# The NANOGrav 15-year data set: Search for Transverse Polarization Modes in
the Gravitational-Wave Background

Gabriella Agazie Center for Gravitation, Cosmology and Astrophysics,
Department of Physics, University of Wisconsin-Milwaukee,
P.O. Box 413, Milwaukee, WI 53201, USA  Akash Anumarlapudi Center for
Gravitation, Cosmology and Astrophysics, Department of Physics, University of
Wisconsin-Milwaukee,
P.O. Box 413, Milwaukee, WI 53201, USA  Anne M. Archibald Newcastle
University, NE1 7RU, UK  Zaven Arzoumanian  X-Ray Astrophysics Laboratory,
NASA Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA  Jeremy
Baier  Department of Physics, Oregon State University, Corvallis, OR 97331,
USA  Paul T. Baker Department of Physics and Astronomy, Widener University,
One University Place, Chester, PA 19013, USA  Bence Bécsy Department of
Physics, Oregon State University, Corvallis, OR 97331, USA  Laura Blecha
Physics Department, University of Florida, Gainesville, FL 32611, USA  Adam
Brazier Cornell Center for Astrophysics and Planetary Science and Department
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Fiore Department of Physics and Astronomy, West Virginia University, P.O. Box
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OR 97331, USA  Ross J. Jennings NANOGrav Physics Frontiers Center Postdoctoral
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Astrophysics, University of Toronto, 50 St. George St., Toronto, ON M5S 3H4,
Canada  David J. Nice Department of Physics, Lafayette College, Easton, PA
18042, USA  Stella Koch Ocker Cornell Center for Astrophysics and Planetary
Science and Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
Ken D. Olum Institute of Cosmology, Department of Physics and Astronomy, Tufts
University, Medford, MA 02155, USA  Timothy T. Pennucci Institute of Physics
and Astronomy, Eötvös Loránd University, Pázmány P. s. 1/A, 1117 Budapest,
Hungary  Benetge B. P. Perera Arecibo Observatory, HC3 Box 53995, Arecibo, PR
00612, USA  Nihan S. Pol Department of Physics and Astronomy, Vanderbilt
University, 2301 Vanderbilt Place, Nashville, TN 37235, USA  Henri A. Radovan
Department of Physics, University of Puerto Rico, Mayagüez, PR 00681, USA
Scott M. Ransom National Radio Astronomy Observatory, 520 Edgemont Road,
Charlottesville, VA 22903, USA  Paul S. Ray Space Science Division, Naval
Research Laboratory, Washington, DC 20375-5352, USA  Joseph D. Romano
Department of Physics, Texas Tech University, Box 41051, Lubbock, TX 79409,
USA  Alexander Saffer Department of Physics and Astronomy, West Virginia
University, P.O. Box 6315, Morgantown, WV 26506, USA  Center for Gravitational
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Physics, Penn State Abington, Abington, PA 19001, USA  Carl Schmiedekamp
Department of Physics, Penn State Abington, Abington, PA 19001, USA  Kai
Schmitz Institute for Theoretical Physics, University of Münster, 48149
Münster, Germany  Brent J. Shapiro-Albert Department of Physics and Astronomy,
West Virginia University, P.O. Box 6315, Morgantown, WV 26506, USA  Center for
Gravitational Waves and Cosmology, West Virginia University, Chestnut Ridge
Research Building, Morgantown, WV 26505, USA  Giant Army, 915A 17th Ave,
Seattle WA 98122  Xavier Siemens Department of Physics, Oregon State
University, Corvallis, OR 97331, USA  Center for Gravitation, Cosmology and
Astrophysics, Department of Physics, University of Wisconsin-Milwaukee,
P.O. Box 413, Milwaukee, WI 53201, USA  Joseph Simon NSF Astronomy and
Astrophysics Postdoctoral Fellow  Department of Astrophysical and Planetary
Sciences, University of Colorado, Boulder, CO 80309, USA  Magdalena S. Siwek
Center for Astrophysics, Harvard University, 60 Garden St, Cambridge, MA 02138
Ingrid H. Stairs Department of Physics and Astronomy, University of British
Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada  Daniel R.
Stinebring Department of Physics and Astronomy, Oberlin College, Oberlin, OH
44074, USA  Kevin Stovall National Radio Astronomy Observatory, 1003
Lopezville Rd., Socorro, NM 87801, USA  Jerry P. Sun Department of Physics,
Oregon State University, Corvallis, OR 97331, USA  Abhimanyu Susobhanan Center
for Gravitation, Cosmology and Astrophysics, Department of Physics, University
of Wisconsin-Milwaukee,
P.O. Box 413, Milwaukee, WI 53201, USA  Joseph K. Swiggum NANOGrav Physics
Frontiers Center Postdoctoral Fellow  Department of Physics, Lafayette
College, Easton, PA 18042, USA  Jacob A. Taylor Department of Physics, Oregon
State University, Corvallis, OR 97331, USA  Stephen R. Taylor Department of
Physics and Astronomy, Vanderbilt University, 2301 Vanderbilt Place,
Nashville, TN 37235, USA  Jacob E. Turner Department of Physics and Astronomy,
West Virginia University, P.O. Box 6315, Morgantown, WV 26506, USA  Center for
Gravitational Waves and Cosmology, West Virginia University, Chestnut Ridge
Research Building, Morgantown, WV 26505, USA  Caner Unal Department of
Physics, Ben-Gurion University of the Negev, Be’er Sheva 84105, Israel  Feza
Gursey Institute, Bogazici University, Kandilli, 34684, Istanbul, Turkey
Michele Vallisneri Jet Propulsion Laboratory, California Institute of
Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA  Division of
Physics, Mathematics, and Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  Sarah J. Vigeland Center for Gravitation, Cosmology
and Astrophysics, Department of Physics, University of Wisconsin-Milwaukee,
P.O. Box 413, Milwaukee, WI 53201, USA  Haley M. Wahl Department of Physics
and Astronomy, West Virginia University, P.O. Box 6315, Morgantown, WV 26506,
USA  Center for Gravitational Waves and Cosmology, West Virginia University,
Chestnut Ridge Research Building, Morgantown, WV 26505, USA  Caitlin A. Witt
Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA),
Northwestern University, Evanston, IL 60208  Adler Planetarium, 1300 S.
DuSable Lake Shore Dr., Chicago, IL 60605, USA  Olivia Young School of Physics
and Astronomy, Rochester Institute of Technology, Rochester, NY 14623, USA
Laboratory for Multiwavelength Astrophysics, Rochester Institute of
Technology, Rochester, NY 14623, USA The NANOGrav Collaboration
<EMAIL_ADDRESS>
###### Abstract

Recently we found compelling evidence for a gravitational wave background with
Hellings and Downs (HD) correlations in our 15-year data set. These
correlations describe gravitational waves as predicted by general relativity,
which has two transverse polarization modes. However, more general metric
theories of gravity can have additional polarization modes which produce
different interpulsar correlations. In this work we search the NANOGrav
15-year data set for evidence of a gravitational wave background with
quadrupolar Hellings and Downs (HD) and Scalar Transverse (ST) correlations.
We find that HD correlations are the best fit to the data, and no significant
evidence in favor of ST correlations. While Bayes factors show strong evidence
for a correlated signal, the data does not strongly prefer either correlation
signature, with Bayes factors $\sim 2$ when comparing HD to ST correlations,
and $\sim 1$ for HD plus ST correlations to HD correlations alone. However,
when modeled alongside HD correlations, the amplitude and spectral index
posteriors for ST correlations are uninformative, with the HD process
accounting for the vast majority of the total signal. Using the optimal
statistic, a frequentist technique that focuses on the pulsar-pair cross-
correlations, we find median signal-to-noise-ratios of 5.0 for HD and 4.6 for
ST correlations when fit for separately, and median signal-to-noise-ratios of
3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the
signal-to-noise-ratios for each of the correlations are comparable, the
estimated amplitude and spectral index for HD are a significantly better fit
to the total signal, in agreement with our Bayesian analysis.

Gravitational waves – Modified theories of gravity – Alternative polarization
modes of gravity – Methods: data analysis – Pulsars: general

##  1 Introduction

Einstein’s theory of general relativity (GR) predicts the existence of
gravitational waves (GWs) with two transverse polarization modes that
propagate at the speed of light (Eardley et al., 1973a, b). Observations by
the LIGO collaboration have shown that GR best describes gravitational
radiation from massive freely accelerating objects in the universe (Abbott et
al., 2016; The LIGO Scientific Collaboration et al., 2021). However, pulsars
and pulsar timing array (PTA) experiments offer a unique opportunity to probe
other possible metric theories of gravity external to Einstein’s GR.

