2022 220 20 October

CME in Xe–Xe collisions

ALICE Collaboration ALICE Collaboration

Charge-dependent two- and three-particle correlations measured in Xe–Xe
collisions at $\sqrt{s_{\mathrm{NN}}}=5.44$ TeV are presented. Results are
obtained for charged particles in the pseudorapidity range $|\eta|<0.8$ and
transverse momentum interval $0.2\leq p_{\rm T}<5.0$ GeV/$c$ for different
collision centralities. The three-particle correlator
$\gamma_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}+\varphi_{\beta}-2\Psi_{\rm
2})\rangle$, calculated for different combinations of charge sign $\alpha$ and
$\beta$, is expected to be sensitive to the presence of the Chiral Magnetic
Effect (CME). Its magnitude is similar to the one observed in Pb–Pb collisions
in contrast to a smaller CME signal in Xe–Xe collisions than in Pb–Pb
collisions predicted by Monte Carlo (MC) calculations including a magnetic
field induced by the spectator protons. These observations point to a large
non-CME contribution to the correlator. Furthermore, the charge dependence of
$\gamma_{\alpha\beta}$ can be described by a blast wave model calculation that
incorporates background effects and by the Anomalous Viscous Fluid Dynamics
model with values of the CME signal consistent with zero. The Xe–Xe and Pb–Pb
results are combined with the expected CME signal dependence on the system
size from the MC calculations including a magnetic field to obtain the
fraction of CME contribution in $\gamma_{\alpha\beta}$, $f_{\rm CME}$. The CME
fraction is compatible with zero for the 30% most central events in both
systems and then becomes positive; averaging over the 0–70% centrality
interval yields an upper limit of 2% (3%) and 25% (32%) at 95% (99.7%)
confidence level for the CME signal contribution to $\gamma_{\alpha\beta}$ in
Xe–Xe and Pb–Pb collisions, respectively.

##  1 Introduction

The theory of the strong interaction applied to many-body systems predicts
that, at sufficiently high densities and temperatures, the protons and
neutrons that compose ordinary matter melt into a plasma where quarks and
gluons are no longer confined into hadrons. This hot and dense state of matter
is called the quark–gluon plasma (QGP) [1]. The transition from normal
hadronic matter to a QGP is supported by Quantum Chromodynamics (QCD)
calculations on the lattice [2, 3, 4, 5], where it is found to occur at a
critical temperature of about 155 MeV, and at a critical energy density
$\epsilon$ of about 0.5 GeV/fm3 [6, 7, 8]. Collisions between heavy ions
accelerated to ultrarelativistic energies can produce the necessary conditions
for such a transition to take place [9, 10, 11].

Heavy-ion collisions may also allow us to access novel QCD phenomena
associated with parity violation in strong interactions [12, 13, 14, 15, 16,
17, 18, 19, 20]. Theoretical expectations indicate that the interaction of
quarks with gluonic fields describing transitions between topologically
different QCD vacuum states changes the quark chirality and leads to a local
chiral imbalance. In the presence of the strong magnetic field produced by the
colliding ions [21, 22, 23], this leads to a charge separation (electric
current) relative to the reaction plane, the plane defined by the impact
parameter and the beam axis. This phenomenon is known as the Chiral Magnetic
Effect (CME) [20].

The effects from local parity violation are quantified via the coefficient
$a_{1,\alpha}$ in a Fourier decomposition of the particle azimuthal
distribution [24, 25]

$\frac{{\rm d}N}{{\rm d}\Delta\varphi_{\alpha}}\sim
1+2v_{1,\alpha}\cos(\Delta\varphi_{\alpha})+2a_{1,\alpha}\sin(\Delta\varphi_{\alpha})+2v_{2,\alpha}\cos(2\Delta\varphi_{\alpha})+...,$
(1)

where $\Delta\varphi_{\alpha}=\varphi_{\alpha}-\Psi_{\rm RP}$,
$\varphi_{\alpha}$ is the azimuthal angle of the particle of charge $\alpha$
(+, $-$), and $\Psi_{\rm RP}$ is the reaction plane angle. The coefficients
$v_{\rm n,\alpha}$ characterise the anisotropic flow, i.e., the azimuthal
anisotropies in particle production relative to $\Psi_{\rm RP}$ due to initial
spatial asymmetries of the collision. The degree of overlap between the two
colliding nuclei is estimated by the centrality, with low percentage values
corresponding to head-on collisions. The first- and second-order flow
coefficients ($v_{1,\alpha}$ and $v_{2,\alpha}$) are called directed and
elliptic flow, respectively. The CME is expected to have an experimentally
accessible signal imprinted in the azimuthal correlations between two
particles relative to the reaction plane [25] of the form
$\gamma_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}+\varphi_{\beta}-2\Psi_{\rm
RP})\rangle$, since $a_{1,\alpha}$ changes sign from event to event and the
average $\langle a_{1,\alpha}\rangle$ over many events is equal to zero. The
charge-dependent difference of $\gamma_{\alpha\beta}$ is commonly used to
search for the CME. In practice, the reaction plane angle is estimated by
constructing the second harmonic symmetry plane angle $\Psi_{\rm 2}$ using
azimuthal particle distributions [26], which is why $\gamma_{\alpha\beta}$ is
often referred to as a three-particle correlator. The $\gamma_{\alpha\beta}$
correlator measures the difference between the correlations projected onto the
reaction plane and perpendicular to it. The contributions from correlations
in- and out-of-plane can also be evaluated by measuring the charge-dependent
two-particle correlator
$\delta_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}-\varphi_{\beta})\rangle$.

The first experimental results in Au–Au collisions at a centre-of-mass energy
per nucleon–nucleon collision $\sqrt{s_{\mathrm{NN}}}=200$ GeV at the
Relativistic Heavy-Ion Collider (RHIC) [27, 28] were compatible with initial
expectations for the existence of the CME. The subsequent first measurements
at the Large Hadron Collider (LHC) in Pb–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [29] showed a surprising agreement with the
results at lower energies, despite the differences in magnitude of the
magnetic field [21, 22, 23]. Considering that the charged-particle density,
$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$, at the LHC is about three times
larger than at RHIC [30, 31], any signal due to CME will be considerably
diluted since it is expected to follow a
$1/(\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta)$ scaling [19]. This effect will
be referred to as dilution in the following. The similarity of the two
measurements was indicative of the existence of background effects, coming
mostly from “flowing clusters" – charge-dependent correlations modified by
elliptic flow [25]. It was shown in Refs. [32, 33] that the local charge
conservation coupled to the anisotropic expansion of the medium could explain
most if not all the measurements.

To study background effects, the CMS Collaboration performed measurements of
charge-dependent correlations in p–Pb collisions at
$\sqrt{s_{\mathrm{NN}}}=5.02$ TeV [34] and the STAR Collaboration in p–Au and
d–Au collisions at $\sqrt{s_{\mathrm{NN}}}=0.2$ TeV [35]. The results suggest
that these correlations are similar to those measured in peripheral Pb–Pb and
Au–Au collisions. These results might further indicate the dominance of
background effects in peripheral collisions.

These measurements highlighted the need to identify ways of isolating the CME
signal from the background. A first attempt was presented by the ALICE
Collaboration in Ref. [36] using the Event Shape Engineering method [37]. This
method utilises the fluctuations in the shape of the initial state of the
system and allows one to select events with the same centrality but different
initial geometry, thus varying the background contributions. The study sets an
upper limit of 26–33% at 95% confidence level for the CME signal contribution
to the charge dependence of $\gamma_{\alpha\beta}$ in the 10–50% centrality
interval. A similar study was performed by the CMS Collaboration [38] and the
results agree with the measurements in Ref. [36]. A recent study by the ALICE
Collaboration [39] found that charge-dependent correlations relative to the
higher harmonic symmetry planes can be used as a proxy for the background,
assuming that the correlations relative to $\Psi_{2}$ and $\Psi_{3}$ can be
factorised. An upper limit of 15–18% at 95% confidence level for the CME
signal has been reported for the 0–40$\%$ centrality interval, consistent with
previous measurements.

Another approach to address the large backgrounds experimentally is to compare
measurements performed in collision systems where the CME contribution is
expected to vary significantly, while the background is similar. The STAR
Collaboration has recently reported the results of the CME search in an
analysis of the three-particle correlator $\gamma_{\alpha\beta}$ measured in
collisions of isobar ${}^{96}_{44}$Ru–${}^{96}_{44}$Ru and
${}^{96}_{40}$Zr–${}^{96}_{40}$Zr nuclei at $\sqrt{s_{\mathrm{NN}}}=200$ GeV
[40]. No anticipated CME signature (i.e., a larger magnitude of
$\gamma_{\alpha\beta}$ in Ru–Ru than in Zr–Zr collisions due to a larger
magnetic field in the former) was observed in that analysis. However, a
quantitative analysis taking into account the small geometrical differences
between the isobar nuclei is needed for the interpretation of the
measurements. One can also try to separate the CME signal and background by
comparing the results from Pb–Pb and Xe–Xe collisions at the LHC since the
differences in $v_{2}$ are typically within 10% in the 5–70% centrality
interval [41] but the magnetic field is expected to be significantly larger in
Pb–Pb collisions [42], leading to a similar increase in the CME contribution.

In this article, measurements of charge-dependent azimuthal correlations from
Xe–Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV are presented. The results
are compared with earlier measurements in Pb–Pb collisions at $\sqrt{s_{\rm
NN}}=5.02$ TeV [39] and calculations from a blast wave parameterisation that
incorporate background effects and from the Anomalous Viscous Fluid Dynamics
(AVFD) model [43, 44, 45]. Furthermore, Monte Carlo (MC) simulations of the
magnetic field induced by spectator protons with different initial conditions
are used to evaluate the expected change in the CME signal between the Xe–Xe
and Pb–Pb collisions. This change is then employed to estimate the fraction of
the CME signal in both collision systems.

##  2 Analysis details

The data set used for these measurements was recorded with the ALICE detector
during the 2017 Xe–Xe run at $\sqrt{s_{\rm NN}}=5.44$ TeV. A detailed overview
of the ALICE detector and its performance are available in Refs. [46, 47]. The
Inner Tracking System (ITS) [48], the Time Projection Chamber (TPC) [49], the
V0 [50], and the Zero Degree Calorimeter (ZDC) [51], the main subsystems used
in this analysis, are briefly described in the following. The ITS and TPC
cover the full azimuth within the pseudorapidity range $|\eta|<0.9$. The ITS
consists of six layers of silicon detectors and is employed for tracking,
vertex reconstruction, and event selection. The TPC is used to reconstruct
charged-particle tracks and to identify particles via specific energy loss,
$\textrm{d}E/\textrm{d}x$. The V0 detector, two arrays of 32 scintillator
tiles covering $-3.7<\eta<-1.7$ (V0C) and $2.8<\eta<5.1$ (V0A), is used for
triggering, event selection, and the determination of centrality [52] and
symmetry plane $\Psi_{\rm 2}$. Both V0 detectors are segmented in four rings
in the radial direction with each ring divided into eight sectors in the
azimuthal direction. Two tungsten-quartz neutron ZDCs, installed 112.5 meters
from the interaction point on each side, are also used for event selection.

The trigger conditions and the event selection criteria can be found in Ref.
[53]. Beam-induced background and pileup events are removed using an offline
event selection, employing information from the V0, ZDC, and tracking
detectors. The primary vertex position is determined from tracks reconstructed
in the ITS and TPC as described in Ref. [47]. Approximately $10^{6}$ Xe–Xe
events in the 0–70% centrality interval, with a primary vertex position within
$\pm 10$ cm from the nominal interaction point along the beam direction, are
used in the analysis. The centrality of the collision is estimated from the
energy deposition measured in the V0 detector [52].

