Close Major Merger Pairs at $z=0$: Bulge-to-Total Ratio and Star Formation Enhancement

We present a study of the bulge-to-total ratio (B/T) of a Ks-band-selected sample of 88 close major-merger pairs of galaxies (H-KPAIR) based on 2-D decomposition of SDSS r-band images with \textsc{galfit}. We investigate the dependence of the interaction-induced specific star formation rate enhancement ($\rm sSFR_{enh}$) on the B/T ratio, and the effects of this dependence on the differences between star-forming galaxies (SFGs) in spiral+spiral (S+S) and spiral+elliptical (S+E) pairs. Of all 132 spiral galaxies in H-KPAIR, the 44 in S+E pairs show higher B/T than those in the 44 S+S pairs, with means of $\rm B/T = 0.35 \pm 0.05$ and $\rm B/T = 0.26 \pm 0.03$, respectively. There is a strong negative dependence of $\rm sSFR_{enh}$ on the B/T ratio and only paired SFGs with $\rm B/T<0.3$ show significant ($>5\sigma$) enhancement. Paired SFGs in S+S pairs show a similar trend, and many disky SFGs ($\rm B/T<0.1$) in S+S have strong sSFR enhancements ($\rm sSFR_{enh}>0.7$~dex). For SFGs in S+E, the sSFR has no clear B/T dependence, nor any significant enhancement in any B/T bin. Disky SFGs in S+S show significant ($>4\sigma$) enhancement in the molecular gas content ($\rm M_{H_2}/M_{star}$), while SFGs in S+E have no such enhancement in any B/T bin. No significant enhancement on total gas content ($\rm M_{gas}/M_{star}$) is found in any B/T bin for paired galaxies. The star formation efficiency of either the total gas ($\rm SFE_{gas} = SFR/M_{gas}$) or the molecular gas ($\rm SFE_{H_2} = SFR/M_{H_2}$) does not depend on the B/T ratio. The only significant ($>4\sigma$) SFE enhancement found for paired SFGs is the $\rm SFE_{gas}$ for disky SFGs in S+S pairs.


INTRODUCTION
It has been well established that galaxy interactions and mergers can induce star formation enhancement (Toomre & Toomre 1972;Larson & Tinsley 1978;Kennicutt et al. 1987;Sanders & Mirabel 1996). In the local universe, the most extreme starbursts such as the ultraluminous infrared galaxies (ULIRGs : L IR ≥ 10 12 L ⊙ ) are exclusively found in the final stage of mergers (Sanders & Mirabel 1996). Significant star formation enhancements are also detected in interacting galaxies in earlier merger stages such as those in optically selected pairs (Kennicutt et al. 1987; Barton et al. 2000;Xu & Sulentic 1991;Nikolic et al. 2004;Ellison et al. 2010;Scudder et al. 2012). Statistical studies based on large surveys found that, among early stage mergers, star-forming galaxies (SFGs) in close major-merger pairs (separation 30 kpc and mass-ratio 3) have the highest star formation rate (SFR) enhancement (Xu & Sulentic 1991;Scudder et al. 2012;Patton et al. 2013). However, Spitzer observations of a sample of Ks-band-selected close major-merger pairs (Xu et al. 2010) found that only ∼ 25% of SFGs in the sample show strong enhancement in specific star formation rate (sSFR = SFR/M star ). Furthermore, the farinfrared (FIR) observations by Spitzer and Herschel show that only SFGs in spiral-spiral (here after S+S) pairs have significantly enhanced sSFR, but not those in spiral-elliptical (here after S+E) pairs (Xu et al. 2010;Cao et al. 2016;Domingue et al. 2016). The GBT HI observations of Zuo et al. (2018) and IRAM CO observations of Lisenfeld et al. (2019) for paired galaxies, selected from H-KPAIR sample of 88 close major-merger pairs that have Herschel FIR observations , found no significant difference between the total gas abundances of SFGs in S+E and in S+S pairs. These results reject the hypothesis that the lack of star formation enhancement in S+E pairs is due to stripping of cold gas of the spiral component by ram-pressure of the hot-gas halo surrounding the elliptical component (Park & Choi 2009;Hwang et al. 2011).
