Environmental Influences on Star Formation in Low-mass Galaxies Observed by the SDSS-IV/MaNGA Survey

Variations in the evolution of galaxies are connected with the diverse environments in which they reside. The Lambda cold dark matter (ΛCDM) model suggests that galaxies in larger mass scales are formed through the hierarchical clustering of lower-mass galaxies (White & Rees 1978). Interactions between galaxies are widely believed to be of critical importance to the growth and evolution of galaxies with $\mathrm{log}({M}_{\star }/{M}_{\odot })\gtrsim 11$ in the low-redshift universe at z < 0.1 (e.g., Toomre & Toomre 1972; Sanders et al. 1988; Schweizer 2000; Ellison et al. 2011; Scudder et al. 2012). Observational studies have found that the star formation activities can be enhanced when the host galaxies are close to their neighboring galaxies (e.g., Patton et al. 2013; Barrera-Ballesteros et al. 2015; Behroozi et al. 2015).

To date, few observational studies have investigated how interactions between low-mass galaxies influence their internal properties. Although low-mass galaxies are numerous, they tend to be faint and therefore difficult to observe. For this reason, most of the existing studies focus on either the Magellanic Clouds or other low-mass galaxies within the Local Group (e.g., Tolstoy et al. 2009; D'Onghia & Fox 2016; Simpson et al. 2018), and most of these low-mass galaxies are under the disturbance of gas stripping. The interaction between the Magellanic Clouds, and possibly the Milky Way, has displaced more than 2 × 10⁹ M_⊙ of gas from these galaxies (Brüns et al. 2005; Barger et al. 2013; Fox et al. 2014). The low-mass galaxies within the Local Group tend to be gas poor and their star formation is either shutting down or has ceased (e.g., Fillingham et al. 2015, 2016, 2018), indicating that they are being influenced by the massive Milky Way and Andromeda galaxies. The existence of nearby higher-mass galaxies is therefore widely accepted to play a crucial role in quenching star formation in low-mass galaxies. Geha et al. (2012) found that the star formation in low-mass galaxies can still be suppressed even when the distance to its higher-mass neighbor galaxy is up to 1.5 Mpc in the low-redshift universe at z < 0.1.

When low-mass galaxies are not under the influence of a massive galaxy, the interaction between low-mass galaxies (hereafter referred to as the dwarf–dwarf interaction) is suggested to be responsible for the elevation of their star formation activities. The TiNy Titans (TNT) project (Stierwalt et al. 2015, hereafter the SBP15 study) started the first systematic study to explore the star formation activities in dwarf–dwarf interacting systems at the low-redshift universe with 0.005 < z < 0.07. This study applies data from the Data Release 7 of Sloan Digital Sky Survey (SDSS DR7; Abazajian et al. 2009), which uses a single fiber with a diameter of 3'' to spectroscopically observe the brightest knot for galaxies. Those spectroscopically observed galaxies in SDSS have r-band Petrosian magnitude r ≤ 17.77 mag; more details on those selection criteria have been introduced in Strauss et al. (2002). For dwarf–dwarf systems that are not accompanied by massive galaxies ($\mathrm{log}({M}_{\star }/{M}_{\odot })\gtrsim 9.7$) within a projected radius of 1500 kpc, the SBP15 study found that their star formation rate (SFR) is elevated by a factor of 2.3 ± 0.7 when the projected separation is less than 50 kpc.

The SBP15 study and other studies greatly assist us in comprehending the evolution of low-mass galaxies in isolated dwarf–dwarf systems. However, these studies often suffer from a few technical limitations. First, the star formation (SF) activity in low-mass galaxies is often explored using only a small sample of dwarf–dwarf systems. Majority of studies only target on individual galaxy pair using data from H i 21 cm observations (e.g., Martin et al. 2002; Lee-Waddell et al. 2018; Stein et al. 2018) or UV surveys (e.g., Paudel et al. 2015; Sengupta et al. 2015; Sacchi et al. 2018). Second, many of the studies that examine the SF activity with larger galaxy samples tend to use single-fiber spectroscopy toward their brightest spot to characterize its SF activity; some of these studies further use photometry infer the star formation properties of the galaxy that is not spectroscopically sampled (such as the SBP15 study). In those studies, the internal properties of galaxies can only be derived through imaging and simulation, thus their interpretation may be biased by the spectroscopic features in the target region. Privon et al. (2017) observe one merging galaxy selected from the SBP15 study using the first Very Large Telescope/Multi Unit Spectroscopic Explorer optical integral field unit (IFU) survey; they find that the total SFR within the full optical extent of the system is 2.7 times higher than the SFR inferred using SDSS single-fiber data. Moreover, Pan et al. (2019) suggest that the degree of interaction-triggered SFR enhancement can be diluted as the radial coverage of the target region increases when they check the radial profile of the SFR for galaxies with stellar mass $\mathrm{log}({M}_{\star }/{M}_{\odot })\geqslant 9$ using data from the fourth-generation SDSS (SDSS-IV)/Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. Several studies also point out that the interaction-triggered SFR enhancement peaks at the galactic center but can also be observed in the outskirts of galaxies with $\mathrm{log}({M}_{\star }/{M}_{\odot })\geqslant 9$ using data from the MaNGA survey (e.g., Pan et al. 2019; Thorp et al. 2019); however, it is unclear whether this feature can be observed in galaxies with lower stellar mass. Overall, the spatially resolved star formation features in a larger-scaled sample of low-mass galaxies are still uncharted, and the global enhancement on star formation induced by the interaction between low-mass galaxies is expected to be further explored.

The shortcoming of single-spectrum studies can be overcome by the new technological breakthrough of integral field spectroscopy, which can obtain multiple spectra over spatially resolvable objects. Benefiting from this technical advancement, we conduct a study on the spatially resolved star formation activities in low-mass galaxies within the stellar mass range of $8\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 10$ at the redshift of 0.01 < z < 0.07. We explore the environmental impacts that dwarf–dwarf galaxy interactions have on their current star formation properties using observations from the SDSS-IV/MaNGA survey. In this work, we intentionally exclude low-mass galaxies that are within a projected distance of 1500 kpc from a massive galaxy, as the star formation in low-mass galaxies can be quenched due to the harassment from a massive neighbor.

This paper is organized as follows. We provide an introduction to the MaNGA survey and its data products in Section 2. We describe the detailed sample selection procedure in Section 3, and we further use the calculation method in Section 4 to determine their SFR and star formation surface density. We explore how the star formation properties of low-mass galaxies are affected in diverse environments using all 386 galaxies included in our sample. The results are described in Section 5 and are further discussed and compared to the SBP15 study in Section 6. Finally, we summarize the conclusions of this work in Section 7. For this work, we adopt a ΛCDM cosmology model with Ω_m = 0.3, Ω_Λ = 0.7, and H₀ = 70 km s⁻¹ Mpc⁻¹ unless otherwise noted.

The MaNGA survey is one of the core projects in SDSS-IV (Smee et al. 2013; Blanton et al. 2017). The 15th data release (DR15) of SDSS (Aguado et al. 2019) brought the 7th MaNGA Product Launch (MPL-7) to the public, which includes 4621 spectroscopically resolved galaxies. An overview of MaNGA is presented by Bundy et al. (2015).

MaNGA selects galaxies from the NASA-Sloan Atlas (NSA) catalog (Blanton, M. http://nsatlas.org/data), and this selection procedure is described in Wake et al. (2017). MaNGA aims to observe 10,000 galaxies by 2020; these selected galaxies span a redshift range of 0.01 ≤ z ≤ 0.15 and are observed over a wavelength range of 3600 ≤ λ ≤ 10300 Å. The MaNGA galaxies are designed to be representative; they are diverse in galaxy type and are evenly distributed by mass between $9\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 11$. These galaxies are observed with IFUs using the SDSS 2.5 m telescope at Apache Point Observatory (Gunn et al. 2006; Drory et al. 2015; Law et al. 2015; Yan et al. 2016a, 2016b). Galaxies in the primary sample (two-thirds of the targets) and secondary sample (one-third of the targets) of MaNGA are spatially resolved out to a radius of 1.5 R_e and 2.5 R_e, respectively. Here, we use R_e to represent the effective radius at which half of the total light is emitted.

The MaNGA data is reduced by the standard SDSS-IV/MaNGA data reduction pipeline (DRP); a detailed description of the DRP is given by Law et al. (2016). This pipeline subtracts the atmospheric contribution using the collected spectroscopic map of the background sky. The correction for the dust attenuation in the Milky Way is performed, and the calibration of fiber spectra after the dithering exposure is determined from the observed data of standard stars. The DRP eventually organizes the data into three-dimensional (3D) data cubes with spaxel size set to 0.5 × 0.5 arcsec². The accuracy of the wavelength calibration during this procedure corresponds to a Δv_calibration ≈ 5 km s⁻¹ uncertainty in the velocity, where the median spectral resolution of these observations is Δv_resolution ≈ 72 km s⁻¹.