The charged-particle tracks reconstructed using the ITS and TPC within
$|\eta|<0.8$ and $0.2\leq p_{\rm T}<5.0$ GeV/$c$ are used to measure the
charge-dependent correlations. Each track is required to have a minimum number
of 70 space points (out of a maximum of 159) with a $\chi^{2}$ per TPC space
point lower than 4, to cross at least 70 TPC readout rows, and to have the
ratio between the number of crossed rows and the number of findable space
points in the TPC larger than 0.8. The selected tracks are also required to
have at least 2 ITS hits and a $\chi^{2}$ per ITS hit smaller than 36. In
addition, tracks are selected with a distance of closest approach (DCA) to the
reconstructed vertex position smaller than 3.2 cm and 2.4 cm in the
longitudinal direction ($z$) and transverse plane ($xy$), respectively. These
selection criteria reduce the contamination from secondary charged particles
(i.e., particles originating from weak decays, conversions, and secondary
hadronic interactions in the detector material) and fake tracks (random
associations of space points) and ensure a track momentum resolution better
than 4% in the considered $p_{\rm T}$ interval [53]. The charged-particle
track reconstruction efficiency is estimated from simulations with the HIJING
event generator [54, 55] combined with the GEANT3 transport model [56]. These
simulations include a detailed description of the detector response. The
$p_{\rm T}$ averaged charge-dependent correlations are corrected for track
reconstruction efficiency.

The charge-dependent correlations are measured using two- and three-particle
correlators expressed as

$\begin{split}\delta_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}-\varphi_{\beta})\rangle&=\langle\cos(\Delta\varphi_{\alpha})\cos(\Delta\varphi_{\beta})\rangle+\langle\sin(\Delta\varphi_{\alpha})\sin(\Delta\varphi_{\beta})\rangle\\\
&=\langle v_{1,\alpha}v_{1,\beta}\rangle+B_{\rm in}+\langle
a_{1,\alpha}a_{2,\beta}\rangle+B_{\rm out},\end{split}$ (2)
$\begin{split}\gamma_{\alpha\beta}\equiv\langle\cos(\varphi_{\alpha}+\varphi_{\beta}-2\Psi_{2})\rangle&=\langle\cos(\Delta\varphi_{\alpha})\cos(\Delta\varphi_{\beta})\rangle-\langle\sin(\Delta\varphi_{\alpha})\sin(\Delta\varphi_{\beta})\rangle\\\
&=\langle v_{1,\alpha}v_{1,\beta}\rangle+B_{\rm in}-\langle
a_{1,\alpha}a_{2,\beta}\rangle-B_{\rm out},\end{split}$ (3)

where $\Delta\varphi_{\alpha(\beta)}=\varphi_{\alpha(\beta)}-\Psi_{2}$, and
$B_{\rm in}$ and $B_{\rm out}$ denote background contributions projected onto
$\Psi_{\rm 2}$ and perpendicular to it, respectively. The term $\langle
v_{1,\alpha}v_{1,\beta}\rangle$ is expected to have negligible charge
dependence at midrapidity [57]. In addition, $\langle v_{1}\rangle$ at
midrapidity is zero for a symmetric collision. While $\gamma_{\alpha\beta}$
suppresses background contributions at the level of $v_{2}$ (i.e., the
relative difference between the particle production in-plane and out-of-
plane), $\delta_{\alpha\beta}$ is dominated by short-range correlations
unrelated to $\Psi_{\rm 2}$ (“non-flow"), such as inter-jet correlations and
resonance decays.

The orientation of the symmetry plane $\Psi_{\rm 2}$ is estimated from the
azimuthal distribution of the energy deposition measured by the V0A detector,
with the $x$ and $y$ components given by

$Q_{\rm 2,x}=\sum_{j}w_{j}\cos(2\varphi_{j}),\;Q_{\rm
2,y}=\sum_{j}w_{j}\sin(2\varphi_{j}),$ (4)

where the index $j$ runs over the 32 sectors of the V0A detector,
$\varphi_{j}$ is the azimuthal angle of sector $j$ defined by the geometric
centre, and $w_{j}$ is the amplitude of the measured signal in that sector.
The symmetry plane resolution is calculated from correlations between the
symmetry planes determined with the TPC, the V0A, and the V0C detectors [26].
The effect of the decorrelation of $\Psi_{2}$ between mid and forward
pseudorapidity has been estimated to be less than 3% for $v_{2}$ [58]. Any
non-uniform detector response is taken into account by adjusting the
components of the ${\bf Q}_{2}$ vector using a recentering procedure (i.e.,
subtraction of the ${\bf Q}_{2}$ vector averaged over many events from the
${\bf Q}_{2}$ vector of each event) [59]. The non-flow contributions to the
charge-dependent azimuthal correlations are greatly suppressed by the large
pseudorapidity separation between the TPC and the V0A ($|\Delta\eta|>2.0$).

The absolute systematic uncertainties were estimated from the variation of the
results with different event and track-selection criteria. The event selection
contributions were determined by varying the range of the reconstructed
collision vertex position from the nominal interaction point along the beam
direction, estimating centrality from the number of hits in the first or
second layer of the ITS, and imposing stricter pileup rejection criteria than
the default selection. Systematic uncertainties related to track selection
criteria were evaluated by changing the ITS hit requirements, varying the
minimum number of TPC space points, changing the minimum number of crossed TPC
readout rows and the ratio between the number of crossed rows and the number
of findable space points in the TPC, rejecting tracks close to the TPC sector
boundaries to which the sensitive readout rows do not extend, and comparing
any differences between results with only positive and only negative charges
for pairs of particles with same charge. Finally, changes of the results due
to uncertainties in the tracking efficiency arising from an imperfect
description in the simulation of the relative abundances of different particle
species and their different reconstruction efficiencies [60] were considered
as part of the systematic uncertainties. The largest contribution to the
systematic uncertainties for $\gamma_{\alpha\beta}$ and $\delta_{\alpha\beta}$
is given by the centrality estimation and track-selection criteria,
respectively. The systematic uncertainties are evaluated for each centrality
interval. The different sources are assumed uncorrelated and are added in
quadrature as an estimate of the total systematic uncertainties if their
deviations from the nominal values are significant according to the Barlow
criterion [61]. The resulting systematic uncertainties increase from central
to peripheral collisions and are summarised in Table 1.

Table 1: Summary of absolute systematic uncertainties on the charge-dependent correlations. The uncertainties depend on centrality, whose minimum and maximum values are listed here. | Opposite charge | Same charge
---|---|---
$\delta_{\alpha\beta}$ | $(6.8-33)\times 10^{-5}$ | $(3.8-13)\times 10^{-5}$
$\gamma_{\alpha\beta}$ | $(1.0-8.3)\times 10^{-5}$ | $(1.4-5.9)\times 10^{-5}$

##  3 Results

Figure 1 compares the $\delta_{\alpha\beta}$ and $\gamma_{\alpha\beta}$
correlators for same- and opposite-charge pairs in Xe–Xe collisions at
$\sqrt{s_{\rm NN}}=5.44$ TeV to those measured in Pb–Pb collisions at
$\sqrt{s_{\rm NN}}=5.02$ TeV [39] as a function of centrality and average
charged-particle multiplicity density
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$ at midrapidity [62,
63]. The results for same-charge pairs denote the average between pairs of
particles with only positive and only negative charges since the two
combinations are consistent within statistical uncertainties. Both correlators
exhibit strong dependence on the charge-sign combination and qualitatively
similar centrality dependence in the two systems. For $\delta_{\alpha\beta}$,
the magnitude of the same- and opposite-charge pair correlations is positive
and increases from central to peripheral collisions. In contrast to the CME
expectation, the correlation for the opposite-charge pairs is stronger than
for the same-charge combinations, indicating that background dominates these
measurements. For $\gamma_{\alpha\beta}$, the magnitude of opposite-charge
pair correlations is close to zero within uncertainties for most of the
centrality intervals, while it decreases from central to peripheral collisions
becoming more negative for same-charge pairs. Thus, the correlation of
opposite-charge pairs is weaker than for same-charge pairs. This ordering is
compatible with a charge separation with respect to the reaction plane
expected in the presence of the CME.

The $\delta_{\alpha\beta}$ for same-charge pairs shows small (if any)
differences between Xe–Xe and Pb–Pb collisions within uncertainties, while the
correlations for opposite-charge pairs have larger magnitude in Xe–Xe
collisions in the 10–70% centrality interval. The $\gamma_{\alpha\beta}$ for
same- and opposite-charge pairs from Xe–Xe and Pb–Pb collisions have similar
magnitudes within uncertainties in the 0–10% and 50–70% centrality ranges,
while the correlations are stronger in Xe–Xe collisions in the 10–50%
centrality interval. These observations can be attributed to the different
number of particles produced in the collision within a given centrality
interval between the two systems that dilutes the correlations. This is
supported by the fact that the $\delta_{\alpha\beta}$ and
$\gamma_{\alpha\beta}$ for same- and opposite-charge pairs from Xe–Xe
collisions are consistent within uncertainties with the corresponding Pb–-Pb
results when reported as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$.

Figure 1: The $\delta_{\alpha\beta}$ (top panels) and $\gamma_{\alpha\beta}$
(bottom panels) correlators as a function of centrality (left panels) and
charged-particle density [62, 63] (right panels) for pairs of particles with
same (closed markers) and opposite (open markers) charges from Xe–Xe
collisions at $\sqrt{s_{\rm NN}}=5.44$ TeV (red circles) compared to Pb–Pb
collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV (black squares) [39]. The Pb–Pb
points are slightly shifted along the horizontal axis for better visibility in
the left panels. Bars (boxes) denote statistical (systematic) uncertainties.
Figure 2: The dependence of $\gamma_{\alpha\beta}$ on the pseudorapidity
difference $|\eta_{\alpha}-\eta_{\beta}|$ (left panel), the transverse
momentum difference $|p_{{\rm T}_{\alpha}}-p_{{\rm T}_{\beta}}|$ (middle
panel), and the average transverse momentum $(p_{{\rm T}_{\alpha}}+p_{{\rm
T}_{\beta}})/2$ (right panel) for pairs of particles with same (closed
markers) and opposite (open markers) charges from 20–30% Xe–Xe collisions at
$\sqrt{s_{\rm NN}}=5.44$ TeV (red circles) compared to results from 30–40%
Pb–Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV (black squares) [39]. The
Pb–Pb and Xe–Xe same-charge points are slightly shifted along the horizontal
axis for better visibility in all panels. Bars (boxes) denote statistical
(systematic) uncertainties.

The $\gamma_{\alpha\beta}$ correlator is also investigated as a function of
the pseudorapidity difference $\Delta\eta=|\eta_{\alpha}-\eta_{\beta}|$, the
transverse momentum difference $\Delta p_{\rm T}=|p_{{\rm T}_{\alpha}}-p_{{\rm
T}_{\beta}}|$, and the average transverse momentum $\langle p_{\rm
T}\rangle=(p_{{\rm T}_{\alpha}}+p_{{\rm T}_{\beta}})/2$ of the pair. Figure 2
presents these results for same- and opposite-charge pairs in the 20–30%
centrality interval compared to measurements performed in 30–40% Pb–Pb
collisions [39]. Different Xe–Xe and Pb–Pb centrality intervals are selected
since they have similar transverse densities
($1/S\,\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\sim 10$ fm-2 with $S$ being
the transverse area) and transverse sizes ($R=\sqrt{S/\pi}\sim 4$ fm) [41],
thus the contribution from dilution effects is comparable. In addition, the
value of $v_{2}/\varepsilon_{2}$ ($\varepsilon_{2}$ is the second-order
eccentricity coefficient and characterises the elliptic shape of the initial
geometry) and the influence of radial flow are similar in the two systems for
these centrality classes [41, 53]. The opposite-charge pair correlations from
Xe–Xe collisions show a weak dependence on $\Delta\eta$ and $\langle p_{\rm
T}\rangle$, while they increase with increasing $\Delta p_{\rm T}$ of the
pair. The correlations for the same-charge pairs do not exhibit any
significant dependence on $\Delta p_{\rm T}$ and $\langle p_{\rm T}\rangle$
within uncertainties. These correlations show a strong dependence on
$\Delta\eta$ with a width of approximately one unit in pseudorapidity
difference. The Xe–Xe and Pb–Pb results are compatible within uncertainties
demonstrating similar behaviour of this observable despite the differences in
the magnetic field.