Simulations of interacting galaxies have shown that a massive bulge can stabilize the disk and suppress the SFR during and after close encounters (Mihos & Hernquist 1996;Di Matteo et al. 2008;Cox et al. 2008). This mechanism may play an important role in the low frequency of star formation enhancement in paired galaxies, in particular those in S+E pairs. However, there has been no observational test of the theoretical prediction in the literature. Indeed, such a test requires accurate estimates of the bulge-to-total (B/T) ratios of paired galaxies. Many works have been carried out on the task of decompositing large samples of galaxies with image fits (such as Simard et al. 2011;Lackner & Gunn 2012;Meert et al. 2015Meert et al. , 2016Kim et al. 2016). Simard et al. (2011) presented a two-dimensional, point-spread-functionconvolved, bulge-disk decompositions in the g and r bands on a sample of 1.1 million SDSS galaxies with gim2d (Simard et al. 2002). Lackner & Gunn (2012) made efforts on low redshift (z < 0.05) galaxies with their own pipeline. Meert et al. (2015) carried out decompositions in the r-band on 670,722 SDSS spectroscopic galaxies, a subsample of Simard et al. (2011), with galfit (Peng et al. 2002), and extended it to the g and i bands in Meert et al. (2016). Kim et al. (2016) provided a recipe for choosing the initial guess values of the input parameters based on galaxy color. However, these works are automated on bulks of sample without individual inspection, therefore, their results on interacting and distorted galaxies may not be reliable.
In this paper, we present our own bulge-disk decomposition for galaxies in the H-KPAIR sample , based on galfit and manual intervention deblending photometry. We study the effects of the central bulge on the star formation enhancement in paired galaxies. Using the H-KPAIR sample and a well matched control sample, we quantify these effects and examine how much the sSFR difference between S+E and S+S pairs is caused by them. The H-KPAIR sample and control sample are introduced in Section 2 and 4, respectively. In Section 3 we describe how we measure the B/T of H-KPAIR galaxies and compare our results with those in the literature. The science analyses are presented in Section 5, followed by a discussion in Section 6 and conclusions in Section 7. Throughout this paper, we adopt the Λ-cosmology with Ω m = 0.3 and Ω Λ = 0.7, and H 0 = 70 km s −1 Mpc −1 .
Our pair sample is identical with the local close majormerger sample H-KPAIR , which is a subsample of a complete and unbiased Ks-band (Two Micron All Sky Survey, 2MASS, Skrutskie et al. 2006;Jarrett et al. 2000a,b) selected sample KPAIR (Domingue et al. 2009). All H-KPAIR galaxies have spectroscopic redshifts in the range of 0.0067 < z < 0.1. The pair sample requires the projected separations range of 5 h −1 kpc ≤ s(p) ≤ 20 h −1 kpc, the radial relative velocity δ(Vz) < 500 km s −1 and the Ks-band magnitude differences within 1 mag (corresponding to a mass ratio no greater than 2.5). H-KPAIR sample contains 44 S+S pairs and 44 S+E pairs, all have Herschel imaging observations in the 6 bands at 70, 110, 160, 250, 350, and 500 µm (Cao et al. 2016). Furthermore, in H-KPAIR, 70 pairs have single dish 21cm HI observations (Zuo et al. 2018) and 78 S galaxies are observed by the IRAM 30m telescope for CO emissions (Lisenfeld et al. 2019).