Modified theories of gravity are often introduced to resolve some of the
current challenges facing fundamental physics, such as the nature of dark
matter, dark energy, and in attempts to reconcile quantum mechanics and
gravity (see, e.g., Berti et al. 2015 and references therein). In metric
theories of gravity, there can be up to six possible GW polarization modes
(Eardley et al., 1973a, b; Will, 1993). PTA searches for non-Einsteinian
polarization modes may provide evidence for modified gravity theories by
uncovering the different correlation patterns associated with such modes
(Chamberlin & Siemens, 2012; Yunes & Siemens, 2013; Gair et al., 2015; Cornish
et al., 2018; Afzal et al., 2023).

Millisecond pulsars (MSPs) emit radio beams from their magnetic poles and are
extremely stable rotators. They appear to us as point sources of periodic
radio bursts that arrive on Earth with a consistency that rivals that of
atomic clocks (Matsakis et al., 1997; Hobbs et al., 2012, 2019). Pulsar timing
experiments exploit the regularity of MSPs to search for low-frequency
($\sim$1-100 nHz) GWs by measuring deviations from the expected arrival time
of radio pulses (Sazhin, 1978; Detweiler, 1979). Moreover, an array of these
MSPs allows us to search for correlations between deviations of times of
arrivals (TOAs) of pulses from MSP pairs (Hellings & Downs, 1983; Foster &
Backer, 1990).

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav),
the European Pulsar Timing Array (EPTA), the Chinese Pulsar Timing Array
(CPTA), and the Parkes Pulsar Timing Array (PPTA) are the PTAs that possess
the most sensitive datasets capable of measuring nHz GWs. NANOGrav, the EPTA,
and the PPTA have seen strong evidence for a common red noise process
(Arzoumanian et al., 2020; Chalumeau et al., 2021; Goncharov et al., 2021).
Most recently in Agazie et al. (2023a) (hereafter referred to as NG15),
NANOGrav has found compelling evidence for quadrupolar correlations (Hellings
& Downs, 1983), while the EPTA and PPTA have seen these correlations at
varying levels of significance (Antoniadis et al., 2023; Reardon et al.,
2023). In this paper, we complement our work in NG15 by searching for evidence
for Scalar Transverse correlations from the non-Einsteinian breathing
polarization mode of gravity. Previous work in (Arzoumanian et al., 2021) has
shown preference for a Scalar-Transverse (ST) and GW-like monopolar
correlations. However, these correlations were not significant as they were
not robust to the solar system ephemeris and were associated with pulsar
J0030$+$0451\. In §2, we review the theoretical background required to
identify and search for a general transverse polarization mode of gravity
using PTAs. In §3, we then describe the analyses performed, both using
Bayesian and frequentist approaches. Lastly, in §4, we present the evidence
for/against the existence of ST correlations.

##  2 Theoretical Background

In this section, we will first review the basics of gravitational wave
polarization modes, §2.1, and proceed to outline the theoretical
considerations needed to predict the signature of such modes in a PTA GWB
signal in §2.2. Finally, in §2.3, we will explicitly describe the model for a
general transverse GWB signal which we will later search for in §3 using the
NANOGrav 15-year data set.

###  2.1 Generalized Polarization Modes in Metric Theories of Gravity

In metric theories of gravity, there can be between two and six independent
polarization modes for GWs (Eardley et al., 1973a). These modes are the
“electric” components of the Riemann tensor $R_{0i0j}$, where $i$ and $j$ are
the spatial components. These components were originally found by Newman &
Penrose (1962) making use of tetrad and spinor calculus.

For the purposes of this work, we assume a coordinate system such that a null
plane-GW travels along the $+z$-axis at the speed of light ($c$), where the
components of the Riemann tensor only depend on the retarded time $u=t-z/c$.
The assumptions lead to the following coefficients which depend on
combinations of the independent electric components of the Riemann tensor:

$\displaystyle\Psi_{2}(u)$ $\displaystyle=-\frac{1}{6}R_{0303}(u)\,,$ (1a)
$\displaystyle\Psi_{3}(u)$
$\displaystyle=-\frac{1}{2}R_{0103}+\frac{i}{2}R_{0203},$ (1b)
$\displaystyle\Psi_{4}(u)$ $\displaystyle=-R_{0101}+R_{0202}+2iR_{0102}\,,$
(1c) $\displaystyle\Phi_{22}(u)$ $\displaystyle=-R_{0101}-R_{0202}\,.$ (1d)

We may relate these to a matrix of the GW polarization modes by

$S^{ij}=\begin{bmatrix}A_{B}+A_{+}&A_{\times}&A_{V1}\\\
A_{\times}&A_{B}-A_{+}&A_{V2}\\\ A_{V1}&A_{V2}&A_{L}\end{bmatrix}\,,$ (2)

where

$\displaystyle A_{+}$ $\displaystyle={\rm Re}(\Psi_{4})\,,$ (3a)
$\displaystyle A_{\times}$ $\displaystyle={\rm Im}(\Psi_{4})\,,$ (3b)
$\displaystyle A_{B}$ $\displaystyle=\Phi_{22}\,,$ (3c) $\displaystyle A_{V1}$
$\displaystyle={\rm Re}(\Psi_{3})\,,$ (3d) $\displaystyle A_{V2}$
$\displaystyle={\rm Im}(\Psi_{3})\,,$ (3e) $\displaystyle A_{L}$
$\displaystyle=\Psi_{2}\,.$ (3f)

Here, $A_{+}$ and $A_{\times}$ represent the two tensor modes of GWs, the only
two allowed by GR. The shear modes are given by $A_{V1}$ and $A_{V2}$, while
the scalar breathing and scalar longitudinal modes are $A_{B}$ and $A_{L}$
respectively. Searching for the coefficients in Eq. (2) allows for a theory-
independent way to perform a test of gravity, without the need to be concerned
with the specifics of any metric theory of gravity. We will utilize this
technique in searches for a GWB using PTAs.

###  2.2 Pulsar Timing and Isotropic Gravitational Wave Background

A GW propagating through the Earth-pulsar line of sight will induce a change
in the expected time of arrival for the pulsar’s radio pulse. These
perturbations were first calculated in the late 1970s (Sazhin, 1978;
Detweiler, 1979) and have since been used to predict the GWB signature. For
pulsar timing, the measured variation in the pulse TOAs can be used to
calculate GW induced residuals, $R_{a}^{\rm GW}$, of pulsar $a$ following the
relation

$R_{a}^{\rm GW}=\int_{0}^{t}dt^{\prime}z_{a}(t^{\prime}),$ (4)

which is the quantity measured directly in PTAs, where $z_{a}$ is the GW
induced redshift. For a detailed explanation of Eq. (4), refer to Arzoumanian
et al. (2021) and Chamberlin & Siemens (2012).

The fractional energy density of the background is given to be

$\Omega_{\rm GW}(f)=\frac{1}{\rho_{c}}\frac{d\rho_{\rm GW}}{d\ln(f)}$ (5)

where $\rho_{\rm GW}$ is the energy of the gravitational wave, $f$ is the
frequency, and $\rho_{c}$ is the critical density necessary for a closed
universe. For the purposes of this analysis, we assume the GWB is produced by
a large number of independent, weak, unresolvable sources isotropically
distributed throughout the sky. Hence, the correlation between the strain
functions is written as

$\langle\tilde{h}_{g}(f,\hat{\Omega})\tilde{h}_{g^{\prime}}^{*}(f^{\prime},\hat{\Omega}^{\prime})\rangle=\frac{\delta(f-f^{\prime})}{2}\frac{\delta^{2}(\hat{\Omega},\hat{\Omega}^{\prime})}{4\pi}\frac{\delta_{gg^{\prime}}}{2}S_{h}(f)\,,$
(6)

where $S_{h}(f)$ is the one-sided power-spectral-density of the GWB; related
to $\Omega_{\mathrm{G}W}(f)$ by

$\Omega_{\rm GW}(f)=\frac{2\pi^{2}}{3H_{0}^{2}}f^{3}S_{h}(f)\,.$ (7)

The spectral characteristics of the GWB are often described via the
_characteristic strain_

$h_{c}(f)=\sqrt{fS_{h}(f)}\,.$ (8)

This quantity is useful, as it includes the effects of the number of cycles
during the GW source in-spiral throughout the frequency band $\sqrt{f}$ as
discussed in Taylor (2021). While several models exist for describing the
nature of $h_{c}(f)$ (NG15), in this work, we will restrict ourselves to that
of a power-law model for each polarization $g$ such that

$h_{g}(f)=A_{g}\left(\frac{f}{f_{\rm yr}}\right)^{\alpha_{g}}\,$ (9)

where $A_{g}$ is a dimensionless amplitude, $f_{\rm yr}$ is the reference
frequency, and $\alpha_{g}$ is the spectral index. Using Eqs. (6), (8), and
(9), we can find the cross-correlation estimator between pulsars $a$ and $b$
(Chamberlin & Siemens, 2012):

$\displaystyle\langle R_{a}^{\rm GW}R_{b}^{\rm GW}\rangle$
$\displaystyle=\int_{f_{L}}^{f_{H}}df\\{S_{ab}(f)\\},$ (10)
$\displaystyle\begin{split}S_{ab}(f)&=\frac{1}{8\pi^{2}f^{3}}\sum_{g}\Gamma^{g}_{ab}(f)h_{g}^{2}(f)\\\
&=\frac{3}{2}\sum_{g}P_{g}\Gamma^{g}_{ab}(f)\ ,\end{split}$ (11)

where $f_{L}$ and $f_{H}$ are lower and upper frequencies and
$\Gamma_{ab}^{g}(f)$ is the _overlap reduction function_ (ORF) which is
related to the spatial geometry of the two pulsars in relation to the Earth
and we have introduce $P_{g}$ defined as

$\displaystyle P_{g}(f)$
$\displaystyle=\frac{A_{g}^{2}}{12\pi^{2}f^{3}}\left(\frac{f}{f_{yr}}\right)^{3-\gamma_{g}}.$

In the above, to align with the more widely used terminology for spectral
index, we have made the reparametrization $\gamma_{g}=3-2\alpha_{g}$.

