# WASP 0346-21: An EL CVn-Type Eclipsing Binary with Multiperiodic Pulsations
in a Triple System

Jae Woo Lee1,2, Kyeongsoo Hong1, Min-Ji Jeong3, and Marek Wolf2 1Korea
Astronomy and Space Science Institute, Daejeon 34055, Republic of Korea
2Astronomical Institute, Faculty of Mathematics and Physics, Charles
University in Prague, 180 00 Praha 8, V Holešovičkách 2, Czech Republic
3Department of Astronomy and Space Science, Chungbuk National University,
Cheongju 28644, Republic of Korea<EMAIL_ADDRESS>
###### Abstract

VLT/UVES spectroscopic and TESS photometric observations for WASP 0346-21
allow the direct determination of its physical properties, along with the
detection of a circumbinary object and oscillating signals. The high-
resolution spectra yielded the radial velocities of all three stars and the
atmospheric parameters of $T_{\rm eff,A}$ = 7225$\pm 42$ K, [M/H] =
0.30$\pm$0.03 dex, and $v_{\rm A}$$\sin i$ = 78$\pm$5 km s-1 of the primary
component. The combined analysis of these observations resulted in the
fundamental parameters of the eclipsing components and the third light of
$l_{3}$ = 0.043$\pm$0.004, which is consistent with the light contribution of
the tertiary star observed in the echelle spectra. WASP 0346-21 A resides
within the overlapping main-sequence domain of $\delta$ Sct and $\gamma$ Dor
variables, while the secondary component of $M_{\rm B}$ = 0.185$\pm$0.013 M⊙,
$R_{\rm B}$ = 0.308$\pm$0.023 R⊙, $T_{\rm eff,B}$ = 10,655$\pm$146 K, and
$L_{\rm B}$ = 1.09$\pm$0.17 L⊙ matches well with the low-mass white dwarf (WD)
model for $Z$ = 0.01, corresponding to the thick-disk population classified by
the Galactic kinematics. Multifrequency analyses were performed on the
residual TESS data after removing the binarity effects. The low frequencies
around 26.348 day-1 and 17.683 day-1 are $\delta$ Sct pulsations originating
from WASP 0346-21 A, and the high frequencies of 97.996 day-1 and 90.460 day-1
are considered to be extremely low-mass WD oscillations. These results
demonstrate that WASP 0346-21 is a hierarchical triple system, consisting of
an EL CVn binary with multiperiodic pulsations in each component and a distant
outer tertiary.

##  1 INTRODUCTION

White dwarfs (WDs) are the final remnants of stars with initial masses up to
about 10 M⊙, corresponding to 95$-$97 % of all stars in our Galaxy. Many of
them are clustered around $\sim$0.6 M⊙ and harbor CO cores and H-rich
envelopes. Considering the age of the Universe, the WD minimum mass that can
be formed from the evolution of a single star is between 0.3 M⊙ and 0.45 M⊙
(Kilic et al. 2007). However, the mass distribution of the stellar remnants
indicates the presence of a non-negligible portion of extremely low-mass (ELM)
WDs with less than 0.3 M⊙ (Kleinman et al. 2013; Kepler et al. 2017), which is
insufficient mass to burn their He cores. The ELM WDs are thought to be
possible products of binary star evolution through stable or unstable mass
transfer (Istrate et al. 2016; Calcaferro et al. 2018; Li et al. 2019).
Observationally, their companions are A/F main-sequence (MS) stars,
millisecond pulsars, and WDs.

EL CVn-type stars are eclipsing binaries (EBs) composed of an ELM WD precursor
(pre-He WD) and an A/F dwarf (Maxted et al. 2014). Their MS binary precursors
are mainly predicted to have orbital periods shorter than $\sim$3 days (Lagos
et al. 2020). The pre-He WDs spend their lives in a constant luminosity phase,
moving almost consistently toward higher temperatures through stable H-shell
burning prior to reaching the WD cooling track (Chen et al. 2017). The light
curves of the EL CVn binaries display total eclipses at the primary minima due
to the occultation of the pre-He WDs and ellipsoidal variations outside
eclipses through the tidal deformation of the MS stars. Based on the light
curve morphology, more than 80 EL CVn-like EBs have been discovered through
various ground- and space-based photometric surveys (van Kerkwijk et al. 2010,
Carter et al. 2011, Breton et al 2012, Maxted et al. 2014, Faigler et al.
2015, Rappaport et al. 2015, van Roestel 2017, Wang et al. 2019, Lee et al.
2020, Peng et al. 2024). Their orbital periods ($P_{\rm orb}$) range from 0.46
to 23.9 days, but most of them have $P_{\rm orb}\lesssim 3$ days. Tokovinin et
al. (2006) showed that 96 % of the MS binary stars with $P_{\rm orb}<3$ days
are at least triplets. Lagos et al. (2020) found tertiary objects in all of
their EL CVn targets in a range of $P_{\rm orb}$ = 0.793–2.173 days, which
implies that short-period EL CVn EBs are possible triple systems.

The number of EL CVn candidates is steadily increasing, but with the exception
of six double-lined EBs, most have no or insufficient spectroscopic data to
reliably measure their physical properties. Some of them are known to display
different classes of pulsations: $\delta$ Sct and/or $\gamma$ Dor variables in
the A/F primary components, and very short-period oscillations of a few
hundred seconds in the pre-He WD companions (cf. Hong et al. 2021; Kim et al.
2021). Such pulsating EL CVn EBs are promising targets for detailed studies of
ELM WDs and intermediate-mass MS stars because of the strong synergy of their
asteroseismology and binary properties. This article focuses on WASP 0346-21
(1SWASP J034623.68-215819.5; TIC 121078334, HD 23692, TYC 5887-800-1, Gaia DR3
5087757377681887232; $T_{\rm p}$ = $+$9.343; $V\rm_{T}$ = $+$9.620,
$(B-V)\rm_{T}$ = $+$0.337). We found significant pulsation signals in the
time-series TESS data of this target.

Using archival WASP data analysis, Maxted et al. (2014) announced WASP 0346-21
to be a potential EL CVn-type EB with the following light curve parameters: an
orbital period of $P_{\rm orb}$ = 0.9285752 days, an inclination of $i$ = 79.1
deg, a mass ratio of $q_{\rm ph}$ = 0.165, a light ratio of $L_{\rm B}/L_{\rm
A}$ = 0.08, and relative radii of $r_{\rm A}$ = 0.3650 and $r_{\rm B}$ =
0.0628. They also estimated the effective temperatures of the binary
components to be $T_{\rm eff,A}$ = 7400$\pm 200$ K and $T_{\rm eff,B}$ =
9950$\pm 400$ K from a model fit to the observed flux distribution. We aim to
explore the pulsation characteristics of WASP 0346-21 and to determine its
stellar properties from a combined modeling of the TESS photometric data and
the archival echelle spectra. These provide valuable information for
understanding how short-period binaries with ELM WDs form and evolve, and for
probing their interiors using asteroseismic tools. Throughout the paper, the
primary and secondary components represent the more massive MS star (A) and
hotter WD companion (B), respectively.

##  2 TESS PHOTOMETRY AND ECLIPSE TIMINGS

WASP 0346-21 was observed during Sectors 4 (S4) and 31 (S31) of the TESS
mission (Ricker et al. 2015). The S4 observations were made in a 2-min cadence
mode from October 19 to November 14 2018, while the S31 ones were obtained in
both 20-s and 2-min modes from October 22 to November 16 2020. The
observational gap between S4 and S31 is approximately 708 days. This study
utilized the SAP-FLUX data collected from the MAST
archive111https://archive.stsci.edu/. The TESS data used are available at
http://dx.doi.org/10.17909/ak4z-xn20. The raw measurements were detrended and
normalized by applying a quadratic fit to the outside-eclipse portions of the
TESS light curves. These data on the flux scale were converted to magnitude
units by taking the average brightness at two quadratures as $T_{\rm p}$ =
$+$9.343 (Paegert et al. 2022). As a consequence, 31,441 and 95,045 individual
points were secured in 2-min and 20-s observing modes, respectively, with a
total period of nearly 760 days. The CROWDSAP values222fraction of target flux
measured in the photometric aperture. for S4 and S31 are 0.99725157 and
0.99575806, respectively, indicating that the TESS measurements of WASP
0346-21 have little contamination by nearby sources.

The resultant time-series data of WASP 0346-21 are plotted in Figure 1, where
the top panel shows 2-min cadence data from both sectors and the other panels
detail 20-s cadence measurements from S31. In this figure, our target star
appears as a detached binary exhibiting different eclipse depths and short
periodic oscillations. Using the 2-min and 20-s cadence data, respectively,
from S4 and S31, we fitted each eclipse curve with the method of Kwee & van
Woerden (1956), and obtained 47 primary and 48 secondary mid-eclipse times,
compiled in Table 1. The primary minima were used to yield the linear
ephemeris suitable for the TESS light curve of WASP 0346-21, as follows:

$\mbox{Min I}=\mbox{BJD}~{}2459145.207499(\pm 0.000083)+0.92857541(\pm
0.00000035)E.$ (1)

The TESS orbital period agrees within error with that (0.9285752$\pm$0.0000003
days) of Maxted et al. (2014) found in archival WASP data. However, when the
TESS data are phased with the epoch of HJD 2455178.3330$\pm$0.0002 in Table 2
of Maxted et al. (2014), their orbital phases are shifted by about 0.18. This
may be the result of changes in the orbital period of WASP 0346-21. Currently
we do not have enough minimum epochs to check this possibility. Future
continuous and systematic mid-eclipse timings are needed to study the orbital
period change.

##  3 VLT/UVES SPECTROSCOPY AND DATA ANALYSIS

Spectroscopic observations for WASP 0346-21 were conducted from 2014 October 2
to 9 with the VLT 8.2-m telescope and the high-resolution UVES spectrograph
(Dekker et al. 2000) at Paranal Observatory in Chile. The echelle spectra were
made sequentially using the UVES blue and red arms in the wavelength ranges of
3282–4563 $\rm\AA$ and 5655–9464 $\rm\AA$, with resolving powers $R$ of $\sim
49,620$ and $\sim 51,690$, respectively. We collected the spectra processed by
the UVES pipeline from the ESO
portal333https://archive.eso.org/scienceportal/home. The reduced spectra were
formed by co-adding and merging three 120-s exposures. Most of them, with an
integration time of 360 s, have a signal-to-noise ratio (SNR) of around 50–70.
The normalization of the archival data was performed by fitting a cubic
spline. The Barycentric Julian Date (BJD) and velocity corrections were
applied to the UVES spectra.

In EL CVn-type binaries, the spectral features of the secondary components are
difficult to measure due to the low luminosity of the stars. Phase-folded
trailed spectra are useful for tracking and revealing absorption lines caused
by the orbital motions of binary components (e.g., Hong et al. 2015; Lee et
al. 2020). Therefore, we closely examined the trailed spectra to find sets of
absorption lines where both components are observable. The result showed that
the absorption lines of the component stars clearly exist in two specific
regions of 4440–4520 $\rm\AA$ (blue; Mg II 4481 $\rm\AA$) and 6310–6390
$\rm\AA$ (red; Si II at 6347 $\rm\AA$ and 6371 $\rm\AA$).

