FINDING THE FIRST COSMIC EXPLOSIONS. III. PULSATIONAL PAIR-INSTABILITY SUPERNOVAE

Population III (Pop III) stars ended the cosmic Dark Ages and began to reionize (Whalen et al. 2004; Kitayama et al. 2004; Alvarez et al. 2006; Abel et al. 2007; Wise & Abel 2008) and chemically enrich (Mackey et al. 2003; Smith & Sigurdsson 2007; Smith et al. 2009; Chiaki et al. 2013; Ritter et al. 2012; Safranek-Shrader et al. 2013) the early intergalactic medium (IGM). They also populated early galaxies (Johnson et al. 2008, 2009; Greif et al. 2008, 2010; Jeon et al. 2012; Pawlik et al. 2011, 2013; Wise et al. 2012) and might be the origin of supermassive black holes (Bromm & Loeb 2003; Johnson & Bromm 2007; Djorgovski et al. 2008; Milosavljević et al. 2009; Alvarez et al. 2009; Lippai et al. 2009; Tanaka & Haiman 2009; Park & Ricotti 2011, 2012; Johnson et al. 2012, 2013c; Whalen & Fryer 2012; Agarwal et al. 2012; Park & Ricotti 2013; Latif et al. 2013a, 2013b; Schleicher et al. 2013; Choi et al. 2013; Reisswig et al. 2013; Volonteri 2012).

Unfortunately, little is known for certain of the properties of the first stars. Individual Pop III stars will not be visible to next-generation instruments such as the James Webb Space Telescope (JWST; Gardner et al. 2006) or the Thirty-Meter Telescope (TMT; but see Rydberg et al. 2013, about detecting the H ii regions of the first stars). Attempts to constrain the Pop III initial mass function (IMF) from stellar archaeology are problematic because of the many processes that can enrich ancient, dim stars with metals over cosmic time (e.g., Cayrel et al. 2004; Beers & Christlieb 2005; Frebel et al. 2005; Lai et al. 2008; Joggerst et al. 2010; Caffau et al. 2012). Simulations are far from being able to model the formation of Pop III stars at z ∼ 20 from first principles (e.g., Abel et al. 2002; Bromm et al. 2002; Nakamura & Umemura 2001; Turk et al. 2009; Stacy et al. 2010, 2012; Clark et al. 2011; Hosokawa et al. 2011; Smith et al. 2011; Greif et al. 2011, 2012; Hosokawa et al. 2012; Susa 2013; Hirano et al. 2013) and therefore do not yet predict their final masses or numbers in a given halo (for recent reviews, see Whalen 2012; Glover 2013).

Several groups have now turned to Pop III supernovae (SNe) as potential probes of the primordial IMF because they can be observed at high redshifts and their masses can be deduced from their light curves. The first studies focused on pair-instability (PI) SNe, the extremely energetic thermonuclear explosions of 140–260 M_☉ stars (Heger & Woosley 2002; Scannapieco et al. 2005; Whalen et al. 2008b; Gal-Yam et al. 2009; Cooke et al. 2012; Joggerst & Whalen 2011; Whalen et al. 2013d). They found that Pop III PI SNe could be detected at z ≳ 20 by JWST and the TMT and at z ∼ 10–20 in all-sky near infrared (NIR) surveys by the Wide-Field Infrared Survey Telescope (WFIRST) and the Wide-Field Imaging Surveyor for High-Redshift (WISH; Fryer et al. 2010; Kasen et al. 2011; Whalen et al. 2013a, 2013e; Pan et al. 2012; Hummel et al. 2012; Dessart et al. 2013; de Souza et al. 2013). Other simulations have now shown that Pop III core-collapse SNe can be seen out to z ∼ 10–15 with JWST (Whalen et al. 2013f) and that Type IIn SNe and supermassive thermonuclear explosions (Whalen et al. 2013c, 2013g, 2013h; Johnson et al. 2013b) are visible at z ∼ 10–20.

Until now, pulsational pair-instability (PPI) SNe, in which the PI fails to unbind the star and instead heaves off its outer layers in a series of violent ejections, have been overlooked as cosmic beacons at high redshifts. These episodes vary in energy and mass but the first ejection is usually the most massive one, with later pulsations ejecting less massive shells at higher velocities. The later shells can overtake the first, producing collisions that are very luminous in the UV. Three PPI SN candidates have been found at low redshifts, SN 1000-1216 at z = 3.9 (Cooke et al. 2012), SN2009ip (Margutti et al. 2014; Smith et al. 2013), and perhaps SN 2006oz at z = 0.376 (Leloudas et al. 2012). This mechanism has also been invoked to explain superluminous SNe such as SN 2006gy (Smith & McCray 2007; Woosley et al. 2007). At early epochs, the large UV fluxes of PPI SNe would be redshifted into the NIR today and could rival those of PI SNe. Indeed, other types of shell-collision explosions are now known to be visible at z ∼ 10–20 (Tominaga et al. 2011; Moriya et al. 2013; Tanaka et al. 2012, 2013; Whalen et al. 2013b). PPI SNe may be more numerous than PI SNe in the early universe, depending on the primordial IMF.

