SN 2010ay IS A LUMINOUS AND BROAD-LINED TYPE Ic SUPERNOVA WITHIN A LOW-METALLICITY HOST GALAXY

SN 2010ay was discovered by the CRTS (Drake et al. 2009) on 2010 March 17.38 UT (Drake et al. 2010) and designated CSS100317:123527+270403, with an unfiltered magnitude of m ≈ 17.5 mag and located ≲1'' of the center of a compact galaxy, SDSS J123527.19+270402.7, at z = 0.067 (Table 1). We adopt a distance D_L = 297.9 Mpc to the host galaxy²⁰ and note that the Galactic extinction toward this galaxy is E(B − V) = 0.017 (Schlegel et al. 1998). Pre-discovery unfiltered images from CRTS revealed an earlier detection of the SN on Mar 5.45 UT at m ≈ 18.2 mag and a non-detection from February 17.45 UT at m ≳ 18.3 mag (Drake et al. 2010).

Table 1. SN 2010ay Host Galaxy SDSS J123527.19+270402.7

Parameter	Value
R.A.	12h35m2719 (J2000)
Decl.	+27°04'027 (J2000)
Redshift (z)	0.0671
Petrosian radius	1355
Photometrya
u'	19.56 ± 0.03 mag
g'	19.02 ± 0.01 mag
r'	19.02 ± 0.01 mag
i'	18.69 ± 0.01 mag
z'	18.87 ± 0.04 mag
U	19.50 ± 0.06 mag
B	19.02 ± 0.05 mag
V	19.13 ± 0.05 mag
R	18.94 ± 0.05 mag
I	18.90 ± 0.06 mag
Extinction
E(B − V)MWb	0.017 mag
E(B − V)hostc	0.2 mag

Notes. SDSS host galaxy properties and ugriz photometry. ^aModel magnitudes from SDSS DR8 (Aihara et al. 2011). Host galaxy photometry has not been corrected for extinction. UBVRI photometry has been converted from the SDSS ugriz measurements using the transformation of Blanton & Roweis (2007). ^bThe Milky Way extinction as determined by Schlegel et al. (1998), assuming R_V = 3.1. ^cThe host galaxy extinction determined from the SDSS spectrum centered on the galaxy nucleus, via the Balmer decrement as described in Section 2.3.1.

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A spectrum obtained on March 22 UT revealed the SN to be of Type Ic with broad features, similar to the GRB-associated SN 1998bw spectrum obtained near maximum light (Filippenko et al. 2010). This classification was confirmed by Prieto (2010), who additionally reported photometry for the SN (see Table 2). After numerically subtracting the host galaxy emission, they estimate an unusually luminous absolute magnitude of V ≈ −19.4 mag.

The field of SN 2010ay was serendipitously observed with the PS1 3π survey in the weeks preceding its discovery. Pan-STARRS1 is a wide-field imaging system at Haleakala, Hawaii, dedicated to survey observations (Kaiser et al. 2002). The PS1 optical design (Hodapp et al. 2004) uses a 1.8 m diameter f/4.4 primary mirror and a 0.9 m secondary. The telescope illuminates a diameter of 33. The Pan-STARRS1 imager (Tonry & Onaka 2009) comprises a total of 60 4800 × 4800 pixel detectors, with 10 μm pixels that subtend 0.258 arcsec. The PS1 observations are obtained through a set of five broadband filters designated as g_P1, r_P1, i_P1, z_P1, and y_P1. These filters are similar to those used in previous surveys, such as Sloan Digital Sky Survey (SDSS; Fukugita et al. 1996). However, the g_P1 filter extends 20 nm redward of g', the z_P1 filter is cutoff at 930 nm, and SDSS has no corresponding y_P1 filter (Stubbs et al. 2010).

The field of SN 2010ay was observed on 2010 February 21 (r_P1 band) and February 25 (i_P1 band; Figure 1). On each night, four exposures were collected following the strategy of the PS1-3π survey (K. C. Chambers et al. 2012, in preparation). Following the CRTS discovery and announcement of SN 2010ay, we geometrically registered SDSS pre-explosion images to the PS1 images and performed digital image subtraction using the ISIS package (Alard 2000). Photometric calibration was performed using many field stars in the SDSS catalog with magnitudes r ≈ 13–19 mag. No residual flux was found in the difference r_P1-band image from 2010 February 21 with an upper limit of r > 22.0 mag. However, we detect residual flux at the position of SN 2010ay in the i_P1-band residual image from 2010 February 25 with a magnitude of i' = 21.1 ± 0.3 mag.

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The field was again observed in the i_P1 band on 2011 March 25 and the r_P1 band on 2011 March 29, but no residual flux was detected in the subtractions at the SN position to limits of i' ≳ 22.2 and r' ≳ 21.9.

In Table 2 and Figure 2, we compile photometry from the PS1 detections, our optical observations, and the circulars to construct a light curve for SN 2010ay.

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We obtained an optical spectrum (∼3000–11000 Å) of SN 2010ay on April 1 UT, from the ISIS blue arm instrument of the 4.2 m WHT at the Roque de Los Muchachos Observatory. The spectrum was taken at the parallactic angle, and the exposure time was 1800 s. We obtained a second 1800 s optical spectrum (∼3600–9600 Å) using the Gemini Multi-Object Spectrograph (GMOS) on the 8.1 m Gemini North telescope on 2010 April 11.4 UT. We employed standard two-dimensional long-slit image reduction and spectral extraction routines in IRAF.²¹ We do not apply a correction for atmospheric differential refraction, because the displacement should be ≲05 at the airmass of the observations, ≈1.0.