###  2.3 Restriction to Transverse Modes

As discussed in §2.1, there exist between two and six possible independent
polarization modes for a GW in metric theories of gravity. Calculating the
effects of longitudinal modes requires additional steps and assessments such
as accurate knowledge of distances to the pulsars, handling the frequency
dependence of the ORF, as well as having a significant number of pulsars at
small-angular separations to capture the unique ORF signature of such
polarization modes (Arzoumanian et al., 2021). Thus, we will restrict
ourselves to the three transverse modes, $A_{+}$ $A_{\times}$, and $A_{B}$,
for the purposes of this paper.

Given only the transverse tensor and scalar modes, we may generalize Eq. (11)
(O’Beirne et al., 2019; Arzoumanian et al., 2021) as

$\displaystyle S_{ab}(f)=\frac{3}{2}\left(P_{\rm TT}\Gamma^{\rm
TT}_{ab}+P_{\rm ST}\Gamma^{\rm ST}_{ab}\right).\,$ (13)

It is worth pointing out that the effect of dipole radiation of binary sources
in non-GR metric theories of gravity (O’Beirne et al., 2019), is accounted for
by treating the spectral index $\gamma_{g}$ as a free parameter in our
statistical models.

The ORFs for the TT and ST modes have been calculated previously in Chamberlin
& Siemens (2012) and Gair et al. (2015),

$\displaystyle\Gamma^{\rm TT}_{ab}$
$\displaystyle=\frac{\delta_{ab}}{2}+\frac{3}{2}\left(\frac{1}{3}+k_{ab}\left(\ln{k_{ab}}-\frac{1}{6}\right)\right)\,,$
(14a) $\displaystyle\Gamma^{\rm ST}_{ab}$
$\displaystyle=\frac{\delta_{ab}}{2}+\frac{1}{8}\left(3+\cos{\xi_{ab}}\right)\,,$
(14b)

with $\xi_{ab}$ being the angular distance on the sky between pulsars $a$ and
$b$ and

$k_{ab}=\frac{1}{2}\left(1-\cos{\xi_{ab}}\right)\,.$ (15)

Figure 1: A plot of transverse ORFs as a function of angular separation. The
blue curve describes the Hellings and Downs curve, which is produced by the TT
polarization mode, while the orange curve describes the shape of the
correlations induced by the ST polarization mode of gravity.

A plot of the transverse ORFs as a function of angular separation is shown in
Figure 1. Where $\Gamma^{\rm TT}_{ab}$ is represented by the more widely known
Hellings and Downs (HD) curve (Hellings & Downs, 1983), and henceforth the TT
mode will be represented by HD. With this structure in hand, we may proceed to
the analysis of the NG15yr data and the investigation of the general
transverse modes.

##  3 Searches for a General Transverse GWB in the NANOGrav 15 Year Data Set

In this section, we complement our previous work in NG15 by analyzing the
NANOGrav 15 year data set for statistical significance of HD plus ST
correlations. We first describe the pulsar noise modeling in §3.1, and then we
present the results of the Bayesian and frequentist analyses in §3.2 and §3.3
respectively. We will take an agnostic approach to the mixing between the HD
and the ST polarization modes of gravity by allowing each mode to possess its
own independent power-spectral-density as suggested by Eq. (13).

###  3.1 Noise Modeling Details

Through individual pulsar analyses we obtain posteriors for both the red and
white noises intrinsic to each pulsar. In all of the analyses, these intrinsic
noises are modeled as a power-law with varying spectral index as well as
varying amplitudes. We model the power spectra using frequency bins from
$1/T_{\text{obs}}$ to $30/T_{\text{obs}}$ for $T_{\text{obs}}$ being the
longest observational baseline among the considered pulsars in the data set.
The white noise is described by three parameters: a linear scaling of TOA
uncertainties, noise added in quadrature to the TOA uncertainties, and noise
common to a given epoch at all frequency subbands. These parameters are called
EFAC, EQUAD, and ECORR, respectively and are set to their fixed values in
NG15. For detailed explanations of these parameters, refer to (Agazie et al.,
2023b).

The common red noise process is modeled as a power-law model in three ways:
CURN, HD, and ST, all of which are modeled using frequency bins from
$1/T_{\text{obs}}$ to $14/T_{\text{obs}}$. Adapted from the naming convention
in NG15, $\mathrm{CURN}$ refers to the modeling of the red noise common
process as an uncorrelated process (i.e.,
$\Gamma_{ab}^{\text{CURN}}=\delta_{ab}$). Whereas HD and ST refer to modeling
of the red noise common process as a correlated process with HD and ST curves
as their respective correlation signatures.

The upper and lower bounds of the model parameters we use are shown below.
Note that the subscript “int” refers to the intrinsic red noise processes
while the subscript $g$ refers to the common red noise process (i.e., CURN,
HD, or ST).

$\displaystyle\begin{split}log_{10}A_{\text{int}}&\sim\text{Uniform}(-20,-11),\\\
log_{10}A_{\text{g}}&\sim\text{Uniform}(-18,-11),\\\
\gamma_{\text{int}},\gamma_{g}&\sim\text{Uniform}(0,7).\end{split}$ (16)

Refer to NG15 and Agazie et al. (2023b) for a more detailed explanation of the
noise modeling adapted for the analyses of the NANOGrav 15 year data set.

###  3.2 Bayesian Analyses

Figure 2: Bayes factors for various model comparisons between ST, HD, and
CURN. Overall, the HD model is preferred over CURN and ST. Modeling ST
alongside HD give about equal odds over HD and ST only. All model comparisons
are agnostic with respect to the spectral index of each model. See §3.1 for
more details. The uncertainties are estimated using bootstrapping and Markov
model techniques of Heck et al. (2019). All Bayes factors are presented as the
model at the end of an arrow over the starting model of an arrow. For example,
for the arrow pointing from CURN to ST, the values are BFs for
${ST}\divslash{CURN}$.

(a)

(b)

Figure 3: (a) Bayesian probability posterior distributions of $\log_{10}A_{g}$
and $\gamma_{g}$ from a HD correlated model ($\color[rgb]{0,0,1}blue$) and a
ST correlated model ($\color[rgb]{1,.5,0}orange$) showing the
1$\sigma$/2$\sigma$/3$\sigma$ credible regions. Plotted for comparison is CURN
($\color[rgb]{.5,.5,.5}grey$) posterior distributions for $\log_{10}A_{g}$ and
$\gamma_{g}$ parameters. Each correlated signal is able to explain the total
signal. (b) Bayesian probability posterior distributions of $\log_{10}A_{g}$
and $\gamma_{g}$ for HD ($\color[rgb]{0,0,1}blue$) and ST
($\color[rgb]{1,.5,0}orange$) from a HD+ST correlated model showing
1$\sigma$/2$\sigma$/3$\sigma$ credible regions. Plotted for comparison is CURN
($\color[rgb]{.5,.5,.5}grey$) posterior distributions for $\log_{10}A_{g}$ and
$\gamma_{g}$ parameters. The plots suggest that the posterior distribution for
ST is uninformative and HD adequately describes the total signal recovered by
CURN.

Our Bayesian analyses follow §3.1 as well as NG15. In short, in terms of a
likelihood function, all the various noise modelings follow from (Johnson et
al., 2023)

$p(\bm{\delta
t}\mid\bm{\eta})=\frac{1}{\sqrt{\det(2\pi\bm{K})}}\exp\left(-\frac{1}{2}\bm{\delta
t}^{T}\bm{K}^{-1}\bm{\delta t}\right)\,,$ (17)

where

$\bm{K}=\bm{D}+\bm{F}\bm{\phi}\bm{F}^{T},$ (18)

and we then use the Woodbury matrix identity to invert this covariance matrix.
We find

$\bm{K}^{-1}=\bm{D}^{-1}-\bm{D}^{-1}\bm{F}\bm{\Theta}\bm{F}^{T}\bm{D}^{-1}\,,$
(19)

with

$\bm{\Theta}=\left(\bm{\phi}^{-1}+\bm{F}^{T}\bm{D}^{-1}\bm{F}\right)^{-1}\,.$
(20)

In the above, $\bm{F}$ is a matrix with alternating columns of sine and cosine
components representing a discrete Fourier transform of the red noise
processes, $\bm{D}$ is covariance matrix for the white noise parameters,
$\bm{\phi}$ is the covariance matrix of the red noise components.

