# EVIDENCE OF X-RAY EMISSION FROM THE WARM HOT INTERGALACTIC MEDIUM

Giulia Cerini  Corresponding authors: Giulia Cerini<EMAIL_ADDRESS>Nico Cappelluti<EMAIL_ADDRESS>Massimiliano Galeazzi,
<EMAIL_ADDRESS> Nico Cappelluti  Corresponding authors: Giulia Cerini,
<EMAIL_ADDRESS>Nico Cappelluti<EMAIL_ADDRESS>Massimiliano
Galeazzi<EMAIL_ADDRESS> Massimiliano Galeazzi  Corresponding authors:
Giulia Cerini<EMAIL_ADDRESS>Nico Cappelluti,
<EMAIL_ADDRESS>Massimiliano Galeazzi<EMAIL_ADDRESS> Eugenio
Ursino  Department of Physics, Purdue University Fort Wayne, 2101 East
Coliseum Boulevard Fort Wayne, IN 46805, USA

##  1 Summary paragraph

The Universe has evolved from an initial diffuse, uniform gas to a complex
structure that includes both voids and high-density galaxy clusters connected
by gaseous filaments, known as the Cosmic Web, and traced by 3D surveys of
galaxies [1, 2]. The filamentary structure contains a significant fraction of
the baryonic matter and is predicted to be mostly in the form of a moderately
high temperature plasma, the Warm Hot Intergalactic Medium [3, 4, 5]. Plasma
at this temperature and ionization level emits mostly in soft X-rays. The
filamentary structure, however, is hard to detect because the other sources
contributing to the Diffuse X-ray Background are much brighter and, currently,
there are very few reported detections of emission from the filaments [6, 7].
We report the first high-confidence level indirect detection of X-ray emission
from the Warm Hot Intergalactic Medium. Applying the Power Spectrum Analysis
to XMM-Newton and eROSITA data, we separated its contribution from other
sources modeled in previous studies [8, 9]. Our result is in good agreement
with numerical simulations [10] and fills a critical gap in the picture of the
large-scale structure of the Universe, in which filamentary gas, galaxies and
dark matter interact and co-evolve.

##  2 Main

High redshift measurements point to about $4\%$ of the matter-energy density
of the Universe to be in the form of baryons, while the rest consists of dark
matter and dark energy [11, 12, 13]. In contrast, the amount of baryons
measured in the local Universe’s structures is less than 2$\%$ [14, 15, 16].
Hydrodynamic simulations tracking the evolution of the Universe in the
framework of the commonly accepted $\Lambda$-Cold Dark Matter ($\Lambda CDM$)
cosmological paradigm suggest that, starting at a redshift of $z\sim 2$,
following the process of structure formation, diffuse baryons in the
Intergalactic Medium (IGM) condensed into a filamentary web, the Warm Hot
Intergalactic Medium (WHIM), forming the backbone of the Cosmic Web and
containing much of the ”missing baryons” [3, 4, 17, 18, 19] (Fig. 1-left).
These filaments, with a density about 10 to 1000 times the average baryon
density $\bar{\rho_{b}}\sim 10^{-7}cm^{-3}$ (thus ranging from
$10^{-6}cm^{-3}$ to $10^{-4}cm^{-3}$), underwent shocks that heated them up to
temperatures of $T\sim 10^{5}-10^{7}\ K$, and were enriched with metals
through galactic outflows triggered by Supernova and Active Galactic Nuclei
(AGN) feedback. At these temperatures and densities, baryons are in the form
of highly ionized plasma, making them visible only in the low energy X-ray and
UV bands, mostly through excitation lines of highly ionized heavy elements
[6]. In the past years UV observations confirmed the presence of the ”warm”
phase of the the intergalactic medium [20, 21, 22]. However, the study of the
”hot” phase in the inner regions of the filaments, where the bulk of the
missing baryon mass is expected and predicted to emit soft X-rays, has been
more challenging.

Simulated WHIM

Figure 1: Detecting the signature of the Cosmic Web in X-rays. Left: starting
at a redshift of $z\sim 2$, diffuse baryons in the IGM condense into a
filamentary web [18]. Center: the filaments are not individually visible in
X-ray images due to the overlap of many of them along the line of sight; the
image represents the simulated X-ray emission, in the band 0.4-0.6 keV, due to
the filaments at different redshifts [10](units are in $photons\
cm^{-2}s^{-1}$). Right: WHIM signature obtained from the angular power
spectrum analysis of simulated X-ray images [10] (the one in the band 0.4-0.6
keV is shown in the center). The signal peaks around $1\ arcmin$ in the
$0.4-0.6\ keV$ energy band, and around $10\ arcmin$ in the $0.7-0.9\ keV$
energy band.

In recent years, significant effort has gone towards detecting and
characterizing the WHIM, including several ad-hoc missions designed to achieve
this goal [23, 24, 25, 26, 27]. Among the methods to detect the WHIM, we
highlight the spectroscopic search of absorption along the line of sight of
distant bright sources [28, 29, 30, 31]. However, given the sensitivity of
existing X-ray observatories, less than a handful of sources are bright enough
to achieve a statistically significant detection. The clearest WHIM detections
in absorption were obtained by observing two absorbers of highly ionized
oxygen (O VII) in the X-ray spectrum of the bright X-ray blazar 1ES 1553+113
[32] with XMM-Newton, even if one of them was thought to likely originate from
foreground WHIM filaments (indeed, spectroscopic redshift confirmations showed
the presence of a spiral galaxy in the proximity of the system, leading to the
suspect that the system was actually generated in the group of that galaxy
[33]), and studying the emission of the luminous quasar H1821+643 through the
combination of Chandra LETG data and previous UV measurements [34].

Another effort has been done in searching for individual filaments in emission
[7, 35, 36, 37] where, however, the inferred temperature of the filament is
too high to be considered a true representation of the WHIM.

A third option is to identify redshifted X-ray emission lines emitted by the
filaments[6], but the emission of individual filaments is very weak with
respect to other foreground and background X-ray emissions like the Solar Wind
Charge eXchange (SWCX), Local Hot Bubble (LHB), Milky Way CGM (MW-CGM), and
signal from unresolved point sources, also collectively known as Diffuse X-ray
Background (DXB, Fig. 2).

DXB components

Figure 2: The X-ray signal from the Cosmic Web filaments is embedded in the
foreground and background from other components of the Diffuse X-ray
Background.

In recent years a new method, based on the thermal Sunyaev-Zeldovich effect
from the gas filaments, has revealed powerful to detect and investigate the
WHIM [38, 39, 40], leading to surprisingly high- confidence level results,
even if they do not offer any information about the metallicity of the
filaments.

