# A Possible Gamma-Ray Enhancement Event in Tycho’s Supernova Remnant

Yi Xing  Shanghai Astronomical Observatory, Chinese Academy of Sciences, 80
Nandan Road, Shanghai 200030, China  Zhongxiang Wang  Department of Astronomy,
Yunnan University, Kunming 650091, China  Shanghai Astronomical Observatory,
Chinese Academy of Sciences, 80 Nandan Road, Shanghai 200030, China  Xiao
Zhang  School of Astronomy & Space Science, Nanjing University, 163 Xinlin
Avenue, Nanjing 210023, China  Key Laboratory of Modern Astronomy and
Astrophysics, Nanjing University, Ministry of Education, China  Yang Chen
School of Astronomy & Space Science, Nanjing University, 163 Xinlin Avenue,
Nanjing 210023, China  Key Laboratory of Modern Astronomy and Astrophysics,
Nanjing University, Ministry of Education, China

###### Abstract

We report a possible $\gamma$-ray enhancement event detected from Tycho’s
supernova remnant (SNR), the outcome of a type Ia supernova explosion that
occurred in year 1572. The event lasted for 1.5 years and showed a factor of
3.6 flux increase mainly in the energy range of 4–100 GeV, while notably
accompanied with two 478 GeV photons. Several young SNRs (including Tycho’s
SNR) were previously found to show peculiar X-ray structures with flux
variations in one- or several-year timescales, such an event at $\gamma$-ray
energies is for the first time seen. The year-long timescale of the event
suggests a synchrotron radiation process, but the hard $\gamma$-ray emission
requires extreme conditions of either ultra-high energies for the electrons
upto $\sim$10 PeV (well above the cosmic-ray “knee” energy) or high
inhomogeneity of the magnetic field in the SNR. This event in Tycho’s SNR is
likely analogous to the $\gamma$-ray flares observed in the Crab nebula, the
comparably short timescales of them both requiring a synchrotron process, and
similar magnetohydrodynamic processes such as magnetic reconnection would be
at work as well in the SNR to accelerate particles to ultra-relativistic
energies. The event, if confirmed, helps reveal the more complicated side of
the physical processes that can occur in young SNRs.

acceleration of particles — gamma-rays: ISM — ISM: individual objects (Tycho’s
SNR) — ISM: supernova remnants

##  1 Introduction

In 1572, a supernova explosion was recorded by Tycho Brahe, of which the
remnant is referred to as Tycho’s supernova remnant (SNR; hereafter Tycho).
This supernova is believed to have a type Ia origin (Baade, 1945; Ruiz-
Lapuente et al., 2004; Krause et al., 2008), i.e., the thermonuclear explosion
of a CO white dwarf whose mass has reached close to the Chandrasekhar limit
($\sim$1.4$\,M_{\odot}$) through mass accretion (Livio & Mazzali, 2018). Being
young and one of a few known type Ia SNRs in our Galaxy, Tycho has been well
studied. While the distance is uncertain, estimated to be in a range of 2–5
kpc (Hayato et al. 2010; Tian & Leahy 2011; we adopt 2.5 kpc in this work),
the SNR has a shell-like shape with a size of $\sim$8 arcmin in diameter in
high-resolution images of multiple wavelengths (Reynoso et al., 1997; Kothes
et al., 2006; Hwang et al., 2002; Williams et al., 2013; Lopez et al., 2015).
The shell is expanding, of which the ejecta was found to have an expansion
velocity of $\sim$4700 km s-1 (Hayato et al., 2010), carrying much of the
energy released in the supernova explosion. At the shell front, acceleration
of high-energy electrons is suggested to be seen (Bamba et al., 2005), which
is considered as evidence for cosmic ray production.

Through the diffusive shock acceleration process (Bell, 1978; Blandford &
Ostriker, 1978; Drury, 1983), cosmic rays below the so-called “knee” ($\sim$3
PeV) are widely believed to arise primarily from SNRs in our Galaxy. High-
energy $\gamma$-ray studies of SNRs can thus help find possible evidence on
the origin of cosmic rays (Drury et al., 1994). Specifically for Tycho, its
high-energy and very-high-energy (VHE) $\gamma$-ray emission has been detected
(Acciari et al., 2011; Giordano et al., 2012; Archambault et al., 2017). With
the focus on the $\gamma$-ray detection, models to explain the observed
emission from Tycho have been proposed (Atoyan & Dermer, 2012; Morlino &
Caprioli, 2012; Berezhko et al., 2013; Zhang et al., 2013; Slane et al.,
2014). Most of them indicate that the hadronic process, the collisions of
high-energy hadrons (protons and ions), is responsible for the $\gamma$-ray
production. X-ray studies of Tycho have also revealed intriguing features, in
particular the stripe-like structures that are suggested as evidence of
particles accelerated to PeV energies (Eriksen et al., 2011). Very recent
results from analysis of the long-term data show that these X-ray stripes in
the southwestern region of the SNR were variable, and are interpreted as the
indication of the magnetic field amplification and/or significant magnetic
turbulence changes (Okuno et al., 2020; Matsuda et al., 2020). In addition,
rapid deceleration of the expanding shell was found in year 2009–2015 in
particular (Tanaka et al., 2020).

Likely related to these features and their implications, here we report a
possible $\gamma$-ray enhancement phenomenon seen in this SNR. In section 2,
detailed analysis of the data obtained with the Large Area Telescope (LAT)
onboard Fermi Gamma-ray Space Telescope (Fermi) is presented. In section 3,
the results from the analysis are summarized and the implications of the
results are discussed.

##  2 LAT Data Analysis

###  2.1 Analysis of the 11.6-yr Fermi LAT data

We selected LAT events from the latest Pass 8 database in an energy range of
60 MeV to 500 GeV during the time period from 2008-08-04 15:43:36 (UTC) to
2020-03-05 01:16:35 (UTC). The region of interest (RoI) is $20^{\circ}\times
20^{\circ}$, centered at the position of Tycho. Only the events with quality
flags of ‘good’ and zenith angles smaller than 90 degrees were used; the
latter is to prevent the Earth’s limb contamination. Both of these are
recommended by the LAT
team111http://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/.

