# Radio Detection of PSR J1813$-$1749 in HESS J1813$-$178: The Most Scattered
Pulsar Known

F. Camilo South African Radio Astronomy Observatory, 2 Fir Street, Observatory
7925, South Africa F. Camilo<EMAIL_ADDRESS>S. M. Ransom National Radio
Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475, USA
J. P. Halpern Department of Astronomy, Columbia University, 550 West 120th
Street, New York, NY 10027-6601, USA  D. Anish Roshi Arecibo Observatory,
Arecibo, PR 00612, USA  University of Central Florida, Orlando, FL 32816, USA

(Received May 4; Accepted June 1, 2021)

###### Abstract

The 44.7 ms X-ray pulsar in the supernova remnant G12.82$-$0.02/HESS
J1813$-$178 has the second highest spin-down luminosity of known pulsars in
the Galaxy, with $\dot{E}=5.6\times 10^{37}$ erg s-1. Using the Green Bank
Telescope, we have detected radio pulsations from PSR J1813$-$1749 at 4.4–10.2
GHz. The pulse is highly scattered, with an exponential decay timescale $\tau$
longer than that of any other pulsar at these frequencies. A point source
detected at this position by Dzib et al. in several observations with the
Jansky Very Large Array can be attributed to the pulsed emission. The steep
dependence of $\tau$ on observing frequency explains why all previous
pulsation searches at lower frequencies failed ($\tau\approx 0.25$ s at 2
GHz). The large dispersion measure, $\mbox{DM}=1087$ pc cm-3, indicates a
distance of either 6.2 or 12 kpc according to two widely used models of the
electron density distribution in the Galaxy. These disfavor a previously
suggested association with a young stellar cluster at the closer distance of
4.8 kpc. The high X-ray measured column density of $\approx 10^{23}$ cm-2 also
supports a large distance. If at $d\approx 12$ kpc, HESS J1813$-$178 would be
one of the most luminous TeV sources in the Galaxy.

ISM: individual objects (HESS J1813$-$178, G12.82$-$0.02) — ISM: supernova
remnants — pulsars: individual (PSR J1813$-$1749)

##  1 Introduction

HESS J1813$-$178 is a bright TeV source (Aharonian et al., 2005, 2006)
coincident with the young shell-type radio supernova remnant (SNR)
G12.82$-$0.02 and the 2–10 keV X-ray source AX J1813$-$178 (Brogan et al.,
2005). It is also detected at 20–100 keV as IGR J18135$-$1751 (Ubertini et
al., 2005). Chandra and XMM-Newton resolved the X-ray emission into a point
source and bright surrounding nebula (Funk et al., 2007; Helfand et al.,
2007), evidently a pulsar and its wind nebula (PWN). In subsequent X-ray
timing observations, Gotthelf & Halpern (2009) and Halpern et al. (2012)
discovered the $P=44.7$ ms pulsar, with characteristic age
$\tau_{c}=P/2\dot{P}=5600$ yr and spin-down luminosity
$\dot{E}=4\pi^{2}I\dot{P}/P^{3}=5.6\times 10^{37}$ erg s-1, second in power in
the Galaxy only to the Crab pulsar.

Close in projection to PSR J1813$-$1749 is the young stellar cluster Cl
1813$-$178 at a kinematic distance of 4.8 kpc, discovered by Messineo et al.
(2008, 2011), who proposed this as a possible birth place of the pulsar
progenitor. But Halpern et al. (2012) argued that the discrepant measurements
of optical extinction to the cluster and X-ray absorption to the pulsar/PWN,
and X-ray absorption to a neighboring source of known distance, are evidence
that the distance to HESS J1813$-$178 is greater than that to Cl 1813$-$178,
possibly as large as 12 kpc.

Radio pulsation searches at the Green Bank Telescope (GBT) at 1.4 GHz and 2
GHz failed to detect a radio pulsar, with period-averaged flux density limits
of $<0.07$ mJy and $<0.006$ mJy, respectively (Halpern et al., 2012). Despite
these non-detections, a time-variable point source at the X-ray position of
PSR J1813$-$1749 in 4.86 GHz images from the Very Large Array (VLA) was
reported by Dzib et al. (2010). The measured flux density was $0.18\pm 0.02$
mJy in 2006. Additional Jansky VLA (JVLA) observations by Dzib et al. (2018)
in 2012, 2017, and 2018 continued to detect a moderately variable point source
at 6 GHz and 10 GHz with flux densities of $\approx 0.12$ mJy and $\approx
0.06$ mJy, respectively. In addition, Dzib et al. (2018) performed another
pulsar search at 1.4 GHz using the 100 m Effelsberg Telescope, obtaining an
upper limit of $<0.065$ mJy. Since the extrapolation of the steep spectrum of
the JVLA 6 GHz and 10 GHz detections to the lower frequencies of the pulsation
searches greatly exceeds the flux upper limits of those searches, it is
difficult to understand the non-detection of the pulsar and the nature of the
compact radio source.

We report pulsation searches using the GBT at frequencies of 4.4–10.2 GHz that
finally detect a highly dispersed and scattered pulse that can be attributed
to the JVLA imaged point source. In Section 2 we describe the observations,
and explain the lack of detection of pulsations at lower frequencies in terms
of scattering. Section 3 discusses the pulsar dispersion measure (DM) distance
and its implications for the luminosity of the TeV source, the location of the
scattering material, as well as other properties. Suggestions for further work
on this pulsar are presented in Section 4.

##  2 Observations

###  2.1 GUPPI

On 2012 July 20 we used the GUPPI spectrometer (DuPlain et al., 2008) to
sample an 800 MHz band centered at 4.8 GHz, recording data from each of 512
frequency channels every 0.163 ms. The integration lasted for 70 minutes. We
used standard pulsar search techniques implemented in PRESTO (Ransom, 2001),
searching in DM up to 3360 pc cm-3, twice the total Galactic value predicted
for this line of sight by the Cordes & Lazio (2002) electron distribution
model. A strong detection at a barycentric period of $44.712592(12)$ ms was
obtained, as shown in Figure 1, 2.3 $\sigma$ from an extrapolation of the
incoherent X-ray ephemeris of PSR J1813$-$1749 (Halpern et al., 2012), which
would predict $P=44.712535(22)$ ms. The large DM of 1087 pc cm-3 implies a
distance of $12\pm 2$ kpc according to the Cordes & Lazio (2002) model, or 6.2
kpc in the Yao et al. (2017) model. A long, exponential scattering tail is
evident even at this high frequency, making PSR J1813$-$1749 clearly an
extremely scattered pulsar.