In both our Gemini and WHT spectra, broad absorption features associated with the SN are clearly detected in addition to narrow emission lines typical of star-forming galaxies. We distinguish the host galaxy emission from the continuum dominated by the highly broadened SN emission by subtracting a high-order spline fit to the continuum. Both SN and host galaxy spectral components are shown in Figure 3. As illustrated in the figure, the broad, highly blended spectral features of SN 2010ay resemble those of the Type Ic-BL SN 2010bh (associated with GRB 100316D) at a similar epoch (Chornock et al. 2010). In particular, the broadening and blueshift of the feature near 6355 Å are similar for SN 2010ay and SN 2010bh and are broader and more blueshifted than in SN 1998bw at a comparable epoch. We discuss the comparison between these two SNe further in Sections 3.3 and 6.2.

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Additionally, we obtained 60 s gri-band images of SN 2010ay on 2010 April 11.4 UT using GMOS. The data were reduced using the gemini package in IRAF, and photometry was performed using the standard GMOS zero points.²² We measure that [g, r, i] = [18.90, 18.32, 18.04] ± 0.1 mag.

Imaging photometry is not available at the epoch of our WHT spectrum. However, the spectrum was flux-calibrated against observations of the standard star Feige 34, which was observed the same night and at approximately the same low airmass as the SN. For the observations of both the standard star and SN, the slit was placed at the parallactic angle. We perform synthetic photometry on the spectrum to extract the flux at the central frequency of the R band (6527 Å) and find R = 18.2 ± 0.2 mag. We then subtract the host galaxy flux numerically.

2.3.1. Host Galaxy Features

We observed SN 2010ay with the EVLA (Perley et al. 2009) on three epochs, 2010 March 26, 2010 April 29, and 2011 May 7. All EVLA observations were obtained with a bandwidth of 256 MHz centered at 4.9 GHz. We used calibrator J1221+2813 to monitor the phase and 3C 286 for flux calibration. Data were reduced using the standard packages of the Astronomical Image Processing System. We do not detect a radio counterpart to SN 2010ay in these observations and place upper limits of F_ν ≲ 46, 42, 30 μJy (3σ) for each epoch, respectively, corresponding to upper limits on the spectral luminosity spanning L_ν ≲ (3.6–5.5) × 10²⁷ erg cm⁻² s⁻¹.

As shown in Figure 4, these limits are comparable to the peak luminosities observed for ordinary SNe Ib/c (Berger et al. 2003a; Soderberg 2007; Chevalier & Fransson 2006; Soderberg et al. 2010, and references within) and a factor of 10²–10³ less luminous than the radio afterglows associated with GRBs 020903, 030329, and 031203 at early epochs (Berger et al. 2003b; Soderberg et al. 2004a, 2004b; Frail et al. 2005). In comparison with the radio luminosities observed for the relativistic SNe 1998bw (Kulkarni et al. 1998) and 2009bb (Soderberg et al. 2010), SN 2010ay is a factor of ≳ 10 less luminous. The peak radio luminosity observed for GRB 100316D was a factor of a few higher than the first EVLA non-detection of SN 2010ay (E. Margutti et al. 2012, in preparation). The only relativistic explosion with detected radio emission below our EVLA limits is the weak and fast-fading XRF 060218 (Soderberg et al. 2006a).

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We construct an R-band light curve for SN 2010ay using the observations described in Section 2.3 (Table 2). We convert the i_P1- and r'-band data points to the R band using the fiducial light-curve method of Soderberg et al. (2006b), assuming the unextincted i' − R and r' − R colors observed for the Type Ic-BL SN 1998bw at the appropriate epoch (Galama et al. 1998). Photometry for the unfiltered CRTS images was reported by Drake et al. (2010) after transformation to the synthetic V band (A. J. Drake 2011, private communication); we therefore convert to the R band assuming the V − R color of SN 1998bw at the appropriate epoch. For the Pan-STARRS1 photometry, the host galaxy flux was subtracted using a template image. For all other photometry, we have subtracted the flux of the host galaxy numerically assuming the magnitude reported in Table 1. A total (Galactic + host) reddening of E(B − V) = 0.2 mag has been assumed (see Section 2.3.1).

To estimate the explosion date of SN 2010ay, we have fit an expanding fireball model to the optical light curve (Figure 2), following Conley et al. (2006). In this model, the luminosity increases as

$$\begin{equation} L\propto \Bigg (\frac{t-t_0}{1+z}\Bigg)^n. \end{equation} \tag{ 1 }$$

We derive an explosion date t₀ of 2010 February 21.3 ± 1.3. Here, we have assumed an index n = 2. This suggests that the PS1 3π i_P1-band pre-discovery detection image of SN 2010ay was taken ∼4 days after the explosion. Observations by the PS1 survey have therefore provided a valuable data point for estimating the explosion date and also for constraining the rise time of SN 2010ay, as well as other nearby SNe (e.g., SN 2011bm; Valenti et al. 2012).

