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Text: We followed a methodology similar to Kelly & Kirshner ( 2012 ) to measure u -band surface brightnesses at the locations of the 17 SNe Ibn whose host galaxies were observed by SDSS ( SDSS Collaboration 2017 ) . 2 Because we include all classified SNe Ibn in a predefined area of the sky , this should be an unbiased sample . Indeed , we do not observe any correlation between our mea-   ( 2011 ) sured surface brightnesses and redshift . We downloaded the background - subtracted u -band images from SDSS , sometimes multiple frames per field , using Astroquery ( Ginsburg et al . 2018 ) and calculated variance images according to the SDSS frame data model . We stacked the images of each host , weighting by inverse variance , and performed aperture photometry on the stacked image and the total variance image using a 5 × 5 pixel ( 1 . 98 × 1 . 98 ) square aperture centered on the location of the SN . Although the physical size of this aperture varies by more than an order of magnitude within our sample , we chose it as a compromise between increasing our statistical uncertainties by including too few pixels and increasing our systematic uncertainties by including significant surface brightness gradients , where the relevant scale for the latter is set by the typical SDSS seeing of 1 . In comparison , Kelly & Kirshner 2012 used a 20 pixel aperture . 2 also approximately matches the 2 kpc aperture we use for the HST images of PS1 - 12sk in Section 2 . The results are listed in Table 2 and shown in Figure 2 . Equations ( 1)-(2 ) are not strictly applicable to these measurements , because the SDSS u filter does not overlap with the 280 nm filter used to derive them . However , u -band luminosity is still dominated by young stars , but with significant contamination from older populations ( Hopkins et al . 2003 ) . Hopkins et al . ( 2003 ) calibrated star formation rate to u -band luminosity , but because their relationship is nonlinear , we can not rewrite it in terms of star formation rate density and surface brightness . Cram et al . ( 1998 ) produced a linear calibration between U -band luminosity and the formation rate of > 5 M stars only . To convert this to a full star formation rate , we multiply by the ratio of mass from stars > 0.5 M to mass from stars > 5 M according to the Salpeter ( 1955 ) initial mass function , which we find to be 22 . This ratio is very sensitive to the 0.5 M lower limit but results in a relationship very close to Equation ( 1 ) . Rather than trust this modified calibration , we take this to mean that Equation ( 1 ) can be used with u -band measurements and apply it to our results in Table 2 . Because all of the hosts are at redshifts z < 0.11 , we again neglect K - corrections .<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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