We adopt SFR of H-KPAIR galaxies in Cao et al. (2016), which are derived from L IR (8-1000 µm; Sanders & Mirabel 1996) using the formula of Kennicutt (1998), with an additional correction factor of 10 −0.20 for the conversion from the Salpeter IMF to the Kroupa IMF (Calzetti 2013), where the L IR is generated from SED fits with the dust emission model of Draine & Li (2007) In Cao et al. (2016) the stellar mass M star of H-KPAIR galaxies was estimated from the Ks-band luminosity using a constant mass-to-light ratio M star /L K (Xu et al. 2004;Domingue et al. 2009;Xu et al. 2012). This is because for normal galaxies both the near infrared (NIR) emission and the stellar mass are dominated by the old stellar populations and therefore the M star /L K ratio is nearly independent of the galaxy types (Gavazzi et al. 1996). On the other hand Bell & de Jong (2001) showed a color dependence of the M star /L K ratio caused by variations of the star formation history, although it is significantly weaker than that for the mass-to-light ratio in optical bands. In this paper, we improve the stellar mass estimate by including a g-r color dependence in the M star /L K ratio. To derive the g-r color for a galaxy, we make 25 mag arcsec −2 isophotal photometry using sextractor (Bertin & Arnouts 1996) on the SDSS r-band image and apply the same isophotal aperture to the g-band image. For H-KPAIR sample, we visually check and optimize the segmentations for all the pairs. When sextractor fails to make good deblending for a merger, we manually draw polygon apertures for them and use the 25 mag arcsec −2 isophot of the whole merger to determine the outer boundaries of the apertures for both galaxies. We exploit the stellar mass derived in GALEX-SDSS-WISE LEGACY CATALOG (GSWLC; Salim et al. 2016Salim et al. , 2018 for the calibration of the relation between M star /L K and g-r. Among 1320 of our control galaxies, 1180 have M star measurements in the GSWLC-2 (Salim et al. 2016(Salim et al. , 2018. For them we carry out a linear regression between the M star,GSWLC,cor /L K and the g-r color, where the M star,GSWLC,cor is the stellar mass in GSWLC-2 after correcting the difference between the cosmology parameters used in GSWLC-2 and in this paper. After excluding the 3σ outliers iteratively and assuming M star,GSWLC,cor is a good M star estimator, we obtain the following relation: The result is shown in Figure 1. The M star of galaxies in our samples are calculated using the formula in Equation 1.

TWO-COMPONENT MODEL FITS (GALFIT) OF H-KPAIR
We carry out two-component two-dimensional fits on SDSS r-band images with galfit (Peng et al. 2002). The Sérsic (1968) and Exponential (Freeman 1970) light profiles are adopted for the bulge and the disk, respectively. This method has been well tested (e.g., Meert et al. 2015;Kim et al. 2016) on the task of decomposing the bulge and the disk of SDSS local galaxies. We constrain the Sérsic index of the "bulge" component in the range of 1 ≤ n ≤ 8.
Because some of our galaxies are on the edge of the field, or even be cut into multiple parts found in differ- ent fields, we use the SDSS SAS mosaic tool 6 , which can stitch together several sky-subtracted, calibrated frames 7 to form a coherent image over a specify patch of sky using the swarp (Bertin et al. 2002). According to Meert et al. (2015), the image should have at least 20 half-light radii to provide enough pixels for background. We use images of 909 × 909 pixels uniformly for the fits of nearly all of our sample galaxies, corresponding to 0. • 1 square sky, since the half-light radii of them are no more than 45 pixels derived from sextractor. The only exception is galaxy J20471908+0019150 (of pair J2047+0018), the largest galaxy in our sample (size ∼ 3 ′ ), for which an image of 1818 × 1818 pixels is used. The image mask is generated based on the sextractor segmentation image. We first run sextractor with the detect threshold set at 25 mag arcsec −2 to detect all the "source" out of sky background. Then we identify our target galaxies visually and set segmentation area of other sources for mask. We also edit mask areas manually when sextractor fails to deblend the sources.
The point-spread-function (psf) is generated from the PsField files 8 using the code readatlasimages-v5 4 11 provided by SDSS 9 .
We calculate an equivalent gain GAIN eq and let galfit generate the Poisson-noise sigma image itself. GAIN eq is defined as GAIN eq = GAIN/cimg, where 6 dr12.sdss.org/mosaics/ 7 data.sdss.org/datamodel/files/BOSS PHOTOOBJ/frames/RERUN/RUN/ 8 data.sdss.org/datamodel/files/PHOTO REDUX/RERUN/RUN/objcs/CAM 9 classic.sdss.org/dr7/products/images/read psf.html GAIN is the original CCD gain and cimg the calibration factor from DN into nanomaggie, both are listed in the SDSS website 10 .