We use Bayesian analyses to compare several models of interest via Bayes
factor estimation, Figure 2, and to obtain posterior distributions for
$\log_{10}A_{g}$ and $\gamma_{g}$ for HD and ST signals, Figure 3. In Figure
2, we observe that correlated Bayesian models are preferred over the
uncorrelated model. The most favored model is a GWB with HD correlations with
a Bayes factor of 200. When ST is modeled alongside HD, Bayes factors are
uninformative given they are on the order of unity when compared to each
correlation alone.

We can use the transitive nature of Bayes factors as a consistency check of
our results. For instance, going around the bottom half of Figure 2 we can
take the Bayes factor of $\rm{ST}\divslash\rm{CURN}$ and multiply by the Bayes
factor of $\rm{HD}\divslash\rm{ST}$ to obtain the Bayes factor of
$\rm{HD}\divslash\rm{CURN}$. This results in $90\times 2.2=198$, which is
consistent with the Bayes factor for $\rm{HD}\divslash\rm{CURN}$ of $\sim 200$
we obtained by directly comparing those two models.

We note that in Figure 3 when fitting for one correlation signature that both
HD correlations and ST correlations are able to explain the total signal. This
agrees with the large Bayes factors favoring these models over CURN. However,
the recovered power spectral estimates for ST are poor when modeled alongside
HD. To check the consistency of the power spectral estimates we see that
$\log_{10}A_{\rm{CURN}}=-14.17^{+0.12}_{-0.13}$ and
$\gamma_{\rm{CURN}}=3.35^{+0.32}_{-0.32}$ (median values with 68% credible
interval). The ST values are $\log_{10}A_{\rm{ST}}=15.03^{+0.87}_{-1.92}$ and
$\gamma_{\rm{ST}}=3.33^{+1.53}_{-1.53}$, while the HD values are
$\log_{10}A_{\rm{HD}}=14.24^{+0.18}_{-0.56}$ and
$\gamma_{\rm{HD}}=3.17^{+0.51}_{-0.61}$. We see that values for CURN and HD
are more consistent with each other. While the ST spectral estimates do
overlap with the median of the CURN spectral estimates, we observe the 68%
credible region for $\gamma_{\rm{ST}}$ and $\log_{10}A_{\rm{ST}}$ expand over
about 43% and 31% of the prior region, respectively. Therefore, the addition
of the ST correlation yields no additional information and we see that the HD
signal in this model explains most of the total signal.

###  3.3 Optimal Statistic Analyses

Figure 4: Distributions of the recovered amplitudes from single-component
noise marginalized optimal statistic (SCOS)(_left_) and multi-component noise
marginalized optimal statistic (MCOS)(_right_) for HD
($\color[rgb]{0,0,1}blue$) and ST ($\color[rgb]{1,.5,0}orange$) correlations.
Additionally, CURN ($\color[rgb]{.5,.5,.5}grey$) is plotted for comparison to
determine the consistency with the common red noise process.  Figure 5:
Distributions of the S/N for HD ($\color[rgb]{0,0,1}blue$) and ST
($\color[rgb]{1,.5,0}orange$) correlations from the multi-component (MCOS) and
single component (SCOS) noise marginalized optimal statistic techniques. The
dashed lines correspond to the median values and the first and third
quartiles. The median S/N values for HD are greater than ST, but are within
their inter-quartile range.

The optimal statistic (Anholm et al., 2009; Chamberlin et al., 2015) allows
for a robust and computationally inexpensive analysis of the correlation
content of a PTA data set. The amplitude and the uncertainty of the pair-wise
cross correlations are estimated by maximizing the ratio of the likelihood of
the fiducial GWB over the _noise-only_ model. The fiducial model contains a
GWB signal along with intrinsic red and white noise components while the
noise-only model includes the intrinsic noises and a common uncorrelated red
noise process. We have employed the _noise-marginalized_ version of the
optimal statistic technique in which $10^{4}$ random draws from the posteriors
of all of the model parameters of a CURN model are used to estimate the
required power spectra. Additionally, since our goal is to search for a
general transverse GWB signal in which two non-orthogonal types of
correlations might simultaneously exist in the data set, a chi-squared
statistic fitting for both HD and ST correlations is used to find the optimal
estimators of the _signal-to-noise-ratio_ (S/N or SNR) and the amplitude of
the correlated signal ($\hat{A}_{g}$) for each polarization mode. Note that
$\hat{A}_{g}$ differs from ${A}_{g}$ as the former is an optimal estimator of
the latter. See Vigeland et al. (2018) and Sardesai & Vigeland (2023) for more
details.

The estimated amplitudes for single component (SCOS) and multi-component
(MCOS) noise marginalized optimal statistics are shown in Figure 4. We see
that for SCOS that the amplitude reconstruction of the HD correlations is in
excellent agreement with the CURN amplitude posterior, whereas the estimated
amplitude for ST correlations is only consistent with CURN. For MCOS the
correlations are fit for simultaneously so the total power is split and the
fit correlations are shifted towards smaller amplitude values and less
consistent with CURN. However, the HD correlations explain most of the total
CURN signal when both correlations are present.

The SNR for SCOS and MCOS are shown in Figure 5. We note that the median SNRs
for HD correlations, 5.0 and 3.5 for SCOS and MCOS, respectively, are larger
than the median SNRs for ST correlations, 4.6 and 3.0 for SCOS and MCOS,
respectively. The difference in median SNR values are not significant as the
medians lie within the inter-quartile ranges of each other. While the SNR
values are similar for HD and ST correlations, as noted before, the
consistency of the estimated HD amplitude with CURN suggest that HD, not ST,
correlations make up most of the common red noise process.

##  4 Discussion

NANOGrav’s 15-year data set shows compelling evidence for quadrupolar HD
inter-pulsar correlations. In this work, we explored the possibility of
deviations from the HD curve caused by the presence of an additional scalar-
transverse (ST) mode.

Our Bayesian analyses show the Bayes factor for HD over ST is $\sim 2$, and
the Bayes factor for a model with both correlations compared to a model with
just HD is $\sim 1$. Taking the spectral parameter recovery into account, as
in Figure 3, we found each correlation, when fit for individually, is in
agreement with CURN. We also found more informative $\log_{10}A_{g}$ and
$\gamma_{g}$ recovery for HD than ST, and HD parameters show better agreement
with CURN spectral parameters when correlations are included together. While
these analyses do not rule out the possibility of ST correlations in our data,
they show there is no statistical need for an additional stochastic process
with ST correlations.

This is also the case for our frequentist analyses. When fitting the
interpulsar correlation data for a single correlation signature, we find that
HD correlations completely account for the total signal due to the amplitudes
consistency with CURN, but ST correlations are only somewhat consistent. When
we fit for both correlations simultaneously, we still see that HD correlations
are able to explain most of the total signal. For the SNR, we find that the
median values for HD correlations are larger than ST correlations, but are
similar and lie within inter-quartile ranges.

Even though we cannot fully rule out ST correlations, Einsteinian polarization
modes with HD correlations are present in all metric theories of gravity.
Thus, even though we do not find a convincing Bayes factor favoring HD
correlations over ST correlations and they have similar SNR values in our
frequentist analyses, there is no metric theory that predicts only ST GWs. In
addition, we no longer report higher SNR and Bayes factors for ST correlations
as we did in Arzoumanian et al. (2021). We have seen a larger increases in
favor of HD correlations than ST correlations in both SNR and Bayes factors.
These changes are consistent with simulations in Arzoumanian et al. (2021)
and, with no evidence indicating otherwise, we expect this trend to continue
with additional data.

We also performed dropout analysis tests, similar to what was done in
Arzoumanian et al. (2021), to determine if particular pulsars play a role in
the observed ST significance. We found that J0030$+$0451 and J0613$-$0200 are
responsible for a majority of the ST significance. When we remove these two
pulsars from the analysis, we find that the Bayes factor for
$\rm{HD}\divslash\rm{CURN}$ increases to $\sim 600$, while the Bayes factor
for $\rm{ST}\divslash\rm{CURN}$ is reduced to $\sim 30$. We suspect improved
noise modeling (as used in Falxa et al. (2023) and Agazie et al. (2023b)) on
these and other pulsars will shed some light on this, and we leave this for
future work.

Other recent work (Allen, 2023; Allen & Romano, 2022) has shown that the HD
correlation signature has a cosmic variance. This idea is not addressed within
this manuscript, but introduces increasing complexity in detecting alternative
polarizations of gravity. An alternative polarization mode now not only needs
to be disentangled from the HD correlations, but also the variance of the HD
correlations to be detected. Impacts of these effects will be addressed in
future work.

