SNe Ia: Can Chandrasekhar Mass Explosions Reproduce the Observed Zoo?
FFigure 1: A Saturday hike in the San Gabriel Mountains above Pasadena in 1985. Left toright are: E. Baron, Hans Bethe, and Gerry Brown. Photo credit: Jerry Cooperstein.
SNe Ia: Can Chandrasekhar Mass ExplosionsReproduce the Observed Zoo?
E. Baron
Homer L. Dodge Dept. of Physics & Astronomy, University of Oklahoma, 400 W. Brooks,Rm 100, Norman, OK 73072-2061, USAHamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
Abstract
The question of the nature of the progenitor of Type Ia supernovae (SNe Ia) isimportant both for our detailed understanding of stellar evolution and for theiruse as cosmological probes of the dark energy. Much of the basic features ofSNe Ia can be understood directly from the nuclear physics, a fact which Gerrywould have appreciated. We present an overview of the current observationaland theoretical situation and show that it not incompatible with most SNe Iabeing the results of thermonuclear explosions near the Chandrasekhar mass.
Keywords:
Type Ia supernovae, Synthetic spectra
Preprint submitted to Nuclear Physics A October 8, 2018 a r X i v : . [ a s t r o - ph . S R ] A ug . Introduction I have been fascinated listening to all of the talks and the remembrances ofGerry. It is especially interesting to see the wide scientific range of all of theNuclear Theory Group alumni. My relationship with Gerry was complex. Un-like most of Gerry’s students whom he actively recruited, when I asked Gerryif I could work with him, he was noncommittal. I had done just okay in TomKuo’s Quantum Mechanics course and poorly on the QM section of the quali-fier and I’m sure he used that as a filter to decide which students to take on.Nevertheless, Gerry did give me a chance and he helped me through many ofthe bewildering aspects of graduate school. Actually, once I joined the NuclearTheory Group as a graduate student I worked much of the time with JerryCooperstein (Coop) and our work preceded quite well. When a promised fel-lowship fell through, I had to scramble to find my first postdoc. I returned tothe Nuclear Theory Group for my second postdoc. In a weak economy, findinga permanent position was difficult and Gerry worked hard on my behalf. In theend, Gerry always came through for me. Gerry’s strong sense of fair play thatmany of us have remarked on, definitely worked on my behalf.I also want to take a minute to discuss our collaborators on the supernovaproblem during my time at Stony Brook. First I want to mention the role thatCoop played in both my and Gerry’s scientific work on the core collapse problem.Gerry trusted Coop implicitly. If Coop said it then Gerry took it seriously. Andwhile Gerry was my thesis adviser, my day-to-day interactions were with Coop.It is indeed a shame that Coop couldn’t make it to this meeting.The other person to mention is, of course, Hans Bethe. Gerry’s collaborationwith Hans was really important to him. He was proud that Hans was hiscollaborator. Gerry, Hans, Coop, and I certainly enjoyed the January “breaks”at Caltech, Santa Barbara, and Santa Cruz (Fig 1).2 . SNe Ia Basics
Type Ia supernovae as observational phenomena are exceedingly regular,particularly when compared with the much more diverse class of core collapsesupernovae. In astronomer’s units the maximum brightness of SNe Ia in the B band, M B is -19.25 with a 1- σ dispersion of 0.50 mag. For ordinary SNeIIP M B = − .
75 with a 1- σ dispersion of 0.98 mag [88]. This regularity ledquickly to the understanding that the progenitors of SNe Ia were likely thethermonuclear explosion of near Chandrasekhar mass white dwarfs [20].In fact the energy source of the visible display of SNe Ia and that of tradi-tional core-collapse supernovae are very different. In core collapse the underlyingenergy source is gravitational potential energy, which is released during the col-lapse of the iron core of a massive star to become a proto-neutron star. Froman astronomical viewpoint, the core collapse display, that is the observed lightcurve and spectra in the UV+Optical+IR (UVOIR) is for the most part pow-ered by energy deposited by the shock and stored in the thermal and ionizationenergy of hydrogen and other elements.In thermonuclear supernovae, SNe Ia, the explosion energy is provided by thethermonuclear fusion of the C+O white dwarf to iron group and intermediatemass elements. The rough structure that any model for a SN Ia must reproduceis shown in Figure 2. However, the optical display seen by astronomers isnot due to the thermal energy produced by the thermonuclear fusion of theexplosion. While this energy unbinds the star and produces the kinetic energyof the explosion, the initial high density and compact radius of a white dwarfmeans that it is opaque to radiation until it has expanded in radius by abouta factor of a million. This means the volume has increased by 10 and thusall the stored thermal energy has been exhausted in p dV work. Thus, theoptical display for SNe Ia comes not from the fusion itself, but rather from theradioactive decay of Ni, where the γ -rays and positrons are thermalized andproduce the optical light curves and spectra.It is important to understand that the thermonuclear explosion of a nearly3 igure 2: The final element distribution of a classical deflagration to detonation model. This isa delayed-detonation model which reproduces the light curves and spectra for Branch-normalsupernovae [33, 41, 43, 45]. The C/O white dwarf is from the core of an evolved 5M (cid:12) mainsequence star. Through accretion, this core approaches the Chandrasekhar limit. An explosionbegins spontaneously when the core has a central density of 2 . × g cm − and a massclose to 1 .