The standard galfit two-component fits is carried out for most H-KPAIR galaxies. Simultaneous fits of both galaxies in a pair are carried out for 61 close pairs, and galaxies in the other 16 well separate pairs are fitted individually. These fits yield reasonably good results, as illustrated by the examples shown in Figure 2 and Figure 3. However, the standard galfit process fails to work for several extremely distorted and merging pairs, either producing large chi-squares or not converging at all. For these cases (11 merging pairs), the following special procedure is performed. Firstly, we assume that bulges in these systems can still be well fitted by 2-D models. This is because, compared to the disks, bulges which are dynamically "hot" respond to tidal interactions more subtly. The triggered morphological distortions such as surface-brightness excess in the outer regions and slightly off-enteric inner isophotes (Kormendy 1977;Aguilar & White 1986;Davoust & Prugniel 1988;Mora et al. 2019) shall have minimal effect on the 2-D model-fits for the estimate of the bulge luminosity. Accordingly, for each system, galfit is carried out in order to obtain the model fluxes of bulges while neglecting the goodness of the fits of the disks. And then, secondly, the total flux of each galaxy in a pair is measured by deblending photometry with sextractor 25 mag arcsec −2 or hand-drawn polygon apertures (see Section 2). An example is shown in Figure 4). The central isophotes (the red contours) of galaxies in this example show that the bulges are not strongly distorted. Nevertheless, the B/T ratios so obtained may have larger uncertainties than those from ordinary galfit. Indeed, among the 11 merging pairs, three galaxies have the model bulge flux larger than the total flux from polygon aperture photometry. Since these are likely bulge-dominated galaxies, they are regarded as having B/T = 1.
The galfit results are listed in Table 1. Note that for pairs with the two galaxies fitted simultaneously, the reduced chi-square χ 2 /ν is listed in the row of the first galaxy of each pair. For those only the bulge is fitted and the total flux obtained from 25 mag arcsec −2 isophot or polygon aperture (with flag bit 2), the m GAL is taken from the photometry, and the disk magnitude m D is calculated by subtracting the bulge flux from the total flux. Other disk parameters of these galaxies are not available, and their χ 2 /ν are not listed. We note that, even though galfit exploits psf deconvolved images, 10 data.sdss.org/datamodel/files/BOSS PHOTOOBJ/frames/RERUN/RUN/CAMCOL/frame.html any model component with radius significantly below the seeing (with a median FWHM of 1. ′′ 32) shall be taken with caution.  . This is an example of simultaneous fits of both galaxies in a pair using two Sérsic-bulge + disk models.  for the photometry on total fluxes of the two galaxies, and isophotal contours of the pair. The red contour levels are at 18. 5, 19, 19.5, and the green contour levels are at 20, 20.5, 21 mag arcsec −2 (no smoothing). The most inner isophot is still larger than the FWHM of the psf. This is an example of bulge fits and deblending photometry on distorted galaxies. The compact, undistorted, high Sérsic index component-bulge-is constrained well by the brightest pixels on the galaxy center, and is fitted well, although an exponential ellipse cannot represent the distorted disk reasonably.    · · · · · · · · · · · · 2 Table 1 continued  Note-The columns are: (1) galaxy name; (2) redshift (after the correction for Virgocentric flow); (3) galaxy morphology: 'S' for Spiral, 'E' for Elliptical, and interaction type : 'J' for JUS, 'I' for INT, 'M' for MER; (4) magnitude taken from sextractor 25 mag arcsec −2 isophot or polygon aperture; (5) model magnitude taken from galfit, except for distorted galaxies (with flag bit 2) for which this is exactly the same as observed magnitude; (6) Bulge−to−Total ratio (B/T); (7) bulge magnitude; (8) bulge Sérsic index; (9) bulge effective radius, noting that all the radii (re or rs) less than 0.05 are recorded as 0.0 in this table due to the limit of decimal places; (10) bulge axis ratio; (11) bulge position angle (the counterclockwise angle between the major axis of the ellipse and North, and the same for disk position angle); (12) disk magnitude; (13) disk scale length; (14) disk axis ratio; (15) disk position angle; (16) reduced Chi−square; (17) binary flag in decimal number: Bit 0 (0, 0x0) -galaxy fitted separately, Bit 1 (1, 0x1) -galaxy fitted in pair, Bit 2 (2, 0x10) -distorted galaxy with the bulge fitted by model and the total flux measured by photometry, Bit 3 (4, 0x100) -the fitted bulge is brighter than the total flux of the galaxy obtained in aperture photometry, Bit 4 (8, 0x1000) -the magnitude difference between model and isophot is significant.