Figure 1: Radio discovery of PSR J1813$-$1749 on 2012 July 20 in a 70-minute
GBT observation with the old C-band receiver using GUPPI (4.4–5.2 GHz). The 44
ms pulse has a clear scattering tail, which is unprecedented among pulsars at
5 GHz, and a nominal DM of 1102 pc cm-3. This peak DM (based on $\chi^{2}$) is
biased high because of scattering at the bottom of the wide band — the best-
fit DM is 1087 pc cm-3 (see Section 2.3). The best-fit barycentric spin period
of this detection is $P=44.71259(1)$ ms, at epoch $\mbox{MJD}=56128.15$.

We made another observation of PSR J1813$-$1749 on 2015 January 12, in the
frequency range 5.2–6.0 GHz, this time using a new C-band receiver. The pulsar
was clearly detected in the 30 minute observation (Figure 2) with a period of
$44.722438(35)$ ms, this time with a somewhat narrower profile consistent with
expectation from the typical $\nu^{-4}$ dependence of the scattering timescale
on observing frequency $\nu$. A formal measurement of the scattering timescale
is made in Section 2.3. The period derivative between the two radio detections
is $\dot{P}=1.2570(37)\times 10^{-13}$, very close to the earlier X-ray
measured value of $1.26545(64)\times 10^{-13}$ (Halpern et al., 2012).

Figure 2: PSR J1813$-$1749 on 2015 January 12 in a 30-minute GBT observation
with the new C-band receiver using GUPPI (5.2–6.0 GHz). For this detection at
$\mbox{MJD}=57034.72$, $P=44.72244(4)$ ms.

###  2.2 VEGAS

On 2015 January 10 we also observed PSR J1813$-$1749 with the new VEGAS
spectrometer (Prestage et al., 2015), using 0.5 ms sampling. A 60 minute
observation in C-band (3.8–8.2 GHz) and a 45 minute observation in X-band
(7.8–10.2 GHz) each detected the pulsar (Figures 3 and 4). The broader
bandpass of VEGAS provides a higher signal-to-noise ratio (S/N) pulse profile
in C-band, and a weaker pulse at X-band, with no scattering evident. These
higher-quality data show that the pulse shape is complex. Rather than a single
narrow pulse with an exponential tail, there appear to be two components
intrinsic to the pulse profile.

Figure 3: PSR J1813$-$1749 on 2015 January 10 in a 60-minute GBT observation
with the new VEGAS spectrometer in C-band (3.8–8.2 GHz). For this detection at
$\mbox{MJD}=57032.57$, $P=44.722434(8)$ ms.

Figure 4: PSR J1813$-$1749 on 2015 January 10 in a 45-minute GBT observation
with VEGAS in X-band (7.8–10.2 GHz). For this detection at
$\mbox{MJD}=57032.62$, $P=44.72239(3)$ ms.

A fit to all the radio and prior X-ray measured periods is shown in Figure 5,
which yields an overall $\dot{P}=1.2668(5)\times 10^{-13}$. The fit is not
perfect, however, likely because of intervening glitches and/or timing noise.
This $\dot{P}$ is within 3.2 $\sigma$ of a longer-term average value based
only on X-ray measurements (Ho et al., 2020).

Figure 5: Timing of PSR J1813$-$1749\. Filled circles are X-ray measurements
from Halpern et al. (2012); open circles are radio measurements reported here.

###  2.3 Pulse Broadening of PSR J1813$-$1749

In order to estimate the amount of pulse broadening for PSR J1813$-$1749, we
performed a simultaneous fit to the C-band and X-band VEGAS profiles (Figures
3 and 4) using the emcee package for MCMC analyses (Foreman-Mackey et al.,
2013). We assumed a simple one-sided exponential pulse broadening model, with
scattering timescale $\tau(\nu)$ proportional to $\nu^{-4}$ (Oswald et al.,
2021). Since we do not know the intrinsic pulse shape in these observing
bands, we fitted a two-gaussian model to the X-band data (see the top gray
line in Figure 6), and assumed that this is the infinite frequency pulse
profile.

Figure 6: Scattering fit to PSR J1813$-$1749 profiles at C- and X-bands. The
lower four black traces are the observed profiles in four C-band subbands
(cf., Figure 3), and the upper two black traces are two X-band subband
profiles (cf., Figure 4). The gray trace is the assumed infinite-frequency
intrinsic pulse profile based on a fit to the X-band data (Figure 4). The red
traces are model profile fits of the six subbands (see Section 2.3 for
details).

We split the C-band data into four equal subbands as a function of $\nu$, and
the X-band data into two equal subbands (black traces in Figure 6). Splitting
into subbands is necessary because the timescale of scattering within the
broad bands varies considerably from bottom to top as a result of the strong
$\nu^{-4}$ dependence of $\tau$. The MCMC fits included multiple nuisance
parameters since the correct relative scalings between any of the six fitted
profiles, the absolute alignment between the two different observations, and
the true DM of the pulsar (the measured value is slightly biased by
scattering) are all unknown.

The model-dependent estimate of the pulse broadening timescale at 1 GHz is
$\tau_{\rm 1\,GHz}=4.14\pm 0.11$ s, where the quoted error is purely
statistical. Systematics resulting from the low-S/N subband detections, the
unknown intrinsic profile shape, and the simple scattering model could
substantially modify that value. In any case, this scattering timescale
(equivalent to 1.1 s at 1.4 GHz and 0.26 s at 2 GHz) would smear out almost
all of the pulsed flux for this 44 ms pulsar at lower frequencies, accounting
for its non-detection in pulsed searches at 1.4 GHz and 2 GHz (see Section 1).
Even at 4.4 GHz (the bottom of the discovery radio band, cf. Figure 1), the
implied 11 ms scattering timescale is 25% of the rotation period.