We have now modeled Pop III PPI SNe and their spectra and light curves with the Los Alamos Radiation Adaptive Grid Eulerian (RAGE) and SPECTRUM codes. In Section 2 we review the PPI SN mechanism and discuss our numerical methods and explosion models in Section 3. Pair pulsations and their collisions are examined in Section 4. In Section 5, we calculate NIR light curves for the collision in the observer frame, and we conclude in Section 6.

It is generally known that Pop III stars from 140 to 260 M_☉ die as PI SNe, but they can actually encounter the PI at ∼100 M_☉ (and at masses as low as 85 M_☉ if they are rotating; Chatzopoulos & Wheeler 2012). At these lower masses, runaway O and Si burning triggered by the PI may not unbind the star. Its outer layers, which are weakly bound if it dies as a red supergiant, are ejected instead. We now examine this process in greater detail by considering the PPI SN from Woosley et al. (2007) as an example. The progenitor was a 110 M_☉ solar-metallicity star whose evolution was modeled in the Kepler stellar evolution code (Weaver et al. 1978; Woosley et al. 2002). Mass loss was heavily suppressed over its lifetime to approximate the evolution of a Pop III star. At the onset of the PI the mass of the star is 74.6 M_☉, with a 49.9 M_☉ He core. It dies as a red supergiant, with a radius of 1.1 × 10¹⁴ cm and a luminosity of 9.2 × 10³⁹ erg s⁻¹.

Loss of thermal pressure support in the core due to the conversion of photons into e⁺–e⁻ pairs causes it to contract, radiate neutrinos and light, and increase in temperature from ∼10⁹ K to 3.04 × 10⁹ K, well above the usual 2.0 × 10⁹ K at which O burns stably in massive stars. Explosive nuclear burning ensues, consuming 1.49 M_☉ of O and 1.55 M_☉ of C and releasing 1.4 × 10⁵¹ erg. Most of this energy goes into expanding the star but ∼10% is channeled into the expulsion of the weakly bound outer layers of the core and surrounding envelope (24.5 M_☉, mostly He and some H). This first shell is ejected at velocities of 100–1000 km s⁻¹. As shown in Figure 2 of Woosley et al. (2007), the ejection of the envelope looks like a weak SN, with a brief breakout luminosity of 10^42.7 erg s⁻¹ followed by a 10^41.9 erg s⁻¹ plateau that is powered primarily by He recombination.

What remains after the initial outburst is a 50.7 M_☉ star that is slightly more massive than the original He core. It again contracts, emits neutrinos, and becomes hotter. After another 6.8 yr the core again encounters the PI and ejects another shell into space. This shell is less massive, 5.1 M_☉, but more energetic, 6.0 × 10⁵⁰ erg. It is soon followed by an even less massive but slightly faster shell that quickly overtakes it and collides with it, as shown in the left and right panels of Figure 1. This initial collision is luminous but buried in an optically thick medium and could not be observed. Nine years later the core contracts a final time, entering a stable Si burning phase that produces an Fe core that later collapses. If the core is rapidly rotating it could create a gamma-ray burst (GRB), either by forming a rapidly spinning neutron star (millisecond magnetars; e.g., Metzger et al. 2011) or a black hole accretion disk system (collapsars; e.g., MacFadyen & Woosley 1999). In this study we consider only the collision of the second two shells with the first and examine the NIR, radio, and X-ray signatures of Pop III GRBs elsewhere (Whalen et al. 2008a; Mesler et al. 2012, 2013).

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Light curves and spectra for PPI SNe are calculated in three stages. First, we map the Kepler blast profiles from Woosley et al. (2007) shown in the right panel of Figure 1 into the RAGE code and evolve them out to 9 yr. We then post process our RAGE profiles with the SPECTRUM code to construct light curves and spectra. Finally, these spectra are convolved with filter response functions, cosmological redshifting and absorption by the neutral IGM at high z to obtain NIR light curves in the observer frame.