Statistical approaches have also been used to identify and study the
filaments. For instance, using XMM-Newton deep fields, the angular auto-
correlation function was adopted [41] to collect evidence of WHIM emission in
the energy band $0.4-0.6\ keV$. More recently, the use of power spectrum
analysis has become the statistical tool of choice for the analysis of diffuse
emission at all wavelengths, as it allows to properly disentangle the
different components and emitting populations contributing to it [42, 9, 8,
43, 44]. While the current high-resolution X-ray spectrometers are dispersive
and have limited effective area, images in narrow energy bands can be
generated (Fig. 1-center). Individual filaments cannot be identified due to
the overlap of all the filaments along the line of sight, but the combined
signal from all the filaments generates a characteristics angular pattern in
the surface brightness fluctuations, whose signature is imprinted in the
angular power spectrum. Given the expected temperature and distribution of the
WHIM, the signal changes as a function of energy and is significant only below
$1\ keV$ [45, 46, 6]. According to previous studies involving the auto-
correlation function in the energy band $0.4-0.6\ keV$ [41], and the power
spectrum in the energy band $0.5-2.0\ keV$ [9], the WHIM filaments show a
characteristic signal at angles of a few arcminutes. The results from the
numerical simulations used in this work [10] are in agreement with the
previous ones, but were obtained in the two narrow energy bands $0.4-0.6\ keV$
and $0.7-0.9\ keV$, and show a peak around $1-10\ arcmin$ that changes with
the energy range (Fig. 1-right). This outcome will be furtherly investigated
in follow-up researches, but can be reasonably due to the contribution of
filaments at different redshift and projection effects. Indeed, the dominant
X-ray flux due to the WHIM is expected to originate from gas at redshift
between 0.1 and 0.6 [6]. Photons at higher energies emitted at larger
distances are redshifted. Therefore, in the energy band $0.4-0.6\ keV$ we are
detecting photons originating at redshift $z\sim 0$, as well as photons
generated at redshift $z\gtrsim 0.2$, whose energy at the emission was
$\gtrsim 0.7\ keV$. On the other hand, the photons in the $0.7-0.9\ keV$
energy range originate from filaments at lower redshifts and, consequently,
allow us to see the WHIM in the nearby Universe. The difference in the angular
scales involved in statistical approaches like the power spectrum has recently
been found also in the redshift evolution of the auto-correlation function
obtained from CAMELS hydrodynamic simulations [47]. For this particular
investigation, the focus was in the two most prominent WHIM emission lines,
the OVII triplet and the OVIII singlet, for which line surface brightness maps
where built, and 3D and 2D 2-point auto-correlation functions were computed at
different redshifts. Their results from the 2D analysis at $z=0.04$ show a
plateau at angular scales of size $\lesssim 10\ arcmin$ and fall off in the
range $\sim 10-10^{2}\ arcmin$, while at $z=0.54$ they exhibit a sharper peak
at scales of size $\lesssim 1arcmin$ and a steeper decrease up to $\sim 10\
arcmin$. On the other hand, this difference was not found in the 3D results,
that show a pattern more similar to the latter at all redshifts. This was
expalained with projections effects that magnify a feature that was difficult
to catch in the 3D analysis, namely the core-shaped profile (a similar feature
was previously seen also in IllustrisTNG simulations [48]). In addition, the
angular scale of the filaments decreases with the increasing redshift, and
this contributes to the change of the AcF and, consequently, the power
spectrum, as a function of redshift. It is also worth mentioning that the
results obtained from the simulations adopted in this work [10] were
demonstrated to be in excellent agreement with the results of other works.
Indeed, they showed that, the power spectrum in the energy band $0.4-0.6\ keV$
due to all gas, regerdless of the temperature and density, is in excellent
agreement with the values obtained in other works and measured by the Atacama
Cosmology Telescope (ACT) [49], the South Pole Telescope (SPT) [50] and Planck
[51]. The reliability of these simulations was demonstrated in the past also
from the analysis of the X-ray properties of galaxy clusters and groups [4].

To reduce systematics and properly remove the signal from other sources of
DXB, we used a combination of data from both deep and extended surveys, namely
from XMM-Newton (XMM-CDFS, XMM-COSMOS and XMM-Stripe82) and eROSITA (eFEDS -
Table 1). [52, 53, 54, 55, 56, 57]. This is important because the DXB source
populations show characteristic angular patterns [9, 58], with point sources
imprinting a clear signal at small scales (of the order of $\sim 10^{2}\
arcsec$), and diffuse/local sources dominating the largest angular scales.
With their different Field of View (FoV) and depth (a so-called wedding cake
approach) these fields provided the best combination of scales to properly
model all the components of the signal and, at the same time, mitigate effects
of cosmic variance to achieve high statistical significance. The study was
conducted in 4 energy bands - $0.4-0.6\ keV$, $0.7-0.9\ keV$, $0.9-1.3\ keV$
and $2.0-5.0\ keV$ (see sec. 4) - to look both at the energy ranges of the
WHIM signal and in a frequency domain where its contribution is negligible, in
order to isolate its signatures.

In the past decades it has been demonstrated that the signal measured in the
power spectrum of the DXB can be analyzed based on population synthesis models
and recent observational results, properly combined to predict the amplitude
and shape of all its components [9, 8, 44, 58]. The amplitude and shape of the
power spectrum of the DXB can be interpreted as the superposition of galactic
and extragalactic components. Extragalactic components include Shot Noise (SN)
from individual undetected AGN and galaxies below the sensitivity of the
observation, clustering of galaxies and AGN below the limiting flux [59], and
clustering of undetected diffuse hot cosmological gas in large scale
structures. The large scale structure is further divided in the contribution
from the WHIM filaments that we are searching for, and hotter/denser
structures associated with galaxy clusters and groups (also referred to as
IGM). Another component to take into account is the cross-correlation of each
individual cosmological population (AGN, galaxies and the IGM) as they share
the same environments. The galactic contribution comes primarily from the
structure of the MW-CGM. Indeed, the emission from the LHB and SWCX can be
described as a constant flux on the detector [9] and therefore contribute to
the Poisson noise only (that has been removed, as explained in Sec. 4).

To obtain a ”clean” signal from the filaments, background flares were removed
from XMM-Newton and eROSITA observations, and for each energy band, the images
were masked to remove resolved point sources and extended X-ray sources,
background-subtracted and exposure-corrected (see sec. 4). For the same fields
and same energy band, all the pointings were co-added in order to produce the
final images and calculate the power spectrum for each field, for a total of
16 datasets (4 fields, 4 energy bands). For each dataset, after the removal of
Poisson noise, point sources, instrumental and cosmic foreground, we checked
that no edge effects affected the clean power spectrum [60], from which we
subtracted all the well known components, leaving only the contribution from
the MW-CGM and, if present, the WHIM (see Figs. 5, 6, 7 and 8 in Sec. 3).
While the different fields have completely different characteristics in terms
of solid angle and sensitivity, and despite the data come from two different
missions, the resulting power spectra were all consistent with each other,
giving us confidence about having removed all the foreground components of the
signal in the same way. Fig. 9 in Sec. 3 shows the model-subtracted power
spectra for all the fields under analysis in all the energy bands under
investigation. In order to assess the consistency of the results, for every
energy range we performed Two-Sample T-Tests to compare the mean and standard
deviation of every pair of data-sets, and check whether or not the average
difference between the two measurements is statistically significant from
zero. In all cases the T-statistic was lower than the critical value on the
test distribution at a confidence level of 99.9$\%$ and, consequently, we
failed to reject the Null Hypothesis and established that there is no
significant difference between the population means. At this point, for each
energy band, the power spectra from all four fields were averaged, using a
weighted average with the statistical uncertainty as a weight.