To extract the radial velocities (RVs) of WASP 0346-21, we employed the
RaveSpan code (Pilecki et al. 2017). This program provides three methods for
RV measurements: broadening function (BF; Rucinski 2002), simple cross-
correlation (CCF; Simkin 1974; Tonry & Davis 1979), and 2D cross-correlation
(TODCOR; Mazeh & Zucker 1994). In this study, we applied the BF method to all
archival spectra, which showed superior results compared to CCF and TODCOR in
preliminary RV measurements. The template spectrum for this technique was
adopted from the library of synthetic local thermodynamic equilibrium (LTE)
spectra by Coelho et al. (2005). The BF profiles for three orbital phases are
illustrated as samples in Figure 2. Except for the BFs obtained at the
conjunction phase of 0.013, the others exhibit three apparent peaks. Unlike
the primary and secondary peaks, which show changes in RVs, the central third
peaks appear to be constant throughout the observing runs. This implies that
the additional sharp line profiles originate from a tertiary object and that
WASP 0346-21 is a triple-lined RV system (cf. Lu et al. 2001). We measured the
weighted mean RVs in each spectral region by fitting Gaussian and rotational
profile functions to the peaks in the BFs several times. These are presented
in Table 2 and depicted in Figure 3. We applied a sine wave to each RV curve
of the binary components, and obtained a spectroscopic mass ratio of $q_{\rm
sp}$ = 0.1179 from the sinusoidal semi-amplitudes of $K_{\rm A}$ = 27.6 km s-1
and $K_{\rm B}$ = 234.1 km s-1.

We calculated the atmosphere parameters of WASP 0346-21 A by comparing
synthetic spectral grids formed from all possible combinations with the UVES
spectrum observed at phase 0.013, where the secondary companion is completely
hidden behind the primary star. For this work, we used the Grid Search in
Stellar Parameters (GSSP444The GSSP package is available at
https://fys.kuleuven.be/ster/meetings/binary-2015/gssp-software-package)
software package by Tkachenko (2015). This package program allows five key
stellar parameters to be optimized at once: effective temperature ($T_{\rm
eff}$), surface gravity ($\log g$), metallicity ([M/H]), projected rotational
rate ($v$$\sin i$), and microturbulence velocity ($v_{\rm{mic}}$). The
synthetic spectra were generated by applying stellar atmosphere models
computed with the LLmodels code (Shulyak et al. 2004) to the radiative
transfer code SynthV (Tsymbal 1996), both of which are in the GSSP package.
Maxted et al. (2014) used models fitted to the observed flux distribution and
inferred the primary’s temperature $T_{\rm eff,A}$ to be $7400\pm 200$ K.
Thus, for the synthetic stellar models the temperature range was given as
6800–8000 K with a step of 100 K. The surface gravity was assigned $\log$
$g_{\rm A}$ (cgs) = 4.13, calculated from our binary modeling in the next
section. The micro and macro turbulence velocities were kept fixed at 1.0 km
s-1 and 4.21 km s-1, respectively, by the empirical relations provided in the
iSpec code (see Blanco-Cuaresma et al. 2014). [M/H] and $v_{\rm A}$$\sin i$
ranges were applied from $-0.8$ to $+0.8$ dex in 0.1 dex steps and 60–100 km
s-1 in 1 km s-1 steps, respectively. Initially, the UVES spectrum was
automatically normalized using the SUPPNet software555The SUPPNet is available
at https://rozanskit.com/suppnet/ (Różański et al. 2022).

The best fitting model was obtained by applying the $\chi^{2}$ minimization
method to the observed spectrum and the grids of synthetic spectra. In this
calculation, we used the UVES blue part of the spectral range 3700–4500
$\rm\AA$, which contains unique absorption lines (H9, H8, Ca II K, Hϵ, Hδ, Hγ)
for determining atmospheric parameters. Then, the observed spectrum was
manually re-normalized by comparison with the resulting synthetic spectrum
using the SUPPNet software. This grid search process was repeated until the
$\chi^{2}$ value among the GSSP results was minimal. The optimal values of
$T_{\rm eff,A}$, [M/H], and $v_{\rm A}$$\sin i$ were determined by polynomial
fitting the lowest $\chi^{2}$ values in grids of each parameter obtained from
the $\chi^{2}$ statistics, and their errors were estimated from the
corresponding $\pm 1\sigma$ confidence level values (cf. Lehmann et al. 2011):
$T_{\rm eff,A}$ = 7225$\pm 42$ K, [M/H] = 0.30$\pm$0.03 dex, and $v_{\rm
A}$$\sin i$ = 78$\pm$5 km s-1. Figure 4 shows the UVES spectrum at the primary
eclipse and its optimal model.

##  4 BINARY MODELING

High-precision TESS data for WASP 0346-21 showed nearly identical light curves
for both S4 and S31. The space-based observations present an ellipsoidal
variation outside eclipses and a box shape with overlapping relatively very
short oscillations in the primary eclipses. The light curve shape resembles
that of the EL CVn type (Maxted et al. 2014; Wang et al. 2020). Maxted et al.
(2014) analyzed the WASP survey data and the observed flux distribution of
WASP 0346-21, and classified the variable star as an EL CVn-type binary with
typical characteristics of a short $P_{\rm orb}$ = 0.9285752 days and a low
$q_{\rm ph}$ = 0.165. However, the spectroscopic elements are not known for
this system, so its binary properties are considered preliminary. To reliably
determine a binary star model for WASP 0346-21, we analyzed in detail the
archival TESS data and spectroscopic measurements using the Wilson-Devinney
(W-D) program (Wilson & Devinney 1971; Kallrath 2022) that is based on the
Roche model and allows for proximity effects in the RVs.

The combined synthetic modeling of the two datasets was performed in an almost
identical way for WASP 0131+28 (Lee et al. 2020). In this synthesis, the
surface temperature and rotation parameter of the cooler but more massive
component were set to be $T_{\rm eff,A}$ = 7225 $\pm$ 42 K and $F_{\rm A}$ =
0.819$\pm$0.071, respectively, obtained from synthetic model fits to the
observed UVES spectrum. The secondary companion WASP 0346-21 B was assumed to
be in synchronous rotation ($F_{\rm B}$ = 1.0) after some trials. The
logarithmic law for limb darkening was applied and its coefficients $x$ and
$y$ were adopted from the updated values of van Hamme (1993). The gravity-
darkening $g_{\rm A,B}$ and albedo $A_{\rm A,B}$ parameters were all assigned
as 1.0 from the components’ temperatures.

In general, a simultaneous binary modeling of light and RV curves is possible.
However, as previously mentioned, the orbital period of WASP 0346-21 may have
changed, and there is a time gap of about 1471 days between the RVs and TESS
measurements. For this reason, our combined analysis was carried out through
two steps (Lee et al. 2018): in the first step, the time-series TESS data were
analyzed applying the spectroscopic results. In the second, the ground-based
RV curves were analyzed with the light curve solution computed in the first
step. The modeling process was calculated iteratively until the corrections of
the free parameters were smaller than their corresponding uncertainties and
both types of observations were reasonably fitted. The binary modeling was
performed for various Roche models, but only detached configurations showed
satisfactory results. The best-fit solutions from this modeling are summarized
in Table 3. The synthetic RV and light curves are illustrated as red solid
curves in Figures 3 and 5, respectively. The third light of $l_{3}\approx$ 4.3
% was detected in the binary modeling, which may result from the presence of a
tertiary object, as discussed in the last section.

The combination of the light and RV parameters yielded the absolute dimension
for WASP 0346-21 collected in Table 4. This calculation used $T_{\rm eff}$⊙ =
5780 K and $M_{\rm bol}$⊙ = +4.73 as the solar surface temperature and
bolometric magnitude, respectively. We took the empirical bolometric
corrections (BCs) expressed as a function of temperature $\log T_{\rm eff}$
(Flower 1996; Torres 2010). The physical properties of WASP 0346-21 A and B
correspond approximately to an F0 main sequence and an ELM WD, respectively.
The distance to the WASP 0346-21 system was measured by adopting $V$ = 9.581
$\pm$ 0.03 and $E$($B-V$) = 0.033 $\pm$ 0.006 from the TESS Input Catalogue
(Paegert et al. 2022), and by applying $A_{\rm V}$ $\simeq$ 3.1$E(B-V)$ and
$l_{3}$ = 0.0425. Our EB-based distance of 269 $\pm$ 8 pc agrees within a
2-$\sigma$ error with 290 $\pm$ 5 pc taken from the Gaia DR3 parallax of 3.447
$\pm$ 0.063 mas (Gaia Collaboration 2022).

##  5 PULSATIONAL CHARACTERISTICS

The more massive primary star of WASP 0346-21 lies inside the main-sequence
instability domain of A/F-type pulsating variables on the Hertzsprung-Russell
(H-R) diagram, and the hotter secondary companion is located among extremely
low-mass pre-He WD variables (pre-ELMVs; Córsico et al. 2019; Hong et al.
2021, Lee et al. 2022a). For a reliable frequency analysis, we subtracted our
binary model in Table 3 from the time-series TESS observations, and analyzed
the light curve residuals with iterative, sequential pre-whitening on the
amplitude spectrum using the PERIOD04 software (Lenz & Breger 2005). Details
of this procedure were presented in a paper by Lee et al. (2014). Figure 6
displays the corresponding residuals for the full 2-min cadence data, clearly
showing the multiperiod oscillations.

To see if there are any changes in oscillation frequencies and amplitudes
between S4 and S31, with a time gap of about 2 years, and between two exposure
times of 2 min and 20 s, we divided the entire frequency range into two
overlapping parts of 0$-$80 day-1 and 70$-$$f_{\rm Ny}$, and separately
analyzed the overall residuals by each sector and cadence. The Nyquist limit
$f_{\rm Ny}$ is $\sim$360 day-1 and $\sim$2164 day-1, respectively, in 2-min
and 20-s cadences. In this process, we extracted all peak signals with SNR $>$
4 (Breger et al. 1993), and used 1.5 times the Rayleigh criterion of $\Delta
f_{\rm res}$ = 1.5/$\Delta T$ = 0.058 day-1 for frequency resolution (Loumos &
Deeming 1978), where $\Delta T$ = 26 days is the time span of each sector
used. The amplitude spectra for three datasets (2-min S4 and S31, and 20-s
S31) are displayed in the first to third panels of Figure 7. We can see strong
low-frequency signals between 15 day-1 and 30 day-1, and noticeable signals,
albeit with significantly lower amplitude, between 90 day-1 and 100 day-1.

Ten significant frequencies with amplitudes higher than $\sim$0.4 mmag were
detected identically in the three separate datasets and agreed with each other
within a 0.01 day-1 interval, which is about 6 times less than the frequency
resolution of $\Delta f_{\rm res}$. In the 2-min cadence data, the amplitudes
of the two most dominant frequencies, 26.348 day-1 and 17.683 day-1, were
suppressed by approximately 0.66 mmag and 0.78 mmag, respectively, in S31
compared to S4, and the 97.996 day-1 and 90.460 day-1 signals in the high-
frequency region were reduced by 0.005 mmag and 0.010 mmag, respectively,
within their 1-$\sigma$ errors. On the other hand, the 2-min and 20-s exposure
time data for Sector 31 had amplitudes that were consistent with each other
within uncertainties. In sum, there were no significant differences in the
frequencies and high-frequency amplitudes between datasets, but the dominant
low frequencies differed significantly in amplitudes between S4 and S31.