3.1. RAGE

3.2. SPECTRUM

Density, velocity, and temperature profiles for the collision between the second two pair pulsations and the first are shown in Figure 2. It is clear from the density profiles in Figures 1 and 2 that the first shell is trailed by a relatively dense wind-like shroud that roughly has an r⁻² profile but is basically stationary. As the second ejection plows through this envelope it rapidly decelerates and begins to shock the trailing edge of the first shell. The shocked gas piles up in a thin, hot dense layer at the leading edge of the second ejection. It is visible as the density spike at ∼10¹⁵ cm at 69 days, at 1.8 × 10¹⁶ cm at 1.6 yr, and at 4.0 × 10¹⁶ cm at 5.4 yr. This thin layer is the origin of all the luminosity from the collision, which we show in the left panel of Figure 3.

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Unlike Type IIn SNe, in which the collision between the ejecta and a shell are more abrupt, collisions between consecutive pair pulsations are more gradual because the first ejection has no distinct inner surface. Instead, the second ejection radiates more strongly as it becomes more mass loaded as it sweeps up the first shell. This is why the luminosity ramps up over a period of ∼10 days before reaching a maximum of ∼7.0 × 10⁴³ erg s⁻¹. The collision radiates strongly for ∼ 3 yr as the relative kinetic energy of the shells is converted into heat and then light. Approximately 90% of the kinetic energy is radiated away as the second shell advances from 10¹⁵ cm to 2 × 10¹⁶ cm. The rebrightening that is visible at ∼600 days is due to an abrupt pileup of gas in the shocked layer that is visible as the density spike at 1.8 × 10¹⁶ cm at 1.6 yr. This bump in luminosity peaks at ∼10⁴³ erg s⁻¹ and lasts about 500 days.

The ripples in the bolometric luminosity, which are also manifest in the NIR light curves, are due to the classic radiative instability described by Chevalier & Imamura (1982) and Imamura et al. (1984). As the second two pulses plow up the first, a reverse shock forms, detaches from the forward shock, and backsteps into the flow in the frame of the forward shock. But if the postshock gas can radiatively cool, as this gas does, the reverse shock loses pressure support and recedes back toward the forward shock. As the forward shock plows up more material the cycle repeats. The fluctuations in overall luminosity are due to this cycle, and since the bolometric luminosity varies by up to 50% we infer that flux from the reverse shock is at times similar to that of the forward shock. The STELLA light curves from Woosley et al. (2007) also exhibit this radiative instability. In a multidimensional simulation, the narrow region between the colliding shells in which the radiative instability occurs would likely be broken up by Rayleigh–Taylor (RT) instabilities, and this might reduce or remove altogether the fluctuations in the light curve. These instabilities would also disrupt the density structures emitting most of the radiation from the collision, and it is unclear how this would change the luminosity.

RAGE and STELLA yield similar bolometric luminosities early in the collision, but there are some differences. From 200 to 600 days the RAGE luminosities fall below 10⁴³ erg s⁻¹ before rebrightening, while the STELLA light curve falls more gradually. There are also features in the peak luminosities in RAGE that are distinct from those in STELLA. These discrepancies can be attributed to differences in resolution, atomic physics and hydrodynamic schemes, and opacities between the two codes. Differences between the opacities in OPLIB and in STELLA in particular could change photon diffusion times through the flow and the duration of the light curves. However, the two codes exhibit similar bolometric luminosities overall. The steeper decline in the RAGE light curve suggests that PPI SNe may be more easily detected at high z than STELLA might predict because of the greater variability after redshifting.

It might be thought that the PPI SN would not appear to be a transient at high redshift because its bolometric luminosity is relatively uniform for a year in the rest frame. This emission would last 10–20 yr for z = 10–20 events in the observer frame. But the spectra evolve considerably over this time, as we show in the right panel of Figure 3 and the temperatures in Figure 1. At ∼70 days the shock is hottest, ∼5 eV or 55,000 K, and its spectrum cuts off at about 500 Å. At this stage the collision radiates strongly in the UV, like Type IIn SNe. As the collision proceeds and more of the relative kinetic energy of the shells is dissipated, the shock cools and its spectrum softens. At 1.6 yr, when the collision temporarily rebrightens, the shock has cooled to ∼11,000 K and its spectrum cuts off at ∼2000 Å. By 5.4 yr the collision has cooled to ∼1500 K and its spectrum has evolved into the optical and IR. At this point the shells have become transparent and their photons have escaped into the IGM, as shown by the flat material temperatures in Figure 2.

