PTF 10bzf (SN 2010ah): A BROAD-LINE Ic SUPERNOVA DISCOVERED BY THE PALOMAR TRANSIENT FACTORY

P48 observations of the PTF 10bzf field were performed with the Mould-R filter. A high-quality image produced by stacking several images of the same field (obtained between 2009 May and 2009 June) was used as a reference and subtracted from the individual images. Photometry was performed relative to the r-band magnitudes of 10 SDSS reference stars in the field, including r−i color term corrections, using an aperture of 2 arcsec radius, and applying aperture corrections to account for systematic errors and errors introduced by the subtraction process. Aperture corrections are all below ≈0.04 mag. All the P48 photometry is listed in Table 2. The P48 calibrated light curve of PTF 10bzf is plotted in Figure 2.

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P60 observations were carried out in the B, g, r, i, z bands. We also observed the PTF 10bzf field with the 1 m telescope at the Wise observatory²⁶ using BVRI filters (see Table 2). For both P60 and Wise observations, image subtraction was performed using the common point-spread function method via the "mkdifflc" routine (Gal-Yam et al. 2004, 2008). Errors on the P60 and Wise data are estimated by using "artificial" sources at a brightness similar to that of the real SN, with the scatter in their magnitudes providing an estimate of the error due to subtraction residuals. The measured magnitude was calibrated against the magnitudes of SDSS stars in the same field (see Figure 1). The calibration procedure described in Jordi et al. (2006) was used for the BVRI data. Calibration errors were summed in quadrature with the subtraction errors.

Gemini North GMOS²⁷ (Hook et al. 2004) spectra were taken on 2010 March 2 (Program ID: GN-2010A-Q-20), using a 1'' slit, with the B600 and R400 gratings. The observations had an exposure time of 450 s (see Table 2), the airmass was 1.236, the sky position angle was 191°, and the standard star was Feige34. Standard data reduction was performed with IRAF V2.14, using the Gemini 1.10 reduction packages. The Gemini spectrum of PTF 10bzf is shown in Figure 3. A redshift of z = 0.0498 ± 0.0003 was derived from the host galaxy emission lines of O iii, Hα, Hβ, N ii, and S ii. The spectrum (black line in Figure 3) resembles that of SN 1998bw at a similar epoch (red line in Figure 3 and Galama et al. 1998) and shows very broad lines, leading us to classify this SN as a broad-line Ic.

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PTF 10bzf was also observed by Keck I/LRIS²⁸ using a 1'' slit, with the 400/8500 grating plus 7847 Å central wavelength on the red side and with the 400/3400 grism on the blue side. The exposure time was 2 × 80 s on the red side and 1 × 240 s on the blue side (see Table 2). Keck data were reduced using the standard long-slit reduction packages developed in the IRAF environment (Figure 4).

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Both Gemini and Keck spectra were used to derive synthetic photometry in SDSS r-, g-, and i-bands (Table 2). Synthetic photometry was performed as described in Poznanski et al. (2002).

A two-epoch observation of PTF 10bzf was performed as part of a Swift Target of Opportunity program.²⁹ Swift/XRT did not detect any X-ray counterpart to PTF 10bzf (Kasliwal & Cenko 2010). The corresponding upper limits are reported in Table 2, where we have converted the 0.3–10 keV XRT count rates into fluxes assuming a photon index of Γ = 2 and correcting for Galactic absorption (N_H ≈ 10²⁰ cm⁻²).

During the first epoch, PTF 10bzf was detected by Swift/UVOT (Kasliwal & Cenko 2010) and was observed to fade in the subsequent observation. The measured magnitudes in Swift/UVOT filters are reported in Table 2.

In the radio band, PTF 10bzf was followed up by the Allen Telescope Array (Welch et al. 2009), by the Combined Array for Research in Millimeter-wave Astronomy (CARMA; Carpenter 2010), and by the Westerbork Synthesis Radio Telescope (WSRT; Kamble et al. 2010). No radio source was detected by any of these telescopes (Table 2).