As a quality check, in Figure 5 we compare the setractor 25 mag arcsec −2 isophotal photometry magnitude and model magnitude (the sum of the bulges and the disks) of 155 galaxies that are fitted using standard galfit. Because the isophotal photometry may miss fluxes from the outskirts of galaxies, especially of ellipticals, while the galfit models are extended to infinity, there is an offset between the isophotal and model magnitudes. For paired galaxies in our sample, the galfit magnitude m GAL are on average brighter than the isophotal magnitudes by −0.11 mag with a standard deviation of 0.17 mag. There are 7 galaxies with large mag GAL − mag iso deviations from the mean (> 2σ) and they are flagged with it Bit 4 (8, 0x1000) in Table 1. The only one with > 3σ deviation is contaminated from a nearby galaxy. We note that the galfit results of these galaxies should be taken with caution.
Bulges can be separated into pseudo-bulges and classical bulges. The pseudo-bulges have Sérsic index n = 1-2 (Kormendy & Kennicutt 2004). While the classical bulges may stabilize the gas disk and suppress the star formation in paired galaxies (Mihos & Hernquist 1996) and in normal galaxies (Martig et al. 2009), the pseudobulges are commonly associated with bars and nuclear disks or rings (Kormendy & Kennicutt 2004) which are disk phenomena, and which themselves may be triggered by interaction and associated with enhanced nuclear star formation (Chown et al. 2018;Erwin et al. 2021). Therefore, we treat all galaxies in our pair sample with bulge Sérsic index n ≤ 2 as disk-only and assign B/T = 0 to them hereinafter. It is worth noting that some pseudo-bulges are not related to nuclear star for- mation and are mostly found in late-type spirals with relatively low B/T ratios (Kim et al. 2016). Treating them as disky galaxies (i.e. B/T = 0) shall not introduce significant bias in our results. For the sSFR enhancement analysis, we are only interested in the B/T ratios of spiral galaxies. Figure 6 presents the histograms of B/T ratio distributions of spiral galaxies in S+S and S+E pairs separately. We find spiral galaxies in S+E pairs have larger bulges (at a mean B/T = 0.35 ± 0.05) than their counterparts in S+S pairs (at a mean B/T = 0.26 ± 0.03) statistically. In particular, 50% (44/88) of spirals in S+S pairs are disky galaxies with B/T < 0.1, while the number in S+E pairs is 32% (14/44). On the other hand, 34% (15/44) of spirals in S+E pairs are bulge dominated with B/T > 0.5, while this percentage for those in S+S pairs is 24% (21/88).

CONTROL SAMPLE
In order to quantify the sSFR enhancement, a control sample of single spiral galaxies is selected from the catalog of Meert et al. (2015). For each paired spiral galaxy 10 control galaxies are selected. Every control galaxy must meet the following criteria: 1. Should be identified as spiral in Galaxy Zoo (Lintott et al. 2008).
2. Not in any interacting system, namely no neighbor galaxy in the SDSS database which has projected distance ≤ 100 kpc and observed redshift difference ≤ 1000 km s −1 .
4. The L K matches that of the paired galaxy within 0.1 dex (or 0.2 dex for controls of 5 H-KPAIR galaxies which have too few control candidates).
5. The B/T ratio matches that of the paired galaxy with δ(B/T) < 0.1, except for paired galaxies of B/T ≥ 0.8 whose controls shall also have B/T ≥ 0.8.
6. Match of local density: we adopt a local density indicator N 1Mpc , which is the count of galaxies brighter than M r = −19.5 and with redshifts differing less than 1000 km s −1 from that of the target galaxy, in the surrounding sky area of radius = 1 Mpc (the count includes the target galaxy itself if it is brighter than M r = −19.5). By means of N 1Mpc , we classify galaxies into 4 environmental categories: field (N 1Mpc ≤ 3), small group (4 ≤ N 1Mpc ≤ 6), large group (7 ≤ N 1Mpc ≤ 10), and cluster (N 1Mpc > 10). The control galaxy shall be in the same environmental category of the paired galaxy.
7. Has the closest redshift, among all qualified candidates, to that of paired galaxy.
Finally, we have a control sample of 1320 (1167 unique) galaxies which are 10-to-1 matched to the 132 paired spiral galaxies in H-KPAIR. We allow galaxies to be included more than once in the control sample as long as there is no duplication among matches to any given paired galaxy. The M star of control galaxies are estimated from the L K and g-r color using the same method as that for paired galaxies (see Section 2).