Future prospects for performing tests of gravity using PTA data are
compelling. Large observational baselines as well as the addition of more
millisecond pulsars to the observing array will enable more robust and
sensitive searches for additional GW polarization modes. In this work, we
reported on one test of gravity in which we searched for evidence for a scalar
transverse polarization mode. While we did not find substantial evidence for
or against this mode, the situation may change in the future due to the nature
of the PTA data sets. It is also important to note that a number of the
observed pulsars are dominated by white and intrinsic red noise process which
could be suppressing a GW-sourced signal. For the case of a GWB, as we obtain
more data on these pulsars, we will be able to provide more definitive answers
about the possibility of the existence or absence of additional polarization
modes of gravity.

##  5  Acknowledgments

Author contributions: An alphabetical-order author list was used for this
paper in recognition of the fact that a large, decade timescale project such
as NANOGrav is necessarily the result of the work of many people. All authors
contributed to the activities of the NANOGrav collaboration leading to the
work presented here, and reviewed the manuscript, text, and figures prior to
the paper’s submission. Additional specific contributions to this paper are as
follows. G.A., A.A., A.M.A., Z.A., P.T.B., P.R.B., H.T.C., K.C., M.E.D.,
P.B.D., T.D., E.C.F., W.F., E.F., G.E.F., N.G., P.A.G., J.G., D.C.G., J.S.H.,
R.J.J., M.L.J., D.L.K., M.K., M.T.L., D.R.L., J.L., R.S.L., A.M., M.A.M.,
N.M., B.W.M., C.N., D.J.N., T.T.P., B.B.P.P., N.S.P., H.A.R., S.M.R., P.S.R.,
A.S., C.S., B.J.S., I.H.S., K.S., A.S., J.K.S., and H.M.W. through a
combination of observations, arrival time calculations, data checks and
refinements, and timing model development and analysis; additional specific
contributions to the data set are summarized in Agazie et al. (2023c). D.M.D
led the search and coordinated the writing of the paper. D.M.D, N.L., A.S.,
S.C.S., and J.A.T. performed the Bayesian and frequentist analysis. J.B. and
K.D.O cross-checked the Bayes factor values. B.B., J.S.H., K.D.O., X.S.,
J.P.S., S.R.T., and S.J.V. provided feedback and guidance on searches and
analysis. N.L. and X.S. provided first insights to dropping J0030+0451 and
J0613-0200. D.M.D, N.L., A.S., S.C.S., and J.A.T. wrote the paper.

Acknowledgments: The work contained herein has been carried out by the
NANOGrav collaboration, which receives support from the National Science
Foundation (NSF) Physics Frontier Center award numbers 1430284 and 2020265,
the Gordon and Betty Moore Foundation, NSF AccelNet award number 2114721, an
NSERC Discovery Grant, and CIFAR. The Arecibo Observatory is a facility of the
NSF operated under cooperative agreement (AST-1744119) by the University of
Central Florida (UCF) in alliance with Universidad Ana G.
M$\acute{\text{e}}$ndez (UAGM) and Yang Enterprises (YEI), Inc. The Green Bank
Observatory is a facility of the NSF operated under cooperative agreement by
Associated Universities, Inc. L.B. acknowledges support from the National
Science Foundation under award AST-1909933 and from the Research Corporation
for Science Advancement under Cottrell Scholar Award No. 27553. P.R.B. is
supported by the Science and Technology Facilities Council, grant number
ST/W000946/1. S.B. gratefully acknowledges the support of a Sloan Fellowship,
and the support of NSF under award #1815664. The work of R.B., R.C., D.D.,
N.La., X.S., J.P.S., and J.A.T. is partly supported by the George and Hannah
Bolinger Memorial Fund in the College of Science at Oregon State University.
M.C., P.P., and S.R.T. acknowledge support from NSF AST-2007993. M.C. and
N.S.P. were supported by the Vanderbilt Initiative in Data Intensive
Astrophysics (VIDA) Fellowship. K.Ch., A.D.J., and M.V. acknowledge support
from the Caltech and Jet Propulsion Laboratory President’s and Director’s
Research and Development Fund. K.Ch. and A.D.J. acknowledge support from the
Sloan Foundation. Support for this work was provided by the NSF through the
Grote Reber Fellowship Program administered by Associated Universities,
Inc./National Radio Astronomy Observatory. Support for H.T.C. is provided by
NASA through the NASA Hubble Fellowship Program grant #HST-HF2-51453.001
awarded by the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., for NASA, under
contract NAS5-26555. K.Cr. is supported by a UBC Four Year Fellowship (6456).
M.E.D. acknowledges support from the Naval Research Laboratory by NASA under
contract S-15633Y. T.D. and M.T.L. are supported by an NSF Astronomy and
Astrophysics Grant (AAG) award number 2009468. E.C.F. is supported by NASA
under award number 80GSFC21M0002. G.E.F., S.C.S., and S.J.V. are supported by
NSF award PHY-2011772. K.A.G. and S.R.T. acknowledge support from an NSF
CAREER award #2146016. The Flatiron Institute is supported by the Simons
Foundation. S.H. is supported by the National Science Foundation Graduate
Research Fellowship under Grant No. DGE-1745301. N.La. acknowledges the
support from Larry W. Martin and Joyce B. O’Neill Endowed Fellowship in the
College of Science at Oregon State University. Part of this research was
carried out at the Jet Propulsion Laboratory, California Institute of
Technology, under a contract with the National Aeronautics and Space
Administration (80NM0018D0004). D.R.L. and M.A.Mc. are supported by NSF
#1458952. M.A.Mc. is supported by NSF #2009425. C.M.F.M. was supported in part
by the National Science Foundation under Grants No. NSF PHY-1748958 and
AST-2106552. A.Mi. is supported by the Deutsche Forschungsgemeinschaft under
Germany’s Excellence Strategy - EXC 2121 Quantum Universe - 390833306. P.N.
acknowledges support from the BHI, funded by grants from the John Templeton
Foundation and the Gordon and Betty Moore Foundation. The Dunlap Institute is
funded by an endowment established by the David Dunlap family and the
University of Toronto. K.D.O. was supported in part by NSF Grant No. 2207267.
T.T.P. acknowledges support from the Extragalactic Astrophysics Research Group
at Eötvös Loránd University, funded by the Eötvös Loránd Research Network
(ELKH), which was used during the development of this research. S.M.R. and
I.H.S. are CIFAR Fellows. Portions of this work performed at NRL were
supported by ONR 6.1 basic research funding. J.D.R. also acknowledges support
from start-up funds from Texas Tech University. J.S. is supported by an NSF
Astronomy and Astrophysics Postdoctoral Fellowship under award AST-2202388,
and acknowledges previous support by the NSF under award 1847938. C.U.
acknowledges support from BGU (Kreitman fellowship), and the Council for
Higher Education and Israel Academy of Sciences and Humanities (Excellence
fellowship). C.A.W. acknowledges support from CIERA, the Adler Planetarium,
and the Brinson Foundation through a CIERA-Adler postdoctoral fellowship. O.Y.
is supported by the National Science Foundation Graduate Research Fellowship
under Grant No. DGE-2139292.

