SN 2006bt: A PERPLEXING, TROUBLESOME, AND POSSIBLY MISLEADING TYPE Ia SUPERNOVA

The light curves of SN 2006bt have already been published by H09b. The light curves were fit by both H09a and H09b, finding Δm₁₅(B) = 1.09 ± 0.06 mag and Δm₁₅(V) = 0.54 ± 0.04 mag. They similarly found the SALT2 (Guy et al. 2007) and MLCS2k2 (with R_V = 1.7); Jha et al. 2007) fit parameters of x1 = 0.069 ± 0.104, c = 0.162 ± 0.008 and Δ = −0.325 ± 0.052, A_V = 0.428 ± 0.053 mag, respectively. The light-curve fits indicate that SN 2006bt has a slightly slow decline, and a red color (SALT2) or relatively high extinction (MLCS2k2). The MLCS2k2 fit has a reduced χ² of ∼ 1.36 for 98 separate observations, including pre-maximum data in multiple passbands. The SALT2 templates used by H09b do not cover the late-time photometry and the best fit has a reduced χ² of ∼ 2 with 70 observations. However, estimates of the time of maximum and the best-fit light-curve models using either method are quite comparable. An analysis of the light-curve fits alone would lead one to conclude that SN 2006bt is not a particularly discrepant object and can be included in any cosmological analysis.

However, the host galaxy, CGCG 108-013, is an S0/a galaxy (with d = 139 Mpc) and SN 2006bt has a projected galactocentric distance (PGCD) of 33.7 kpc (equivalent to 7.8R_eff, where R_eff = 64 is defined by the Petrosian radius where 50% of the flux is contained within a circle of radius R_eff; see Section 5), making SN 2006bt have the fourth largest PGCD of SNe Ia in the CfA3 sample of 185 SNe Ia. The SN environment is thus expected to have little dust (excluding possible circumstellar dust). Additionally, H09a shows the relationship between host morphology, PGCD, and light-curve fit parameters. In the CfA3 sample, SN 2006bt has among the largest values for x1, c, and A_V, and the smallest values of Δ for all SNe hosted in early-type galaxies. Furthermore, SN 2006bt is a clear outlier in the trend of smaller c or A_V with increasing PGCD (see Figures 18 and 19 in H09a).

From the light curves, we can see that SN 2006bt evolves slightly differently from other SNe with similar B-band decline rates. In Figure 1, the light curves of SN 2006bt are compared to those of SN 2006ax, an object with Δm₁₅(B) = 1.08  ±   0.05 mag and minimal (A_V < 0.04 mag) host-galaxy extinction. These objects have very similar UBV light curves; however, the r and i light curves have some slight differences. In the r band, SN 2006bt lacks the "shoulder" at 15–20 days after maximum brightness seen in average and high-luminosity SNe Ia. In the i band, SN 2006bt has a shoulder, but lacks the deep "trough" and subsequent prominent second maximum seen in most SNe Ia.

In Figure 1, the light curves of SN 2006bt are also compared to those of SN 2005mz, a fast-declining SN Ia (Δm₁₅(B) = 1.96 ± 0.14 mag) with moderate host-galaxy extinction (A_V = 0.27 ± 0.09 mag). Although this object lacks a shoulder in either the r or i bands, it declines much faster in all bands.

Figure 3 presents the color curves of SNe 2005mz, 2006ax, and 2006bt. We have corrected the color curves of SN 2005mz for host-galaxy extinction as determined by MLCS fits (A_V = 0.27 mag and R_V = 1.7), and all objects for Milky Way extinction as determined by Schlegel et al. (1998), which indicates E(B − V) = 0.051 mag for SN 2006bt. The curves of SN 2006bt generally fall between the curves of SNe 2005mz and 2006ax for t < 35 days and above both curves for t>35 days. Reddening the color curves of SN 2006ax by A_V = 0.428 mag with R_V = 1.7, the best-fit value for SN 2006bt from H09a using MLCS, the B − V color curves of SNe 2006ax and 2006bt are very well matched. This is consistent with the "Lira relation" (Phillips et al. 1999), which uses the late-time colors of SNe Ia to predict their host-galaxy reddening. However, this same correction does not account for the differences in the V − r and V − i color curves of SNe 2006ax and 2006bt. Given the shapes of their color curves, reddening alone cannot account for the differences between these objects. Furthermore, the color curves of SNe 2005mz and 2006bt differ by more than reddening alone.