We constructed a source model based on the Fermi LAT 10-year source catalog
(Ballet et al., 2020), by including all the sources within 20 degrees away
from Tycho. The spectral forms and parameters of these sources are provided in
the catalog. In our analysis, we fixed the spectral parameters of the sources
5 degrees away from the target at the values given in the catalog, and set
those of the sources within 5 degrees as free parameters. We included the
background Galactic and extragalactic diffuse spectral models
(gll_iem_v07.fits and iso_P8R3_SOURCE_V2_v1.txt respectively) in the source
model, and their normalizations were set as free parameters. The emission from
Tycho was described with a simple power law $\sim E^{-\Gamma}$, where $E$ is
the photon energy and $\Gamma$ is the photon spectral index.

Figure 1: 300-day binned light curve of Tycho (top panel), in which data
points with TS$\geq$9 are shown. The corresponding power-law index and TS are
shown in the middle and bottom panels respectively.

We performed the binned likelihood analysis to the LAT data in the energy
range of 0.3–500 GeV during the whole selected time period. In the energy
range $<$0.3 GeV, the instrument response function of LAT has relatively large
uncertainties and the background emission along the Galactic plane is strong
(Abdollahi et al., 2020). A photon index of $\Gamma=2.23\pm$0.07 and a 0.3–500
GeV flux of $F_{0.3-500}=4.3\pm 0.5\times 10^{-9}$ photons s-1 cm-2 were
obtained (Table 1), which are consistent with those given in the Fermi LAT
10-year source catalog. The Test Statistic (TS) value obtained is 245.

###  2.2 Variability and spectral analysis

To check the long-term emission properties of Tycho, we first extracted the
$\gamma$-ray light curves of the source. Because Tycho is faint, we initially
constructed 0.3–500 GeV light curves of 100, 200, 300, 400, and 500-day bins.
The 200- and 300-day binned light curves relatively well show possible
variations, as the time bins can avoid to either have many flux upper limits
(when too small) or smear out possible changes (when too large). For example,
there are only three data points in the 300-day binned light curve (Figure 1)
with TS$<$9 (resulting in flux upper limits in this case), and most of them
are in the range of 10$<$TS$<$30\. Also notably the data point at MJD 56330
has TS$\sim 60$ and a hard spectral index, suggesting possible emission
changes.

Figure 2: Left: Spectra of Tycho obtained from the whole data (11.6 yrs; dots)
and 300-day data in MJD 56180–56480 (squares) in the energy range of 0.2–500
GeV. The corresponding power-law fits obtained from the binned likelihood
analysis are shown as dotted and dashed lines respectively. Right: Spectra of
Tycho in the energy range of 0.2–500 GeV in time period II (red squares) and
the remaining time periods (black dots). The red dashed and black dotted lines
are the best-fit power-law models obtained from the binned likelihood analysis
for the two spectra. When we do not include the two $\sim$478 GeV photon
events (see Section 2.3), the data point in the energy range of 273.9–500 GeV
is turned to be a flux upper limit (the green square). In the both panels, the
open signs are the flux upper limits.

We thus extracted a spectrum from the 300-day data centered at MJD 56330 by
performing likelihood analysis in 13 evenly divided energy bands in logarithm
in 0.2–500 GeV energy range. The spectrum of the same energy bands from the
whole data was also extracted. The spectral normalizations of the sources
within 5 degrees from the target were set as free parameters, while all the
other parameters of the sources in the source model were fixed at the values
obtained from the above binned likelihood analysis. For the obtained spectral
data points, we kept those with TS greater than 9, and derived 95% flux upper
limits otherwise. The spectra are shown in the left panel of Figure 2. The
spectral points of the whole data set are given in Table 2.

Comparing the two spectra in Figure 2, possible differences are seen in the
energy range of 4.1–25 GeV. The three spectral data points covering the energy
range appear higher in the 300-day spectrum than those in the whole-data
spectrum, although their uncertainties are large. It can be noted that the
last data point (at $\sim$370 GeV) in the two spectra is not an upper limit.
This flux data point is actually due to the two $\sim$478 GeV photons (see
section 2.3).

The energy range of $\geq$4.1 GeV was thus chosen for determining the time
range containing possible flux variations of Tycho. A 300-day binned smooth
light curve was constructed, for which each data point was shifted by 10 days
forward (instead of 300 days). This type of smooth light curves helps reveal
possible fine structures of variations. From the smooth light curve, we
determined the time range of MJD 56000–56530 (defined as time period II) in
which Tycho showed an emission enhancement. This time period was set by
requiring the TS values in time bins greater than 30 (Figure 3). The time
periods before and after it (1318 and 2383 days respectively) were defined as
time period I and III respectively.

We then extracted the $\gamma$-ray spectra of Tycho in the energy range of
0.2–500 GeV during the time period II and the remaining time periods. The
spectra are shown in the right panel of Figure 2, and the data points are
provided in Table 2. We note that during time period II, the last spectral
data point, a flux measurement, is in 273.9–500 GeV band, which includes the
two $\sim$478 GeV events (see section 2.3). If we exclude the two events, the
data point turns to be a flux upper limit instead.

Figure 3:  300-day binned light curve (top panel) and TS curve (bottom panel)
of Tycho in the energy range of 4.1–100 GeV, where each data point is
constructed by shifting 10 days (instead of 300 days) forward and each
horizontal bar indicates the length of 300 days. Only the flux data points
with TS$\geq$9 are shown in the top panel. The TS curve shows a time period of
530 days for having TS$\geq 30$, for which we define as time period II (MJD
56000–56530). When extend the energy range of the data to 500 GeV, which thus
include two $\sim$478 GeV events (with the arrival times indicated by two
arrows), the TS values during time period II are further increased (indicated
by the dotted curve).

###  2.3 Energy distribution of photon events

During the time period II, there are two events with energies of 478.5 and
478.3 GeV at MJD 56242 and 56329 respectively. The event class Source,
recommended for most analyses with good sensitivity for point sources, was
used in our analysis. At $\sim$500 GeV, the 68% containment angle for the
event class is about 0.1 degree. We ran gtfindsrc to determine the position of
the $\gamma$-ray emission in the energy range of $\geq 100$ GeV during the
time period II. The position has R.A. = 6$\fdg$22 and Decl. = 64$\fdg$13, with
an 1$\sigma$ uncertainty of 0$\fdg$04\. Tycho is 0$\fdg$05 away from the
position, within the 2$\sigma$ error circle (consistent with the containment
angle). The two $\sim$478 GeV events are the only high-probability ones in
association with Tycho among detected photons in the high energy band. We note
that the energy resolution at $\sim$500 GeV is less than 10%, set as the 68%
containment half width of the reconstructed incoming photon energy.

