Progress toward the Laboratory Simulation of Young Supernova

THE ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 127 : 305È310, 2000 April ( 2000. The American Astronomical Society. All rights reserved. Printed in U.S.A.

PROGRESS TOWARD THE LABORATORY SIMULATION OF YOUNG SUPERNOVA REMNANTS R. P. DRAKE,1 T. B. SMITH,1 J. J. CARROLL III,1 Y. YAN,1 S. G. GLENDINNING,2 KENT ESTABROOK,2 D. D. RYUTOV,2 B. A. REMINGTON,2 R. J. WALLACE,2 AND R. MCCRAY3 Received 1999 January 19 ; accepted 1999 August 3

ABSTRACT Progress in experiments to simulate the hydrodynamics of supernova remnants (SNRs) in the laboratory is reported. The experiment design involves shock heating of a dense material, which expands to become the ejecta that drive a blast wave through low-density foam. In the design, a variety of issues, such as radiative preheat of the unshocked matter, had to be addressed. A careful analysis of the scaling between hydrodynamic systems shows that the experiment is a good, scaled model of a local region in a young SNR. Measurements of the basic hydrodynamic behavior for two blast-wave velocities are nearly complete. Measurements of hydrodynamic instabilities at the contact surface between the ejecta and the low-density matter will commence in the near future. Subject headings : hydrodynamics È instabilities È supernova remnants È shock waves 1.

INTRODUCTION

and explodes it, just as the energy from a supernova event drives a blast wave through a star and explodes the star. In the SNR, the ejecta from the star expands into the circumstellar matter, driving a blast wave forward and decompressing from the spherical expansion. This decompression leads to the formation of a reverse shock in the stellar ejecta. In the experiment, we provide a vacuum gap to accomplish the decompression, so that the ejecta from the plug become a highÈMach number, Ñowing plasma, which then impacts low-density foam. The impact of the ejecta drives a forward shock through the foam ; a reverse shock forms in the ejecta. In SN 1987A, the forward shock is now beginning to collide with the ring. In the experiment, the forward shock collides with the dense, plastic end plate. We will see below that the ejecta-foam interaction turns out to be a good, scaled simulation of the SNR. The collision of the shocked foam with the end plate is a good simulation of only some initial aspects of the ring collision in SN 1987A, because radiative e†ects soon become dominant there (Borkowski et al. 1997). In the following, we summarize the details of the design and discuss one of the key design issuesÈthe choice of foam density. Then we discuss the scaling between the SNR and the experiment. After that we summarize the status of the experiments and describe our plans for further experiments to observe the growth of the Rayleigh-Taylor instability in this system.

Despite our ability to observe emission from supernova remnants (SNRs) at many wavelengths, and to model them in two dimensions, (and, occasionally, three dimensions) with hydrodynamic and MHD models, their structure continues to hold many mysteries. It is unclear why the radio and X-ray emission in many objects appears to extend to the forward shock (Pye et al. 1981 ; Reynolds & Gilmore 1986 ; Dickel, van Breugel, & Strom 1991). It is unclear why the magnetic Ðeld near the forward shock is radial, as indicated by the polarization of the radio emission (Dickel et al. 1991 ; Jun & Norman 1996). It is unclear why the structure in Tycho extends as far as it does toward the forward shock (Seward, Gorenstein, & Tucker 1983 ; Dickel et al. 1991 ; Chevalier, Blondin, & Emmering 1992). It is unclear what the origin of the knots in Cas A may be (Anderson & Rudnick 1995 ; Reed et al. 1995 ; Keohane, Rudnick, & Anderson 1996). The impending collision of the ejecta of SN 1987A with its ring seems likely to provide further puzzles (Borkowski, Blondin, & McCray 1997a, 1997b). Finding additional approaches toward understanding the behavior of SNRs is evidently worthwhile. Here we discuss laboratory experiments that can both provide a well-scaled simulation of certain hydrodynamic e†ects in SNRs and provide good tests of computational hydrodynamic models. Two years ago, at the Ðrst International Workshop on Laboratory Astrophysics with Large Lasers, we discussed the preliminary conceptual design of an experiment to simulate hydrodynamic e†ects in SNRs. Figure 1 shows our essential approach, only the outline of which had become clear at that time. The energy source, for our simulation experiments, is the nearly Planckian distribution of X-rays produced within a laser-heated, gold cavity. In this experiment, the characteristic temperature of the distribution is about 215 eV. The X-rays strike a plastic ““ plug, ÏÏ so called because it plugs a hole in the wall of the cavity. The energy deposited by the X-rays drives a shock through the plug