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Considering the PGCD, the early-type host, the non-standard color curves, and a lack of Na D absorption in any spectrum (see Section 4), we believe the MLCS-fit extinction of A_V = 0.428 mag to be unrepresentative of the true host-galaxy extinction. Given these factors, the extinction is most likely very small, and for the remainder of our analysis, we assume that there is no host-galaxy extinction.

Since SN 2006bt has slightly odd light and color curves as well as a host-galaxy extinction very different from its MLCS-fit extinction (which indicates that SN 2006bt is not well modeled by the training set of MLCS), it is worth investigating the possibility that SN 2006bt does not follow the WLR. The MLCS model would indicate that SN 2006bt had a peak absolute magnitude in V that is 0.428 mag (equivalent to the fit value for A_V) brighter than its true value.

We plot the relationship between Δm₁₅(B) and M_V in Figure 4 for a subsample of the CfA3 sample (H09b). Using the extinction derived from MLCS, SN 2006bt is slightly overluminous relative to the relationship fit by Phillips et al. (1999), but it is within the scatter around the relationship. With no extinction correction, SN 2006bt is slightly underluminous for its light-curve shape; however, it is not a significant outlier.

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Despite an atypical set of light curves, SN 2006bt is not a significant outlier to the WLR using either no extinction or the MLCS-determined extinction value. For SN 2006bt, H09a measured distance moduli of μ = 35.981, 35.944, 35.784, and 35.993 mag with distance fitters SALT, SALT2, MLCS with R_V = 3.1, and MLCS with R_V = 1.7, respectively. Using the cosmic microwave background (CMB)-corrected redshift for CGCG 108-013 of z_CMB = 0.0330 and H₀ = 65 km s⁻¹ Mpc⁻¹ (to match the analysis of H09a), CGCG 108-013 has a Hubble-flow luminosity distance modulus of μ = 35.968 mag.⁷ Therefore, three out of the four distance fitters provide values within 0.03 mag of the expected value if CGCG 108-013 is in the Hubble flow. We can also measure the distance modulus with the formula μ = V_peak − M_V,peak − A_V,host − A_V,MW. Using the values measured and assumed by H09a, we find μ = 36.254 and 35.826 mag for A_V = 0 and 0.428 mag, respectively. These values differ from the Hubble-flow distance modulus by 0.286 and −0.146 mag, respectively, corresponding to the offset from the WLR in Figure 4. Obviously, fitting all light curves of SN 2006bt provides a better estimate of the distance to SN 2006bt than using only V-band data.

Although SN 2006bt appears to have a somewhat odd light curve, it is still a relatively good standardizable candle. SN 2006bt is both intrinsically faint and red for its light-curve shape. All light-curve fitters correct for its red color by effectively brightening its apparent magnitudes. Since intrinsic color variation and dust extinction are not orthogonal, deviations from the model in MLCS are regarded as dust extinction (see Conley et al. 2007 for a discussion of how MLCS and SALT treat color). We discuss the implications of including SN 2006bt-like objects in a cosmological analysis in Section 6.2.

SN 2006bt was located between CGCG 108-013 and 2MASX J15562803+2002482, two objects at similar, but significantly different, recession velocities (cz = 9628 ± 55 and 13, 894 ± 30 km s⁻¹, respectively). To determine the most likely host galaxy, we cross-correlated all spectra obtained at t < 7 days with a library of SN Ia spectra using SNID (Blondin & Tonry 2007). We determined two likely redshifts for each spectrum: the redshift from the best-fitting template and the average redshift from all SN 1991bg-like objects (since SN 2006bt has a very similar spectrum to this class of objects; see Section 4.2). The best-fitting template spectrum was of SN 1986G for all but one spectrum. Performing these fits, we find cz_SN = 9397 ± 109 and 8682 ± 73 km s⁻¹ for the best-fit template and SN 1991bg-like templates, respectively. Considering the velocity dispersion of the galaxy and the peculiarity of SN 2006bt, we believe that these values are consistent with SN 2006bt being associated with CGCG 108-013 and inconsistent with SN 2006bt being associated with 2MASX J15562803+2002482. For the remainder of the paper, we assume that the redshift of SN 2006bt is that of CGCG 108-013.