Figure 3: Centrality evolution of the difference between same- and opposite-
charge pair correlations for $\delta_{\alpha\beta}$ (top panel) and
$\gamma_{\alpha\beta}$ (bottom panel) compared to model calculations: blast
wave (BW) parameterisation [64] coupled to local charge conservation (LCC)
effects (blue curves) and Anomalous Viscous Fluid Dynamics (AVFD) [44, 43]
(green curves). The BW+LCC model is tuned to reproduce the centrality
dependence of $\Delta\delta_{\alpha\beta}$, while AVFD is tuned to describe
simultaneously the centrality dependence of $\Delta\delta_{\alpha\beta}$ and
$\Delta\gamma_{\alpha\beta}$. Bars (boxes) denote statistical (systematic)
uncertainties on the data points, while the thickness of the curves represents
the uncertainties on the model calculations.

To get insight into the origin of the charge-dependent effects observed in
Xe–Xe collisions, two different approaches were investigated. The first one
relies on a blast wave (BW) model based on a parameterisation from Ref. [64].
Input parameters of the model are tuned to describe the $p_{\rm T}$ spectra
[65] and the $p_{\rm T}$-differential $v_{2}$ values [66] of charged pions and
kaons, as well as of protons and antiprotons, measured in the same collision
system and centre-of-mass energy. To account for the main source of background
in the measurements reported in this article, the model was further extended
by including effects from local charge conservation (LCC). This was done by
generating sources uniformly at the surface of the ellipse that surrounds the
centre of the system and allowing them to decay into particles with opposite
charge. In this extension of the BW model, the number of sources that emit
oppositely-charged pairs is tuned separately for each centrality interval to
reproduce the centrality dependence of
$\Delta\delta_{\alpha\beta}\equiv\delta^{\mathrm{opp.}}_{\alpha\beta}-\delta^{\mathrm{same}}_{\alpha\beta}$,
the correlator that is mainly sensitive to background effects. This is
illustrated in the upper panel of Fig. 3, where the BW curve is represented by
the blue, solid line that goes through the experimental data points. The tuned
model is then used to extract the expectation for the centrality dependence of
$\Delta\gamma_{\alpha\beta}\equiv\gamma^{\mathrm{opp.}}_{\alpha\beta}-\gamma^{\mathrm{same}}_{\alpha\beta}$,
shown in the lower panel of Fig. 3. The width of the band reflects the
uncertainty obtained by propagating the corresponding uncertainties of the
model parameters using a sub-sampling method. It can be seen that the BW model
describes fairly well the measured data points for all centrality intervals.
This is in contrast to the picture that emerged in Pb–Pb collisions, where
following a similar procedure the same model underestimated the measurements
of $\Delta\gamma_{\alpha\beta}$ by as much as $\approx$ 40$\%$ [39].

Additional insight can be obtained by comparing the results with calculations
from the Anomalous Viscous Fluid Dynamics (AVFD) model [43, 44, 45]. It relies
on a Glauber model description of the initial state of the collision and
accounts for the development of the early-stage electromagnetic fields as well
as for the propagation of anomalous fermion currents. The expanding medium is
described using a 2+1 dimensional viscous hydrodynamics (VISH2+1) code [67]
which is coupled to a hadron cascade model (UrQMD) [68, 69]. Within AVFD, the
final-state CME signal induced by the initial chirality imbalance is
controlled by the axial current density $n_{5}/\mathrm{s}$. At the same time,
the relevant background in AVFD is governed by the amount of positive and
negative charged partners emitted from the same fluid element relative to the
total multiplicity of the event, i.e., the LCC percentage. The model was first
calibrated to describe the centrality dependence of both the charged-particle
density [63] and the elliptic flow [41]. As a second step, the dependence of
$\Delta\delta_{\alpha\beta}$ and $\Delta\gamma_{\alpha\beta}$ on both the CME
signal and the background was determined, by analysing samples with either
increasing values of $n_{5}/\mathrm{s}$ or LCC percentage, respectively [42].
These results made it possible to extract the combination of
$n_{5}/\mathrm{s}$ and LCC percentage that describes the data and led to a
quantitative simultaneous description of the centrality dependence of
$\Delta\delta_{\alpha\beta}$ and $\Delta\gamma_{\alpha\beta}$ [42]. This is
illustrated in the two panels of Fig. 3. Also in this case, the width of the
band reflects the uncertainty obtained by propagating the corresponding
uncertainties of the model parameters using a sub-sampling method. The
experimental data points can be described by large values of LCC contribution,
between 40$\%$ and 60$\%$ for peripheral and more central Xe–Xe collisions,
respectively. In addition, the values of $n_{5}/\mathrm{s}$ extracted from
this procedure did not exhibit any significant centrality dependence and were
compatible with zero within uncertainties [42]. Similar to the conclusion
extracted from the BW model, the study within the AVFD framework indicates
that the experimental measurements in Xe–Xe collisions are dominated by
background.

Figure 4: Difference between opposite- and same-charge pair correlations for
$\gamma_{\alpha\beta}$ divided by $v_{2}$ [41] as a function of centrality
(left) and charged-particle density (right) compared to results from Pb–Pb
collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV [39]. The Pb–Pb points are slightly
shifted along the horizontal axis for better visibility in the left panel.
Bars (boxes) denote statistical (systematic) uncertainties.

The charge separation effect can be further studied using the difference
between opposite- and same-charge pair correlations
$\Delta\gamma_{\alpha\beta}$ and the CME signal expectations from MC
calculations employed as guidance. A comparison between
$\Delta\gamma_{\alpha\beta}$ divided by $v_{2}$ [41] in Xe–Xe collisions and
that measured in Pb–Pb collisions [39] is presented as a function of
centrality and charged-particle density [62, 63] in Fig. 4. The value of
$\Delta\gamma_{\alpha\beta}/v_{2}$ is positive for all centralities and its
magnitude increases from central to peripheral collisions. Furthermore, it is
slightly higher in Xe–Xe than Pb–Pb collisions in the 10–60% centrality
interval. However, the Xe–Xe and Pb–Pb data points fall approximately onto the
same curve when reported as a function of
$\langle\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta\rangle$.

The expected centrality dependence of the CME signal in Xe–Xe and Pb–Pb
collisions is estimated from MC Glauber [70] simulations including a magnetic
field [36]. In these calculations, the 208Pb nucleus is spherical while the
129Xe nucleus is deformed with a deformation parameter $\beta_{2}=0.18\pm
0.02$ [52]. The centrality classes are determined from the multiplicity of
charged particles in the acceptance of the V0 detector, which is generated
according to a negative binomial distribution with parameters taken from Ref.
[71]. The magnetic field is calculated at the origin from the number of
spectator protons using Eq. (A.6) from Ref. [19] with the proper time
$\tau=0.1$ fm/$c$. Figure 5 shows the centrality dependence of
$\langle(eB)^{2}\cos(2(\Psi_{\rm B}-\Psi_{2}))\rangle$ ($\Psi_{\rm B}$ is the
direction of the magnetic field $\vec{B}$), which is the expected CME signal
contribution in $\gamma_{\alpha\beta}$, for the two collision systems. The
expected CME signal is stronger in Pb–Pb than Xe–Xe collisions in a given
centrality interval due to the smaller magnetic field strength and a larger
decorrelation between $\Psi_{\rm B}$ and $\Psi_{2}$ in Xe–Xe collisions.
Similar results are found using TRENTo [72] initial conditions. This
observation coupled to the agreement of $\Delta\gamma_{\alpha\beta}$ between
the two collision systems (see Fig. 4) points to a large background
contribution to $\gamma_{\alpha\beta}$ in Xe–Xe collisions.

Figure 5: The expected CME signal as a function of centrality from MC Glauber
simulations for Xe–Xe and Pb–Pb collisions [70] (see text for details).

The large differences in the CME signal expectations and the small variations
in $v_{2}$ ($<10$% for the 5–70% centrality interval) [41] between the two
collision systems can be used to disentangle the potential CME signal from the
background in Xe–Xe and Pb–Pb collisions. Assuming that both the CME signal
and the background scale with $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$, the
charge dependence of $\gamma_{\alpha\beta}$ for the two collision systems can
be expressed using a two-component approach similar to the one proposed in
Ref. [73]

$\displaystyle\Gamma^{\rm Xe-Xe}$ $\displaystyle=sB^{\rm Xe-Xe}+bv_{2}^{\rm
Xe-Xe},$ (5) $\displaystyle\Gamma^{\rm Pb-Pb}$ $\displaystyle=sB^{\rm Pb-
Pb}+bv_{2}^{\rm Pb-Pb},$ (6)

where
$\Gamma\equiv\gamma_{\alpha\beta}\,\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$,
$B\equiv\langle(eB)^{2}\cos(2(\Psi_{\rm B}-\Psi_{2}))\rangle$, and $v_{2}$ is
taken from Ref. [41] and $\gamma_{\alpha\beta}^{\rm Pb-Pb}$ from Ref. [39].
The $s$ and $b$ parameters quantify the signal and background contributions,
respectively, and do not depend on collision system as a result of the
assumption that both scale with $\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$.
While this scaling is expected for $b$ since it is dominated by flowing
clusters [25], the domains responsible for $s$ are small and thus they can be
considered as “usual" clusters which scale with
$\mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta$. These parameters can be used to
calculate the fractions of the CME signal (denoted as $f_{\rm CME}$) in Xe–Xe
and Pb–Pb collisions as

$f_{\rm CME}=\frac{sB}{sB+bv_{2}}.$ (7)

The smaller CME signal in Xe–Xe collisions also results in a tighter limit on
$f_{\rm CME}$ in Xe–Xe than in Pb–Pb collisions. It is worth noting that the
CME fractions in the two collision systems are correlated because both are
calculated with the same $s$ and $b$ parameters, extracted from the data using
Eqs. 5 and 6.

Figure 6: Centrality dependence of the CME fraction extracted using Eq. 7 with
the expected CME signal from MC Glauber [70] (closed markers) and TRENTo [72]
(open markers) models (see text for details). The TRENTo points are slightly
shifted along the horizontal axis for better visibility.

Figure 6 presents the centrality dependence of $f_{\rm CME}$ in Xe–Xe and
Pb–Pb collisions for the two models used in this study. The uncertainties in
the CME fractions are obtained adding in quadrature the statistical and
systematic uncertainties in Eqs. 5 and 6. The $f_{\rm CME}$ does not depend
significantly on the proper time used to calculate the magnetic field since
varying the value from 0.1 fm/$c$ to 0.01 fm/$c$, 0.5 fm/$c$, and 1 fm/$c$
yields similar CME fractions. The $f_{\rm CME}$ is compatible with zero up to
30% centrality in both systems and then becomes positive for midcentral and
peripheral collisions with larger values in Pb–Pb than in Xe–Xe. The CME
fraction for the 0–30% centrality interval in Pb–Pb collisions agrees with the
one reported in Ref. [39]. Fitting the data points in the centrality range
0–70% with a constant function neglecting any centrality dependence gives
$f_{\rm CME}=-0.003\pm 0.010$ ($f_{\rm CME}=-0.001\pm 0.012$) and $f_{\rm
CME}=0.147\pm 0.061$ ($f_{\rm CME}=0.150\pm 0.062$) for MC Glauber (TRENTo)
initial conditions in Xe–Xe and Pb–Pb collisions, respectively. These results
are consistent with zero CME fraction in Xe–Xe collisions and correspond to
upper limits on $f_{\rm CME}$ of 2% (3%) and 25% (32%) at 95% (99.7%)
confidence level for the 0–70% centrality interval in Xe–Xe and Pb–Pb
collisions, respectively. The limits are estimated assuming Gaussian
uncertainties.