The Expanded Very Large Array³⁰ (EVLA; Perley et al. 2009) provided the deepest upper limit of 33 μJy for a radio counterpart associated with PTF 10bzf (Chomiuk & Soderberg 2010, and Table 1).

Starting on 2010 November 27.49, we observed PTF 10bzf with the EVLA in its C configuration, through an EVLA exploratory program (PI: A. Corsi).³¹ We observed for 2 hr, at a center frequency of 4.96 GHz, and with a total bandwidth of 256 MHz. No radio source was detected at the SN position; the corresponding upper limit is reported in Table 2. A compact source (J1146+5356) near PTF 10bzf was observed every 6 minutes for accurate phase calibration, while 3C 286 was observed at the end of the run for the bandpass and flux density calibration. Data were reduced and imaged using the Astronomical Image Processing System (AIPS) software package.

We also reduced with the AIPS archival data that were taken on 2010 May 21.21 (PI: A. Soderberg), for a 1 hr integration time at 6 GHz (with a 1 GHz bandwidth). We find no source at the position of PTF 10bzf and derive a 3σ upper limit comparable to the one obtained by Chomiuk & Soderberg (2010) during the first epoch (see Table 2).

Our photometric monitoring program missed the photometric maximum. However, by performing synthetic photometry on the Gemini spectrum taken on 2010 March 2 (about a week after the discovery), and the Keck spectrum taken on 2010 March 7 (about 12 days after the discovery), we derive g−r−i magnitudes of PTF 10bzf at these epochs (see Table 2). As evident from Figure 2, PTF 10bzf was likely around maximum light during the Gemini observation. The R-band apparent magnitude of PTF 10bzf, as derived from the synthetic photometry on the Gemini spectrum, is R = 18.4 ± 0.3 (AB system or R = 18.2 ± 0.3 in the Vega system). This gives us an approximate estimate of the SN absolute magnitude around R-band peak time of M_R = −18.3 ± 0.3 (AB system or M_R = −18.5 ± 0.3 in the Vega system).

In Figure 2 and Table 1 we summarize the properties of the spectroscopically confirmed broad-line Type Ic SNe associated with GRBs, of the broad-line Type Ic SNe 2003jd and 2002ap, as examples of "normal" broad-line Ics, and finally of the broad-line Type Ic SN 2009bb (Pignata et al. 2011; Soderberg et al. 2010), as prototype of engine-driven SNe with no clear GRB association.

SNe 1998bw (Iwamoto et al. 1998), 2003dh (Mazzali et al. 2003), and 2003lw (Mazzali et al. 2007), all of which produced GRBs, were brighter and more energetic than other broad-line Type Ic SNe for which a high-energy signal was either not detected (e.g., SNe 1997ef and SN 2002ap; see Mazzali et al. 2000, 2002) or was an XRF (SN 2006aj; Mazzali et al. 2006b). As evident from Table 1 and Figure 2, PTF 10bzf was more luminous than the broad-line Type Ic SN 2002ap (with a difference in R-band absolute magnitude at peak of M_{R; 10bzf} − M_{R, 2002ap} = −1.0 ± 0.4), comparable (within the errors) to the engine-driven SN 2009bb and to the broad-line Ic SN 2003jd at maximum R-band light, and less luminous than the GRB-associated SN 1998bw (M_{R, 10bzf} − M_{R, 1998bw} = 0.9 ± 0.3 at R-band maximum light).

