kpc.

The highest mass galaxies in the sample are at closer projected separations in
comparison to the rest of the sample with 70% of the highest mass galaxies
being within 20 kpc. The cause of this may be due to clustering effects where
high mass galaxies tend to be at the centers of galaxy clusters (Cooray &
Sheth, 2002; Zehavi et al., 2002). As we will show in § 4.3, the central sSFR
enhancement is strongest at small projected separation which means that higher
sSFR in the centers of the massive galaxies may be driven by their close
projected separations.

The results we obtain from the tailored-control method is largely consistent
with the mass-binning method. Between the two methods we see that the
$\Delta$log(sSFR) profile is independent of the total stellar mass of the
galaxies. In the next two sections, we will use the tailored-control method to
study how the difference profiles behave as a function of the mass ratio (§
4.2) and projected separation (§ 4.3).

###  4.2. Dependency on Mass Ratio

Figure 7.— Same as Figure 4 except the difference profiles are split by
projected separation.

While the centrally enhanced star formation in close galaxy pairs seems mostly
mass-independent, the mass ratio of the galaxy pair, like the projected
separation, may be an important parameter that controls the level of
enhancement (Ellison et al., 2008).

The mass ratio here is defined as,

$\Delta{\rm log}(M)={\rm log}(M_{\rm target})-{\rm log}(M_{\rm comp}),$ (7)

where $M_{\rm target}$ is the stellar mass of the MaNGA target galaxy and
$M_{\rm comp}$ is the stellar mass of its identified companion galaxy. In the
inside-IFU sample, we have stellar masses for the MaNGA target galaxy but not
the other identified pairs. Because of this, we leave the inside-IFU
companions out of this analysis.

In the top left of Figure 6, we split the $\Delta$log(sSFR) profiles into four
mass ratio bins from $|\Delta$log(M)$|$ $=$ 0.0$-$1.0. Here,
$|\Delta$log(M)$|$ $\leq$ 0.5, represents equal mass major mergers while
$|\Delta$log(M)$|$ $\geq$ 0.5 represents minor mergers. We see that there is a
clear preference for pairs in major merger to have higher sSFR enhancements in
their centers, $\sim$0.3$-$0.4 dex, while minor mergers show a weaker sSFR
enhancement of $\sim$0.0$-$0.2 dex. The effect can be seen more clearly with
the data extracted from the central 0.5 $R_{\rm eff}$ in the top right panel.
Here the $\Delta$log(sSFR) falls linearly with wider mass ratios, reaching
zero enhancement to the sSFR at $|\Delta$log(M)$|$ $=$ 1.5$-$1.75.

We not only use the mass ratio to study how a major merger behaves differently
from a minor merger but also to study how the more massive galaxy of a pair
behaves differently from the less massive galaxy of the pair. We expect that
either component of a similar mass pair will behave in a similar fashion;
however, in a minor merger the large central galaxy may not respond to the
merger event in the same way as its less massive companion. The two different
scenarios can be differentiated with our definition of the mass ratio in
equation 7; when the MaNGA target is the more massive companion of the pair,
its mass ratio is positive and when MaNGA target is the less massive companion
of pair the mass ratio is negative. To distinguish between these scenarios, we
refer to the more massive galaxy of a pair as the primary companion and the
less massive galaxy of a pair as the secondary companion.

In bottom left panel of Figure 6, we split the profiles by mass ratio in four
bins. The primary companions are the pairs with $\Delta$log(M) $\geq$ 0.0 and
the secondary companions are the pairs with $\Delta$log(M) $\leq$ 0.0. When
splitting the mass ratio like this we see that major mergers still higher
levels of sSFR enhancement in comparison to minor mergers; however, we also
see that the less massive companion of the pair sees a higher
$\Delta$log(sSFR) in comparison to the more massive companion of a pair. In
major mergers, the sSFR enhancement is $\sim$0.1 dex higher in secondary
companions in comparison to primary companions. In minor mergers the sSFR
enhancement is $\sim$0.2 dex higher in secondary companions in comparison to
primary companions.

In bottom right panel of Figure 6 we see that the sSFR enhancement is
strongest in galaxies close to a 1:1 mass ratio ($\Delta$log($M$) $=$ 0.0).
These galaxies feature a central enhancement of $\sim$0.4 dex which is 0.2 dex
higher than the average central enhancement of the whole sample. This
enhancement falls with wider mass ratios with a different slope for primary
and secondary companions. At $\Delta$log($M$) $=$ -1.0, the sSFR is enhanced
by 0.2 dex while at $\Delta$log($M$) $=$ 1.0 the sSFR enhancement is zero.