##  4 Summary

The charge-dependent two- and three-particle correlators
$\delta_{\alpha\beta}$ and $\gamma_{\alpha\beta}$ have been measured in Xe–Xe
collisions at $\sqrt{s_{\mathrm{NN}}}=5.44$ TeV. The charge dependence of
these correlators is strongly correlated with centrality, increasing from
central to peripheral collisions, and is qualitatively similar to those
reported in Pb–Pb collisions. The difference between the Xe–Xe and Pb–Pb
results mostly arises from dilution effects since the data points from both
collision systems fall approximately onto the same curve when presented as a
function of charged-particle density. Monte Carlo simulations with different
initial state models predict a significantly larger magnitude of the CME
signal in Pb–Pb than Xe–Xe collisions, which implies that the dominant
contribution to $\gamma_{\alpha\beta}$ in Xe–Xe collisions is due to
background effects. The magnitude of the charge dependence of
$\gamma_{\alpha\beta}$ is described over the entire centrality range by a
blast wave parameterisation that incorporates local charge conservation tuned
to reproduce the components of the background. This magnitude is also
reproduced by Anomalous Viscous Fluid Dynamics calculations with large
contributions from local charge conservation effects and values of the CME
signal close to zero, thus indicating that the background is the dominant
contribution to the three-particle correlator. In order to get a quantitative
estimate of the signal and background contributions, the measured values of
$\gamma_{\alpha\beta}$ in Xe–Xe and Pb–Pb collisions are compared using a two-
component approach. This procedure allows one to estimate the fraction of the
CME signal in both collision systems. Averaging over the 0–70% centrality
interval, an upper limit of 2% (3%) and 25% (32%) is estimated at 95% (99.7%)
confidence level for the CME contribution to the charge dependence of
$\gamma_{\alpha\beta}$ in Xe–Xe and Pb–Pb collisions, respectively.

## References

  * [1] F. Karsch and E. Laermann, “Thermodynamics and in medium hadron properties from lattice QCD”, World Scientific (2004) 1–59, arXiv:hep-lat/0305025.
  * [2] F. Karsch, E. Laermann, and A. Peikert, “Quark mass and flavor dependence of the QCD phase transition”, Nucl. Phys. B 605 (2001) 579–599, arXiv:hep-lat/0012023.
  * [3] F. Karsch, E. Laermann, and A. Peikert, “The Pressure in two flavor, (2+1)-flavor and three flavor QCD”, Phys. Lett. B 478 (2000) 447–455, arXiv:hep-lat/0002003.
  * [4] F. Karsch, “Lattice results on QCD thermodynamics”, Nucl. Phys. A 698 (2002) 199–208, arXiv:hep-ph/0103314.
  * [5] C. R. Allton et al., “The QCD thermal phase transition in the presence of a small chemical potential”, Phys. Rev. D 66 (2002) 074507, arXiv:hep-lat/0204010.
  * [6] A. Bazavov et al., “Equation of state and QCD transition at finite temperature”, Phys. Rev. D 80 (2009) 014504, arXiv:0903.4379 [hep-lat].
  * [7] A. Bazavov et al., “The chiral and deconfinement aspects of the QCD transition”, Phys. Rev. D 85 (2012) 054503, arXiv:1111.1710 [hep-lat].
  * [8] S. Borsanyi et al., “The QCD equation of state with dynamical quarks”, JHEP 11 (2010) 077, arXiv:1007.2580 [hep-lat].
  * [9] CMS Collaboration, S. Chatrchyan et al., “Measurement of the pseudorapidity and centrality dependence of the transverse energy density in PbPb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. Lett. 109 (2012) 152303, arXiv:1205.2488 [nucl-ex].
  * [10] ALICE Collaboration, J. Adam et al., “Direct photon production in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Lett. B 754 (2016) 235–248, arXiv:1509.07324 [nucl-ex].
  * [11] ALICE Collaboration, J. Adam et al., “Measurement of transverse energy at midrapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. C 94 no. 3, (2016) 034903, arXiv:1603.04775 [nucl-ex].
  * [12] T. Lee, “A Theory of Spontaneous T Violation”, Phys. Rev. D 8 (1973) 1226–1239.
  * [13] T. Lee and G. Wick, “Vacuum Stability and Vacuum Excitation in a Spin 0 Field Theory”, Phys. Rev. D 9 (1974) 2291–2316.
  * [14] P. Morley and I. Schmidt, “Strong P, CP, T Violations in Heavy Ion Collisions”, Z. Phys. C 26 (1985) 627.
  * [15] D. Kharzeev, R. Pisarski, and M. H. Tytgat, “Possibility of spontaneous parity violation in hot QCD”, Phys. Rev. Lett. 81 (1998) 512–515, arXiv:hep-ph/9804221.
  * [16] D. Kharzeev and R. D. Pisarski, “Pionic measures of parity and CP violation in high-energy nuclear collisions”, Phys. Rev. D 61 (2000) 111901, arXiv:hep-ph/9906401.
  * [17] D. E. Kharzeev, “Topology, magnetic field, and strongly interacting matter”, Ann. Rev. Nucl. Part. Sci. 65 (2015) 193–214, arXiv:1501.01336 [hep-ph].
  * [18] D. Kharzeev and A. Zhitnitsky, “Charge separation induced by P-odd bubbles in QCD matter”, Nucl. Phys. A 797 (2007) 67–79, arXiv:0706.1026 [hep-ph].
  * [19] D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, “The Effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation”’, Nucl. Phys. A 803 (2008) 227–253, arXiv:0711.0950 [hep-ph].
  * [20] K. Fukushima, D. E. Kharzeev, and H. J. Warringa, “The Chiral Magnetic Effect”, Phys. Rev. D 78 (2008) 074033, arXiv:0808.3382 [hep-ph].
  * [21] V. Skokov, A. Illarionov, and V. Toneev, “Estimate of the magnetic field strength in heavy-ion collisions”, Int. J. Mod. Phys. A 24 (2009) 5925–5932, arXiv:0907.1396 [nucl-th].
  * [22] A. Bzdak and V. Skokov, “Event-by-event fluctuations of magnetic and electric fields in heavy ion collisions”, Phys. Lett. B 710 (2012) 171–174, arXiv:1111.1949 [hep-ph].
  * [23] W.-T. Deng and X.-G. Huang, “Event-by-event generation of electromagnetic fields in heavy-ion collisions”, Phys. Rev. C 85 (2012) 044907, arXiv:1201.5108 [nucl-th].
  * [24] S. Voloshin and Y. Zhang, “Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions”, Z. Phys. C70 (1996) 665–672, arXiv:hep-ph/9407282.
  * [25] S. A. Voloshin, “Parity violation in hot QCD: How to detect it”, Phys. Rev. C70 (2004) 057901, arXiv:hep-ph/0406311.
  * [26] A. M. Poskanzer and S. A. Voloshin, “Methods for analyzing anisotropic flow in relativistic nuclear collisions”, Phys. Rev. C58 (1998) 1671–1678, arXiv:nucl-ex/9805001.
  * [27] STAR Collaboration, B. I. Abelev et al., “Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation”, Phys. Rev. Lett. 103 (2009) 251601, arXiv:0909.1739 [nucl-ex].
  * [28] STAR Collaboration, B. I. Abelev et al., “Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions”, Phys. Rev. C 81 (2010) 054908, arXiv:0909.1717 [nucl-ex].
  * [29] ALICE Collaboration, B. Abelev et al., “Charge separation relative to the reaction plane in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. Lett. 110 no. 1, (2013) 012301, arXiv:1207.0900 [nucl-ex].
  * [30] ALICE Collaboration, K. Aamodt et al., “Charged-particle multiplicity density at mid-rapidity in central Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. Lett. 105 (2010) 252301, arXiv:1011.3916 [nucl-ex].
  * [31] ALICE Collaboration, K. Aamodt et al., “Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV”, Phys. Rev. Lett. 106 (2011) 032301, arXiv:1012.1657 [nucl-ex].
  * [32] S. Schlichting and S. Pratt, “Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation observables”, Phys. Rev. C 83 (2011) 014913, arXiv:1009.4283 [nucl-th].
  * [33] S. Pratt, S. Schlichting, and S. Gavin, “Effects of Momentum Conservation and Flow on Angular Correlations at RHIC”, Phys. Rev. C 84 (2011) 024909, arXiv:1011.6053 [nucl-th].
  * [34] CMS Collaboration, V. Khachatryan et al., “Observation of charge-dependent azimuthal correlations in $p$-Pb collisions and its implication for the search for the chiral magnetic effect”, Phys. Rev. Lett. 118 no. 12, (2017) 122301, arXiv:1610.00263 [nucl-ex].
  * [35] STAR Collaboration, J. Adam et al., “Charge-dependent pair correlations relative to a third particle in $p$ \+ Au and $d$\+ Au collisions at RHIC”, Phys. Lett. B 798 (2019) 134975, arXiv:1906.03373 [nucl-ex].
  * [36] ALICE Collaboration, S. Acharya et al., “Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV”, Phys. Lett. B777 (2018) 151–162, arXiv:1709.04723 [nucl-ex].
  * [37] J. Schukraft, A. Timmins, and S. A. Voloshin, “Ultra-relativistic nuclear collisions: event shape engineering”, Phys. Lett. B719 (2013) 394–398, arXiv:1208.4563 [nucl-ex].
  * [38] CMS Collaboration, A. M. Sirunyan et al., “Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in $p\mathrm{Pb}$ and PbPb collisions at the CERN Large Hadron Collider”, Phys. Rev. C 97 no. 4, (2018) 044912, arXiv:1708.01602 [nucl-ex].
  * [39] ALICE Collaboration, S. Acharya et al., “Constraining the Chiral Magnetic Effect with charge-dependent azimuthal correlations in Pb–Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 and 5.02 TeV”, JHEP 09 (2020) 160, arXiv:2005.14640 [nucl-ex].
  * [40] STAR Collaboration, M. Abdallah et al., “Search for the chiral magnetic effect with isobar collisions at $\sqrt{s_{NN}}$=200 GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider”, Phys. Rev. C 105 no. 1, (2022) 014901, arXiv:2109.00131 [nucl-ex].
  * [41] ALICE Collaboration, S. Acharya et al., “Anisotropic flow in Xe–Xe collisions at $\sqrt{s_{\rm{NN}}}=5.44$ TeV”, Phys. Lett. B 784 (2018) 82–95, arXiv:1805.01832 [nucl-ex].
  * [42] P. Christakoglou, S. Qiu, and J. Staa, “Systematic study of the chiral magnetic effect with the AVFD model at LHC energies”, Eur. Phys. J. C 81 no. 8, (2021) 717, arXiv:2106.03537 [nucl-th].
  * [43] S. Shi, Y. Jiang, E. Lilleskov, and J. Liao, “Anomalous Chiral Transport in Heavy Ion Collisions from Anomalous-Viscous Fluid Dynamics”, Annals Phys. 394 (2018) 50–72, arXiv:1711.02496 [nucl-th].
  * [44] Y. Jiang, S. Shi, Y. Yin, and J. Liao, “Quantifying the chiral magnetic effect from anomalous-viscous fluid dynamics”, Chin. Phys. C 42 no. 1, (2018) 011001, arXiv:1611.04586 [nucl-th].
  * [45] S. Shi, H. Zhang, D. Hou, and J. Liao, “Signatures of Chiral Magnetic Effect in the Collisions of Isobars”, Phys. Rev. Lett. 125 (2020) 242301, arXiv:1910.14010 [nucl-th].
  * [46] ALICE Collaboration, K. Aamodt et al., “The ALICE experiment at the CERN LHC”, JINST 3 (2008) S08002.
  * [47] ALICE Collaboration, B. B. Abelev et al., “Performance of the ALICE Experiment at the CERN LHC”, Int. J. Mod. Phys. A 29 (2014) 1430044, arXiv:1402.4476 [nucl-ex].
  * [48] ALICE Collaboration, K. Aamodt et al., “Alignment of the ALICE Inner Tracking System with cosmic-ray tracks”, JINST 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det].
  * [49] J. Alme et al., “The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events”, Nucl. Instrum. Meth. A 622 (2010) 316–367, arXiv:1001.1950 [physics.ins-det].
  * [50] ALICE Collaboration, E. Abbas et al., “Performance of the ALICE VZERO system”, JINST 8 (2013) P10016, arXiv:1306.3130 [nucl-ex].
  * [51] R. Arnaldi et al., “The zero degree calorimeters for the ALICE experiment”, Nucl. Instrum. Meth. A 581 (2007) 397–401. [Erratum: Nucl.Instrum.Meth.A 604, 765 (2009)].
  * [52] ALICE Collaboration, S. Acharya et al., “Centrality determination using the Glauber model in Xe–Xe collisions at $\sqrt{s_{\rm NN}}=5.44$ TeV”, ALICE-PUBLIC-2018-003 (2018) 1–23. {http://cds.cern.ch/record/2315401}.
  * [53] ALICE Collaboration, S. Acharya et al., “Transverse momentum spectra and nuclear modification factors of charged particles in Xe–Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV”, Phys. Lett. B 788 (2019) 166–179, arXiv:1805.04399 [nucl-ex].
  * [54] X.-N. Wang and M. Gyulassy, “HIJING: A Monte Carlo model for multiple jet production in pp, pA and AA collisions”, Phys. Rev. D44 (1991) 3501–3516.
  * [55] M. Gyulassy and X.-N. Wang, “HIJING 1.0: A Monte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions”, Comput. Phys. Commun. 83 (1994) 307, arXiv:nucl-th/9502021.
  * [56] R. Brun et al., “GEANT Detector Description and Simulation Tool”, CERN-W5013 1 (1994) 1. https://cds.cern.ch/record/1082634.
  * [57] U. Gürsoy, D. Kharzeev, E. Marcus, K. Rajagopal, and C. Shen, “Charge-dependent Flow Induced by Magnetic and Electric Fields in Heavy Ion Collisions”, Phys. Rev. C 98 no. 5, (2018) 055201, arXiv:1806.05288 [hep-ph].
  * [58] ATLAS Collaboration, G. Aad et al., “Longitudinal Flow Decorrelations in Xe+Xe Collisions at $\sqrt{s_{\mathrm{NN}}}=5.44$ TeV with the ATLAS Detector”, Phys. Rev. Lett. 126 no. 12, (2021) 122301, arXiv:2001.04201 [nucl-ex].
  * [59] I. Selyuzhenkov and S. Voloshin, “Effects of non-uniform acceptance in anisotropic flow measurement”, Phys. Rev. C 77 (2008) 034904, arXiv:0707.4672 [nucl-th].
  * [60] ALICE Collaboration, S. Acharya et al., “Transverse momentum spectra and nuclear modification factors of charged particles in pp, p–Pb and Pb–Pb collisions at the LHC”, JHEP 11 (2018) 013, arXiv:1802.09145 [nucl-ex].
  * [61] R. Barlow, “Systematic errors: Facts and fictions”, in Conference on Advanced Statistical Techniques in Particle Physics, pp. 134–144.  7, 2002.  arXiv:hep-ex/0207026.
  * [62] ALICE Collaboration, J. Adam et al., “Centrality dependence of the charged-particle multiplicity density at midrapidity in Pb–Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV”, Phys. Rev. Lett. 116 no. 22, (2016) 222302, arXiv:1512.06104 [nucl-ex].
  * [63] ALICE Collaboration, S. Acharya et al., “Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe–Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV”, Phys. Lett. B 790 (2019) 35–48, arXiv:1805.04432 [nucl-ex].
  * [64] F. Retiere and M. A. Lisa, “Observable implications of geometrical and dynamical aspects of freeze out in heavy ion collisions”, Phys. Rev. C70 (2004) 044907, arXiv:nucl-th/0312024.
  * [65] ALICE Collaboration, S. Acharya et al., “Production of pions, kaons, (anti-)protons and $\phi$ mesons in Xe–Xe collisions at $\sqrt{s_{\rm NN}}=5.44$ TeV”, arXiv:2101.03100 [nucl-ex].
  * [66] ALICE Collaboration, S. Acharya et al., “Anisotropic flow of identified hadrons in Xe–Xe collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.44 TeV”, JHEP 10 (2021) 152, arXiv:2107.10592 [nucl-ex].
  * [67] H. Song and U. W. Heinz, “Suppression of elliptic flow in a minimally viscous quark-gluon plasma”, Phys. Lett. B 658 (2008) 279–283, arXiv:0709.0742 [nucl-th].
  * [68] S. A. Bass et al., “Microscopic models for ultrarelativistic heavy ion collisions”, Prog. Part. Nucl. Phys. 41 (1998) 255–369, arXiv:nucl-th/9803035.
  * [69] M. Bleicher et al., “Relativistic hadron–hadron collisions in the ultrarelativistic quantum molecular dynamics model”, J. Phys. G 25 (1999) 1859–1896, arXiv:hep-ph/9909407.
  * [70] M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, “Glauber modeling in high energy nuclear collisions”, Ann. Rev. Nucl. Part. Sci. 57 (2007) 205–243, arXiv:nucl-ex/0701025.
  * [71] ALICE Collaboration, S. Acharya et al., “Centrality determination in heavy ion collisions”, ALICE-PUBLIC-2018-011 (2018) 1–28. {https://cds.cern.ch/record/2636623}.
  * [72] J. S. Moreland, J. E. Bernhard, and S. A. Bass, “Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions”, Phys.Rev. C92 no. 1, (2015) 011901, arXiv:1412.4708 [nucl-th].
  * [73] W.-T. Deng, X.-G. Huang, G.-L. Ma, and G. Wang, “Test the chiral magnetic effect with isobaric collisions”, Phys. Rev. C 94 (2016) 041901, arXiv:1607.04697 [nucl-th].