The 3D data cubes are further processed by the SDSS-IV/MaNGA data analysis pipeline (DAP). The overview of the DAP is provided by Westfall et al. (2019). More specifically, the analysis of the emission-line properties in DAP is introduced by Belfiore et al. (2019). The DAP simultaneously fits the stellar continuum and emission lines using the latest version of the penalized pixel-fitting program package (pPXF; Cappellari 2017). A hybrid binning approach is applied in this procedure, where stellar kinematics are derived using the Voronoi binned data and emission lines are modeled using individual spaxels. The flux of emission lines is determined through both numerical integration and a single Gaussian profile. The products from the DAP include two-dimensional (2D) position maps of the stellar kinematics, emission-line properties, and stellar continuum features. Additionally, the associated statistical uncertainties and data quality flags are provided in the DAP. However, it needs to be noted that the Gaussian-fitted gas velocity for each emission line is underestimated in the DAP when the signal-to-noise ratio (S/N) is less than 10. This underestimation is caused by the formal error in pPXF, as the covariance between the fluxes and the gas kinematics is currently ignored. Extra corrections are suggested to rectify this underestimation.

Furthermore, Belfiore et al. (2019) demonstrates that Gaussian-fitted emission-line fluxes are statistically well fit in DAP when $1.5\leqslant {\rm{S}}/{\rm{N}}\leqslant 30$, and elevated uncertainties are found at a higher S/N region due to the limitation of using the single Gaussian profile. However, it is also pointed out that the average S/N for Hα emission is around 29.5 at the radial distance R ≤ 1 R_e for MaNGA galaxies. To ensure that there are sufficient data for the later analysis, the numerically integrated flux for each emission line in the DAP product is adopted for this investigation.

We select low-mass galaxies with stellar mass 8 ≤ log(M_⋆/M_⊙) ≤ 10 and redshift 0.01 < z < 0.07 from the MPL-7 (Figure 1), which is publicly available in the SDSS-IV DR15. The position (R.A., decl., and redshift z) and stellar mass for our galaxy sample are extracted from the NSA galaxy catalog (Blanton, M. http://nsatlas.org/data) catalog, where the stellar mass of galaxy is calculated by applying a K-correction software package (Blanton & Roweis 2007, 2017) with the Hubble constant of H₀ = 100 km s⁻¹ Mpc⁻¹. Because our investigation adopts a different the Hubble constant of H₀ = 70 km s⁻¹ Mpc⁻¹, we apply an h-scale factor to achieve consistency in stellar mass for each selected galaxy (Croton 2013).

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We identify the neighboring galaxies for our selected sample using the NSA galaxy catalog, which includes all galaxies with $r\leqslant 17.77\,\mathrm{mag}$ that have been spectroscopically observed in SDSS DR13 at redshift z < 0.15. To categorize the environmental conditions for our sample, we use the projected separation (d_proj) and the difference in line-of-sight velocity (Δv_LOS) to describe the physical and line-of-sight kinematic separations. We further determine the relative stellar mass scale of the neighboring galaxies using the stellar mass ratio M_Neighbor/M_MaNGA for each MaNGA target galaxy. We call a neighboring galaxy a "minor" neighbor if M_Neighbor/M_MaNGA ≤ 4; otherwise we call it a "major" neighbor. This scheme is inspired by the commonly accepted definition of galaxy major and minor mergers (e.g., Rodriguez-Gomez et al. 2015), in which the merger events are classified using the stellar mass ratio of the two involved galaxy components. The nearest major neighbor for each of our selected galaxy is required to be at a projected separation of at least 1500 kpc so that all our selected low-mass galaxy systems are isolated from their neighboring higher-mass galaxies and their star formation activities will not be affected by the disturbance of gas stripping.

Our pair candidates are selected to include low-mass galaxies that are in various stages of dwarf–dwarf interaction; their nearest neighbors (hereafter the first neighbor) are minor neighbors with d_proj ≤ 1500 kpc and Δv_LOS ≤ 300 km s⁻¹. To further rule out the influence on star formation from other minor neighbors, all other minor neighbors are required to be at least 150 kpc away from both components in the selected dwarf–dwarf galaxy system. For target galaxies that are not found to have any neighbors in the NSA catalog within the projected radius of 1500 kpc, they are extremely isolated and will be classified under the "Control" category.

After excluding galaxies with bad quality on the MaNGA DRP and DAP product from our sample, we radially bin their 2D nebular emission-line maps so that we can further compare their properties in the inner (0 ≤ R/R_e ≤ 0.5), middle (0.5 ≤ R/R_e ≤ 1.0), and outer (1.0 ≤ R/R_e ≤ 1.5) regions. Although a subset of the MaNGA galaxies was observed out to a radius of R ≈ 2.5 R_e, most only have spatially resolved spectra out to R ≈ 1.5 R_e. To keep the consistency, we thus set a cutoff threshold of the radial distance R = 1.5 R_e for this investigation. For each selected target galaxy, at least half of their spaxels in the data cube need to be "valid" spaxels within each of these three radially binned regions. In this work, a spaxel with S/N ≥ 3 and Hα emission equivalent width EW ≥ 1 Å is considered to possess valid data and is referred to as a "valid" spaxel. The fraction with the number of valid spaxels as the numerator and all spaxels as the denominator for all radially binned regions are presented in Table 1. It should be noted that our sample only include galaxies with the semiminor axis (b) to semimajor axis (a) ratio b/a ≥ 0.3. We exclude galaxies with an extremely thin body (e.g., edge-on galaxies) so that we can compare how the star formation varies at different radii from the galactic center for our selected galaxies.

Table 1.  Information for Galaxies in Our Sample

									Star Formation Surface Densityd				Fraction of Valid Spaxelsf
PlateIFU	MaNGA-ID	Category	Rea	b/aa	$\mathrm{log}({M}_{\star }/{M}_{\odot })$ b	${d}_{\mathrm{proj}}$ c	${\rm{\Delta }}{v}_{\mathrm{LOS}}$ c	${M}_{\mathrm{ratio}}$ c	${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{in}}$	${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{mid}}$	${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{out}}$	${\mathrm{SFR}}_{\mathrm{fiber}}$ e	${f}_{\mathrm{in}}$	${f}_{\mathrm{mid}}$	${f}_{\mathrm{out}}$
			(arcsec)			(kpc)	(km s−1)		(${M}_{\odot }\,{\mathrm{yr}}^{-1}\,{\mathrm{arcsec}}^{-2}$)			(${M}_{\odot }\,{\mathrm{yr}}^{-1}$)
8338-6101	1-574691	Pair	5.78	0.56	9.78	16	181	0.11	0.0482	0.0134	0.0026	0.3183	59/59	178/178	284/284
8329-6104	1-592743	Pair	6.63	0.86	9.72	16	31	0.97	0.0178	0.0123	0.0062	0.1362	117/117	358/358	592/595
9510-12701	1-584931	Pair	11.87	0.77	9.50	21	149	0.03	0.0012	0.0009	0.0006	0.0081	339/338	1026/1026	1106/1700
8941-6101	1-604928	Pair	3.41	0.52	9.54	25	57	0.39	0.0379	0.0249	0.0094	−999.0000	17/17	58/58	102/102
8085-12701	1-38368	Pair	10.94	0.57	9.54	29	256	0.33	0.0066	0.0060	0.0022	0.0520	219/219	648/648	904/1082
9493-9101	1-384936	Pair	4.34	0.73	9.17	35	31	0.30	0.0100	0.0018	0.0005	0.0614	44/44	118/131	173/216
8318-1901	1-284321	Pair	2.87	0.60	9.57	36	55	0.54	0.0010	0.0005	0.0002	0.0046	15/15	46/46	68/74
8261-6102	1-258315	Pair	5.55	0.86	9.64	42	121	0.04	0.0042	0.0031	0.0011	0.0231	83/83	250/250	422/422
8331-3704	1-251043	Pair	5.59	0.44	9.73	44	129	0.02	0.0016	0.0013	0.0006	0.0085	46/46	122/128	160/217
7968-3704	1-635629	Pair	4.22	0.48	9.23	44	73	0.65	0.0203	0.0135	0.0056	0.0580	28/28	80/80	133/133

Notes.