We also see that the $\Delta$log(sSFR) in the outskirts ($R$ $>$ 1.5 $R_{\rm
eff}$) of the pairs have a dependence on the mass ratio in the bottom right of
Figure 6. Primary companions show a positive enhancement of 0.0$-$0.4 dex to
the sSFR in their outskirts, while secondary companions feature a suppression
to the sSFR in their outskirts of about 0.0$-$0.3 dex. Again we note that only
37% of the MaNGA sample is designed to extend beyond 1.5 $R_{\rm eff}$;
however, a similar result has been observed in the hydrodynamical simulations
of Moreno et al. (2015) and Moreno et al. (2020).

From the mass ratio, we see two different effects. First, we see that the
central enhancement to the sSFR is strongest for pairs with 1:1 mass ratios.
Second, we see that secondary companions show steeper enhancement profiles
with higher levels of sSFR enhancement in their centers and stronger levels of
sSFR suppression in their disks with respect to primary companions. Finally,
we see that primary companions feature sSFR enhancement at wide radii while
secondary companions feature sSFR suppression at wide radii.

###  4.3. Dependency on Projected Separation

A number of previous studies have shown that the sSFR enhancement increases as
projected separation decreases (e.g., Li et al., 2008; Ellison et al., 2008;
Scudder et al., 2012; Patton et al., 2013), in agreement with simulations
(Scudder et al., 2012).

Figure 7 shows the profile and the central level of sSFR enhancement as a
function of the projected separation ($r_{\rm p}$) from our MaNGA data. The
$\Delta$log(sSFR) profiles show only a weak dependency on the projected
separation. The pairs below a separation of 25 kpc have $\Delta$log(sSFR)
profiles which lie $\sim$0.1 dex above the sample median while the profiles of
the pairs beyond 25 kpc are $\sim$ 0.1 dex below the sample median.

A dependence on the projected separation can be seen more clearly when looking
at the data extracted from the inner 0.5 $R_{\rm eff}$. The level of the
enhancement gradually increases with closer separation from 50 kpc to 10 kpc.
While $\Delta$log(sSFR) falls at higher separations, there is still a
substantial level of enhancement between 40 and 50 kpc, $\sim$0.15 dex. Within
10 kpc, the $\Delta$log(sSFR) enhancement jumps to $\sim$0.3 dex. Our data
shows that the sSFR enhancement persists out to at least $r_{\rm p}=50$ kpc,
which is the limit of our pair selection.

##  5\. Discussion

###  5.1. Radial Profiles of Enhancement

Figure 8.— The mean radial profile of $\Delta$log(sSFR) (Top) and
$\Delta$log(SFR) (Bottom) between pairs and controls of this work with the
tailored control method (Black) compared against those of Pan et al. (2019)
(Red), a pair sample, and Thorp et al. (2019) (Blue), a post-merger sample.

In Figure 8 we compare the $\Delta$log(sSFR) profile and $\Delta$log(SFR) as a
function of galactocentric radius between our work and previous works using
the MaNGA data. Thorp et al. (2019) studies a sample of 36 post-mergers from
the MaNGA sample. The centers of the post-merger galaxies feature a greater
level of sSFR enhancement in their centers compared to our galaxies pairs of
$\Delta$log(SFR) $=$ 0.40$-$0.45, roughly 0.2 dex higher than our paired
galaxies. Between 0.4$-$1.0$R_{\rm eff}$ the post-merger galaxies and our
pairs are in closer agreement, being 0.05$-$0.1 dex higher than our paired
galaxies. Beyond 1.0 $R_{\rm eff}$ the post-merger galaxies have a higher
$\Delta$log(SFR) by about 0.1$-$0.2 dex. The heightened level of sSFR
enhancement in the centers of post-merger galaxies in comparison to merging
galaxies seems consistent with the idea that a second and greater burst of
star formation occurs as the two merging galaxies coalesce into a single
galaxy.