In Figure 2, we compare the light curve of SN 2010ay to the SN Ib/c light-curve template of Drout et al. (2011) after stretching by a factor of (1 + z). The template provides a reasonable fit to the optical evolution of SN 2010ay. Fitting the template to our photometry, we derive (reduced χ² = 0.3) a date of R-band peak of 2010 March 18 ± 2 UT (MJD 55, 273 ± 2) and an R-band peak magnitude of M_R ≈ −19.7 mag before extinction correction. As discussed in Section 2.3.1, based on the Balmer decrement observed for the host galaxy emission lines, we assume an extinction of E(B − V) = 0.2 mag. Applying this correction, the peak absolute magnitude is M_R ≈ −20.2 ± 0.2 mag. We note that this fitted value is ≈0.2 mag fainter than that estimated from the data point near peak. Here, the uncertainty is dominated by the template fitting.

Regardless of the extinction correction, SN 2010ay is more luminous than all the 25 SNe Ib/c in the sample of Drout et al. (2011), except for SN 2007D (M_R ≈ −20.65 mag, which was also significantly extincted: A_V ∼ 1.0 mag). Assuming an intrinsic V − R color of zero at peak (e.g., 1998bw: Galama et al. 1998; Patat et al. 2001), SN 2010ay is also more luminous than any of the 22 GRB and XRF-producing SNe in the compilation of Cano et al. (2011b), all corrected for extinction, and is 1.5 standard deviations from the mean luminosity. The peak magnitude is only ∼1 mag below that of the Type Ic SN 2007bi (M_R = −21.3 ± 0.1 mag), which Gal-Yam et al. (2009) report as a candidate pair-instability SN.

We use the available photometry for SN 2010ay discussed above to derive the mass of ⁵⁶Ni required to power the optical light curve under the assumption that the emission is powered by radioactive decay. Using the relation between M_Ni and M_R found by Drout et al. (2011), log (M_Ni) = (− 0.41M_R − 8.3) M_☉, we estimate that SN 2010ay synthesized a nickel mass of M_Ni = 0.9^+0.1_−0.1 M_☉. We have estimated the uncertainty in the M_Ni estimate by propagation of the uncertainty in the template fitted peak magnitude—systematic uncertainties are not included. If we instead adopt the most luminous individual data point in the light curve as the peak value, rather than the smaller peak value from template fitting, we find M_Ni ≈ 1.2 M_☉.

The M_Ni estimate for SN 2010ay is larger than that of all but one (SN 2007D) of the 25 SNe Ib/c in the Drout et al. (2011) compilation and significantly larger than the estimate for GRB–SN 2010bh, M_Ni = 0.12 ± 0.01 M_☉ (Cano et al. 2011a). On the other hand, M_Ni of SN 2010ay is at least 3 times smaller than for SN 2007bi (M_Ni ≈ 3.5–4.5 M_☉; Young et al. 2010). A pair-instability SN should produce M_Ni ≳ 3 M_☉ (Gal-Yam et al. 2009).

As illustrated in Figure 3, the broad, highly blended spectral features of SN 2010ay at the time of the WHT observations (14 days after R-band peak; see Section 3.1) resemble those of SN 2010bh at a similar time (10.0 days after peak; Chornock et al. 2010). In particular, the blueshift of the feature near 6355 Å is larger than in SN 1998bw and more similar to SN 2010bh. This feature is commonly associated with Si ii λ6355 (e.g., Patat et al. 2001). However, this feature has two clearly detectable absorption minima in SN 2010ay, but not in SN 2010bh. This could be due to increased blending in SN 2010bh or the absence of contaminating lines. The red ends of the SN 2010ay and SN 2010bh spectra (rest wavelength >7500 Å) have similar P Cygni features, but the emission and absorption components in SN 2010bh are each blueshifted by ∼200 Å more than in the spectrum of SN 2010ay. Chornock et al. (2010) attribute this feature to the Ca ii near-IR (NIR) triplet, with a gf-weighted line centroid of 8479 Å, and find a velocity that is high but consistent with the early-time velocity of Si ii λ6355 ((30–35) × 10³ km s⁻¹).

We measure the absorption velocity from the minimum of the Si ii λ6355 absorption feature (v_Si). We smooth the spectrum using an inverse-variance-weighted Gaussian filter (Blondin et al. 2006, with dλ/λ = 0.005) and measure the minimum position of the redmost component of the absorption profile. The blue component of the absorption profile shifts blueward over time, suggesting that it is produced by a combination of ions separated by several 10³ km s⁻¹, such as He i λ5876 and Na i D, whose relative optical depth changes with time.

The absorption velocity inferred from the Si ii λ6355 feature is ∼2 times faster than that of SN 1998bw at similar times, and more similar to that of SN 2010bh (Figure 3). For SN 1998bw, Patat et al. (2001) measured ∼10 × 10³ km s⁻¹ at +13 days. For SN 2010bh, Chornock et al. (2010) measured v_Si ≈ 26 × 10³ km s⁻¹ at +10.0 days after explosion. Prieto (2010) reported a velocity of v_Si ≈ 22.6 × 10³ km s⁻¹ from the Si ii λ6355 feature in a spectrum of SN 2010ay taken at +4 days; Prieto (2010) does not discuss the details of their methodology for the velocity measurement. From our [WHT, Gemini] spectra taken [ + 14, +24] days after R-band peak (see Section 3.1), we estimate v_Si ≈ [19.2, 18.3] × 10³ km s⁻¹.