Our first spectrum was obtained 3 days before B-band maximum. Using this spectrum, Filippenko & Foley (2006) noted that SN 2006bt was somewhat peculiar. In Figure 5, we present this spectrum as well as spectra of SNe 1986G (Δm₁₅(B) = 1.65 mag) and 2006ax (Δm₁₅(B) = 1.08 mag) at a similar phase. Despite having the same value of Δm₁₅(B), SNe 2006ax and 2006bt exhibit very different spectra at this epoch, with SN 2006bt having a much stronger Si ii λ5972 feature and a depression at ∼ 4100 Å corresponding to Ti ii. These features are indicative of a relatively cool photosphere and are hallmarks of the low-luminosity SN 1991bg-like class of SNe Ia (e.g., Filippenko et al. 1992a; Leibundgut et al. 1993). Although there is some dispersion in the spectra of objects with the same light-curve shape (Benetti et al. 2004; Matheson et al. 2008), differences of this magnitude have never before been seen within normal SNe Ia of the same light-curve shape.

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The earliest spectrum of SN 2006bt is more similar to the spectrum of SN 1986G, a low-luminosity SN Ia and a member of the SN 1991bg-like class of objects (Phillips et al. 1987). SN 1986G has stronger Si ii λ5972 and Ti ii features, indicating that SN 2006bt is slightly hotter than SN 1986G. (However, we do caution that the uncertain reddening correction of SN 1986G may cause the relative strengths of its features to be incorrect.)

At this phase, the minimum of the Si ii λ6355 absorption feature is blueshifted by 12,500 km s⁻¹, which is the same as SN 1986G and within the typical range of slower declining SNe Ia (although it is slightly larger than the velocity of SN 2006ax at that phase). The minimum of the Ca ii near-infrared triplet (seen in Figures 2 and 9) is blueshifted by 15,900 km s⁻¹, which is also normal. There is no obvious high-velocity structure associated with either feature.

Despite having a slow optical decline rate, SN 2006bt has a pre-maximum spectrum most similar to those of fast decliners. SN 2006bt has a relatively cool photosphere, which may explain the lack of a shoulder in r and a prominent second maximum in i (Kasen 2006), but is contradictory given the slow decline (Kasen & Woosley 2007).

There is no indication of Na D absorption at either zero velocity (consistent with the low value of E(B − V) measured by Schlegel et al. 1998) or the host-galaxy recession velocity in any of our spectra, indicating a small or negligible extinction.

In Figure 6, we present our t = 35 day spectrum compared to spectra of SNe 1986G and 2006ax at a similar phase. The differences between SN spectra become smaller with time, and by t = 35 days, the spectrum of SN 2006bt is very similar to spectra of both SNe 1986G and 2006ax at this time.

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There have been several attempts to classify SNe Ia into distinct groups based on their spectra (e.g., Nugent et al. 1995; Benetti et al. 2005; Branch et al. 2006). Most methods rely (at least in one dimension) on the strength of Si ii λ5972 relative to that of Si ii λ6355. This is easily measured by the parameter $\mathcal {R}$(Si) (Nugent et al. 1995), but Branch et al. (2006) advocates measuring the equivalent widths of these lines. In addition to $\mathcal {R}$(Si), Benetti et al. (2005) divided SNe Ia based on a combination of light-curve shape and the velocity gradient of the Si ii λ6355 feature, $\dot{v}$. Branch et al. (2006) defines four subclasses, namely shallow silicon (SS), core normal (CN), broad line (BL), and cool (CL), while Benetti et al. (2005) defines three subclasses called low-velocity gradient (LVG), high-velocity gradient (HVG), and faint (FAINT). The classification systems have much overlap, with SS and CN objects mostly being in the LVG, BL objects mostly being in the HVG, and CL mapping directly to FAINT.

At maximum light, SN 2006bt has W(5750) = 29 Å, W(6100) = 120 Å, $\mathcal {R}{\rm (Si)} = 0.44$, and $\dot{v} = 51$ km s⁻¹ day⁻¹. These values place SN 2006bt within the LVG group (although toward the high end of the range of $\dot{v}$; see Figure 7) and between the CL and BL groups, with its closest neighbors (using the updated values of Branch et al. 2009) being the BL SN 1999cc (W(5750) = 26 Å; W(6100) = 121 Å) followed by CL SN 1989B (W(5750) = 25 Å; W(6100) = 126 Å). Despite being closest to a BL object in the equivalent width space, the shape of the Si ii absorption and the borderline values should place SN 2006bt in the CL group.