Although the peak epoch is not well known, we can estimate the ⁵⁶Ni mass in PTF 10bzf by interpolating between the R-band light curves of SN 2002ap (for which $M_{^{56}\rm Ni}\approx 0.09$ M_☉; Mazzali et al. 2002) and SN 1998bw (for which $M_{^{56}\rm Ni}\approx 0.5$ M_☉; Nakamura 1999; Nakamura et al. 2001). We find that for PTF 10bzf $M_{^{56}\rm Ni}\approx 0.20\hbox{--}0.25$ M_☉. The ⁵⁶Ni mass can also be estimated using the empirical relation derived by Drout et al. (2010) from the properties of a large sample of Type Ic SNe (including broad-line and engine-driven SNe):

$$\begin{equation} \log (M_{^{56}\rm Ni}/M_{\odot })\simeq -0.41\times M_{\rm R}-8.3, \end{equation} \tag{ 1 }$$

where $M_{\rm ^{56}Ni}$ is the mass of ⁵⁶Ni estimated using the formalism of Valenti et al. (2008; see also Arnett 1982) and M_R is the extinction-corrected peak magnitude in the R-band (see also Perets et al. 2010). For PTF 10bzf, using Equation (1), we get $M_{\rm ^{56}Ni}\approx 0.2\,M_{\odot }$, compatible with what was obtained by interpolation. This is comparable to SN 2002aj, associated with XRF 060218 (Mazzali et al. 2006b), and significantly less than all other GRB-associated SNe (see Table 1).

Estimating the kinetic energy requires modeling. However, we can use line velocity as a proxy for it. In Figures 3 and 4 we show a spectroscopic sequence of broad-line Type Ic SNe, from 2002ap to 1998bw. The first (Figure 3) shows spectra near maximum light, the second (Figure 4) shows spectra obtained about 5 days after maximum. In addition, we show the only near-peak spectrum available of SN 1997ef, a broad-line SN without a GRB (Mazzali et al. 2000). We have ordered the SNe by peak luminosity. This ordering, however, reveals a sequence also in line velocity and blending. The spectra of SN 1998bw are the most affected by line broadening, as seen, for example, in the almost complete absence of the re-emission peak near 4500 Å and by the complete blending of the O i 7773 and the Ca ii IR triplet. PTF 10bzf is intermediate between SN 1998bw and the two non-GRB SNe 1997ef and 2002ap in both of these respects.

We have measured the velocity of the Si ii 6355 Å absorption, which traces reasonably closely the position of the photosphere, in the two available spectra of PTF 10bzf (see Figures 3 and 4). The results are shown in Figure 5, where they are compared to the photospheric velocity of a number of Ib/c SNe, with and without a GRB or an XRF. PTF 10bzf appears to be intermediate in velocity between the GRB-associated SNe (in red) and the non-GRB ones, both broad-lined (blue) and narrow-lined (green). Note that, typically, the measured Si ii line velocity is somewhat larger than the photospheric velocity, so the photospheric velocity of PTF 10bzf is likely lower than the values shown in Figure 5. This makes PTF 10bzf more similar to non-GRB-associated SNe.

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We can use this line velocity measurement, together with an estimate of the width of the light curve of PTF 10bzf, to derive an approximate estimate of the kinetic energy and ejecta mass for PTF 10bzf. As evident from Figure 2, the light curve of PTF 10bzf has to be stretched in time by a factor of ≈1.12 to match the shape of the SN 1998bw light curve. Moreover, as evident from Figure 5, the velocity of PTF 10bzf may be a factor of ≈0.9 smaller than SN 1998bw. Using the formula for the light curve width as a function of ejecta mass and kinetic energy, as delineated by Arnett (1982), we obtain for PTF 10bzf: M = (7 ± 2) M_☉ and E_K = (17 ± 5) × 10⁵¹ erg.

PTF 10bzf thus appears to have an E_K/M ratio of ≈2.5. This is larger than non-GRB SNe such as 1997ef (which had E_K/M ≈ 2) or 2002ap (for which E_K/M ≈ 1.25), but smaller than SN 1998bw (E_K/M ≈ 3). We thus conclude that PTF 10bzf probably lacks the mass and energy required to initiate a GRB.

The Swift/XRT upper limit for PTF 10bzf at 8.5 days constrains any X-ray source associated with PTF 10bzf to have a flux <1.3 × 10⁻¹⁴ erg s⁻¹ cm⁻², which at the redshift of PTF 10bzf corresponds to an isotropic luminosity of <7.4 × 10⁴⁰ erg s⁻¹.