Figure 3 shows the results for all four energy bands, both in the form of
power spectrum (left) and root mean square RMS fluctuations (right). To
analyze the data, we first assume that only one component (the MW-CGM) is
contributing. If that is the case, the curve should be fitted with a single
power law model $P=a\theta^{k}$, consistently with what was demonstrated in
the past for the galactic cirrus and galactic foregrounds [61, 62, 63]. As the
plots in the top row of Fig. 3 show, this is, indeed, true for the energy band
$0.9-1.3\ keV$, where the data can be fitted with a simple power law with
statistics $\chi^{2}/d.o.f.=27.57/26$ (see Table 2 in sec. 3). On the other
hand, for the energy band $2.0-5.0\ keV$ the statistics
$\chi^{2}/d.o.f.=54.60/26$ suggests that the simple power law fit must be
rejected at $3.34\sigma$ confidence level (see Table 2 in sec. 3). This result
does not surprise, since the contribution from the MW-CGM to the DXB is still
expected at energies $\gtrsim 1\ keV$ but is negligible at higher energies,
and the mean model-subtracted power spectrum is presumably a residual signal
for which we cannot find a best fit model. In addition, the value of the
exponent of the power law obtained for the $0.9-1.3\ keV$ energy band -
$2.68\pm 0.04$ \- is in agreement with the typical values in the range $(2,3)$
found for cloud distributions [61, 62, 63]. It is also worth mentioning that
our results are not in conflict with the recent study about the influence of
the foreground absorption on the patchiness of the MW-CGM conducted with eFEDS
[64]. If, indeed, the observed patchiness of the soft X-ray diffuse emission
within the eFEDS field is primarily a consequence of absorption, this has
important consequences in the spectral analysis, while the angular power
spectrum does not change.

The two lower energy bands, $0.4-0.6\ keV$ and $0.7-0.9\ keV$, cannot be
similarly fitted with a single power law component (see the plots in the top
row of Fig. 3). For these bands, we obtained $\chi^{2}/d.o.f.=94.64/26$ and
$\chi^{2}/d.o.f.=130.52/26$, respectively. These results suggest that the
hypothesis of a single power law model must be rejected at $>6\sigma$
confidence level (see Table 2 in sec. 3).

Up to this point we have shown that, once all other known components have been
removed, in addition to the contribution from the MW-CGM, there is a second
component that becomes significant below $1\ keV$. To confirm that this
component is, indeed, the signature of the WHIM and represents the hot
filaments in the Cosmic Web, we combined our data with predictions from
cosmological simulations [10]. The two plots in the bottom row of Fig. 3 show
the same data we have described before, but this time the model includes two
components, a power law to represent the MW-CGM, and the expected WHIM signal
derived from cosmological simulations [10] (Fig. 1-right). In the fit, while
the power law is free to change, the WHIM component has fixed shape and
amplitude, and the degrees of freedom have been reduced by 1. With the
addition of the second cosmological signal, the data in the two lower energy
bands are in good agreement with the fit (see Table 2 in 3), with
$\chi^{2}/d.o.f.=30.25/25$ and $\chi^{2}/d.o.f.=27.00/25$ for the $0.4-0.6\
keV$ and $0.7-0.9\ keV$ bands, respectively. Also for the two lower energy
bands we found values of the exponent of the power law due to the MW-CGM
consistent with those obtained for the galactic cirrus[61], namely $k=2.48\pm
0.06$ and $2.54\pm 0.05$, respectively. To compare the two models, in both the
lower energy bands we computed $\Delta\chi^{2}$, $\Delta BIC$ and $\Delta AIC$
(see Table 2 in 3). In all cases the results suggest that the model with the
WHIM component is favored at $>6\sigma$ confidence level (see Table 2 in 3).
So far, even if the spectral resolution of the data does not allow the direct
detection of the emission-line signal produced by the WHIM, this result turns
to be the highest-confidence level detection of the WHIM in emission. It is
also the only high-confidence level signal, so far available, obtained from
the combination of data from different and larger regions of the sky, instead
of single smaller areas. In Fig. 4 we show the WHIM signal, obtained after
subtracting the best fit power law from the mean model-subtracted power
spectra, compared to the simulated WHIM signal.

Finally, from the RMS fluctuations $\sqrt{q^{2}P(q)/2\pi}$, shown in all the
four energy bands in the right panels of Fig. 3, we reconstructed the energy
spectrum of the WHIM fluctuations. To this aim, we picked the value of
$\sqrt{q^{2}P(q)/2\pi}$ at an angular scale of $1.5\ arcmin$ (=$90\ arcsec$)
in the three lower energy bands (above $1\ keV$ the contribution from this
component is negligible). Plotting $\sqrt{q^{2}P(q)/2\pi}$ as a function of
the energy at the chosen angular scale, (see Fig. 10 in sec. 3), we were able
to obtain the energy spectrum of the fluctuations due to the WHIM. Using the
Simulated Observations of X-ray Sources (SOXS) package, we compared our energy
spectrum with different APEC models (Fig. 10 in sec. 3), and obtained the
following possible ranges for the fitting parameters: $kT\in(0.15,0.30)\ keV$,
$\rho\in(1,50)\bar{\rho_{b}}$, $z\in(0.1,0.4)$, and metallicity
$Z\in(0.01,0.40)Z_{\odot}$ (see Fig. 10 in sec. 3 for more details). These
values are all consistent with the physical properties of the WHIM [4, 65, 32,
19].

Mean model-subtracted power spectra

Figure 3: Mean model-subtracted power spectra obtained averaging, in every
energy band, the four model-subtracted power spectra, derived from the
analysis conducted in the four fields. The plots in the top row show the best
fit lines found adopting a power law $P=a\theta^{k}$, while the plots in the
bottom row display the best fit lines from the 2-component model
$P=a\theta^{k}+P_{WHIM}$, with $P_{WHIM}$ being the blue and green continuous
curves with error bars in the plots at the bottom. In both rows, the plots on
the left show the power spectra, while the plots on the right contain the RMS
fluctuations. The data in the energy bands 0.4-0.6, 0.7-0.9, 0.9-1.3, and
2.0-5.0 keV are shown in black, red, magenta and purple, respectively. The
continuous straight lines show the best lines.

Whim signal

Figure 4: Both the panels show the observed (black and red data) and simulated
WHIM signals (blue and green continuous curves with error bars). The plot on
the left contains the power spectrum of the WHIM, while the plot on the right
displays the WHIM RMS fluctuations, both obtained after subtracting the best
fit power law from the mean model-subtracted power spectra.

##  3 Extended Data

Clean power spectra and modeled components in the 0.4-0.6 keV

Figure 5: Red data: Clean power spectra for XMM-CDFS [52, 53], XMM-COSMOS
[54], XMM-Stripe82 [55, 56] and eFEDS [57] in the energy band 0.4-0.6 keV (the
data have been obtained after masking the images in all fields, subtracting
the background, dividing by the exposure and removing spurious signals). Red
continuous line: power spectrum of the shot noise. Magenta continuous line:
power spectrum from unresolved emission from infra-cluster/group gas. Blue
continuous line: power spectrum due to galaxy clustering. Green continuous
line: AGN clustering component. Orange continuous line: cross-power component.

Clean power spectra and modeled components in the 0.7-0.9 keV

Figure 6: Red data: Clean power spectra for XMM-CDFS [52, 53], XMM-COSMOS
[54], XMM-Stripe82 [55, 56] and eFEDS [57] in the energy band 0.7-0.9 keV (the
data have been obtained after masking the images in all fields, subtracting
the background, dividing by the exposure and removing spurious signals). Red
continuous line: power spectrum of the shot noise. Magenta continuous line:
power spectrum from unresolved emission from infra-cluster/group gas. Blue
continuous line: power spectrum due to galaxy clustering. Green continuous
line: AGN clustering component. Orange continuous line: cross-power component.

