# Analysis of Previously Classified White Dwarf-Main Sequence Binaries Using
Data from the APOGEE Survey

Kyle A. Corcoran Department of Astronomy, University of Virginia,
Charlottesville, VA 22904, USA  Hannah M. Lewis Department of Astronomy,
University of Virginia, Charlottesville, VA 22904, USA  Borja Anguiano
Department of Astronomy, University of Virginia, Charlottesville, VA 22904,
USA  Steven R. Majewski Department of Astronomy, University of Virginia,
Charlottesville, VA 22904, USA  Marina Kounkel Department of Physics and
Astronomy, Western Washington University, Bellingham, WA 98225, USA  Devin J
McDonald Department of Astronomy, University of Virginia, Charlottesville, VA
22904, USA  Keivan G. Stassun Department of Physics and Astronomy, Vanderbilt
University, Nashville, TN 37235, USA  Katia Cunha  Steward Observatory,
Department of Astronomy, University of Arizona, Tucson, AZ 85721, USA
Observatório Nacional, Rio de Janeiro, Brasil  Verne Smith  NSF OIR Lab,
Tucson, AZ 85719, USA  Carlos Allende Prieto  Instituto de Astrofísica de
Canarias, E-38205 La Laguna, Tenerife, Spain  Universidad de La Laguna, Dpto.
Astrofísica, E-38206 La Laguna, Tenerife, Spain  Carles Badenes Department of
Physics and Astronomy and Pittsburgh Particle Physics, Astrophysics and
Cosmology Center (PITT PACC), University of Pittsburgh, Pittsburgh, PA 15260,
USA  Nathan De Lee  Department of Physics, Geology, and Engineering
Technology, Northern Kentucky University, Highland Heights, KY 41099
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN
37235, USA  Christine N. Mazzola  Department of Physics and Astronomy and
Pittsburgh Particle Physics, Astrophysics and Cosmology Center (PITT PACC),
University of Pittsburgh, Pittsburgh, PA 15260, USA  Penélope Longa-Peña
Centro de Astronomía, Universidad de Antofagasta, Antofagasta 1270300, Chile
Alexandre Roman-Lopes Departamento de Astronomía, Universidad de La Serena,
1700000 La Serena, Chile

(Accepted December 21, 2020)

###### Abstract

We present analyses of near-infrared, spectroscopic data from the Apache Point
Observatory Galactic Evolution Experiment (APOGEE) survey for 45 previously
confirmed or candidate white dwarf-main sequence (WDMS) binaries identified by
the optical SDSS and LAMOST surveys. Among these 45 systems, we classify three
as having red giant primaries in the LAMOST sample and fourteen to be young
stellar object contaminants in the photometrically identified SDSS sample.
From among the subsample of 28 systems that we confirm to have MS primaries,
we derive and place limits on orbital periods and velocity amplitudes for
fourteen. Seven systems have significant velocity variations that warrant a
post-common-envelope (PCE) binary classification – four of which are newly
classified, three of which are newly confirmed, and five for which we can
derive full orbital parameters. If confirmed, one of these newly discovered
systems (2M14544500+4626456) will have the second longest orbital period
reported for a typical, compact PCE WDMS binary ($P=15.1$ days). In addition
to the seven above, we also recover and characterize with APOGEE data the well
known PCE WDMS systems EG UMa and HZ 9. We also investigate the overall
metallicity distribution of the WDMS sample, which is a parameter space not
often explored for these systems. Of note, we find one system
(2M14244053+4929580) to be extremely metal-poor (${\rm[Fe/H]}=-1.42$) relative
to the rest of the near-solar sample. Additionally, the PCE systems in our
sample are found to be, on average, higher in metallicity than their wide-
binary counterparts, though we caution that with this small number of systems,
the sample may not be representative of the overall distribution of WDMS
systems.

binaries: close, spectroscopic – stars: white dwarfs, low-mass

††journal: AJ††software: APOGEE reduction software (Nidever et al., 2015),
ASPCAP (García Pérez et al., 2016; Jönsson et al., 2020), The Joker (Price-
Whelan et al., 2017, 2020), TOPCAT (Taylor, 2005), astro-gala (Price-Whelan,
2017)

