supernovae wavelet spectral index method: a step toward
TRANSCRIPT
Cedarville UniversityDigitalCommons@Cedarville
The Research and Scholarship Symposium The 2014 Symposium
Apr 16th, 11:00 AM - 2:00 PM
Supernovae Wavelet Spectral Index Method: AStep Toward Precision CosmologyAndrew J. WagersCedarville University, [email protected]
Lifan WangTexas A & M University - College Station, [email protected]
Steve AsztalosX-ray Instrumentation Associates, LLC, [email protected]
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Wagers, Andrew J.; Wang, Lifan; and Asztalos, Steve, "Supernovae Wavelet Spectral Index Method: A Step Toward PrecisionCosmology" (2014). The Research and Scholarship Symposium. 36.http://digitalcommons.cedarville.edu/research_scholarship_symposium/2014/poster_presentations/36
Andrew J. WagersCedarville UniversityEmail: [email protected]: 937-766-7692
ContactBailey, S., Aldering, G., Antilogus, P., Aragon, C., Baltay, C., et al. 2009, A&A, 500, L17Bongard, S., Baron, E., Smadja, G., Branch, D., & Hauschildt, P. H. 2006, ApJ, 647, 513Bongard, S., Baron, E., Smadja, G., Branch, D., & Hauschildt, P. H. 2008, ApJ, 687, 456Branch, D., Dang, L. C., & Baron, E. 2009, PASP, 121, 238Hachinger, S., Mazzali, P. A., & Benetti, S. 2006, MNRAS, 370, 299Holschneider, M, Kronland-Martinet, R., Morlet, J., Tchamitchian. P., 1989, in Wavelets, Time-Frequency Methods and Phase Space, ed. J.-M. Combes, A. Grossmann & P. Tchamitchian (Berlin: Springer-Verlag), 289Nugent, P., Phillips, M., Baron, E., Branch, D., & Hauschildt, P. 1995, ApJ, 455, L147Phillips, M. M. 1993, ApJ, 413, L105Shensa, M. J. 1992, Proc. IEEE Transactions on Signal Processing, 40, 2464Starck, J.-L., Murtagh, F., & Bijaoui, A. 1995, Astronomical Data Analysis Software and Systems IV, 77, 279Starck, J.-L., Siebenmorgen, R., & Gredel, R. 1997, ApJ, 482, 1011Wagers, A., Wang, L., & Asztalos, S. 2010, ApJ, 711, 711Wagers, A., PhD Thesis, 2012, Texas A&M Univ.
References
The first thing that can be noticed about the WSIM is that it reproduces previous results. It had been previously shown that the Si II spectral feature with wavelength 5750 Å correlates strongly with the decline rate of the SN magnitude (Hachinger et al. 2006), WSIM successfully reproduces this (see Figure 5). Also, Branch et al. (2009) established subgroups of SNe Ia by plotting the two spectral features against each other, these groups are retained by the WSIM (see Figure 6).
The plots mentioned above use spectra near maximum brightness, however the WSIM is not restricted to maximum brightness. The spectral indexes can be traced over the course of the explosion. Spectral features can be seen weakening and even disappearing, or (as in Figure 7) they can be seen strengthening. This evolution of the spectral features is due to changes in opacity in the explosion causing different compositional layers to be revealed.
The evolution of correlations between the spectral features with each other and with the decline rate can be explored (see Figure 8). It is clear that several strong correlations are present near maximum but there is also a second epoch of strong correlation 2-3 weeks after maximum. It is during these epochs that the most information can be extracted from the spectra. Lastly, Principal Components Analysis (PCA) was performed on the spectral index data and decline rates at each epoch. The PC1 coefficients are plotted in Figure 9 showing that epochs within 1 week of maximum all contribute nearly equally to the variation in the data.
Introduction
The Wavelet Spectral Index Method (WSIM) uses the á trous wavelet (Holtschneider et al. 1989; Shensa 1992; Starck et al. 1995, 1997) to decompose each supernova spectrum into different components representing variations on each scale (see Figure 3). The lower scales contain mainly noise in the data while the higher scales contain information from the overall shape of the spectrum (i.e. the continuum). If only the components of the scales related to spectra feature widths are selected than the confounding variations have essentially been removed. Also, with proper normalization, a natural reference (the zero flux line) arises so that the ambiguity of the continuum line is removed.
Five spectral features were chosen and the spectral index was defined as the area enclosed between the zero flux line and the normalized flux, downward features were given negative indexes (see Figure 4). Spectra were gathered from depositories freely available as well as a few unpublished spectra (ex. Harvard CfA SN Archive). These spectra were all run through the WSIM. The spectral catalog used contained spectra from as early as ~10 days before maximum to over two weeks after maximum. The results will be explained in the next section.
