SPECTROPOLARIMETRY OF EXTREMELY LUMINOUS TYPE Ia SUPERNOVA 2009dc: NEARLY SPHERICAL EXPLOSION OF SUPER-CHANDRASEKHAR MASS WHITE DWARF^*

The top panel of Figure 1 shows the total flux spectrum of SN 2009dc at t = +5.6 days (blue) compared with the spectra of normal SN 2003du (gray; Stanishev et al. 2007) and overluminous SN 2006gz (black; Hicken et al. 2007). SN 2003du is a well-studied normal Type Ia SN (z = 0.00638; Gerardy et al. 2004; Anupama et al. 2005; Stanishev et al. 2007). SN 2006gz is an overluminous Type Ia SN, which is a candidate for super-Chandrasekhar mass SN (z = 0.0236; Hicken et al. 2007). Compared with normal Type Ia SNe, the spectrum of SN 2009dc is unique in the following points: (1) very low line velocities and (2) the presence of the carbon line (see also Yamanaka et al. 2009).

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The velocity of the Si ii λ6355 line is v = 7200 km s⁻¹, lower than that of SN 2003du at a similar epoch (10,200 km s⁻¹ at +6.2 days) and SN 2006gz (11,200 km s⁻¹ at +6 days). The Si line velocity of SN 2009dc is close to that of SN 2003fg (8000 km s⁻¹ at +2 days; Howell et al. 2006).

The C ii λ6578 line is clearly present in the spectrum of SN 2009dc at +5.6 days. The velocity is v = 6700 km s⁻¹, which is also very low for a Type Ia SN. The C lines are rarely seen in Type Ia SNe (Marion et al. 2006; Tanaka et al. 2008b). Even if they are seen, the detection is limited almost exclusively to the very early phases: the earliest detection was in SN 1990N at −15 days (Mazzali 2001), and the detection is usually at <−10 days for other SNe (Thomas et al. 2007). In fact, the C ii line was also visible in SN 2006gz, but disappeared at −10 days. In SN 2003fg, the C ii line was marginally present at +2 days.

Figure 2 shows the total flux spectrum of SN 2009dc at t = +89.6 days compared with SN 2003du at t = 84.0 days (Stanishev et al. 2007). This epoch is a transition phase when the SN spectrum evolves from a photospheric spectrum to a nebular spectrum. In the spectra of both SNe, continuum emission is nearly absent, and emission features start to dominate the spectrum. Line features of SN 2009dc are narrower than those of SN 2003du even at this epoch.

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Observed Stokes Q and U at t = +5.6 days are shown in the middle panels of Figure 1. Polarization data are binned into 20 Å. It clearly shows a variation in the polarization degree at the Si ii λ6355 and the Ca ii IR triplet lines. The change in the degree of polarization at these lines is ∼ 0.5% (see Section 4.2 for more details), which is broadly consistent with the past measurements for other Type Ia SNe (Wang et al. 1997, 2003b, 2007; Leonard et al. 2005; Chornock & Filippenko 2008). A smaller fluctuation is also seen at the O i λ7774.

Except for these lines, the degree of polarization is Q ∼ −0.5% and U ∼ −0.2%. No significant polarization variation is detected at the C ii line and in the wavelength region of <6000 Å, where the S ii lines and many Fe ii–Fe iii lines are present.

The polarization data at t = +5.6 days are plotted in the Q–U plane in Figure 3. This also shows that the majority of the data is confined around Q ∼ −0.5% and U ∼ −0.2%. And, the polarization around the Si ii and Ca ii lines deviates from this point, making a loop in the Q–U plane. This is also inferred from the large variation in θ at these lines (Figure 1, see Section 4.2 for more details). According to the classification of spectropolarimetry types by Wang & Wheeler (2008), SN 2009dc shows type N1 for the continuum (no significant dominant axis) and type L for the Si ii and Ca ii lines (large polarization change at the line).