In order to understand the association of the two $\sim$478 GeV events with
Tycho and also check if there are other related events with slightly lower
energies, we calculated the association probabilities of the photon events for
Tycho. We chose a circular region centered at Tycho with 3-degree radius,
which approximately corresponds to the 68% containment angle of the Point
Spread Function (PSF) of the LAT at 200
MeV222https://www.slac.stanford.edu/exp/glast/groups/canda/lat_Performance.htm.
The association probabilities of the events in this region for all the sources
in our source model (i.e., the 20-degree radius RoI centered at Tycho) were
calculated, using the LAT data analysis tool gtsrcprob. The two 478.5 and
478.3 GeV events are highly associated with Tycho, having the probabilities of
94% and 98% coming from Tycho, respectively.

We set the energy bins the same as those for the above spectrum extraction. In
each energy bin, the probabilities of the events for Tycho were added (i.e.,
the weighted counts from Tycho). In the left panel of Figure 4, we show the
probability results for time periods I+III and II: the values in the former
are generally higher than those in the latter, but when the lengths of the
time periods are considered, the values in 4.1–45 GeV are higher in the latter
than in the former (very similar to the spectrum results shown above). In
addition, the two $\sim$478 GeV events constitutes the last data point with
the added probability close to 2. It can be noted that between 45–274 GeV,
there is an obvious gap with very low probability values.

Another figure can be plotted is photon events with high association
probabilities. We counted the numbers of events in the 3-degree radius region
with $\geq$68% association probabilities for Tycho. The same energy bins were
used. The counts results are shown in the right panel of Figure 4. In time
period I+III, when we scale its counts with the length ratio between time
period I+III and time period II, the counts are mostly $<$1 in the energy bins
between 2.2–82 GeV. On the other hand in time period II, the counts are mostly
$>$1 in the energy bins between 4.1–45 GeV and the highest is 6 at 10 GeV.
Also similarly to the above probability plot, the last data point is close to
2 due to the two $\sim$478 GeV photons and the gap between 45–274 GeV is
visible. Thus the two photons were isolated events, not coming together with a
beam of similarly high energy events from Tycho.

Figure 4: Left: Added probabilities of photon events for Tycho in the energy
range of 0.2–500 GeV. The black circles are values in time period I+III, while
the open circles are values scaled to the length of time period II. The red
pluses are values in time period II. Right: Photon counts with $\geq$68%
association probabilities for Tycho. The symbols are the same as those in the
left panels. Due to high backgrounds, few photons are assigned with high
probability values below 4 GeV (indicated by the vertical dotted line). There
is a gap with very low or no photons between 45–274 GeV in time period II,
indicating that the two $\sim$478 GeV photons (the last data point) are
isolated events.

###  2.4 Analysis of the 4.1–100 GeV LAT data

As the two $\sim$478 GeV events can significantly affect the results such as
by increasing the TS value or changing the spectrum, we used the energy range
of 4.1–100 GeV in our binned likelihood analysis to avoid inclusion of the two
$\sim$478 GeV events. The obtained 4.1–100 GeV fluxes are $4.0\pm 0.9\times
10^{-10}$ photons s-1 cm-2 and $1.1\pm 0.2\times 10^{-10}$ photons s-1 cm-2
during time period II and time period I plus III, respectively (Table 1). The
integrated flux in the former is thus higher than that in the latter at a
3$\sigma$ confidence level. We checked the normalization factors of the
Galactic background, the dominant background for Galactic sources (the
Galactic latitude of Tycho is 1.4 degrees), and they were 1.03$\pm$0.02 and
1.001$\pm$0.008 in the two time periods, consistent with each other. For
completeness of the results, we also obtained the fluxes in the energy range
of 0.3–500 GeV in time period I, II, and III, and the values are also given in
Table 1.

A TS map helps show if a significant detection (with a high TS value at a
source’s position) is due to the presence of the source at the position or
not. To carefully examine the detection of the enhanced emission, we
calculated the 4.1–100 GeV TS maps centered at Tycho in the three time
periods. The three TS maps are shown in Figure 5. At the position of Tycho,
there is always the point-source emission present without any additional
emission sources. The highest TS value of $\simeq$50 was found in time period
II, comparing to 15 and 41 in time period I and III respectively (note that
the latter two have time durations 2.5 and 4.5 times longer than that of the
former). The results clearly indicate that there was enhanced emission in time
period II.

Also noted is that the $\gamma$-ray field around Tycho is rather clean. There
is only one faint unidentified source (J0034.6+6438; see Figure 5) 1.1 degrees
away from Tycho. Its emission is described with a power law with
$\Gamma\simeq$2.43. It is not variable with a TS value of 80 in the LAT source
catalog. Considering that the 95% containment angle of the LAT PSF is
$\simeq$1 degree at 4
GeV333https://www.slac.stanford.edu/exp/glast/groups/canda/lat_Performance.htm,
this source did not likely contaminate the enhancement detection. The
2$\sigma$ positional uncertainty for the $\gamma$-ray emission of Tycho is
0.05 degrees. Within the error region, no blazars (the dominant $\gamma$-ray
sources in the sky) are known to be located. Thus no evidence shows that the
enhancement would be caused by a background source.

Figure 5: TS maps of the $3^{\circ}\times 3^{\circ}$ region centered at Tycho
in the energy range of 4.1–100 GeV from the data of time period I (top left
panel), time period II (top right panel), and time period III (bottom panel).
The white (or black) plus in each panel marks the position of Tycho, and the
green plus marks a catalog source that is included in the source model and
thus removed when calculating the TS maps. The image scale of the TS maps is
0.05∘ pixel-1.

##  3 Results and Discussion

Using the Fermi LAT data, we have conducted detailed analysis for studying the
$\gamma$-ray emission of Tycho. We found that the long-term flux and TS values
in the energy range of 4.1–100 GeV, obtained from 300-day time bin LAT data,
effectively demonstrate the enhancement in emission from Tycho (Figure 3).
During a time period of 530 days ($\simeq$1.5 yr between MJD 56000–56530), the
TS values are greater than 30, higher than every of those in the remaining
time periods (time periods I and III with lengths of 1318 and 2383 days
respectively). Interestingly, there are two $\sim$478 GeV photon events
received from the direction of Tycho during time period II, and the
association probabilities, respectively 94% and 98%, with Tycho are very high.
Because of the rareness of such high-energy photons (Ackermann et al., 2016),
the two events can significantly affect the results. For example, if we extend
the energy range to 500 GeV, the TS values in time period II are further
increased due to the two events (Figure 3).