2.

ISSUES FOR EXPERIMENT DESIGN

In the detailed design of the experiment, we examined each component of the system just described, using both analytic calculations and hydrodynamic simulations to evaluate how best to produce a good simulation experiment. The simulations were performed using the radiationhydrodynamics code LASNEX (Zimmerman & Kruer 1975), used frequently for inertial conÐnement fusion research. The design tradeo†s are described in detail in (Drake et al. 1998). Here we describe the resulting target and examine one issue, the radiative preheating of the underdense foam, in more detail. The basic structure of the target was developed over a period of several years (Glendinning et al. 1992 ; Kau†man et al. 1994 ; Louis et al. 1995 ; Peyser et al. 1995 ; Remington et al. 1995 ; Dimonte et al. 1996). It has been used successfully for many hydrodynamic experiments. In this

1 Atmospheric Oceanic and Space Sciences, University of Michigan, 2455 Hayward Street, Ann Arbor, MI 48109 ; rpdrake=umich.edu. 2 Lawrence Livermore National Laboratory, P.O. Box 808, Livermore, CA 94551 ; glendinning1=llnl.gov. 3 JILA, Campus Box 440, University of Colorado, Boulder, CO 80309 ; dick=jila.Colorado.edu.

305

FIG. 1.ÈSchematic of the experiment design, and its relation to SN 1987A. The arrows illustrate the X-rays that ablate the cylindrically symmetric, plastic ““ plug ÏÏ that is mounted on a washer attached to the wall of a gold hohlraum. The plug is separated by a gap from a cylinder of low-density foam. The foam is mounted on an endplate. The image of SN 1987A is based on observations with the Hubble Space T elescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.

FIG. 2.ÈSimulations of the system shown in Figure 1, for two values of the initial foam density. (aÈd) 40 mg cm~3 foam. (eÈh) 10 mg cm~3 foam

