Starburst fractions (f SB ) of galaxies as a function of e b. Solid and dotted lines represent isolated and interacting galaxies, respectively. Red and blue represent bright and faint galaxies, respectively. 

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... we examine the correlation between bulge elongation and nuclear star formation activity. We first show a fraction of non-barred galaxies with nuclear starburst activity (fSB) as a function of bulge ellipticity (e b ) in the bottom panel of Fig. 2. The fSB increases with e b . The number distribu- tion in the top panel shows that the peak of the distribution is around e b = 0.3, and the number of galaxies decreases at e b > 0.4. We use several statistical tools to examine the significance of the correlation between bulge ellipticity and starburst fraction. The Spearman correlation test between the two gives a correlation coefficient ρcorr = 1.0 and the probability of obtaining the correlation by chance of pcorr < 0.001, suggesting a significant correlation. We also apply the Kolmogorov-Smirnov (K-S) test and the Anderson-Darling (A-D) k-sample test directly to the distributions of sSFRs of galaxies (not the fraction) for two subsamples divided by bulge ellipticity (i.e. e b > 0.4 and e b 0.4). We could reject the hypothesis that the sSFR distributions of the two sam- ples are extracted from the same parent population with a confidence level of 98%. This confirms a significant difference in the star formation activity between the two subsamples with different bulge ellipticities. Fig. 3(a) shows that fSB depends more strongly on the u − r colour than on Mr. Here, note that fixing the u − r colour is needed to carefully investigate the relationship be- tween bulge elongation and nuclear star formation. We di- vided samples into relatively blue and red at u − r ≈ 1.8 mag, which is similar to the peak of u − r colour of spi- ral galaxies separating morphological type Sb vs. SC/Irr (See Fig. 7 in Strateva et al. 2001;Baldry et al. 2004). For blue galaxies with u − r < 1.8 mag, bright galaxies have higher fSB at fixed colour. These galaxies might be the re- sult of gas-rich major mergers that show high star forma- tion rates during late stages of merging (Kennicutt 2012;van Dokkum 2005). Fig. 3(b) shows that bulges are more elongated as galaxies become redder and fainter. e b has low values when galaxies become brighter than Mr ≈ −20.4 mag. This value is similar to a characteristic luminosity in the r -band, M⋆ ≈ −20.4 mag, of the SDSS sample ( Blanton et al. 2003). Galaxies brighter than the character- istic luminosity show that the number density, stellar mass, gas contents and other parameters dramatically change com- pared to galaxies with lower luminosities than the charac- teristic luminosity ( Blanton et al. 2009). Since fSB and e b are intricately correlated with the magnitude and colour of host galaxies, we divided the samples into bright or faint galaxies, and blue or red galaxies in order to separate the intricate relationships between the parameters in our subse- quent analysis. The fSB and e b contours indicate the fraction and the median value at each point, respectively. We obtain the contours by dividing each panel into 60 by 60 bins and by applying the spline kernel method to extract smoothed distributions. The contours represent 2σ level, and the un- certainties for fSB and e b are calculated by 1000 times re- sampling bootstrap ...

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... Section 2.3 in Park et al. (2008) and Section 2.3 in Park & Choi (2009) for detailed descriptions. Due to ρ20/¯ ρ at the locations in massive clusters is over 50 (Park & Choi 2009), we constrain the sample considering the environmen- tal effects and the number of galaxies based on the follow- ing criteria. We select galaxies at intermediate density (1 < ρ20/¯ ρ < 30), then divide them into isolated (Rn > 3rvir,n) and interacting (Rn < 0.7rvir,n) galaxies. As we explained above, Rn/rvir,n is the parameter used to perceive how far the host galaxies are from their neighbouring galaxies' virial radius. When Rn/rvir,n < 1, a host galaxy is located within the virial radius of its nearest neighbour galaxy. Fig. 7 shows that fSB of each galaxy sample divided by environment and luminosity generally increases with e b despite large error bars, but the trend between fSB and e b does not depend significantly on galaxy ...

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... than on Mr. Here, note that fixing the u − r colour is needed to carefully investigate the relationship be- tween bulge elongation and nuclear star formation. We di- vided samples into relatively blue and red at u − r ≈ 1.8 mag, which is similar to the peak of u − r colour of spi- ral galaxies separating morphological type Sb vs. SC/Irr (See Fig. 7 in Strateva et al. 2001;Baldry et al. 2004). For blue galaxies with u − r < 1.8 mag, bright galaxies have higher fSB at fixed colour. These galaxies might be the re- sult of gas-rich major mergers that show high star forma- tion rates during late stages of merging (Kennicutt 2012;van Dokkum 2005). Fig. 3(b) shows that bulges are more ...

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... ρ < 30), then divide them into isolated (Rn > 3rvir,n) and interacting (Rn < 0.7rvir,n) galaxies. As we explained above, Rn/rvir,n is the parameter used to perceive how far the host galaxies are from their neighbouring galaxies' virial radius. When Rn/rvir,n < 1, a host galaxy is located within the virial radius of its nearest neighbour galaxy. Fig. 7 shows that fSB of each galaxy sample divided by environment and luminosity generally increases with e b despite large error bars, but the trend between fSB and e b does not depend significantly on galaxy ...