Clean power spectra and modeled components in the 0.9-1.3 keV

Figure 7: Red data: Clean power spectra for XMM-CDFS [52, 53], XMM-COSMOS
[54], XMM-Stripe82 [55, 56] and eFEDS [57] in the energy band 0.9-1.3 keV (the
data have been obtained after masking the images in all fields, subtracting
the background, dividing by the exposure and removing spurious signals). Red
continuous line: power spectrum of the shot noise. Magenta continuous line:
power spectrum from unresolved emission from infra-cluster/group gas. Blue
continuous line: power spectrum due to galaxy clustering. Green continuous
line: AGN clustering component. Orange continuous line: cross-power component.

Clean power spectra and modeled components in the 2.0-5.0 keV

Figure 8: Red data: Clean power spectra for XMM-CDFS [52, 53], XMM-COSMOS
[54], XMM-Stripe82 [55, 56] and eFEDS [57] in the energy band 2.0-5.0 keV (the
data have been obtained after masking the images in all fields, subtracting
the background, dividing by the exposure and removing spurious signals). Red
continuous line: power spectrum of the shot noise. Magenta continuous line:
power spectrum from unresolved emission from infra-cluster/group gas. Blue
continuous line: power spectrum due to galaxy clustering. Green continuous
line: AGN clustering component. Orange continuous line: cross-power component.

Model-subtracted power spectra

Figure 9: Red data: Model-subtracted power spectra for XMM-CDFS [52, 53].
Green data: Model-subtracted power spectra for XMM-COSMOS [54]. Purple data:
Model-subtracted power spectra for XMM-Stripe82 [55, 56]. Grey data: Model-
subtracted power spectra for eFEDS [57]. The results in the energy bands
0.4-0.6, 0.7-0.9, 0.9-1.3, 2.0-5.0 keV are shown with circles, triangles,
squares and asterisks, respectively.

Energy spectrum of the WHIM fluctuations

Figure 10: Black data: Energy spectrum of the fluctuations due to the WHIM;
Magenta continuous line: APEC model with temperature $kT=0.15\ keV$, redshift
$z=0.4$ and metallicity $Z=0.01Z_{\odot}$; Blue continuous line: APEC model
due to the sum of different filaments at redshifts $z=0.0,0.1,0.2,0.3,0.4$,
temperatures and metallicities in the ranges $(0.15,0.30)keV$ and
$(0.01,0.20)Z_{\odot}$, respectively; Green continuous line: APEC model with
with $kT=0.25\ keV$, $z=0.0$ and metallicity $Z=0.40Z_{\odot}$. All the
normalization values of the APEC models correspond to a gas density $\rho$ in
the range $(1,50)\bar{\rho_{b}}$, through the relation
$norm=\frac{10^{-14}}{4\pi[D_{A}(1+z)]^{2}}\int{n_{e}n_{H}dV}$, where $D_{A}$
is the angular diameter distance to the source, $dV$ is the volume element,
$n_{e}$ and $n_{H}$ are the electron and H densities, respectively. In
particular, for the blue continuous line, we obtained a gas density $\rho\sim
10\bar{\rho_{b}}$. Despite the lack of points to conduct significant
statistics, we can notice that the data are included in an area with APEC
parameters consistent with the physical properties of the WHIM.

Sample of targets used in this investigation

Target | Area ($deg^{2}$) | Exposure (Ms) | S${}_{lim}(0.5-2)/10^{-15}$ (cgs)
---|---|---|---
XMM-CDFS | 0.25 | 3.45 | 0.66($2.0-10keV$)
XMM-COSMOS | 2.13 | 1.5 | 1.7
XMM-STRIPE82 | 20 | 0.8 | 5
eFEDS | 140 | 0.36 | 7

Table 1: Sample of targets used in this investigation. The table entries are:
field name (the first column), FoV area (second column), exposure time (third
column), sensitivity (fourth column)[52, 53, 66, 54, 55, 56, 57].

Statistical tests results

Energy band (keV) | Model 1, $P=a\theta^{k}$ | Model 2, $P=a\theta^{k}+P_{WHIM}$ | $\Delta$BIC | $\Delta$AIC | $\Delta\chi^{2}$ | Confidence
---|---|---|---|---|---|---
$\chi^{2}$ | d.o.f. | $\chi^{2}_{red}$ | Confidence | $\chi^{2}$ | d.o.f. | $\chi^{2}_{red}$ | Confidence
0.4-0.6 | 94.64 | 26 | 3.64 | $>6\sigma$ | 30.25 | 25 | 1.21 | $1.24\sigma$ | 63.58 | 62.39 | 64.39 | $>6\sigma$
0.7-0.9 | 130.52 | 26 | 5.02 | $>6\sigma$ | 27.00 | 25 | 1.08 | $0.92\sigma$ | 101.61 | 101.52 | 103.52 | $>6\sigma$
0.9-1.3 | 27.57 | 26 | 1.06 | $0.88\sigma$ |  |  |  |  |  |  |  |
2.0-5.0 | 54.60 | 26 | 2.10 | $3.34\sigma$ |  |  |  |  |  |  |  |

Table 2: Results of the statistical tests. The table entries are: energy band
(first column), results obtained from model 1 (second column), results
obtained from models 2 (third column), $\Delta BIC$, $\Delta AIC$,
$\Delta\chi^{2}$ and $\Delta\chi^{2}$-obtained confidence level (fourth,
fifth, sixth and seventh columns, respectively). For both models, we listed
the $\chi^{2}$, the d.o.f., the $\chi^{2}_{red}$ and the confidence level.

##  4 Methods

###  4.1 Data assembly

For the purpose of this work, we used the fields listed in Table 1 in sec. 3
and numerical simulations [10]. For the XMM-Newton and eROSITA fields, count
maps were created in the bands $0.4-0.6\ keV$, $0.7-0.9\ keV$, $0.9-1.3\ keV$
and $2.0-5.0\ keV$, together with background, exposure maps and masks to
remove resolved point and extended sources. For every field, the masked,
background-subtracted, exposure- corrected images obtained for every pointing
were merged and mosaic images were created using the python
reproject.mosaicking sub-package. The final images have the following FoV:
$0.25\ deg^{2}$ for XMM-CDFS, $2\ deg^{2}$ for XMM-COSMOS, $17\ deg^{2}$ for
XMM-Stripe82 and $140\ deg^{2}$ for eFEDS. The simulated images were obtained
in the $0.4-0.6\ keV$ and $0.7-0.9\ keV$ energy band, and have a FoV of $1\
deg^{2}$.