SIMULATION OF YOUNG SNRs target, 18 ^ 2 kJ of laser energy at 0.35 km laser wavelength, in a 0.97 ^ 0.02 ns FWHM, Ñat-topped pulse, heats a 3 mm long by 1.6 mm diameter gold cylindrical cavity, known as a ““ hohlraum, ÏÏ to a radiation temperature of 215 ^ 5 eV. There is a 700 km-diameter hole at the center of the hohlraum wall. The X-rays ablate, shock, and explode the plug in this hole. The plug is plastic, 205 ^ 5 km thick, and has the ““ top hat ÏÏ shape seen in Figure 1Èthe 50 km protrusion into the hohlraum is of an 800 km diameter. Outside the hohlraum, there is a vacuum gap between the plug and the foam. The gap, which allows decompression, is 150 ^ 5 km wide. The foam is SiO , of density 40 mg cm~3, 2 about 1 of the initial density of the plug. In the design of 40 the target, the minimum density of the foam was constrained by radiation preheat, as we discuss next. When the shock that is driven by X-ray ablation breaks out of the plug, radiation from its surface, now at a temperature of about 20 eV, irradiates the foam. Later, the layer of shocked, compressed foam, which is at about 30 eV, emits radiation into the unshocked foam in front of it. The heat transported by this radiation must produce small enough e†ects that it does not signiÐcantly alter the structure of the shock, if the experiment is to be a successful simulation of hydrodynamic phenomena in an SNR. Here, in Figure 2, we compare simulations of a reference example, for which this is the case, with an example for which the foam density is too low. Figures 2aÈ2d and 2eÈ2h show the density, pressure, ion temperature, and velocity, respectively, calculated by the LASNEX radiation-hydrodynamic code for two cases. The case on the left (Fig. 2aÈ2d) uses the 40 mg cm~3 foam that we chose for the experiments. The case on the right uses 10 mg cm~3 foam. Each frame in the Ðgure shows the proÐle at three di†erent times : 2, 4, and 6 ns (measured from the rising edge of the initial X-ray heating pulse). The proÐles are the same in the two cases at 2 ns, as the shock driven by X-ray ablation is still traversing the plug, compressing and accelerating the matter there. At 4 and 6 ns, one can see the ejecta expanding from left to right, with increasing velocity, the stagnated ejected forming a reverse shock, and the forward shock in the foam. In the lower density foam (Fig. 2eÈ2h), the ion temperature is signiÐcant in advance of the shock, as is the pressure, and one can see in the velocity and density that there has been some acceleration and compression of the foam there. In this case, the shock has become a radiative precursor shock. The radiation mean free path has become large enough that a heated region develops in front of the shock. The simulations produced the desired, lowpreheat behavior for densities º 20 mg cm~3 ; we chose 40 mg cm~3 for the experiment. Most of the calculations needed for design of the target were possible using one-dimensional simulations of the proposed system. To evaluate the geometric details, we performed additional simulations in two dimensions, also using LASNEX. This led us, for example, to choose to make the foam diameter the same as the diameter of the plug, rather than larger or smaller. We also decided, based on two-dimensional simulations, not to tamp the radial expansion of the foam. The interaction with the tamper appeared more likely to interfere with the measurements than a free radial expansion would. The expanding material tends to lag behind the forward shock in the foam, and is at reduced density, so it has a small quantitative e†ect on the observation of the shock structure using radiography.

3.

307

SCALING FROM THE LABORATORY TO THE SNR

We have also studied more closely the scaling between hydrodynamic systems. Our intent is that the planar laboratory experiment be a good simulation of a local segment of an SNR, over a timescale on which spherical divergence is not important. A detailed study of this issue is reported in Ryutov et al. (1998) ; here we summarize the applicable results. SNR evolution is frequently studied as a hydrodynamic problem, to which the Euler equations apply. This requires that four conditions be satisÐed : (1) the plasma behavior must be localized, (2) energy transport by heat conduction must be small compared with convective energy transport, (3) momentum transport by viscosity must be small compared with convective momentum transport, and (4) global radiation cooling must be small. In the SNR, magnetization, along with entanglement of the magnetic Ðeld and/or microÑuctuations, is believed to satisfy the Ðrst three conditions. Global radiation cooling is often small (satisfying the fourth condition). In cases where global radiation cooling is signiÐcant, the hydrodynamic description using the Euler equations is known to be inadequate. In the laboratory simulation experiment, we satisfy the Ðrst three conditions by using a dense plasma with sufficiently rapid collisions. Radiation cooling in the laboratory system is also small. Thus, the Euler equations apply to both systems. The remaining question is what scaling must be established between two such systems for their behavior to be identical. The case of very strongly driven systems, in which a highÈ Mach number Ñowing plasma or forward shock produces the subsequent behavior, is a fairly simple one. For two such systems to evolve identically, there are three requirements. First, the initial geometric structure of the two systems must be identical. Second, the dimensionless time dependence of the drive (the normalized shape of the drive in time), must be identical. SpeciÐcally, if in a given system the driving velocity is v , and the spatial scale of some subd is of interest, is h, then the timestructure whose evolution scale on which the evolution will occur in that system is q \ h/v . This allows one to connect the evolution of two d systems. For example, a structure of 1017 cm size disparate driven at 104 km s~1 in an SNR evolves on a 108 s (about 3 yr) timescale ; the corresponding evolution of a geometrically identical structure of 0.01 cm size driven at 100 km s~1 in the laboratory occurs on a 1 ns timescale. These latter numbers are those that we have actually achieved in a planar experiment in the laboratory, with the intent that the dynamics there will correspond to those in a small angular segment of an SNR, over a timescale short enough that spherical divergence is not signiÐcant. The more general case, in which the system may involve weak shocks or small Mach numbers, is discussed in detail in Ryutov et al. (1998). Two systems with identical geometric structure and with an identical temporal structure of any external drive, will have a scaled, identical development if they both have the same ““ Euler number, ÏÏ Eu \ l8 Jr/p. Here l8 , r, and p are the magnitude of the initial velocity, density, and pressure at some chosen locations, respectively. Eu must be evaluated in the same way in the two systems, and it is the relative value, not the numerical value, that has signiÐcance. We have deÐned this quantity as the Euler number because the Euler equations are unchanged under a transformation between two systems for which this number is the same. Figure 3, from Ryutov et al. (1998), shows lines