The MCMC-fit value of the dispersion measure is $\mbox{DM}=1087\pm 0.5$ pc
cm-3, where the quoted error is purely statistical. This is model dependent
(e.g., it assumes that there is no intrinsic frequency evolution of the pulse
profile, and that $\tau(\nu)\propto\nu^{-4}$) and there is some covariance
with other fit parameters. We estimate a systematic DM error of $\approx 3$ pc
cm-3.

###  2.4 Pulsed Flux Density of PSR J1813$-$1749

We obtain the period-averaged flux density $S_{\nu}$ for PSR J1813$-$1749 at
C-band and X-band by applying the standard modified radiometer equation to the
VEGAS detections (Section 2.2).

Prior to doing the VEGAS pulsar observations, we optimized the pointing and
focusing of the subreflector/receiver system. The on-line calibration
procedure for these observations returned a system temperature of 18.8 and
29.7 K for C-band and X-band, respectively. In turn, the nominal GBT gain for
these bands is 1.87 and 1.8 K Jy-1.

Using the above in the modified radiometer equation with parameters
appropriate for the VEGAS observations (Figures 3 and 4) yields $S_{\rm
6\,GHz}\approx 0.06$ mJy and $S_{\rm 9\,GHz}\approx 0.06$ mJy. These are crude
estimates; e.g., the C-band value may be biased low by scattering, and the
X-band detection suffers from low S/N.

##  3 Discussion

###  3.1 Scattering Timescale and JVLA Point Source

PSR J1813$-$1749 doubtless accounts for the JVLA point source with $S_{\rm
6\,GHz}\approx 0.12$ mJy and $S_{\rm 10\,GHz}\approx 0.06$ mJy (Dzib et al.,
2018). Firstly, these flux densities are comparable to those estimated from
the pulsed detections (Section 2.4).

Also, despite the extreme pulse scattering, angular broadening is not expected
to be detectable in the existing images. A scattering timescale $\tau$
corresponds to angular broadening of the image with FWHM

$\theta=\sqrt{{8\,{\rm ln}\,2\,c\,(d-s)\,\tau\over d\,s}}$ $None$

for a source at a distance $d$ scattered by a thin screen at a distance $s$
(Cordes & Lazio, 1997). Our fitted scattering timescale at 6 GHz is $\tau_{\rm
6\,GHz}=3.2$ ms. Assuming $d=6.2$ kpc, and $s=d/2$, the predicted angular
broadening is $\theta_{\rm 6\,GHz}\approx 0.\\!^{\prime\prime}034$, which is
much smaller than the typical $1.\\!^{\prime\prime}6\times
0.\\!^{\prime\prime}8$ beam size of the Dzib et al. (2018) JVLA B-array
observations, consistent with their detection of the pulsar as an unresolved
source.

###  3.2 Distance, Associations, and Energetics

Arguments pertaining to the distance and possible associations with PSR
J1813$-$1749/G12.82$-$0.02 were detailed by Halpern et al. (2012), and are
summarized here. The young stellar cluster Cl 1813$-$178 is centered
$4.\\!^{\prime}4$ southwest of G12.82$-$0.02. Messineo et al. (2011) concluded
that Cl 1813$-$178 is one of several clusters belonging to the massive star
forming region W33 at $(\ell,b)=(12\fdg 8,-0\fdg 2)$, and determined that it
has an age of 4–4.5 Myr, which is ideal for the production of neutron stars.
They derived a spectrophotometric distance to Cl 1813$-$178 of $3.6\pm 0.7$
kpc, and a kinematic distance of $4.8\pm 0.3$ kpc from the radial velocity of
the brightest star in the cluster. At 4.8 kpc, the $2.\\!^{\prime}5$ diameter
of the SNR corresponds to a radius of 1.7 pc. Subsequent to the above work,
Immer et al. (2013) measured a distance of $2.4^{+0.17}_{-0.15}$ kpc to the
main W33 complexes using trigonometric parallaxes of water masers, in
contradiction to a previously assumed kinematic distance of 3.7 kpc, which
suggests that Cl 1813$-$178 is not associated with W33.

In any case, the absorbing column densities to PSR J1813$-$1749 and Cl
1813$-$178 are discrepant. The X-ray measured $N_{\rm H}=(10\pm 1)\times
10^{22}$ cm-2 to G12.82$-$0.02 (Helfand et al., 2007) is very high. An even
larger value of $N_{\rm H}=(13.1\pm 0.9)\times 10^{22}$ cm-2 was derived by Ho
et al. (2020) analyzing the same and newer data. In comparison, the average
visual extinction to Cl 1813$-$178 of $A_{V}=9.1$ (Messineo et al., 2011)
corresponds to an equivalent X-ray absorption of $N_{\rm H}=2\times 10^{22}$
cm-2 according to the relation $N_{\rm H}=2.21\times 10^{21}A_{V}$ cm-2 (Güver
& Özel, 2009). The highest extinction for a cluster member is $A_{V}=17$
(equivalent to $N_{\rm H}=3.8\times 10^{22}$ cm-2), which still does not come
close to matching the X-ray $N_{\rm H}$. Taking into account the observed
column density of molecular gas together with its velocity information from
CO, it appears that the X-ray absorption is consistent with any distance in
the range 5–12 kpc. The wide possible range is due to the uncertain partition
of molecular gas between the near and far branches of the double-valued
rotation curve. The newly measured DM is consistent with such distances as it
predicts $d=12\pm 2$ kpc according to the Cordes & Lazio (2002) electron
distribution model or 6.2 kpc in the Yao et al. (2017) model.