In order to check whether the B/T ratios obtained using our method and those estimated by Meert et al. (2015) are consistent with each other, we make the following comparison. For each paired galaxy we pick out from the 10 matching control galaxies the one with the smallest χ 2 /ν in the table of Meert et al. (2015) and derive its B/T ratio using the same method that we used for H-KPAIR galaxies. In Figure 7, our results on the B/T ratios of the 132 such galaxies in the control sample are compared with the corresponding values in Meert et al. (2015). A good overall agreement is found. The average difference between the two results is only 0.002 with a standard deviation of 0.169. It is worth noting that, same as for paired galaxies, we assign B/T = 0 to all control galaxies with bulge Sérsic index n ≤ 2. However, there is a minor difference between paired and control samples in this treatment: For paired sample our galfit results give the n values in real numbers, while for the control sample, whose galfit results are taken from Meert et al. (2015), the n values are reduced to integers. This means that some of the control galaxies with n = 2 originally have the bulge Sérsic index in the range of 2 ≤ n < 2.5. In order to constrain the uncertainties due to this minor mismatch between the paired and control samples, we test our results with an alternative control sample in which galaxies with n < 2 (instead of n ≤ 2) are assigned B/T = 0. In this case, the treatment actually applies only to control galaxies with original bulge Sérsic index n < 1.5. No significant difference is found in any of our results when this alternative control sample is used.
The SFR of control galaxies is calculated from the Wide-field Infrared Survey Explorer (WISE, Wright et al. 2010a,b) w4-band 22 µm luminosity L 22µm , using the method given by Salim et al. (2016). Namely we estimate the total IR luminosity by fit the luminosity-dependent IR templates of Chary & Elbaz (2001) to match the L 22µm , then use the conversion given by Kennicutt (1998), adjusted to the Chabrier IMF using the 1.58 conversion factor (Salim et al. 2007). This yields the formula log(SFR WISE ) = log(L IR,CE ) − 9.966. (2) The SFR WISE so defined is different from the SFR of paired galaxies which are estimated using Herschel data . In order to make the two SFRs consistent with each other, we carried out the following analysis: Among the control galaxies of Cao et al. (2016), which are one-to-one matched to H-KPAIR spirals, 82 galaxies have both Herschel and AllWISE 22 µm SFRs detection. We selected the H-KPAIR control sample  instead of the pair members to avoid any pair blending issues in the 22 µm photometry. We carry out linear regression between SFR Herschel and SFR WISE of these galaxies, which is presented in Figure 8. The result shows that log(SFR Herschel ) = 0.89 × log(SFR WISE ) + 0.16. (3) This conversion is applied to the SFR WISE of our control galaxies to facilitate the comparison with paired galaxies. It is worth noting that the slightly non-linear relation between SFR Herschel and SFR WISE is likely due to the fact that the 22 µm emission in WISE w4band is predominantly powered by massive ionizing stars (> 10 M ⊙ ; Calzetti et al. 2007) while the total IR luminosity used in the estimate of SFR Herschel has significant contributions from intermediate and low mass stars and therefore decreases less rapidly when the massive star formation rate vanishes (Buat & Xu 1996). When a control galaxy has no detection in the WISE w4-band, the SFR upper limit is estimated from the upper limit of L 22µm .