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Stokes Q and U at the Ca ii IR triplet seem to have substructures, i.e., the main peak around 8300 Å and a small peak at 8450 Å. To identify these peaks, the positions of three lines (λ8498, 8542, 8662) are marked with the Doppler shifts of v = 7200 km s⁻¹ (photospheric component) and v = 12,000 km s⁻¹ (high-velocity component) in Figure 1. It is found that the small peak at 8450 Å originates from the photospheric component of the reddest Ca ii λ8662, while the main peak is a combination of the photospheric component of the other two lines and the high-velocity component of the three lines. Similar substructures were also seen in the polarization spectrum of SN 2004S at +9 days (Chornock & Filippenko 2008), but polarization of the high-velocity component is smaller than the photospheric component in SN 2004S.

We also mark these two velocity components for the Si ii line. Stokes U has a strong peak at a similar high velocity (v = 12,000 km s⁻¹), and polarization variation is seen up to v ∼ 15,000 km s⁻¹. Note that the total flux has the absorption minimum at v = 7200 km s⁻¹ and does not show a strong blue wing.

Figure 2 shows the polarization spectrum at t = +89.5 days. Given the low signal-to-noise ratio (S/N), the data are binned into 100 Å. The overall polarization level is similar to that at t = +5.6 days (Q ∼ −0.5% and U ∼ −0.2%). No significant variation (with ≳0.5 % level) of polarization is detected at the lines. Also, the polarization angle θ is nearly constant. Spectropolarimetry type at this epoch is type N1.

The spectropolarimetric data suffer from ISP both in our Galaxy and the host galaxy. To discuss intrinsic properties of the SN polarization, ISP must be corrected. In this section, we give an estimate of ISP.

There are several possible methods to estimate ISP. When only single-epoch data are available, and if there is a dominant axis (a straight line in the Q–U plane) in the polarization data, we may assume global axisymmetry of the SN ejecta and take an ISP at either end of the line in the Q–U plane (Howell et al. 2001; Wang et al. 2001, 2003a; Tanaka et al. 2008a). Another method is assuming complete depolarization at strong emission lines (e.g., Kawabata et al. 2002; Leonard et al. 2005; Wang et al. 2006; Maund et al. 2007). This method is justified because the emission part of P Cygni profile consists largely of line-scattered, depolarized photons. However, it must be carefully done because depolarization is not necessarily complete (Tanaka et al. 2009).

To avoid the uncertainty caused by these methods, we use spectropolarimetric data taken at t = 89.5 days. As shown in Figure 2, the spectrum at this epoch does not have clear continuum light, and electron scattering is not important. In addition, the emission features, which are intrinsically unpolarized, dominate the spectrum. Thus, the light from SN at this epoch is assumed to be intrinsically unpolarized, and the observed polarization can be considered as ISP origin.

For the wavelength dependence of ISP, we assume the following relation, which is valid for the Milky way like dust (Serkowski et al. 1975):

$$\begin{equation} P(\lambda)\ =\ P_{\rm max}\exp [ -K \ln ^2 (\lambda _{\rm max}/ \lambda)]. \end{equation} \tag{ 1 }$$

Here λ_max is the wavelength at the peak of the ISP, P_max is the degree of the ISP at λ_max, and K is given as K = 0.01 + 1.66 λ_max(μm) (Whittet et al. 1992). We assume λ_max = 5500 Å as a conventional choice.

The best simultaneous fit of the Stokes Q and U at t = +89.5 days can be obtained (χ²/dof = 1.1) when Q_ISP = −0.50% and U_ISP = −0.25% at 5500 Å, i.e., P_ISP,max = 0.56%, θ_ISP = 103°. This ISP is shown in red dashed lines in Figures 1 and 2 and in a gray circle in Figure 3. Note that the uncertainty of the ISP is ∼0.15%, which is a typical error of the Stokes Q and U (χ²/dof ≲ 2.0 with this uncertainty range).