37 M (cid:12) [40]. The transition from deflagration to detonation is triggered at a densityof 2 . × g cm − . Adapted from Baron et al. [4]. Ni, or, if the densities are high enough,electron capture will be significant and non-radioactive iron group elements willbe produced in the central regions.In addition, the explosion itself is complex, in all scenarios it begins with asubsonic burning phase (deflagration). However, Rayleigh Taylor instabilitieswill lead to a well-mixed distribution of the elements in contrast to what is ob-served in SNe Ia spectra [31]. This behavior is shown in Figure 3. The favoredsolution to this problem is the deflagration to detonation transition (DDT) sce-nario, where the explosion begins as a deflagration, allowing the material topre-expand, but the deflagration transitions to a detonation at some density[29, 30, 51–53, 55, 56]. The detonation shock wave travels both forward andbackward through the star burning any mixed unburned material and produc-ing a layered structure. Figure 4 shows one realization of the DDT model.Several variations on this scenario exist, including the gravitationally confineddetonation [48, 74, 85] and the pulsating reverse detonation [2, 13–15]. Whilethe deflagration to detonation transition occurs in terrestrial situations wherethe burning occurs in a confined region, with walls for the pressure waves to re-flect off of, it is unknown if it naturally occurs in the unconfined stellar medium,but see Ref. [86].At first glance, SNe Ia seem remarkably homogeneous in their observationalcharacteristics. Nevertheless, observations carried out since the 1980’s haveincreasingly revealed a widespread diversity in spectra and light curves requiringa whole new understanding of the field. Empirically, considerable order wasbrought to the understanding of SNe Ia with the development of the Phillipsrelation [34, 81, 82], which is understood as due to a variation in the total amountof radioactive nickel produced in the supernova causing higher temperature andhence opacity variations which leads to variations in the diffusion time. Thecorrelation in the brightness (nickel mass) and the diffusion time leads to thePhillips relation [50, 54, 75]. Yet, while the light curve shape relation allows5 igure 3: 3-D models: Pure deflagration leads to low energy explosion, and lots of clumps ofunburned material particularly near center. Adapted from Gamezo et al. [31].Figure 4: 3-D models: Delayed detonation, the initial deflagration phase allows the star topre-expand. The detonation “sphericizes” the incomplete burning left from the deflagration.Adapted from Gamezo et al. [30]. pEW max (Si II l p E W m a x ( S i II l ) A ng s t r o m s CNCN HVBLBL HVSSCL91bg91T
CfA Sample
Figure 5: Branch et al. diagram of the Si II pseudo-equivalent widths based on measurementsof CfA spectra published by Blondin et al. [7]. The CN, CL, SS, and BL classes are indicatedby the different symbols. High velocity (HV) SNe [102], which are essentially the same as theHVG class [5] are concentrated mostly among the BL objects. 1991bg-like events correspondthe CL class, and 1991T-like events to the SS class. us to use SNe Ia as standard candles, it does not explain all of the observeddiversity.This diversity observed on top of the Phillips relation is sometimes generi-cally referred to as the second parameter problem, and is partially captured inthe work of Branch et al. [8–12] who plotted pseudo-equivalent widths of theSi II λ igure 6: A detailed NLTE calculation of the model W7 compared to the observed spectrumof SN 1994D March 21. The observed spectrum has been corrected for redshift assuming avelocity of 448 km s − and a reddening of E ( B − V ) = 0 .