In addition to the broadening of the spectral features and the blueshift of the Si ii λ6355 line, additional lines of evidence suggest a high photospheric expansion velocity for SN 2010ay. We measure v_Si ≈ [21.7, 20.1] × 10³ km s⁻¹ from the Ca ii NIR triplet on the smoothed [WHT, Gemini] spectra, relative to a line center at 8479 Å. This is within a few × 10³ km s⁻¹ of the v_Si we measure from Si ii λ6355 at these epochs. Furthermore, we do not detect the broad emission "bump" near 4500 Å in either of our spectra. This feature was also absent in SN 2010bh but was identified in SN 2003dh, SN 2006aj, and several Ic-BLs not associated with GRBs and normal SNe Ic; Chornock et al. (2010) suggest that the absence of this feature indicates a high expansion velocity if it is due to blending of the iron lines to the blue and red of 4500 Å.

We compare the late-time expansion velocity of SN 2010ay to other SNe Ic-BL and GRB–SNe with detailed, multi-epoch velocity measurements from the literature in Figure 5. We note that the velocities for SNe 1997ef, 2003dh, and 2003lw plotted in the figure were estimated by Mazzali et al. (2006) via spectral modeling, rather than measured directly from the minimum of the Si ii λ6355 absorption feature; however, these velocities should be equivalent to within a few 10³ km s⁻¹, as the minimum of the Si ii feature is typically well fit by the photospheric velocity of the spectral models (see, e.g., Mazzali et al. 2000; Kinugasa et al. 2002). In this figure, we also fit power-law gradients to the time evolution of the velocity of these SNe with the form v_Si = v³⁰_Si(t/30)^α, where t is the time since explosion in days and v³⁰_Si is the velocity at 30 days in units of 10³ km s⁻¹. These parameters are listed in Table 4. Figure 5 illustrates that most SNe are well described by a single power law.²³ However, due to lack of late-time spectroscopy, the v³⁰_Si measurement amounts to an extrapolation for some objects (particularly 2006aj), and contamination from different ions or detached features will add uncertainty to velocities measured from the Si ii λ6355 feature.

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SNe 2010ay and 2010bh share high characteristic velocities at 30 days after explosion and velocity gradients that are low relative to other broad-lined SNe Ic with and without associated GRBs. For SN 2010ay, v³⁰_Si = 21 ± 2 is 2–4 times larger than for other SNe Ic-BL without associated GRBs (v³⁰_Si = 6 ± 2 for 1997ef, 5 ± 2 for 2002ap, 10 ± 1 for 2003jd, 9 ± 2 for 2007bg, and 10.3 ± 0.7 for 2007ru) and is similar to the GRB–SN 2010bh (v³⁰_Si = 24 ± 3). No other GRB–SN or SN Ic-BL has v³⁰_Si > 15. The SNe Ic-BL and GRB–SNe with the most shallow velocity gradients among these 12 objects have α < −0.5; they are SN 2006aj (α = −0.3 ± 0.2), SN 2007bg (α = −0.3 ± 0.2), SN 2010ay (α = −0.4 ± 0.3), and SN 2010bh (α = −0.22 ± 0.07). This places SN 2010ay in the company of two GRB–SNe in having a slowly evolving absorption velocity and SN 2007bg (whose unusually fast decline rate distinguishes it from other SNe Ic-BL; Young et al. 2010). The velocities of SNe 2010ay and 2010bh, respectively, decline about 2 and 4 times more slowly than the other SNe Ic-BL (mean and standard deviation: α = −0.8 ± 0.4) and about 1.5 and 3 times more slowly than the other GRB–SNe (α = −0.7 ± 0.2). The slow Si ii λ6355 absorption velocity evolution of SN 2010ay at late times resembles the slow evolution of the Fe ii lines of the spectroscopically normal Type Ic SNe 2007gr and 2011bm at late times (Valenti et al. 2012).

Given the high peak luminosity of SN 2010ay (Section 3.1), we also consider the velocity of the candidate pair-instability SN 2007bi. Velocity measurements for SN 2007bi are only available at late times (>50 days; Young et al. 2010). Fitting to these late-time Si ii λ6355 velocity measurements, we find that SN 2007bi has a characteristic velocity ∼3 times smaller than 2010ay (v³⁰_Si = 8 ± 2) and the late-time velocity gradient is ∼2 times more shallow (α = −0.2 ± 0.2).

We use the scaling relations provided by Drout et al. (2011), based on the original formalism of Arnett (1982) and modified by Valenti et al. (2008), to derive the total mass of the ejecta and the kinetic energy

$$\begin{eqnarray} &&M_{\rm ej}=0.8\bigg (\frac{\tau _c}{8 \,\rm d}\bigg)^2\bigg (\frac{v_{\rm Si}}{\rm 10{,}000\,km\,s^{-1}}\bigg) \,M_{\odot } \end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray} &&E_{K}=0.5\bigg (\frac{\tau _c}{8 \,\rm d}\bigg)^2\bigg (\frac{v_{\rm Si}}{\rm 10{,}000\,km\,s^{-1}}\bigg)^3 \times 10^{51}\,{\rm erg}. \end{eqnarray} \tag{ 3 }$$

We assume the fitted peak magnitude for SN 2010ay (M_R = −20.2 ± 0.2; Section 3.1), the absorption velocity we measure from our WHT spectrum at 14 days after maximum light (v_Si = 19.2 × 10³ km s⁻¹; Section 3.3), and a characteristic time (light-curve width) consistent with the data and the mean value from the Drout et al. (2011) sample of SNe Ic-BL (τ_c = 14 days).