^aThe effective radius (R_e) and the semiminor to semimajor axis ratio (b/a) derived from the elliptical Petrosian analysis in the MaNGA DAP. ^bThe stellar mass in logarithm derived from the K-correction fit in the NSA catalog (Blanton, M.; http://nsatlas.org/data). ^cProjected separation (d_proj), line-of-sight kinematic separation (${\rm{\Delta }}{v}_{\mathrm{LOS}}$), and stellar mass ratio ${M}_{\mathrm{Neighbor}}/{M}_{\mathrm{Candidate}}$ (${M}_{\mathrm{ratio}}$) to the first neighbor. ^dThe star formation surface density within the inner, middle, and outer regions are represented by "${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{in}}$," "${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{mid}}$," and "${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{out}}$," respectively. ^eThe star formation rate within the 3'' SDSS single fiber is represented by "${\mathrm{SFR}}_{\mathrm{fiber}}$." The ${\mathrm{SFR}}_{\mathrm{fiber}}$ is derived from the product of ${\rm{\Sigma }}{\mathrm{SFR}}_{\mathrm{fiber}}$ and the area of the 3'' fiber (see Section 6.1.2). It needs to be noted that six galaxies (PlateIFU = 8941-6101, 7991-12701, 9883-3701, 9024-6102, 7443-6102, and 9891-1901) in our sample are not observed by the SDSS single-fiber survey; their $\mathrm{SFR}$ within the fiber thus are not able to be recovered using the MaNGA IFU data. For these six galaxies, their ${\mathrm{SFR}}_{\mathrm{fiber}}$ are given by "−999.0000." in this table. These six galaxies are also excluded in the discussion of star formation activity within the fiber coverage in Section 6.1.2. ^fThe number fraction of valid spaxels within the inner region, middle region and outer region is represented by ${f}_{\mathrm{in}}$, ${f}_{\mathrm{mid}}$, and ${f}_{\mathrm{out}}$, respectively. In the fraction value for each region, the number in front of the slash sign presents the number of valid spaxels, while the number of all observed spaxels is presented by the number after the slash sign.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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The calculation method for star formation properties is elaborated in Section 4, in which the nonvalid spaxels are masked out. The dominant ionization mechanism throughout the IFU sight is examined for each selected target galaxy using the [N ii] Baldwin–Phillips–Terlevich (BPT; Baldwin et al. 1981) diagnostic map with classification lines in Kewley et al. (2001) and Kauffmann et al. (2003a), in which EW ≥ 1 Å are required for each involved emission line. To simplify the ionization condition and the star formation behavior, target galaxies with spaxels dominantly ionized by active galactic nuclei (AGNs) are excluded in this investigation. After calculating the star formation properties, one pair candidate with d_proj ≈ 1000 kpc and two control galaxies are found to possess star formation activities that are more than 10 times stronger than the average level of control galaxies within our entire radial coverage. These three galaxies are moved from their original category to the "Robust" category (hereafter referred to as the "RB" category), and their extreme star formation behavior will be discussed separately in Section 6.2.

A general visual check is further conducted using the SDSS SkyServer and the MaNGA Marvin interface (Cherinka et al. 2019) on those selected MaNGA galaxies, as the NSA catalog does not include galaxies that have not been spectroscopically observed using the 3'' single fiber. After the visual check, three galaxies in the "Control" category and one galaxy in the "Pair" category are suspected to possess an extra neighboring galaxy with d_proj ≤ 30 kpc. Information on the redshift and stellar mass of those recovered neighbors are missing due to the lack of spectroscopy data, so that their line-of-sight kinematic separation Δv_LOS and stellar mass ratio to the associated target galaxies remain vague. We exclude those four galaxies from their original category and classify them under the "Recovered" category (the "RC" category).

Two pair candidates have been observed twice by MaNGA; their MaNGA IDs are 1-235530 and 1-178443. For these repeatedly observed galaxies, their latest observations will be kept in the "Pair" category for the later analysis and discussions, and the older version of their observations will be moved to the "Repeated" category (the "RP" category). All of those repeated observations will be used to provide a supplemental exploration of the uncertainties in our calculation about the star formation properties in galaxies.

The 386 target galaxies in our sample consist of 90 control galaxies, 287 pair candidates, 3 "Robust" galaxies, 4 Recovered pairs, and 2 with repeat observations in the "RP" category. Two of the pair candidates (PlateIFU = 9045-3702 and 9045-12702) belong to the same galaxy pair with d_proj ≈ 1300 kpc and Δv_LOS = 19 km s⁻¹. In this system, the galaxy with identifier PlateIFU = 9045-12702 is 3.23× more massive than the galaxy with identifier PlateIFU = 9045-3702. We designate both of these two galaxies to the "Pair" category, and we explore how these respective galaxies affect their companion separately. The information for those galaxies can be found in the complete machine-readable table, a portion of which is shown in Table 1. Figure 1 displays the distribution of redshift and stellar mass for our control galaxies and pair candidates. Those control galaxies in our sample have a median stellar mass of $\mathrm{log}(M/{M}_{\odot })=9.3$ at a median redshift of z = 0.038; our pair candidates have a median stellar mass of $\mathrm{log}(M/{M}_{\odot })=9.5$ at a median redshift of z = 0.030. These pair candidates have a median line-of-sight kinematic separation of Δv_LOS = 80 km s⁻¹. The stellar mass ratio for galaxies in the "Pair" category spans a 0.004 ≤ M_Neighbor/M_Candidate ≤ 4 range with a median value of (M_Neighbor/M_Candidate)_median = 0.4 (see Figure 2).

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4.1. Dust Extinction

4.2. SFR and Surface Density

The SFR describes the total mass of stars formed per unit time. There are several indicators of the current SFR, which has been thoroughly reviewed in Kennicutt (1998). Strong recombination emission lines (especially Hα) are widely adopted to describe current star formation activity in galaxies, because they are good tracers of ionization imprints that massive stars leave on their surrounding gas. In this study, we apply the intrinsic Hα energy flux F_i(λ_Hα) to calculate the current SFR using the luminosity–SFR relation in Kennicutt (1998),

$$\begin{eqnarray}&&\displaystyle \frac{{L}_{{\rm{H}}\alpha }}{\mathrm{erg}\,{{\rm{s}}}^{-1}}=\left(\displaystyle \frac{{\nu }^{2}}{\mathrm{erg}\,{{\rm{s}}}^{-1}\,{{M}_{\odot }}^{-1}\,\mathrm{yr}}\right)\cdot \left(\displaystyle \frac{\mathrm{SFR}}{M\odot \,{\mathrm{yr}}^{-1}}\right),\end{eqnarray} \tag{ 1 }$$

where ν² is the ${L}_{{\rm{H}}\alpha }$–SFR calibrator. The Hα luminosity is calculated from ${L}_{{\rm{H}}\alpha }=4\pi {d}^{2}\times {F}_{{\rm{i}}}({\lambda }_{{\rm{H}}\alpha })$, where d is the distance to the host galaxy using redshift and Hubble's law. The redshift (z_Hα) adopted in the calculation of d is extracted from the MaNGA DAP product, which is the flux-weighted mean redshift of the Hα emission line within an angular radius of 125 at the galactic center. Accordingly, the uncertainty for Gaussian-fitted Hα emission-line velocity within the same angular radius is extracted from the DAP product. More specifically, the included valid spaxels within this region are also required to have ${\rm{S}}/{\rm{N}}\geqslant 10$, so that the velocity uncertainty is underestimated in this data product. The MaNGA wavelength calibration (Δv_calibration ≈ 5 km s^−1; Law et al. 2016) is also considered when we estimate the uncertainty for z_Hα. Eventually, the median fractional uncertainty of z_Hα is around 0.05%.

The original L_Hα–SFR calibrator in Kennicutt (1998) is estimated using solar metallicity (Z_⊙) and a Salpeter initial mass function (IMF) over the mass range of 0.1 ≤ M/M_⊙ ≤ 100. However, it has been pointed out by Weilbacher & Fritze-v. Alvensleben (2001) that the SFR in dwarf galaxies is overestimated when using the calibrator in Kennicutt (1998), as higher metallicity can be translated into higher SFR and dwarf galaxies generally have a subsolar metallicity. To explore the calibrator for galaxies that do not have solar metallicity, Weilbacher & Fritze-v. Alvensleben (2001) conducted a series of simulations over the metallicity range 0.001 ≤ Z ≤ 0.04 (1/20 ≲ Z/Z_⊙ ≲ 2), and a Salpeter IMF is adopted over two mass ranges (0.15 ≤ M/M_⊙ ≤ 85 and 0.15 ≤ M/M_⊙ ≤ 120). In this work, we presume a calibrator of Z = 0.4 Z_⊙ of ${\nu }^{2}=(2.311\pm 0.238)\times {10}^{41}\,{{\rm{s}}}^{-1}\,{{M}_{\odot }}^{-1}\,\mathrm{yr}$. This adopted calibrator represents the average value of the simulated calibrators over 0.15 ≤ M/M_⊙ ≤ 85 and 0.15 ≤ M/M_⊙ ≤ 120, and the half-difference between these two simulated calibrators is used to describe the uncertainty of our adopted calibrator. This selection is made because our galaxies and the LMC have similar stellar masses ($\mathrm{log}({M}_{\star ,\mathrm{LMC}}/{M}_{\odot })\approx 9.5$ in van der Marel et al. 2009), and the LMC has a metallicity of Z_LMC ≈ 0.008 (Glatt et al. 2010).