06. Adapted from Baron et al. [1].
Phillips relation, it may not be too far afield to expect that variations in the zeroage main sequence mass (ZAMS) of the progenitor, its primordial metallicityand the history of the binary system, may well account for much of the “secondparameter” diversity described above.In spite of the detailed diversity of SNe Ia, they remain important cosmo-logical probes and their basic layered structure well reproduces the observeddetailed spectra for normal SNe Ia. Figure 6 shows a detailed non-local ther-modynamic equilibrium (NLTE) spectral calculation of the parameterized W7model compared to the observed spectrum of the core normal SN 1994D andFigure 7 shows an extremely detailed NLTE calculation of a standard delayeddetonation model compared to the full UV–IR spectrum of the nearby, normalSN 2011fe.Observations in the 21st Century have seen the discovery of an uncomfort-ably large number of peculiar “classes” of SNe Ia identified by their prototypes:8 igure 7: Detailed NLTE spectrum of delayed detonation model compared to the maximumlight spectrum of SN 2011fe. The observed spectrum covers the entire wavelength range fromthe UV to the IR. Adapted from Baron et al. [4]. (rare, photometrically-peculiar events that do not follow the Phillips re-lation, showing a rise time typical of a SN Ia, but with an unusually slower de-cline and high photospheric temperature [16, 64, 97]); (a BL-HVG eventwith an extremely slow decline rate but with an apparently modest Ni yield of0.6 solar masses [3, 58]); (events that are spectroscopically similar to nor-mal SNe Ia, but have lower maximum-light velocities, low luminosities for theirdecline rates, yet generally hotter photospheres [28, 63, 83]); (SNe Ia-likeevents with a strong CSM interaction [6, 18, 21, 23, 36, 37, 57, 101]); and (SNe Ia with broad light curves like a hot, luminous event and lacking a promi-nent secondary maximum in the near-IR, but displaying spectra at maximumsimilar to those of low-luminosity SNe Ia [27, 67]). Moreover, several SNe Ia(2003fg, 2006gz, 2007if, 2009dc) have been observed whose brightness and lightcurve shape have led them to be classified as super-Chandrasekhar explosions[39, 46, 47, 77, 94, 96, 100] which may be due to double degenerate explosionswhere the mass of the binary exceeds a Chandrasekhar mass, or possibly due tosupermassive white dwarfs due to rotational support [104, 105].In fact this wide range of diversity has led to the suggestion that the param-9 igure 8: The Bolometric light curve of a classic delayed detonation model, compared tothe pulsational delayed detonation model used for SN 2001ay. The dashed lines show theinstantaneous gamma-ray luminosity used in Arnett’s law. Adapted from Baron et al. [3]. eter responsible for the second parameter variation is the mass ejected in theexplosion itself. This is due either to dynamical mergers of binary white dwarfs[24, 78–80] or due to pure deflagration leading to a bound remnant with lowejected mass [26, 49, 60].While these paths may in fact exist in nature, even among the wide variety ofobserved supernovae, there is opportunity for the Chandrasekhar mass scenarioto explain some of the observed diversity. Particularly, pulsational delayeddetonations (PDDs) allow for variation in the Ni distribution that explaindeviations from the Phillips relation.For example, SN 2001ay, the slowest known decliner, was significantly un-derbright for its decline rate [3, 58]. By increasing the C/O ratio, and assuminga PDD we were able to move the nickel distribution further out, increasing thekinetic energy and thus, the amount of p dV work done, leading to a slow de-cline ratio, normal brightness, and the observed fast spectra [3]. The bolometriclight curve of the model is shown in Figure 8 and the detailed NLTE syntheticspectrum is compared to the observations in Figure 9.10 igure 9: Pulsating Delayed Detonation. SN 2001ay, Max Light, M V = -19.07 mag. Adaptedfrom Baron et al. [3]. Similarly, the SN Iax class supernova 2012Z, can be explained by a PDD ina Chandrasekhar mass white dwarf, where the burning to the iron group takesplace almost exclusively during the deflagration phase, leading to a central non-radioactive core, some Ni mixing during the fallback of the bound shell, butthe layered structure characteristic of a detonation in the intermediate masselements, as well as for the low velocity spectra with narrow lines, indicating asmall differential spread in velocities [99]. Figure 10 shows the mean half widthsof the 1 . µ m Fe II feature for a variety of normal and SNe Iax supernovae.Both the models of SN 2001ay and SN 2012Z, show that while the primaryunderstanding of the Phillips relation is the correlation of the total mass of Ni produced in a Chandrasekhar mass explosion, additional variation canbe accommodated by variations on the spatial distribution of Ni, leading toChandrasekhar mass explosions that do not obey the Phillips