##  1 Introduction

White dwarf stars are the endpoint of stellar evolution for almost every main
sequence star. Because most main sequence stars exist in binary systems
(Duquennoy & Mayor, 1991; Raghavan et al., 2010; Yuan et al., 2015), it is
common for the more massive star to evolve into a white dwarf, leading to a
detached white dwarf-main sequence (WDMS) binary. The way in which the more
massive star evolves is dictated by its separation from the progenitor binary,
but there are two main formation scenarios followed by these systems. For a
majority ($\sim$75%) the separation is sufficient for the stars to evolve
independently of one another, resulting in a wide binary (Willems & Kolb,
2004). The remaining fraction ($\sim$25%) of systems can undergo a stage of
common envelope (CE) evolution, which causes the orbit to shrink
significantly. Orbital energy can then be deposited into the envelope, which
is ejected from the system, leaving behind a close, post-CE (PCE) binary
(Webbink, 2008).

The two populations of WDMS binaries also yield a bimodal distribution in
their orbital periods. This was shown in population synthesis studies (e.g.,
Willems & Kolb, 2004; Camacho et al., 2014; Cojocaru et al., 2017), which
predict that wide WDMS binaries should have orbital periods of $P\\!>\\!100$
days. For instance, Farihi et al. (2010), using high-resolution imaging of 90
white dwarfs with known or suspected low-mass stellar and substellar
companions, confirmed observationally that these systems exhibit a bimodal
distribution in projected separation; further, they predict that all spatially
unresolved, low-mass stellar and substellar companions in their survey will be
found to be in short-period orbits. Indeed, observations of close PCE WDMS
binaries show a distribution peaking at $\sim$8 hours (Miszalski et al., 2009;
Nebot Gómez-Morán et al., 2011). It is worth noting, however, that five self-
lensing PCE WDMS binaries with early-type companions and larger than typical
separations have been found, and four of these have orbital periods of $P>400$
days (Kawahara et al., 2018; Masuda et al., 2019). While still PCE WDMS
binaries, these may represent a population with a distinct formation pathway
from the typical, more-compact PCE systems.

Apart from the normal migration from intermediate to short periods occurring
in the course of normal CE evolution, PCE systems can evolve to even shorter
orbital periods through angular momentum loss due to magnetic braking and/or
gravitational wave emission. As is outlined in Ren et al. (2018) and
references therein, it is possible for the PCE system to undergo a second CE
stage, eventually producing double-degenerate WDs, cataclysmic variables, or
super-soft X-ray sources. However, a complete understanding of the variety of
these late evolutionary pathways must rest on a better foundational picture of
the CE phase, which itself is still relatively poorly understood (e.g.,
Ivanova et al., 2013). To guide these theoretical studies, more well-
characterized systems at all phases of CE and PCE evolution are needed to
place firm observational constraints. However, identifying systems in the CE
phase is challenging, and most efforts are pointed at categorizing and
characterizing PCE systems, which are then used to infer the parameters (e.g.,
envelope ejection efficiencies, angular momentum loss, envelope binding
energy) of the more “hidden” CE phase (e.g., Ivanova et al., 2013). Of the
different kinds of PCE systems (e.g., hot subdwarf B stars, extremely low mass
white dwarfs, etc.), PCE WDMS are arguably the most common. Thus, PCE WDMS
systems can play a crucial role in the study of CE evolution (Zorotovic et
al., 2011), and are fundamental tools for understanding the range of
astrophysically interesting endpoints of that evolution — e.g., from Type Ia
supernovae to gravitational wave sources (e.g., Toloza et al., 2019).