- - - - c 9.42807(1e-05) 1689.91613(0.00097) 1.8(1.7) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1439 (T001439) - - - - - $\equiv 0.0$ $\equiv
0.0$ -0.3(0.71) - 4.62(0.56) - b 27.644(0.00012) 1703.4747(0.0029) 7.0(1.0)
0.157(0.083) 2.0(2.7) - - - - - - TOI 1443 (T001443) - - - - - 0.029(0.0044)
$\equiv 0.0$ -3.5(1.4) - 5.0(1.0) - b 23.540678(5.8e-05) 1693.25(0.05)
1.4(2.2) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1444 (T001444) - - - - -
$\equiv 0.0$ $\equiv 0.0$ -0.3(0.5) - 3.76(0.38) - b 0.4702743(1.1e-06)
1711.3675(0.0011) 3.02(0.62) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
16.067(0.017) 713.2(1.5) 2.67(0.72) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI
1451 (T001451) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.09(0.61) -0.22(0.76)
4.58(0.52) 6.39(0.73) b 16.537944(4.5e-05) 1694.3115(0.0015) 3.82(0.68)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1456 (332231) - - - - - $\equiv
0.0$ $\equiv 0.0$ 1.13(0.98) 1.0(1.0) 3.85(0.89) 10.4(0.81) b
18.712024(2.3e-05) 1692.2582(0.00071) 16.0(1.0) 0.069(0.034) 0.04(0.87) - - -
- - - TOI 1467 (T001467) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.75(0.64) -
4.6(0.5) - b 5.97199(0.00083) 1766.985(0.003) 0.0(1.8) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1471 (12572) - - - - - -0.058(0.0011) $\equiv
0.0$ -13.31(0.59) -3.86(0.38) 3.61(0.45) 5.02(0.31) b 20.772858(4.7e-05)
1767.4228(0.0013) 2.01(0.41) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
52.56363(0.00016) 1779.1904(0.0014) -0.1(0.5) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 1472 (T001472) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.3(1.3) -
5.9(1.1) - b 6.36381(0.00091) 1765.6074(0.0022) 6.0(1.9) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1473 (6061) - - - - - -0.018(0.0061)
2.7e-05(1.2e-05) -2.6(0.7) -2.0(1.9) 5.21(0.54) 11.5(1.4) b 5.2549(0.0011)
1769.7863(0.0027) 3.63(0.87) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1601
(T001601) - - - - - $\equiv 0.0$ $\equiv 0.0$ 1.2(1.2) - 6.95(0.99) - b
5.33175(0.00014) 1793.2753(0.0016) 107.8(1.9) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 1611 (207897) - - - - - 0.00165(0.00095) 3.4e-07(1.8e-07) 0.52(0.39)
442.69(0.55) 2.39(0.28) 4.11(0.56) b 16.20166(1.6e-05) 1796.49559(0.00067)
4.26(0.38) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1669 (T001669) - - - - -
-0.03(0.006) $\equiv 0.0$ -3.7(1.4) - 4.3(1.1) - b 500.0(13.0) 2325.0(9.6)
15.5(1.8) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c 2.6800535(6.2e-06)
1816.94479(0.00083) 0.1(1.9) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1691
(T001691) - - - - - $\equiv 0.0$ $\equiv 0.0$ 0.48(0.88) - 3.74(0.74) - b
16.7369(3e-05) 1818.091(0.001) 3.8(1.4) $\equiv 0.0$ $\equiv\pi/2$ - - - - - -
TOI 1694 (T001694) - - - - - $\equiv 0.0$ $\equiv 0.0$ -2.8(0.9) - 1.2(2.9) -
b 3.770107(8.5e-05) 1817.26629(0.00061) 14.3(1.1) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - c 393.1(4.7) 2170.5(4.3) 28.84(0.98) $\equiv 0.0$ $\equiv\pi/2$ - -
- - - - TOI 1710 (T001710) - - - - - -0.0125(0.0032) $\equiv 0.0$ -2.3(1.4)
0.7(0.69) 4.9(1.2) 7.92(0.49) b 24.283377(2.6e-05) 1836.96292(0.00051)
4.87(0.86) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1716 (237566) - - - - -
$\equiv 0.0$ $\equiv 0.0$ -0.7(0.5) -1.2(0.76) 3.68(0.41) 6.4(0.7) b
8.0824(4.5e-05) 1843.853(0.0028) 1.47(0.62) $\equiv 0.0$ $\equiv\pi/2$ - - - -
- - TOI 1723 (T001723) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.6(1.8) -0.8(1.1)
7.1(1.4) 7.11(0.92) b 13.72641(0.00046) 1852.7024(0.0017) 2.7(1.3) $\equiv
0.0$ $\equiv\pi/2$ - - - - - - TOI 1726 (63433) - - - - - $\equiv 0.0$ $\equiv
0.0$ -0.4(7.9) -5.2(9.8) 15.0(29.0) 5.0(1.1) b 7.1079384(6.6e-06)
1845.37353(0.00055) 12.5(3.2) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
20.543847(2.1e-05) 1844.05899(0.00058) 4.1(2.3) $\equiv 0.0$ $\equiv\pi/2$ - -
- - - - TOI 1736 (T001736) - - - - - -0.183(0.002) $\equiv 0.0$ -131.05(0.76)
-89.89(0.43) 4.33(0.43) 6.2(0.3) b 7.073076(1.7e-05) 1792.795(0.001)
4.01(0.44) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c 571.25(0.46) 1701.81(0.79)
197.55(0.59) 0.3685(0.0021) 2.8312(0.0077) - - - - - - TOI 1742 (156141) - - -
- - 0.0392(0.0015) -4.05e-05(5.2e-06) 5.39(0.45) -0.56(0.51) 3.1(0.3)
6.57(0.32) b 21.269084(5.1e-05) 1725.3518(0.0021) 2.25(0.44) 0.3(0.1)
-0.64(0.56) - - - - - - TOI 1751 (146757) - - - - - $\equiv 0.0$ $\equiv 0.0$
0.33(0.63) -0.4(0.7) 4.7(0.5) 5.42(0.74) b 37.46852(0.00013) 1733.635(0.002)
4.15(0.73) 0.327(0.083) 2.1(2.9) - - - - - - TOI 1753 (T001753) - - - - -
$\equiv 0.0$ $\equiv 0.0$ -0.2(1.3) - 5.1(1.1) - b 5.3846104(9.9e-06)
1684.503(0.002) 6.0(2.0) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1758
(T001758) - - - - - $\equiv 0.0$ $\equiv 0.0$ 0.1(1.2) - 5.0(1.0) - b
20.705127(5.6e-05) 1806.6974(0.0013) 1.8(1.7) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 1759 (T001759) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.5(2.2) -
2.9(0.44) - b 18.85018(0.00031) 1745.4658(0.0011) 0.0(1.8) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - TOI 1775 (T001775) - - - - - $\equiv 0.0$ $\equiv
0.0$ 0.1(3.3) - 12.3(2.5) - b 10.2405549(9.6e-06) 1877.5645(0.00047) 29.8(4.6)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1776 (95072) - - - - -
0.0019(0.0018) -1.61e-05(5.4e-06) 0.18(0.68) -1.78(0.55) 4.01(0.44) 3.56(0.51)
b 2.799868(2.3e-05) 1871.4976(0.0038) 0.68(0.51) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - TOI 1778 (77946) - - - - - -0.0072(0.0019) -1.34e-05(5.5e-06)
-2.18(0.63) 178.1(0.6) -3.38(0.39) 5.55(0.55) b 6.527363(2.7e-05)
1875.9989(0.0021) 3.4(0.53) 0.211(0.072) -0.16(0.67) - - - - - - TOI 1794
(T001794) - - - - - $\equiv 0.0$ $\equiv 0.0$ -0.3(0.8) - 3.2(0.73) - b
8.765528(3.5e-05) 1715.312(0.002) 2.8(1.3) $\equiv 0.0$ $\equiv\pi/2$ - - - -
- - TOI 1797 (93963) - - - - - $\equiv 0.0$ $\equiv 0.0$ -3.8(1.6) 0.4(1.7)
10.02(0.98) 10.99(0.97) b 1.0376109(8.5e-06) 2635.926(0.003) 1.6(1.4) $\equiv
0.0$ $\equiv\pi/2$ - - - - - - c 3.6451389(4.4e-06) 1902.874(0.00068) 7.2(1.2)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1798 (T001798) - - - - -
0.0061(0.0025) $\equiv 0.0$ -0.7(0.5) - 4.73(0.39) - b 8.02154(2.8e-05)
1741.5942(0.0022) 2.3(0.7) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - c
0.4378146(1.4e-06) 1738.6343(0.00097) 5.24(0.66) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - TOI 1799 (96735) - - - - - $\equiv 0.0$ $\equiv 0.0$ -1.65(0.43)
0.0(3.3) 3.16(0.35) 8.0(11.0) b 7.085738(8.3e-05) 1904.8318(0.0072) 1.4(0.6)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1801 (HIP57099) - - - - -
-0.0688(0.0081) 9.3e-05(3.4e-05) -10.1(3.8) - 9.0(2.0) - b 10.643985(2.6e-05)
1903.548(0.002) -2.2(3.2) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1807
(HIP65469) - - - - - $\equiv 0.0$ $\equiv 0.0$ 2.1(7.5) - 1.5(2.3) - b
0.54937097(7.2e-07) 1899.345(0.00038) 2.18(0.51) $\equiv 0.0$ $\equiv\pi/2$ -
- - - - - TOI 1823 (TIC142381532) - - - - - -0.025(0.0052) $\equiv 0.0$
14.9(2.9) 5.1(1.9) 5.3(1.5) 6.9(1.4) b 38.8(0.01) 2645.70502(0.00071)
14.4(1.7) 0.062(0.057) 1.3(2.2) - - - - - - TOI 1824 (T001824) - - - - -
-0.007(0.0031) $\equiv 0.0$ -0.1(0.98) 0.68(0.94) 1e-06(0.28) 5.85(0.46) b
22.808533(5.5e-05) 1879.5467(0.0011) 3.93(0.62) $\equiv 0.0$ $\equiv\pi/2$ - -
- - - - TOI 1836 (148193) - - - - - -0.017(0.019) -7e-05(3.6e-05) 2.3(2.4) -
6.04(0.76) - b 20.380845(2.8e-05) 1933.16603(0.00078) 5.0(1.2) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - c 1.7727471(7.9e-06) 2739.67(0.003) -0.3(1.3)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 1842 (T001842) - - - - -
-0.0269(0.0073) $\equiv 0.0$ -0.13(0.97) - 5.13(0.77) - b 9.5739181(9.9e-06)
1933.33614(0.00081) 21.7(1.9) 0.276(0.064) 1.18(0.17) - - - - - - TOI 1898
(83342) - - - - - $\equiv 0.0$ $\equiv 0.0$ -6.9(0.7) -15.0(3.0) 3.76(0.59)
4.9(9.9) b 45.52234(6.1e-05) 1894.2511(0.0008) 22.9(1.1) 0.485(0.039)
1.239(0.088) - - - - - - TOI 2019 (T002019) - - - - - $\equiv 0.0$ $\equiv
0.0$ 0.57(0.66) - 3.93(0.55) - b 15.3444(0.0057) 1942.942(0.009) 7.97(0.95)
0.099(0.069) 1.0(1.0) - - - - - - TOI 2045 (T002045) - - - - - -0.099(0.014)
$\equiv 0.0$ 0.0(0.0) - -2.4(8.5) - b 9.077534(8.5e-05) 1765.5949(0.0014)
54.7(4.6) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 2076 (T002076) - - - - -
$\equiv 0.0$ $\equiv 0.0$ -0.5(7.4) -13.0(19.0) 17.3(4.3) 14.0(4.0) b
10.355096(1.8e-05) 1743.744(0.001) 5.2(2.7) $\equiv 0.0$ $\equiv\pi/2$ - - - -
- - c 21.015327(2.3e-05) 1748.68944(0.00063) 5.2(2.9) $\equiv 0.0$
$\equiv\pi/2$ - - - - - - d 35.125686(8.6e-05) 1938.2931(0.0014) 0.3(2.2)
$\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 2088 (T002088) - - - - - $\equiv
0.0$ $\equiv 0.0$ -0.2(1.6) - 7.1(1.3) - b 124.72997(0.00065)
1769.6066(0.0027) 0.26(0.92) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 2114
(T002114) - - - - - $\equiv 0.0$ $\equiv 0.0$ -4.0(10.0) - 21.0(28.0) - b
6.20973(0.00019) 2719.0476(0.0011) 10.0(14.0) $\equiv 0.0$ $\equiv\pi/2$ - - -
- - - TOI 2128 (155060) - - - - - 0.0016(0.0025) 1.84e-05(7.7e-06) -0.38(0.61)
3.09(0.65) 3.81(0.37) 6.01(0.51) b 16.34136(0.00013) 1987.2663(0.0017)
1.1(0.5) $\equiv 0.0$ $\equiv\pi/2$ - - - - - - TOI 2145 (HIP86040) - - - - -
$\equiv 0.0$ $\equiv 0.0$ 29.0(4.3) - -25.6(3.3) - b 10.261127(1.1e-05)
2013.2801(0.0006) 370.7(6.4) 0.21(0.018) 1.682(0.049) - - - - - -