The degree of ISP is also constrained by the total extinction: P/E(B − V) < 9% (Serkowski et al. 1975). In the line of sight to SN 2009dc, the extinction by our Galaxy is E(B − V)_Gal = 0.071 mag (Schlegel et al. 1998). The extinction by the host galaxy is not certain. In our spectrum, narrow Na i D lines are detected, and their equivalent widths are EW= 0.5 and 1.0 Å for our Galaxy and the host galaxy, respectively (these are slightly lower than the values reported by Marion et al. 2009). If we assume a host extinction proportional to the EW, the host extinction is E(B − V)_host = 0.14 mag. Alternatively, if we use the relations by Turatto et al. (2003), we obtain E(B − V)_host = 0.15 mag or 0.47 mag. Thus, the upper limit for the ISP is P < 0.63% in our Galaxy and P < 1.3% (tightest when E(B − V) = 0.14 mag) in the host galaxy. The ISP estimated above is consistent with these upper limits.

Figure 4 shows the ISP-corrected, bias-corrected total polarization P at t = 5.6 days. Assuming the ISP estimated with the later epoch data, the continuum polarization is found to be <0.3% measured at the line-free region at 6500–7300 Å. Although there is a fluctuation in polarization around 6600 Å (this is less significant in the original Stokes Q and U, Figure 1), there is no corresponding line. Thus, we take this part as an upper limit of the continuum polarization.

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The small degree of continuum polarization is consistent with other normal Type Ia SNe (e.g., Wang et al. 1997, 2003b, 2006; Leonard et al. 2005; Chornock & Filippenko 2008). The small degree of continuum polarization indicates that the overall shape of the photosphere is nearly spherically symmetric. If a pure electron-scattering ellipsoid is assumed and if it is viewed near 90°, the axis ratio of the photosphere deviates less than 10% from unity (Höflich 1991; Wang et al. 1997).

Variation of polarization degree at the lines is clearly detected at Si ii λ6355 and the Ca ii IR triplet, and O i λ7774 in the data taken at t = +5.6 days (Figure 1). The line polarization means that the distribution of these elements is not spherically symmetric. The degree of the total polarization is 0.5% ± 0.1% for the Si ii line and 0.7% ± 0.1% for the Ca ii line (ISP-corrected P, Figure 4). The polarization change at the O i line is affected by the choice of the ISP (P ≲ 0.3% in ISP-corrected P, Figure 4), but fluctuation in the original Stokes Q and U is ∼0.2% (Figure 1). The degree of the line polarization is similar to that of normally luminous Type Ia SNe with normal expansion velocities.

If we look at the ISP-corrected polarization (Figure 4), the smaller polarization change is also marginally seen at Si ii–Fe iii absorption at 4800 Å and Si ii λ5789. But these are not significant, and their significance does depend on the choice of the ISP.

Polarization at the Si ii, Ca ii, and O i lines is plotted in the Q–U plane in Figure 5. In these plots, the ISP is not corrected for, and the position of the ISP at 5500 Å is shown by the gray circle. Colors of the points represent the Doppler velocity measured from 6355 Å (Si ii), 8567 Å (Ca ii), and 7774 Å (O i). As already shown in Section 3.2, polarization change at the Si and Ca lines is detected not only at photospheric velocity (v = 7200 km s⁻¹) but also at higher velocities (v ≳ 12,000 km s⁻¹). This is more clearly seen in the polarized flux (PF_λ in Figure 4), which has a peak at high velocity (v ∼ 12,000 km s⁻¹).

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In the Q–U plane (Figure 5), polarization at the Si ii and Ca ii lines shows a "loop." It can also be inferred by the large variation in the ISP-corrected position angle θ at the line (Figure 4). A similar structure in the Q–U plane has been discovered in several Type Ia SNe, e.g., SN 2001el (Wang et al. 2003b) and SN 2004S (Chornock & Filippenko 2008). The presence of the loop means that the polarization degree and position angle do depend on the velocity, i.e., the depth in the ejecta. Thus, it suggests that the distribution of the element is not axisymmetric. If the distribution were axisymmetric, the data would be distributed in a straight line in the Q–U plane.

Interestingly, the loop of the Si ii line and the Ca ii line shares a similarity: it goes counterclockwise for the larger blueshift (higher velocity, see the left and center panels of Figure 5). This is in contrast to the behavior of the O i line, whose loop is not prominent (the right panel of Figure 5). The marginal loop of the O i line goes to a direction different from that of the Si ii and Ca ii lines.