DEPENDENCE OF sSFR ENHANCEMENT ON B/T RATIO
For individual spiral galaxies in the pair sample, we define an sSFR enhancement index sSFR enh as follow- Comparison between log(SFR Herschel ) and log(SFRWISE) for control galaxies in Cao et al. (2016). The solid line is the linear regression, and the dashed lines represent the 1σ region. ing: where sSFR pg is the sSFR of the paired spiral galaxy, and sSFR med,ctrl the median of the sSFR of the 10 control galaxies. Following Cao et al. (2016), spiral galaxies with log(sSFR/yr −1 ) < −11.3 are regarded as in the red sequence and thus excluded from the analysis. The remaining 98 SFGs in the H-KPAIR sample are divided into 4 B/T bins: disky galaxies (B/T = 0-0.1), galaxies with small bulge (B/T = 0.1-0.3), galaxies with large bulge (B/T = 0.3-0.5), and bulge dominant galaxies (B/T = 0.5-1). Their sSFR enhancement is plotted against the B/T ratio in Figure 9. We use Kaplan-Meier (K-M) estimator (Kaplan & Meier 1958;Feigelson & Nelson 1985) to take into account information in the upper limits. It shows that, for paired SFGs on the whole, there is a significant dependence of sSFR enh on B/T ratio. In particular, only galaxies in the first two bins (with B/T < 0.3) have the average sSFR enh significantly above zero while the average sSFR enh of the last two bins (with B/T > 0.3) are consistent with no enhancement, supporting the hypothesis that large bulges suppress interaction-induced star formation (Mihos & Hernquist 1996). Then, we divide the paired SFGs into S+S and S+E subsamples. For the SFGs in S+S pairs, the averages of sSFR enh in the four B/T bins show a similar but stronger trend of anticorrelation as that for the total sample. Very strong sSFR enhancements (sSFR enh > 0.7 dex) are found almost exclusively in disky SFGs (B/T < 0.1) in S+S pairs. On the other hand, for the SFGs in S+E pairs, sSFR enh vs B/T relation is rather flat, and none of the average sSFR enh in individual bins is significantly above zero. Particularly, even in the first two B/T bins with small B/T ratios, where nearly half of SFGs in S+S pairs show strong enhancements (sSFR enh 0.5), SFGs in S+E pairs show no sSFR enhancement in general. Star formation is fueled by cold gas, and sSFR can be decomposed into two terms sSFR = M gas /M star × SFE gas , where SFE gas = SFR/M gas is the star formation efficiency of gas. Cao et al. (2016) derived the total gas mass (M gas ) with a fixed gas-to-dust ratio of 100. They found significantly enhanced SFE gas for SFGs in S+S pairs, but not for those in S+E pairs, compared to a control sample. On the other hand, they found no significant difference among the gas content (M gas /M star ) among SFGs in S+S, in S+E pairs, and in control sample.
In Figure 10 we show the means of the log(M gas /M star ) in the four B/T ratio bins for 96 H-KPAIR SFGs with SFR detections, and of 95 SFR detected SFGs of the control sample in Cao et al. (2016). Both the paired galaxies and the normal galaxies show a trend of the gas content decreasing with increasing B/T ratio. Consistent with Cao et al. (2016), we find no significant difference among the gas contents of SFGs in S+S and S+E pairs and in control sample, in any of the B/T bins.  In Figure 11 the means of log(SFE gas ) in four B/T bins are plotted for the same four samples. The SFGs in S+S pairs have systematically higher SFE than those in S+E pairs as Cao et al. (2016) showed, especially in the bin 1 (B/T < 0.1) and bin 2 (0.1 ≤ B/T < 0.3), the differences are beyond 2σ. The enhanced SFE from SFGs in S+S pairs compared to that of control samples found in Cao et al. (2016) comes also mainly from these two bins (B/T < 0.3).
There are two kinds of cool gas in a galaxy: atomic gas and molecular gas. The connection of SFR with molecular gas is more direct than with atomic gas. Lisenfeld et al. (2019) carried out CO observation of 78 spiral galaxies in H-KPAIR and found that, compared with normal galaxies, paired SFGs in H-KPAIR sample show significant enhancement in M H2 /M star ratio but not in SFE H2 . When separated into S+S and S+E subsamples, SFGs in S+S pairs show higher M H2 /M star (0.21±0.11 dex) and SFE H2 (0.18±0.06 dex) than those in S+E pairs.
In Figure 12 we plot the means of the log(M H2 /M star ) in the four B/T ratio bins for the 69 SFGs with WISE w4-band detection out of 78 H-KPAIR galaxies observed by Lisenfeld et al. (2019) in CO. Also plotted are the means of the M H2 /M star ratios of 93 normal SFGs with WISE w4-band detection that have CO data in the COLD GASS sample (Saintonge et al. 2011a,b) and B/T ratio data in Meert et al. (2015).  Figure 11. Plot of means of log(SFEgas) and errors in four B/T bins. The meaning of the symbols are the same as in Figure 10.