The bottom panel in Figure 7 is the PERIOD04 periodogram for all 2-min cadence
residuals combined from both S4 and S31. We extracted signals with a SNR
greater than 5 as possible pulsation frequencies, which is a detection
threshold corresponding to a 0.1 % false alarm probability for 2-min cadence
TESS data simulated by Baran & Koen (2021). A total of 58 candidate pulsations
were acquired, and their frequencies $f_{i}$, amplitudes $A_{i}$ and phases
$\phi$ are summarized in Table 5. The model curve synthesized from all
extracted frequencies is shown as a red solid on the lower panel in Figure 6.
Possible combination terms for these signals were carefully examined. We used
the frequency resolution of $\Delta f_{\rm res}$ = 0.058 day-1 corresponding
to the duration of one sector, because the 2-year observational gap between S4
and S31 was too long (Breger & Bischof 2002; Kim 2023). The resultant
combinations are presented in the last column of Table 5.

We believe that the four frequencies ($f_{11}$, $f_{16}$, $f_{41}$, $f_{47}$)
below 4 day-1 are likely to be orbital harmonics or instrumental artifacts
that were not removed by detrending. Excluding these sidelobes, the low
frequencies correspond to pulsation periods of $P_{\rm pul}$ = 37$-$100 min.
Their pulsation constants and period ratios are in ranges of $Q$ =
0.014$-$0.038 days and $P_{\rm pul}/P_{\rm orb}$ = 0.028$-$0.075,
respectively, which are typical values for $\delta$ Sct pulsators in EBs
(Zhang et al. 2013; Kahraman Aliçavuş et al. 2017). The pulsation constants of
the two strongest frequencies $f_{1}$ and $f_{2}$ are about 0.021 days and
0.031 days, respectively. Compared to 1.5 $M_{\odot}$ models of Fitch (1981),
they can be identified as fundamental (F) and second harmonic (2H) radial
$p$-modes, in the same order.

##  6 DISCUSSION AND CONCLUSIONS

We present a characterization of WASP 0346-21 by analyzing the VLT/UVES high-
resolution spectra and the TESS photometric data in S4 and S31. The BF
profiles for the echelle spectra revealed the presence of a new tertiary
object in addition to the two binary components. We measured the RVs of the
three stars by the BF fits. The third body’s RVs exhibit an average velocity
of 36.7$\pm$0.6 km s-1 during the 7.2-day spectroscopic observation period,
with no trend in observation time or orbital phase. Using the GSSP package, we
compared the observed UVES spectrum at the primary eclipse with all possible
synthetic models, and utilized the $\chi^{2}$ minimization method to find the
atmospheric parameters of $T_{\rm eff,A}$ = 7225$\pm 42$ K, [M/H] =
0.30$\pm$0.03 dex, and $v_{\rm A}$$\sin i$ = 78$\pm$5 km s-1.

The light and RV curve analysis combined with the atmospheric parameters
allows us to characterize each component of the EB system. The modeling
results for WASP 0346-21 indicate the existence of the third light $l_{3}$ =
0.043$\pm$0.004 in the TESS data. This value roughly corresponds to the
average contribution (4.7 %) of the tertiary component (C) to the total system
light estimated from the BF profiles for the red region spectra (e.g.,
Rucinski & Pribulla 2008; Nelson 2022). Then, the $l_{3}$ source might be
identified as WASP 0346-21 C detected in the UVES spectra. The physical
properties of WASP 0346-21 AB were derived from the light and RV parameters as
follows: masses of $M_{\rm A}$ = 1.57$\pm$0.05 M⊙ and $M_{\rm B}$ =
0.19$\pm$0.01 M⊙, radii of $R_{\rm A}$ = 1.78$\pm$0.04 M⊙ and $R_{\rm B}$ =
0.31$\pm$0.02 M⊙, effective temperatures of $T_{\rm eff,A}$ = 7225$\pm$42 K
and $T_{\rm eff,B}$ = 10,655$\pm$146 K, and luminosities of $L_{\rm A}$ =
7.7$\pm$0.4 L⊙ and $L_{\rm B}$ = 1.1$\pm$0.2 L⊙. The low $q$ and $M_{2}$
combination of the short-period eclipsing pair is fully consistent with being
an EL CVn binary (Maxted et al. 2014; Chen et al. 2017; Lee et al. 2020).

WASP 0346-21 A and B are marked as star symbols on the H-R diagram in Figure
8. Here, the solid and dash oblique lines denote the instability edges of the
$\delta$ Sct and $\gamma$ Dor variables, respectively. The gray and black
lines are WD evolution tracks for metallicities $Z$ = 0.001 and 0.01 with
masses between 0.183 M⊙ and 0.190 M⊙ (Istrate et al. 2016). As shown in this
diagram, WASP 0346-21 A is located within an overlapping main sequence region
of the two pulsation types, and its secondary companion of 0.185 $\pm$ 0.013
$M_{\odot}$ is in full agreement with the low-mass He WD model for $Z$ = 0.01
and is currently thought to be evolving towards higher temperatures at the
constant $L$ stage. During the pre-He WD phase, the lifetime ($t$) of WASP
0346-21 B depends on its mass $M_{\rm WD}$, which is calculated to be $\sim$8
$\times$ 108 yr from the $M_{\rm WD}-t$ relation by Chen et al. (2017). The
post-mass transfer EBs such as R CMa and EL CVn binaries have been proposed to
be formed from the stable Roche-lobe overflow channel (Chen et al. 2017; Lee
et al. 2018). This evolution channel predicts that there is a close
correlation between $P_{\rm orb}$ and $M_{\rm WD}$ (Rappaport et al. 1995; Lin
et al. 2011). WASP 0346-21 B is well-matched with the relationship between the
two in a paper of Lin et al. (2011). This implies that WASP 0346-21 AB is a
post-mass transfer binary produced through a stable mass transfer evolution
during its red giant phase.

To find out the population membership of WASP 0346-21, we obtained its space
motion ($U,V,W$) and Galactic orbit ($J_{\rm z}$, $e$) using the same solar
values and procedure as Lee et al. (2020). These were calculated by applying
the astrometric data from the Gaia DR3 (Gaia Collaboration 2022) and our
center-of-mass $\gamma$ velocity for the eclipsing components. We plotted the
kinematical data of our target star on the $U-V$ and $J_{\rm z}-e$ diagrams in
Figure 9, together with the other double-lined EL CVn stars: EL CVn (Wang et
al. 2020), KOI-81 (Matson et al. 2015), WASP 0131+28 (Lee et al. 2020), WASP
0247-25 (Maxted et al. 2013; Kim et al. 2021), WASP 0843-11 (Hong et al.
2021), and WASP 1625-04 (Lee et al. 2022b). The location of WASP 0346-21 lies
within the thick-disk regions in the two diagrams, which are useful for the
population classification of WDs (Pauli et al. 2006). The classification of
WASP 0346-21 into the thick-disk population ($Z\approx 0.01$; Chen et al.
2021) is concurrent with the metallicity $Z$ = 0.01 obtained from the He-core
WD model fit.

Using a relation of $v_{\rm sync}$ = $2\pi R$/$P_{\rm orb}$, we computed the
synchronized rotations of the binary components to be $v_{\rm A,sync}$ = 97.0
$\pm$ 0.5 km s-1 and $v_{\rm B,sync}$ = 16.8 $\pm$ 1.3 km s-1, respectively.
Our measured rotation $v_{\rm A}$ indicates that WASP 0346-21 A is spinning
0.82 times slower than its synchronous value $v_{\rm A,sync}$. The sub-
synchronization mechanism is currently not well understood in the post-mass
transfer EL CVn EBs (Wang et al. 2020; Kim et al. 2021). However, Fuller &
Felce (2023) reported that the slow rotation in close binaries could be caused
by the action of a circumbinary object. In addition, binary evolution theories
indicate that EL CVn binaries are inner close pairs of hierarchical triplets
descended from short-period ($P_{\rm orb}<$ $\sim$3 days) main-sequence
binaries. Consistent with this prediction, Lagos et al. (2020) found potential
tertiary objects in their observations of all five EL CVn stars. These
results, together with the third-light detection, imply that WASP 0346-21 C,
discovered in the UVES spectra, is a circumbinary star that is physically
associated with WASP 0346-21 AB. The tertiary object may have played a
significant role in the evolution of the initial binary into the present
closer pair through re-distribution of angular momentum between them (Eggleton
& Kisseleva-Eggleton 2006; Tokovinin et al. 2006).

The echelle spectral analysis and binary modeling presented in this paper
indicate that WASP 0346-21 is a triple system (AB)C, which comprises a post-
mass transfer binary (AB) with a short period of $<$ 1 day and a distant
tertiary companion (C) with a light contribution of 4.3 % in the TESS band.
The fundamental stellar parameters and pulsational characteristics of the
eclipsing components, and their locations in the H-R diagram demonstrate that
the low frequencies from 14 day-1 to 39 day-1 are mostly $\delta$ Sct
pulsations arising from WASP 0346-21 A, and that both high frequencies of
97.996 day-1 and 90.460 day-1 are oscillating signals associated with the pre-
ELM WD companion (Breger 2000; Córsico et al. 2019). Then, WASP 0346-21 is the
first triple system to be spectroscopically detected and the sixth EBs to
exhibit both $\delta$ Sct and pre-ELMV multiperiod pulsations, among the EL
CVn stars. These discoveries make WASP 0346-21 a key object for studying the
dynamical evolution and asteroseismology of the post-mass transfer binaries.

This article is based on VLT/UVES spectra made with ESO under programme
094.D-0027(A) and photometric data collected by the TESS mission. We
appreciate the helpful comments and suggestions of the anonymous referee. This
research has made use of the Simbad database maintained at CDS, Strasbourg,
France, and was supported by the KASI grant 2024-1-832-01 and the project
Cooperatio - Physics of the Charles University in Prague.