Significant progress has been made in recent years to identify WDMS binaries
using large area spectroscopic sky surveys at optical wavelengths, such as the
Sloan Digital Sky Survey (SDSS; York et al., 2000; Stoughton et al., 2002) and
the Large sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) survey
(Zhao et al., 2012). These systems are identified in the optical through a
variety of different methods, such as through $\chi^{2}$-fits of WDMS template
spectra covering a vast range of temperatures, gravities, and companion
spectral types (see Rebassa-Mansergas et al., 2010), through application of a
wavelet transform (Chui, 1992) that efficiently identifies WDMS spectral
features (see Ren et al., 2014), and through color-color cuts such as those in
Rebassa-Mansergas et al. (2013). Presently, the most up-to-date catalog of
spectroscopically-confirmed WDMS systems identified using SDSS, that by
Rebassa-Mansergas et al. (2016a), contains 3294 WDMS binaries. The
photometrically selected catalog of WDMS candidates identified using SDSS from
Rebassa-Mansergas et al. (2013) contains 3419 systems. Meanwhile, Ren et al.
(2018) created a catalog with an additional 876 WDMS binaries identified using
LAMOST spectra, 793 of which are claimed to be genuine WDMS systems. From
these and other works (such as the White Dwarf Binary Pathways Survey —
Parsons et al. 2016; Rebassa-Mansergas et al. 2017), the total number of
systems classified as PCE WDMS binaries stands at $\sim$300 systems, while
only $\sim$120 of these have derived orbital periods.

Fortunately, that number can be increased through a serendipitous channel. The
Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et
al., 2017) is a high resolution ($R\sim 22,500$) infrared (1.5 – 1.7 $\mu$m)
spectroscopic survey that primarily targets red giant stars to study stellar
populations across the Milky Way. However, because of the simple,
photometrically-based selection criteria used for APOGEE targeting (Zasowski
et al., 2013, 2017), some WDMS systems have received APOGEE observations by
chance. Because of APOGEE’s multi-epoch observing strategy, most of these
systems have high-quality time series radial velocity (RV) information for at
least three, and, in some cases, as many as 50 “visits” (i.e., epochs). For
systems with 6 or more visits, these data can be used to constrain or derive
orbital parameters for these binary systems.

Here we present the 45 systems previously classified as WDMS binaries or
candidate WDMS binaries via optical SDSS and LAMOST studies that have also
been observed by APOGEE as of November 2019. Although this is a relatively
small subsample drawn from these optical catalogs, the high quality APOGEE
data — which include not only time series RVs, but also the spectroscopically-
derived stellar atmospheric parameters and chemistry of the primaries — not
only permit some glimpses into various sources of contamination in these
previous, optical WDMS catalogs, but also contribute to the small, but growing
census of WDMS systems having detailed characterization of their individual
stellar constituents and orbital geometries. In particular, of the 21 systems
that are confirmed here using APOGEE stellar parameters to have MS primaries,
twelve have sufficient RV visit information (6+ visits) from APOGEE to allow
us to derive, or place limits on, the Keplerian orbital parameters. The
remaining nine systems have more than two visits, which allows us to attempt
to place limits on the orbital paramters. This pilot APOGEE assessment of the
specific set of previously known WDMS systems also lends insights into the
potential of the greater APOGEE database for not only the identification of
previously unknown WDMS and PCE binaries, but to contribute in a major way to
the relatively small number of such systems having well characterized system
architectures.

##  2 The APOGEE Survey

The SDSS-III APOGEE (Majewski et al., 2017) and SDSS-IV (Blanton et al., 2017)
APOGEE-2 (Majewski et al., in prep.) surveys are now in their ninth year of
observations with the 2.5-m Sloan Telescope (Gunn et al., 2006) at Apache
Point Observatory in the Northern Hemisphere and their third year of
observations with the 2.5-m du Pont Telescope at Las Campanas Observatory in
the Southern Hemisphere. The combined survey databases now encompass more than
2 million spectra of nearly 600,000 distinct stars. The vast majority of
APOGEE targets receive at least three visits, to build up signal-to-noise
(S/N) and with the intent that RV variations can be used to identify stars in
binary or higher multiplicity systems. Fainter stars will receive more visits
as a means to build up signal sufficient to enable precision chemical
abundance analysis on the combined spectra; however, the individual visits,
even for faint stars, typically accumulate sufficient flux that good RVs can
be derived for more extensive time series exploration. At the other extreme, a
small fraction of APOGEE targets have only one visit for various reasons, but
primarily because many of these were obtained as “bonus” targets through
APOGEE-2 co-observing with the dark time SDSS-IV MaNGA project (Bundy et al.,
2015).