The main discernable difference in emission of Tycho during time period II,
from that in the remaining time periods (i.e., time period I plus III), can be
seen to occur in the energy range of 4–25 GeV (Figure 2). The results from the
binned likelihood analysis (Table 1) indicate that the emission appears
marginally softer (larger $\Gamma$ value). The flux in this time period is
$4.0\pm 0.9\times 10^{-10}$ photons cm-2 s-1 (in the energy range of 4.1–100
GeV), higher by a factor of $\sim$3.6 than that in the remaining time periods,
which is $1.1\pm 0.2\times 10^{-10}$ photons cm-2 s-1. Correspondingly, the TS
value in time period II is 49, only slightly smaller than TS of 57 from the
latter (data of totally 3701 days). From the spectral analysis, we note that
the two $\sim$478 GeV photon events determine whether the highest energy data
point (273.9–500 GeV) in the spectrum in time period II is a flux measurement
or a flux upper limit (Figure 2; see also Table 2).

Given these, we conclude that there is approximately a 1.5-yr time period in
which Tycho showed enhanced $\gamma$-ray emission in the energy range of 4–25
GeV. Based on the fluxes obtained from the binned likelihood analysis to the
data in time period II and the remaining time periods, the enhancement has a
significance of 3$\sigma$. However, our analyses involve the initial search
(from 5 light curves of from 100-day to 500-day bins) for possible signals and
determination of the optimal energy and time windows for the signal. Although
it is hard to evaluate a trial factor, i.e., the number of independent tests
(e.g., Choudalakis 2011), in the analyses, we may at least consider it to be
much larger than 10, such as arising in the initial search and the search for
the time range of the signal (cf., Figure 3). Thus the significance should be
lowered to be less than 2$\sigma$. Nevertheless, we did find evidence from the
spectral analysis and TS maps, plus the unusual two $\sim$478 GeV photons,
indicating a possible enhancement event in Tycho. Such an event would be the
first time seen in a young SNR, suggesting occurrences of complicated physical
processes in young SNRs. Below we discuss the possible models that might
explain the enhancement and their difficulties.

Tycho is young and there has been discussion in regard to young SNRs noting
that they may show $\gamma$-ray flux variations due to the changeable ambient
environments their shock front goes through (Berezhko et al., 2011, 2015;
Yasuda & Lee, 2019). In particular, the number density of the target hadrons
in the collision process could have significant changes in the space
surrounding a young SNR. Previously on the observational side, X-ray hot spots
or filaments in the young SNRs RX J1713.7$-$3946 and Cassiopeia A were found
to show yearly intensity variations, which is interpreted as evidence for
amplification of the magnetic field (to $\sim$1 mG) at the shocks Uchiyama et
al. 2007; Uchiyama & Aharonian 2008; but also see Bykov et al. 2008). Also,
the known youngest SNR G1.9+0.3 ($\sim$100 yrs) in our Galaxy has been found
to be brightening at radio frequencies (Murphy et al., 2008) and the remnant
of supernova 1987A (occurred in year 1987 in the Large Magellanic Cloud) was
brightening at both radio and X-ray frequencies (Zanardo et al., 2010; Helder
et al., 2013; Frank et al., 2016). The phenomena either suggest magnetic field
amplification or the increasing volume and number of cosmic rays (Brose et
al., 2019) in the former, or reveal the interaction between the shock front
and the preexisting equatorial ring (formed from the progenitor system of the
supernova) in the latter. In this respect, our results add a different,
previously unknown case to young SNRs by showing that a $\gamma$-ray emission
enhancement in a time period of more than a year can occur, in addition to the
baseline, long-term emission variations. While the latter are understood to
reflect the physical processes SNRs go through (Reynolds, 2017), what this
Tycho case reflects is intriguing.

###  3.1 Hadronic model

There must have been a temporary change of the high-energy emitting processes
related to Tycho in the time period around 2012 March to 2013 August (MJD
56000–56530). The baseline (or steady) $\gamma$-ray emission of Tycho is
considered to arise from the hadronic process (Morlino & Caprioli, 2012; Zhang
et al., 2013; Slane et al., 2014). The relativistic protons from the shock
front have a long lifetime $\tau_{\rm pp}=6\times 10^{7}(n_{\rm t}/1\,{\rm
cm}^{-3})^{-1}$ yr, where $n_{\rm t}$ is the number density of the target gas.
Thus the $\gamma$-ray enhancement would have been only caused by the change of
the target, for which a probable scenario was that the shock front swept up
some dense clumps, and more protons were available as the target in the
hadronic process. In such a case, a transition layer around the boundary of a
shocked clump is formed, which is a highly turbulent region and will prevent
low energy particles from diffusively penetrating into the clump due to the
amplification of the magnetic field (Inoue et al., 2012; Gabici & Aharonian,
2014). Then a hard $\gamma$-ray spectrum (with a small spectral index) arises
from the shocked clump. Applying this scenario, the increased $\gamma$-ray
flux of Tycho in time period II could have been explained (Figure 6).

Here we assume that the energetic protons accelerated by the shock take away
the explosion energy $E_{\rm sn}$ with a fraction of $\eta$ and are uniformly
distributed in the SNR shell. The shell is between the forward shock (at
radius $R_{s}$) and the contact discontinuity (at radius $R_{\rm CD}$), and
has width $\Delta R=R_{s}-R_{\rm CD}$, where $R_{\rm CD}=rR_{s}$ and $r=0.93$
is adopted (Warren et al., 2005). We consider that a dense clump with radius
$R_{c}$ and density $n_{c}$ was swept up by the SNR shock at the beginning of
time period II. The $\gamma$-ray emission in this period is a sum of two
components: one is the emission from the SNR shell (or the steady component),
and the other is from the shocked clump.