The X-ray flux of GRB 980425 about 1 day after the burst was ≈3 × 10⁻¹³ erg s⁻¹ cm⁻², and it declined at a rate ∝t^−0.2 (Nakamura 1999; Pian et al. 2000). Rescaling it at 8.5 days and taking into account the SN 1998bw distance, we obtain an X-ray isotropic luminosity of ≈3 × 10⁴⁰ erg s⁻¹, a factor of ∼2.4 below our X-ray luminosity upper limit on PTF 10bzf.

For GRB 030329, an X-ray flux upper limit of <2.6 × 10⁻¹² erg s⁻¹ cm⁻² was set at an epoch of about 8 days since the burst, using RXTE observations (Tiengo et al. 2003). From broadband afterglow modeling, the predicted X-ray flux at 8 days was ≈4 × 10⁻¹³ erg s⁻¹ cm⁻² (see Figure 4 in Tiengo et al. 2003), which at the redshift of GRB 030329 corresponds to an isotropic luminosity of ≈3 × 10⁴³ erg s⁻¹, a factor of ≈400 higher than our upper limit on PTF 10bzf.

GRB 031203 had an estimated X-ray flux of ≈10⁻¹³ erg s⁻¹ cm⁻² around 8 days (derived by extrapolating from the XMM-Newton observations; see Figure 1 in Watson et al. 2004). This corresponds to an isotropic X-ray luminosity of ≈3 × 10⁴² erg s⁻¹, a factor of ≈40 higher than our X-ray luminosity upper limit on PTF 10bzf.

For GRB/XRF 060218, Swift/XRT measured a flux of ≈1.3 × 10⁻¹³ erg s⁻¹ cm⁻² around 8 days since trigger (see the upper panel of Figure 2 in Campana et al. 2006). This gives an isotropic X-ray luminosity of ≈3 × 10⁴¹ erg s⁻¹, a factor of ∼4 above our PTF 10bzf upper limit.

Finally, Swift/XRT observations set an upper limit of ≈3 × 10⁻¹⁴ erg s⁻¹ cm⁻² on GRB 100316D X-ray flux around 8 days since the burst (see Figure 6 in Starling et al. 2010), i.e., an isotropic luminosity upper limit of ≈2 × 10⁴¹ erg s⁻¹, a factor of ∼3 greater than our upper limit on PTF 10bzf.

In conclusion, at ≈8 days since trigger, all GRBs with a spectroscopically confirmed associated SN had an X-ray isotropic luminosity larger than our upper limit on PTF 10bzf, except for GRB 980425.

The novelty of SN 1998bw was in the discovery of prompt radio emission just a few days after GRB 980425 (Kulkarni et al. 1998). The brightness temperature suggested that the radio photosphere moved relativistically (Γ ⩾ 2), with a total energy of ≈10⁵⁰ erg (Li & Chevalier 1999), about two orders of magnitude less than the total kinetic energy of the explosion, which was estimated to be ≈3 × 10⁵² erg (Iwamoto et al. 1998). None of these last features, together with the spatial and temporal association with a GRB, were ever observed for a nearby SN before SN 1998bw, thus suggesting the presence of a central engine powering this explosion.

SN 2003dh, associated with GRB 030329, showed an isotropic energy of ≈4 × 10⁵² erg, which led to the classification of this event as an "hypernova" (Mazzali et al. 2003). The radio afterglow of GRB 030329 was ≳ 100 times more luminous than SN 1998bw (Berger et al. 2003a). Berger et al. (2003a) modeled such emission as due to the contribution of a second jet component, wider than the one generating the burst itself, and having an isotropic kinetic energy of ≈5.6 × 10⁵¹ erg.

SN 2003lw, associated with GRB 031203, had a total kinetic energy of ≈6 × 10⁵² erg (Mazzali et al. 2006b). The spectral peak luminosity in radio was ≈10²⁹ erg s⁻¹ Hz⁻¹, about a factor of 100 less luminous than the radio afterglow of GRB 030329, but comparable to the radio peak luminosity of SN 1998bw. The kinetic energy in the afterglow component giving rise to the radio emission was estimated to be ≈1.7 × 10⁴⁹ erg (Soderberg et al. 2004).