####  4.1.1 XMM-Newton data

For XMM-CDFS, centered at R.A.=$03^{h}32^{m}28.2^{s}$ and
dec=$-27^{\circ}48^{\prime}36.0"$ (J2000), we used 33 pointings, for a nominal
exposure of $3.45\ Ms$ and a total area of $\sim 0.25\ deg^{2}$ [53]. The XMM-
COSMOS field, centered at R.A.=$10^{h}00^{m}28.6^{s}$ and
dec=$+02^{\circ}12^{\prime}21.0"$ (J2000), covers an area of $\sim 2\ deg^{2}$
and consists of 56 pointings, for a total exposure of $1.5\ Ms$ [54]. Finally,
for XMM-Stripe82, we combined the 7 observations coming from the $\sim 17\
deg^{2}$ area [55] of the Announcement Opportunity 13 (AO13), each consisting
in 22 pointings, spanning over $14^{\circ}<R.A.<28^{\circ}$,
$-0.63^{\circ}<dec<0.63^{\circ}$ (J2000). For all the XMM-Newton fields we
used data coming from PN and MOS cameras, and performed the reduction of the
datasets using the Extended Source Analysis Software (ESAS) package, following
the standard data processing procedure for XMM-Newton EPIC observations of
extended objects and diffuse background [67] , and the Science Analysis System
(SAS) package.

In order to investigate the DXB, we first removed all resolved sources in the
fields. For CDFS we used 59 images (32 PN images and the 27 longest exposure
among MOS1 and MOS2) and a combination of 3 catalogs. The first catalog we
generated contains 322 XMM-detected point sources using the XMM-SAS tools
emosaic_prep, emosaicproc, eboxdetect, and region. Using ds9, we converted the
images units to galactic coordinates. For the second catalog, instead, we used
the Chandra CDFS-7 Ms source catalog, that reaches a much better sensitivity
($10^{-17}\ erg\ s^{-1}\ cm^{-2}$). It contains the coordinates, redshifts,
full-band fluxes, classifications, and many other useful properties for 740
detected sources. Finally, the third catalog contains 46 extended sources
(galaxy clusters and groups [68]). The last two catalogs were reformatted to
match the XMM-SAS standard and were merged with the source lists generated by
the XMM tools listed above. While the radii of XMM-detected sources are
automatically calculated by the XMM tools, to determine the correct cut-out
radius of point sources from the Chandra CDFS-7 Ms source and the extended
source catalogs , we had to take into account the fact that XMM-Newton has a
different Point Spread Function (PSF) than Chandra. The appropriate cut-out
radius was computed using the linear depeence of the PSF on the off-axis angle
[69]. The same approach for the computation of the cut-out radius of resolved
point sources was followed for XMM-COSMOS and XMM-Stripe82. For the former, we
used the Chandra-COSMOS Legacy Survey Multiwavelength Catalog [70], that
includes 4016 X-ray sources, 97% of which have identifications in the optical
and Near-Infrared bands. For the latter, the resolved point sources were
removed with the Sloan Digital Sky Survey Stripe 82 Chandra Source Match
Catalog (SDSS82CXO) and Sloan Digital Sky Survey Stripe 82 XMM-Newton Source
Match Catalog (SDSS82XMM).

For all the three fields fields, the events registered by the CCDs aboard XMM-
Newton were cleaned before being processed. One major contamination comes from
the Soft Proton (SP) flaring, due to low energy protons entering the telescope
from the Van Allen belt. This causes sudden flares in the count rate in the
instrument and can lead to a loss of observing time from hundreds of seconds
to hours. To remove this contamination we used the XMM-ESAS routines epchain
and pn-filter, that filter the event files from SP flaring and create cleaned
events. The cleaned event files were then used by XMM-SAS to create the image
count maps with the tool evselect. In particular, we sorted events in arrival
time to create odd- and even-listed event files, henceforward A and B subsets,
from which (A+B)/2 and (A-B)/2 maps were obtained. In particular, the
difference between the two subsets does not contain celestial signals or any
stable instrumental effects, allowing to evaluate the random noise [63, 71,
72, 43]. For every field, the A and B substets were created in all the four
energy bands. In addition, we generated exposure maps and background maps to
subtract other spurious signals, such as cosmic rays and electronic noise
[73].

The count maps were then masked, background-subtracted and divided by the
exposure to get the count rate maps. The masked, background-subtracted,
exposure- corrected images obtained for every pointing were merged and mosaic
images were created. In addition, the final count rate maps were divided by
the solid angle of the pixels, in order to get the X-ray surface brightness in
$counts\ s^{-1}\ sr^{-1}$.

####  4.1.2 eROSITA data

The eFEDS raw event files were obtained from the eROSITA-DE Early Data
Release. These data are made of 4 event files, each corresponding to a
35-square-degree quadralgular patch. The data reduction and analysis was
performed using the eROSITA Science Analysis Software System (eSASS) package
[74, 75]. For each event file, the command evtool was used to select all
photons in the energy bands of interest, converting them into image count
maps. To quantify and remove the random noise we used the same A-B subsets
approach adopted for the XMM fields. The corresponding exposure maps were
created with the expmap routine, while the background maps were created
combining the tools erbox and erbackmap [57]. As for the XMM fields, we
subtracted the background maps from the image count maps, that were also
divided by the exposure maps and by the solid angle of the pixels, in order to
get the same units for the X-ray surface brightness. Resolved point sources
and extended X-ray sources were masked out in the X-ray surface brightness
maps [76, 75]. We used a circular mask to remove every point source at its
position. The radius of the circular mask was given by the ape-radius
parameter in the adopted source catalog [76], which is the instrumental PSF
with size $3^{\prime}$. Finally, the four masked, background-subtracted
exposure-corrected image count maps were reprojected onto the same World
Coordinate System (WCS) and merged together into a single field in all the
energy bands under analysis.

####  4.1.3 Numerical simulations

The X-ray images adopted for the evaluation of the WHIM power spectrum come
from hydrodynamical simulations [4, 10], performed with the TREESPH code
GADGET-2 [77], using a $\Lambda CDM$ model with cosmological constant
$\Omega_{\Lambda}=0.7$, matter density $\Omega_{m}=0.3$, baryon density
$\Omega_{b}=0.04$, Hubble constant $H_{0}=100\ h\ km\ s^{-1}\ Mpc^{-1}$,
$h=0.7$ and $\sigma_{8}=0.8$. The code follows the evolution of $480^{3}$ dark
matter and baryonic gas particles, from $z=49$ to $z=0$. The physical
processes included in the model are gravity, non-radiative hydrodynamics, star
formation, feedback from supernovae, taking into account the effects of weak
galactic outflows, radiative gas coolong and heating by a uniform, time-
dependent, photoionizing ultraviolet background. The output of the simulation
consists of 102 $192\ h^{-1}\ Mpc$-side boxes with redshifts between $z=9$ and
$z=0$. The metallicity model with the best agreement with constraints from
X-ray observations and $Ly\alpha$ observations [3] was chosen. The images with
the X-ray flux were obtained stacking the simulation boxes in the redshift
interval from $z=0$ to $z=3$, then projecting the product of X-ray flux from
the single particles to a mesh, using 3-dimensional smoothing kernel as a
weight [78]. For every baryonic particle in the simulation, we know density,
volume and position, and the metallicity is assigned using a probability
distribution function of density and redshift that was previously adopted in
other hydrodinamic simulations [79], from which the X-ray emission can be
obtained. The apec model for the X-ray Spectral Fitting Package XSPEC was
adopted to generate tables of the energy spectrum as a function of temperature
and metallicity. Through an interpolation on temperature and metallicity, and
multiplying by $\rho^{2}$, the X-ray spectrum for every particle can be
created and, finally, summing on the redshifted energy bins, the contribution
to the bands $0.4-0.6\ keV$ and $0.7-0.9\ keV$ can be computed (the X-ray
emission of the single particle was smoothed over the volume elements
associated with the particle’s position). The simulation particles were
filtered by their density and temperature, in order to obtain images of X-ray
emission due to the WHIM, with $10^{5}<T<10^{7}\ K$ and $\rho<1000\
\bar{\rho_{b}}$.