Pan et al. (2019) studies a set of 205 paired galaxies in the MaNGA sample,
focusing on the sSFR enhancement as a function of the merger interaction
stage. The $\Delta$log(sSFR) profiles of the galaxies pairs in Pan et al.
(2019) are $\sim$0.10$-$0.15 dex above the profiles in our sample. Our paired
galaxies show a slight sSFR suppression in their disks past 1.0 $R_{\rm eff}$
while the galaxy pairs in Pan et al. (2019) show an enhancement of $\sim$0.15
dex to the sSFR in their disks.

The reason for the discrepancies between our samples may be that Pan et al.
(2019) includes a set of 96 pairs which are too close to be separately de-
blended by SDSS and instead were visually identified by their morphology. 82
of these pairs are post-merger galaxies. Pan et al. (2019) showed that pairs
with disturbed morphology have higher $\Delta$log(SFR) when compared to pairs
without morphological distortions. Further, Thorp et al. (2019) showed that
post-merger galaxies have $\Delta$log(SFR) profiles which are elevated over
our sample’s profiles. From this, infer that the lower $\Delta$log(sSFR) seen
in our sample is due to our sample’s lack of post-merger galaxies.

###  5.2. Central Enhancement vs. Merger Parameters

While in this work we find that $\Delta$log(sSFR) has essentially no
dependence on the stellar mass of the galaxy, Li et al. (2008) found that
lower mass galaxies experience greater levels of enhancement than higher mass
galaxies. Galaxies in the mass range log($M/M_{\odot}$) $\geq$ 9.72 were shown
to experience an enhancement $\sim$0.4 dex higher than galaxies in the mass
range log($M/M_{\odot}$) $\geq$ 10.6.

The source of the difference is unclear; between our works we utilize
different methods for determining the sSFR enhancement in galaxy pairs. Li et
al. (2008) defines their enhancement function as the average sSFR of the
paired galaxies at a given separation, weighted by the number of companions,
subtracted by the average sSFR of the whole sample. While we do not find the
same dependency between the sSFR enhancement and stellar mass, the sSFR
enhancement as a function of projected separation between our studies is in
good agreement (see Figure 9).

The dependency of the SFR enhancement on the mass ratio was studied in Ellison
et al. (2008). They found that pairs with mass ratios of 2:1 have higher SFR
enhancements of $\sim$0.1 dex over pairs with wider 10:1 mass ratios. We find
that pairs with mass ratios of $\Delta$log($M$) $=$ 0.25 (1.8:1) are 0.2 dex
over pairs with mass ratios of $\Delta$log($M$) $=$ 1.0 (10:1). Ellison et al.
(2008) also saw tentative evidence for SFR enhancement in the secondary
companions of minor pairs. We not only confirm that secondary companions of
minor pairs feature SFR enhancement, but also that the enhancement is higher
than the primary component of pairs at the same mass ratios.

The observations are also consistent with simulations. Moreno et al. (2015)
used Gadget-3, a smoothed particle hydrodynamics code, to study the spatial
extent of the star formation enhancement. The merger simulations showed that
the star formation enhancement was largely concentrated in the centers (R $<$
1 kpc) of the paired galaxies and that the off-nuclear regions (1 $<$ R $<$ 10
kpc) showed a suppression to the star formation. Moreno et al. (2015) also
found that lower mass secondary galaxies (in mergers with stellar mass ratios
of 2.5:1) have higher levels of sSFR enhancement in their centers and have
stronger levels of sSFR suppression in their disks. This is in good agreement
with our work, we found that secondary companions show moderately higher
levels of sSFR enhancement in their centers in comparison to primary
companions at the same mass ratio. Further, the outskirts of our primary
companions feature positive enhancement to their sSFR while the secondary
companions show a strong suppression to the sSFR in their outskirts.

Figure 9.— (Top) $\Delta$log(SFR) extracted from the inner 0.5 $R_{\rm
eff}$over projected separation from this study (Black), Ellison et al. (2008)
(Red), Scudder et al. (2012) (Blue), Patton et al. (2013) (Green), and
Bustamante et al. (2020) (Purple). (Bottom) $\Delta$log(sSFR) extracted from
the inner 0.5 $R_{\rm eff}$over projected separation from this study (Black),
Li et al. (2008) (Red), and Patton et al. (2020) (Blue).