The total kinetic energy of SN 2006aj was ≈2 × 10⁵¹ erg (Mazzali et al. 2006a), smaller than the other GRB-associated SN. The radio afterglow of XRF 060218 peaked at about 5 days since the trigger, the peak luminosity being about a factor of 10 less bright than SN 1998bw at peak (Soderberg et al. 2006a). The kinetic energy and Lorentz factor around the time of the radio peak were estimated to be ≈2 × 10⁴⁸ erg and Γ ≈ 2.3, respectively (Soderberg et al. 2006a).

SN 2010bh, the latest spectroscopically confirmed SN associated with a GRB, had a kinetic energy of ≈1.39 × 10⁵² erg (Cano et al. 2011). Radio upper limits at about 2 days since the burst constrain the radio spectral luminosity to be below 8 × 10²⁷ erg s⁻¹ Hz⁻¹, a factor of 2–10 lower than the radio afterglow luminosities observed for SN 1998bw, GRB 031203, and XRF 060218 on comparable timescales (Wieringa et al. 2010).

At a redshift of z = 0.0498, the deepest early-time radio upper limit for PTF 10bzf was obtained by Chomiuk & Soderberg (2010). This sets a limit on the spectral luminosity of L_5 GHz < 1.6 × 10²⁷ erg s⁻¹ Hz⁻¹, at about three weeks after the explosion. This is ≈20 times lower than the radio luminosity observed on a similar timescale for the Type Ic SNe 1998bw and 2009bb (Soderberg et al. 2010), the only two SNe which showed clear evidence for energetic and mildly relativistic outflows (Chomiuk & Soderberg 2010). However, we note that this upper limit is comparable to the radio luminosity of GRB 060218 at a similar epoch (Soderberg et al. 2006a).

Using the early-time radio upper limit, we constrain the mean expansion speed v_r of the radio photosphere. Under the reasonable assumption that radio emission arises from a synchrotron spectrum with ν_a ∼ ν_p (where ν_a is the self-absorption frequency and ν_p is the peak frequency), and under the hypothesis of equipartition, the peak time t_p and peak luminosity L_p of the radio emission directly measure the average expansion speed (Berger et al. 2003b; Chevalier 1998; Kulkarni et al. 1998; Scott & Readhead 1977):

$$\begin{eqnarray} && {v_{\rm r}} \sim 3.1 \times 10^4 \left(\frac{L_{\rm p}}{10^{26} \,{\rm erg\, s}^{-1}}\right)^{17/36}\left(\frac{t_{\rm p}}{10\,{\rm days}}\right)^{-1}\nonumber\\ && \qquad\quad \times \left(\frac{\nu _{\rm p}}{5\,{\rm \,GHz}}\right)^{-1}\,{\rm km\,s}^{-1}\,. \end{eqnarray} \tag{ 2 }$$

Figure 6 shows L_5 GHz at peak versus t_pν_p for different values of v_r, compared with the Allen telescope, WSRT, and EVLA upper limits on PTF 10bzf. Assuming that the radio emission peaked at ≈18 days, the WSRT and EVLA observations constrain the expansion velocity to be less than 10⁵ km s⁻¹.

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Estimating the expansion velocities for non-detections has the caveat that the radio peak epoch is in reality unknown. However, as noted by Berger et al. (2003b), observations performed at ∼10–20 days since explosion sample the radio peak time of Type Ic SNe reasonably well. For example, SN 1983N peaked in radio at ∼30 days after explosion, while the radio light curve of SN 1998bw showed a double-peak profile, with the first peak around 10 days after explosion and the second around 30 days after explosion. This justifies our use of radio upper limits taken within ≈3 weeks since discovery to constrain the expansion speed. We also note, however, that if PTF 10bzf peaked at a few days after the explosion like SN 2002ap, the EVLA and WSRT upper limits would not be deep enough to rule out a relativistic expansion.