Using these values, the total mass ejected was M_ej ≈ 4.7 M_☉, and the total kinetic energy of the explosion was E_K ≈ 10.8 × 10⁵¹ erg. Hereafter we refer to the definition E_{K, 51} = E_K/10⁵¹ erg.

The systematic uncertainties associated with this modeling dominate the statistical uncertainties. In particular, the models rely on the assumptions of homologous expansion, spherical symmetry, all ⁵⁶Ni centralized at the center of the ejecta, optically thick ejecta, and constant opacity.

We note that an earlier measurement of the absorption velocity is preferred for optical modeling. Since we have argued that SN 2010ay and SN 2010bh have similar characteristic velocities (v³⁰_Si), if we instead adopt a higher velocity of 25, 000 km s⁻¹ as measured for SN 2010bh by Cano et al. (2011a), we estimate M_ej ≈ 6.1 M_☉ and E_{K, 51} ≈ 23.9 for SN 2010ay.

The M_ej and E_{K, 51} of SN 2010ay are consistent with the mean for SNe Ic-BL in the Drout et al. (2011) sample (4.7^+2.3_−1.8 M_☉ and 11⁺⁶₋₄, respectively), because the authors assumed a velocity (v_Si = 2 × 10⁴ km s⁻¹) similar to the late-time velocity we measure. For comparison, SN 2010bh had a total ejecta mass of ∼2 M_☉ and a total kinetic energy of E_{K, 51} ≈ 13 (Cano et al. 2011a).

The ratio of Ni to total ejecta mass is ∼0.2 for SN 2010ay, significantly higher than the values typical of SNe Ic-BL and GRB–SNe. For comparison, the ratio is just ∼0.05 for SN 2010bh. Adopting the values derived from bolometric light-curve modeling by Cano et al. (2011a), the M_Ni and M_Ni/M_ej ratios for other GRB–SNe are ∼0.5 M_☉ and ∼0.06–0.22 (1998bw), ∼0.4 M_☉ and ∼0.08 (2003dh), ∼0.15 M_☉ and ∼0.07–0.1 (2006aj), and ∼0.2 M_☉ and ∼0.06 (2009bb). This ratio for SN 2010ay is larger than that of all but 4 of the 25 SNe of Drout et al. (2011): the Type Ic SNe 2004ge (M_Ni/M_ej ∼ 0.4) and 2005eo (M_Ni/M_ej ∼ 0.2), the Type Ib SN 2005hg (∼0.4), and the Type Ic-BL SN 2007D (∼0.6).

The large value of M_Ni we estimate for SN 2010ay raises the question of whether a process other than Ni decay may be powering its light curve (e.g., Chatzopoulos et al. 2009). An independent test of the physical process powering the light curve is the decay rate of the late-time light curve, which should be ≈0.01 mag day⁻¹ for SNe powered by radioactive decay of ⁵⁶Co. For SN 2007bi, Gal-Yam et al. (2009) derive M_Ni = 3.5 M_☉ from the measured peak magnitude and find that the late-time light curve is consistent with the decay rate of ⁵⁶Co. While the Pan-STARRS1 3π survey also observed the field in 2011 March, the SN was not detected in our subtracted images, and the limits are not constraining in the context of ⁵⁶Co decay (see Section 2.2 and Table 2). Another possible process is a radiation-dominated shock that emerges due to interaction with an opaque circumstellar medium (CSM), as has recently been proposed by Chevalier & Irwin (2011) for the ultraluminous SNe 2006gy and 2010gx (Pastorello et al. 2010; Quimby et al. 2011). However, while this class of ultraluminous objects shares some spectroscopic similarities to SNe Ic (Pastorello et al. 2010), they show peak luminosities ∼4–100 times higher than SN 2010ay (Chomiuk et al. 2011; Quimby et al. 2011).

In the free-expansion scenario, a shock discontinuity separates the forward and reverse shocks, located at the outer edge of the stellar envelope. The bulk ejecta is in free expansion, while the thin layer of post-shock material is slightly decelerated, R∝t^0.9 (Chevalier & Fransson 2006). At a given frequency, the bell-shaped light curves of the SN synchrotron emission may be described as (Chevalier 1998)

$$\begin{equation} L_{\nu }\approx 1.582\times L_{\nu ,p} \left(\frac{\Delta t}{t_p}\right)^a [1-e^{-(\Delta t/t_p)^{-(a+b)}}], \end{equation} \tag{ 4 }$$

where L_{ν, p} is the flux density at the spectral peak at epoch t_p. Assuming an electron index of p ≈ 3, consistent with radio spectra of SNe Ib/c (Chevalier & Fransson 2006), the exponents are a ≈ 2.3 and b ≈ 1.3. The time-averaged shock wave velocity is $\overline{v}\approx R/\Delta t$, where R is the shock wave radius defined as

$$\begin{eqnarray} R&\approx &2.9\times 10^{16}\left(\frac{\epsilon _e}{\epsilon _B}\right)^{-1/19} \left(\frac{L_{\nu ,p}}{10^{28} \rm \,erg \,s^{-1} \,Hz^{-1}}\right)^{9/19}\nonumber \\ &&\times \left(\frac{\nu _p}{5\,{\rm GHz}}\right)^{-1} \,\rm cm. \end{eqnarray} \tag{ 5 }$$