The distribution in energy of the accelerated protons is assumed to have a
power-law form with a high-energy cutoff

$dN/dE=N_{0}E_{p}^{-\alpha_{p}}\times\mathrm{exp}(-E_{p}/E_{c,p}),$ (1)

where $E_{p}$, $\alpha_{p}$, and $E_{c,p}$ are the proton energy, the power-
law index, and the cutoff energy, respectively. The normalization $N_{0}$ is
determined by the total energy in protons $\eta E_{\rm sn}$. Modeling the
steady component, the proton index $\alpha=2.2$, the ambient density
$n_{0}=0.1/(\eta/10\%)\,{\rm cm}^{-3}$, and the cutoff energy $E_{c,p}=20$ TeV
can be obtained (blue line in Figure 6). Given that the main differences
between the spectra of the steady and the enhanced emission are in the energy
range of 4–20 GeV, we take 10 GeV as the reference energy value. To produce
the enhanced component around 10 GeV, the protons with energies above 100 GeV
need to diffusively penetrate the transition layer and reach the clump, which
constrains the thickness of the transition layer $L_{tr}=0.003$ pc and the
magnetic field of it $B_{tr}=10$ $\mu$G. To fit the data, $R_{c}=0.05$ pc and
$n_{c}=1.2\times 10^{4}/(\eta/10\%)\,{\rm cm}^{-3}$ are obtained (giving the
orange line in Figure 6).

This scenario seems to be supported by the blast waves’ reaching the wall of a
surrounding bubble (Zhou et al., 2016) and rapid deceleration of the SNR shell
(Tanaka et al., 2020), both of which likely indicate the interaction of the
blast waves with clumps of dense gas and the latter notably occurred in a time
period covering the enhancement. However, the time duration of a flux
enhancement in this scenario should be much longer than that of time period
II, as the shocked clumps in downstream of the shock have a survival time
described by the so-called cloud crushing timescale $\tau\approx 4\times
10^{3}(\chi/10^{5})^{1/2}$ yr ($\chi=n_{c}/n_{0}$; Klein et al. 1994). We note
that a similar scenario, but with the cosmic-ray precursor interacting with
the gas shell surrounding an SNR, has been proposed by Federici et al. (2015),
and it predicts a flux increase at a few hundred GeV energies (which fits the
enhancement event in Tycho). Still the same problem exists, as the time
duration should be much longer.

Figure 6: Model fits to the $\gamma$-ray spectra of Tycho. The green pentagons
and black squares are the data points in the time period I plus III (steady
emission) and time period II (enhanced emission), respectively. The highest-
energy data point (orange square) that includes the two $\sim$478 GeV photons
is also shown. For comparison, the $\gamma$-ray spectra previously obtained
with LAT and Very Energetic Radiation Imaging Array System (VERITAS)
(Archambault et al., 2017) are shown as blue and red dots, respectively. A
model spectrum from the shocked clump in the hadronic process is shown as the
orange curve, which can explain the enhanced emission when it is added to the
model spectrum (blue curve) for the steady emission. The added spectrum is
shown as the green curve.

###  3.2 Inverse Compton scattering process

The other often-considered $\gamma$-ray emission process is inverse Compton
(IC) scattering, in which low-energy photons surrounding an SNR, consisting of
the cosmic microwave background (CMB), infrared background (IB), and star
light (SL), are boosted to the gamma-ray domain by the relativistic electrons.
To produce photons of $\sim$10 GeV energies via the IC scattering process, the
electron energy needs to be 1 TeV at least. Due to the long lifetime of the
TeV electrons ($\tau_{\rm IC}\sim 10^{6}$ yrs), the IC scattering process has
difficulties generating year-timescale variations, unless the magnetic field
could reach the order of milli-Gauss. In such a strong magnetic field, the
electrons will suffer severe synchrotron energy loss, resulting in a
sufficiently short lifetime $\tau_{\rm syn}=1.4\ (E/1\ {\rm TeV})(B/3\ {\rm
mG})^{-2}$ yr. Then extremely high synchrotron emission (for example, with
10–20 keV flux of $\sim 10^{-8}\ \mathrm{erg\ cm^{-1}\ s^{-1}}$) will be
produced at the same time, which are several orders of magnitude higher than
the observed ($1.3\times 10^{-11}\ \mathrm{erg\ cm^{-1}\ s^{-1}}$; Tamagawa et
al. 2009). To avoid this inconsistency, one may reduce the density of the
relativistic electrons and increase that of the IB or SL photons. However in
order to explain the enhancement around 10 GeV emission, the energy density of
IB (SL) would need to be $6000\ {\rm eV\,{\rm cm}^{-3}}$ ($30000\ {\rm
eV\,{\rm cm}^{-3}})$, which is unphysically high in the interstellar
environment of Tycho. Thus, the IC scattering process can be ruled out.

###  3.3 Synchrotron emission modeling

While high-energy electrons in the magnetic field can also produce soft
$\gamma$-rays via the synchrotron process, photon energies are limited to be
lower than the so-called synchrotron burnoff limit ($\sim$160 MeV; Guilbert et
al. 1983; de Jager et al. 1996). In order to exceed this limit, the particle
acceleration and cooling need to be decoupled. A possible process that can
provide additional relativistic electrons in young SNRs is the magnetic
reconnection (MR; Matsumoto et al. 2015). When the SNR shock sweeps up some
compact molecular clumps, the magnetic field around the interface between the
shock and clumps can be amplified (Inoue et al., 2012). The MR process may be
accompanied with the shock-clump interaction. We also note that an MR
detonation scenario has been specifically proposed for Tycho (and the Crab
nebula), which actually suggests a year-long timescale for the reconnection
process (Zhang et al., 2018).

Alternatively, the $\sim$10 GeV emission could be ascribed to the synchrotron
process in inhomogeneous magnetic fields. The evidence for the magnetic field
amplification in SNRs, the variable X-ray structures (hot spots or filaments),
implies that the magnetic field in an SNR should have significantly different
strengths at different locations. Specifically in Tycho, the X-ray stripes and
their year-scale time variability also indicate high inhomogeneity of the
magnetic field (Okuno et al., 2020; Eriksen et al., 2011; Matsuda et al.,
2020). In a recently discussed scenario for the presence of some discrete
compact magnetic blobs, it has been shown that the maximum energy of
synchrotron photons can be boosted to multi-GeV energies depending on the
ratio of the magnetic field in the blobs to that in the background (Khangulyan
et al., 2020). For example, a synchrotron spectrum can extend to energies
beyond 10 GeV for the ratio of $\sim$100\. If the $\gamma$-ray emitting
magnetic blobs survive or decrease in the field strength at yearly timescale,
the $\gamma$-ray enhancement might be explained.