###  4.2 Power spectrum formalism

From the X-ray surface brightness maps, the fluctuation fields $\delta
F_{X}=F_{X}(x)-<F_{X}>$ can be obtained. $F_{X}(x)$ represents the masked,
background-subtracted, exposure-corrected X-ray data, and $<F_{X}>$ is the
average value of the datasets. Through the discrete Fast Fourier Transform
(FFT), provided by the python numpy.fft subpackage, we computed the Fourier
transform $\Delta_{X}(\textbf{q})$ through the integral $\int\delta
F_{X}(x)\exp(-i\textbf{x}\cdot\textbf{q})d^{2}x$, with x coordinate vector in
the real space, $\textbf{q}=2\pi\textbf{k}$ wave-vector,
$|\textbf{k}|=1/\theta$, and $\theta$ angular scale. The 1D power spectrum
$P_{X}(q)=<|\Delta_{X}(\textbf{q})|^{2}>$ can then be computed, where the
average is taken over all the independent Fourier elements which lie inside
the radial interval $[q,q+dq]$. The error associated to the power spectrum was
obtained through the Poissonian estimator
$\sigma_{P_{X}}=P_{X}(q)/\sqrt{0.5N_{q}}$, with $N_{q}/2$ number of
independent measurements of $\Delta_{i}(q)$ out of a ring with $N_{q}$ data
(only one half of the Fourier plane is independent, since the flux is a real
quantity). The RMS fluctuations on scales $\theta=2\pi/q$ are usually computed
as $\sqrt{q^{2}P(q)/2\pi}$, where $P(q)$ is the 1D power spectrum of the image
under analysis. As previously mentioned, in order to quantify the random
noise, we created signal maps $1/2(A+B)$ and noise maps $1/2(A-B)$. The final,
clean power spectrum $P_{X}$ was evaluated as $P_{1/2(A+B)}-P_{1/2(A-B)}$.
Since $P_{1/2(A-B)}$ is the power spectrum of fluctuations due to Poisson
noise, it is essentially a flat spectrum (white noise).

###  4.3 Modeling the power spectra of the DXB fluctuations

####  4.3.1 Shot noise and Point Spread Function

The shot noise (SN) is produced by discrete sources that occasionally enter in
the beam. Indeed, apart from the bright detected sources, that were removed
from the images, there do exist faint objects that are not detectable and yet
add a further noise component to the power spectrum. Their contribution can be
estimated starting from the Log N-Log S and limited fluxes. It has been shown
that [63], if the resolved sources are removed down to a flux $S_{lim}$, the
shot noise component can be evaluated as
$P_{SN}=\int_{0}^{S_{lim}}S^{2}\frac{dN_{X}}{dS}dS$, where $dN_{X}/dS$ is the
differential Log N-Log S [80] of all the X-ray point sources - namely AGN,
galaxies and stars. Since the sensitivity of the survey is usually
inhomogeneous accross the FoV, $S_{lim}$ is a function of the sky coordinates.
To take into account this effect, for every field we scaled the number counts
by the corresponding selection functions $\eta(S)$ [54, 9, 56, 57]:
$\frac{dN_{X}}{dS}_{(SN)}=(1-\eta(S))\frac{dN_{X}}{dS}$.

####  4.3.2 Point Spread Function

All the astronomical components of the power spectrum are affected by the
telescope (PSF), whose effect consists in a multiplicative factor applied to
the effective power spectrum. For the XMM-Newton fields we modeled the effect
due to the PSF multiplying at every frequency [81] the power spectrum of each
modeled component by the factor $P_{PSF}(k)=1/[1+(k/0.02)^{2}]^{1.6}$, with
$k$ angular frequency. For eFEDS, instead, we simulated an image of randomly
distributed X-ray point sources with the SImulation of X-ray TElescopes
(SIXTE) software package [82] and computed its power spectrum. The power
spectrum of randomly distributed point sources is essentially a flat spectrum,
while the telescope PSF makes the power spectrum fall off at scales
$\theta<\sigma$ (or, equivalently, wave numbers $k>1/\sigma$), where $\sigma$
is the Gaussian width of the telescope PSF. The power spectrum of the PSF can
be modeled normilizing to 1 the power spectrum obtained from the simulated
image. The SIXTE software simulated the image of point sources generating a
number of photons that then are propagated through the representation of the
optics of the eROSITA telescope, resulting in a list of impact times,
positions and energies. Finally the read-out and the event list are simulated.

####  4.3.3 AGN and galaxy clustering, intergalactic medium and cross
correlation terms

The AGN (and, similarly, the galaxy) clustering is related to the unresolved
DXB production rate $dS/dz$, with $S$ the X-ray flux and $z$ the redshift, and
the evolving 3D power spectrum of the AGN $P_{3,AGN}(q)$, through the Limber’s
equation [83]. The power spectrum due to AGN can be related to the matter
power spectrum through the redshift dependent linear biasing factor [84]:
$P_{3,AGN}(k,z)=b(z)^{2}P_{3,M}(k,z)$, with $P_{3,M}(k,z)$ 3D matter power
spectrum. The latter can be estimated using the tool CAMB
111Source:http://camb.info/ [85]. The 2D power spectrum can then be obtained
with
$P_{2,AGN}(k)=\int_{0}^{z}(\frac{dS}{dz})^{2}\times\dfrac{P_{3,AGN}(k[2\pi
d_{A}\times(1+z)]^{-1}),z}{c\ dt/dz\ [d_{A}\times(1+z)]^{2}}\frac{dz}{1+z}$,
where $d_{A}$ is the angular diameter distance. For the Galaxy clustering the
procedure is similar. In both cases the flux originating from undetected
sources $\frac{dS}{dz}$ can be obtained from DXB synthesis models [9] and can
be computed as $\frac{dS}{dz}=\int_{0}{\infty}(1-\eta(S))\
\int_{z}{z+dz}\frac{L^{\prime}}{4\pi
d_{L}^{2}}\phi(L^{\prime},z)\frac{dV}{dz}dL^{\prime}dz$, with $d_{L}$
luminosity distance, $L^{\prime}$ luminosity measured in the energy bands
$0.4(1+z)-0.6(1+z)$ keV, $0.7(1+z)-0.9(1+z)$ keV, $0.9(1+z)-1.3(1+z)$ keV and
$2.0(1+z)-5.0(1+z)$ keV, and $\frac{dV}{dz}$ comoving volume element. [9].

From the analysis of the unresolved DXB from the Chandra observations in the
CDFS [9], it was found that another significant contribution to the total DXB
signal arises from clustering of unresolved galaxy clusters and groups. In
this work we followed the same approach and the same hydrodinamical
simulations [86] to model this component, namely the X-ray surface brightness
originating by the intergalactic gas at temperature $T>10^{7}\ K$, and density
$\rho>10^{3}\rho_{c}$. We also adopted the same procedure for the computation
of the cross-correlation terms.