The APOGEE reduction software (Nidever et al., 2015) derives RVs for each star
using a two-step process. First, each visit spectrum is cross-correlated
against a grid of synthetic spectra. This provides an “estimated RV” for each
visit which is then used to correct the visit spectra to a common velocity
needed for combination to a single, higher S/N spectrum for each source. The
latter can then serve as an intermediate template against which the relative
velocity of each visit spectrum can be rederived, and the whole process
repeated in an iterative fashion to arrive at the best combined spectrum as
well as a set of relative RVs. In principle, these well-matching, intermediate
cross-correlation template spectra created from the combination of individual
visits to a star should yield more precise RVs for that same star than if a
synthetic template or the spectrum of another star were employed. Moreover,
this method does not require fore-knowledge of the spectral type of the star
to obtain high quality RVs. On the other hand, it is the case that for some
stars (typically the fainter ones) this procedure does not improve on results
obtained using synthetic cross-correlation templates, and so the reduction
pipeline chooses the better result from the two methods at each iteration in
the visit combination/relative RV determination stage of the data processing.

Due to the intrinsic resolution of the APOGEE spectrographs and the fact that
they are bench-mounted in tightly controlled vacuum and cryogenic environments
(Wilson et al., 2019), the median visit RV precision for APOGEE main survey
stars is around 100 m s-1 (Nidever et al., 2015). This is better than is
usually employed for the study of stellar binaries, and enables the detection
of more subtle RV variability induced by more widely separated and/or lower
mass companions (e.g., Troup et al., 2016; Price-Whelan et al., 2020).

After determination of the per-epoch RVs, the APOGEE reduction pipeline
collates the spectra from all epochs after shifting them each to the rest
frame velocity. The final, coadded spectra are then run through the APOGEE
Spectral Parameters and Chemical Abundances Pipeline (ASPCAP; García Pérez et
al., 2016; Jönsson et al., 2020) to derive exquisite information on the
effective temperatures ($T_{\rm eff}$), gravities ($\log{g}$), and
metallicities of each APOGEE target (e.g., Holtzman et al., 2015, 2018).
Majewski et al. (2017) presents many example spectra of stars spanning large
ranges in spectral type and metallicity to showcase the quality of APOGEE
spectra, and the publicly available APOGEE spectra can be viewed along with
their ASPCAP fits on a per-target basis via the SDSS
website.111https://dr16.sdss.org/infrared/spectrum/search The ASPCAP results
for the luminous primaries of the WDMS candidates presented here are included
in Table 1 (see columns 6-8), which also gives the 2MASS names for the sources
(column 1), the survey in which each system was first identified as a WDMS
candidate (LAMOST or SDSS, column 2), the Gaia magnitude (column 3), and the
2MASS $H$ magnitude and $(J-K)$ color (columns 4 and 5, respectively). We use
these data to make an initial global assessment of these 45 systems in Section
3, aided in part by ancillary information provided by previous studies. That
ancillary information is summarized in the final column of Table 1.

##  3 Global Assessment of the Previously Identified WDMS Systems

As is to be expected, we find here some fraction of contaminants among systems
previously identified as WDMS candidates, based on optical spectroscopic and
photometric surveys. In this section we identify some categories of
contamination, made evident by exploration of the observed global properties
of the systems in Table 1.

Figure 1 shows both the Gaia-based $H$-band absolute magnitude and the ASPCAP-
based spectroscopic gravities $\log{g}$ as a function of ASPCAP effective
temperature, $T_{\rm eff}$. The full sample of APOGEE DR16 stars are shown in
black and the 45 WDMS candidates as the larger colored dots. The WDMS
candidates cluster in three general locations in these observational planes.
The majority of the candidates do indeed lie on the main sequence, as one
would hope for WDMS candidates. Among those systems with MS primaries, the
vast majority are at temperatures typical of M dwarfs; only one
(2M18454771+4431148) is at a hotter temperature ($T_{\mathrm{eff}}\sim 5240$
K), a temperature typical of a late G type star. All of these WDMS candidates
on the lower MS have spectroscopically-derived metallicities that are near-
solar (within 0.4 dex), consistent with their locations in Figure 1.