However, in order to fit the enhanced part of the emission (cf., Figure 6)
with the synchrotron radiation, the electron energies are required to be as
high as $\sim 10$ PeV (assuming a magnetic strength of 1 mG). Such high
energies are above the “knee” energy and would have extremely short lifetimes
of $\sim 1$ day. It is hard to explain the year-long enhancement event with
such a short-lifetime radiation process.

In any case, we note that this possible $\gamma$-ray enhancement event in
Tycho shares similar features with the $\gamma$-ray flares in the Crab nebula
(Tavani et al., 2011; Abdo et al., 2011). Both occurred at GeV energies and
their timescales are too short to be explained by the processes other than the
synchrotron. The complication in the Crab nebula lies at the young pulsar in
the center, which keeps powering the nebula. For Tycho, it stands out among
the young SNRs with the features of the variable X-ray strips, blast-
waves–bubble-wall interaction, and rapid deceleration of the expansion. These
features could be the reason that induces the enhancement event, while
detailed studies are needed in order to fully understand the physical
processes behind the event.

We thank anonymous referee for critical comments that helped shape up the
manuscript, and J. Fang for helpful discussion about properties of pulsar wind
nebulae and supernova remnants. This research made use of the High Performance
Computing Resource in the Core Facility for Advanced Research Computing at
Shanghai Astronomical Observatory. This work was supported by Key Research and
Development Project (Grant No. 2016YFA0400804) and the National Natural
Science Foundation of China (11633007, U1738131). Z.W. acknowledges the
support by the Original Innovation Program of the Chinese Academy of Sciences
(E085021002) and the Basic Research Program of Yunnan Province No.
202101AS070022. X.Z. and Y.C. thank the support of National Key R&D Program of
China under nos. 2018YFA0404204 and 2017YFA0402600 and NSFC grants under nos.
U1931204, 12173018, and 12121003.

Table 1: Likelihood analysis results for Tycho | 0.3–500 GeV | 4.1–100 GeV
---|---|---
Time | MJD | $\Gamma$ | $F/10^{-9}$ | TS | $\Gamma$ | $F/10^{-10}$ | TS
period |  |  | (photons cm-2 s-1) |  |  | (photons cm-2 s-1) |
Total | 54682–58913 | 2.23$\pm$0.07 | 4.3$\pm$0.5 | 245 | – | – | –
I | 54682–56000 | 2.4$\pm$0.1 | 4.9$\pm$1.1 | 53 | – | – | –
II | 56000–56530 | 1.8$\pm$0.1 | 2.6$\pm$0.9 | 69 | 2.4$\pm$0.3 | 4.0$\pm$0.9 | 49
III | 56530–58913 | 2.31$\pm$0.09 | 5.0$\pm$0.7 | 140 | – | – | –
I$+$III | – | 2.35$\pm$0.08 | 4.9$\pm$0.6 | 192 | 1.9$\pm$0.3 | 1.1$\pm$0.2 | 57
Table 2: Spectra obtained from the data in the whole time period, time period
I plus III, and time period II.

| Whole data | Period I$+$III | Period II
---|---|---|---
$E$ | Band | $F/10^{-12}$ | TS | $F/10^{-12}$ | TS | $F/10^{-12}$ | TS
(GeV) | (GeV) | (erg cm-2 s-1) |  | (erg cm-2 s-1) |  | (erg cm-2 s-1) |
0.27 | 0.2–0.4 | 2.3$\pm$0.8 | 12.8 | 2.1$\pm$0.9 | 9.1 | 6.8 | 4.4
0.49 | 0.4–0.7 | 2.0$\pm$0.5 | 15.6 | 2.4$\pm$0.6 | 20.0 | 1.8 | 0.0
0.90 | 0.7–1.2 | 1.8$\pm$0.4 | 21.3 | 1.9$\pm$0.4 | 20.5 | 3.0 | 1.2
1.64 | 1.2–2.2 | 1.8$\pm$0.3 | 36.6 | 1.9$\pm$0.3 | 35.7 | 2.5 | 1.6
3.00 | 2.2–4.1 | 1.9$\pm$0.3 | 58.6 | 2.0$\pm$0.3 | 56.3 | 2.8 | 3.0
5.48 | 4.1–7.4 | 0.9$\pm$0.3 | 18.9 | 0.7$\pm$0.3 | 10.7 | 2.6$\pm$1.0 | 12.0
10.00 | 7.4–13.5 | 0.7$\pm$0.3 | 15.1 | 0.8 | 3.5 | 3.4$\pm$1.3 | 22.0
18.3 | 13.5–24.7 | 1.4$\pm$0.4 | 32.9 | 1.2$\pm$0.4 | 21.2 | 2.9$\pm$1.5 | 13.3
33.3 | 24.7–45.0 | 1.5$\pm$0.6 | 27.1 | 1.6$\pm$0.6 | 23.7 | 5.2 | 3.4
60.8 | 45.0–82.2 | 1.0 | 1.4 | 1.2 | 1.7 | 3.0 | 0.0
111.0 | 82.2–150.0 | 1.2 | 0.0 | 1.5 | 0.0 | 5.4 | 0.0
202.7 | 150.0–273.9 | 1.3 | 0.0 | 1.6 | 0.0 | 20.9 | 0.0
370.1 | 273.9–500.0 | 4.3$\pm$2.5 (3.3) | 16.7 (0.0) | 3.8 | 0.0 | 27$\pm$18 (18) | 23.9 (0)

Note: a) $F$ is the energy flux ($E^{2}dN/dE$), and fluxes without
uncertainties are 95$\%$ upper limits. b) Values in parentheses were obtained
without including the two $\sim$478 GeV photons.

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# Design, Fabrication, and Experimental Demonstration of Junction Surface Ion
Traps

D. L. Moehring, C. Highstrete, D. Stick, K. M. Fortier, R. Haltli, C. Tigges,
and M. G. Blain  Sandia National Laboratories, Albuquerque, New Mexico 87185,
USA<EMAIL_ADDRESS>
###### Abstract

We present the design, fabrication, and experimental implementation of surface
ion traps with Y-shaped junctions. The traps are designed to minimize the
pseudopotential variations in the junction region at the symmetric
intersection of three linear segments. We experimentally demonstrate robust
linear and junction shuttling with greater than $10^{6}$ round-trip shuttles
without ion loss. By minimizing the direct line of sight between trapped ions
and dielectric surfaces, negligible day-to-day and trap-to-trap variations are
observed. In addition to high-fidelity single-ion shuttling, multiple-ion
chains survive splitting, ion-position swapping, and recombining routines. The
development of two-dimensional trapping structures is an important milestone
for ion-trap quantum computing and quantum simulations.