Further evidence for a large distance comes from a comparison with the X-ray
absorption to the bright LMXB GX 13+1 that lies only $0\fdg 7$ from
G12.82$-$0.02 along the Galactic plane. The distance to GX 13+1 was estimated
as $7\pm 1$ kpc (Bandyopadhyay et al., 1999) from the spectroscopic
classification (K5III) of its companion star and extinction variously
estimated as $A_{V}=13.2$–17.6, while its X-ray column density is less than
one-third that to PSR J1813$-$1749\. This suggests that the latter is farther
than 7 kpc, compatible with the DM derived values. The H II regions of the
intervening W33 complex may, however, contribute to the scattering of PSR
J1813$-$1749, similar to the conclusion of Dexter et al. (2017) concerning
other pulsars and H II regions in the inner Galaxy.

If HESS J1813$-$178 is located at $d=12$ kpc, its $>200$ GeV luminosity would
be $\approx 3\times 10^{35}$ erg s-1, which is $<1\%$ of the $\dot{E}$ of PSR
J1813$-$1749\. It and HESS J1640$-$465 associated with PSR J1640$-$4631
(Gotthelf et al., 2014), also at a distance of 12 kpc, would have nearly the
same luminosity and would be two of the most powerful TeV sources in the
Galaxy.

###  3.3 Comparison with Other Pulsars

Figure 7: Scattering timescale at 1 GHz versus dispersion measure for pulsars
with the highest DM. Open circles are from the ATNF Pulsar Catalog (Manchester
et al., 2005), supplemented with recent measurements from MeerKAT (Oswald et
al., 2021). Labelled pulsars (filled circles) are discussed in Section 3.3.

Figure 7 graphs scattering timescale against dispersion measure for the
highest DM pulsars. Data are from the ATNF Pulsar
Catalog111https://www.atnf.csiro.au/research/pulsar/psrcat/ (Manchester et
al., 2005) version 1.64, supplemented with recent measurements from MeerKAT
(Oswald et al., 2021). Although there is a general correlation of $\tau_{\rm
1\,GHz}$ with DM among pulsars, the spread in $\tau_{\rm 1\,GHz}$ at a given
DM is several orders of magnitude (Löhmer et al., 2001; Lewandowski et al.,
2015). This could be due to the placement of the scattering material or
inadequacy of the isotropic thin-screen model. The scattering timescale of PSR
J1813$-$1749 makes it the most scattered pulsar known, although it falls
within the spread of the correlation with DM. It is not more of an outlier in
Figure 7 than, e.g., PSR J1841$-$0500, the intermittent pulsar discovered by
Camilo et al. (2012).

The Galactic Center (GC) magnetar PSR J1745$-$2900 has $\mbox{DM}=1778$ pc
cm-3, the highest of any known radio pulsar, but its scattering timescales of
$\tau_{\rm 4.8\,GHz}=3.3\pm 0.6$ ms and $\tau_{\,\rm 1\,GHz}=1.3$ s (Spitler
et al., 2014) are smaller than those of PSR J1813$-$1749\. Bower et al. (2014)
used the equality of the image broadening of PSR J1745$-$2900 and Sgr A∗ to
argue that they are scattered by the same screen, which Equation (1) places at
2–3 kpc from Earth rather than near the GC. Such a determination of the
scattering location cannot yet be made for PSR J1813$-$1749 because its image
size has not been measured.

What else we know from pulsars close to the line of sight is summarized in
Table 1, which lists data on four pulsars at $<0\fdg 5$ angular distance from
PSR J1813$-$1749\. All four have DM distances greater than the parallax
distance of W33, but none is as distant as PSR J1813$-$1749\. The two with the
largest DM (other than PSR J1813$-$1749) are closest to the Galactic plane,
but do not have scattering timescales measured. The two with reported
scattering measurements have timescales much smaller than that of PSR
J1813$-$1749\. Together, these data argue that PSR J1813$-$1749 lies behind
additional, distant scattering material that is not associated with the W33
complex and not traversed by the other pulsars’ sightlines.

Table 1: Pulsars within $0\fdg 5$ of PSR J1813$-$1749 Name | $\ell$ | $b$ | DMaaUncertainties on the last digits are in parentheses. |  $d$bbDM distance from the Yao et al. (2017) model. |  $\tau_{\,\rm 1\,GHz}$aaUncertainties on the last digits are in parentheses. | $\theta$
---|---|---|---|---|---|---
(PSR) | (∘) | (∘) | (pc cm-3) | (kpc) | (s) | (∘)
J1811$-$1736 | 12.82 | $0.43$ | 473.93(4) | 4.4 | 0.042(1) | 0.45
J1812$-$1733 | 12.90 | $0.38$ | 509.8(1) | 4.5 | 0.102(1) | 0.41
J1813$-$1749 | 12.81 | $-0.02$ | 1087(3) | 6.2 | 4.14(11) | …
J1814$-$1744 | 13.02 | $-0.21$ | 792(16) | 5.0 | … | 0.28
J1815$-$1738 | 13.17 | $-0.27$ | 724.6(2) | 4.9 | … | 0.44

###  3.4 Proper Motion and Age

Recently, Ho et al. (2020) reported a proper motion of $0.0655\pm 0.0114$
arcsec yr-1 for PSR J1813$-$1749 using three Chandra images over 10 years.
This implies a high tangential velocity of $v_{t}=1490$ km s-1 at the 4.8 kpc
distance assumed in previous studies, but an even larger $v_{t}=1925$ km s-1
if it is at the Yao et al. (2017) distance of 6.2 kpc. This would be larger
than any well-measured velocity for a neutron star (cf., Deller et al. 2019),
a result that invites skepticism as well as exploration of its implications.

For one, PSR J1813$-$1749 is only $\approx 20^{\prime\prime}$ from the center
of the radio shell of G12.82$-$0.02, unlike other high-velocity pulsars that
have either escaped their shells or show other morphological evidence of high
velocity in the structure of their PWNe (for a review, see Kargaltsev et al.
2017). These properties might, however, be reconciled if G12.82$-$0.02 has a
very young age of $\approx 300$ yr. This would possibly make PSR J1813$-$1749
the youngest known neutron star in the Galaxy. If so, it would also be
interesting if such a young SNR is accompanied by dense plasma that could
cause the extreme scattering of the radio pulses. Note from Equation (1) that
for a scattering screen very close to the pulsar ($s\approx d$), a given image
broadening would correspond to a very large scattering timescale $\tau$.