relation.There does remain a question of whether there are enough white dwarfs inbinary systems to grow to the Chandrasekhar mass. Calculations of supernovaerates suggest that including both the single degenerate channel and the double11 igure 10: Mean Half Width, MHW, for the 1 . µ m feature for SNe Ia (blue) and SN 2012Z(red). In addition, the MHW is given for theoretical models of the series 5p0z22 with (leftline) and without mixing (right line) [45]. Adapted from Stritzinger et al. [99].Figure 11: Gerry Brown and Hans Bethe relaxing in the San Gabriel Mountains during a 1982visit to Caltech. Photo credit: Jerry Cooperstein. degenerate channel still produces too few supernovae compared to the observedgalaxy-cluster rate [19]. Chandraskehar mass WD explosions are triggered bycompressional heating near the WD center. Because the compressional heat re-lease increases rapidly towards the Chandrasekhar mass, exploding stars shouldhave a very narrow range in masses [42]. The donor star may be either a redgiant or a main sequence star, a helium star, or the accreted material may orig-inate from a tidally disrupted WD [84, 103]. We differentiate between dynamicmerger models where a prompt explosion occurs on a dynamic timescale dueto heating of merging material [often called violent mergers 61, 79, 80] and asecular merger in which the matter of the disrupted companion is accreted bythe primary WD on a quasi-hydrostatic time-scale. The former leads to an ex-12losion of a relatively low density configuration. The latter might share manycharacteristics with the standard high-density, single-degenerate M Ch explo-sion models. Efforts have been made to expand the progenitor distribution byincluding sub-Chandrasekhar explosions [90–93]. Sub-Chandrasekhar mass ex-plosions are triggered by helium detonation which produce iron group elementsat the surface making the spectra either too blue [44, 76] or too red [59, 78, 98].Others have studied channels where two white dwarfs collide in globular clus-ters or multiple systems [24, 32, 38, 62, 87, 89]. While there is some evidencethat the classical red giant mode of the single degenerate channel may be rare[17, 25, 65, 95] there are uncertainties on the nature of the environment as wellas uncertainties on the nature of the progenitor white dwarf [22]. Additionally,there is some solid evidence for the single degenerate scenario [23, 73]. Thestudy of delay time distributions (DTD) also somewhat favors the double de-generate scenario [68–70] in that the observed DTD seems to be proportionalto t − . In the single degenerate scenario, the DTD should decline sharply aftera few billion years since for longer times the primary will have smaller mainsequence mass and hence produce lower mass white dwarfs. However the ev-idence based solely on delay times is not conclusive [35, 71]. Thus, while thetotal mass ejected in the explosion may be a parameter in some SNe Ia events, itis interesting to see just how much of the observered diversity may be explainedwithin the Chandrasekhar mass scenario by variations in the Ni distribution.
3. Conclusions
While the Phillips relation implies strong homogeneity, which is well ac-counted for in the Chandrasekhar mass model combined with fundamental nu-clear physics, it is unclear just how much of the observed diversity can be ac-commodated in the Chandrasekhar mass paradigm. Nevertheless, some peculiarSNe Ia that don’t obey the Phillips relation can in fact be modeled within theChandrasekhar mass paradigm and fit many of the observations. This does notmean that nature does not take advantage of other channels available.13inally, Figure 11 shows Gerry and Hans as I fondly remember them.
Acknowledgments
I wish to acknowledge my collaborators Peter Hauschildt, Peter Hoeflich,Mark Phillips, and David Branch for much advice and helpful discussions. Ithank Mark Phillips and Chris Burns for helping to construct Figure 5. I alsowish to thank my Nuclear Theory Group friends who supported me duringnearly a decade at Stony Brook. This incomplete list includes Jerry Cooperstein,Tom Ainsworth, Hans Hansson, Karen Kolehmainen, Prakash, Dany Page, andJim Lattimer. The work has been supported in part by support for programsHST-GO-12298.05-A, and HST-GO-122948.04-A provided by NASA through agrant from the Space Telescope Science Institute, which is operated by the As-sociation of Universities for Research in Astronomy, Incorporated, under NASAcontract NAS5-26555. This work was also supported in part by the NSF grantAST-0707704 and grants SFB 676 and GRK 1354 from the DFG. This researchused resources of the National Energy Research Scientific Computing Center(NERSC), which is supported by the Office of Science of the U.S. Departmentof Energy under Contract No. DE-AC02-05CH11231; and the H¨ochstleistungsRechenzentrum Nord (HLRN). We thank both these institutions for a generousallocation of computer time.
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