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UPM 1851-3840 | 282.8074922 | -38.6741419 | -161.2 | 82.0 | 6.2 | 6.2 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 10.575 | 9.983 | 9.704 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1852-2751 | 283.0031728 | -27.8602172 | 82.6 | -174.6 | 7.9 | 8.8 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.419 | 11.857 | 11.593 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1858-3548 | 284.6541453 | -35.8062356 | -102.9 | 178.4 | 6.7 | 6.7 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 11.275 | 10.871 | 10.760 |  $\cdots$ |  $\cdots$ |  bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable ccSuperCOSMOS plate magnitudes suspect
UPM 1859-1701 | 284.8129344 | -17.0311458 | -127.7 | -164.7 | 8.3 | 8.3 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 10.923 | 10.345 | 10.034 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1900-0511 | 285.2324742 | -5.1836367 | -90.8 | -168.3 | 7.2 | 7.0 | 13.538 | 11.997 | 11.474 | 10.426 | 9.765 | 9.570 | 1.571 | 43.5 |
UPM 1902-3731 | 285.5237094 | -37.5289453 | 163.2 | -82.3 | 12.1 | 12.2 | 18.665 | 16.574 | 15.884 | 13.833 | 13.187 | 12.935 | 2.741 | 158.4 |
UPM 1907-0221 | 286.7786636 | -2.3570300 | -23.4 | -192.6 | 7.2 | 7.1 | 13.359 | 12.590 | 12.326 | 11.287 | 10.812 | 10.740 | 1.303 | 76.8 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1917-2949 | 289.4523744 | -29.8228444 | -70.6 | -223.4 | 10.8 | 10.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 11.927 | 11.374 | 11.094 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1920-1606 | 290.0811403 | -16.1009153 | -175.4 | 68.9 | 10.9 | 11.0 |  $\cdots$ |  $\cdots$ | 17.198 | 16.119 | 15.579 | 15.625 |  $\cdots$ | 574.5 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1920-2206 | 290.1098181 | -22.1062475 | 122.9 | -161.4 | 14.4 | 9.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.085 | 11.542 | 11.280 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1923-4026 | 290.7523894 | -40.4484822 | -154.6 | -96.7 | 7.7 | 9.5 |  $\cdots$ | 16.086 | 14.192 | 12.847 | 12.337 | 12.100 | 3.239 | 88.5 |
UPM 1925-0916 | 291.4896428 | -9.2686953 | -58.8 | -197.4 | 6.4 | 6.2 |  $\cdots$ | 14.429 |  $\cdots$ | 12.428 | 11.800 | 11.617 | 2.001 | 121.9 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1925-3712 | 291.4461181 | -37.2007175 | 138.7 | -165.4 | 15.2 | 15.1 |  $\cdots$ |  $\cdots$ | 13.683 | 12.134 | 11.536 | 11.289 |  $\cdots$ | 47.8 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1931-4001 | 292.9411467 | -40.0227744 | -3.1 | -185.0 | 1.9 | 1.9 | 14.966 | 12.936 | 11.356 | 10.714 | 10.092 | 9.861 | 2.222 | 50.2 |
UPM 1933-2916 | 293.3358858 | -29.2750011 | -90.4 | -159.5 | 2.9 | 5.1 | 15.935 | 13.822 | 11.914 | 10.767 | 10.151 | 9.882 | 3.055 | 34.6 |
UPM 1940-0508 | 295.1044458 | -5.1410269 | 22.0 | -181.3 | 8.1 | 8.0 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 11.602 | 11.074 | 10.825 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1943-0035 | 295.9131372 | -0.5899383 | -256.9 | 22.2 | 11.4 | 10.0 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.195 | 11.669 | 11.372 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1947-3542 | 296.7613983 | -35.7157425 | 24.0 | -180.4 | 2.5 | 2.6 | 16.879 | 14.954 | 13.555 | 12.269 | 11.659 | 11.436 | 2.685 | 86.0 |
UPM 1950-0135 | 297.6302547 | -1.5941806 | 223.2 | 2.3 | 10.2 | 10.1 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.355 | 11.803 | 11.575 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1952-0813 | 298.1828144 | -8.2235433 | 103.0 | -220.6 | 7.8 | 9.1 | 15.568 | 13.655 | 11.782 | 10.585 | 9.968 | 9.683 | 3.070 | 32.6 |
UPM 1953-0508 | 298.3124231 | -5.1386344 | -45.1 | -196.0 | 7.3 | 7.1 |  $\cdots$ | 14.484 | 13.942 | 12.870 | 12.395 | 12.296 | 1.614 | 160.4 |
UPM 1954-0139 | 298.6503828 | -1.6506567 | -93.6 | -164.6 | 9.0 | 9.1 | 16.468 | 15.236 | 14.497 | 13.541 | 12.951 | 12.815 | 1.695 | [213.2] | ffSubdwarf candidate selected from RPM diagram; plate distance [in bracket] is incorrect
UPM 1955-3426 | 298.9125511 | -34.4337736 | -92.3 | -161.9 | 4.8 | 4.7 | 15.620 | 15.545 |  $\cdots$ | 12.908 | 12.406 | 12.128 | 2.637 | 116.8 |  bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable ccSuperCOSMOS plate magnitudes suspect
UPM 1957-3801 | 299.4516389 | -38.0268108 | 119.4 | -160.3 | 6.6 | 17.2 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.317 | 11.721 | 11.521 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 1958-3348 | 299.6281386 | -33.8102706 | 122.5 | -132.4 | 5.7 | 5.0 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.145 | 11.624 | 11.377 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2007-0132 | 301.7682706 | -1.5366978 | 6.6 | -184.1 | 16.4 | 16.1 |  $\cdots$ | 15.506 |  $\cdots$ | 12.448 | 11.871 | 11.591 | 3.058 | 71.5 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2007-0312 | 301.9236269 | -3.2085131 | -159.3 | -86.5 | 7.3 | 7.2 | 16.388 | 14.715 | 12.952 | 11.235 | 10.702 | 10.462 | 3.480 | 41.6 |
UPM 2009-0041 | 302.4692369 | -0.6924347 | 115.0 | -191.9 | 14.0 | 14.7 | 17.493 | 15.536 | 13.355 | 12.277 | 11.749 | 11.497 | 3.259 | 72.2 |
UPM 2009-3305 | 302.2734844 | -33.0964475 | 60.3 | -179.0 | 22.0 | 16.9 | 17.666 | 15.906 | 14.344 | 13.039 | 12.533 | 12.329 | 2.867 | 129.1 |
UPM 2011-0002 | 302.9155206 | -0.0494872 | 82.3 | -262.2 | 10.4 | 10.7 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 11.420 | 10.819 | 10.684 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2011-0010 | 302.7694014 | -0.1825764 | -141.8 | -130.9 | 11.1 | 8.4 |  $\cdots$ |  $\cdots$ | 12.726 | 11.881 | 11.339 | 11.119 |  $\cdots$ | 79.4 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2011-0139 | 302.8264014 | -1.6649031 | 129.2 | -127.5 | 15.9 | 16.0 | 17.948 | 15.746 | 13.609 | 12.433 | 11.860 | 11.584 | 3.313 | 67.8 |
UPM 2012-0133 | 303.1161578 | -1.5506017 | 236.9 | -65.7 | 14.0 | 13.5 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 11.962 | 11.370 | 11.068 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2014-0124 | 303.6403675 | -1.4061056 | 144.1 | -231.7 | 7.8 | 7.9 |  $\cdots$ |  $\cdots$ | 12.139 | 11.284 | 10.729 | 10.508 |  $\cdots$ | 59.2 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2014-0624 | 303.5245169 | -6.4119417 | 3.3 | -220.4 | 17.6 | 17.2 | 17.444 | 15.620 | 14.056 | 12.989 | 12.373 | 12.223 | 2.631 | 131.8 |
UPM 2014-1634 | 303.6036331 | -16.5819139 | -167.7 | -192.2 | 12.1 | 13.4 |  $\cdots$ | 13.477 |  $\cdots$ | 12.772 | 12.137 | 12.020 | 0.705 |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2019-0754 | 304.8205911 | -7.9011086 | 127.5 | -157.6 | 6.9 | 7.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.462 | 12.101 | 12.066 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2020-0826 | 305.0236797 | -8.4449589 | 174.3 | -48.6 | 11.2 | 8.1 |  $\cdots$ | 14.934 | 12.955 | 11.903 | 11.347 | 11.099 | 3.031 | 62.7 |
UPM 2024-0638 | 306.0952239 | -6.6395264 | 75.9 | -247.6 | 10.9 | 11.1 | 16.931 | 14.871 | 13.039 | 11.878 | 11.357 | 11.085 | 2.993 | 64.4 |
UPM 2045-0612 | 311.4779600 | -6.2101506 | -143.8 | -120.3 | 10.0 | 10.1 |  $\cdots$ | 15.646 | 13.667 | 12.937 | 12.409 | 12.167 | 2.709 | 122.0 |