The PPI SN is similar to the Type IIn SNe studied by Whalen et al. (2013b) in that it is bright in the UV at early stages of the collision, when the shock has large radii, ∼10¹⁵ cm. This radius is also similar to the inner radii of shells of the Type IIn events in Whalen et al. (2013b) when the ejecta crashes into them. With similar shock temperatures and radii upon collisions, the initial total luminosities for PPI SNe and Type IIne might be expected to be comparable, and inspection of Figure 2 in Whalen et al. (2013b) confirms this to be the case. As the shock approaches radiation breakout from the first shell, one would expect low-energy photons to filter out first and later be followed by higher energy photons because opacities are generally greater at shorter wavelengths. But the temperature of the shock rises in the early stages of the collision so both processes harden the spectrum as radiation fully emerges from the shell.

We note that it is primarily bound–bound and bound–free emissions from the shocked region between the second two shells and the first that comprise the spectrum. In our models, the collision does not produce temperatures that are high enough for bremsstrahlung X-rays, as might occur in more energetic events. The spectra are basically blackbody with emission and absorption lines from the shells. These latter features are prominent in the spectra at later times, which appear to be blackbody but are sheared off at short wavelengths.

Although our model does not produce X-rays, they might be emitted in real events by non-local-thermodynamic-equilibrium (non-LTE) processes in the shock. If ions in the shocked region between the shells decouple from electrons at early times they could rise to higher temperatures than in our models because they cannot efficiently radiate away the heat deposited by the shock. Under these circumstances the shock might emit X-rays at later times. Efforts are now underway to implement three-temperature physics in RAGE, in which ions, electrons, and photons are evolved at separate temperatures, to capture non-LTE processes. Although such X-rays would not be detected from high-z explosions due to absorption by the neutral IGM, they might be visible in local events.

We also note that although the spectrum at times appears to be blackbody, one cannot fit a blackbody to the effective temperature of the shock to estimate the NIR flux from a high-redshift SN in lieu of an actual spectrum calculation. The UV that is redshifted into the NIR comes from the short wavelength limit of the spectrum, which, unlike the longer wavelengths, is poorly approximated by a blackbody because of absorption by the shells. A blackbody fit based on the lower wavelengths would overestimate flux at these short wavelengths and predict too much NIR luminosity today.

To obtain NIR light curves from the spectra, we first cosmologically redshift and dim them. They are then corrected for absorption by the neutral IGM at high redshift according to the prescription of Madau (1995). Several models for absorption by the neutral IGM exist in the literature but they yield similar transmission factors, as discussed by de Souza et al. (2013). We then convolve the spectra with filter response functions for JWST and WFIRST with the synthetic photometry code of Su et al. (2011) to compute NIR light curves.

We show light curves for the PPI SN in four JWST filters (1.5 μm, 2 μm, 2.77 μm, and 4.44 μm at z = 7, 10, 15, 20, and 30) in Figure 4. The PPI SN is visible at z ≳ 30 to JWST, whose photometry limit is AB mag 32. The light curves all exhibit rapid rise times that correspond to the breakout of radiation from the first shell. Breakout is followed by a gradual rise in luminosity as the shock grows in radius. But this rise and later decline has fluctuations that are due to hydrodynamics. As the shock expands it runs into density structures that cause it to intermittently brighten. Fluctuations in densities and shock temperatures also result in variations in opacities in front of the shock. Such features are present in Type IIn NIR light curves at early times as SN ejecta plows up density structures in the collision zone (see Figure 10 in Whalen et al. 2013b).

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The PPI SN shock is brighter but a little cooler than the Type IIn collisions examined by Whalen et al. (2013b). At z = 15, the PPI SN is about 2 mag brighter than the Type IIn, but at 4.44 μm rather than 3.56 μm. The collision between the faster SN ejecta and the shell in Type IIne creates higher shock temperatures but happens at somewhat smaller radii, and is therefore less luminous. We note that the SN considered by Whalen et al. (2013b) only had an energy of 2.4 × 10⁵¹ erg and was therefore a conservative case. In many Type IIne the ejecta can have much more energy and the collision could be superluminous (e.g., SN 2006gy; Moriya et al. 2013) and nearly as bright in the NIR as a PPI SN at high redshift.

At z ≳ 15 the PPI SN is slightly dimmer than the nominal detection limit of WFIRST at 4 μm, AB mag 27. However, simple spectrum stacking could extend this limit down to 29. If so, WFIRST could detect these events out to z ∼ 20 at 2–4 times the rate of PI SNe, or perhaps hundreds over its mission lifetime as discussed in Section 6 of Whalen et al. (2013a). The possibility of building up the Pop III IMF and tracing cosmic star formation rates (SFRs) at high redshift by detecting large numbers of primeval SNe underscores the need for all-sky NIR missions such as WFIRST and WISH.

