An investigation on the FWHM of absorption features of type Ia supernovae

Abstract

We present an investigation of the full width at half maximum (FWHM, or γ) of absorption features of Type Ia supernova (SNe Ia). We found that, the average value of FWHM can be well predicted with the rest wavelength (λ). The velocity also plays an important role, as objects with a higher velocity tend to have a larger FWHM. Temperature may be the third factor, as we found that, at the same velocity (but different phases), a normal-velocity (NV) object tends to have a larger FWHM than high-velocity (HV) object. Also, 1991T/1999aa-like objects that are believed to have relatively high temperatures show the largest FWHMs if compared at the same velocity. Generally speaking, FWHM evolves very slowly with time and shows no correlation with Δm15, but 1991T/1999aa-like objects are characterized by relatively fast decreasing FWHM. On the other hand, we found that, objects with relatively small FWHMs shows a tighter correlation between absorption depth (A) and Δm15, possibly a sign of higher degree of homogeneity. We also found that A/γ of Si II λ5972 has a strong correlation with Δm15, and more importantly, a relatively slow time evolution, making it a useful luminosity estimator even in the absence of phase information.

Figures (5)

• Figure 1: Time evolutions of the FWHMs ($\gamma$) of SN 2011fe (upper left panel, NV subtype), SN 2002bo (upper right panel, HV subtype), SN 1999aa (lower left panel, 1991T/1999aa subtype) and SN 1999by (lower right panel, NV subtype). Marker specifiers: the square, pentagram, hexagram, triangle, plus and cross mark the absorption features Si II $\lambda$4130, Si II $\lambda$5972, Si II $\lambda$6355, S II $\lambda$5454, S II $\lambda$5620, Ca II HK and Ca II NIR, respectively.
• Figure 2: Shown in the upper panel are fitting results of the ratios of FWHMs and wavelengths ($R=\gamma/\lambda_0$) for several lines. Data are mostly from the sample presented in Zhao21Zhao24 and fitted with second-order polynomials. But, the sample size is too large, and we are only interested in the overall trend, so they are not fully presented in Tab.\ref{['Tab1']} & \ref{['Tab2']}. Shown below is also the ratio, but scaled by a factor of $e^{-0.29(E_{exc}-E_{exc}^{Si6})}$, where '$E_{exc}$' is the line's excitation energy (i.e. $\frac{hc}{\lambda_0}$), and '$E_{exc}^{Si6}$' is that of line Si II $\lambda$6355.
• Figure 3: . Correlation between the velocity and FWHM of Si II $\lambda$ 6355. Left panel: A sample at phases near maximum light, i.e. $|t|\leq 1$ days. Each point represents an individual object. Right panel: Some typical objects, at phases $\leq$ +6 days. Classifications are according to Wang09.
• Figure 4: Upper panel: decline rate of FWHM of Si II $\lambda$6355 ($\Delta\gamma^{Si6}/\Delta t$) as a function of the decline rate of brightness ($\Delta m_{15}$). Here $\Delta\gamma^{Si6}$ is calculated by $\Delta\gamma^{Si6}=\gamma^{Si6}_{t1}-\gamma^{Si6}_{t2}$, with $t_1\approx -4$ days and $t_2\approx 0$ days. $\Delta t$ is calculated by $\Delta t=t_2-t_1$. Lower panel: $\Delta m_{15}$ vs. the FWHM of Si II $\lambda$5972 of SNe Ia at the time of B-band maximum light.
• Figure 5: Upper left panel shows the absorption depth of Si II $\lambda$5972 ($A^{Si5}$) as a function of the decline rate ($\Delta m_{15}$). Plus signs mark the inliers which have relatively small residuals from the fit, i.e. $\Delta A^{Si5}=|A^{Si5}-A^{Si5}_{fitted}|\leq 0.07$, where $A^{Si5}_{fitted}$ is given by the best-fit linear relation. Black circles mark the outliers which have relatively large residuals, i.e. $\Delta A^{Si5}=|A^{Si5}-A^{Si5}_{fitted}|> 0.07$. All objects are measured at $|t|\leq 1$ days, each point represents an individual object. The straight dash line in this panel is only a guiding line, not a fitting line. Upper right panel shows $A^{Si5}$ as a function of the FWHM ($\gamma^{Si5}$). Markers in this panel and the lower right panel are the same as for the upper left panel. Lower left panel shows the temporal evolution of the ratio of depth to FWHM of line Si II $\lambda$5972 ($A^{Si5}/\gamma^{Si5}$). The dash line in this panel is a fitting line with a large sample (data not completely presented in this paper, for the same reason as in Fig.\ref{['Fig2']}). Lower right panel shows the correlation between $A^{Si5}/\gamma^{Si5}$ and the decline rate. The straight dash line in this panel is also a guiding lines.