In the context of the fireball model, the emission from an off-axis GRB is expected to be visible in the radio band long past the GRB explosion (at timescales of the order of ∼1 yr; see Levinson et al. 2002). In fact, at sufficiently late times, the relativistic fireball is expected to enter the sub-relativistic phase, during which the jet starts spreading, rapidly intersecting the viewer's line of sight as the ejecta approach spherical symmetry.

To model the late-time radio emission from an off-axis GRB during the non-relativistic phase, we use the analytical model of Waxman (2004b) for a fireball expanding in a wind medium (see, e.g., Levinson et al. 2002 for the constant ISM case). In this model the radio luminosity is approximated as (see also Perna & Loeb 1998; Livio & Waxman 2000; Paczynski 2001; Granot et al. 2002; Berger et al. 2003b; Soderberg et al. 2006b; van Eerten et al. 2010)

$$\begin{eqnarray} &&\nonumber L_{\rm r}\sim 2.1\times 10^{29}\left(\frac{\epsilon _{\rm e}\epsilon _{\rm B}}{0.01}\right)^{3/4}\left(\frac{\nu }{10\,{\rm GHz}}\right)^{-\frac{(p-1)}{2}}\left(\frac{t}{t_{\rm NR}}\right)^{-3/2}\\ &&\times A^{9/4}_{*} E^{-1/2}_{51}{\rm \,erg\,s}^{-1}\,{\rm Hz}^{-1},\quad \end{eqnarray} \tag{ 3 }$$

where E₅₁ is the beaming-corrected ejecta energy, A_* defines the circumstellar density in terms of the progenitor mass-loss rate $\dot{M}$ and wind velocity v_w such that $\dot{M}/4\pi {v_{\rm w}}=5\times 10^{11}A_*$ g cm⁻¹ (Waxman 2004b; Soderberg et al. 2006b), and

$$\begin{equation} t_{\rm NR} \sim 0.3 \left(\frac{E_{51}}{A_*}\right){\rm \,yr} \end{equation} \tag{ 4 }$$

is the time of the non-relativistic transition. Note that in the above formulation it is assumed that the fireball spreads sideways at approximately the speed of light. By imposing t_NR ≲ t_obs and L_r ≳ L_obs, we can use the EVLA observations of PTF 10bzf (see Table 2) to exclude the values of (beaming-corrected) energy and wind density that would give a radio luminosity above the upper limits of PTF 10bzf, at the times of our observations. The exclusion regions obtained in this way are plotted in yellow in Figure 7. We can compare these constraints with the energy and density derived from the broadband afterglow modeling of GRB 980425, GRB 030329, and GRB 031203 (see Soderberg et al. 2006b; Waxman 2004a, and references therein), also plotted in Figure 7. From such a comparison we conclude that a GRB fireball possibly associated with PTF 10bzf could not have the same (beaming-corrected) energy and wind density as GRB 030329 and GRB 031203. In fact, if this was the case, such a fireball would have been in its non-relativistic (spherical) phase at the times of our radio observations (so that its radio emission would be observable by any off-axis observer), and its radio luminosity would be greater than our upper limits for PTF 10bzf.

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We stress that our Figure 7 only constrains the portion of the parameter space where t_NR ≲ t_obs. This provides an estimate of the values of the fireball parameters ruled out by our observations, which does not depend critically on the adopted model. Constraining the portion of the parameter space where t_NR ≳ t_obs requires detailed modeling. In fact, before t_NR, the sideways expansion and the deceleration of the jet depend on the spatial distribution within the jet of the energy density and the Lorentz factor. These distributions are poorly constrained by current observations. And, for given distributions, an accurate calculation of jet expansion and deceleration must be carried out numerically.