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The true peculiar nature of SN 2006bt is apparent when comparing a temperature-dependent spectral parameter such as $\mathcal {R}$(Si) with a light-curve parameter such as Δm₁₅(B). In Figure 7, we show these values for the sample of Benetti et al. (2005; open symbols) and for SN 2006bt (filled circle). In this parameter space, SN 2006bt is a large outlier, indicating that it has a relatively cool photosphere and a slow decline rate.

In our earliest spectra, there is a small feature redward of Si ii λ6355 (see Figure 8). In our first spectrum (when the feature is strongest and the signal-to-noise ratio of the spectrum is highest), its minimum is at 6465 Å. This feature is present in our second and third spectra, although with less significance. These three spectra come from different instruments and telescopes, indicating that it is not an artifact of data reduction. The feature has mostly disappeared in our fourth spectrum (t = 0.0 days).

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An intriguing possibility is that this feature is from C ii λ6580 absorption. If this is the case, the minimum of the absorption would be blueshifted by 5200 km s⁻¹, which is much lower than that of other features and may indicate a misidentification. This feature has been detected in a handful of objects (e.g., Branch et al. 2003) with the best cases being SNe 2006D (Thomas et al. 2007), 2006gz (Hicken et al. 2007), and 2009dc (Yamanaka et al. 2009), but all detections so far have been at much larger velocities and typically at much earlier phases. For instance, the minimum of the C ii λ6580 feature in SN 2006gz was blueshifted by ∼ 15,500 km s⁻¹ at t = −14 days (which was a larger velocity than the Si ii feature at that phase) and had completely disappeared by t = −12 days.

C ii has four relatively strong features in the optical: λλ4267, 4745, 6580, and 7234. Unfortunately, C ii λ4267 would be on the edge of a strong Mg ii feature and C ii λ4745 is on top of a Ti ii feature (although it may still be detectable with SYNOW; see Section 4.6). Only the two reddest lines are in relatively uncontaminated regions of the spectrum. As seen in Figure 8, there is a very shallow feature in our earliest spectrum at the wavelength that corresponds to C ii λ7234 blueshifted by ∼ 5000 km s⁻¹.

Observations have shown that high-velocity features are common in SNe Ia (e.g., Mazzali et al. 2005). The data can be explained by circumstellar interaction, dense blobs of material "detached" from the rest of the ejecta, or a differing covering fraction of the ejecta (Gerardy et al. 2004; Mazzali et al. 2005; Tanaka et al. 2006). If there is a single carbon blob ejected at an angle away from our line of sight, the absorption velocity seen in the spectra would correspond to the component of the velocity vector along our line of sight. For an angle of 45° (65°) relative to our line of sight, we infer a true velocity of 7450 km s⁻¹ (12,300 km s⁻¹) in such a scenario. This potential asymmetry may help explain other aspects of this SN (see Section 6.1). Alternatively, there may be a significant amount of carbon-rich material close to the SN. For this scenario, viewing-angle effects necessitate that our line of sight be in the plane of the circumstellar accretion disk.

Besides the possible detection of carbon lines, SN 2006bt shares other characteristics with SNe 2006D and 2006gz. SN 2006D had a relatively narrow light curve similar to that of SN 1986G, but not as narrow as that of SN 1991bg (Thomas et al. 2007). The t = −5 day spectrum from Thomas et al. (2007) is reproduced in Figure 5. The early-time spectra of SNe 2006D and 2006bt are relatively similar, both having relatively large $\mathcal {R}$(Si). SN 2006bt has slightly larger velocities for the Si and Ca features and stronger Ti ii features than SN 2006D.

SN 2006gz had very broad light curves (Δm₁₅(B) = 0.69 ± 0.04), no shoulder in r, and no second maximum in i (Hicken et al. 2007). The colors were also very red, but Hicken et al. (2007) attributed this to a large amount of host-galaxy extinction (E(B − V)_host = 0.18 mag). SN 2006gz had spectra indicative of a very hot photosphere unlike SN 2006bt.