We note that with only modest gravitational lensing PPI SNe could be found in the Cluster Lensing and Supernova Survey with Hubble (CLASH) at z ∼ 7–12 because the H band (1.63 μm) photometry limit of the Wide-Field Camera 3 is ∼AB mag 27.3. However, it is not clear if there are enough PPI SN at this epoch to be enclosed by the volume that is lensed by the clusters in the survey. For the mean of the SFRs discussed in the next section, Whalen et al. (2013i) find that up to a dozen SNe from 5 < z < 12 may already have been found by CLASH. For most IMFs it is unlikely that any of these events would be a PPI SN.

Pop III PPI SNe can be used to probe the primordial universe because they are visible at z ≳ 30 to JWST and at z ≳ 20 to WFIRST. They will complement PI SNe, Type IIne, and supermassive Pop III SNe, which are visible out to similar redshifts. PPI SN light curves are easily distinguished from those of other Pop III SNe, and their variability over likely protogalactic survey times will clearly identify them as transients in future surveys. Besides revealing the properties of early stars, Pop III SNe will pinpoint the positions of ancient galaxies on the sky that otherwise might not have been discovered. They will also constrain SFRs in the first galaxies, which will yield important clues about their evolution at early times.

Although we have considered a solar-mass progenitor as a proxy for a Pop III star, this will not have a large effect on the energetics of the PPI or the NIR light curve of the collision. The energetics of the central engine primarily depend on the entropy profile of the core of the star at the end of its life, which is similar for solar-metallicity and Pop III stars of equal mass (e.g., Chieffi & Limongi 2004; Woosley & Heger 2007; see also Figure 1 of Whalen & Fryer 2012). But metals could enhance cooling in the shocked gas between the shells and lead to denser and thinner structures with lower temperatures and luminosities. Metals also impose a more complex line structure on the spectra of the collision than would be present in zero-metallicity explosions. All of this, together with the somewhat larger opacity in the surrounding envelope due to the metals, suggests that the NIR luminosities in our simulation are a lower limit to those for Pop III events.

While our fiducial model demonstrates that PPI SNe will be visible out to z ∼ 20 in future observational campaigns, more work must be done to determine the range of stellar masses for which PPI SNe can be detected at high redshift. Although Pop III stars from 85 to 140 M_☉ can die in pulsational explosions, only those with He core masses from 40 to 50 M_☉ will produce very luminous events because the timescales between their pulsations are short enough for the shells to actually collide (on the order of years). Also, for this range in mass the collisions occur at radii of ∼10¹⁶ cm, where most of their energy is emitted in the UV and optical. As noted above, RT instabilities will induce mixing at the interface between the colliding shells and alter their luminosity. Future studies should be multidimensional, and focus on explosions in this mass range.

Detection rates for PPI SNe at high-redshift hinge on the cosmic SFR. Current estimates of the cosmic SFR from GRBs (Ishida et al. 2011; Robertson & Ellis 2012), SNe (Cooke et al. 2012), early galaxies (Campisi et al. 2011), and simulations (Tornatore et al. 2007; Trenti & Stiavelli 2009; Wise et al. 2012; Johnson et al. 2013a; Pawlik et al. 2013; Xu et al. 2013; Hasegawa & Semelin 2013; Muratov et al. 2013) vary by more than two orders of magnitude above z ∼ 10 (see also Section 4 of Whalen et al. 2013i). Assuming fairly conservative SFRs, 5–10 Pop III PI SNe could be found by JWST over its lifetime (Hummel et al. 2012). Depending on the slope of the IMF, twice as many PPI SNe could be found. Wide-field campaigns by WFIRST and WISH might discover hundreds of these events.

D.J.W. acknowledges support from the Baden-Württemberg-Stiftung by contract research via the programme Internationale Spitzenforschung II (grant P- LS-SPII/18). J.S. and J.L.J. were supported by LANL LDRD Director's Fellowships. M.S. thanks Marcia Rieke for making the NIRCam filter curves available and was partially supported by NASA JWST grant NAG5-12458. Work at LANL was done under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under contract No. DE-AC52-06NA25396. All RAGE and SPECTRUM calculations were performed on Institutional Computing (IC) and Yellow network platforms at LANL (Pinto, Mustang, and Moonlight). At Santa Cruz, research was supported by NASA (NNX09AK36G) and the DOE-HEP Program (DE-SC0010676).