On the other hand, countervailing evidence against such a young age is found
in the broadband spectral energy distribution of HESS J1813$-$178, which is
more like those of evolved SNRs, and has been modelled most recently with an
age of 2500 yr (Zhu et al., 2018). In summary, there would be obstacles to
attributing the scattering of PSR J1813$-$1749 to a very young age.

##  4 Conclusions and Suggestions for Further Work

Pulsation searches at high radio frequency were necessary to overcome the
extremely long scattering timescale of PSR J1813$-$1749, the largest among
known pulsars. The GBT pulsed radio detection at 4.4–10.2 GHz with
$\mbox{DM}=1087$ pc cm-3 provides additional evidence of a larger distance
than once assumed, now favoring $d\approx 6$–14 kpc. If at the higher end of
this range, HESS J1813$-$178 may be one of the most luminous TeV source in the
Galaxy, at the expense of $<1\%$ of the spin-down power of PSR J1813$-$1749\.
A complete census of pulsars in the Galaxy, even energetic ones such as PSR
J1813$-$1749, remains a challenging prospect if there are more lines of sight
with such long scattering timescales.

Previous modelling of the spectral energy distribution of HESS J1813$-$178 as
leptonic emission from an evolving PWN in an expanding SNR (Fang & Zhang,
2010; Zhu et al., 2018) used a distance of 4.7 kpc. Models should also be
recalculated for the now favored larger distances. However, it is not
universally accepted that the PWN is the source of the TeV emission, as
opposed to the SNR shell or hadronic interactions with the environment (Torres
et al., 2014).

Since the DM distance still has a large uncertainty, it would be worthwhile to
obtain a more sensitive observation of 21 cm H I absorption against
G12.82$-$0.02 to pin down a kinematic distance. Future Chandra observations
are needed to confirm or disprove the reported high proper motion of PSR
J1813$-$1749, which would imply a very young age for the system, and possibly
be related to the extreme pulse scattering timescale. VLBI at 5 GHz could also
measure proper motion, as well as image broadening that could be used to
deduce the location of the scattering medium.

Finally, the detection in Figure 3 indicates that the combination of C-band
and VEGAS can produce high-S/N pulse profiles in only a few minutes of
observing time, opening opportunities to obtain a phase-connected timing
solution for PSR J1813$-$1749\. This might lead to the determination of its
spin-down braking index, which is an important parameter to model the
broadband (spectral) evolution and energetics of its PWN and HESS J1813$-$178.

This material is based upon work supported by the Green Bank Observatory which
is a major facility funded by the National Science Foundation operated by
Associated Universities, Inc. We thank Ryan Lynch for assistance with VEGAS
data analysis. The National Radio Astronomy Observatory is a facility of the
National Science Foundation operated under cooperative agreement by Associated
Universities, Inc. SMR is a CIFAR Fellow and is supported by the NSF Physics
Frontiers Center award 1430284. We are grateful to Michael Kramer and Ralph
Eatough for obtaining trial observations at Effelsberg. GBT

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# PPINtonus: Early Detection of Parkinson’s Disease Using Deep-Learning Tonal
Analysis

Varun Reddy
Academy of Engineering and Technology

(6/2/2022)

###### Abstract

PPINtonus is a system for the early detection of Parkinson’s Disease (PD)
utilizing deep-learning tonal analysis, providing a cost-effective and
accessible alternative to traditional neurological examinations. Partnering
with the Parkinson’s Voice Project (PVP), PPINtonus employs a semi-supervised
conditional generative adversarial network to generate synthetic data points,
enhancing the training dataset for a multi-layered deep neural network.
Combined with PRAAT phonetics software, this network accurately assesses
biomedical voice measurement values from a simple 120-second vocal test
performed with a standard microphone in typical household noise conditions.
The model’s performance was validated using a confusion matrix, achieving an
impressive 92.5 % accuracy with a low false negative rate. PPINtonus
demonstrated a precision of 92.7 %, making it a reliable tool for early PD
detection. The non-intrusive and efficient methodology of PPINtonus can
significantly benefit developing countries by enabling early diagnosis and
improving the quality of life for millions of PD patients through timely
intervention and management.

##  1 Background

Parkinson’s Disease (PD) is a progressive neurodegenerative disorder that
primarily affects motor function due to the loss of dopamine-producing neurons
in the substantia nigra, a region of the brain. The cardinal motor symptoms of
PD include tremors, rigidity, bradykinesia (slowness of movement), and
postural instability. These symptoms significantly impact the quality of life
of individuals and typically worsen over time. In addition to motor symptoms,
non-motor symptoms such as cognitive impairment, mood disorders, and sleep
disturbances also occur, further complicating disease management.

Early detection of PD is crucial as it allows for the timely initiation of
therapies that can alleviate symptoms and potentially slow the disease
progression. However, early-stage PD is often challenging to diagnose because
the symptoms can be subtle and may overlap with other conditions. Traditional
diagnostic methods for PD involve clinical evaluations, including neurological
examinations and the patient’s medical history. While these methods are
effective, they rely heavily on the expertise of medical professionals and are
subjective to some extent.

Advanced imaging techniques such as computed tomography (CT) and magnetic
resonance imaging (MRI) are also used to aid in the diagnosis of PD. These
methods provide detailed images of the brain, allowing for the identification
of structural abnormalities Theodoros (2008). However, the primary limitation
of these techniques is their high cost and the need for specialized equipment
and trained personnel Ogbole et al. (2018). This makes them less accessible,
especially in developing countries with limited healthcare resources. To
address the need for more accessible diagnostic tools, researchers have
explored various biomarkers that can be indicative of PD. Among these, vocal
biomarkers have gained significant attention. PD affects the muscles involved
in speech production, leading to changes in voice quality, pitch, loudness,
and articulation Sapir et al. (2011). These changes occur early in the disease
process, making vocal analysis a promising avenue for early PD detection. ML
models have been increasingly applied to analyze vocal biomarkers for PD
detection. These models can process large amounts of data and identify
patterns that may not be apparent to human observers. Traditional ML
approaches have been employed to classify vocal features extracted from speech
recordings. Despite the potential of ML models in PD detection, several
challenges remain. One major challenge is the variability in vocal features
among different individuals, which can be influenced by factors such as age,
gender, and the presence of other medical conditions. This variability can
make it difficult for models to generalize across different populations Arora
et al. (2015). Additionally, traditional ML models often require extensive
feature engineering, which involves manually selecting and transforming raw
data into a format suitable for model training. This process can be time-
consuming and may not capture the full complexity of the data. Deep learning
models, particularly neural networks, offer an alternative approach by
automatically learning hierarchical representations of data. CNNs and RNNs
have been used to analyze speech signals and detect PD Liao et al. (2020).
These models can learn directly from raw audio data, reducing the need for
manual feature engineering Marti et al. (2019). However, the performance of
deep learning models is heavily dependent on the availability of large,
annotated datasets. In the context of PD detection, obtaining a sufficiently
large and diverse dataset of vocal recordings is challenging, which limits the
effectiveness of these models.