## References

  * Baran & Koen (2021) Baran, A. S., & Koen, C. 2021, AcA, 71, 113
  * Blanco-Cuaresma et al. (2014) Blanco-Cuaresma, S., Soubiran, C., Heiter, U., et al. 2014, A&A, 569, A111
  * Breger (2000) Breger, M. 2000, in ASP Conf. Ser. 210, Delta Scuti and Related Stars, ed. M. Breger and M. Montgomery (San Francisco, CA: ASP), 3
  * Breger & Bischof (2002) Breger, M., & Bischof, K. M. 2002, A&A, 385, 537
  * Breger et al (1993) Breger, M., Stich, J., Garrido, R., et al. 1993, A&A, 271, 482
  * Breton et al (2012) Breton, R. P., Rappaport, S. A., van Kerkwijk, M. H., & Carter, J. A. 2012, ApJ, 748, 115
  * Cakirli (2015) Çakirli, Ö. 2015, New Astron., 38, 55
  * Calcaferro et al (2018) Calcaferro, L. M., Althaus, L. G., & Corsico, A. H. 2018, A&A, 614, A49
  * Carter et al (2011) Carter, J. A., Rappaport, S., & Fabrycky, D. 2011, ApJ, 728, 139
  * Chen et al (2017) Chen, X., Maxted, P. F. L., Li, J., & Han, Z. 2017, MNRAS, 467, 1874
  * Chen et al (2021) Chen, D.-C., Yang, J.-Y., Xie, J.-W., et al. 2021, AJ, 162, 100
  * Coelho et al (2005) Coelho, P., Barbuy, B., Melendez, J., Sciavon, R. P., & Castilho, B. V. 2005, A&A, 443, 735
  * Corsico et al (2019) Córsico, A. H., Althaus, L. G., Miller Bertolami, M. M., & Kepler, S. O. 2019, A&ARv, 27, 7
  * Dekker et al. (2000) Dekker, H., D’Odorico, S., Kaufer, A., et al. 2000, Proc. SPIE, 4008, 534
  * Eggleton & Kisseleva-Eggleton (2006) Eggleton, P. P., & Kisseleva-Eggleton, L. 2006, Ap&SS, 304, 75
  * Faigler et al (2015) Faigler, S., Kull, I., Mazeh, T., et al. 2015, ApJ, 815, 26
  * Fitch (1981) Fitch, W. S. 1981, ApJ, 249, 218
  * Flower (1996) Flower, P. J. 1996, ApJ, 469, 355
  * Fuller & Felce (2023) Fuller, J., & Felce, C. 2023, MNRAS, 527, L103
  * GAIA (2022) Gaia Collaboration 2022, VizieR Online Data Catalog, I/355
  * Hong et al (2015) Hong, K., Lee, J. W., Kim, S.-L., et al. 2015, AJ, 150, 131
  * Hong et al (2021) Hong, K., Lee, J. W., Koo, J.-R., et al. 2021, AJ, 161, 137
  * Istrate et al (2016) Istrate, A. G., Marchant, P., Tauris, T. M., et al. 2016, A&A, 595, A35
  * Kahraman Alicavus et al (2017) Kahraman Aliçavuş, F., Soydugan, E., Smalley, B., & Kubát, J. 2017, MNRAS, 470, 915
  * Kallinger et al (2008) Kallinger, T., Reegen, P., & Weiss, W. W. 2008, A&A, 481, 571
  * Kallrath (2022) Kallrath, J. 2022, Galaxies, 10, 17
  * Kepler et al (2017) Kepler, S. O., Koester, D., Romero, A. D., Ourique, G., & Pelisoli, I. 2017, in ASP Conf. Ser. 509, 20th European White Dwarf Workshop, ed. P. E. Tremblay, B. Gaensicke, & T. Marsh (San Francisco, CA: ASP), 421
  * Kilic et al (2007) Kilic, M., Stanek, K. Z., & Pinsonneault, M. H. 2007, ApJ, 671, 761
  * Kim (2023) Kim, S.-L. 2023, ApJ, 948, 16
  * Kim et al (2021) Kim, S.-L., Lee, J. W., Lee, C.-U., et al. 2021, AJ, 162, 212
  * Kleinman et al (2013) Kleinman, S. J., Kepler, S. O., Koester, D., et al. 2013, ApJS, 204, 5
  * Kwee & van Woerden (1956) Kwee, K. K., & van Woerden, H. 1956, BAN, 12, 327
  * Lagos et al (2020) Lagos, F., Schreiber, M. R., Parsons, S. G., et al. 2020, MNRAS, 499, L121
  * Lee et al (2022a) Lee, J. W., Hong, K., Kim, H.-Y., & Park, J.-H. 2022a, MNRAS, 515, 4702
  * Lee et al (2018) Lee, J. W., Hong, K., Koo, J.-R., & Park, J.-H. 2018, AJ, 155, 5
  * Lee et al (2022b) Lee, J. W., Hong, K., & Park, J.-H. 2022b, MNRAS, 511, 654
  * Lee et al (2014) Lee, J. W., Kim, S.-L., Hong, K., Lee, C.-U., & Koo, J.-R. 2014, AJ, 148, 37
  * Lee et al (2020) Lee, J. W., Koo, J.-R., Hong, K., & Park, J.-H. 2020, AJ, 160, 49
  * Lehmann et al. (2011) Lehmann, H., Tkachenko, A., Semaan, T., et al. 2011, A&A, 526, A124
  * Lenz & Breger (2005) Lenz, P., & Breger, M. 2005, Comm. Asteroseismology, 146, 53
  * Li et al (2019) Li, Z., Chen, X., Chen, H.-L., & Han, Z. 2019, ApJ, 871, 148
  * Lin et al (2011) Lin, J., Rappaport, S., Podsiadlowski, P., et al. 2011, ApJ, 732, 70
  * Loumos & Deeming (1978) Loumos, G. L., & Deeming T. J. 1978, Ap&SS, 56, 285
  * Lu et al (2001) Lu, W., Rucinski, S. M., & Ogyoza, W. 2001, AJ, 122, 402
  * Matson et al (2015) Matson, R. A., Gies, D. R., Guo, Z., et al. 2015, ApJ, 806, 155
  * Maxted et al (2014) Maxted, P. F. L., Bloemen, S., Heber, U., et al. 2014, MNRAS, 437, 1681
  * Maxted et al (2013) Maxted, P. F. L., Serenelli, A. M., Miglio, A., et al. 2013, Natur, 498, 463
  * Mazeh & Zucker (1994) Mazeh, T., & Zucker, S. 1994, Ap&SS, 212, 349
  * Nelson (2022) Nelson, R. H. 2022, RMxAA, 58, 223
  * Paegert (2022) Paegert, M., Stassun, K. G., Collins, K. A., et al. 2022, VizieR Online Data Catalog, IV/39
  * Pauli et al (2006) Pauli, E.-M., Napiwotzki, R., Heber, U., Altmann, M., & Odenkirchen, M. 2006, A&A, 447, 173
  * Peng et al (2024) Peng, Y., Wang, K., & Ren, A. 2024, New Astron., 107, 102153
  * Pilecki et al (2017) Pilecki, B., Gieren, W., Smolec, S., et al. 2017, ApJ, 842, 110
  * Pols et al (1998) Pols, O. R., Schroder, K.-P., Hurley, J. R., Tout, C. A., & Eggleton, P. P. 1998, MNRAS, 298, 525
  * Rappaport et al (2015) Rappaport, S., Nelson, L., Levine, A., et al. 2015, ApJ, 803, 82
  * Rappaport et al. (1995) Rappaport, S., Podsiadlowski, P., Joss, P. C., Di Stefano, R., & Han, Z. 1995, MNRAS, 273, 731
  * Ricker et al (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, JATIS, 1, 014003
  * Rolland et al. (2002) Rolland, A., Costa, V., Rodríguez, E., et al. 2002, Comm. Asteroseismology, 142, 57
  * Rozanski et al (2022) Różański, T., Niemczura, E., Lemiesz, J., et al. 2022, A&A, 659, A199
  * Rucinski (2002) Rucinski, S. M. 2002, AJ, 124, 1746
  * Rucinski & Pribulla (2008) Rucinski, S. M., & Pribulla, T. 2008, MNRAS, 388, 1831
  * Shulyak et al. (2004) Shulyak, D., Tsymbal, V., Ryabchikova, T., et al. 2004, A&A, 428, 993
  * Simkin (1974) Simkin, S. M. 1974, A&A, 31, 129
  * Soydugan et al. (2006) Soydugan, E., İbanoǧlu, C., Soydugan, F., Akan, M. C., & Demircan, O. 2006, MNRAS, 366, 1298
  * Tkachenko (2015) Tkachenko, A. 2015, A&A, 581, A129
  * Tokovinin et al (2006) Tokovinin, A., Thomas, S., Sterzik, M., & Udry, S. 2006, A&A, 450, 681
  * Tonry & Davis (1979) Tonry, J., & Davis, M. 1979, AJ, 84, 1511
  * Torres (2010) Torres, G. 2010, AJ, 140, 1158
  * Tsymbal (1996) Tsymbal, V. 1996, in ASP Conf. Ser. 108, M.A.S.S., Model Atmospheres and Spectrum Synthesis, ed. S. J. Adelman, F. Kupka, & W. W. Weiss (San Francisco, CA: ASP), 198
  * van Hamme (1993) van Hamme, W. 1993, AJ, 106, 209
  * van Kerkwijk et al (2010) van Kerkwijk, M. H., Rappaport, S. A., Breton, R. P., et al. 2010, ApJ, 715, 51
  * van Roestel et al (2018) van Roestel, J., Kupfer, T., Ruiz-Carmona, R., et al. 2018, MNRAS, 475, 2560
  * Wang et al. (2020) Wang, L., Gies, D. R., Lester, K. V., et al. 2020, AJ, 159, 4
  * Wang et al (2019) Wang, K., Zhang, X., Luo, Y., & Luo, C. 2019, MNRAS, 486, 2462
  * Warner et al. (2003) Warner, P. B., Kaye, A. B., & Guzik, J. A., 2003, ApJ, 593, 1049
  * Wilson & Devinney (1971) Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605
  * Zhang et al (2013) Zhang, X. B., Luo, C. Q., & Fu, J. N. 2013, ApJ, 777, 77

Figure 1: TESS observations of WASP 0346-21 obtained during Sectors 4 and 31.
The top panel represents 2-min cadence data (blue and green) from both
sectors, and the other panels detail 20-s cadence measurements (cyan) from
Sector 31. The gray lines are the sum of the two model curves computed from
the binary star parameters of Table 3 and the 58-frequency fit of Table 5.
Figure 2: Sample BF profiles for three orbital phases ($\phi$) obtained with
the RaveSpan code. The solid black line indicates the BF profile, which is
fitted with three rotational profile functions representing the primary
(blue), secondary (green), and third (cyan) components. In the top panel, the
secondary companion (B) is not visible as it is obscured by the primary
component.  Figure 3: RV curves of WASP 0346-21 with fitted models. The blue,
green, and cyan colors denote the primary (A), secondary (B), and third (C)
components, respectively. The circles and squares are the RV measurements in
the blue (4440–4520 $\AA$) and red (6310–6390 $\AA$) spectral ranges,
respectively. The solid curves represent the results of our binary model using
the W-D code, and the dotted line denotes the average RV of $+$36.7 km s-1 for
the third component.  Figure 4: Spectra of WASP 0346-21 at a conjunction phase
of 0.013. The black and red solid lines represent the observed UVES and best-
fitting synthetic spectra, respectively.  Figure 5: The top panel displays the
phased light curve of WASP 0346-21 with the fitted model. The blue and green
circles are the 2-min cadence measurements from Sectors 4 and 31,
respectively, and the red solid curve is computed with our W-D fit. The middle
and bottom panels represent the corresponding residuals for 2-min and 20-s
cadence data, respectively, from the synthetic curve.  Figure 6: Light curve
residuals distributed in BJD after subtraction of the binarity effects from
the 2-min cadence TESS observations. The lower panel presents a short section
of the residuals marked using the inset box in the upper panel. The synthetic
curve is computed from the 58-frequency fit to the residuals.  Figure 7:
PERIOD04 periodograms for the binary-subtracted light residuals. The first to
third panels show the amplitude spectra for the residuals in each sector (4
and 31) and cadence (2 min and 20 s), while the bottom panel is obtained using
the entire 2-min cadence data. In each panel, the amplitude spectrum at
frequencies above 80 day-1 is blown-up to show pre-He WD pulsations and is
shown as a gray line.  Figure 8: Position in the H-R diagram of WASP 0346-21 A
and B (star symbols). The green solid line is the zero-age main sequence (Pols
et al. 1998), and the coloured oblique solid and dash lines denote the
instability strips of $\delta$ Sct (Rolland et al. 2002; Soydugan et al. 2006)
and $\gamma$ Dor stars (Warner et al. 2003; Çakirli 2015), respectively. The
gray and black lines represent the evolutionary tracks of He-core WDs with
different metallicities ($Z$) and masses ($M$) from the models of Istrate et
al. (2016).  Figure 9: (a) $U-V$ and (b) $J_{z}-e$ diagrams for WASP 0346-21
(star symbols) and the other double-lined EL CVn binaries (circles). The dot
and solid eclipses in the left panel represent the thin and thick disk
contours, respectively, and the solid box in the right panel indicates the
thick-disk region (Pauli et al. 2006). Our target star represents a thick-disk
population together with WASP 0247-25.