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of constant Euler number and some speciÐc cases. The SNR and our laboratory experiment, labelled ““ SNR- lab, ÏÏ have the same Euler number and thus are well scaled in this sense. The conditions of a related experiment (Kane et al. 1997), relevant to the supernova explosion (labelled ““ SN ÏÏ and ““ SN-lab ÏÏ), are also shown.

10

SNR

8

Eu

v˜ (cm/s)

10

=3

Lab for SNR

10

6

= Eu

4.

SN 0.3

Lab for SN 10

4

10

5

10

6

7

10 p / ρ (cm/s)

10

8

Vol. 127

10

9

FIG. 3.ÈA Euler number can be deÐned for a given hydrodynamic system by choosing a velocity, density, and pressure, as discussed in the text. The Euler number is not an absolute measure but instead is a useful comparator. Identical hydrodynamic systems, when evaluated in the same way, have equal Euler number, Eu. Here we show lines of constant Eu for some systems of interest on axes of representative velocity (l8 or v ) and a quasi-sonic velocity, Jp/r. The speciÐc parameters for the systems dare also plotted.

PROGRESS AND PLANS IN THE EXPERIMENTS

We have now completed a Ðrst sequence of experiments. We have characterized the evolution of the laboratory hydrodynamic system in one dimension, at two di†erent drive velocities. To vary the drive velocity, we vary the density of the plug, which changes the velocity of the initial shock in the plug and of the subsequent ejecta. We vary the density by changing the fraction of bromine within the plastic plug, and have used 2 atomic per cent and 6 at. per cent Br. A certain amount of Br is needed to absorb the small fraction of gold M-band ( D 2 keV) X-rays produced in the hohlraum, so as to prevent them from preheating the low-density foam. We diagnose the experimental system using X-ray radiography. Two laser beams irradiate a plate of either Sc or Fe, producing K-shell X-rays at 4.3 or 6.7 keV, respectively. This provides a source of X-rays for backlighting ; some of the X-rays emitted by the plate are transmitted through the target and are imaged to a gated detector.

Space 1 ns

Time

Fiducials

205 m thick

275 m thick

500 m

FIG. 4.ÈUltraviolet emission from the outer surface of the plug, in time and space. The earliest signal shows the emergence of the shock from the usual, 205 km thick plug. The Ðducials establish the timing of the data.

No. 2, 2000

SIMULATION OF YOUNG SNRs

309

FIG. 5.ÈSchematic design of an experiment to observe Rayleigh-Taylor (and related) instabilities grow at the contact surface between the ejecta from the plug and the low-density foam.