The uncertainty of Hα-based SFR has five sources: Hα redshift ${z}_{{\rm{H}}\alpha }$, the emission-line flux of Hα and Hβ before the dust extinction ${F}_{{\rm{o}}}({\lambda }_{{\rm{H}}\alpha })$ and ${F}_{{\rm{o}}}({\lambda }_{{\rm{H}}\beta })$, the extinction factor R_V, and the L_Hα–SFR calibrator ν². Overall, our selected galaxies possess a fractional SFR uncertainty of 12.4% for each spaxel. This uncertainty is mainly contributed by the uncertainty of the extinction factor and L_Hα–SFR calibrator, as the median fractional uncertainties for ${F}_{{\rm{o}}}({\lambda }_{{\rm{H}}\alpha })$ and ${F}_{{\rm{o}}}({\lambda }_{{\rm{H}}\beta })$ in the MaNGA DAP product are only in the scale of 1.4% and 6.8% for each spaxel.

The 2D SFR map for all selected galaxies are displayed in Figure 16; the three radially binned regions are separated by the ellipses with different radii in terms of R_e. The total SFR (SFR_total) for each radially binned region can be obtained simply by adding up the calculated SFR for each valid spaxel within the respective region; the number of valid spaxels for each radially binned region is displayed in Table 1. It needs to be pointed out, however, that the calculated total SFR above are area dependent because the radially binned region with larger radial distance contains more spaxels. The area-weighted SFR for each galaxy, also known as the star formation surface density (ΣSFR), is subsequently determined for each radially binned region (Figure 3) using the relation ${\rm{\Sigma }}\mathrm{SFR}\,={\mathrm{SFR}}_{\mathrm{total}}/({A}_{\mathrm{spaxel}}\cdot {N}_{\mathrm{spaxel}})$, where N_spaxel is the number of spaxels within this region, and A_spaxel = 0.5 × 0.5 arcsec² is the angular area for each spaxel in MaNGA. The summation for the SFR_total considerably reduces the uncertainty of SFR_total. The fractional uncertainty of Hα-based ΣSFR in the inner, middle, and outer regions for each selected galaxy is typically on the scale of 1.8%, 1.1%, and 1.0%, respectively. Furthermore, the repeated observations in our sample exhibit an average ΣSFR percentage difference of 8.3%, 5.5%, and 5.7% for the inner, middle and outer regions, respectively.

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5.1. Environmental Impact on the Star Formation Strength in Low-mass Galaxies

There is a tight proportional correlation between SFR and stellar mass for galaxies within any given stellar mass range, which is well known as the SF main sequence (e.g., Noeske et al. 2007; Wang et al. 2019). In this investigation, we adopt the stellar-mass-weighted ΣSFR (ΣSFR/M_⋆) to represent the SF strength, so that the impact of the stellar mass can be removed.

Figure 3 presents the distribution of ΣSFR and stellar mass for our control galaxies and pair candidates. The ΣSFR and stellar mass of control galaxies are adopted to estimate the average level of SF strength for each radial binned region. The average control level for each radially binned region is represented by the average value and the associated standard deviation of the mean (also known as the standard error) for SF properties in control galaxies after removing the 3σ outliers (σ represents the standard deviation). We found that the average SF strength of our control galaxies is $\mathrm{log}({\rm{\Sigma }}\mathrm{SFR}/{M}_{\star })\,=-11.16\pm 0.06$, −11.36 ± 0.06, and −11.70 ± 0.05 in their inner, middle and outer regions, respectively (see Figure 4). The unit of ΣSFR/M_⋆ is ${\mathrm{yr}}^{-1}\,{\mathrm{arcsec}}^{-2}$. We use these average control levels to compare the SF activity of our pair candidates.

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Our pair candidates probe different potential environmental influences on their star formation, including the projected separation (d_proj), line-of-sight kinematic separation (Δv_LOS), and stellar mass ratio (M_Neighbor/M_Candidate) between the MaNGA target galaxies and their associated nearest neighbor. We divided our pair candidates into different bins according to their environmental conditions and illustrate their ΣSFR as a function of stellar mass in each environmental bin in Figure 3. Pair candidates with a stellar mass ratio of 0.25 ≤ M_Neighbor/M_Candidate ≤ 4 are accompanied by neighboring galaxies with a comparable stellar mass; pair candidates with a stellar mass ratio of 0.1 ≤ M_Neighbor/M_Candidate < 0.25 correspond to the more massive galaxy in each associated galaxy pair. And the pair candidates with a stellar mass ratio of M_Neighbor/M_Candidate < 0.1 are accompanied by extremely small neighboring galaxies. We separated the pair candidates into three evenly spaced Δv_LOS groups so that we could estimate its influence on the SF activity of our galaxy sample. These Δv_LOS groups include 0 ≤ Δv_LOS ≤ 100 km s⁻¹, 100 ≤ Δv_LOS ≤ 200 km s⁻¹, and 200 ≤ Δv_LOS ≤ 300 km s⁻¹. We binned the SF strength for each of these Δv_LOS groups in ascending order of d_proj, which is included in Figure 5.

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For pair candidates with Δv_LOS > 100 km s⁻¹ in Figure 5, we were only able to explore the SF trends for pair candidates with stellar mass ratio 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0 because there were too few galaxies in the other stellar mass ratio bins. Throughout all three radially binned regions, the pair candidates with stellar mass ratio 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0 and 200 ≤ Δv_LOS ≤ 300 km s⁻¹ have a relatively flat SF trend that is well matched to the control level; this implies that the SF activities in these galaxies are no longer affected by their companions when Δv_LOS > 200 km s⁻¹.

For galaxies with an intermediate line-of-sight kinematic separation (100 ≤ Δv_LOS ≤ 200 km s⁻¹) in Figure 5, the estimated SF trend for galaxies with a stellar mass ratio of 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0 matches with the control level at 300 ≤ d_proj ≤ 700 kpc; however, there is an increase in star formation in all three radially binned regions at 850 ≤ d_proj ≤ 1250 kpc because of five galaxies with extremely strong SF. We also find that the SF strength drops at 100 ≤ d_proj ≤ 200 kpc for those galaxies with a stellar mass ratio of 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0. No evidences suggest that the SF becomes elevated at small projected separations.

We find that pair candidates with Δv_LOS ≥ 100 km s⁻¹ generally have weaker SF compared to the average control level, which is illustrated in Figure 5 where the circular symbols represent the estimated ΣSFR/M_⋆ for our pair candidates. Overall, we do not observe SF enhancement for dwarf–dwarf systems with Δv_LOS ≥ 100 km s⁻¹ at small projected separation in Figure 5.

We explore the global SF trends for pair candidates with Δv_LOS ≤ 100 km s⁻¹ in all three stellar mass ratio bins as a function of projected separation. Galaxies with a stellar mass ratio of 0.1 ≤ M_Neighbor/M_Candidate < 0.25 generally show a decreasing SF trend throughout the entire d_proj range, and their SF strength is greater than the control level only when d_proj ≤ 400 kpc (see Figure 5). We find that the SF activity for galaxies with a stellar mass ratio of 0 < M_Neighbor/M_Candidate < 0.1 is lower than the average control level in Figure 5, especially when d_proj ≤ 400 kpc. For those galaxies in the 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0 stellar mass ratio bin, we observe an enhancement in their SF strength when d_proj ≤ 100 kpc (see Figure 5).

Furthermore, we use the fractional change in star formation strength (${f}_{{\rm{\Delta }}\mathrm{SF}}$) to describe how the SF activity in these pair candidates varies compared to the average control level (Figure 6). The f_ΔSF in Figure 6 is calculated from

$$\begin{eqnarray}&&{f}_{{\rm{\Delta }}\mathrm{SF}}=\displaystyle \frac{{({\rm{\Sigma }}\mathrm{SFR}/M)}_{\mathrm{Pair}}-{({\rm{\Sigma }}\mathrm{SFR}/M)}_{\mathrm{Control},\mathrm{mean}}}{{({\rm{\Sigma }}\mathrm{SFR}/M)}_{\mathrm{Control},\mathrm{mean}}},\end{eqnarray} \tag{ 2 }$$

where (ΣSFR/M_⋆)_Pair is the average SF strength calculated using the moving-average method for our pair candidates and (ΣSFR/M_⋆)_Control,mean is the average SF strength of our control galaxies. A positive f_ΔSF at a small projected separation suggests that the star formation activities in this pair candidates are stronger than the average control level, thus we can use the maximum f_ΔSF within this d_proj region to represent the scale of enhancement on SF strength. Similarly, the minimum f_ΔSF can be adopted to describe the scale of suppression on SF strength if a galaxy in a close pair possesses a negative f_ΔSF.