Here, we make the assumption that the radio-emitting region is half of the total volume enclosed by a spherical blast wave. Next, we estimate the internal energy, E, of the radio-emitting material from the post-shock magnetic energy density, E ≈ B²R³/12_B, where we maintain the assumption of equipartition. As shown by Chevalier (1998), the amplified magnetic field at peak luminosity is also directly determined from the observed radio properties,

$$\begin{eqnarray} B&\approx & 0.43 \left(\frac{\epsilon _e}{\epsilon _B}\right)^{-4/19} \left(\frac{L_{\nu ,p}}{10^{28} \,{\rm erg\,s^{-1}\,Hz^{-1}}}\right)^{-2/19} \nonumber \\ &&\times \left(\frac{\nu _p}{5\,{\rm GHz}}\right) \,\rm G. \end{eqnarray} \tag{ 6 }$$

Finally, the mass-loss rate of the progenitor star, $\dot{M}$, may be derived from the number density of emitting electrons. Here, we normalize the wind profile according to ρ∝Ar⁻² and A_* = A/5 × 10¹¹ g cm⁻. This normalization of A_* implies that an A_* of 1 corresponds to typical Wolf–Rayet progenitor wind properties of $\dot{M}=10^{-5}\,M_{\odot }\,\rm yr^{-1}$ and a progenitor wind velocity of v_w = 10³ km s⁻¹:

$$\begin{eqnarray} A_* &\approx & 0.15 \bigg(\frac{\epsilon _B}{0.1}\bigg)^{-1} \bigg(\frac{\epsilon _e}{\epsilon _B}\bigg)^{-8/19} \left(\frac{L_{\nu ,p}}{10^{28} \,{\rm erg\,s^{-1}\,Hz^{-1}}}\right)^{-4/19} \nonumber \\ &&\times \bigg(\frac{\nu _p}{5\,{\rm GHz}}\bigg)^2 \left(\frac{\Delta t}{10 \,\rm days}\right)^2 \,{\rm cm}^{-1}, \end{eqnarray} \tag{ 7 }$$

where we assume a shock compression factor of ∼4 and a nucleon-to-electron ratio of 2.

We built a two-dimensional grid of fiducial radio light curves according to Equation (4) in which we vary the parameters $L_{\nu _p}$ and ν_p over a reasonable range of parameter space, bounded by t_p ≈ [1, 3000] days and F_{ν, p} ≈ 0.04–1000 mJy. We identify the fiducial light curves associated with a radio luminosity higher than the EVLA upper limits for SN 2010ay at each epoch as these are excluded by our observations. We extract the physical parameters associated with these excluded light curves (R, B, E, A_*) to define the parameter space excluded by our radio observations. The parameter space for ν_p and F_{ν, p} is bounded by the respective values for which the model exceeds relativistic velocities, βΓ ∼ few.

As shown in Figure 6, our deep EVLA limits enable us to rule out a scenario in which there is copious energy, E ≳ 10⁴⁸ erg, coupled to a relativistic outflow, in this two-dimensional E − v parameter space. The excluded region includes GRB–SNe 1998bw and 060218, as well as the relativistic SN 2009bb. It does not exclude the standard scenario in which a small percent of the energy is coupled to fast-moving material within the homologous outflow, as is typically observed for ordinary SNe Ib/c (E ≈ 10⁴⁷ and v ≈ 0.2c; Soderberg et al. 2010).

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Next we consider the effects of circumstellar density since lower mass-loss rates produce fainter radio counterparts. As shown in Figure 7, the EVLA limits for SN 2010ay exclude the region of parameter space populated by SNe 1998bw and 2009bb with mass-loss rates of A_* ∼ 0.1; however, the low-density environment of GRB 060218 lies outside of our excluded region due to its lower CSM density, A_* ∼ 0.01, which gives rise to a lower luminosity radio counterpart.

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In the case of relativistic deceleration the ejecta are confined to a thin jet and are physically separated from the homologous SN component. Deceleration of the jet occurs on a timescale of Δt ≈ (E₅₁/A_*) years in a wind-stratified medium (Waxman 2004). On this same timescale, any ejecta components that were originally off-axis spread sideways into the observer's line of sight. While the early EVLA limits constrain the properties of the on-axis ejecta according to the free-expansion model described above, the late-time EVLA upper limits constrain any radio emission from a GRB jet originally pointed away from our line of sight.

For this scenario, we adopt the semianalytic model of Soderberg et al. (2006c) for off-axis GRB jets. In Figure 4, we compare the radio upper limits for SN 2010ay with the predictions for an off-axis jet with standard parameters (E_K ≈ 10⁵¹ erg, A_* = 1, _e = _B = 0.1, and θ_j = 5°) and assuming a viewing angle of θ_oa = 30°, 60°, or 90°. Our EVLA upper limits rule out all three of these model light curves. We derive the two-dimensional parameter space (energy and CSM density) that is excluded based on our EVLA upper limit at Δt ≈ 1.2 years. We note that this model accommodates the full transition from relativistic to non-relativistic evolution. We built a collection of model light curves spanning parameter range A_* ≈ [0.01–100] and E ≈ [10⁴⁹–10⁵²] erg, maintaining the assumption of p = 3 and _e = _B = 0.1. Here, we adopted a jet opening angle of θ_j = 5° and an off-axis viewing angle of θ_oa = 90° (the most conservative scenario). We note that van Eerten & MacFadyen (2011) have developed off-axis GRB afterglow light-curve models based on hydrodynamic simulations that reproduce the semianalytic models presented here to within factors of a few (see also van Eerten et al. 2010).