(a)

(b)

Figure 1: Confirmed or candidate WDMS systems shown against all of APOGEE.
Note that not all of the 45 systems are shown due to either missing parallaxes
(left) or ASPCAP parameters (right). We highlight in both plots the RG (yellow
triangles) and YSO (magenta squares) contaminants as well as the remaining,
cleaned sample with MS primaries (blue circles). Left: Gaia-based $H$-band
absolute magnitude as a function of the ASPCAP $T_{\rm eff}$. Right: Kiel
diagram with the ASPCAP $\log(g)$ as a function of ASPCAP $T_{\rm eff}$.

However, one of the systems in the “lower MS” group, (2M14244053+4929580),
actually lies below the MS at $T_{\mathrm{eff}}\sim 4110$ K in both panels of
Figure 1. This “subdwarf” location is consistent with the ASPCAP derived
metallicity for this star ([Fe/H] = $-1.42$), which shows it to be a rare (see
Figure 9, below), metal-poor WDMS candidate. This metallicity is near the mean
value of the Galactic halo (Beers et al., 2005), suggesting that this WDMS
system belongs to this population. Nevertheless, surprisingly, an analysis of
the kinematics of this star (Sec. 6) shows this binary to actually have a
disk-like orbit.

Yet another star in our sample, 2M05303840$-$0525436, has a derived ASPCAP
metallicity that is relatively low ([Fe/H] = $-0.8$), but in this case we
believe that this metallicity is likely incorrect, because this star is likely
a pre-main sequence, young stellar object (YSO; see below). In addition, the
spectrum of this star has been flagged by ASPCAP as having potential problems
due to cross-talk from a bright neighboring spectrum, as well as landing in
parts of the APOGEE detectors that have been identified to have problems with
persistence (see Wilson et al., 2019, for an explanation). We discuss the
subdwarf 2M14244053+4929580 and the overall metallicity distribution function
of the cleaned WDMS sample in more detail in Section 6.

Three other stars in Table 1 (2M01090044+5203369, 2M19202987+4000013, and
2M22145972$-$0820200) have both absolute magnitudes and spectroscopically-
derived gravities indicating that the primaries are, in fact, on the red giant
branch. LAMOST had classified 2M01090044+5203369 and 2M22145972$-$0820200 as
confirmed WDMS binaries, while 2M19202987+4000013 was reported as a candidate
WDMS system. Recently, Frasca et al. (2016), as part of their analysis of the
stellar parameters of targets in the Kepler field, also identified the system
2M19202987+4000013 to have a red giant primary. These three systems, while not
WDMS, are still potentially interesting as potential symbiotic star candidates
(e.g., Lewis et al., 2020).

A third group of systems that can be seen in Figure 1 are those with low
$T_{\mathrm{eff}}$, but both higher luminosities and lower surface gravities
as compared to normal MS stars of the same temperature. The properties of
these systems are consistent with young stellar objects (YSOs). All twelve of
these stars are located either in the youngest (1–3 Myr) regions of the Orion
Complex (Kounkel et al., 2018), or in NGC 2264, which is another $\sim$3 Myr
massive cluster (Dahm, 2008). Moreover, all twelve of these systems are
designated as YSOs in the SIMBAD database (Wenger et al., 2000). Two
additional systems in Table 1 that do not have derived ASPCAP parameters (due
to insufficient S/N or other problems) and therefore do not appear in Figure
1, 2M05343005$-$0449506 and 2M06402564+0959597, are also identified in SIMBAD
to be YSOs. Given their extreme youth, it is very unlikely that any of these
systems have white dwarf companions.

All fourteen of the YSO contaminants were found in the catalog derived from
SDSS photometric data, for which the WDMS candidates were selected on the
basis of several color–color selections. However, none of these stars are
among those SDSS candidates having previous spectroscopic confirmation by
Rebassa-Mansergas et al. (2016a). Clearly the original optical photometric
selection used to select WDMS candidates is also sensitive to YSOs, as
evidenced by their prominence in our sample. The main signature of accreting
young stars (i.e., Classical T Tauri stars) is strong H$\alpha$ emission, with
a 10% width of the line in excess of 200 km s-1, and with equivalent widths
that can reach as high as 200 Å. Weak-Lined T Tauri stars (WTTS, i.e., YSOs
that have already stopped accreting and likely have depleted their
protoplanetary disks) also can have an H$\alpha$ equivalent width as high as
40 Å in late M stars (e.g., White & Basri, 2003). Apparently such strong
Balmer emission, particularly H$\alpha$, confounds the various automated WDMS
candidate finding algorithms previously employed.