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The SF activity in pair candidates with a stellar mass ratio of 0 < M_Neighbor/M_Candidate < 0.1 and Δv_LOS ≤ 100 km s⁻¹ is suppressed throughout the entire projected separation range explored in this study (d_proj ≤ 1500 kpc) in all three radially binned regions (see Figure 6 and Table 2). For pair candidates with a stellar mass ratio of 0 < M_Neighbor/M_Candidate ≥ 0.1, we observe an elevated SF strength that peaks in the inner region and diminishes with increasing galactic radii when Δv_LOS ≤ 100 km s⁻¹ (see Table 3 and Figure 6).

Table 2.  The Scale of Suppression on SF Strength for Pair Candidates with ${\rm{\Delta }}{v}_{\mathrm{LOS}}\leqslant 100\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and a Stellar Mass Ratio of ${M}_{\mathrm{Neighbor}}/{M}_{\mathrm{Candidate}}\lt 0.1$

		${f}_{{\rm{\Delta }}\mathrm{SF},\min }$
Projected Separation	Stellar Mass Ratio	Inner Region	Middle Region	Outer Region
${d}_{\mathrm{proj}}\leqslant 400\,\mathrm{kpc}$	${M}_{\mathrm{Neighbor}}/{M}_{\mathrm{Candidate}}\lt 0.1$	−0.84 ± 0.24	−0.83 ± 0.23	−0.83 ± 0.16

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Table 3.  The Scale of Enhancement on SF Strength for Pair Candidates with ${\rm{\Delta }}{v}_{\mathrm{LOS}}\leqslant 100\,\mathrm{km}\,{{\rm{s}}}^{-1}$ and a Stellar Mass Ratio of ${M}_{\mathrm{Neighbor}}/{M}_{\mathrm{Candidate}}\geqslant 0.1$

		${f}_{{\rm{\Delta }}\mathrm{SF},\max }$
Projected Separation	Stellar Mass Ratio	Inner Region	Middle Region	Outer Region
dproj ≤ 400 kpc	0.1 ≤ MNeighbor/MCandidate < 0.25	1.30 ± 0.61	1.23 ± 0.60	0.71 ± 0.34
dproj ≤ 100 kpc	0.25 ≤ MNeighbor/MCandidate ≤ 4	1.75 ± 0.96	1.45 ± 0.73	0.93 ± 0.41

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The SF strength and the fractional change in SF strength trends with increasing projected separation in Figures 5 and 6 distinctly indicate that the SF activities in dwarf–dwarf system are under the impact of stellar mass ratio when Δv_LOS ≤ 100 km s⁻¹. The observed weak SF activity in pair candidates with a stellar mass ratio of M_Neighbor/M_Candidate < 0.1 and Δv_LOS ≤ 100 km s⁻¹ at d_proj ≤ 400 kpc suggests that the SF strength in low-mass galaxies can be significantly reduced when their associated nearest neighbor is over 10 times smaller in mass scale, which could be caused by the fact that these small neighboring galaxies do not have enough gas storage to fuel the SF for their higher-mass companion. This assumption is further supported by the observed feature that galaxies with a higher stellar mass ratio tend to possess higher SF strength at d_proj ≤ 400 kpc. The greater SF strength for galaxies with a stellar mass ratio of 0.1 ≤ M_Neighbor/M_Candidate < 0.25 is also consistent with the fact that the SF in galaxies with larger mass scales can be elevated in a minor merger event (e.g., Weistrop et al. 2012; Kaviraj 2014).

Galaxies with 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0 and 0 ≤ Δv_LOS ≤ 100 km s⁻¹ also show a greater dispersion on SF strength as the projected separation decreases. This large dispersion is also reflected by the large uncertainties on their fraction of SF strength at d_proj ≤ 100 kpc throughout all the three radially binned regions in Figure 6. Those features suggest that galaxies under that environmental condition present strong diversity in their SF activity, which matches the well-accepted opinion that the SF activities in these galaxies are generally vicious and ceases shortly after their gas is drained during the interaction (e.g., Geach et al. 2018). The observed feature also implies that the interaction between low-mass galaxies is also responsible for the quenching of star formation in a dwarf–dwarf system. However, another possibility is that some of these galaxies may only be "projected pairs" that are not actually physically interacting. Jian et al. (2012) points out that about 36% of their simulated galaxy pairs that consist of galaxies with a B-band magnitude of −21 ≤ M_B ≤ −19 mag fail to interact in the end, even though they match all their selection criteria for close pairs (d_proj ≤ 50h⁻¹ and 0 ≤ Δv_LOS ≤ 500 km s⁻¹). This so-called "close-pair contamination" is suggested to result from the projection effect, where the high relative 3D velocities between the galaxy pairs are responsible for the failure of interaction in those contaminated pairs. Our pair candidates may also be "contaminated" in that way, which can be responsible for the weak SF activities observed in some close dwarf–dwarf galaxy systems.

Moreover, we observe that both the control galaxies and pair candidates in our sample tend to be predominantly central star forming with a decreasing ΣSFR/M_⋆ at larger galactic radii. On average, the SF strength in the inner region is 1.6 times stronger than the middle region and is 3.5 times stronger than the outer region.

5.2. Environmental Impact on the Neutral Gas Fraction in Low-mass Galaxies

Diemer et al. (2019) found that the star formation activity within galaxies is tightly correlated with their H i mass (${M}_{{\rm{H}}{\rm{i}}}$). Diemer et al. (2019) also found that galaxies with higher stellar mass tended to have lower neutral gas fraction (f_gas), where ${f}_{\mathrm{gas}}=1.4{M}_{{\rm{H}}{\rm{i}}}/(1.4{M}_{{\rm{H}}{\rm{i}}}+{M}_{\star })$. To explore the connection between the H i gas content and star formation in our galaxy sample, we further examine the neutral gas fraction for our sample.

The H i-MaNGA program is an H i 21 cm radio survey that is in the process of observing the MaNGA galaxies using the Green Bank Telescope (Masters et al. 2019). Their released data provide detected H i mass for around one-third of our selected galaxies and estimation of upper limits for around one-fifth of our galaxies (Figure 7). In their program, they observe MaNGA galaxies using the L band (1.15–1.73 GHz); the beam has an FWHM of 88 at these frequencies. Because of the relatively large beam size of their H i observations in comparison to the angular size and separation of our pair candidates, some of our close pairs are both enclosed within their beam. When this occurs, we derive their neutral gas fraction using the total stellar mass of these close pairs (right panel in Figure 7). Otherwise, we derive the neutral gas fraction for our pair candidates only using their own stellar masses (middle panel in Figure 7).

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Blanton & Moustakas (2009) found that the optical extent of galaxies generally is on the scale of at least 2 ≤ R_optical/R_e ≤ 4, where R_e is the effective radius at where half of the light of the galaxy is emitted. Moreover, Swaters et al. (2002) suggest that the H i content is R_{H i} = (1.8 ± 0.8)R_optical times larger than the optical content for late-type dwarf galaxies with major diameter greater than 15 in the B band. When determining the H i mass of the MaNGA galaxy and its nearest minor neighbor, we assume that their maximum optical component extends out to ${R}_{\mathrm{optical}}=4\,{R}_{{\rm{e}}}$ and that their maximum H i radio component extends out to ${R}_{{\rm{H}}{\rm{i}}}\lesssim (1.8+3{\sigma }_{{R}_{{\rm{H}}{\rm{i}}}})\,{R}_{\mathrm{optical}}$ or R_{H i} ≲ 4.2 R_optical so that we can estimate whether or not the pair candidate and its nearest minor neighbor are both enclosed within the H i radio beam. We extract the effective radius of the minor neighbors for each pair candidate from the NSA galaxy catalog. When we examine the neighborhood of our pair candidates, we check whether the Δθ_beam = 88 H i beam overlaps with our pair candidate and its associated companion galaxy. For pair candidates in close pairs with θ_sep + R_{H i,nbr,max} ≤ Δθ_beam/2, we determine the neutral gas fraction of the pair by ${f}_{\mathrm{gas}}=1.4{M}_{{\rm{H}}{\rm{i}}}/(1.4{M}_{{\rm{H}}{\rm{i}}}+{M}_{\star ,\mathrm{total}}),$ with ${M}_{\star ,\mathrm{total}}$ the total stellar mass of the pair candidate and its associated neighbor, where θ_sep is their angular separation and where we used the effective radius of the neighboring galaxy to determine the maximum radial extent of its H i emission (${R}_{{\rm{H}}{\rm{i}},\mathrm{nbr},\max }$). Overall, pairs that are within a projected separation of d_proj ≤ 200 kpc tend to both be enclosed within the H i beam coverage. Therefore, the neutral gas fraction for the close pair that is both enclosed within the H i beam represents an average fraction for both of the galaxies in that pair, whereas the neutral gas fraction for a galaxy pair with a greater angular separation is representative of only the pair candidate observed by MaNGA. In Figure 7, we show the neutral gas fraction of our control galaxies and pair candidates as a function of their stellar mass; we include close pairs within the H i beam in the right-hand panel, and the middle panel only displays the neutral gas fraction for distant pairs where their companion galaxies lie outside of the H i beam.