Table 5: Fitted Parameters

Note. — * Denotes a TKS publication. Upper limitd are given as 3$\sigma$ upper
limits. Note that mass marked as mp$\sin{(i)}$ lack an inclination measurement
and should be treated as a lower limit.

Note. — The first line for each target displays fitted parameters for the
system as a whole such as RV offset for each instrument, linear and quadratic
terms, etc. Values in parenthesis represent the 1-$\sigma$ errors for each
value. BJD is given relative to the TESS standard $T_{\text{0}}$-2457000.

Table 6: GP Fitted Parameters

TOI (TKS ID) |  $\eta_{1}$ (HIRES) |  $\eta_{1}$ (APF) | $\eta_{2}$ | $\eta_{3}$ | $\eta_{4}$
---|---|---|---|---|---
1759 (T001759) | $5.1^{+1.6}_{-1.1}$ | – | $178^{+140}_{-171}$ | $36.63^{+0.9}_{-0.53}$ | $0.487^{+0.049}_{-0.049}$
260 (HIP 1532) | $3.12^{+0.72}_{-0.6}$ | – | $274^{+170}_{-170}$ | $36.6^{+0.8}_{-0.44}$ | $0.474^{+0.051}_{-0.048}$
1174 (T001174) | $6.4^{+5.2}_{-6.3}$ | – | $145^{+100}_{-99}$ | $11.49^{+0.35}_{-0.35}$ | $0.501^{+0.051}_{-0.05}$
1272 (T001272) | $0.032^{+0.094}_{-0.018}$ | – | $81^{+210}_{-42}$ | $28.31^{+0.63}_{-0.62}$ | $0.5^{+0.052}_{-0.051}$
2076 (T002076) | $36.7^{+8.7}_{-7.4}$ | $55^{+14}_{-11}$ | $161^{+77}_{-37}$ | $7.367^{+0.02}_{-0.022}$ | $0.381^{+0.057}_{-0.049}$
1473 (6061) | $3.7^{+2.5}_{-3.1}$ | $9.6^{+2.2}_{-2.2}$ | $27^{+30}_{-11}$ | $13.87^{+0.81}_{-0.87}$ | $0.488^{+0.052}_{-0.05}$
1430 (235088) | $2.1^{+3.0}_{-1.9}$ | $0.95^{+4.8}_{-0.76}$ | $15.5^{+300}_{-7.7}$ | $7.6^{+1.6}_{-2.3}$ | $0.498^{+0.051}_{-0.05}$
1726 (63433) | $15^{+16}_{-15}$ | $44.7^{+7.4}_{-5.9}$ | $91^{33}_{-40}$ | $6.382^{+0.021}_{-0.016}$ | $0.367^{+0.045}_{-0.05}$
1807 (HIP 65469) | $33^{+5}_{-4}$ | – | $64.6^{+7.9}_{-7.6}$ | $8.728^{+0.021}_{-0.022}$ | $0.333^{+0.028}_{-0.027}$
1347 (T001347) | $12.4^{+2.9}_{-1.9}$ | – | $111^{+76}_{-40}$ | $16.47^{+0.12}_{-0.17}$ | $0.460^{+0.052}_{-0.05}$
1824 (T001824) | $5.16^{+0.68}_{-0.58}$ | $4.68^{+0.73}_{-0.68}$ | $10.3^{2.9}_{-2.3}$ | $8.36^{+0.47}_{-0.51}$ | $0.518^{+0.048}_{-0.046}$

Note. — Not all systems have APF data.

$\eta_{1}$ \- GP amplitude for given instrument.

$\eta_{2}$ \- GP exponential scaling.

$\eta_{3}$ \- GP period.