These facts suggest that the distributions of Si and Ca are correlated. In addition, the distribution of these elements is different from that of O, which may have a complementary distribution. But all of these elements share similar velocity space. This configuration can be understood if intermediate-mass elements have a non-axisymmetric, large-scale clumpy distribution, with some clumps sticking out to the O-rich layer (Wang et al. 2006; Wang & Wheeler 2008).

Summarizing the spectropolarimetric properties, the explosion geometry of SN 2009dc seems to be similar to normally luminous Type Ia SNe with normal expansion velocities. The explosion is globally spherical with clumpy distribution of intermediate-mass elements.

The clumpy structure of intermediate-mass elements discussed in Section 4.2 seems to be common in Type Ia SNe (Wang et al. 2006; Wang & Wheeler 2008; Chornock & Filippenko 2008). In this section, we discuss the property of line polarization of SN 2009dc comparing with other Type Ia SNe.

Wang et al. (2007) presented the largest spectropolarimetric sample of Type Ia SNe. They showed a correlation between the polarization degree of the Si ii line and the decline parameter of the light curve Δm₁₅(B), the difference in the B-band magnitude at maximum and at 15 days after the maximum (brighter SNe decline more slowly, and thus, have smaller Δm₁₅(B), e.g., Phillips 1993; Phillips et al. 1999). The data taken from Wang et al. (2007) are plotted in blue points in Figure 6. The time evolution is not corrected for. With two exceptions (SNe 2004dt and 1999by), they suggested that the brighter SNe (with smaller Δm₁₅(B)) show the smaller line polarization.

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Wang et al. (2007) limited their sample to the data taken at premaximum phases. From the literature, we have added three spectropolarimetric examples at postmaximum phases (green points in Figure 6): SN 1997dt (+21 days, $P_{\rm Si\,\mathsc {ii}} = 0.4 \% \pm 0.2\%$; Leonard et al. 2005), SN 2003du (+18 days, $P_{\rm Si\,\mathsc {ii}} = 0.2 \% \pm 0.05 \%$; Leonard et al. 2005), and SN 2004S (+4 days, $P_{\rm Si\,\mathsc {ii}} = 0.3 \% \pm 0.05 \%$; Chornock & Filippenko 2008). Their Δm₁₅(B) is 1.04 ± 0.15 mag (Jha et al. 2006), 1.02 ± 0.05 mag (Anupama et al. 2005; Stanishev et al. 2007), and 1.14 ± 0.01 mag (Misra et al. 2005; Krisciunas et al. 2007), respectively. We must be careful about the time evolution of polarization. It is thought that the degree of polarization decreases with time (Wang et al. 2003b, 2007; Patat et al. 2009), but the number of multi-epoch spectropolarimetric observations is not sufficient to clarify the common property of the time evolution.

Keeping this caveat in mind, we can still see the trend that brighter SNe have smaller line polarization. As is inferred from spectral models for Type Ia SNe (Mazzali et al. 2007), brighter SNe have the thinner Si-rich layers, i.e., the degree of the line polarization is smaller in SNe with the thinner Si-rich layers. In addition, SNe with high Si II line velocities tend to have a high Si II line polarization (Leonard et al. 2005; Wang et al. 2006; Patat et al. 2009). In high-velocity SNe, the Si-rich layer is thought to be thick (Stehle et al. 2005; Tanaka et al. 2008b). We thus suggest that the Si line polarization can be used as an indicator of thickness of the Si-rich layers, or that enough thick Si-rich layers are required to produce the sufficient Si ii line polarization.

SN 2009dc is an extremely luminous SN, synthesizing ≳1.2 M_☉ of ⁵⁶Ni (Δm₁₅(B) = 0.65 ± 0.03 mag; Yamanaka et al. 2009). Despite the large production of ⁵⁶Ni, we have detected a moderate degree of line polarization. The degree of the Si line polarization (0.5% ± 0.1%, red point in Figure 6) is higher than expected from the trend seen in other Type Ia SNe (blue and green points). This fact suggests that SN 2009dc has enough thick, clumpy Si-rich layers above ≳1.2 M_☉ of ⁵⁶Ni-rich layers.