Figure 9 compares the enhancement in both SFR and sSFR as a function of
projected separation. For our data points, we use the mean $\Delta\log{\rm
SFR}$ and $\Delta\log{\rm sSFR}$ measured within a deprojected radius of 0.5
$R_{\rm eff}$ (i.e., the black data points in the right side panel of Figure
7). The literature data is measured from single 1-1.5″-radius SDSS fibers
(Ellison et al., 2008; Scudder et al., 2012; Patton et al., 2013; Bustamante
et al., 2020). We find that our central SFR enhancements for closely separated
pairs are higher than many of the previous studies, our sSFR enhancement is
$\sim$0.1 dex higher than Scudder et al. (2012) and $\sim$0.2 dex higher than
Ellison et al. (2008) and Bustamante et al. (2020). The central enhancement to
the sSFR for closely separated pairs in our sample is $\sim$0.05 dex lower
than Patton et al. (2013). The sSFR enhancement function from Li et al. (2008)
is 0.05$-$0.10 dex above our sample at close separations.

The sSFR as a function of separation was studied with the cosmological
hydrodynamical simulations of IllustrisTNG (Patton et al., 2020). In Figure 9
we show the $\Delta$log(sSFR) enhancements across 2D separation (projected
separation) from the TNG300-1 simulation. Patton et al. (2020) found a sSFR
enhancement which is 1.8$\times$ that of the isolated controls within a
separation of 15 kpc and is statistically significant out to a 2D separation
of $\sim$250 kpc. This enhancement is $\sim$0.05 dex lower than ours; however,
our sSFR enhancement shown in Figure 9 was extracted from a 0.5 $R_{\rm eff}$
aperture while Patton et al. (2020) extracted the sSFR from a 50% half-mass
radius. This means that our extraction radius is effectively twice a small and
is more restricted to the central burst of star formation.

Our sample only covers projected separations within 50 kpc, while previous
surveys cover out to 100$-$200 kpc. While our sample covers a smaller
separation range, the $\Delta$log(SFR) of our sample at 50 kpc is roughly the
same level as Ellison et al. (2008) and Bustamante et al. (2020) at the same
projected separation. From this we see that our sSFR enhancement as a function
of projected separation is consistent with with what has been found in
previous works.

###  5.3. Comparison with Simulations

Our results are consistent with the idea that galaxy merger events trigger a
burst of star formation in the centers of the paired galaxies. In this model,
when two galaxy pairs undergo their first pericenter, the tidal torques
exerted on the disks of interacting galaxies form barred structures. These
barred structures funnel gases into the centers of the galaxies which triggers
a burst of new star formation. Eventually, as the pairs separate from each
other after the first pericenter, the burst of star formation begins to
subside. This is shown in our work and many previous works in Figure 9 where
the sSFR enhancement is greatest for close separations and falls with wider
separations.

We also found that the $\Delta$log(sSFR) is independent of the stellar mass.
This means that the merger event will produce the same amount of new stellar
mass for low mass galaxies as it produces for high mass galaxies. This also
means that the low mass galaxies will experience a greater change in total
stellar mass before and after the merger event so the merger event will have a
greater impact on the mass evolution of low mass galaxies as opposed to high
mass galaxies.

We find that the strength of the central burst of merger induced star
formation is dependent on the relative masses between the two galaxies. Equal
mass galaxies see the strongest bursts of star formation while wide mass
ratios see weaker bursts of star formation. We further find that the strength
of the central burst of star formation differs between the primary and
secondary companion of a pair where the less massive secondary companion
features a higher level of sSFR enhancement in comparison to its higher mass
primary companion.

Moreno et al. (2020) uses galaxy merger simulations to study the origin of the
enhanced star formation in galaxy pairs, whether its an increase in the star
formation efficiency, defined as the ratio between the SFR and the mass of
cold-dense gas, or its an increase in the availability of cold dense gas. They
find that the star formation in secondary galaxies is evenly split between
being efficiency driven or fuel driven systems while primary galaxies are more
likely to be fuel driven systems (71%). Moreno et al. (2020) also finds that
that secondary galaxies feature higher levels of star formation enhancement in
comparison to primary galaxies, which is in agreement with what we find in
this work. This indicates that the reason why primary galaxies behave
differently from secondary galaxies may be due to a difference in the physical
mechanism which drives the enhanced star formation.