$\eta_{4}$ \- GP periodic scaling

Table 7: Summary of HRI Observations  TOI (TKS ID) | Telescope/Instrument (Filter)
---|---
260 (HIP 1532) | Gemini/’Alopeke (562 nm, 832 nm) WIYN/NESSI (562 nm, 832 nm)
| Palomar/PHARO (Br$\gamma$, H-continuous) Gemini/Zorro (832 nm, 562 nm)
| Keck2/NIRC2 (Br$\gamma$)
1173 (T001173) | Gemini/’Alopeke (562 nm, 832 nm) Keck2/NIRC2 (Br$\gamma$)
| SAI-2.5m/Speckle (Ic)
1174 (T001174) | Gemini/’Alopeke (562 nm, 832 nm) 2.2m@CAHA/AstraLux ($z$)
| Shane/ShARCS (J, K-short)
1180 (T001180) | 2.2m@CAHA/AstraLux ($z$) WIYN/NESSI (832 nm) SAI-2.5m/Speckle (Ic)
1184 (T001184) | WIYN/NESSI (562 nm, 832 nm) Shane/ShARCS (J, K-short)
| 2.2m@CAHA/AstraLux ($z$) Gemini/NIRI (Br$\gamma$)
1194 (T001194) | Shane/ShARCS (K-short, J) Gemini/’Alopeke (562 nm, 716 nm)
1244 (T001244) | WIYN/NESSI (562 nm, 832 nm) Shane/ShARCS (K-short, J)
| 2.2m@CAHA/AstraLux ($z$) SAI-2.5m/Speckle (Ic)
| Keck2/NIRC2 (K)
1248 (T001248) | Gemini/’Alopeke (562 nm, 832 nm) Shane/ShARCS (J, K-short)
| Palomar/PHARO (Br$\gamma$)
1249 (T001249) | Gemini/’Alopeke (832 nm, 562 nm) Shane/ShARCS (J, K-short)
| 2.2m@CAHA/AstraLux ($z$)
1269 (T001269) | Shane/ShARCS (K-short, J) WIYN/NESSI (562 nm, 832 nm)
| Palomar/PHARO (Br$\gamma$) 2.2m@CAHA/AstraLux ($z$)
1279 (T001279) | Gemini/NIRI (K, Br$\gamma$) Gemini/’Alopeke (832 nm, 562 nm)
| Shane/ShARCS (J, K-short) Palomar/PHARO (Br$\gamma$)
| 2.2m@CAHA/AstraLux ($z$)
1436 (T001436) | Gemini/’Alopeke (832 nm, 562 nm) 2.2m@CAHA/AstraLux ($z$)
| Keck2/NIRC2 (Br$\gamma$)
1438 (T001438) | Gemini/’Alopeke (562 nm, 832 nm) WIYN/NESSI (832 nm, 562 nm)
| SAI-2.5m/Speckle (Ic)
1443 (T001443) | Gemini/NIRI (Br$\gamma$, K) SAI-2.5m/Speckle (Ic)
1451 (T001451) | Gemini/’Alopeke (562 nm, 832 nm) Gemini/NIRI (Br$\gamma$, K)
| Palomar/PHARO (Br$\gamma$) 2.2m@CAHA/AstraLux ($z$)
1467 (T001249) | Gemini/’Alopeke (562 nm, 832 nm) Keck2/NIRC2 (K)
1472 (T001467) | SAI-2.5m/Speckle (Ic) Gemini/’Alopeke (562 nm, 832 nm)
| Shane/ShARCS (K-short) Keck2/NIRC2 (Br$\gamma$)
1669 (T001669) | Gemini/’Alopeke (832 nm, 562 nm) WIYN/NESSI (832 nm, 562 nm)
| 2.2m@CAHA/AstraLux ($z$) SAI-2.5m/Speckle (880 nm)
1691 (T001691) | Gemini/’Alopeke (832 nm, 562 nm) 2.2m@CAHA/AstraLux ($z$)
1716 (237566) | Gemini/’Alopeke (562 nm, 832 nm) Shane/ShARCS (K-short)
| SAI-2.5m/Speckle (880 nm) Palomar/PHARO (Br$\gamma$)
1723 (T001723) | WIYN/NESSI (832 nm, 562 nm) 2.2m@CAHA/AstraLux ($z$)
| SAI-2.5m/Speckle (880 nm) Shane/ShARCS (K-short)
1742 (156141) | Gemini/’Alopeke (562 nm, 832 nm) Keck2/NIRC2 (Br$\gamma$)
1753 (T001753) | Gemini/’Alopeke (562 nm, 832 nm) Shane/ShARCS (J, K-short)
| Palomar/PHARO (Br$\gamma$)
1758 (T001758) | SAI-2.5m/Speckle (625 nm) Gemini/’Alopeke (832 nm, 562 nm)
| 2.2m@CAHA/AstraLux ($z$)
1775 (T001775) | WIYN/NESSI (832 nm, 562 nm) SAI-2.5m/Speckle (Ic)
| Shane/ShARCS (K-short) Palomar/PHARO (Br$\gamma$)
1776 (95072) | Palomar/PHARO (Br$\gamma$) Shane/ShARCS (Br$\gamma$, J)
| Gemini/’Alopeke (562 nm, 832 nm)
1778 (77496) | Gemini/’Alopeke (562 nm, 832 nm) Shane/ShARCS (K-short)
| Palomar/PHARO (Br$\gamma$) SAI-2.5m/Speckle (880 nm)
1794 (T001794) | Gemini/’Alopeke (832 nm, 562 nm) Palomar/PHARO (Br$\gamma$, H-continuous)
| Shane/ShARCS (K-short) 2.2m@CAHA/AstraLux ($z$)
1798 (T001798) | Gemini/’Alopeke (832 nm, 562 nm) Keck2/NIRC2 (Br$\gamma$)
1799 (96735) | Palomar/PHARO (Br$\gamma$) Shane/ShARCS (K-short, J)
| Gemini/’Alopeke (562 nm, 832 nm)
1823 (TIC142381532) | Shane/ShARCS (J, K-short) Gemini/’Alopeke (562 nm, 832 nm)
| Palomar/PHARO (Br$\gamma$)
2045 (T002045) | Shane/ShARCS (K-short) SAI-2.5m/Speckle (Ic)
2088 (T002088) | 2.2m@CAHA/AstraLux ($z$) SAI-2.5m/Speckle (Ic)
| WIYN/NESSI (832 nm)
2114 (T002114) | Shane/ShARCS (Ks, J) Palomar/PHARO (Br$\gamma$)
2128 (155060) | SAI-2.5m/Speckle (625 nm) Shane/ShARCS (Br$\gamma$, J)
| 2.2m@CAHA/AstraLux ($z$) Palomar/PHARO (Br$\gamma$, H-continuous)