We find no distinct differences in the neutral gas fraction of pair candidates with a stellar mass ratio of M_Neighbor/M_Candidate ≥ 0.1 and control galaxies (see Figure 7). We further check whether the neutral gas fraction of our pair candidates vary with projected separation. We find that the neutral gas fraction of our pair candidates is d_proj independent (see Figure 8). We observe that those pair candidates with a stellar mass ratio of M_Neighbor/M_Candidate < 0.1 possess relatively lower neutral gas fraction and lower SF strength compared to those galaxies with higher stellar mass ratio, which implies that their low neutral gas fraction may be responsible for the weak SF activity in those galaxies. We also find that galaxies with $\mathrm{log}({\rm{\Sigma }}\mathrm{SFR}/{M}_{\star })\geqslant -11$ generally have a neutral gas fraction of f_gas ≥ 0.6.

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6.1. The Comparison with the SBP15 Study

6.1.1. Comparison of Sample Selection Procedures

The SBP15 study selects their galaxies from the SDSS Data Release 7, whereas our galaxy sample is selected from the MPL-7 in SDSS DR15. Their galaxy sample spans a mass range of 7 ≤ log(M_⋆/M_⊙) ≤ 9.7 at the redshift of 0.005 < z < 0.07. The median stellar mass of their sample is log(M_⋆/M_⊙) = 8.9, whereas the pair candidates in our sample have a median stellar mass of log(M_⋆/M_⊙) = 9.5. The isolated dwarf pairs in the SBP15 study are all at least 1.5 Mpc away from galaxies with log(M_⋆/M_⊙) > 9.7. Their galaxy pair sample includes a main sample with a projected separation of less than 50 kpc and extended sample with a projected separation of out to 300 kpc. They use these selected pairs to explore how the SFR in these galaxies varies as a function of projected separation. More than 90% of their galaxy sample have a velocity separation Δv_LOS < 150 km s⁻¹. Isolated dwarf pairs in SBP15 study have a higher-mass compared to the lower-mass companion galaxy with stellar mass ratios of M_⋆,high/M_⋆,low ≤ 10, but most of their pairs have the stellar mass ratio ${M}_{\star ,\mathrm{high}}/{M}_{\star ,\mathrm{low}}\leqslant 5$ and only 4 of 60 pairs have stellar mass ratio $5\,\lt {M}_{\star ,\mathrm{high}}/{M}_{\star ,\mathrm{low}}\leqslant 10$.

We outline our selection procedure in Section 3 above. Here we summarize the differences in the selection criteria used in the SBP15 study and this work. Both our pair candidates and the isolated dwarf pairs in the SBP15 study are not accompanied by massive galaxies within the projected radius of d_proj ≤ 1500 kpc. However, we define the stellar mass of a massive neighboring galaxy differently. The SBP15 study considers all galaxies with $\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 9.7$ to be a massive galaxy; we identify massive galaxies to be ones with a stellar mass ratio that exceeds the stellar mass ratio for each pair candidate and its corresponding neighbor by a stellar mass ratio of M_Neighbor/M_Candidate > 4. Another major difference is in the range of their projected separation. The SBP15 study focuses on pairs that have a projected separation to d_proj ≤ 50 kpc as these galaxies have a higher probability of experiencing a nonnegligible tidally interacting with their companion. They select this limit because SF enhancements in interacting galaxies have been primarily observed in massive galaxy pairs that have separations around half of the virial radius (e.g., Patton et al. 2013). The SBP15 study estimated that their low-mass galaxies have a typical virial radius of r_vir ≈ 120 kpc and therefore they anticipate that interaction signatures will be observable for pairs with a separation range of d_proj ≲ 50 kpc. Because our galaxies span a similar stellar mass range, it is reasonable to assume that they have a similar virial radius to those galaxies in the SBP15 study. We have 22 pair candidates in our sample that have a projected separation of less than half a virial radius (${r}_{\mathrm{vir}}/2\approx 60\,\mathrm{kpc}$); 265 of our pair candidates span a projected separation between $60\leqslant {d}_{\mathrm{proj}}\leqslant 1500\,\mathrm{kpc}$. We include galaxies that span a larger range of projected separations because we are able to spectroscopically explore the SF properties of our galaxy sample out to a larger galactic radius of R = 1.5 R_e, and we did not want to assume a priori that the outskirts of the galaxies are not influenced by their companions at larger separations. In contrast, the SBP15 study only spectroscopically explores their galaxies toward the optically brightest location in their galaxy, which is most often at the central region of their galaxies. Further, we also did not want to assume that the typical separation of half a virial radius or less for SF enhancements occurs in large galaxy pairs applied to low-mass pairs, as Geha et al. (2012) suggest that galaxies with $\mathrm{log}({M}_{\star }/{M}_{\odot })\gt 9$ can still leave imprints on SF activity in their neighboring galaxies at a distance of 1.5 Mpc. In this way, this large projected separation enables us to explore if and at what projected separation the SF becomes enhanced in different radial regions within our galaxy sample. In Section 5.1, we found that the SF in low-mass galaxies can be affected by a low-mass companion galaxy out to a projected separation of d_proj ≲ 400 kpc (see Figure 6).

The galaxies in the SBP15 sample are intentionally selected to be star forming within the 3'' SDSS single fiber, which is classified using the [N ii] BPT line-ratio cutoffs given in Kauffmann et al. (2003a). We do not perform this selection criterion for our sample, but we do examine the ionization mechanism of our galaxies using the MaNGA spatially resolved data. We found that around 75% of our galaxies would be classified as "star forming" using this classification scheme within the SDSS single-fiber coverage. We also compare our calculation results to the single-fiber classifications published by Kauffmann et al. (2003a) on the SDSS CasJobs workbench and our classifications are found to be consistent.

Like the work in the SBP15 study, our exploration of the neutral gas fraction of our sample occurred after our galaxies were already selected for our study. The analysis in the SBP15 study suggests that the enhanced SFR in their isolated dwarfs are not strong enough to deplete their gas, because there are no significant differences in neutral gas fraction between their isolated dwarf pairs and control group. Galaxies in their study are also found to be gas rich (f_gas > 0.6) in general, and their neutral gas fraction is not separation dependent. The neutral gas fraction for our galaxies has a higher dispersion, which could be related to their slightly higher stellar mass than those galaxies in the SBP15 study (Figure 1) as galaxies with higher stellar mass generally have lower neutral gas fraction (e.g., Diemer et al. 2019).

6.1.2. Comparison of SFR Trend

To conduct a comparison with the SFR trends in the SBP15 study, we only use a subset of our sample to better match the sample used in their study. This subset only includes galaxies with a stellar mass of $\mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 9.7$ and pair candidates with a stellar mass ratio of 0.25 ≤ M_Neighbor/M_Candidate ≤ 4.0 and that span a velocity separation of 0 ≤ Δv_LOS ≤ 100 km s⁻¹ to their nearest minor neighbors. We additionally exclude one control galaxy (PlateIFU = 9891-1901) and one pair candidate (PlateIFU = 8941-6101) from this subset because they were not observed in the SDSS single-fiber survey; thus, we are unable to characterize their star formation properties within the 3'' single-fiber radius without making assumptions on where the single fiber would have been positioned. This comparison subset consists of 72 control galaxies and 77 pair candidates.