We have accomplished the following measurements : Using a 6 at. per cent doping of Br, we have measured the following : (1) the position of the forward shock and the position of maximum density of the stagnated ejecta as they move across the foam, (2) the motion of the ejecta across the gap, (3) the emergence of the shock from the plastic slab, and (4) the compressed density and the velocity of the initial shock in the plug. Because the plug as shown in Figure 1 is too opaque to diagnose, this last measurement required a special target. The outer half of the opaque, brominated plastic plug was reduced to 200 km in diameter and was surrounded by a hydrodynamically similar material of the original diameter (700 km). In this case, a Be washer was used. Using a 2 at. per cent doping of Br, we have at this time made the same measurements except for (4), which we will obtain shortly, in this case using a polycarbonate rather than a Be washer to match the lower density of the plug. Data from one of these measurements are shown in Figure 4. We use an optical imaging system and a streak camera to detect the temporal dependence of the UV emission from the outer surface of the plug, imaged in one direction in space. In this case, the experimental package includes only the plug and not the foam or end plate. The outer surface of the plug is coated with a thin Al layer to block emission from the plug until the shock does break out. The diagnostic views the plug face on (from below in Figure 1). When the shock breaks out of the plug, the surface at D 20 eV produces bright emissions. For these measurements, we added a 70 km slab of material to half of the plug, delaying the emission there. The data shown are for a plug with 2 at. per cent Br doping. The shock initially emerged at 2.9 ns after the rising half-maximum of the 1 ns laser pulse. This, then, is the time at which the ejecta from the plug begin crossing the gap. We are in the process of publishing some of these results (Drake et al. 1998a ; Drake et al. 1998b) and analyzing the rest. The goal of these measurements is to provide sufficient data that a purely hydrodynamic initial condition can be deÐned from which the rest of the system evolution can be calculated. The initial condition will be the initial state of

the shock within the plastic slab, at a time late enough that radiation input in no longer signiÐcant. Calculating the subsequent evolution of the system will provide a simple, real test case for any hydrodynamic code. Reproducing the scaling with the plug density will provide a simple scaling test. Our intent is that such calculations will serve as ““ warm-up exercises ÏÏ for modeling of the instability behavior, discussed next. We have Ðnalized the design for a target that will produce hydrodynamic instabilities at the contact surface between the ejecta and the lower density matter, shown in Figure 5. We have switched from SiO foam, which allowed us to simultaneously diagnose both2 the forward and the reverse shocks, to C foam of the same density. This allows us to diagnose the contact surface while producing similar hydrodynamic behavior. The C foam also has a simpler equation of state, which may help the modeling. The surface of the C foam is rippled so as to seed hydrodynamic instabilities. The opaque layer in the ejecta is localized along the line of sight near the center of the target, so that the region where the X-rays are absorbed is narrow. As the Ðgure shows, the absorbing material, though shallow (along the line of sight), is wide (across the line of sight), allowing us to observe the evolution of the contact surface across the entire object. At the time of the writing of this paper, these targets are under construction, and measurements of their behavior will soon follow. 5.

CONCLUSION

In the two years since the last conference, we have progressed considerably from having a few ideas about simulating SNRs. We completed the design of an experimental system, addressing a variety of issues such as radiative preheat of the unshocked matter. We have demonstrated that the experiment produces the qualitative features present in a segment of a young SNR. We have conducted careful analysis of the scaling between hydrodynamic systems, which shows that the experiment is a good, scaled model of a local region in a young SNR. We have made measurements of the evolution of the system in one dimen-

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sion, allowing basic validation of a hydrodynamic simulation. We are about to begin measurements of the evolution of hydrodynamic instabilities at the contact surface between the ejecta and the low-density matter. We look forward to obtaining and analyzing these results and to reporting what we learn.

We acknowledge the support of the Nova technical sta†, without whom this work would not have been possible. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract W 7405 ENG-48 and with support from the University of Michigan.

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