To investigate the details of our SN spectra, we use the supernova spectrum-synthesis code SYNOW (Fisher et al. 1997). Although SYNOW has a simple, parametric approach to creating synthetic spectra, it is a powerful tool to aid line identifications which in turn provide insights into the spectral formation of the objects. To generate a synthetic spectrum, one inputs a blackbody temperature (T_BB), a photospheric velocity (v_ph); and for each involved ion, an optical depth at a reference line, an excitation temperature (T_exc), the maximum velocity of the opacity distribution (v_max), and a velocity scale (v_e). This last variable assumes that the optical depth declines exponentially for velocities above v_ph with an e-folding scale of v_e. The strengths of the lines for each ion are determined by oscillator strengths and the approximation of a Boltzmann distribution of the lower level populations with a temperature of T_exc.

In Figure 9, we present our −3.8 day spectrum of SN 2006bt with a synthetic spectrum generated from SYNOW. This fit is very similar to the fit performed for SN 1986G by Branch et al. (2006) and the optical depths for the fit are presented in Table 2. The main differences are that we include O i (it was excluded from the reference fit because of the short wavelength range of the SN 1986G spectrum), the excitation temperature is 8000 K instead of 7000 K, all ions other than Mg i and Mg ii have lower optical depths, we do not include high-velocity Ca ii and Fe ii, and we do not impose a maximum velocity for Si ii. The model includes low-ionization ions and excludes high-ionization ions, confirming the low-temperature nature of SN 2006bt. No ions at high velocity are included, further limiting the possibility of high-velocity ejecta. There are some differences between the SN 2006bt and SYNOW spectra. It is possible that these differences could be reduced by examining more of the parameter space of SYNOW input parameters. These differences do not affect our conclusions below.

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A slightly higher excitation temperature and lower optical depths in SN 2006bt compared to SN 1986G is consistent with our relatively crude assessment of the spectrum in Section 4.2 where we considered SN 2006bt to be slightly hotter (and more "normal") than SN 1986G. The model for SN 1986G has v_max= 15,000 km s⁻¹, while the model for SN 2006bt imposes no limit. Where nuclear burning may only extend to v = 15, 000 km s⁻¹ in SN 1986G, it appears that it extends to all velocities in SN 2006bt.

Since we may have identified C ii in the pre-maximum spectra of SN 2006bt (see Section 4.5), we created models with and without C ii. In an attempt to match the possible low-velocity features, we included C ii with T_exc = 12, 000 K, v_max = 15, 000 km s⁻¹, and v_e = 200 km s⁻¹. The inclusion of C ii with these parameters improves the model fit. In addition to better fits near C ii λλ6580, 7234, the model is significantly better near C ii λ4745. This shows that it is possible to detect lines in confused regions such as near 4600 Å. Branch et al. (2006) fit this region with high-velocity Fe ii, and again, we caution that the identification of C ii is not definitive.

It has long been believed that the vast majority of SN Ia light curves can be described by a single parameter which directly correlates with the amount of ⁵⁶Ni produced in the explosion (with more ⁵⁶Ni corresponding to more luminous events having broader light curves). Kasen & Woosley (2007) explain this further by noting that objects with larger M_Ni are hotter, making the recombination from Fe iii to Fe ii occur at a later time, and thus have a broader B-band light curve.

Kasen (2006) found that the depth of the trough, the height of the second maximum, and the delay between the first and second maxima in the I band all increase with ⁵⁶Ni mass. This finding would imply that SN 2006bt had a small ⁵⁶Ni mass (model I-band light curves with 0.2 M_☉ ⩽ M_Ni ⩽ 0.3 M_☉ show a similar behavior to the i-band light curve of SN 2006bt), which is in direct conflict with the decline rate of all bands.

The prominence of the second maximum is more generally related to the mass of all Fe-group elements in the ejecta, not just ⁵⁶Ni and the isotopes into which it decays (Kasen 2006). The second maximum can be reduced by decreasing the progenitor metallicity, which decreases the amount of stable Fe-group elements ("stable Fe") produced in the explosion (Timmes et al. 2003); however, the effect is at most ∼ 10%. Since stable Fe is produced via electron capture, it is possible that the explosion simply did not have the physical conditions necessary to form a significant amount of stable Fe through electron capture. Finally, one can smear out the second maximum in I by mixing the stable Fe and ⁵⁶Ni throughout the ejecta (Kasen 2006). This will also cause the maximum of the I band to occur later, which may be the case for SN 2006bt.