It must be cautioned, however, that this discussion relies largely on the small number of spectropolarimetry of SN 1991T-like overluminous Type Ia SN, especially on SN 2001V (Wang et al. 2007, see Matheson et al. 2008 for spectroscopic behavior). To firm the conclusion, more spectropolarimetric observations of SNe with Δm₁₅(B) = 0.7–1.0 mag are necessary.

We have shown that SN 2009dc shows the small continuum polarization and moderate line polarizations. From the relation between Δm₁₅(B) and the Si ii line polarization, it is suggested that SN 2009dc has enough thick, clumpy Si-rich layers. Combined with the low line velocities and the clear detection of the strong C ii line (Yamanaka et al. 2009), we suggest that SN 2009dc has a super-Chandrasekhar mass.

Hillebrandt et al. (2007) suggested a possibility that the extremely luminous Type Ia SN 2003fg is an aspherical explosion of a Chandrasekhar mass white dwarf. In their scenario, the explosion is triggered at an off-center position, and nuclear burning preferentially takes place toward one direction. As a result, the distribution of ⁵⁶Ni is lopsided. With such a lopsided explosion, the extreme luminosity can be explained even with 0.9 M_☉ of ⁵⁶Ni when we observe the SN from the ⁵⁶Ni-rich direction.

Although this explosion model is very aspherical, the expected continuum polarization may not be very large. Kasen & Plewa (2007) presented theoretical predictions of the polarization spectra for a detonating failed deflagration model by Plewa (2007), in which the off-center ignition is followed by a surface detonation. The center of the ⁵⁶Ni distribution is displaced also in this model. The resultant SN can be brighter when it is viewed from the direction in which the detonation takes place. The predicted continuum polarization is small in every line of sight. This is understood as follows. In the ellipsoidal geometry, non-zero polarization is expected because of the difference in the amount of light from the pole and the equator (90° away), having orthogonal polarization directions. In the off-center model, on the other hand, the difference is mainly in 180° away, and thus the resultant net polarization is small.

It is also worth comparing the Si ii line polarization of this off-center ignition model (Plewa 2007; Kasen & Plewa 2007) with the observation (0.5% ± 0.1%). Although the expected polarization depends on the line of sight, Kasen & Plewa (2007) found that the line polarization tends to be high, reflecting the aspherical distribution of intermediate-mass elements. In their model, the Si ii line polarization is greater than 1% in almost half of the possible viewing angles.

Next, we discuss the explosion geometry of a super-Chandrasekhar mass white dwarf. When a super-Chandrasekhar mass is maintained by rapid rotation, the rotation speed is limited by the critical rotation at the surface in the equatorial direction. If the rotation is uniform, the Chandrasekhar mass is only 1.5 M_☉. If the white dwarf mass is as large as 2 M_☉, then the rotation must be differential, and the white dwarf prior to the explosion has an aspherical shape (Uenishi et al. 2003; Yoon & Langer 2005).

The explosion of a super-Chandrasekhar mass white dwarf was first studied by Steinmetz et al. (1992). They explored pure detonation models and found that almost all the materials are burned into Fe-peak elements. This is incompatible with the observed properties of normal and extremely luminous Type Ia SNe.

Recently, Pfannes et al. (2010b) performed simulations of deflagration models of a super-Chandrasekhar mass white dwarf. They found that the deflagration model does not result in a bright enough SN and is unlikely to explain the extremely luminous Type Ia SNe, as noted by Hillebrandt et al. (2007).

Interestingly, Pfannes et al. (2010a) revised the simulations of pure detonation models of the super-Chandrasekhar mass white dwarf. They found that the entire white dwarf is not burned into Fe-peak elements, and that some intermediate-mass elements are synthesized. In their models, the synthesized mass of ⁵⁶Ni is sufficiently large (∼1.5 M_☉) to explain the extremely luminous Type Ia SNe. It is worth testing the spectroscopic and spectropolarimetric properties of this model.

Note that a recently proposed scenario involving the collision of two white dwarfs could also realize super-Chandrasekhar mass ejecta (Rosswog et al. 2009; Raskin et al. 2009). However, this scenario predicts a very aspherical explosion, and thus it may not be consistent with the small continuum polarization level observed in SN 2009dc.