UPM 2047-0429 | 311.8002206 | -4.4950453 | 143.0 | -117.9 | 6.4 | 6.6 | 12.644 | 11.975 | 11.578 | 11.659 | 11.348 | 11.398 | 0.316 |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2047-2232 | 311.9131269 | -22.5408683 | -136.3 | -128.9 | 9.8 | 10.0 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 13.261 | 12.733 | 12.634 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2047-3246 | 311.9777267 | -32.7689467 | -242.1 | 197.9 | 7.2 | 7.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 10.917 | 10.373 | 10.143 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2049-0304A | 312.4151003 | -3.0785519 | 83.1 | -185.7 | 7.0 | 7.3 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.889 | 12.288 | 12.072 |  $\cdots$ |  $\cdots$ |  bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable ddCommon proper motion companion; see Table 4
UPM 2049-0304B | 312.4151678 | -3.0771406 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 14.444 | 13.943 | 13.673 |  $\cdots$ |  $\cdots$ |  aaProper motions suspect bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable ddCommon proper motion companion; see Table 4 eeNot detected during automated search but noticed by eye during the blinking process
UPM 2050-1541 | 312.5709881 | -15.6922022 | 84.2 | -178.4 | 3.2 | 4.7 | 15.656 | 13.702 | 12.131 | 11.456 | 10.862 | 10.580 | 2.246 | 70.2 |
UPM 2050-4535 | 312.5937853 | -45.5929939 | 17.8 | -207.4 | 9.5 | 9.6 | 17.265 | 15.170 | 14.302 | 13.405 | 12.863 | 12.688 | 1.765 | [214.1] | ffSubdwarf candidate selected from RPM diagram; plate distance [in bracket] is incorrect
UPM 2057-0911 | 314.4559047 | -9.1875750 | 129.1 | -168.5 | 8.7 | 8.4 |  $\cdots$ | 12.472 | 11.512 | 11.501 | 10.806 | 10.656 | 0.971 | 87.5 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2058-0332 | 314.6363908 | -3.5394206 | -38.0 | -198.2 | 6.6 | 8.1 | 13.785 | 11.439 | 10.095 | 10.436 | 9.823 | 9.618 | 1.003 | 44.8 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2105-1703 | 316.4376317 | -17.0536781 | 81.7 | -161.3 | 2.1 | 2.3 | 15.955 | 14.016 | 12.396 | 11.385 | 10.749 | 10.506 | 2.631 | 57.4 |
UPM 2115-0631 | 318.8872478 | -6.5276206 | 191.1 | 28.7 | 7.6 | 8.4 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.633 | 12.090 | 11.891 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2118-2101 | 319.5260700 | -21.0311750 | 188.4 | 30.4 | 15.9 | 17.3 | 18.188 | 15.914 | 14.188 | 13.103 | 12.484 | 12.212 | 2.811 | 108.6 |
UPM 2131-3027 | 322.7657644 | -30.4592144 | 47.4 | -173.7 | 3.7 | 3.7 | 17.497 | 15.514 | 13.704 | 12.264 | 11.687 | 11.415 | 3.250 | 65.9 |
UPM 2140-0613 | 325.0265956 | -6.2270500 | -56.1 | -210.2 | 7.9 | 8.2 | 13.765 | 12.664 | 13.526 | 12.762 | 12.356 | 12.341 | -0.098 | 156.2 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2145-4145 | 326.4178564 | -41.7660619 | 137.1 | -125.2 | 1.7 | 2.1 | 16.569 | 13.895 | 12.271 | 11.407 | 10.885 | 10.560 | 2.488 | 55.7 | ccSuperCOSMOS plate magnitudes suspect
UPM 2152-1147 | 328.2452208 | -11.7888700 | 150.3 | -123.1 | 1.9 | 4.1 | 16.766 | 14.875 | 12.787 | 11.466 | 10.888 | 10.632 | 3.409 | 44.4 |
UPM 2154-0143 | 328.6042781 | -1.7273786 | 259.8 | -7.5 | 11.2 | 11.7 | 13.464 | 11.889 | 10.739 | 11.170 | 10.542 | 10.353 | 0.719 | 79.4 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2157-0251 | 329.4304583 | -2.8516900 | 139.8 | -132.6 | 18.1 | 17.9 | 18.051 |  $\cdots$ | 14.875 | 13.480 | 12.902 | 12.672 |  $\cdots$ | 152.1 |
UPM 2222-3528 | 335.5426575 | -35.4820467 | -116.0 | -155.8 | 5.9 | 5.7 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 13.313 | 12.672 | 12.461 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2229-0432B | 337.4473828 | -4.5360572 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.140 | 11.556 | 11.319 |  $\cdots$ |  $\cdots$ |  bbNumber of relations used for distance estimate $<$ 6: plate distance less reliableeeNot detected during automated search but noticed by eye during the blinking process ddCommon proper motion companion; see Table 4 aaProper motions suspect
UPM 2231-1642 | 337.7917883 | -16.7142497 | -123.3 | -139.2 | 1.8 | 1.9 | 16.421 | 14.446 | 12.668 | 11.850 | 11.283 | 11.036 | 2.596 | 76.2 |
UPM 2232-0225 | 338.1181078 | -2.4226789 | 181.2 | -31.2 | 11.1 | 11.5 | 16.226 | 14.169 | 12.605 | 11.514 | 10.938 | 10.684 | 2.655 | 60.9 |
UPM 2233-0003 | 338.2930958 | -0.0525181 | 247.8 | 99.7 | 8.7 | 8.8 |  $\cdots$ | 15.656 |  $\cdots$ | 12.763 | 12.209 | 11.978 | 2.893 | 94.6 | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2237-0118 | 339.3505139 | -1.3070036 | -147.7 | -110.1 | 7.0 | 7.0 | 14.926 | 13.000 | 11.919 | 11.674 | 11.029 | 10.877 | 1.326 | 97.5 |
UPM 2244-4333 | 341.0835264 | -43.5574258 | 183.0 | -51.4 | 14.8 | 15.1 | 17.708 | 15.718 | 14.089 | 13.114 | 12.529 | 12.353 | 2.604 | 138.3 |
UPM 2246-0017 | 341.6494342 | -0.2863092 | 193.6 | -28.5 | 10.3 | 10.3 | 17.545 | 15.654 | 13.935 | 12.665 | 12.130 | 11.873 | 2.989 | 95.3 |
UPM 2248-3255 | 342.1992344 | -32.9243678 | -126.6 | -174.9 | 3.8 | 3.9 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.662 | 12.120 | 11.932 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2250-2908A | 342.5898331 | -29.1365486 | 186.9 | -9.2 | 5.0 | 3.0 | 15.217 | 13.358 | 11.795 | 12.126 | 11.517 | 11.293 | 1.232 | 115.3 |  bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable ddCommon proper motion companion; see Table 4
UPM 2250-2908B | 342.5883269 | -29.1372669 | 182.3 | -17.0 | 3.7 | 3.9 | 15.217 | 13.358 | 11.795 | 13.184 | 12.599 | 12.327 | 0.174 | 155.7 |  aaProper motions suspect ddCommon proper motion companion; see Table 4 bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable eeNot detected during automated search but noticed by eye during the blinking process
UPM 2251-0201 | 342.7661222 | -2.0260436 | 50.1 | -185.5 | 7.6 | 7.6 | 15.605 | 13.598 | 12.627 | 11.995 | 11.372 | 11.176 | 1.603 | 110.8 |
UPM 2305-4612 | 346.2905092 | -46.2043653 | 143.5 | -110.4 | 7.8 | 2.5 | 16.914 | 15.068 | 13.649 | 12.773 | 12.240 | 11.993 | 2.295 | 136.2 |
UPM 2306-0315 | 346.6112989 | -3.2637836 | 181.1 | -55.6 | 10.2 | 10.2 | 17.564 | 15.549 | 13.841 | 12.506 | 11.947 | 11.661 | 3.043 | 80.8 |
UPM 2308-1954 | 347.1959358 | -19.9085208 | 183.6 | -0.3 | 13.0 | 12.1 | 13.693 | 12.059 | 11.387 | 11.479 | 11.092 | 11.006 | 0.580 | 131.5 |  bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable aaProper motions suspect
UPM 2310-0410 | 347.5503997 | -4.1822806 | 155.6 | -93.0 | 11.0 | 11.1 |  $\cdots$ | 15.438 | 14.685 | 13.920 | 13.313 | 13.160 | 1.518 | [263.6] | ffSubdwarf candidate selected from RPM diagram; plate distance [in bracket] is incorrect
UPM 2320-0006 | 350.0481022 | -0.1140686 | 78.7 | -165.2 | 9.3 | 2.5 | 13.636 | 11.776 | 10.884 | 10.299 | 9.637 | 9.479 | 1.477 | 50.0 |
UPM 2325-1715 | 351.4973083 | -17.2589567 | 180.0 | 254.5 | 11.5 | 10.5 | 16.160 | 13.342 | 11.790 | 11.113 | 10.486 | 10.218 | 2.229 | 50.7 |
UPM 2328-0546 | 352.0857586 | -5.7781261 | 183.3 | 62.8 | 6.6 | 7.2 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 10.995 | 10.415 | 10.162 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2329-0510 | 352.4821203 | -5.1685144 | 159.2 | 88.3 | 12.7 | 9.7 | 17.693 | 15.621 | 13.802 | 12.583 | 12.002 | 11.781 | 3.038 | 85.5 |
UPM 2331-0233 | 352.8670611 | -2.5567644 | -189.0 | -114.3 | 8.6 | 11.3 | 17.038 | 14.938 | 13.029 | 11.864 | 11.303 | 11.000 | 3.074 | 58.3 |
UPM 2331-0617 | 352.7987228 | -6.2871728 | 180.6 | 36.1 | 10.3 | 10.3 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 12.722 | 12.079 | 11.904 |  $\cdots$ |  $\cdots$ | bbNumber of relations used for distance estimate $<$ 6: plate distance less reliable