##  1 Introduction

The first requirement for quantum information processing is the ability to
build a “scalable physical system with well characterized qubits” [1]. In
recent years, research in trapped ion quantum information has concentrated
much effort toward creating scalable architectures for trapping and shuttling
large numbers of ions [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. Within this
effort, surface-electrode ion traps are generally regarded as the most
promising long-term approach due to the ability to fabricate complex trap
arrays leveraging advanced semiconductor and microfabrication techniques [14,
15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Two-dimensional ion-trap geometries,
such as those shown here, and ion trap arrays are key developments for
scalable implementations of ion-based quantum computation and simulation [25,
26, 27].

In this paper, we report the design, fabrication, and successful testing of
Y-junction surface ion traps. We demonstrate high-fidelity shuttling protocols
in three different traps of two different trap designs. This includes linear
and junction shuttling, splitting and recombining of ion chains, and ion
reordering. The surface microtraps reported here are both reproducible and
invariable. This is demonstrated by successful ion-shuttling solutions that
are identical for day-to-day operation as well as for multiple congeneric
traps.

##  2 Design and Fabrication

The design principles for the traps discussed here are based in part on
fabrication constraints and techniques described in our previous work [23].
These principles include minimized line of sight exposure between the ion and
dielectric surfaces to ensure shielding of any trapped dielectric charge [28],
and recessed bond pads to limit the projection of the wire-bond ribbons above
the top surface of the trap. In addition, the top metal layout in the vicinity
of the junction and the loading hole is optimized with respect to RF potential
and other characteristics by utilizing lateral shape-modulation of electrode
edges [Fig. 1].

As with all known junction traps, it is not possible to stabilize a trapped
charge with a vanishing RF field and zero ponderomotive potential everywhere
[29]. However, a suitable trade in performance characteristics can be achieved
by optimizing the predicted performance using a figure of merit as a function
of the electrode geometry. The trap geometries chosen here placed particular
emphasis on minimizing the magnitude and slope of the equilibrium
pseudopotential particularly in the junction region while maintaining a
specified ion equilibrium height range. Resulting junction designs are shown
in Figures 1 and 2. The spatial features of the RF electrodes in the junction
region decrease the pseudopotential barrier from greater than 1 eV for
straight RF electrodes to less than 2 meV so that the ion can be transported
through the junction with relatively reduced control voltages and motional
heating [12] [Fig. 3].

Figure 1: Scanning electron microscope (SEM) image of a
Y${}_{\textrm{H}}$-junction trap. In each trap, 47 independent DC electrodes
are routed for wire bonding to the CPGA. Inset: Image of 7 ions trapped above
the loading hole. The average ion-ion spacing in this image is $\approx
3.5~{}\mu$m

Figure 2: SEM image of the central region of the Y${}_{\textrm{H}}$-junction
trap (left) and the Y${}_{\textrm{L}}$-junction trap (right). Note especially
the sharp edges in Y${}_{\textrm{H}}$ that are rounded in Y${}_{\textrm{L}}$.

Figure 3: Two different BE simulations of the trap pseudopotential. Both show
similar results from the junction center ($x=0~{}\mu$m) outward along a linear
segment of the Y${}_{\textrm{H}}$ trap. The loading hole is centered at
$x=853~{}\mu$m.

Another feature of these traps is the (70 $\mu$m $\times$ 86 $\mu$m) loading
hole [Fig. 4]. The presence of the loading hole, in contrast to a solid center
DC electrode, also gives rise to pseudopotential barriers that can be reduced
by modulating the edges of nearby RF and DC electrodes. The distance between
the center of the loading hole and the center of the junction is $853~{}\mu$m.

Electrostatic solutions were calculated using a boundary element (BE) method
to predict device performance. The BE models were created by describing
electrode geometries in the form of planar polygons in three spatial
dimensions in conjunction with additional meta information (i.e. ion
equilibrium position, BE mesh length scale) to control model fidelity. In
these models, the dielectric contribution has been ignored since these
materials are always well shielded by metal. The geometries were determined by
a parametric description in order to facilitate computer optimization.

Optimization of the electrode layout was accomplished by minimizing a design
cost function described by parametric values for a specific geometry. This
cost function was a sum of several positive semi-definite sub-cost terms that
were traded by weighting coefficients. The cost functions included figures of
merit for the ion height and the pseudopotential values and derivatives along
the equilibrium trap axis of one arm of the Y-junction. The sub-cost values at
points along the trap axis were not always treated uniformly – some points in
particular were weighted differently to effect a desired outcome not achieved
by solely varying the trade coefficients. For example, the ion height near the
junction was reduced in cost so as to not trade so heavily against the
pseudopotential minimization.

Two different trap models were fabricated and tested. Trap
“Y${}_{\textrm{L}}$” has lower spatial frequencies on the electrode edge
shapes in the junction region, whereas the second trap “Y${}_{\textrm{H}}$”
has higher spatial frequencies [Fig. 2]. The higher spatial frequencies in
Y${}_{\textrm{H}}$ are predicted to further reduce the pseudopotential by
$\approx 50\%$ compared to Y${}_{\textrm{L}}$. Two trap versions were
fabricated due to a concern over the structural integrity of the cantilevered
electrode segments, caused by dielectric setbacks in the high spatial-
frequency regions of Y${}_{\textrm{H}}$ [23]. This concern was also addressed
by using a dielectric setback of only 2 $\mu$m for Y${}_{\textrm{H}}$, as
opposed to 5 $\mu$m for Y${}_{\textrm{L}}$. In the end, the structural
integrity of the aluminum was not an issue.

Figure 4: SEM image showing the detail of the loading hole and the modulated
edges of nearby electrodes.

##  3 Operation

Each fabricated ion-trap chip is packaged in a 100-pin ceramic pin grid array
(CPGA) providing electrical connections to the RF electrode and 47 independent
DC electrodes. Each trap is installed in a vacuum chamber with a base pressure
$\approx 5\times 10^{-11}$ Torr. The applied DC voltages are varied between
-10 V and +10 V using National Instruments PXI-6733 DAC cards. The applied RF
voltage is varied between 25 - 165 V for trapping in the loading hole and 85 -
120 V for junction shuttling. Trapping lifetimes are several hours when the
ions are Doppler cooled, and approximately one minute without laser cooling.