SN 2006bt may have been a very asymmetric explosion. Although we see no indication of high-velocity ejecta in any of the spectral features, there is the possibility that a carbon blob was ejected ∼ 65° from our line of sight. SN 1999by, a low-luminosity event, showed a very polarized spectrum corresponding to an explosion with an asphericity of 20% viewed along the equator (Howell et al. 2001). Asymmetric explosion models show that peak luminosity depends on viewing angle; however, these models do not exhibit significant differences in ionization with viewing angle (Kasen & Plewa 2007; Sim et al. 2007).

It is also possible that SN 2006bt rose very quickly to maximum, causing a high luminosity with a smaller amount of ⁵⁶Ni (Arnett 1982). There are poor constraints on an explosion date from pre-explosion images (Lee & Li 2006). Our photometry starts only a few days before B maximum, but it does not appear to be faster than other objects with its decline rate. Although a fast rise is still a possibility, it appears to be an unlikely solution.

Given its relatively normal luminosity, SN 2006bt-like objects would still be detected in high-redshift SN surveys, unlike other peculiar objects such as SNe 2002cx (Li et al. 2003) and 2008ha (Foley et al. 2009a; Valenti et al. 2009). Furthermore, given its B − V color curve, a SN 2006bt-like object with some host-galaxy extinction will simply look like a normal object with that extinction plus an additional A_V ≈ 0.5 mag of extinction. At some point too much extinction would lead to the exclusion of these objects from a SN sample; most cosmological analyses avoid SNe Ia having extremely red colors.

Additionally, at high redshift, the rest-frame r and i band will be redshifted out of the optical, requiring observers to rely on rest-frame B − V alone to determine the quality of the light-curve fits and measure the extinction. At low redshift, one could search for objects with large Δm₁₅(B) but no secondary maximum in i and exclude any such objects; however, at high redshift this is not feasible without observing in the near-infrared (James Webb Space Telescope, and depending on the ultimately chosen design, the Joint Dark Energy Mission might be able to measure the rest-frame i band out to z ≈ 1). For an object at z ≳ 0.3 (where i is redshifted out of the optical), one would have to rely on a spectrum (in combination with a light curve) to identify SN 2006bt-like objects. However, with the Si ii lines redshifting out of the optical window at z ≈ 0.5 and the generally low signal-to-noise ratio spectra of high-redshift SNe Ia, it is difficult to detect spectroscopically peculiar objects from high-redshift surveys (Foley et al. 2009b).

If SN 2006bt does come from a very old progenitor and the age of the progenitor is the main reason for its peculiarity, then SN 2006bt-like objects may not exist at high redshift. At z = 0.5 and 1, the universe had an age of ∼ 8.6 and 5.9 Gyr, respectively. If the delay time between formation and explosion is longer than those times, SN 2006bt-like objects will not exist at those redshifts. Foley et al. (2009b) found no SN 1991bg-like objects in a sample of 118 high-redshift SNe Ia, indicating that SN 2006bt-like objects are probably not a large fraction of the early-universe SN Ia population.

We have developed a Monte Carlo simulation to assess the impact of contamination of a population of SN 2006bt-like objects in a SN Ia cosmological sample. For normal SNe Ia, we generate 1000 light curves over a range of light-curve shape parameters from the MLCS2k2 "early" templates (Jha et al. 2007) over 0 < z < 0.8 (500 for z < 0.1 and 500 for z>0.1), with distance modulus, μ_true, calculated in a nominal flat ΛCDM (Ω_M = 0.3 and h = 0.65) cosmology. We parameterize the input extinction by a R_V = 3.1 O'Donnell (1994) law, with A_V drawn from the glos distribution (e.g., Hatano et al. 1998). The light-curve shape parameter Δ is drawn randomly between −0.3 and 1.3. The sampling and signal-to-noise ratio is matched to the expected values for the Pan-STARRS Medium Deep Survey.

Since SN 2006bt has very different light curves from those of other SNe Ia, the MLCS2k2 template light curves had to be modified to create simulated light curves of SN 2006bt-like objects. Specifically, the SN 2006bt-like light curves must be intrinsically underluminous and red compared to a nominal SN Ia with the same light-curve shape. To determine the appropriate modifications, each individual light curve of SN 2006bt was fit separately. The UBVr light curves all had best fits of Δ ≈ −0.15, while the i-band light curve was best fit with Δ = −0.38. The MLCS2k2 model light curves were shifted so that the peak magnitudes were the same as those of SN 2006bt in each band. We created 100 SN 2006bt-like light curves for 0 < z < 0.8 (50 for z < 0.1 and 50 for z>0.1).