We also find that there is a difference in the $\Delta$log(sSFR) offsets at
wide radii between primary and secondary companions. The primary companion
features an enhancement to their sSFR at wide radii while the secondary
companion features a suppression to their sSFR at wide radii. The reason for
this is unclear; however, this means that the primary companions will
experience enhanced stellar mass growth across their disks while the secondary
companions will see only see substantial stellar mass growth in their centers
which will result in more bulge dominated galaxies. Differences in the bulge-
to-total ratio, (B/T), has been observed in previous works like Bluck et al.
(2019) who found that satellites tend to have slighter higher (B/T) ratios in
comparison to central galaxies at the same stellar mass.

##  6\. Summary and Conclusion

In this paper, we have demonstrated the power of a massive integral-field
spectroscopic survey in comparison studies of galaxy properties. The nearby
galaxy populations show consistent behaviors despite of their large diversity
in star formation properties. Stacking was able to detect the signal buried in
the noise by averaging, in the time domain, the likely stochastic star forming
histories of galaxies (which drives the scatter in the sample). We focused on
comparing the azimuthally averaged radial profiles of sSFR between galaxies in
close pairs and a control sample of isolated galaxies. In agreement with
previous studies, we found that, on average, star formation is elevated in
close galaxy pairs. The properties of these purported merger-induced
differences in sSFR can be summarized as follows:

  1. 1.

Star formation is enhanced within the inner 1.0 $R_{\rm eff}$ and it peaks at
a level of 0.20$-$0.25 $\pm$ 0.1 dex (i.e., $\sim$2$\times$ faster star
formation). On the other hand, the outskirts of the paired galaxies ($R_{\rm
eff}$ $=$ 1.0$-$2.5) show a moderate amount of suppression in sSFR at a level
of $\sim$0.1 dex.

  2. 2.

The sSFR difference profile is largely independent of the stellar mass.

  3. 3.

The level of central sSFR enhancement increases smaller projected separations.

  4. 4.

The level of central sSFR enhancement depends on the mass ratio of the galaxy
pair. Galaxies with small mass ratios, $|\Delta$log($M$)$|$ $=$ 0.0$-$0.5, see
an enhancement $\sim$0.1$-$0.2 dex higher than the average. But the
enhancement is still present in pairs with mass ratios as large as
$|\Delta$log($M$)$|$ $=$ 1.0.

  5. 5.

The merger-induced changes in sSFR also seem to differ between the more
massive and the less massive member of a galaxy pair. At the same mass ratio,
the less massive member in a galaxy pair shows a higher sSFR enhancement (by
$\sim$0.1$-$0.2 dex) in comparison to the more massive member.

  6. 6.

At large radii (R/$R_{\rm eff}$ $>$ 1.5), the more massive companion of pairs
show an enhancement to the sSFR while the less massive companion of pairs show
a suppression to the sSFR.

As of 2020 August 24, MaNGA has completed its observations of $\sim$10,000
galaxies. This final sample gives us access to an unprecedentedly large sample
of paired and control galaxies with 2″ spatial sampling up to 2-3 $R_{\rm
eff}$, which will undoubtedly improve the results presented here. In addition,
the less massive members of the inside-IFU pairs can be included in such a
comparison study once we build a better deblended photometric catalog using
SDSS images.

We thank the anonymous referee for the useful comments and suggestions. We
also thank Cheng Li for our useful discussion on how the sSFR enhancement in
galaxy pairs relates to their stellar mass and mass ratio. J.S. and H.F.
acknowledge support from the National Science Foundation (NSF) grant
AST-1614326. YSD would like to acknowledge support from NSFC grant number
10878003. 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 acknowledges support and resources
from the Center for High-Performance Computing at the University of Utah. The
SDSS web site is www.sdss.org. SDSS is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS Collaboration
including the Brazilian Participation Group, the Carnegie Institution for
Science, Carnegie Mellon University, the Chilean Participation Group, the
French Participation Group, Harvard-Smithsonian Center for Astrophysics,
Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli
Institute for the Physics and Mathematics of the Universe (IPMU) / University
of Tokyo, the Korean Participation Group, Lawrence Berkeley National
Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-
Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik
(MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE),
National Astronomical Observatories of China, New Mexico State University, New
York University, University of Notre Dame, Observatório Nacional / MCTI, The
Ohio State University, Pennsylvania State University, Shanghai Astronomical
Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma
de México, University of Arizona, University of Colorado Boulder, University
of Oxford, University of Portsmouth, University of Utah, University of
Virginia, University of Washington, University of Wisconsin, Vanderbilt
University, and Yale University.

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