Another approach that has been explored is the use of hybrid models that
combine traditional ML techniques with deep learning Miao et al. (2019). These
models aim to leverage the strengths of both approaches to improve diagnostic
accuracy. For example, a hybrid model might use deep learning to extract
features from raw audio data and then apply a traditional ML classifier to
make predictions He et al. (2016). While promising, these models still face
data availability and variability challenges.

##  2 Methodology

###  2.1 Data Collection

Our study utilized the UC Irvine Parkinson’s Disease Detection Dataset as the
primary source of biomedical voice measurements. Additionally, we collaborated
closely with vocal specialists at the Parkinson’s Voice Project and biomedical
engineering experts at the Monroe Advanced Technical Academy. The dataset
underwent an extensive preprocessing phase to prepare it for effective model
training. Initially, the data was thoroughly cleaned to remove any
inconsistencies or anomalies that could negatively impact model performance.
This cleaning process was followed by one-hot encoding, a technique used to
convert categorical variables into a numerical format suitable for machine
learning algorithms.

To further enhance our dataset, we generated additional synthetic data using a
Conditional Generative Adversarial Network (cGAN) Goodfellow et al. (2014). A
cGAN consists of two primary components: a generator and a discriminator. The
generator’s role is to produce synthetic data samples that resemble real data,
while the discriminator evaluates these samples to determine their
authenticity. The generator creates synthetic samples conditioned on actual
data features, which are then assessed by the discriminator. Both components
are trained simultaneously in a competitive setting, where the generator
continuously improves its ability to produce realistic data, and the
discriminator enhances its capability to distinguish between real and
synthetic samples. This iterative process continues until the discriminator
can no longer reliably differentiate between real and synthetic data,
indicating that the generator has successfully learned to produce high-quality
synthetic samples Pang et al. (2021). The synthetic data generated by the cGAN
was rigorously validated and subsequently used to augment our training
dataset. This approach significantly increased the volume of data available
for training, enhancing the robustness and generalizability of our neural
network model.

Figure 1: Illustration of a Generative Adversarial Network (Gharakhanian).

By leveraging a diverse set of samples, our model was better equipped to
detect Parkinson’s Disease across a variety of conditions and patient
profiles. In the feature extraction phase, we used PRAAT phonetics software to
derive critical vocal features from the dataset. This software provided
precise measurements of various vocal characteristics, which were further
validated by vocal specialists to ensure their accuracy and relevance in the
context of Parkinson’s Disease detection.

###  2.2 Deep Learning Methodology

The neural network architecture designed for this study includes multiple
fully connected (dense) layers interspersed with ReLU activation functions.
The output layer uses a sigmoid activation function to produce a probability
score indicating the likelihood of PD.

One significant challenge in deploying a deep learning model trained on
controlled data to real-world environments is handling noise. Training data is
typically collected in sound booths using high-quality condenser microphones,
ensuring minimal background noise and high fidelity. However, real-world
applications, especially in developing countries, often involve standard
smartphone microphones in typical household environments, which are prone to
various types of noise. To address this, we incorporate several noise-handling
techniques. Firstly, we apply data augmentation techniques to simulate real-
world conditions during training. This includes adding different types of
noise (e.g., white noise, background chatter, household sounds) to the clean
audio recordings. By training the model on augmented data, it learns to
differentiate between noise and the relevant vocal features indicative of PD.
Additionally, we integrate noise reduction algorithms as a preprocessing step
before feeding the audio data into the model. We employ deep learning-based
denoising autoencoders to reduce background noise, enhancing the clarity of
the extracted vocal features Benba et al. (2021). Furthermore, we employ
microphone calibration techniques to account for the differences in audio
quality between high-end condenser microphones and standard smartphone
microphones. We reduce the discrepancy between training and real-world data by
calibrating the recordings to match the audio profile of high-quality data.
This ensures that the model remains robust and reliable when used in practical
settings with standard equipment Dehak et al. (2010).

Raw audio data is initially preprocessed to extract relevant features using
PRAAT software. Features such as fundamental frequency (F0), jitter, shimmer,
and harmonics-to-noise ratio (HNR) are derived from the audio recordings.
Clean training data is then augmented with various types of noise to simulate
real-world conditions, and noise reduction algorithms are applied to the noisy
data to improve signal quality. The neural network is trained using the
augmented and noise-reduced data, with dropout layers applied to prevent
overfitting. Finally, performance metrics such as accuracy, precision, recall,
and F1-score are calculated and thoroughly analyzed to assess the model’s
effectiveness. Based on these results, a Bayesian optimization technique is
employed to further fine-tune the model’s hyperparameters Tsanas et al. (2012)
Kingma and Welling (2013). This method allows for a systematic search of the
hyperparameter space, ensuring that the model achieves optimal performance and
accuracy by evaluating the trade-offs between different configurations and
converging on the most effective parameter set.