shows a common trend for all samples that M H2 /M star decreases with increasing B/T. However, the trend for paired SFGs is steeper than that for normal galaxies, and paired SFGs with small B/T ratios have significant molecular fraction enhancement while those with B/T > 0.5 have about the same molecular fraction as their counterparts in the normal galaxy sample. Also, spirals in S+E pairs show systematically lower M H2 /M star than those in S+S pairs, as was found previously by Lisenfeld et al. (2019). The enhancement of M H2 /M star for disky (B/T < 0.1) SFGs in S+S pairs is 0.26 dex (> 4σ). In Figure 13 we show the means of log(SFE H2 ) in four B/T bins for the same four samples. It does not show significant trend for any sample and, compared to the single galaxies, no significant SFE H2 enhancement for the paired SFGs is found in any B/T ratio bin. Most results for S+S and S+E subsamples have large errors because of relatively small sample sizes. The only noticeable difference is found in the first bin of B/T < 0.1: the mean SFE H2 of the disky SFGs in S+E pairs is 0.20 ± 0.09 dex lower than that of their counterparts in S+S pairs.

DISCUSSION
Our results show that indeed the sSFR enhancement is suppressed in paired SFGs with large bulges (B/T ≥ 0.3). In particular, very strong sSFR enhancement (sSFR enh 0.7) occurs almost exclusively in disky galaxies with B/T < 0.1. However, given the large scatter of the sSFR enh versus B/T relation, the low frequency of interaction-induced starbursts cannot be explained solely by the B/T dependence.
We find that spiral galaxies in S+E pairs have larger bulges than their counterparts in S+S pairs. This can explain partially the sSFR enh difference between SFGs in S+E and S+S pairs found by Xu et al. (2010) and Cao et al. (2016). But it cannot explain why in a same B/T bin the sSFR enh of SFGs in S+E pairs are systematically lower than those in S+S pairs (Figure 9). Particularly, in the bin of disky galaxies (B/T < 0.1), SFGs in S+E show significantly lower M H2 /M star and SFE H2 than their counterparts in the S+S subsample, and none of them has sSFR enh > 0.7 while only one has sSFR enh > 0.5.
Why do some paired disky SFGs have strong sSFR enhancements while others do not, especially those in S+E pairs? According to Xu et al. (2021), the systematically higher SFE H2 of SFGs in S+S pairs than those in S+E pairs may be explained by the following scenario: The former may have higher chance to be in lowspeed co-planer interactions which can trigger strong nuclear starbursts by tidal torques (Barnes & Hernquist 1996;Hopkins et al. 2009), while the latter are more likely in higher speed, higher incline angle interactions which tend to trigger ring galaxies that have more extended star formation and lower SFE H2 , such as what is observed in the S+E pair Arp 142 (its spiral component has B/T < 0.1). This hypotheses is based on their results that on average S+S pairs have lower local density and lower relative velocity than S+E pairs, therefore are more likely found in the field environment which favors co-planer interactions (Dubois et al. 2014). On the other hand, S+E pairs are more likely found in groups/clusters where the interaction orbits are severely disturbed and randomly oriented. More investigations are needed to explore whether this mechanism can explain the difference in the sSFR enh of disky SFGs in S+S and S+E pairs.

CONCLUSION
In this paper we present a bulge-disk decomposition catalog of a 2MASS Ks-band-selected close majormerger galaxy pair sample (H-KPAIR). The decompositions are derived by two-dimensional, two-component fits on SDSS r-band images using galfit. With this catalog and a control sample of single galaxies selected from a large catalog of SDSS galaxies with galfit results (Meert et al. 2015), we are able to study the dependence of the interaction-induced sSFR enhancement on the B/T ratio, and verify the theoretical prediction that large bulges can suppress the star formation enhancement in interacting galaxies (Mihos & Hernquist 1996). We also investigate the effects of the B/T ratio dependence of the sSFR enhancement on the differences between star-forming galaxies (SFGs) in spiral+spiral (S+S) pairs and spiral+elliptical (S+E) pairs. Our main results are: 1. There is a strong monotonic dependence of sSFR enhancement on the B/T ratio, in the sense that sSFR enhancement decreases with increasing B/T. On average, only paired SFGs with B/T < 0.3 show significant sSFR enhancement.
2. When separated into S+S and S+E subsamples, the S+S subsample shows a similar (albeit slightly stronger) trend. Very strong sSFR enhancements