As shown in Figure 8, we are able to exclude the parameter space associated with typical GRBs, i.e., E ≈ 10⁵¹ erg (beaming corrected) and A_* ≈ 1. GRBs with lower energies and densities are better constrained using the trans-relativistic formalism above. In conclusion, our radio follow-up of SN 2010ay reveals no evidence for a relativistic outflow similar to those observed in conjunction with the nearest GRB–SNe; however, a weak afterglow like that seen from XRF 060218 cannot be excluded.

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We compare the host galaxy of SN 2010ay to the nearby galaxy population of the SDSS spectroscopic survey. The physical properties of the host galaxy, SDSS J123527.19+270402.7, are estimated in the MPA/JHU catalog.²⁴ The total (photometric) galaxy stellar mass (M_*) is given as 3.6^+2.9_−1.3 × 10⁸ M_☉, the aperture-corrected SFR is 1.0^+0.3_−0.2 M_☉ yr⁻¹, and the nuclear (fiber) oxygen abundance (O/H_o) is log (O/H) + 12 = 8.58^+0.02_−0.03 on the scale of Tremonti et al. (2004, T04). The specific star formation rate (SSFR) of the host galaxy is then ≈2.8^+0.9_−0.4 Gyr⁻¹. For consistency, we consider these values of M_*, the oxygen abundance, and the SFR for the host galaxy of SN 2010ay when comparing to other galaxies in the MPA/JHU catalog.

The oxygen abundance and SFR of the host galaxy of SN 2010ay listed in the MPA/JHU catalog are consistent with the values we derive in this paper (see also Kelly & Kirshner 2011). The MPA/JHU catalog lists metallicities on the T04 scale. Using the Kewley & Ellison (2008) conversion to the PP04 scale, the T04 metallicity estimate corresponds to a metallicity of log (O/H) + 12 = 8.38, which is ∼0.2 dex higher than the one we measure (log (O/H) + 12 = 8.19). However, there is a large (∼0.2 dex) rms scatter between the PP04 O3N2 and T04 diagnostics at the regime of log (O/H) + 12_PP04 ∼ 8.2 (Kewley & Ellison 2008). The SFR in the MPA/JHU catalog is also in good agreement with the value we estimate from the Hα luminosity. Although our estimate does not include an aperture correction, the size of the Gemini slit (1) should encompass most of the star formation in the galaxy (Petrosian r = 1355; Table 1).

The mass-to-light ratio of the host galaxy of SN 2010ay is low compared to typical star-forming galaxies. To compare the host galaxy to the general galaxy population, we select a subset of the MPA/JHU catalog by requiring that estimates of M_*, SFR, and O/H_o be available, and we remove active galactic nuclei (AGNs) according to Kauffmann et al. (2003). We consider 167,837 starbursting galaxies following these constraints. The host galaxy ranks in the [4th, 38th, 11th] percentile in [M_*, SFR, O/H_o] among these galaxies. Among the selected galaxies with a stellar mass as low as the host galaxy,²⁵ the median and standard deviation of the B-band²⁶ absolute magnitude are −15.8 ± 1.3 mag. With M_B = −18.35 ± 0.05 mag, the host of SN 2010ay is more luminous than other galaxies with a similar mass at the 2σ level. The discrepancy is due to the blue color of the SN 2010ay host galaxy, which indicates a stellar population that is very young and therefore has a low stellar-mass-to-light ratio. Among the 1184 galaxies in the MPA/JHU catalog that meet the constraints above and have a color similar to the host of SN 2010ay (0.47 < u − r < 0.67, from SDSS fiber magnitudes), the host galaxy has typical properties, with [M_*, SFR, O/H_o] in the [46th, 49th, 54th] percentile.

Based on these properties, we classify the host galaxy of SN 2010ay as a luminous blue compact galaxy (BCG). BCGs span a large range in luminosity (−21 < M_B < −12, where luminous BCGs have M_B < −17) but are distinguished by their blue colors (B − V < 0.45), high SFR (1 < SFR < 20 M_☉ yr⁻¹), and low metallicity (Z_☉/50 < Z < Z_☉/2; Kunth & Östlin 2000; Kong & Cheng 2002). The host galaxy of SN 2010ay has a luminosity (M_B = −18.35 ± 0.05), color (B − V = 0.11 ± 0.07), SFR (1.0^+0.3_−0.2 M_☉ yr⁻¹), and metallicity (Z ∼ 0.3 Z_☉) consistent with all these ranges.²⁷

Our measurement of the metallicity from the Gemini spectrum indicates that the explosion site of SN 2010ay is ∼0.5(0.2) dex lower in metallicity than the median SNe Ic (Ic-BL) in the sample of Modjaz et al. (2011). In that sample, the median PP04 O3N2 metallicity measured at the explosion site of SNe Ic is log (O/H) + 12 ≈ 8.7 and for Ic-BL is ≈8.4 dex, for 12 and 13 objects, respectively. If instead the KD02 metallicity is used, the median of the sample is ≈8.9 dex for SNe Ic (13 objects) and ≈8.7 dex for Ic-BL (15 objects), so the abundance of the SN 2010ay host galaxy is similarly low compared to the median.

