Analysis discovered 5 GRB-SN connections within z ≤ 0.2, and one of them was already known to be a physical association between GRB and SN: GRB 130702A - SN 2013dx. The optical afterglow of GRB 130702A (which was localized by Fermi and with- out Swift) was found by searching large 71 deg2 area inside Fermi error circle (Singer et al., 2013). It could have easily been missed and with it, the emerging SN. The GRB was in between “cosmological” and underluminous, and had a relatively strong after- glow. The optical transient found showed signs of decreasing GRB optical afterglow (one of the reason it was identified with a GRB among numerous other optical sources in the area). Therefore, if a GRB-SN is serendipitously discovered before or close to maxi- mum, it should show signs of decreasing GRB afterglow, unless the GRB is underluminous (Eiso∼ 1048erg) and its afterglow is week. So, the potential missed connections are most probably the ones that involve underluminous GRBs. That being said, it should be noted
that known GRB-SNe were observed with numerous and strongest optical instruments which were “staring” at a predefined position. Normal SNe are discovered by chance and observed by various instruments at various times, and even if a SN has a presence of an additional GRB-decaying-afterglow-like component, it might be missed.
After examination of the data, only SN 2012ba seems to be good candidate for being physical associated with a GRB (120121B). SN 2012ba was of type Ic and reached quickly
a very bright maximum magnitude Rabs ' −18.5, about 11 days after the GRB trigger,
which is very similar to the typical rising time and high luminosities of SNe associated with GRBs. To date there are only two other SNe associated with GRBs and classified as “Ic” (rather than “broad lines” Ic or Hypernovae): SN 2002lt, associated to GRB 021211, and SN 2013ez, associated to GRB 130215A. However, these observations do not imply that GRBs may be associated with “standard type Ic SNe”. We note that in all three cases, 2012ba, 2002lt and 2013ez, SN spectra were secured 20-40 days past maximum, therefore even if the pre-maximum spectra showed significantly broader lines, than observed in the post-maximum spectra, this difference shortly vanished after maximum (if the SN ejecta carry little mass) such that it is not easy to distinguish between the two types of SNe. The isotropic energy of this Fermi GRB-SN candidate is Eiso = 1.39 × 1048erg, which implies that this burst likely belongs to the low-luminosity subclass of GRBs.
Now, it is possible to independently estimate, admittedly on the very scanty statistic of one single object, the rate ρ0 of local low-energetic long GRBs - type Ic SNe. For that a maximum distance of GRB 120121B for it to be detected by Fermi is needed. This can be estimated by examining count curve (in rmfit for example) of the burst in the most illuminated detector. The ratio of unknown peak of the curve (signal coming from maxi- mum distance) to the square root of the known background (noise) is set to Fermi-GBM significance threshold of 4.5 (Band, 2003). From there the calculated peak (at maxi- mum redshift/distance) is compared to the known actual peak (at z = 0.017), and the
maximum redshift is calculated, and from there, the maximum (comoving) volume Vmax.
Background in Fermi-GBM oscillates at different points in orbit and orientation of the spacecraft, and the signal from GRB also depends on the orientation, etc. but the sim- plified approach is good enough for an estimation of zmax which will again be used for final estimation of rates. The maximum redshift for GRB 1202121B to be detected by Fermi-GBM is zmax≈ 0.021.
The estimated rate can then be written as: ρ0 =
NLE VmaxfFT
, (5.1)
where NLE = 1 is the number of found physical connections, fF ≈ 0.7 the average ratio of Fermi-GBM solid angle over the total one, and T = 6 y the Fermi observational period. From there a local rate for this GRB - SN Ic events of ρ0 = 77+289−73 Gpc−3yr−1, where the errors are upper and lower limit determined from the 95% confidence level of the Poisson statistic for a single count (Gehrels, 1986). It is important to note here that Fermi might have detected more SN-GRBs that were missed, not just by direct observations, but also here, simply because the SN wasn’t detected (directly or serendipitously). In other words, other GRBs in the Fermi GRB catalog might be SN-GRBs but the accompanying SN is not in the SN catalogs for the script to match it to the GRB as a potential pair. So, the NLE = 1 in the formula is in a sense a minimum.
There is growing body of evidence that low luminosity GRBs are less beamed that high luminosity GRBs, indeed fb−1 is of the order of 10, or less (Guetta and Della Valle, 2007).
After taking into account this correction derived value is ρ0,b ≤ 770+2890−730 Gpc−3 yr−1, which is consistent with ρ0 = 380+620−225 Gpc−3 yr−1 in (Guetta and Della Valle, 2007), 325+352−177 Gpc−3 yr−1 in (Liang et al., 2007), and 230+490−190Gpc−3yr−1 in (Soderberg et al., 2006b). This analysis confirms the existence of a class of more frequent low-energetic GRBs - SNe Ic, whose rate is larger than the one obtained extrapolating at low redshifts the rate for high-energetic bursts, i.e., ρ = 1.3+0.7−0.6 Gpc−3 yr−1 (Wanderman and Piran, 2010).