Table 1: TESS Eclipse Timings of WASP 0346-21

BJD | Error | Epoch | $O-C$ | Min
---|---|---|---|---
2,458,411.17012 |  $\pm$0.00045 |  $-$790.5 |  $+$0.00148 | II
2,458,411.63412 |  $\pm$0.00023 |  $-$790.0 |  $+$0.00120 | I
2,458,412.09702 |  $\pm$0.00018 |  $-$789.5 |  $-$0.00019 | II
2,458,412.56058 |  $\pm$0.00016 |  $-$789.0 |  $-$0.00092 | I
2,458,413.02630 |  $\pm$0.00030 |  $-$788.5 |  $+$0.00051 | II
2,458,413.49122 |  $\pm$0.00020 |  $-$788.0 |  $+$0.00114 | I
2,458,413.95577 |  $\pm$0.00021 |  $-$787.5 |  $+$0.00141 | II
2,458,414.41820 |  $\pm$0.00007 |  $-$787.0 |  $-$0.00045 | I
2,458,414.88220 |  $\pm$0.00033 |  $-$786.5 |  $-$0.00074 | II
2,458,415.34739 |  $\pm$0.00012 |  $-$786.0 |  $+$0.00016 | I

Note. — This table is available in its entirety in machine-readable form. A
portion is shown here for guidance regarding its form and content.

Table 2: Radial velocities of WASP 0346-21a

BJD | $V_{\rm A}$ | $\sigma_{\rm A}$ | $V_{\rm B}$ | $\sigma_{\rm B}$ | $V_{\rm C}$ | $\sigma_{\rm C}$ | Regionb
---|---|---|---|---|---|---|---
(2,456,000+) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1) |
932.65263 | $58.22$ | 0.23 | $-199.66$ | 0.42 | 35.70 | 0.18 | red
932.65280 | $52.77$ | 0.39 | $-196.74$ | 1.00 | 35.86 | 0.43 | blue
932.70797 | $56.70$ | 0.26 | $-177.41$ | 0.48 | 36.46 | 0.17 | red
932.70811 | $49.11$ | 0.39 | $-178.36$ | 0.81 | 36.85 | 0.53 | blue
932.76111 | $52.22$ | 0.26 | $-130.74$ | 0.35 | 36.71 | 0.19 | red
932.76121 | $44.95$ | 0.38 | $-131.87$ | 0.93 | 36.71 | 0.43 | blue
936.66353 | $17.61$ | 0.25 | $139.44$ | 0.47 | 36.84 | 0.18 | red
936.66363 | $11.26$ | 0.40 | $141.39$ | 0.83 | 36.77 | 0.44 | blue
936.68108 | $16.99$ | 0.29 | $166.09$ | 0.75 | 38.13 | 0.24 | red
936.68119 | $11.15$ | 0.40 | $164.74$ | 0.99 | 37.03 | 0.41 | blue
936.70825 | $12.50$ | 0.28 | $199.35$ | 0.58 | 36.85 | 0.23 | red
936.70838 | $3.83$ | 0.44 | $195.49$ | 1.02 | 36.71 | 0.37 | blue
937.71650 | $5.16$ | 0.30 | $257.21$ | 0.41 | 36.95 | 0.19 | red
937.71668 | $-0.61$ | 0.40 | $255.81$ | 0.99 | 37.67 | 0.43 | blue
939.85328 | $35.78$ | 0.22 | $\dots$ | … | 36.33 | 0.16 | red
939.85338 | $28.38$ | 0.35 | $\dots$ | … | 36.24 | 0.33 | blue

aafootnotetext: $V_{\rm A}$, $V_{\rm B}$, and $V_{\rm C}$ represent the
measured RVs of the primary, secondary, and third stars, respectively, and
$\sigma_{\rm A}$, $\sigma_{\rm B}$, and $\sigma_{\rm C}$ are their
uncertainties.

bbfootnotetext: Blue and red indicate the spectral regions of 4440–4520 $\AA$
and 6310–6390 $\AA$, respectively.

Table 3: Light and RV Parameters of WASP 0346-21

Parameter | Primary | Secondary
---|---|---
$T_{0}$ (BJD) | 2,459,145.207562$\pm$0.000054
$P_{\rm orb}$ (day) | 0.92857550$\pm$0.00000010
$i$ (deg) | 79.01$\pm$0.54
$T$ (K) | 7225$\pm$42 | 10,655$\pm$146
$\Omega$ | 2.865$\pm$0.043 | 3.288$\pm$0.067
$\Omega_{\rm in}$a | 2.012
$F$ | 0.819$\pm$0.071 | 1.0
$X$, $Y$ | 0.642, 0.259 | 0.705, 0.067
$x$, $y$ | 0.526, 0.290 | 0.398, 0.196
$l/(l_{1}+l_{2}+l_{3})$ | 0.8993$\pm$0.0028 | 0.0582
$l_{3}$b | 0.0425$\pm$0.0037
$r$ (pole) | 0.3630$\pm$0.0060 | 0.0635$\pm$0.0046
$r$ (point) | 0.3750$\pm$0.0069 | 0.0638$\pm$0.0047
$r$ (side) | 0.3701$\pm$0.0065 | 0.0636$\pm$0.0046
$r$ (back) | 0.3728$\pm$0.0067 | 0.0638$\pm$0.0047
$r$ (volume)c | 0.3687$\pm$0.0065 | 0.0637$\pm$0.0047
Spectroscopic orbits:
$T_{0}$ (BJD) | 2,456,938.9125$\pm$0.0017
$a$ (R⊙) | 4.831$\pm$0.068
$\gamma$ (km s-1) | 32.26$\pm$0.67
$K_{1}$ (km s-1) | 27.2$\pm$1.7
$K_{2}$ (km s-1) | 231.3$\pm$3.2
$q$ | 0.1175$\pm$0.0075

aafootnotetext: Potential for the inner critical Roche surface.

bbfootnotetext: Value at 0.25 orbital phase.

ccfootnotetext: Mean volume radius.

Table 4: Absolute Parameters of WASP 0346-21  Parameter | Primary | Secondary
---|---|---
$M$ ($M_{\odot}$) | 1.572$\pm$0.049 | 0.185$\pm$0.013
$R$ ($R_{\odot}$) | 1.780$\pm$0.040 | 0.308$\pm$0.023
$\log$ $g$ (cgs) | 4.134$\pm$0.024 | 4.729$\pm$0.072
$\rho$ ($\rho_{\odot}$) | 0.279$\pm$0.021 | 6.4$\pm$1.5
$v_{\rm sync}$ (km s-1) | 97.0$\pm$2.2 | 16.8$\pm$1.3
$v$$\sin$$i$ (km s-1) | 78$\pm$5 |
$T_{\rm eff}$ (K) | 7225$\pm$42 | 10,655$\pm$146
$L$ ($L_{\odot}$) | 7.74$\pm$0.39 | 1.09$\pm$0.17
$M_{\rm bol}$ (mag) | 2.50$\pm$0.05 | 4.63$\pm$0.17
BC (mag) | 0.03$\pm$0.01 |  $-$0.39$\pm$0.03
$M_{\rm V}$ (mag) | 2.47$\pm$0.05 | 5.02$\pm$0.18
Distance (pc) | 269$\pm$8
Table 5: Results of the multiple frequency analysis for WASP 0346-21a,b