We determined our SFRs slightly differently than the SBP15 study. Here we summarize those differences. In our work, we use the data from the MaNGA IFU survey and the location of the single SDSS fiber in the NSA galaxy catalog to recover the SFR within the 3'' fiber (SFR_Fiber) for our galaxies. The position of the SDSS single-fiber observations tends to be at the brightest optical spot of the galaxy, which is most often the center of the galaxy, but is sometimes a bright star-forming knot. The SFR_Fiber is derived from the product of star formation surface density within the fiber coverage (ΣSFR_Fiber) and the area of the 3'' fiber, where the ΣSFR_Fiber is derived using the SFR summed up from all valid spaxels within the fiber coverage (around 37 on average) divided by the area of those included spaxels within the 3'' fiber (Figure 9). Further, to ensure that we account for the fractional area of MaNGA spaxels that are only partially within a 3'' fiber beam coverage, we do this by weighting the star formation of the spaxels on the edge of the region of interest by the fraction of area that is within the beam footprint. Our SFR trend for pair candidates is revealed by using the moving-average method. It should be noted that our pair candidates are the only component galaxy in each galaxy pair that are observed by MaNGA with the exception of one galaxy pair that had both components observed in the MaNGA survey. Therefore, our SFR trend is estimated using the SFR of one member in each galaxy pair, whereas the SBP15 study used both members of the pair. Additionally, we calculate the average SFR of all our control galaxies to construct a uniform average control level as the standard level when we examine the environmental impact on the star formation in low-mass galaxies. Our control galaxies have $\mathrm{log}[{\mathrm{SFR}}_{\mathrm{fiber}}/({M}_{\odot }\,{\mathrm{yr}}^{-1})]=-1.36\pm 0.05$ and $\mathrm{log}[({\mathrm{SFR}}_{\mathrm{fiber}}/{M}_{\star })/{\mathrm{yr}}^{-1}]=-10.46\pm 0.06$.

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The SBP15 study extracted their SFRs from Brinchmann et al. (2004), which were derived by applying the luminosity–SFR relation and calibrator in Kennicutt (1998); this enabled them to calculate the average SFR of both members in the associated dwarf pair. Furthermore, every dwarf pair in the SBP15 study has a matched isolated dwarf with similar stellar mass and redshift. The SFR trend in the SBP15 study for their isolated dwarf pairs and matched isolated dwarfs is estimated from the average SFR in bins of 50 kpc projected separation (left panel of Figure 5 in the SBP15 study); the SFRs for those matched isolated dwarfs are estimated in each separation bin to represent the control level of star formation. Because the SBP15 study and our work use different luminosity–SFR calibrator ν², we apply a ${\nu }_{\mathrm{SFR}}^{2}$-scale factor to achieve consistent SFRs.

In general, the ${\mathrm{SFR}}_{\mathrm{Fiber}}$ trends for our pair candidates and control galaxies match those trends found in the SBP15 study in that we also observe an increase in SFR at small projected separations of ${d}_{\mathrm{proj}}\lesssim 100\,\mathrm{kpc}$ and that our control levels are similar (see Figure 10). Our ${\mathrm{SFR}}_{\mathrm{Fiber}}$ trends support those results in the SBP15 study that the SFR is enhanced within the SDSS single-fiber coverage when the projected separation is less than 100 kpc, but it is also noticeable that some of our pair candidates have significantly high SFRs throughout the entire projected separation range of d_proj ≤ 1500 kpc. We check the stellar mass for those active star-forming galaxies in Figure 9, and it turns out that those galaxies also have higher stellar mass than others. This fact is consistent with the well-accepted tight correlation between SFR and stellar mass (the SF main sequence).

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We further examine the scale of the SF enhancement by normalizing our SFR trend as a function of d_proj with the control level (bottom panel of Figure 10). We find that there is a significant enhancement in the SFR for galaxies with a projected separation of d_proj ≤ 100 kpc that peaks at ${\mathrm{SFR}}_{\mathrm{Fiber},\mathrm{pair}}/{\mathrm{SFR}}_{\mathrm{Fiber},\mathrm{control}}=4.6\pm 2.6$ (see Figure 11). The SBP15 study observed an enhancement of only ${\mathrm{SFR}}_{\mathrm{Fiber},\mathrm{pair}}/{\mathrm{SFR}}_{\mathrm{Fiber},\mathrm{control}}=2.3\pm 0.7$, which is a factor of 2.0 ± 1.3 less than the value in our results. This difference could be in part because we did not have as many extremely low-mass galaxies as the SBP15 study had within the stellar mass range of $7\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 8$, which are generally expected to have weaker star formation according to the star formation main sequence. Further, around 55% of our pair candidates have a higher stellar mass than its associated companion (Figure 12). We refer to the galaxy that has a greater stellar mass in the pair as the "primary" component and the less massive companion as the "secondary" component. Kaviraj (2014) found that during tidal interaction, the primary component in galaxy pairs tends to experience greater SF enhancement than the secondary component. We also observe that the enhancement of SF strength within the SDSS 3'' fiber coverage peaks at ${f}_{{\rm{\Delta }}\mathrm{SF},\mathrm{Fiber}}=1.75\pm 0.95$ for our pair candidates within a projected separation of ${d}_{\mathrm{proj}}\leqslant 100\,\mathrm{kpc}$ (see Figure 11). This is essentially the same as the results on SF enhancement we obtained for the spatially resolved inner region ($R\leqslant 0.5\,{R}_{{\rm{e}}}$) at ${f}_{{\rm{\Delta }}\mathrm{SF},\mathrm{Inner}}=1.75\pm 0.96$ (Figure 6 and Table 3).

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To further check our SF trend, we also explore the distribution of star formation within the entire $R\leqslant 1.5\,{R}_{{\rm{e}}}$, because it is possible that the star formation activities in galaxies are not well represented by their behavior within a single fiber. We use the ${\mathrm{SFR}}_{\mathrm{Fiber}}/{\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}}$ to investigate how much star formation occurring within the fiber region compares to the entire galaxy within the radial coverage of $R\leqslant 1.5\,{R}_{{\rm{e}}}$. The SFR within the entire $R\leqslant 1.5\,{R}_{{\rm{e}}}$ region (${\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}}$) is calculated by adding up the total SFR of all three radially binned regions, in which the total SFR for each binned region is estimated using the product of the respective ΣSFR and the region area. A high SFR fraction ${\mathrm{SFR}}_{\mathrm{Fiber}}/{\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}}$ correlates to a more representative SF behavior within the fiber coverage. On average, our control galaxies have ${({\mathrm{SFR}}_{\mathrm{Fiber}}/{\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}})}_{\mathrm{mean}}=0.18$ (see Figure 13), which suggests that the SDSS 3'' fiber region contributes 18% of the SF budget within the region R ≤ 1.5 R_e for these galaxies. For those pair candidates with SF strength above the control level, their SFR fractions are normally greater than 0.25. Overall, we find that this SFR fraction is independent of the projected separation for our pair candidates, which is shown by the color of the data symbols in the top panel of Figure 10. This SFR fraction is also found to be independent of d_proj for those pair candidates.

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We also use the high-ΣSFR fraction within R ≤ 1.5 R_e to describe how SF spread out within the entire galaxy (the color coding in the bottom panel of Figure 10). The high-ΣSFR fraction (${f}_{\mathrm{high}\mathrm{SF}}$) is calculated from ${f}_{\mathrm{high}\mathrm{SF}}\,={N}_{\mathrm{pix},\mathrm{highSF}}/{N}_{\mathrm{pix},\mathrm{all}}$, where ${N}_{\mathrm{pix},\mathrm{all}}$ is the total amount of spaxels within R ≤ 1.5 R_e and ${N}_{\mathrm{pix},\mathrm{highSF}}$ describes how many spaxels with ΣSFR higher than the average ΣSFR of spaxels in control galaxies. The average star formation surface density of our control galaxies is ${({\rm{\Sigma }}\mathrm{SFR})}_{\mathrm{mean}}=0.005\,{M}_{\odot }\,{\mathrm{yr}}^{-1}\,{\mathrm{arcsec}}^{-2}$ within the radial region of R ≤ 1.5 R_e. On average, our control galaxies have a high-ΣSFR fraction of ${f}_{\mathrm{high}\mathrm{SF}}=28 \%$ (see Figure 13).

For these control galaxies and pair candidates in this comparison subset, we find no distinct differences in the distribution of their SFR fraction ${\mathrm{SFR}}_{\mathrm{Fiber}}/{\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}}$ and ${f}_{\mathrm{high}\mathrm{SF}}$ (see Figure 13). Around 15.2% control galaxies and 18.3% pair candidates have ${f}_{\mathrm{high}\mathrm{SF}}$ higher than the average control level but their ${\mathrm{SFR}}_{\mathrm{Fiber}}/{\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}}$ are lower than the average value in control galaxies, which suggests that these galaxies have strong SF activities occurring outside of the fiber coverage. Therefore, galaxies with high ${f}_{\mathrm{high}\mathrm{SF}}$ do not necessarily have high ${\mathrm{SFR}}_{\mathrm{Fiber}}/{\mathrm{SFR}}_{1.5{R}_{{\rm{e}}}}$. The star formation activities in those galaxies with displaced SF may not be properly represented by their SFR within the fiber coverage.