UPM 2334-4145 | 353.6053231 | -41.7568239 | -20.3 | -187.7 | 2.4 | 3.2 | 17.676 | 15.973 | 15.112 | 14.059 | 13.421 | 13.279 | 1.914 | [273.8] | ffSubdwarf candidate selected from RPM diagram; plate distance [in bracket] is incorrect
UPM 2349-1023 | 357.2962428 | -10.3857086 | 169.5 | 71.8 | 13.1 | 14.1 | 17.811 | 15.720 | 13.845 | 12.954 | 12.352 | 12.065 | 2.766 | 109.4 |
UPM 2356-0453 | 359.1178706 | -4.8861358 | 189.6 | -44.4 | 19.9 | 18.6 | 18.052 | 16.087 | 14.310 | 12.885 | 12.374 | 12.113 | 3.202 | 95.4 |
Table 3: New UCAC3 High Proper Motion Systems estimated to be within 25 pc between Declinations $-$47$\arcdeg$ and 0$\arcdeg$ with 0$\farcs$40 yr-1 $>$ $\mu$ $\geq$ 0$\farcs$18 yr-1 Name | RA J2000.0 | DEC J2000.0 | $\mu_{\alpha}\cos\delta$ | $\mu_{\delta}$ | sig $\mu_{\alpha}$ | sig $\mu_{\delta}$ | $B_{J}$ | $R_{59F}$ | $I_{IVN}$ | $J$ | $H$ | $K_{s}$ |  $R_{59F}$ $-$ $J$ | Est Dist | Notes
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) | (mas/yr) | (mas/yr) | (mas/yr) | (mas/yr) |  |  |  |  |  |  |  | (pc) |
UPM 1349-4228 | 207.2552625 | -42.4784189 | -161.9 | -84.6 | 1.3 | 3.0 | 14.468 | 11.703 |  $\cdots$ | 9.449 | 8.863 | 8.622 | 2.254 | 24.4 |
UPM 1648-3459 | 252.1200667 | -34.9967942 | 178.6 | 142.5 | 4.4 | 4.4 |  $\cdots$ | 14.631 |  $\cdots$ | 10.687 | 10.161 | 9.907 | 3.944 | 22.1 |
UPM 1654-3105 | 253.6846164 | -31.0961000 | -32.4 | -215.9 | 7.4 | 7.2 | 15.122 | 13.553 | 11.977 | 10.072 | 9.482 | 9.237 | 3.481 | 23.8 | aaPossible NLTT star with a position difference $>$ 90$\arcsec$ when compared to UCAC3 position
UPM 1718-2245A | 259.6129147 | -22.7616683 | -160.7 | -160.8 | 7.2 | 6.8 | 15.469 | 13.836 | 13.155 | 10.385 | 9.806 | 9.572 | 3.451 | 25.4 | bbCommon proper motion companion; see Table 4
UPM 1718-2245B | 259.6213031 | -22.7746183 | -161.1 | -154.8 | 10.9 | 9.6 |  $\cdots$ | 14.787 | 13.289 | 10.207 | 9.608 | 9.375 | 4.580 | 13.2 |  bbCommon proper motion companion; see Table 4 ccNot detected during automated search but noticed by eye during the blinking process
UPM 1840-1934 | 280.1299600 | -19.5831464 | 201.2 | -89.8 | 8.8 | 8.1 |  $\cdots$ | 13.733 | 12.400 | 10.264 | 9.706 | 9.450 | 3.469 | 20.7 |
Table 4: Common Proper Motion Candidate Systems Primary | $\mu_{\alpha}\cos\delta$ | $\mu_{\delta}$ | Distance | Secondary/Tertiary | $\mu_{\alpha}\cos\delta$ | $\mu_{\delta}$ | Distance | Separation | $\theta$ | notes
---|---|---|---|---|---|---|---|---|---|---
| (mas/yr) | (mas/yr) | (pc) |  | (mas/yr) | (mas/yr) | (pc) | ($\arcsec$) | ($\arcdeg$) |
UPM 0209-3339A | -86.1 | -166.9 | 49.5 | UPM 0209-3339B | -112.9 | -170.2 |  $\cdots$ | 11.6 | 78.1 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
UPM 0443-4129A | 186.1 | 4.3 | 39.3 | 2MASS J04430760-4128575B | -107.5 | -53.1 |  $\cdots$ | 6.8 | 339.2 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect
UPM 0528-4313A | -75.6 | 164.7 | 70.4 | UPM 0528-4313B | -86.3 | 163.2 | 109.1 | 42.1 | 209.0 | aaNot detected during automated search but noticed by eye during the blinking process
UPM 0659-0052A | -58.3 | -184.1 | 78.2 | UPM 0659-0052B |  $\cdots$ |  $\cdots$ |  $\cdots$ | 13.8 | 151.6 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect
UPM 0704-0602A |  $\cdots$ |  $\cdots$ | 123.4 | UPM 0704-0602B | 99.5 | -153.0 | 37.8 | 12.2 | 359.1 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect ddSuperCOSMOS plate magnitudes suspect
UPM 0747-2537A | -148.5 | 101.9 | 40.6 | UPM 0747-2537B | -151.3 | 102.3 | 47.3 | 12.0 | 237.4 | bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
UPM 0800-0617A | 135.2 | -233.8 | [175.5] | UPM 0800-0617B |  $\cdots$ |  $\cdots$ |  $\cdots$ | 5.8 | 297.2 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect eeSubdwarf candidate selected from RPM diagram; plate distance [in bracket] is incorrect
BD-04 2807A | -142.1 | -37.1 | 19.5 | UPM 1009-0501B | -190.5 | 92.1 |  $\cdots$ | 20.9 | 338.5 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
UPM 1020-0633A | -179.8 | -27.8 | 34.8 | SCR 1020-0634B | -181.5 | -24.2 | 37.5 | 87.3 | 157.2 |
UPM 1031-0024A | -207.4 | -105.6 | 55.1 | UPM 1031-0024B | -142.5 | -96.9 |  $\cdots$ | 7.4 | 91.4 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ffSource not in 2MASS
UPM 1056-0542A | -98.1 | -173.8 | 76.5 | UPM 1056-0542B | -63.9 | -173.3 |  $\cdots$ | 9.0 | 86.2 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
UPM 1142-2055A | -186.7 | 44.2 | 41.2 | UPM 1142-2055B |  $\cdots$ |  $\cdots$ |  $\cdots$ | 8.3 | 167.6 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect
NLTT 28641A | -201.8 | 6.2 |  $\cdots$ | UPM 1149-0019B | -201.5 | 2.2 |  $\cdots$ | 27.3 | 128.2 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
UPM 1159-3623A | -182.1 | -101.4 | 113.1 | UPM 1159-3623B | -172.6 | -92.4 | 132.4 | 13.6 | 303.7 | aaNot detected during automated search but noticed by eye during the blinking process
UPM 1226-2020A | -137.6 | -119.8 | 72.3 | UPM 1226-2020B | -146.3 | -117.3 |  $\cdots$ | 7.0 | 333.3 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
SCR 1226-3515A | -192.3 | 41.0 | 56.5 | UPM 1226-3516B | -200.5 | 38.3 | 127.5 | 49.8 | 191.3 |  aaNot detected during automated search but noticed by eye during the blinking process ggPossible NLTT star with a position difference $>$ 90$\arcsec$ when compared to UCAC3 position
|  |  |  | UPM 1226-3516C | -115.2 | 8.5 | 243.3 | 97.0 | 146.9 |  aaNot detected during automated search but noticed by eye during the blinking process ccProper motions suspect ggPossible NLTT star with a position difference $>$ 90$\arcsec$ when compared to UCAC3 position
UPM 1315-2904A | -190.6 | -27.5 | 89.6 | UPM 1315-2904B | -209.7 | -1.5 | 149.3 | 5.9 | 332.6 | aaNot detected during automated search but noticed by eye during the blinking process
2MASS J13465039-2112266A | -186.8 | -44.0 | 46.8 | UPM 1346-2111B | -112.1 | -60.0 | 86.8 | 82.2 | 350.8 |  aaNot detected during automated search but noticed by eye during the blinking process ccProper motions suspect
UPM 1718-2245A | -160.7 | -160.8 | 25.4 | UPM 1718-2245B | -161.1 | -154.8 | 13.2 | 54.3 | 149.2 | aaNot detected during automated search but noticed by eye during the blinking process
UPM 1724-0318A | 143.7 | -126.7 | 92.0 | UPM 1724-0318B |  $\cdots$ |  $\cdots$ | 169.5 | 5.5 | 325.4 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect
TYC 7897 997 1A | -10.4 | -160.2 | 40.3 | UPM 1749-4404B | 0.0 | -204.9 |  $\cdots$ | 19.8 | 254.0 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect ddSuperCOSMOS plate magnitudes suspect
TYC 8344 154 1A | 51.6 | -179.5 |  $\cdots$ | UPM 1757-4632B | 59.7 | -185.1 |  $\cdots$ | 30.7 | 296.9 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable
UPM 2049-0304A | 83.1 | -185.7 |  $\cdots$ | UPM 2049-0304B |  $\cdots$ |  $\cdots$ |  $\cdots$ | 5.3 | 1.5 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect
2MASS J22294694-0432036A | 160.9 | -86.5 | 50.8 | UPM 2229-0432B |  $\cdots$ |  $\cdots$ |  $\cdots$ | 8.7 | 134.7 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect
UPM 2250-2908A | 186.9 | -9.2 | 115.3 | UPM 2250-2908B | 182.3 | -17.0 | 155.7 | 5.4 | 241.4 |  aaNot detected during automated search but noticed by eye during the blinking process bbNumber of relations used for distance estimate $<$ 6; plate distance less reliable ccProper motions suspect