## References

  * Akana Murphy et al. (2023a) Akana Murphy, J. M., Batalha, N. M., Scarsdale, N., et al. 2023a, AJ, 166, 153, doi: 10.3847/1538-3881/ace2ca
  * Akana Murphy et al. (2023b) —. 2023b, AJ, 166, 153, doi: 10.3847/1538-3881/ace2ca
  * Anderson et al. (2011) Anderson, D. R., Collier Cameron, A., Hellier, C., et al. 2011, ApJ, 726, L19, doi: 10.1088/2041-8205/726/2/L19
  * Armstrong et al. (2020) Armstrong, D. J., Lopez, T. A., Adibekyan, V., et al. 2020, Nature, 583, 39, doi: 10.1038/s41586-020-2421-7
  * Baron et al. (2023) Baron, J., Müller, S., Helled, R., Bouchy, F., & Parc, L. 2023, arXiv e-prints, arXiv:2311.12593, doi: 10.48550/arXiv.2311.12593
  * Beard et al. (2024) Beard, C., Robertson, P., Dai, F., et al. 2024, AJ, 167, 70, doi: 10.3847/1538-3881/ad1330
  * Berger et al. (2020) Berger, T. A., Huber, D., van Saders, J. L., et al. 2020, AJ, 159, 280, doi: 10.3847/1538-3881/159/6/280
  * Berger et al. (2023) Berger, T. A., Schlieder, J. E., & Huber, D. 2023, arXiv e-prints, arXiv:2301.11338, doi: 10.48550/arXiv.2301.11338
  * Blunt et al. (2023) Blunt, S., Carvalho, A., David, T. J., et al. 2023, AJ, 166, 62, doi: 10.3847/1538-3881/acde78
  * Borucki et al. (2010) Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977, doi: 10.1126/science.1185402
  * Borucki et al. (2012) Borucki, W. J., Koch, D. G., Batalha, N., et al. 2012, ApJ, 745, 120, doi: 10.1088/0004-637X/745/2/120
  * Brinkman et al. (2023) Brinkman, C. L., Weiss, L. M., Dai, F., et al. 2023, AJ, 165, 88, doi: 10.3847/1538-3881/acad83
  * Burt et al. (2018) Burt, J., Holden, B., Wolfgang, A., & Bouma, L. G. 2018, AJ, 156, 255, doi: 10.3847/1538-3881/aae697
  * Butler et al. (1996) Butler, R. P., Marcy, G. W., Williams, E., et al. 1996, PASP, 108, 500, doi: 10.1086/133755
  * Chen & Kipping (2017) Chen, J., & Kipping, D. 2017, ApJ, 834, 17, doi: 10.3847/1538-4357/834/1/17
  * Chontos et al. (2022) Chontos, A., Murphy, J. M. A., MacDougall, M. G., et al. 2022, AJ, 163, 297, doi: 10.3847/1538-3881/ac6266
  * Chontos et al. (2024) Chontos, A., Huber, D., Grunblatt, S. K., et al. 2024, arXiv e-prints, arXiv:2402.07893, doi: 10.48550/arXiv.2402.07893
  * Ciardi et al. (2015) Ciardi, D. R., Beichman, C. A., Horch, E. P., & Howell, S. B. 2015, ApJ, 805, 16, doi: 10.1088/0004-637X/805/1/16
  * Covino et al. (2013) Covino, E., Esposito, M., Barbieri, M., et al. 2013, A&A, 554, A28, doi: 10.1051/0004-6361/201321298
  * Crossfield et al. (2016) Crossfield, I. J. M., Ciardi, D. R., Petigura, E. A., et al. 2016, ApJS, 226, 7, doi: 10.3847/0067-0049/226/1/7
  * Dai et al. (2021a) Dai, F., Howard, A. W., Batalha, N. M., et al. 2021a, AJ, 162, 62, doi: 10.3847/1538-3881/ac02bd
  * Dai et al. (2021b) —. 2021b, AJ, 162, 62, doi: 10.3847/1538-3881/ac02bd
  * Dai et al. (2023) Dai, F., Masuda, K., Beard, C., et al. 2023, AJ, 165, 33, doi: 10.3847/1538-3881/aca327
  * Dalba et al. (2020) Dalba, P. A., Gupta, A. F., Rodriguez, J. E., et al. 2020, AJ, 159, 241, doi: 10.3847/1538-3881/ab84e3
  * Damasso et al. (2023) Damasso, M., Locci, D., Benatti, S., et al. 2023, A&A, 672, A126, doi: 10.1051/0004-6361/202245391
  * Dekany et al. (2013) Dekany, R., Roberts, J., Burruss, R., et al. 2013, ApJ, 776, 130, doi: 10.1088/0004-637X/776/2/130
  * Demangeon et al. (2018) Demangeon, O. D. S., Faedi, F., Hébrard, G., et al. 2018, A&A, 610, A63, doi: 10.1051/0004-6361/201731735
  * Desai et al. (2024) Desai, A., Turtelboom, E. V., Harada, C. K., et al. 2024, AJ, 167, 194, doi: 10.3847/1538-3881/ad29ee
  * Dressing & Charbonneau (2013) Dressing, C. D., & Charbonneau, D. 2013, ApJ, 767, 95, doi: 10.1088/0004-637X/767/1/95
  * Eastman et al. (2013) Eastman, J., Gaudi, B. S., & Agol, E. 2013, PASP, 125, 83, doi: 10.1086/669497
  * Edmondson et al. (2023) Edmondson, K., Norris, J., & Kerins, E. 2023, arXiv e-prints, arXiv:2310.16733, doi: 10.48550/arXiv.2310.16733
  * Espinoza et al. (2022) Espinoza, N., Pallé, E., Kemmer, J., et al. 2022, AJ, 163, 133, doi: 10.3847/1538-3881/ac4af0
  * Ford (2006) Ford, E. B. 2006, ApJ, 642, 505, doi: 10.1086/500802
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067
  * Fulton & Petigura (2018) Fulton, B. J., & Petigura, E. A. 2018, AJ, 156, 264, doi: 10.3847/1538-3881/aae828
  * Gavel et al. (2014) Gavel, D., Kupke, R., Dillon, D., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9148, Adaptive Optics Systems IV, ed. E. Marchetti, L. M. Close, & J.-P. Vran, 914805, doi: 10.1117/12.2055256
  * Gelman & Rubin (1992) Gelman, A., & Rubin, D. B. 1992, Statistical Science, 7, 457, doi: 10.1214/ss/1177011136
  * Giacalone et al. (2021) Giacalone, S., Dressing, C. D., Jensen, E. L. N., et al. 2021, AJ, 161, 24, doi: 10.3847/1538-3881/abc6af
  * Hadden & Lithwick (2014) Hadden, S., & Lithwick, Y. 2014, ApJ, 787, 80, doi: 10.1088/0004-637X/787/1/80
  * Haywood et al. (2014) Haywood, R. D., Collier Cameron, A., Queloz, D., et al. 2014, MNRAS, 443, 2517, doi: 10.1093/mnras/stu1320
  * Heidari et al. (2022) Heidari, N., Boisse, I., Orell-Miquel, J., et al. 2022, A&A, 658, A176, doi: 10.1051/0004-6361/202141429
  * Hillenbrand et al. (2015) Hillenbrand, L., Isaacson, H., Marcy, G., et al. 2015, in Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, Vol. 18, 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, 759–766, doi: 10.48550/arXiv.1408.3475
  * Hodapp et al. (2003) Hodapp, K. W., Jensen, J. B., Irwin, E. M., et al. 2003, PASP, 115, 1388, doi: 10.1086/379669
  * Horch et al. (2012) Horch, E. P., Howell, S. B., Everett, M. E., & Ciardi, D. R. 2012, AJ, 144, 165, doi: 10.1088/0004-6256/144/6/165
  * Hord et al. (2023) Hord, B. J., Kempton, E. M. R., Mikal-Evans, T., et al. 2023, arXiv e-prints, arXiv:2308.09617, doi: 10.48550/arXiv.2308.09617
  * Hormuth et al. (2008) Hormuth, F., Hippler, S., Brandner, W., Wagner, K., & Henning, T. 2008, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7014, Ground-based and Airborne Instrumentation for Astronomy II, ed. I. S. McLean & M. M. Casali, 701448, doi: 10.1117/12.787384
  * Howard et al. (2010) Howard, A. W., Johnson, J. A., Marcy, G. W., et al. 2010, ApJ, 721, 1467, doi: 10.1088/0004-637x/721/2/1467
  * Howard et al. (2021) Howard, W. S., Teske, J., Corbett, H., et al. 2021, AJ, 162, 147, doi: 10.3847/1538-3881/ac0fe3
  * Howell et al. (2011) Howell, S. B., Everett, M. E., Sherry, W., Horch, E., & Ciardi, D. R. 2011, AJ, 142, 19, doi: 10.1088/0004-6256/142/1/19
  * Huber et al. (2017) Huber, D., Zinn, J., Bojsen-Hansen, M., et al. 2017, ApJ, 844, 102, doi: 10.3847/1538-4357/aa75ca
  * Isaacson & Fischer (2010) Isaacson, H., & Fischer, D. 2010, ApJ, 725, 875, doi: 10.1088/0004-637X/725/1/875
  * Jeffreys (1946) Jeffreys, H. 1946, Proceedings of the Royal Society of London Series A, 186, 453, doi: 10.1098/rspa.1946.0056
  * Kabáth et al. (2022) Kabáth, P., Chaturvedi, P., MacQueen, P. J., et al. 2022, MNRAS, 513, 5955, doi: 10.1093/mnras/stac1254
  * Kane et al. (2009) Kane, S. R., Mahadevan, S., von Braun, K., Laughlin, G., & Ciardi, D. R. 2009, PASP, 121, 1386, doi: 10.1086/648564
  * Kane et al. (2021) Kane, S. R., Bean, J. L., Campante, T. L., et al. 2021, PASP, 133, 014402, doi: 10.1088/1538-3873/abc610
  * Kempton et al. (2018) Kempton, E. M. R., Bean, J. L., Louie, D. R., et al. 2018, PASP, 130, 114401, doi: 10.1088/1538-3873/aadf6f
  * Knudstrup et al. (2023) Knudstrup, E., Gandolfi, D., Nowak, G., et al. 2023, MNRAS, 519, 5637, doi: 10.1093/mnras/stac3684
  * Kosiarek & Crossfield (2020) Kosiarek, M. R., & Crossfield, I. J. M. 2020, AJ, 159, 271, doi: 10.3847/1538-3881/ab8d3a
  * Kupke et al. (2012) Kupke, R., Gavel, D., Roskosi, C., et al. 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 8447, Adaptive Optics Systems III, ed. B. L. Ellerbroek, E. Marchetti, & J.-P. Véran, 84473G, doi: 10.1117/12.926470
  * Lightkurve Collaboration et al. (2018) Lightkurve Collaboration, Cardoso, J. V. d. M., Hedges, C., et al. 2018, Lightkurve: Kepler and TESS time series analysis in Python, Astrophysics Source Code Library.  http://ascl.net/1812.013
  * Lillo-Box et al. (2012) Lillo-Box, J., Barrado, D., & Bouy, H. 2012, A&A, 546, A10, doi: 10.1051/0004-6361/201219631
  * Lillo-Box et al. (2014) —. 2014, A&A, 566, A103, doi: 10.1051/0004-6361/201423497
  * López-Morales et al. (2016) López-Morales, M., Haywood, R. D., Coughlin, J. L., et al. 2016, AJ, 152, 204, doi: 10.3847/0004-6256/152/6/204
  * Lubin et al. (2022) Lubin, J., Van Zandt, J., Holcomb, R., et al. 2022, AJ, 163, 101, doi: 10.3847/1538-3881/ac3d38
  * Luque & Pallé (2022) Luque, R., & Pallé, E. 2022, Science, 377, 1211, doi: 10.1126/science.abl7164
  * MacDougall et al. (2021) MacDougall, M. G., Petigura, E. A., Angelo, I., et al. 2021, AJ, 162, 265, doi: 10.3847/1538-3881/ac295e
  * MacDougall et al. (2022) MacDougall, M. G., Petigura, E. A., Fetherolf, T., et al. 2022, AJ, 164, 97, doi: 10.3847/1538-3881/ac7ce1
  * MacDougall et al. (2023) MacDougall, M. G., Petigura, E. A., Gilbert, G. J., et al. 2023, arXiv e-prints, arXiv:2306.00251, doi: 10.48550/arXiv.2306.00251
  * Martioli et al. (2022a) Martioli, E., Hébrard, G., Fouqué, P., et al. 2022a, A&A, 660, A86, doi: 10.1051/0004-6361/202142540
  * Martioli et al. (2022b) —. 2022b, A&A, 660, A86, doi: 10.1051/0004-6361/202142540
  * McGurk et al. (2014) McGurk, R., Rockosi, C., Gavel, D., et al. 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9148, Adaptive Optics Systems IV, ed. E. Marchetti, L. M. Close, & J.-P. Vran, 91483A, doi: 10.1117/12.2057027
  * Monet et al. (2003) Monet, D. G., Levine, S. E., Canzian, B., et al. 2003, AJ, 125, 984, doi: 10.1086/345888
  * Montet (2018) Montet, B. T. 2018, Research Notes of the American Astronomical Society, 2, 28, doi: 10.3847/2515-5172/aac2c1
  * Morton (2015) Morton, T. D. 2015, VESPA: False positive probabilities calculator, Astrophysics Source Code Library, record ascl:1503.011.  http://ascl.net/1503.011
  * Morton et al. (2023) Morton, T. D., Giacalone, S., & Bryson, S. 2023, Research Notes of the American Astronomical Society, 7, 107, doi: 10.3847/2515-5172/acd9a6
  * Motalebi et al. (2015) Motalebi, F., Udry, S., Gillon, M., et al. 2015, A&A, 584, A72, doi: 10.1051/0004-6361/201526822
  * Moutou et al. (2021) Moutou, C., Almenara, J. M., Hébrard, G., et al. 2021, A&A, 653, A147, doi: 10.1051/0004-6361/202141151
  * Naponiello et al. (2022) Naponiello, L., Mancini, L., Damasso, M., et al. 2022, A&A, 667, A8, doi: 10.1051/0004-6361/202244079
  * Nardiello et al. (2022) Nardiello, D., Malavolta, L., Desidera, S., et al. 2022, A&A, 664, A163, doi: 10.1051/0004-6361/202243743
  * Orell-Miquel et al. (2023) Orell-Miquel, J., Nowak, G., Murgas, F., et al. 2023, A&A, 669, A40, doi: 10.1051/0004-6361/202244120
  * Pecaut & Mamajek (2013) Pecaut, M. J., & Mamajek, E. E. 2013, ApJS, 208, 9, doi: 10.1088/0067-0049/208/1/9
  * Petigura (2015) Petigura, E. 2015, arXiv e-prints, arXiv:1510.03902, doi: 10.48550/arXiv.1510.03902
  * Reiners et al. (2018) Reiners, A., Zechmeister, M., Caballero, J. A., et al. 2018, A&A, 612, A49, doi: 10.1051/0004-6361/201732054
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003, doi: 10.1117/1.JATIS.1.1.014003
  * Rodriguez et al. (2023) Rodriguez, J. E., Quinn, S. N., Vanderburg, A., et al. 2023, MNRAS, 521, 2765, doi: 10.1093/mnras/stad595
  * Rogers et al. (2023) Rogers, J. G., Schlichting, H. E., & Owen, J. E. 2023, ApJ, 947, L19, doi: 10.3847/2041-8213/acc86f
  * Rosenthal et al. (2021a) Rosenthal, L. J., Fulton, B. J., Hirsch, L. A., et al. 2021a, ApJS, 255, 8, doi: 10.3847/1538-4365/abe23c
  * Rosenthal et al. (2021b) —. 2021b, ApJS, 255, 8, doi: 10.3847/1538-4365/abe23c
  * Rubenzahl et al. (2024) Rubenzahl, R. A., Dai, F., Howard, A. W., et al. 2024, AJ, 167, 153, doi: 10.3847/1538-3881/ad28bb
  * Safonov et al. (2017) Safonov, B. S., Lysenko, P. A., & Dodin, A. V. 2017, Astronomy Letters, 43, 344, doi: 10.1134/S1063773717050036
  * Savel et al. (2020) Savel, A. B., Dressing, C. D., Hirsch, L. A., et al. 2020, AJ, 160, 287, doi: 10.3847/1538-3881/abc47d
  * Savel et al. (2022) Savel, A. B., Hirsch, L. A., Gill, H., Dressing, C. D., & Ciardi, D. R. 2022, PASP, 134, 124501, doi: 10.1088/1538-3873/aca4f910.48550/arXiv.2212.00641
  * Scarsdale et al. (2021) Scarsdale, N., Murphy, J. M. A., Batalha, N. M., et al. 2021, AJ, 162, 215, doi: 10.3847/1538-3881/ac18cb
  * Scott (2019) Scott, N. J. 2019, in AAS/Division for Extreme Solar Systems Abstracts, Vol. 51, AAS/Division for Extreme Solar Systems Abstracts, 330.15
  * Scott et al. (2021) Scott, N. J., Howell, S. B., Gnilka, C. L., et al. 2021, Frontiers in Astronomy and Space Sciences, 8, 138, doi: 10.3389/fspas.2021.716560
  * Serrano et al. (2022) Serrano, L. M., Gandolfi, D., Hoyer, S., et al. 2022, A&A, 667, A1, doi: 10.1051/0004-6361/202243093
  * Stassun et al. (2018) Stassun, K. G., Oelkers, R. J., Pepper, J., et al. 2018, AJ, 156, 102, doi: 10.3847/1538-3881/aad050
  * Strakhov et al. (2023) Strakhov, I. A., Safonov, B. S., & Cheryasov, D. V. 2023, Astrophysical Bulletin, 78, 234, doi: 10.1134/S1990341323020104
  * Strehl (1902) Strehl, K. 1902, Astronomische Nachrichten, 158, 89, doi: 10.1002/asna.19021580604
  * Tayar et al. (2022) Tayar, J., Claytor, Z. R., Huber, D., & van Saders, J. 2022, ApJ, 927, 31, doi: 10.3847/1538-4357/ac4bbc
  * Teske et al. (2021) Teske, J., Wang, S. X., Wolfgang, A., et al. 2021, ApJS, 256, 33, doi: 10.3847/1538-4365/ac0f0a
  * Torres et al. (2004) Torres, G., Konacki, M., Sasselov, D. D., & Jha, S. 2004, ApJ, 614, 979, doi: 10.1086/423734
  * Turtelboom et al. (2022) Turtelboom, E. V., Dressing, C., Weiss, L., Tess-Keck Survey, & Kesprint Consortium. 2022, in Bulletin of the American Astronomical Society, Vol. 54, 102.281
  * Van Zandt & Petigura (2024) Van Zandt, J., & Petigura, E. 2024, arXiv e-prints, arXiv:2403.16340, doi: 10.48550/arXiv.2403.16340
  * Van Zandt et al. (2023) Van Zandt, J., Petigura, E. A., MacDougall, M., et al. 2023, AJ, 165, 60, doi: 10.3847/1538-3881/aca6ef
  * Vogt et al. (1994) Vogt, S. S., Allen, S. L., Bigelow, B. C., et al. 1994, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 2198, Instrumentation in Astronomy VIII, ed. D. L. Crawford & E. R. Craine, 362, doi: 10.1117/12.176725
  * Vogt et al. (2014a) Vogt, S. S., Radovan, M., Kibrick, R., et al. 2014a, PASP, 126, 359, doi: 10.1086/676120
  * Vogt et al. (2014b) —. 2014b, PASP, 126, 359, doi: 10.1086/676120
  * Weiss & Marcy (2014) Weiss, L. M., & Marcy, G. W. 2014, ApJ, 783, L6, doi: 10.1088/2041-8205/783/1/L6
  * Wolfgang et al. (2016) Wolfgang, A., Rogers, L. A., & Ford, E. B. 2016, ApJ, 825, 19, doi: 10.3847/0004-637X/825/1/19
  * Wright (2005) Wright, J. T. 2005, PASP, 117, 657, doi: 10.1086/430369
  * Yee et al. (2017) Yee, S. W., Petigura, E. A., & von Braun, K. 2017, ApJ, 836, 77, doi: 10.3847/1538-4357/836/1/77
  * Zeng et al. (2019) Zeng, L., Jacobsen, S. B., Sasselov, D. D., et al. 2019, Proceedings of the National Academy of Science, 116, 9723, doi: 10.1073/pnas.1812905116