| Frequency $f_{i}$ | Amplitude $A_{i}$ | Phase $\phi_{i}$ | SNRc | Remark
---|---|---|---|---|---
| (day-1) | (mmag) | (rad) |  |
$f_{1}$ | 26.34818$\pm$0.00001 | 1.619$\pm$0.032 | 4.75$\pm$0.06 | 85.94 |
$f_{2}$ | 17.68348$\pm$0.00001 | 1.559$\pm$0.037 | 4.19$\pm$0.07 | 73.11 |
$f_{3}$ | 16.65456$\pm$0.00001 | 1.166$\pm$0.037 | 3.55$\pm$0.09 | 54.10 | $f_{2}-f_{\rm orb}$
$f_{4}$ | 19.90132$\pm$0.00001 | 0.971$\pm$0.038 | 1.75$\pm$0.12 | 43.29 | $f_{3}+3f_{\rm orb}$
$f_{5}$ | 28.09058$\pm$0.00001 | 0.612$\pm$0.028 | 1.56$\pm$0.14 | 37.11 |
$f_{6}$ | 26.24409$\pm$0.00001 | 0.652$\pm$0.033 | 2.78$\pm$0.15 | 34.07 |
$f_{7}$ | 16.57004$\pm$0.00003 | 0.329$\pm$0.037 | 1.72$\pm$0.33 | 15.26 | $f_{2}-f_{\rm orb}$
$f_{8}$ | 15.96747$\pm$0.00002 | 0.444$\pm$0.035 | 1.81$\pm$0.23 | 21.99 |
$f_{9}$ | 14.50208$\pm$0.00002 | 0.401$\pm$0.031 | 0.66$\pm$0.22 | 22.48 | $f_{3}-2f_{\rm orb}$
$f_{10}$ | 17.66355$\pm$0.00002 | 0.428$\pm$0.036 | 3.02$\pm$0.25 | 20.18 | $f_{2}$
$f_{11}$ | 1.07421$\pm$0.00003 | 0.340$\pm$0.041 | 4.61$\pm$0.35 | 14.18 | $f_{\rm orb}$
$f_{12}$ | 16.60748$\pm$0.00003 | 0.362$\pm$0.037 | 3.55$\pm$0.30 | 16.86 | $f_{3}$
$f_{13}$ | 26.34213$\pm$0.00002 | 0.362$\pm$0.032 | 5.05$\pm$0.26 | 19.17 | $f_{1}$
$f_{14}$ | 16.13082$\pm$0.00003 | 0.327$\pm$0.035 | 3.88$\pm$0.32 | 15.85 |
$f_{15}$ | 28.50201$\pm$0.00002 | 0.300$\pm$0.027 | 0.24$\pm$0.26 | 18.94 |
$f_{16}$ | 2.15245$\pm$0.00003 | 0.299$\pm$0.037 | 3.94$\pm$0.37 | 13.70 | $2f_{\rm orb}$
$f_{17}$ | 19.25117$\pm$0.00003 | 0.286$\pm$0.038 | 3.20$\pm$0.39 | 12.94 | $2f_{2}-f_{14}$
$f_{18}$ | 21.27300$\pm$0.00004 | 0.272$\pm$0.037 | 2.46$\pm$0.40 | 12.62 |
$f_{19}$ | 17.62200$\pm$0.00003 | 0.278$\pm$0.036 | 3.45$\pm$0.38 | 13.10 | $f_{10}$
$f_{20}$ | 18.95194$\pm$0.00004 | 0.240$\pm$0.039 | 0.99$\pm$0.47 | 10.57 |
$f_{21}$ | 14.42441$\pm$0.00004 | 0.214$\pm$0.030 | 2.85$\pm$0.41 | 12.15 | $f_{2}-3f_{\rm orb}$
$f_{22}$ | 22.73966$\pm$0.00005 | 0.207$\pm$0.037 | 2.89$\pm$0.52 | 9.63 |
$f_{23}$ | 15.51922$\pm$0.00004 | 0.201$\pm$0.034 | 4.66$\pm$0.49 | 10.23 | $f_{2}-2f_{\rm orb}$
$f_{24}$ | 17.73007$\pm$0.00004 | 0.248$\pm$0.037 | 2.31$\pm$0.43 | 11.53 | $f_{2}$
$f_{25}$ | 37.08501$\pm$0.00004 | 0.196$\pm$0.026 | 0.54$\pm$0.39 | 12.78 |
$f_{26}$ | 14.45765$\pm$0.00004 | 0.196$\pm$0.030 | 0.89$\pm$0.45 | 11.05 | $f_{2}-3f_{\rm orb}$
$f_{27}$ | 33.13303$\pm$0.00004 | 0.175$\pm$0.025 | 5.48$\pm$0.42 | 12.00 | $2f_{7}$
$f_{28}$ | 15.06981$\pm$0.00005 | 0.173$\pm$0.033 | 5.56$\pm$0.56 | 9.01 | $f_{14}-f_{\rm orb}$
$f_{29}$ | 16.62178$\pm$0.00005 | 0.201$\pm$0.037 | 0.51$\pm$0.53 | 9.38 | $f_{3}$
$f_{30}$ | 17.58988$\pm$0.00005 | 0.188$\pm$0.036 | 2.52$\pm$0.57 | 8.86 | $f_{19}$
$f_{31}$ | 38.76764$\pm$0.00004 | 0.162$\pm$0.025 | 1.32$\pm$0.46 | 10.92 | $2f_{4}-f_{\rm orb}$
$f_{32}$ | 22.85869$\pm$0.00006 | 0.153$\pm$0.037 | 5.93$\pm$0.71 | 7.05 |
$f_{33}$ | 16.91802$\pm$0.00007 | 0.146$\pm$0.037 | 0.67$\pm$0.74 | 6.76 | $2f_{4}-f_{32}$
$f_{34}$ | 15.52936$\pm$0.00005 | 0.172$\pm$0.034 | 2.71$\pm$0.57 | 8.74 | $f_{2}-2f_{\rm orb}$
$f_{35}$ | 15.90096$\pm$0.00007 | 0.134$\pm$0.034 | 3.07$\pm$0.75 | 6.70 | $f_{31}-f_{32}$
$f_{36}$ | 26.76464$\pm$0.00006 | 0.130$\pm$0.032 | 2.11$\pm$0.72 | 6.92 |
$f_{37}$ | 35.15393$\pm$0.00005 | 0.125$\pm$0.026 | 2.34$\pm$0.61 | 8.21 | $2f_{30}$
$f_{38}$ | 17.22793$\pm$0.00009 | 0.109$\pm$0.036 | 2.06$\pm$0.96 | 5.24 | $f_{25}-f_{4}$
$f_{39}$ | 21.19250$\pm$0.00008 | 0.120$\pm$0.037 | 4.56$\pm$0.90 | 5.55 | $f_{31}-f_{19}$
$f_{40}$ | 26.69991$\pm$0.00007 | 0.119$\pm$0.032 | 2.94$\pm$0.79 | 6.34 |
$f_{41}$ | 3.23351$\pm$0.00008 | 0.115$\pm$0.035 | 4.20$\pm$0.89 | 5.62 | $f_{4}-f_{3}$
$f_{42}$ | 15.31097$\pm$0.00008 | 0.116$\pm$0.034 | 1.68$\pm$0.85 | 5.91 |
$f_{43}$ | 36.61512$\pm$0.00006 | 0.114$\pm$0.026 | 2.36$\pm$0.66 | 7.61 | $f_{20}+f_{2}$
$f_{44}$ | 28.67571$\pm$0.00006 | 0.113$\pm$0.027 | 0.04$\pm$0.70 | 7.18 |
$f_{45}$ | 17.69393$\pm$0.00006 | 0.161$\pm$0.037 | 3.70$\pm$0.67 | 7.51 | $f_{2}$
$f_{46}$ | 22.16505$\pm$0.00008 | 0.115$\pm$0.036 | 2.29$\pm$0.93 | 5.40 | $f_{31}-f_{3}$
$f_{47}$ | 1.70530$\pm$0.00010 | 0.106$\pm$0.040 | 2.47$\pm$1.11 | 4.52 | $f_{5}-f_{1}$
$f_{48}$ | 24.73803$\pm$0.00009 | 0.105$\pm$0.035 | 5.75$\pm$0.98 | 5.09 |
$f_{49}$ | 28.08824$\pm$0.00002 | 0.316$\pm$0.028 | 6.09$\pm$0.26 | 19.17 | $f_{5}$
$f_{50}$ | 27.99998$\pm$0.00007 | 0.109$\pm$0.028 | 0.82$\pm$0.76 | 6.56 | $f_{1}+f_{47}$
$f_{51}$ | 22.30011$\pm$0.00009 | 0.108$\pm$0.037 | 4.33$\pm$1.00 | 5.00 | $f_{18}+f_{\rm orb}$
$f_{52}$ | 17.15799$\pm$0.00007 | 0.135$\pm$0.036 | 2.11$\pm$0.78 | 6.40 | $f_{25}-f_{4}$
$f_{53}$ | 17.08872$\pm$0.00009 | 0.112$\pm$0.037 | 4.06$\pm$0.96 | 5.21 | $f_{8}+f_{\rm orb}$
$f_{54}$ | 13.36270$\pm$0.00007 | 0.100$\pm$0.026 | 4.77$\pm$0.77 | 6.48 | $f_{21}-f_{\rm orb}$
$f_{55}$ | 34.46275$\pm$0.00007 | 0.096$\pm$0.026 | 1.25$\pm$0.79 | 6.37 | $2f_{38}$
$f_{56}$ | 31.68340$\pm$0.00006 | 0.095$\pm$0.023 | 0.92$\pm$0.72 | 6.95 | $f_{3}+f_{28}$
$f_{57}$ | 97.99553$\pm$0.00007 | 0.056$\pm$0.015 | 2.18$\pm$0.77 | 6.49 |
$f_{58}$ | 90.45982$\pm$0.00008 | 0.051$\pm$0.016 | 2.86$\pm$0.89 | 5.60 |

aafootnotetext: Frequencies, amplitudes, and phases are the values from the
equation $Z$ = $Z_{0}$ \+ $\Sigma_{i}$ $A_{i}\sin$(2$\pi f_{i}t+\phi_{i}$).

bbfootnotetext: Parameters’ errors were obtained following Kallinger et al.
(2008).

ccfootnotetext: Calculated in a range of 5 day-1 around each frequency.


# ProAI: An Efficient Embedded AI Hardware for Automotive Applications
– a Benchmark Study

Sven Mantowsky1, Falk Heuer1, Syed Saqib Bukhari1, Michael Keckeisen2, Georg
Schneider1
1ZF Friedrichshafen AG, Artificial Intelligence Lab, Saarbrücken, Germany 2ZF
Friedrichshafen AG, Autonomous Mobility Systems, Germany

###### Abstract

Development in the field of Single Board Computers (SBC) have been increasing
for several years. They provide a good balance between computing performance
and power consumption which is usually required for mobile platforms, like
application in vehicles for Advanced Driver Assistance Systems (ADAS) and
Autonomous Driving (AD). However, there is an ever-increasing need of more
powerful and efficient SBCs which can run power intensive Deep Neural Networks
(DNNs) in real-time and can also satisfy necessary functional safety
requirements such as Automotive Safety Integrity Level (ASIL). “ProAI” is
being developed by ZF mainly to run powerful and efficient applications such
as multitask DNNs and on top of that it also has the required safety
certification for AD. In this work, we compare and discuss state of the art
SBC on the basis of power intensive multitask DNN architecture called
Multitask-CenterNet with respect to performance measures such as, FPS and
power efficiency. As an automotive supercomputer, ProAI delivers an excellent
combination of performance and efficiency, managing nearly twice the number of
FPS per watt than a modern workstation laptop and almost four times compared
to the Jetson Nano. Furthermore, it was also shown that there is still power
in reserve for further and more complex tasks on the ProAI, based on the
CPU/GPU utilization during the benchmark.

##  1 Introduction

The progress in the field of Deep Neural Networks (DNNs) have increased
exponentially since the advent of AlexNet [12] back in 2012. In last decade
significant progress has been made in several domains such as natural language
processing [16] and computer vision [8][5]. Their applications are already
established in different areas; strongly including the automotive sector like
Advanced Driver Assistance Systems (ADAS) and Autonomous Driving (AD). For the
development of deep learning-based methods Graphics Processing Units (GPUs)
are mainly used, which have enormously large parallel computing power.
Furthermore, other processing units are also developed for these methods such
as Tensor Processor Units (TPU 111https://cloud.google.com/tpu/docs/tpus) or
even entire workstations that make parallel use of GPUs possible (such as
Nvidia DGX-2 222https://www.nvidia.com/de-de/data-center/dgx-2/). However, the
high computing power also requires a lot of electrical power that cannot be
provided under mobile circumstances in vehicles.

Figure 1: Example of ZF’s Single Board Computer: the ProAI.

Development in the field of Single Board Computers (SBC) has been increasing
for several years for achieving the best possible balance between computing
performance and power consumption mainly for mobile platforms. There are many
manufacturers who produce chips for these boards, such as Texas Instruments,
Xilinx, Qualcomm and NVIDIA. The boards with GPU support are providing
computing power that is required for mobile platforms, because they combine
high core density of the processors with lower energy consumption. However,
there is a persistent need of even more powerful and efficient Single Board
Computers which on one side can run multiple Deep Neural Networks (DNNs)
together in real-time, and on the other side, can satisfy necessary functional
safety requirements for autonomous driving such as Automotive Safety Integrity
Level (ASIL) [10].

ProAI is being developed by ZF mainly to solve these issues. It is
specifically designed for running powerful and efficient applications such as
multitask DNNs [17, 2, 6, 11] in real-time for autonomous driving. On top of
that, ProAI already has ASIL certification. An example of ProAI board is shown
in Figure 1. For benchmarking ProAI and comparison with other hardware, the
Multitask-CenterNet architecture [9] is used here. It is a power intensive
architecture, which can perform multiple perception related tasks such as
semantic segmentation, object detection, and human pose estimation in
parallel. It can be used with different configurations that range from single
to multiple tasks in parallel.

This paper provides the following main contributions: i) Presentation of the
mobile single board computer “ProAI” [1] for DNNs. ii) Benchmark result for
the ProAI are presented for the Multitask-CenterNet architecture. For this
benchmark, power, latency, and frames per second (FPS) metrics are addressed
which are suitable to judge the performance of mobile platforms. iii)
Comparison of ProAI with different platforms including the NVIDIA Jetson Nano
(as another mobile platform) and a typical workstation laptop. Altogether in
this paper we show on one hand the advantage of a modern multitasks network
architecture such as the Multitask-CenterNet for mobile application in
vehicles and on the other hand the potential of ZF’s ProAI as compared to
other platforms for such power intensive DNN architectures.