The Wavelet Spectral Index Method (WSIM)
There is much to do with the WSIM. The WSIM was developed with the goal of developing a system to generate synthetic SNe Ia spectra. The purpose of this was to test photometric techniques to gather information about SNe Ia that would normally be gathered via the spectra. Another natural application was to develop a correction to the Hubble diagram using the PCA results. The WSIM method can also be extended into other regions of the spectra such as the near infrared which has shown some promise in correlating spectral features to the decline rate. Ultimately, the WSIM could be extended outside SNe research and even outside astronomy itself since there are very few assumptions about the data being analyzed.
Future Work
The wavelet spectral index method is a useful tool in studying Type Ia Supernovae (SNe Ia), their evolution, and the correlations between peak magnitude and spectral features. The Wavelet Spectral Index Method (WSIM) eliminates much of the uncertainty inherent in the equivalent width methods used previously. Strong correlations have been found between several spectral features near maximum and the rate of decline after maximum. These correlations can be used in two ways: 1) to better calibrate the maximum magnitude of an individual SNe Ia, and 2) develop synthetic spectra that correlate to different light curve shapes. Lastly, the WSIM can be expanded to other areas of research since it is not dependent on what type of spectra is being studied.
Summary
In order to measure distances in the universe, astronomers use objects that have well known brightness. These objects are referred to as “standard candles.” One such standard candle is the Type Ia supernova (SN Ia). These supernovae are believed to originate from a White Dwarf with a giant companion. The white dwarf’s gravity pulls material off of it companion, when the white dwarf has reached a mass of ~1.4 times the mass of the sun it becomes unstable and explodes. It has been shown that SNe Ia have very uniform peak magnitudes.
It was shown that some of the variation in peak magnitude correlates with the decline rate of the brightness of the explosion (Philips 1993). Other work has shown that certain spectral lines, and ratios of spectral line strengths correlate with peak magnitude (Bailey et al. 2009; Bongard et al. 2006, 2008; Hachinger et al. 2006; Nugent et al. 1995). Unlike galaxies and most stars, SNe Ia have lots of overlapping spectral features with P Cygniprofiles. This makes measurement of the line strengths prone to large uncertainties. The method put forth here circumvents many of the inherent problems of the typical methods.
Results
Supernovae Wavelet Spectral Index Method:A Step Toward Precision Cosmology
Andrew J. Wagers, PhD1; Lifan Wang, PhD2,3; Stephen Asztalos, PhD4
1Cedarville University, 2Texas A&M Univ., 3Purple Mtn. Obs.; 4X-ray Instrumentation Assoc.
Figure 2. An artist’s impression of a SNe Ia progenitor (from spacetelescopes.org).
Figure 1. A distant supernova (from hubblesite.org).
X(5750)
Core NormalBroad LineCoolShallow Silicon
epochs ofstrong
correlation epochs ofstrong
correlation
Original Spectrum Shot Noise
“Continuum-like”
Wavelet Scales Used
Scale 2
Scale 3
Scale 1
Scale 4 Scale 5
Scale 6 Scale 7 Scale 8
Scale 9 Residual
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Figure 3: The original supernova spectrum and the components resulting from decomposing the spectrum with an á trous wavelet (Wagers 2010).
Figure 4: The sum of scales 3, 4, and 5 are combined to show the spectral features. The features used are highlighted showing the region that was used to calculate the spectral index (Wagers 2010).
Figure 5: The spectral index of the Si II absorption feature at the wavelength of 5750 Å is plotted verses the decline rate of the magnitude from maximum to 15 days after maximum showing a strong correlation (from Wagers et al. 2010).
Figure 6: The spectral index of the Si II absorption feature at the wavelength of 5750 Å is plotted verses the spectral index of the Si II feature at 6150 Å. The subgroups of Branch et al. (2009) are reproduced in a similar upside-down “y” shape. This work has added the category of “Known Peculiar” to represent those SNe that are particularly strange. There is some mixing between the “Cool” and “Broad Line” SNe, this is due primarily to the normalization as demonstrated by the dashed gray lines which show how the point circled by the gray open circle would vary if the 5750 Å feature was artificially strengthened/weakened (from Wagers 2012).
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Figure 7: The evolution of the Si II spectral feature at a wavelength of 5750 Å is plotted for the collection of SNe from 10 days before maximum to 25 days after maximum. The colors indicate Branch et al. (2009) subgroups. The lower plots show residuals from a simple fit to the data of that subgroup (from Wagers 2012).
Figure 8: Correlations are calculated between the spectral indexes and the decline rate of the SNe. Two regions of strong correlations are found near maximum and 1-2 weeks after maximum (from Wagers 2012).
Figure 9: The coefficients for each spectral index and the decline rate in the first principal component are shown for epochs between 10 days before maximum to 25 days after maximum. This data should prove useful for developing Hubble corrections and synthetic spectra.
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