###  2.3 Real Time PD Detection

Real-time detection of Parkinson’s Disease (PD) through vocal analysis
involves selecting the most effective vocal tests to extract reliable
Biomedical Voice Measurements (BVMs). These measurements are crucial for the
machine learning model to accurately predict the presence of PD. Research
indicates that certain types of vocal tasks are more effective at revealing
the subtle vocal characteristics affected by PD Hinton et al. (2012). The
primary vocal tests used for PD detection include sustained vowel phonations,
sentence readings, and complex speech tasks Theodoros (2008). Each test type
provides unique insights into different aspects of vocal function affected by
PD. Sustained vowel phonations involve prolonged pronouncing vowels such as
/a/, /i/, and /u/. This test is simple to administer and has been shown to
effectively reveal abnormalities in vocal fold vibration and control. Research
indicates that patients with PD exhibit increased jitter (frequency variation)
and shimmer (amplitude variation) during sustained phonation due to the
reduced ability to maintain a stable pitch and volume Skodda et al. (2011).
These measurements are critical BVMs for the model. Sentence readings involve
having the patient read predefined sentences aloud. This task assesses more
complex speech functions, including prosody (intonation), articulation, and
rhythm. Sentences are designed to include a variety of phonemes and stress
patterns to challenge the patient’s speech control. Studies have shown that PD
patients often have a reduced range of pitch and volume modulation, as well as
increased pauses and hesitations Sapir et al. (2011). These features can be
quantified as BVMs and used to train the machine learning model. Complex
speech tasks include spontaneous speech, narrative tasks, and rapid repetition
of syllables (e.g., ”pa-ta-ka”). These tasks are more demanding and can
highlight the motor planning deficits characteristic of PD. For instance,
diadochokinetic rate (the ability to make rapid, alternating movements) can be
measured during syllable repetition tasks. PD patients typically show a slower
rate and irregular rhythm, which are valuable BVMs for the model. Extensive
research has demonstrated the efficacy of these vocal tests in identifying PD-
specific vocal impairments. Sustained vowel phonations are particularly useful
for their simplicity and sensitivity to vocal tremors and stability issues.
Sentence readings provide a broader assessment of speech control and are
effective in capturing prosodic abnormalities. While more challenging to
administer, complex speech tasks offer comprehensive insights into the
neuromuscular control of speech Rusz et al. (2011).

Table 1: Various Biomedical Vocal Features and Their Descriptions Feature |  Description
---|---
Fundamental Frequency (F0) |  Average pitch of the voice, indicating vocal fold vibration rate.
Jitter |  Frequency variation between cycles, indicating vocal stability.
Shimmer |  Amplitude variation between cycles, indicating vocal amplitude regularity.
Harmonics-to-Noise Ratio (HNR) |  Ratio of harmonic to noise components, indicating voice quality.
Formant Frequencies (F1, F2, F3) |  Resonant frequencies of the vocal tract, crucial for vowel sounds.
Intensity |  Loudness of the voice, reflecting vocal energy.
Voice Onset Time (VOT) |  Interval between consonant release and vocal fold vibration.
Speech Rate |  Speed of speech, indicating motor control of speech production.
Diadochokinetic Rate (DDK) |  Rate of rapid, alternating movements, assessing neuromuscular coordination.
Pitch Range |  Range between the highest and lowest pitches, indicating vocal flexibility.
Speaking Fundamental Frequency (SFF) |  Mean pitch during continuous speech.
Maximum Phonation Time (MPT) |  Longest time a vowel can be sustained, indicating respiratory control.
Cepstral Peak Prominence (CPP) |  Measure of voice quality, higher values indicate clearer voice.
Voice Range Profile (VRP) |  Range of pitch and intensity, indicating vocal capacity.
Phonation Threshold Pressure (PTP) |  Minimum subglottal pressure needed to initiate phonation.
Amplitude Perturbation Quotient (APQ) |  Measure of short-term amplitude variations.
Normalized Noise Energy (NNE) |  Ratio of noise energy to total energy in the voice signal.

A study by Rusz et al. (2011) quantitatively analyzed the speech of early
untreated PD patients and found that these patients exhibited significant
deviations in fundamental frequency (F0), jitter, shimmer, and harmonics-to-
noise ratio (HNR) compared to healthy controls. These deviations were most
pronounced during sustained vowel phonations but were also evident during
sentence readings and complex speech tasks. Another study by Skodda et al.
(2011) highlighted the importance of prosodic features, such as intonation and
speech rate, which are best captured during sentence readings and spontaneous
speech tasks. The combination of different vocal tasks ensures a comprehensive
assessment of the patient’s speech abilities, thereby providing a robust set
of BVMs for the machine-learning model.

Figure 2: Figure 2: Differences in specific BVMs between Parkinson’s patients and healthy individuals (Rusz) Table 2: Sample Vocal Test Tasks for Real-Time PD Detection Task Code |  Speech Data |  Description
---|---|---
TASK 1 |  Sustained phonation of /i/ |  At a comfortable pitch and loudness, as constant and long as possible, at least 5 s.
TASK 2 |  Rapid syllable repetition |  Steady repetition of /pa/-/ta/-/ka/ syllables, repeated at least 5 times on one breath.
TASK 3 |  Sustained vowels /a/, /i/, /u/ |  Approximately 5-second sustained vowels at a comfortable pitch and loudness.
TASK 4 |  Sentence reading |  Reading a phonemically balanced text of 136 words.
TASK 5 |  Monologue |  Speaking for approximately 90 s about a familiar topic (e.g., recent events, interests).
TASK 6 |  Stress pattern reading |  Reading the same text containing 8 variable sentences of 71 words with varied stress patterns.
TASK 7 |  Emotional sentence reading |  Reading 10 sentences with specific emotions in a neutral tone, covering various emotional states.
TASK 8 |  Rhymed text reading |  Reading rhymes of 34 words following the example set by the examiner.

##  3 Proposed Model Architecture

Vocal Test Administration through PPINtonus software Data Acquisition via
Parselmouth (PRAAT python library) Preprocessing Noise Reduction Data
Augmentation Microphone Calibration Feature Extraction Neural Network
Classification Model Training Process Evaluation and Fine-Tuning

##  4 Results

The Generative Adversarial Network (GAN) model was trained over 10000 epochs,
and its performance was evaluated based on the loss of both the generator and
the discriminator. Throughout the training process, the generator loss
demonstrated a consistent decrease, starting at approximately 0.5 and
following a negative log curve to stabilize around 0.1. Similarly, the
discriminator loss exhibited a comparable trend, beginning at 0.5 and settling
at around 0.1. These diminishing loss values indicate that the GAN effectively
learned to generate realistic synthetic data that closely resembles the real
data used during training.