The paper is further organized as follows: In Section 2 we present technical
specifications of ProAI in comparison to different mobile platforms. In
Section 3 the architecture of the Multitask-CenterNet is described. Section 4
highlights the dataset, metrics and benchmark method used in this paper. In
Section 5 the benchmark on different platforms are shown and discussed.
Finally the paper is concluded in Section 6.

##  2 ProAI – Single Board Computer with GPU

|  Jetson Nano |  Dell Precision 7530 | ProAI
---|---|---|---
Perform [GFLOPS] |  472$@$FP16 235$@$FP32 7.3$@$FP64 |  38.5$@$FP16 2468$@$FP32 77.14$@$FP64 |  2820$@$FP16 1410$@$FP32 705$@$FP64
CPU |  Quad-core ARM Cortex-A72 64-bit$@$ 1.5GHz |  Intel® Core™ i7- 8850H, 6 Cores$@$ 2.6GHz |  Octa-core ARMv8 64-bit
GPU |  Maxwell 2.0 GM20B | Pascal GP107 | Volta GV10B
GPU- Memory |  4GB LPDDR4 $@$1600MHz 25.6GB/s |  4GB GDDR5 $@$1502MHz 96.13GB/s |  32GB LPDDR4 $@$1600MHz 127GB/s
GPU- Clock (boost) | 921 MHz | 1557 MHz | 1377 MHz
GPU- Cores | 128 Cores | 768 Cores |  512 Cores & 64 Tensor Cores
CUDA | .52 | 6.1 | 7.2
Internal Memory | SDHC slot |  32GB DDR4 RAM 1TB HDD |  32GB eMMC 5.1
Video Encode |  1x4Kp30 2x1080p60 4x1080p30 4x720p60 9x720p30 (H.265& H.264) |  4x4Kp120 4x5Kp60 (H.264&HEVC) |  4x4Kp60 8x4Kp30 16x1080p60 32x1080p30 (H.265) 4x4Kp60 8x4Kp30 14x1080p60 30x1080p30 (H.264)
Video Decode |  1x4Kp60 1x4Kp30 4x1080p60 8x1080p30 9x720p60 (H.265& H.264) |  4x4Kp60 H.264 HEVC MVC VC-1 |  2x8Kp30 6x4Kp60 12x4Kp30 26x1080p60 52x1080p30 (H.265) 4x4Kp60 8x4Kp30 16x1080p60 32x1080p30 (H.264)
Camera | MIPI CSI | USB | CAN, USB
GPU Power (max) | 5-10W | 75W | 15-30W
Table 1: Comparison between different Platforms used in this work: NVIDIA
Jetson Nano, Dell Precision 7530 Workstation and ZF’s ProAI.

This section first gives a technical overview of Single Board Computers and
then further details about ZF’s ProAI.

###  2.1 Single Board Computers (SBC)

Single Board Computers form a complete system in themselves, just like laptop
or desktop computers. In contrary to laptop or desktop computers, all of SBC
components are installed on the same board. Their architecture is geared
towards efficiency and therefore mostly built on ARM-based central processing
chips. They cannot perform as many functions as a powerful desktop computer,
but they represent a great compromise between energy consumption and computing
power. These boards are available with a wide variety of processing units such
as Central Processing Unit (CPU), Multiprocessing Unit (MPU), Graphics
Processing Unit (GPU) or Field Programable Gate Array (FPGA) and several
combinations thereof. Due to their compact design and their significantly
lower power consumption, they are very well suited for mobile applications,
such as robotics, drones, and vehicle technology. One of the most popular SBCs
is the Raspberry PI 333https://www.raspberrypi.org/. It offers the performance
of a small laptop, for the size of a mobile phone. It is well suited for
multimedia, HD streaming or games, as well as the possibility of text and
image processing in 4K resolution at a refresh rate of up to 60Hz. However,
when it comes to deep learning, memory and neural network model sizes are the
limitations. SBCs with focus on machine learning often have a dedicated GPU
and therefore a clear advantage in terms of computing power. Due to the
immense parallelization possibilities of the GPU’s, boards like the NVIDIA
Jetson NANO offer a much better opportunity for the computational needs of
deep and complex neural networks. Above all, the NVIDIA GPU architecture
offers a great advantage over other manufacturers: the CUDA library. This
opens up the possibility of calculating all arithmetic operations on the GPU.
In a perception task like semantic segmentation are innumerable calculations
during the inference procress. In practical applications, for example in
automotive sector, there are usually additional requirements such as
compatibility with the CAN-BUS, automotive-grade software (e.g. AUTOSAR),
quality ensurance, safety and security. Many design guidelines, hardware and
software requirements must be considered during the development process to
obtain ASIL certification in accordance with the ISO 26262/AEC-Q100 standard
[10]. This certification is necessary in European area, to allow vehicles with
new electrical components to drive on public roads. Most of the existing
boards do not fulfil these requirements.

###  2.2 ProAI

ZF has taken up the current challenges of SBC and successfully developed an
automotive-grade single board computer that both meets the quality and safety
requirements, and furthermore provides the required computing power for a wide
range of Deep Learning applications. Regarding the nature of the board which
is suitable for ADAS and Deep Learning based tasks it has been given the name
“ProAI”. In addition to a very competent octa-core CPU (ARM-architecture), a
powerful NVIDIA graphics processor provides the ”computational heart” of
ProAI. Some essential parameters are listed in Table 1 and compared with other
GPU-based platforms like NVIDIA’s Jetson Nano and the workstation used in this
work. Based on the parameter values, the potential of ProAI can already be
projected, which will be demonstrated in further detail in the following
sections.

As a summary of Table 1, the most important key aspects are the performance of
the CPU and GPU. ProAI outshines especially with an 8-core ARM CPU and a GPU
Volta architecture with 32GB GPU memory, due to the share system memory, at a
power consumption of max 30W (GPU). The computing power of ProAI exceeds the
P2000 GPU of the workstation while using FP16 (half precision) by the factor
73, while using FP64 almost by 9 times. When using FP32, the workstation GPU
is stronger than the ProAI, as it is apparently optimized primarily for
workstation tasks like rendering. Further, the LPDDR4 memory also has a
significantly higher read/write rate than the other platforms, which makes the
data connection between CPU and GPU significantly faster.

Benchmark result for the ProAI and other platforms are presented for a
multitask DNN. For this purpose, we selected the Multitask-CenterNet
architecture, which is briefly explained in the next section.

##  3 The Multitask-CenterNet (MCN) Architecture – A Brief Description

In most cases, multitask networks are built on a common backbone, in order to
extract basic features. Branches for the various tasks, which can consist of
several layers, emerge from the backbone. The selection of the emerging point
can prove difficult, because in order to achieve the best possible result,
this point is different for every task. The multitude of possible combinations
to solve such problems is shown in [4], where different approaches are
presented.

Figure 2: Architecture of Multitask-CenterNet (MCN) [9]. The network has a
single image input and a shared backbone. On top are separate prediction
heads, one for each task. In this case, Object Detection (Det), Semantic
Segmentation (Seg) and Pose Estimation (Pos) are shown.

The Multitask-CenterNet (MCN) [9] is based on the CenterNet architecture [17].
The MCN uses a common backbone like a ResNet50 or ResNet101 [7] and several
different prediction heads for perception related tasks. An illustration of
the MCN architecture is show in Figure 2.

To evaluate the performance of the MCN architecture on SBCs, we used three
different heads: object detection (Det), semantic segmentation (Seg) and human
pose estimation (Pos). The advantage of the MCN architecture is very clear;
while the necessary expensive computational operations in the backbone only
need to be performed once, each prediction head acts independently. Moreover,
each head is optimized for its own respective task. Especially in the field of
autonomous driving, the possibility of using these tasks concurrently is
required to design a robust and versatile agent. This network forms an ideal
benchmark basis, as it is both state-of-the-art and directly related to the
automotive domain. Using single tasks, semantic segmentation reached 49% mIoU
and detection achieved 36.7% mAP. With the combination of segmentation and
detection, the MCN achieved an accuracy of 48.9% mIoU (Seg) and 36.7% mAP
(Det), which is an improvement compared to using the tasks separately. When
adding the third task, human pose estimation, the accuracy of both
segmentation and detection tasks drops to 41.7% mIoU (Seg) and 25.1% mAP
(Det). This is most likely due a class imbalance of the setup, where the COCO-
dataset has a total of 80 classes where only one of the classes contains pose-
estimation labels (class: ”person”). The training of non-human classes for
detection and segmentation is at least one reason for the loss of accuracy. A
detailed explanation with further details of the MCN architecture and its
results for different setups are presented in the work [9]. In the rest of the
paper prediction accuracy is not considered in the benchmark, as it is
independent of the platform. The next section will define the dataset, metrics
and benchmark method that are used in this paper.

##  4 Dataset, Metrics and Benchmark Method

In this section the dataset and metrics used in this benchmark are presented
before explaining the process and content of the benchmark itself.

###  4.1 Dataset and Metrics

When selecting the dataset, various aspects had to be taken into account.
Regarding the area of application, a data set from the automotive context is
important. However, this harbors some difficulties with regard to the tasks
used within the Multitask-CenterNet (detection, segmentation, human pose
estimation). Many datasets often use common label types like semantic
segmentation or bounding boxes but missing out on human pose labels, where
data fusion is inevitable if the goal is to train a multitask network. This
represents a challenge of its own, especially in terms of accuracy, which is
why this is also a separate research area in combination with domain
adaptation in the field of deep learning. Furthermore, the goal of this
benchmark is the comparability of different hardware platforms to the ProAI
under as similar conditions as possible. In addition, we find similar general
conditions are more important for performance-oriented benchmarks with regard
to the data than the actual context of the data.

The aforementioned points are ideally combined in the COCO dataset [15]. The
dataset provides a wide variety of labels for object detection, semantic
segmentation and human pose estimation and is commonly used with a variety of
different DNN and publications, which is the ideal basis for this benchmark.

The most essential part for mobile applications is efficiency and the amount
of throughput per second of the hardware. Therefore, the metrics frames-per-
second (FPS), inference time, memory usage and energy efficiency (W) (Wtotal
and W/fps) were used for the benchmark. For the benchmark evaluation, we use
the specifications given in Table 1 as the maximum GPU power consumption.

###  4.2 Benchmark Method

Algorithm 1 DataLogger
Custom software to measure relevant system data for inferencing models.
Reading sensor data and adding it to a structure which directly writes it to a
file.

while model inferencing do

init data_struct

data_struct $\leftarrow{}$ cpu utilization

data_struct $\leftarrow{}$ memory utilization

data_struct $\leftarrow{}$ system temperature

if OS == linux then

gpu utilization = tegrastats()

else

gpu utilization = nvidia-smi()

end if

data_struct $\leftarrow{}$ gpu utilization

print(data_struct)

log_to_csv(data_struct)

end while

For the benchmark of SBCs, the NVIDIA Jetson Nano and ZF ProAI are used
against a modern workstation laptop, which can be regarded as a stationary
platform with a total of 230W of total power. However, it must be taken into
account that the mobile platforms have ARM-based CPUs, whereas the workstation
laptop has an x64_x84 CPU architecture, which means that the results of pre-
and post-processing (in particular the FPS and inference time) can only be
compared to a limited extent. The laptop uses an Intel i7-8850H as CPU and a
NVIDIA P2000 as GPU. First two different networks were compared with the
Multitask-CenterNet: the SSD300 [13] for object detection and the DeeplabV3
[3] for semantic segmentation, both with a ResNet50 Backbone. These two
network architectures are representative networks of their areas of use and
are frequently used in the literature. We used standard implementations of
each network without further improvement regarding network inference or pre-
and post-processing steps. Additionally, in order to see the influence of the
different tasks of the Multitask-CenterNet, several combinations of them were
used during the benchmark: 1) Seg: only semantic segmentation, 2) Det: only
object detection (Det), 3) Det + Pos: both object detection and human pose
estimation together, and 4) Seg + Det + Pos: all heads combined together. The
necessary arithmetic operations are directly related to the complexity of the
network, which is different for the tasks presented, especially semantic
segmentation has a high computational requirement. The utilization of the CPU
and GPU can therefore provide information about how much computing power is
still available for other applications during the inference.