All light curves were fit using MLCS2k2 (Jha et al. 2007), which provided estimates of A_V, Δ, and μ. The fitting was performed with both the glos and flatnegav (a flat prior which includes negative values of A_V) priors. Fits of all light curves, including those for SN 2006bt-like objects, had a reduced χ² ⩽ 2, indicating that all would nominally be included in a cosmological analysis.

To demonstrate how MLCS2k2 interprets our SN 2006bt-like model light curves as a function of redshift, we produced noise-free light curves spanning the redshift interval 0 < z < 0.8. The light curves were fit by MLCS2k2 with a flatnegav prior (in this signal-to-noise ratio regime, the prior is inconsequential and the uncertainty is dominated by the MLCS model uncertainty). The resulting distance modulus residuals and derived A_V are presented in Figure 12. The derived distance modulus residuals are close to zero near z = 0, but increase to ∼ 0.1 mag at z = 0.1. After that, the residuals generally linearly decrease with increasing redshift, deviating by ∼ 0.5 mag at z = 0.8. At redshifts where either the mapping of observed filters to rest-frame filters during the K-correction process changes or when a rest-frame filter is no longer used in K-corrections (the filter "drops out"), there are large discontinuities in the residuals. These discontinuities are partly the result of our model for SN 2006bt and the normal SN Ia template model and partly the result of having the observer-frame light curves derived from a single rest-frame filter.

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The derived value for A_V has a very similar (but inverted) function with redshift. Since our model assumes A_V = 0 mag at all redshifts, the derived value corresponds to the difference between the true distance modulus and the derived distance modulus, modulo the difference in peak absolute magnitude for SN 2006bt and the canonical SN Ia with the same Δ. Although the distance modulus residuals appear to be quite large, the distance modulus is compared to the input cosmological model. When fitting an observed sample, one can only look for outliers from the best fit, and the inclusion of SN 2006bt-like objects will influence such a fit. Furthermore, a deviation of a few tenths of a magnitude from the residual of the best-fit cosmology is expected for several objects in a high-redshift SN sample.

To examine the impact of SN 2006bt-like objects on cosmological parameter estimation, we defined seven distinct samples. The first sample had no contamination from SN 2006bt-like objects. The remaining samples had 1%, 5%, or 10% contamination at all redshifts, or only for z < 0.1 (consistent with a very long delay time for such objects). The distance moduli found using MLCS2k2 were used to constrain the cosmological parameters Ω_M and w with the assumption of flatness. We also combined the SN data with the prior from the baryon acoustic oscillations (BAO; Eisenstein et al. 2005), further constraining the cosmological parameters. Since we fit the light curves using two separate extinction priors, we have a total of 14 different estimates of Ω_M and w with and without BAO constraints. The parameters are listed in Table 3.

As SN 2006bt-like objects become a larger share of the SN sample, the estimate of w consistently increases (becoming closer to 0). The value derived from the uncontaminated sample is w = −0.927^+0.067_−0.070 and −0.893^+0.069_−0.072 for the glos and flatnegav priors, respectively, while the 10% contaminated (at all redshifts) sample yields w = −0.725^+0.055_−0.055 and −0.813^+0.065_−0.066 for the same priors, respectively. This trend is true if the SN 2006bt-like objects are spread throughout redshift or restricted only to low redshifts, but which of these two samples has more bias depends on the prior. For the SN-only cosmological fits, the value of Ω_M is typically biased to lower values, but only the fits with the glos prior are substantially biased. The 1σ contours for the uncontaminated and 10% contaminated samples are shown in Figure 13.

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From our basic simulations, we see that SN 2006bt-like objects can have a large impact on derived cosmological parameters; however, if the fraction of SN 2006bt-like objects in the sample is low, the bias can be much smaller than other systematic biases (if 1% of the low-redshift sample in contaminated by SN 2006bt-like objects, w shifts by only 0.007). We have identified one object with these peculiar properties out of 185 objects in the CfA3 sample, but we have not examined all objects with the same scrutiny. Within the CfA3 sample, 20% of SNe Ia have measured A_V larger than that of SN 2006bt, which is a very conservative upper bound to the fraction of the contamination of the low-redshift sample.