The neural network was trained using a dataset comprising both real and GAN-
generated synthetic data. Over the course of 100 epochs, the model’s training
and validation accuracy were monitored closely. The training accuracy showed a
steady improvement, starting from approximately 75 % and reaching 92.5 %. The
validation accuracy followed a similar trajectory, increasing from around 55 %
to 85 %. The alignment of the training and validation accuracy curves suggests
that the model generalizes well to unseen data and does not overfit,
demonstrating robustness and reliability in its predictive capabilities.

The consistency and reliability of different vocal tests in extracting
accurate BVMs were assessed. Sustained vowel phonation emerged as the most
effective test, achieving an accuracy of 85 %. This test is particularly
useful in capturing stable and clear vocal features. Rapid syllable repetition
and emotional sentence reading also performed well, with accuracies of 83 %
and 82 %, respectively. Sentence reading yielded an accuracy of 80 %, while
monologue tasks had a slightly lower accuracy of 78 %. These results highlight
that sustained vowel phonation and rapid syllable repetition are especially
effective in providing reliable BVMs for Parkinson’s Disease detection.

The integration of real data with GAN-generated synthetic data significantly
enhanced the model’s ability to detect Parkinson’s Disease (PD). The final
model achieved an accuracy of 92.5 %, with a precision of 92.7 % and a recall
of 1.0. The low false negative rate, corroborated by a confusion matrix
analysis, underscores the model’s reliability in identifying PD. The
application of data augmentation and noise reduction techniques ensured that
the model remained robust when tested in real-world conditions using standard
microphones. Additionally, the preprocessing steps, including microphone
calibration, contributed to the consistency and accuracy of the extracted
BVMs, making the system suitable for practical deployment in diverse
environments.

Table 3: Confusion Matrix for PD Detection Model | Predicted Positive | Predicted Negative | Total
---|---|---|---
Actual Positive | 950 | 0 | 950
Actual Negative | 77 | 1023 | 1100
Total | 1027 | 1023 | 2050

Figure 3: cGAN model able to model pre-existing training data over 10,000
epochs Figure 4: (a) Training and validation accuracy over 100 epochs. (b)
Training and validation loss over 100 epochs. Figure 5:  Accuracy of various
vocal tests in extracting reliable Biomedical Voice Measurements (BVMs) for
Parkinson’s Disease detection.

##  5 Discussion

While PPINtonus shows promising results in detecting PD through vocal
analysis, several areas can be improved. Enhancing the diversity of training
data through advanced data augmentation techniques can help the model
generalize better. This includes simulating various environmental noises,
different microphone qualities, and varying speech patterns to mimic real-
world conditions more closely. Further research into the most informative BMVs
could improve model accuracy. Advanced feature selection methods, such as
recursive feature elimination or PCA, can identify and retain the most
relevant features. Implementing real-time feedback mechanisms for patients
during vocal tests could ensure better compliance and more accurate data
collection. This could involve interactive interfaces that guide the user
through the vocal tests.

The training data is primarily collected in controlled environments using
high-quality microphones. Real-world applications, especially in third-world
countries, may involve lower-quality audio recordings, which could affect
model performance Li et al. (2019). The model’s effectiveness is constrained
by the available dataset size. Larger and more diverse datasets are needed to
validate the model’s robustness and generalizability across different
populations and dialects. While the model performs well on the current
dataset, its performance on unseen, real-world data needs further validation.
This includes testing across different demographic groups and geographical
regions to ensure broad applicability. The current model may require
significant computational resources, which could be a limitation for
deployment on edge devices in resource-constrained environments. Several
optimizations are necessary to enable the deployment of the model on edge
devices in third-world countries Lohr (2007). Utilizing lightweight neural
network architectures, such as MobileNets or EfficientNet, which are designed
for mobile and edge computing, can help in achieving the desired performance
with lower computational overhead. Leveraging edge AI frameworks like
TensorFlow Lite or PyTorch Mobile can facilitate the deployment of the model
on edge devices. These frameworks are optimized for low-latency and low-power
consumption environments Alsop (2021).

Designing intuitive user interfaces that guide users through the vocal tests
and provide real-time feedback, ensuring better data quality and user
engagement Becker et al. (2017). Integrating the model with existing
healthcare systems and electronic health records facilitates seamless data
flow and provides healthcare providers with actionable insights. Implementing
mechanisms for continuous learning and model updates based on new data and
feedback, ensuring that the model remains up-to-date and accurate over time.
By addressing these areas, we can improve the model’s performance, overcome
current limitations, and optimize it for deployment on edge devices in
resource-constrained environments, thereby making it accessible and beneficial
for a broader population.

##  6 Conclusion

This research explores the use of deep learning models for the early detection
of PD through vocal analysis. The study employed a comprehensive dataset of
BVMs and integrated synthetic data generated by a cGAN to enhance the training
process. The neural network trained on this enriched dataset achieved high
accuracy, precision, and recall, demonstrating the potential of this approach
in accurately identifying PD. The effectiveness of various vocal tests was
evaluated, revealing that sustained vowel phonation and rapid syllable
repetition provided the most reliable BVMs for PD detection. While the results
are promising, the study acknowledges several limitations, such as the
controlled nature of the training data and the computational demands of the
model. To address these issues, future work should focus on expanding the
dataset to include more diverse and real-world audio samples, particularly
from third-world countries. Optimizing the model for deployment on edge
devices through techniques like model pruning, quantization, and the use of
lightweight architectures such as MobileNets or EfficientNet is essential.
This research establishes a solid foundation for using vocal analysis in PD
detection, demonstrating significant potential for improving early diagnosis
and intervention. By addressing the identified limitations and optimizing the
model for real-world deployment, particularly in resource-constrained
environments, this approach can become a valuable tool in global healthcare
efforts to manage and treat PD.

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