We searched for a possible GRB in coincidence with PTF 10bzf using the interplanetary network (IPN) data. We searched for bursts with a localization error box including PTF 10bzf. Since the exact explosion epoch of PTF 10bzf is not known, we searched in a time window extending from 2010 February 12 to 2010 February 23 (the discovery day of PTF 10bzf). We conservatively extend such a time window to include one full week prior to our last non-detection of PTF 10bzf. Therefore, our time window starts ≈11 days before the SN discovery (i.e., ≈18 days before its R-band maximum light).

For comparison, we note that the engine-driven SN 2009bb reached its maximum light about two weeks after the estimated explosion date (Soderberg et al. 2010), evolving somewhat faster than SN 1998bw in the pre-peak phase (Pignata et al. 2011). As evident from Figure 2, our last upper limit on 2010 February 19 (R > 21.3) indicates that PTF 10bzf probably also evolved more rapidly than SN 1998bw in its pre-peak phase. Using the R-band light curve as a proxy for L(t), and assuming a pre-peak luminosity evolution L(t)∝(t − t₀)^1.8 (where t₀ is the explosion time; see e.g., Pignata et al. 2011), t₀ should be in between ≈2010 February 17.80 and ≈2010 February 23.50 (i.e., the PTF discovery date) to account for the ≳ 2.44 mag drop observed between our last non-detection of PTF 10bzf and its discovery. However, we conservatively extend our time interval for the GRB search to 2010 February 12, one week prior to our last non-detection (on 2010 February 19.443).

Between 2010 February 12 and 2010 February 23, a total of 14 confirmed bursts were detected by the spacecraft of the IPN³² (Mars Odyssey, Konus-Wind, RHESSI, INTEGRAL (SPI-ACS), Swift-BAT, MESSENGER, Suzaku, AGILE, and Fermi (GBM)). Here confirmed means that they were observed by more than one detector on one or more spacecraft and could be localized at least coarsely.

The localization accuracies of these 14 bursts varied widely, but none of them was found to be consistent with the position of PTF 10bzf. One burst was observed by the Fermi GBM alone (error circles with 1σ statistical-only error radii of 10.5 deg), while another five were observed by the GBM and other spacecraft. Four events were observed by a distant IPN spacecraft and could be triangulated to annuli or error boxes with dimensions as small as ∼10'. Five GRBs were observed within the coded field of view of the Swift-BAT (3' initial localization accuracy), and in some cases by other IPN spacecraft as well.

PTF 10bzf is not spatially associated with any of these GRBs. The total area of the localizations of the 14 confirmed bursts, containing the 3σ error regions, was ≈1.3 sr. Therefore, there is only ≈10% chance coincidence between these bursts and PTF 10bzf.

Next, based on our GRB sample, we can put a limit on the fluence of any GRB associated with PTF 10bzf. We considered three distinct sets of events: IPN bursts, Fermi GBM-only bursts, and Swift-BAT-only bursts. The IPN is sensitive to bursts with fluences down to about 6 × 10⁻⁷ erg cm⁻² (50% efficiency—see Hurley et al. 2010) and observes the entire sky with a temporal duty cycle close to 100%. The Fermi GBM detects bursts down to a 8–1000 keV fluence of about 4 × 10⁻⁸ erg cm⁻² and observes the entire unocculted sky (≈8.8 sr) with a temporal duty cycle of more than 80%. The weakest burst observed by the BAT had a 15–150 keV fluence of 6 × 10⁻⁹ erg cm⁻², and the BAT observes a field of view of about 2 sr with a temporal duty cycle of about 90%.

If the SN produced a burst below the IPN threshold, and above the Fermi one, it is possible that both Swift and Fermi did not detect it: considering their spatial and temporal coverages, the non-detection probabilities are about 0.86 and 0.44, respectively. Finally, if the SN produced a burst below the Fermi threshold, but above the Swift one, the non-detection probability is about 0.86. We note that a burst with an isotropic energy release comparable to that of the sub-energetic GRB 980425, E_iso ≈ 6 × 10⁴⁷ erg, placed at the distance of PTF 10bzf, would be observed with a fluence of ≈10⁻⁷ erg cm⁻², which is below the IPN threshold, but above the Fermi GBM one.