##  5 Data availability

The entire XMM-Newton and eROSITA data used in this work are available in the
public XMM-Newton and eROSITA archives, namely, the XMM-Newton Science Archive
(http://nxsa.esac.esa.int/nxsa-web/) and the eROSITA Early Data Release (EDR)
archive (https://erosita.mpe.mpg.de/edr/). In particular, we used all the 33
pointings of XMM-CDFS, the 56 pointings of XMM-COSMOS, and the 7 observations
of the $\sim\ 17\ deg^{2}$ AO13 Stripe82 area, each one consisting of 22
pointings [55]. We also used all the 4 event files corresponding to the
35-square-degree quadralgular patches composing eFEDS.

##  6 Code availability

The codes for the simulations [4, 87, 86] can be accessed at
https://wwwmpa.mpa-garching.mpg.de/gadget/, while the power spectrum analysis
and the models of the DXB components used in this work are available upon
request from the corresponding authors. The SOXS package for the simulated
X-ray observations of astrophysical sources, used for the APEC model, is
available at https://hea-www.cfa.harvard.edu/soxs/.

## Acknowledgments

This research has made use of the SIXTE software package [82] provided by
ECAP/Remeis observatory (https://github.com/thdauser/sixte). In particular, we
deeply acknowledge Sicong Huang for providing us the XMM-COSMOS and XMM-
Stripe82 images, as well as Stefano Marchesi for his support on the SIXTE
simulations.

## Author contributions

Giulia Cerini developed all the codes for the power spectrum analysis, reduced
the XMM-COSMOS and XMM-Stripe82 data images, elaborated, together with Nico
cappelluti, the pipelines to model all the DXB components, extracted the WHIM
signal, and conducted the statistical tests to assess the significance of the
results. Nico Cappelluti developed the theoretical framework and techniques
for the decomposition of the DXB in its components, and reduced the eFEDS
images. Massimiliano Galeazzi designed the project suggesting the analysis in
narrow energy bands. Eugenio Ursino provided the numerical simulations,
reduced the XMM-CDFS images and, together with Massimiliano Galeazzi,
conducted the preliminary test of the method using the auto-correlation
function. All authors contributed to the the interpretation of the power
spectra, gave theoretical support for the results, and commented on the
manuscript.

### Corresponding authors

Giulia cerini, Nico Cappelluti, Massimiliano Galeazzi

<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
## Ethics declaration

The team has a strong history of supporting diversity and fostering an
inclusive workplace to ensure all current and prospective members of the
organizations are valued for the unique contributions they bring to support
program requirements at their highest levels of performance, and are committed
to the vision represented by NASA’s core value of inclusion in project
activities throughout the full life cycle. At the institutional level,
Diversity and Inclusion efforts fall into three main categories: bring
practices, community outreach, and training. Both the University of Miami and
Purdue University at Fort Wayne advance their goals through regular training,
issuance of guidelines to all partner institutions, regular collection and
reporting of metrics, issuance of anonymous surveys, and the establishment of
well-defined lines of authority to align practices with diversity and
inclusion objectives.

### Competing interests

The authors declare no competing interests.

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# Design Methodologies for Reliable and Energy-efficient PCM Systems

Shihao Song  Department of Electrical and Computer Engineering
Drexel University
Philadelphia, Pennsylvania, USA
<EMAIL_ADDRESS>Anup Das  Department of Electrical and Computer
Engineering
Drexel University
Philadelphia, Pennsylvania, USA
<EMAIL_ADDRESS>
###### Abstract

Phase-change memory (PCM) is a scalable and low latency non-volatile memory
(NVM) technology that has been proposed to serve as storage class memory
(SCM), providing low access latency similar to DRAM and often approaching or
exceeding the capacity of SSD. The multilevel property of PCM also enables its
adoption in neuromorphic systems to build high-density synaptic storage. We
investigate and describe two significant bottlenecks of a PCM system. First,
writing to PCM cells incurs significantly higher latency and energy penalties
than reading its content. Second, high operating voltages of PCM impacts its
reliable operations. In this work, we propose methodologies to tackle the
bottlenecks, improving performance, reliability, energy consumption, and
sustainability for a PCM system.

###### Index Terms:

phase change memory (PCM), non-volatile memory (NVM), DRAM, hybrid memory,
tiered memory, neuromorphic computing, performance, energy, reliability,
bitline parasitic, NBTI, endurance

††publicationid: pubid: 978-0-7381-4307-1/20/$31.00 ©2020 IEEE

##  I Introduction

Emerging non-volatile memory (NVM) technologies have been extensively studied,
which is due to two reasons. First, there is a gap of orders of magnitude
between access latencies of SSD (e.g., 0.1-1 ms) and DRAM (e.g., 10-100 ns).
Thus, there has been continuous research on finding a new layer of memory
hierarchy, e.g., storage class memory (SCM) [1], to fill the large performance
gap. Second, conventional dynamic random access memory (DRAM) technology is
experiencing significant scalability issues [2]. Therefore, a promising NVM
technology should be scalable and provide near-DRAM access latency in order to
supplant or supplement DRAM for a high-performance and high-capacity main
memory system.

Examples of emerging non-volatile memory technologies include phase-change
memory (PCM), resistive random access memory (RRAM), ferroelectric random
access memory (FeRAM), and magnetic random access memory (MRAM). This work
focuses on phase-change memory (PCM), which is considered the most mature NVM
technology [3].

However, there are key bottlenecks in PCM. First, PCM shows near-DRAM read
latency, but its write latency is much higher than DRAM. This is because the
SET operation (0 $\rightarrow$ 1 programming) requires much longer latency
than RESET operation (1 $\rightarrow$ 0 programming). Qureshi et al. propose
PreSET [4], a mechanism to proactively SET the memory location (preparing an
all-ones data pattern) well in advance of the anticipated write. This enables
a PCM write to perform only short-latency RESETs, improving system
performance. However, RESET operations consume much more energy than SET
operations. Our recent work [5] shows that PreSET can incur significant energy
penalties. Second, PCM requires high voltages and currents to operate, leading
to accelerated aging of CMOS transistors in the peripheral circuits within
each PCM bank. Each peripheral circuit consists of a sense amplifier (to read
PCM cells) and a write driver (to program PCM cells). Aging of peripheral
circuits impacts PCM reliability because a failed peripheral circuit cannot
serve reads and writes [6, 7].

This work addresses performance, energy consumption, and reliability issues in
PCM. We make the following key contributions.

  * •

We propose _data content aware PCM writes_ (DATACON) [5], a mechanism that
lowers the latency and energy consumption of PCM writes by redirecting these
requests to the best overwritten memory locations.

  * •

We propose MNEME [6], a novel hybrid DRAM-PCM system architecture to improve
performance and reliability. MNEME consists of a segmented bitline
architecture and a prediction-based page management policy.

  * •

We extend our study to neuromorphic hardware that uses PCM as synaptic storage
elements. We propose RENEU [8], a reliability-oriented approach to map machine
learning applications to neuromorphic hardware, improving reliability without
degrading performance.

##  II Methodologies

###  II-A DATACON

The key observation of PreSET [4] is that overwriting an all-ones memory
content incurs the least write latency because only short-latency RESETS are
required. However, we observe that overwriting an all-ones memory content is
not energy-efficient when the fraction of SET bits in the write data is less
than 60%, whereas overwriting an all-zeros memory content gives the best
energy efficiency.