6.2. SF Activities in Recovered and Robust Galaxies

6.2.1. Robust Galaxies RB1–RB3

There are three Robust galaxies (RB1–RB3 in Figure 14) that are found to have a ${\rm{\Sigma }}\mathrm{SFR}/{M}_{\star }$ over 10 times higher than the average control level throughout the three radially binned regions. The RB1 galaxy originates from the "Pair" category, and the d_proj is around 957 kpc to its nearest neighbor. The RB2 galaxy and RB3 galaxy are originally in the "Control" category. None of these RB galaxies have extra-close neighbors in their surrounding environments.

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Figure 14 reveals that these RB galaxies are all relatively compact, as their effective radius are all found to be around 5''. The strength of Hα emission compared to the stellar continuum can be traced by the equivalent width (EW) of the Hα line; the Hα EW are all significantly higher in the galactic center for these RB galaxies. Their spatially resolved SFR maps also demonstrate that their SF activities are all concentrated in the central region. We further adapt the BPT diagnostic diagram with those classification lines in Kewley et al. (2001) and Kauffmann et al. (2003a) to investigate the ionization mechanism in those galaxies; all involved emission lines are required to have equivalent width greater than 1 Å. The region labeled as "Star-forming" (SF) is ionized by the SF activity, and the "Active galactic nuclei" (AGN) area is powered by AGNs or other ionization mechanisms that are much more energetic than SF activities. The "Composite" (COMP) area is a mixture of the region powered by AGNs and SF. The spatially resolved BPT maps show that the ionization in these RB galaxies is all dominated by SF activities.

6.2.2. Recovered Galaxies RC1–RC4

Four galaxies are found to have recovered close neighbors through a visual check on the SDSS SkyServer. These "recovered" (RC) pairs are photometrically identified and recovered neighbors for those MaNGA galaxies were not present in the NSA galaxy catalog. These galaxies in the "RC" category are shown in the bottom four rows of Figure 14. The RC1 galaxy originates from the "Pair" category and its nearest neighbor in the NSA catalog is d_proj ≈ 1400 kpc away; the rest of the three RC galaxies are originally in the "Control" category. For each recovered galaxy, we estimate their projected separations using their R.A. and decl. position information provided by SDSS SkyServer photometry data. We do not know the redshift and stellar mass of these recovered neighbors due to the lack of spectroscopy observation. The line-of-sight kinematic separations and stellar mass ratios are vague for these recovered galaxy pairs, which makes it difficult to examine to which environmental bins in Figure 5 they belong.

The star formation strength of those recovered galaxies is not significantly enhanced compared with the average control level for any radially binned region (Figure 15). The SFR within the fiber coverage for RC1–RC3 galaxies is considerably higher than the average level of control galaxies (SFR_Fiber ≈ 0.04 ${M}_{\odot }\,{\mathrm{yr}}^{-1}$). However, it is unclear whether this active star formation is triggered by the interaction because although these galaxies are spatially close to their companions on the sky, we do not know their line-of-sight kinematic separation.

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We explore the environmental influences on star formation activities in low-mass galaxies using the SDSS-IV/MaNGA spatially and spectroscopically resolved data set for 386 low-mass galaxies with stellar mass $8\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 10$ at a redshift of 0.01 < z < 0.07. We use these observations specifically to explore how different configurations of projected separation, line-of-sight kinematic separation, and the stellar mass ratio of galaxy pairs impact their star formation strength at different galactic radii compared to the isolated control galaxy sample. In this study, we intentionally exclude low-mass MaNGA galaxies that are accompanied by a higher-mass neighboring galaxy (M_Neighbor/M_MaNGA > 4) within a projected distance of d_proj ≤ 1500 kpc as tidal interactions with a massive galaxy can trigger the star formation within a gas-rich satellite galaxy and can ultimately quench its star formation by stripping its gas. We identify the neighboring galaxies for our sample using the NSA galaxy catalog, which includes all galaxies with r-band Petrosian magnitude r ≤ 17.77 and spectroscopically determined redshift at z < 0.15 in the 13th data release of SDSS (SDSS DR13). Our pair candidates have projected separations of d_proj ≤ 1500 kpc and line-of-sight kinematic difference of Δv_LOS ≤ 300 km s⁻¹ to their nearest low-mass neighboring galaxies with stellar mass ratio of M_Neighbor/M_Candidate ≤ 4. Galaxies in our control group do not have neighboring galaxies at any given stellar mass in the NSA galaxy catalog within a projected radius of d_proj ≤ 1500 kpc. Our sample of low-mass galaxies are predominantly classified as star forming, with a mass-weighted star formation surface density that diminishes with radial distance from their galactic center.

We radially bin our selected galaxies into inner (0–0.5 R_e), middle (0.5–1.0 R_e), and outer (1.0–1.5 R_e) regions to investigate the variation of their star formation strength (${\rm{\Sigma }}\mathrm{SFR}/{M}_{\star }$) as a function of radial distance from their galactic center, where R_e is the effective radius where half of the light is emitted by the galaxy. We use the fractional change in star formation strength (f_ΔSF in Equation (2)) to describe how much the star formation activities in our selected galaxies are enhanced (f_ΔSF > 0) or suppressed (f_ΔSF < 0) under different environmental conditions compared to the average level of control galaxies. We summarize our conclusions as follows:

• 1.  
  Low-mass galaxies that are within Δv_LOS ≤ 100 km s⁻¹ of a lower-mass companion at M_Neighbor/M_Candidate < 0.1 tend to have weaker star formation activity when d_proj ≤ 400 kpc compared to the average level of those control galaxies with f_ΔSF ≈ −0.87 throughout the galaxy.
• 2.  
  Low-mass galaxies with Δv_LOS ≤ 100 km s⁻¹ possess enhanced star formation at d_proj ≤ 400 kpc when their neighboring galaxies have 4–10 times smaller stellar mass. We find that their star formation is elevated by an average level of f_ΔSF = 1.30 ± 0.61, 1.23 ± 0.60, and 0.71 ± 0.34 in the inner, middle and outer regions, respectively.
• 3.  
  We observe the strongest interaction-induced enhancement on star formation when the low-mass galaxies that are paired with other low-mass neighboring galaxies that have compatible stellar mass (with stellar mass ratio 0.25 ≤ M_Neighbor/M_Candidate ≤ 4). When these galaxies are within Δv_LOS ≤ 100 km s⁻¹ and d_proj ≤ 100 kpc from their companion, we find that their star formation is enhanced by ${f}_{{\rm{\Delta }}\mathrm{SF}}=1.75\pm 0.96$, 1.45 ± 0.73, and 0.93 ± 0.41 in the inner, middle and outer regions, respectively, compared to our isolated control sample.
• 4.  
  We find that the neutral gas fraction of our pair candidates and control sample does not vary with projected separation for close kinematic pairs with Δv_LOS ≤ 100 km s⁻¹. We also find that the pair candidates with stellar mass ratio M_Neighbor/M_Candidate ≥ 0.1 have a similar neutral gas fraction to the control group. All star-forming low-mass galaxies with $\mathrm{log}({\rm{\Sigma }}\mathrm{SFR}/{M}_{\star })\geqslant -11$ have a neutral gas fraction that is ${f}_{\mathrm{gas}}\leqslant 0.6$. Galaxies in our sample tend to have a lower neutral gas fraction when they are accompanied by a lower-mass companion with a stellar mass that is over 10 times smaller.
• 5.  
  We compared our spectroscopically and spatially resolved results with SFRs derived within the SDSS 3'' single-fiber footprint for selected pair candidates with a stellar mass of $8\leqslant \mathrm{log}({M}_{\star }/{M}_{\odot })\leqslant 9.7$. We found that their average SFR becomes significantly higher than the control sample when ${\rm{\Delta }}{v}_{\mathrm{LOS}}\leqslant 100\,\mathrm{km}\,{{\rm{s}}}^{-1}$, ${d}_{\mathrm{proj}}\leqslant 100\,\mathrm{kpc}$, and stellar mass ratio $0.25\leqslant {M}_{\mathrm{Neighbor}}/{M}_{\mathrm{Candidate}}\leqslant 4.0$, peaking at ${\mathrm{SFR}}_{\mathrm{Fiber},\mathrm{pair}}/{\mathrm{SFR}}_{\mathrm{Fiber},\mathrm{control}}=4.6\pm 2.6$. The star formation strength of these galaxies within the fiber coverage is enhanced by ${f}_{{\rm{\Delta }}\mathrm{SF},\mathrm{Fiber}}=1.75\pm 0.95$.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the US 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 website is www.sdss.org.

SDSS-IV 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, Observatário 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.

The Hα-based SFRs for all selected galaxies are calculated using the methods in Section 4. The complete set of the 2D SFR maps for all galaxies in our sample is presented in Figure 16.

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View extended figure (10 panels)