The complete software is implemented in Python in combination with the deep
learning framework Pytorch [14]. In order to use the models on the NVIDA-GPU,
the frameworks CUDA and cuDNN are required. Several other libraries are used
to implement the image pre- and post-processing (e.g. OpenCV, Numpy). Since
the main task of SBCs for deep learning in the automotive area is mostly to
inference models and not the training process itself, we only measured timings
and utilization during the inference process while using pretrained weights.
The pretrained weights for the Multitask-CenterNet were provided by us, the
other weights were provided by the Pytorch framework itself. As inferencing
data, the test set “COCO test2017” is used, which includes 41k images. For our
benchmark, only 5k images of the test dataset is used for the benchmark
itself. This is a sufficient amount of data to test memory and inference
timings of each model. Custom software is used to record the test metrics. All
necessary system values are queried with a frequency of 0.5Hz and displayed
live in a terminal as well as logged to a file, in order to be able to use
those values afterwards. Since ProAI and Jetson Nano have ARM-based systems
with a linux operating system, whereas the workstation PC uses windows as
operating system, the code slightly differs due to specific terms of the
operating system (mostly affects how to read the GPU utilization). A
simplified process of the measurement is shown in Algorithm 1.

Figure 3: Qualitvative results of different models. a) original image b)
result of Single Shot Detector (SSD) with ResNet backbone c) result of
DeeplabV3 (the tennis racket is not segmented because the model was pretrained
on only 21 classes of COCO Dataset which does not include the class tennis
racket) d) result of the Multitask-CenterNet (MCN).

##  5 Benchmark Results and Discussion

Figure 4: Comparison of different networks on all platforms. The Results show
inference with pre- and postprocessing. The most right result shows the
inference when SSD and Deeplab are running simultaneously on P2000 and ProAI
(Jetson Nano board could not run both models simultaneously, due to
insufficient amount of memory). Figure 5: Benchmark Results: Left: The FPS for
each task and platform is shown, distinguished between model performance
(monochrome) and complete process performance (dotted). Middle: Shows the
efficiency with FPS per watt and the same distinction as in the left graph.
Right: Shows the GPU (monochrome) and CPU (dotted) utilization for each task.

In this section the performance evaluation and comparison of each platform is
presented, including ZF ProAI, the NVIDIA Jetson Nano and a workstation laptop
with a P2000 GPU.

First the qualitative results of the Multitask-CenterNet (detection, semantic
segmentation and human pose estimation) compared to state of the art networks
(SSD300 for object detection and DeeplabV3 for semantic segmentation) are
shown in Figure 3. Since the networks used for this comparison were only
pretrained on 21 classes of the COCO dataset444Pretrained weights available on
www.pytorch.org an image with the class ”person” was chosen to get a fair
comparison, as it was available in each of the training processes of all
networks.

We have split the quantitative benchmark results into two parts: performance
of the MCV against state of the art models (SSD and DeepLab) on different
platforms, and performance of different MCN settings on different platforms. A
detailed comparison of the MCN network against SSD and DeepLab for different
platform results are presented in Figure 4. In all measurements, both the
inference time of the network itself and the pre- and post-processing of the
results were considered. Additionally, to enable a realistic statement, a
batch size of one was used during inference, as with the application of a
(single) camera. The DeeplabV3 performance was the worst on all platforms
which was not very surprising due to the computationally intensive
segmentation task. The SSD, on the other hand, had the highest throughput on
the workstation (12.46 FPS) and the ProAI (9.85) as expected. But on the
Jetson Nano the Multitask-CenterNet was with 0.95 FPS slightly faster than the
SSD with 0.87 FPS. This was quite surprising, due to the fact, that the
Multitask-CenterNet combine detection and semantic segmentation in this
particular case. In order to create a more realistic comparison to the
Multitask-CenterNet, the inference of the SSD and DeeplabV3 was run
simultaneously (to have two different task running simultaneously). This
scenario clearly shows the advantage of the Multitask-CenterNet, especially on
platforms with very limited resources. The Jetson Nano board could not run
both models simultaneously, due to an insufficient amount of memory, but the
Multitask-CenterNet with very promising results. Also the ProAI achieves much
better results with the Multitask-CenterNet than with SSD and Deeplab in
parallel. When comparing the workstation and the ProAI when running those two
models in parallel, the difference between ProAI and workstation is even
smaller in comparison to a single model inference.

The detailed results regarding the different settings of Multitask-CenterNet
for different platforms are shown in Figure 5. FPS and FPS/Watt are
distinguished between the performance of the model prediction itself, in which
only the GPU computing part is very high, and the whole process including
image loading, network prediction and pre-/post-processing. The frames-per-
second, which are derived from the inference time, are best on the workstation
laptop with the Quadro P2000 GPU, as expected. The Jetson Nano has a
significantly slower prediction time using all task combined, which makes the
differences between detection only and all tasks at the same time hardly
recognizable (Figure 5 – left). Despite the big differences in computing
power, ProAI only has 3.5 FPS less in total compared to the workstation
laptop.

Considering the efficiency, the ratio between FPS and power consumption of the
respective platform, ProAI is ahead by a clear margin (Figure 5 – middle). For
this relation, the FPS derived by the inference time and the maximum GPU
consumptions from Table 1 were used. The ProAI achieves almost twice as much
FPS/Watt in all task combinations in the analysis except segmentation (Seg).
The reason for the backlog in the area of segmentation is mainly found in the
post-processing step, since the complex calculation of the predicted heatmaps
and up-sampling steps is CPU based until now. Therefore, there is an advantage
for the power station with the significantly more powerful CPU.

Another important part is the utilization of CPU and GPU of the systems.
Striking is the similar CPU load of the two ARM-based boards in contrast to
the x64_86 CPU of the workstation laptop (Figure 5 – right). In addition to
the significantly faster post-processing on the workstation laptop, this
additionally shows the greater computing power of the Intel CPU over the ARM
processor. However, it must be considered that the Intel CPU has a max.
consumption of 45 W, whereas ARM processors only use a few watts in total.
However, in contrast to the other two platforms, ProAI has a significantly
lower GPU utilization, despite the lower number of cores compared to the
P2000. The high utilization of the GPU with three tasks on the Jetson Nano
board shows that it has nearly reached its limit and has not much potential
left for more than three tasks with the Multitask-CenterNet. With a maximum
GPU utilization of 46% on ProAI, there is still a lot of free potential which
can be used for further tasks or the parallel calculation of other networks.

##  6 Conclusion

The requirements for single board computers in ADAS are enormously high, both
in terms of the computationally expensive and complex applications and in
terms of the necessity of quality and safety requirements. ZF shows with the
development of its ProAI that such an SBC can meet all necessary requirements
for example running power intensive multitask deep learning models. Using the
Multitask-CenterNet (MCN) architecture, the performance of ProAI is compared
to another SBC as well as a stationary platform. This architecture enables
significantly better performance on platforms that are particularly limited in
terms of resources, as is often the case with edge devices. ZF ProAI
demonstrated with a clear lead that high efficiency and performance can be
combined in a single SBC. Nevertheless, the utilization results of the ARM
processor have shown that there is further potential for improvement,
especially in the area of pre- and post-processing. Furthermore, the
innovation cycles in high performance CPUs and GPUs are very short. Today we
already see the next generations coming up which have again enormous increase
of efficiency and performance. This will enable even more complex algorithms
by lower power consumption.

## Acknowledgment

This work is in part funded by the German Federal Ministry for Economic
Affairs and Energy (BMWi) through the grant 19A19013Q, project ”KI Delta
Learning”.

##  7 References

## References

  * [1] ZF Friedrichshafen AG.  Zf proai.  https://www.zf.com/products/en/trucks/products_51218.html.
  * [2] Rich Caruana.  Multitask learning.  Mach. Learn., 28(1):41–75, July 1997.
  * [3] Liang-Chieh Chen, George Papandreou, Florian Schroff, and Hartwig Adam.  Rethinking atrous convolution for semantic image segmentation.  CoRR, abs/1706.05587, 2017.
  * [4] Michael Crawshaw.  Multi-task learning with deep neural networks: A survey.  CoRR, abs/2009.09796, 2020.
  * [5] Alberto Garcia-Garcia, Sergio Orts-Escolano, Sergiu Oprea, Victor Villena-Martinez, Pablo Martinez-Gonzalez, and Jose Garcia-Rodriguez.  A survey on deep learning techniques for image and video semantic segmentation.  Applied Soft Computing, 70:41–65, 2018.
  * [6] Kaiming He, Georgia Gkioxari, Piotr Dollár, and Ross B. Girshick.  Mask R-CNN.  CoRR, abs/1703.06870, 2017.
  * [7] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun.  Deep residual learning for image recognition.  CoRR, abs/1512.03385, 2015.
  * [8] Peter Henderson, Riashat Islam, Philip Bachman, Joelle Pineau, Doina Precup, and David Meger.  Deep reinforcement learning that matters.  CoRR, abs/1709.06560, 2017.
  * [9] Falk Heuer, Sven Mantowsky, Syed Saqib Bukhari, and Georg Schneider.  Multitask-centernet (mcn): Efficient and diverse multitask learning using an anchor free approach.  ICCV - Embedded and Real-World Computer Vision in Autonomous Driving (ICCV-ERCVAD, 2021.
  * [10] ISO.  Road vehicles – Functional safety, 2011.
  * [11] Alexander Kirillov, Kaiming He, Ross B. Girshick, Carsten Rother, and Piotr Dollár.  Panoptic segmentation.  CoRR, abs/1801.00868, 2018.
  * [12] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton.  Imagenet classification with deep convolutional neural networks.  Advances in Neural Information Processing Systems, 25:1097–1105, 2012.
  * [13] Wei Liu, Dragomir Anguelov, Dumitru Erhan, Christian Szegedy, Scott E. Reed, Cheng-Yang Fu, and Alexander C. Berg.  SSD: single shot multibox detector.  CoRR, abs/1512.02325, 2015.
  * [14] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Köpf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala.  Pytorch: An imperative style, high-performance deep learning library.  CoRR, abs/1912.01703, 2019.
  * [15] Andreas Veit, Tomas Matera, Lukas Neumann, Jiri Matas, and Serge J. Belongie.  Coco-text: Dataset and benchmark for text detection and recognition in natural images.  CoRR, abs/1601.07140, 2016.
  * [16] Tom Young, Devamanyu Hazarika, Soujanya Poria, and Erik Cambria.  Recent trends in deep learning based natural language processing.  CoRR, abs/1708.02709, 2017.
  * [17] Xingyi Zhou, Dequan Wang, and Philipp Krähenbühl.  Objects as points.  CoRR, abs/1904.07850, 2019.