Calcium ions are loaded by first generating a stream of neutral calcium atoms
through the loading hole [Fig. 4], which are then photoionized using a
resonant 423 nm laser on the 4s1S${}_{0}\leftrightarrow$ 4p1P1 transition and
an ionizing 375 nm laser [30]. By placing the source of the atomic beam
beneath the chip, we minimize neutral atom plating on the top surface of the
chip, virtually eliminating any chance of shorting adjacent trap electrodes.
This is essential for consistent day-to-day trap operations [31].

The height of the ions above the top trap surface can be directly measured
after shuttling the ions from the loading hole. This is accomplished by
imaging the ion directly and imaging the reflected photons off the aluminum
center trap electrode [Figure 5]. The translation of the imaging lens between
the two images confirms the expected $\approx 70~{}\mu$m height of the ion
above the trap surface [20, 32].

Figure 5: Left: Direct image of the ion (upper) and indirect image of the ion
reflected by the aluminum trap surface (lower). Right: Elapsed-time image of
an ion shuttling $\approx 40$ microns up each arm in a Y${}_{\textrm{H}}$
trap. This 10 second image captures $\approx 40,000$ round-trip junction
shuttles. Rather than shuttling into the exact center of the junction, the
ions are intentionally steered along a smooth path between the linear
sections.

In total, one Y${}_{\textrm{L}}$ trap and two Y${}_{\textrm{H}}$ traps [Fig.
2] were tested, with initial work performed on the Y${}_{\textrm{L}}$ trap.
Here, trapping and linear shuttling tests were completed as in [23] with
greater than $10^{5}$ linear shuttles without ion loss. Junction shuttling was
also tested in the Y${}_{\textrm{L}}$ trap, and despite the lower spatial
frequency electrode variations, we performed $10^{6}$ round-trip shuttles
without ion loss. In a given round-trip, the ion traveled up each leg of the
Y-junction by $\approx 30~{}\mu$m, resulting in a total of $3\times 10^{6}$
passes through the junction.

Following these initial successes, testing began in two congeneric
Y${}_{\textrm{H}}$ traps in two independent test systems. As the
Y${}_{\textrm{H}}$ trap design differs from Y${}_{\textrm{L}}$ only in the
junction region, successful loading and linear shuttling voltage solutions
used for Y${}_{\textrm{L}}$ were demonstrated to work also in each
Y${}_{\textrm{H}}$ trap. In contrast, voltage solutions for ion transfer
through the modified junction electrodes required a new shuttling routine.
Interestingly, successful junction shuttling was observed in each
Y${}_{\textrm{H}}$ trap with a voltage-solution modification consisting of a
-0.5 volt adjustment on only the center electrode [33, 34].

Multiple ions were also shuttled with these solutions from the loading hole,
thrice through the junction, and back to the loading hole. One round trip
reverses the order of ions within the linear chain, however this is difficult
to prove unequivocally as all ions were the same isotope (40Ca+). All of the
above mentioned tests utilized high-degree-of-freedom voltage solutions which
used up to 25 DC electrodes at a given time for linear shuttling and 35 DC
electrodes for junction shuttling.

After success with the high-degree-of-freedom solutions, we tested voltage
solutions with a reduced number of DC electrodes. This is convenient for
parallel shuttling of ions in multiple harmonic wells with minimal crosstalk.
It is also convenient to use voltage shuttling solutions with a constant
center DC electrode [33]. With solutions utilizing only the nearest 7 DC
electrodes at any one time in the linear regions and the central 13 DC
electrodes in the junction region (including the center electrode), ions were
shuttled to all functional regions of each trap. Ions survive these routines
with or without Doppler cooling during shuttling.

As in the Y${}_{\textrm{L}}$ trap, a single ion in a Y${}_{\textrm{H}}$ trap
successfully completed $10^{6}$ round-trip shuttles around the junction
without ion loss. With the ion moving $40$ microns up each arm, $10^{6}$
shuttles took about 4 minutes, whereas moving $250$ microns up each arm took
about 24 minutes. In the latter case, the ion traveled a total distance of
$1.5$ km at an average speed of $1~{}$m/s. Utilizing Doppler cooling during
the junction shuttling routine, the emission of photons from the ion resulted
in the trace of the ion path shown in Figure 5. Importantly, voltage solutions
successful in one Y${}_{\textrm{H}}$ trap were also successful in a second
identically constructed Y${}_{\textrm{H}}$ trap, even though the two traps
were tested in different vacuum chambers with independent RF and DC voltage
sources – only lasers were shared between the two setups. These solutions have
been successfully used without modification for over six months.

Finally, complex shuttling routines were implemented for multiple ions in
several locations on a given trap. For instance, three ions were consecutively
loaded, independently shuttled into each arm of the junction, and Doppler
cooled in a triangular configuration for over an hour without loss. Linear ion
chains were also split and recombined as seen in Fig. 6. By performing
independent junction shuttling between splitting and recombining, two ions
were unequivocally observed to exchange position in a linear chain.

Figure 6: Left: Ions within the same harmonic well separated by approximately
6 microns. Right: Ions separated by 4 electrodes (approximately 370 microns).
The splitting and recombining of two ions was explicitly observed hundreds of
times without error.

##  4 Conclusion

Reliable and repeatable micro-fabrication of complex ion-trapping structures
has been demonstrated, indicating that a scalable system of trapped ions for
quantum computation and quantum simulation is conceivable. By further
utilizing the device design and integration capabilities of multi-layer
fabrication techniques, the robust fabrication of more complex 2D and 3D trap
arrays is imminent [25]. For example, multi-level metalization (up to four
levels of metal) is being employed to accommodate nested trap electrodes and
to minimize electrode cross-talk, thereby enabling fundamentally new trap
array concepts.

##  5 Acknowledgments

The authors thank the members of Sandia’s Microsystems and Engineering
Sciences Application (MESA) facility for their fabrication expertise and Mike
Descour for helpful comments on the manuscript. This work was supported by the
Intelligence Advanced Research Projects Activity (IARPA). Sandia National
Laboratories is a multi-program laboratory managed and operated by Sandia
Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the
U.S. Department of Energy’s National Nuclear Security Administration under
contract DE-AC04-94AL85000.

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