We propose _data content aware PCM writes_ (DATACON), a mechanism that lowers
the latency and energy of PCM writes by redirecting these requests to memory
locations that contain all-ones or all-zeros based on the number of SET bits
in the write data. DATACON operates in three steps. First, for every write
request, DATACON counts the number of SET bits in the write data. Second, if
the fraction of SET bits in the write data is less than 60%, DATACON will
select a memory location containing all-zeros as the request’s new write
address. Otherwise, a memory location containing all-ones should be selected.
DATACON keeps track of the address translation of the original write address
to the new write address, guaranteeing the correctness for future read
requests. Third, DATACON re-initializes unused memory locations, i.e., to SET
or RESET one unused memory location to prepare an all-ones or all-zeros memory
content. The re-initialization step employs our _partition-level parallelism_
(PALP [9]) mechanism, avoiding interference with regular read and write
requests.

We evaluate DATACON with SPEC CPU2017, NAS, and state-of-the-art machine
learning workloads. Results demonstrate that DATACON improves the effective
access latency by 31%, overall system performance by 27%, and total memory
system energy consumption by 43% compared to the best performance-oriented
state-of-the-art techniques.

###  II-B MNEME

A peripheral circuit is several orders of magnitude larger than the size of a
PCM cell. To achieve higher chip density, many PCM cells share one peripheral
circuit through a wire called a bitline. We observe that the farther a PCM
cell from the peripheral circuit, the more parasitic components are associated
with the cell. The voltage drop (called the _IR drop_) induced by parasitic
components need to be compensated by supplying extra voltage generated by the
on-chip voltage regulators. This implies that cells nearer to their peripheral
circuit can be accessed faster due to reduced latencies for voltage regulators
to generate fewer voltages. Furthermore, since the lower voltage is required
to access nearer cells, the aging of peripheral circuits is reduced, thus
improving PCM reliability. A similar phenomenon is also observed and reported
for DRAM [10].

MNEME system architecture considers a computing system with PCM supplementing
DRAM, forming a hybrid main memory subsystem. The first key component of MNEME
is a segmented bitline architecture where each long bitline in DRAM and PCM is
split into a near segment and a far segment using an isolation transistor.
This new architecture creates intra-memory asymmetries for both DRAM and PCM.
For instance, cells inside the near segment in PCM can be accessed faster, and
the reduced voltage level also improves PCM reliability. Conversely, when
accessing cells in the far segment in PCM, higher access latency and degraded
reliability are expected. Thus, from the reliability and performance
perspective, access-intensive pages should be placed in the near segment in
PCM or DRAM.

Conventional page management policy such as Nimble [11] does not perform well
in the segmented bitline DRAM-PCM architecture. This is due to two reasons.
First, Nimble does not consider intra-memory asymmetries. Second, Nimble
induces significant migration overhead, which is because Nimble randomly
selects a memory tier, e.g., the far segment in PCM or the near segment in
DRAM, to place a new memory page during its initial allocation. Nimble then
migrates pages among memory tiers based on their run-time access intensity.
MNEME extends its page management policy in the following ways. First, MNEME
exploits both inter-memory and intra-memory asymmetries. Second, MNEME
implements a prediction-based page management policy. A new page’s access-
intensity is predicted then placed in a matching memory tier during its
initial allocation. For instance, a page that is predicted to be write-
intensive should be placed in the near segment in DRAM because of the lower
operating voltage and faster access latency. This eliminates unnecessary page
migrations during program execution and improves system-wide reliability as
well as performance.

We evaluate MNEME with single-core and multi-programmed workloads from the
SPEC CPU2017 Benchmark suites. Our results show that MNEME significantly
improves the performance and reliability of state-of-the-art hybrid memory
systems.

###  II-C RENEU

Neuromorphic hardware is designed for executing spiking neural networks (SNN).
Recently, non-volatile memory technologies such as phase-change memory are
used to implement synaptic storage in neuromorphic hardware [12]. PCM brings
certain advantages such as multilevel storage and high integration density.

We analyze the internal circuitry of a (pre-synaptic) neuron and observe that
due to PCM’s high operating voltages, the CMOS transistors inside the neuron
are stressed at elevated voltages when propagating excitations through PCM
synapse, leading to accelerated CMOS aging. This impacts the lifetime
reliability of the neuromorphic hardware. In our study, we concentrate CMOS
aging considering Time-Dependent Dielectric Breakdown (TDDB), Negative-Bias
Temperature Instability (NBTI), and Hot-Carrier Injection (HCI) failure
mechanisms. These are the dominant failure mechanisms in 45nm and below
technology nodes [13, 14].

Our key observation is that CMOS aging in a neuron circuitry is dependent on
the number of spikes/excitations propagated by the neuron. Thus, we formulate
and express a single neuron’s failure mechanisms in terms of the number of
spikes propagated by it. We consider a tile-based neuromorphic hardware and
extend the formulation to incorporate all the neurons in a tile. To this end,
we consider a tile is faulty if any of the neurons in it fails. Similarly, a
single faulty tile leads to the failure of the neuromorphic hardware.
Formulating failure mechanisms as a series failure model enables us to apply
mapping techniques to minimize the maximum aging, e.g., a mapping technique
that balances the aging among all the tiles.

We propose RENEU (REliability-aware NEUromorphic Computing), a reliability-
oriented approach to map spiking neural networks to neuromorphic hardware,
improving system-side reliability without compromising key performance metrics
such as execution time. RENEU first partitions an SNN model into clusters,
where each cluster with a fixed number of neurons and synapses can fit its
entirety to a tile. Incorporating the reliability formulation, RENEU then uses
the clustered SNN model to find the cluster-to-tile mapping based on Particle
Swarm Optimization (PSO).

We evaluate RENEU using different machine learning applications on a state-of-
the-art neuromorphic hardware. Results demonstrate an average 38% reduction in
circuit aging, leading to an average 18% improvement in the hardware’s
lifetime compared to current practices. RENEU only introduces a marginal
performance overhead of 5% compared to our performance-oriented mapping
mechanism [15].

##  III Conclusion

We introduce DATACON and MNEME to address performance, energy consumption, and
reliability issues of conventional PCM-based computing systems. We also extend
our study on PCM to neuromorphic hardware and propose RENEU to improve its
lifetime reliability. We evaluate our methodologies using state-of-the-art
workloads, and results show that they significantly improve performance,
energy consumption, and reliability for PCM-enabled systems. In future
research, we plan to extend our study on PCM to the following potential
fields.

  1. 1.

GPU-PCM architecture. GPUs are facing challenges such as limited on-board DRAM
space. We plan to explore the performance and power bottleneck when
supplanting or supplementing DRAM with PCM.

  2. 2.

Managed programming languages and in-PCM computing. Recent research shows that
the garbage collection mechanism in managed programming languages such as Java
induce significant performance penalties. We plan to explore in-memory
computing techniques to mitigate performance bottleneck for managed
programming languages executed on PCM-based computing systems.

## Acknowledgment

This work is supported by 1) the National Science Foundation Faculty Early
Career Development Award CCF-1942697 (CAREER: Facilitating Dependable
Neuromorphic Computing: Vision, Architecture, and Impact on Programmability)
and 2) the National Science Foundation Award CCF-1937419 (RTML: Small: Design
of System Software to Facilitate Real-Time Neuromorphic Computing).

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