The metallicity of the environment of SN 2010ay is more similar to previously studied nearby GRB–SN progenitors. A metallicity identical to our measurement was measured at the explosion site of SN 2010bh (Levesque et al. 2011): log (O/H) + 12 = 8.2. In the survey of Levesque et al. (2010a), and adding the measurement for SN 2010bh, the GRB–SN host galaxies have an average and standard deviation PP04 O3N2 metallicity of log (O/H) + 12 = 8.1 ± 0.1 on the PP04 scale, which is consistent with the SN 2010ay environment. Among the 17 LGRB host galaxies surveyed in Savaglio et al. (2009), the average metallicity is somewhat lower, 1/6 Z_☉ or log (O/H) + 12 ∼ 7.9, but these are at an average redshift of z ∼ 0.5 that is much higher than SN 2010ay.

This evidence suggests that the host galaxy of SN 2010ay has chemical properties more consistent with LGRBs/GRB–SNe than SNe Ic-BL without associated GRBs; however, selection effects may mitigate this discrepancy. SNe found in targeted surveys of luminous galaxies have host galaxy properties biased toward higher metallicities, due to the luminosity–metallicity (L − Z) relation (Tremonti et al. 2004). LGRBs are found in an untargeted manner through their gamma-ray emission and therefore are not biased by this relation.

SN 2010ay joins a growing list of SNe Ic-BL that have been discovered in low-metallicity host galaxies. Given the systematic uncertainty in strong-line oxygen abundance diagnostics (∼0.07 dex), we will consider host galaxies with metallicity log (O/H)_PP04 + 12 < 8.3 (Z ≲ 0.4 Z_☉) to be in the low-metallicity regime of SN 2010ay. Among the 15 SNe Ic-BL (9 discovered by untargeted searches) in the surveys of Modjaz et al. (2008) and Modjaz et al. (2011), 4 were found in low-metallicity environments: SN [2007eb, 2007qw, 2005kr, 2006nx] at log (O/H)_PP04 + 12 = [8.26, 8.19, 8.24, 8.24]. All of these SNe were discovered by untargeted searches. Young et al. (2010) measure the metallicity of the host galaxy of the broad-lined Ic SN 2007bg to be log (O/H)_PP04 + 12 = 8.18, although this SN has light curve and spectral properties that distinguish it from normal SNe Ic-BL (Section 3.3). Furthermore, Arcavi et al. (2010) find that SNe Ic-BL are more common in dwarf (M_r ⩾ −18) host galaxies, which the authors attribute to a preference for lower metallicities.

The star formation properties of the host galaxy of SN 2010ay also resemble the host galaxies of LGRBs. If we consider those galaxies in the MPA/JHU catalog with masses similar to the host galaxy of SN 2010ay (as defined above), then the median SFR and O/H_o of these galaxies is 0.13 M_☉ yr⁻¹ and log(O/H_o)+12 = 8.36, respectively. The host galaxy of SN 2010ay is in the [96th, 77th] percentile for [SFR, O/H_o] among these galaxies. This indicates that, while the host galaxy of SN 2010ay falls within 1σ of the mass–metallicity (M − Z) relation for star-forming galaxies, its SFR is extreme for its mass. The 39 LGRB host galaxies in the survey of Savaglio et al. (2009) are similarly low in mass and have high SFRs, with an average stellar mass of M_* ∼ 10⁹ M_☉ and SSFR ∼3.5 Gyr⁻¹.

The host galaxy of SN 2010ay falls below the L − Z relation for nearby star-forming galaxies, as illustrated by Figure 9. We have transformed the k-corrected gri magnitudes from the MPA/JHU catalog to B band (Blanton & Roweis 2007). At the luminosity of the host galaxy of SN 2010ay, the median metallicity and standard deviation of the SDSS galaxies on the T04 scale are log (O/H) + 12 = 8.93 ± 0.17; the host galaxy of SN 2010ay falls in the 3rd percentile. In other words, the host galaxy of SN 2010ay is a 2σ outlier from the L − Z relation. Similarly, Levesque et al. (2010a) and Han et al. (2010) suggest that the host galaxies of LGRBs fall below the L − Z relation as defined by normal star-forming galaxies, BCGs, and the host galaxies of SNe Ic.

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Mannucci et al. (2011) have explained the offset of LGRB host galaxies from the M − Z relation as a preference for LGRBs to occur in host galaxies with high SFR, as characterized by the fundamental metallicity relation (FMR) of Mannucci et al. (2010; see also Lara-López et al. 2010). Using the extended FMR for low-mass galaxies from Mannucci et al. (2011), the host galaxy of SN 2010ay should have a metallicity of log (O/H) + 12 = 8.20 given its stellar mass and SFR. The FMR is calibrated to the Nagao et al. (2006) metallicity scale, which is similar to that of PP04 at this metallicity. Given the intrinsic scatter in the extended FMR on the order of ∼0.05 dex, this value is consistent with the PP04 value we measure from our Gemini spectrum: log (O/H) + 12 = 8.19. Kocevski & West (2011) similarly explain the offset of LGRB host galaxies from the M − Z relation as an SFR effect but suggest that the long GRB host galaxies have even higher SFR than would be implied by the FMR.

SN 2010ay is an example of an SN Ic-BL where the host galaxy is consistent with the M − Z relation for star-forming galaxies but deviates from the L − Z relation due to its low stellar-mass-to-light ratio (Section 6.1). Its 2σ discrepancy from the L − Z relation would be hard to explain as an SFR rate effect alone because among galaxies in the MPA/JHU catalog without AGNs (as defined above) and with M_B within 0.1 mag of the host galaxy of SN 2010ay, the host galaxy has an SFR in the 26th percentile (<1σ discrepancy).