Meanwhile, at shorter wavelengths, an excess of flux in YSOs can also be a
signature of magnetospheric accretion (e.g., Calvet & Gullbring, 1998; Ingleby
et al., 2013), produced by the accretion shocks heating up small spots on the
photosphere to temperatures as high as 90,000 K immediately after the shock.
Even WTTS systems have NUV luminosities three times higher than what is
observed for MS stars of the same spectral type. Given their propensity for UV
emission, it is understandable how photometric selection criteria that search
for WDMS systems might also recover some YSOs. Ultimately, it seems that a
check of other WDMS candidate properties, such as detection of Li I
absorption, placement on the HR diagram, and/or a Galactic position consistent
with nearby star forming regions, is needed to identify YSO contaminants from
these optically-based WDMS candidate catalogs. It is also worth noting that
while WDMS are multiple systems by definition, comparable photometric or
spectroscopic signals could originate from single YSOs without any binary
companions.

That about a third of our sample of WDMS candidates turn out to be YSOs may
seem surprising, but this should not be interpreted as implying that the SDSS-
based (or even the LAMOST-based) WDMS catalog is similarly fractionally
contaminated by YSOs. Both the SDSS-based WDMS catalog as well as the APOGEE
survey have numerous strong selection biases that complicate interpretation of
contamination fractions. For example, the SDSS survey by and large avoided
observations of the Galactic midplane, where YSOs are most concentrated. On
the other hand, APOGEE observations are highly biased towards the Galactic
plane, and, to further amplify that bias toward finding YSOs, the APOGEE
survey included a specific focus on star forming regions as part of its
targeting, in particular through several APOGEE Ancillary Science projects
(Zasowski et al., 2013, 2017; Cottaar et al., 2014; Cottle et al., 2018).
These competing biases make it difficult to interpret the 27% YSO
contamination of our initial sample, except as a strong alert to this false
positive class.

A similar comment may be made regarding the fraction of misidentified giant
stars among the WDMS candidates: The $\sim$6% fraction of giant star systems
in our sample, which all come from the LAMOST-based WDMS search, may be
inflated by the strong focus on giant stars in APOGEE targeting. Again, the
primary relevant conclusion to be drawn is that the prior WDMS candidate
catalogs contain some contamination by misidentified systems with red giant
primaries.

Table 1: General information on the 45 WDMS systems/candidates observed by APOGEE. APOGEE ID | Source Survey | $G^{a}$ | $H^{b}$ | $\left(J-K\right)^{b}$ | $T_{\rm eff}\\!^{b}$ | $\log\left(g\right)^{b}$ |  [Fe/H]b |  Notesc
---|---|---|---|---|---|---|---|---
|  | [mag] | [mag] | [mag] | [K] | [cgs] |  |
2M01090044$+$5203369 | LAMOST | 11.692 |  8.290$\pm$0.018 |  1.098$\pm$0.032 |  4033$\pm$65 |  1.486$\pm$0.047 |  0.254$\pm$0.007 | RG
2M01575656$-$0244460 |  SDSSd | 15.041 |  12.103$\pm$0.024 |  0.829$\pm$0.035 |  3871$\pm$86 |  4.739$\pm$0.103 |  0.114$\pm$0.016 |
2M03160020$+$0009462 | LAMOST | 15.363 |  12.069$\pm$0.024 |  0.797$\pm$0.037 |  3574$\pm$77 |  5.290$\pm$0.111 |  0.017$\pm$0.019 |
2M03452349$+$2451029 |  LAMOSTd | 14.476 |  11.201$\pm$0.030 |  0.880$\pm$0.034 |  3776$\pm$64 |  4.789$\pm$0.110 |  0.048$\pm$0.011 |
2M04322373$+$1745026 | LAMOST | 13.362 |  10.161$\pm$0.019 |  0.840$\pm$0.027 |  3344$\pm$64 |  5.283$\pm$0.110 |  0.187$\pm$0.017 |
2M05242983$+$0023460 |  SDSSd | 15.836 |  12.016$\pm$0.023 |  0.974$\pm$0.035 |  3439$\pm$67 |  4.193$\pm$0.122 |  -0.204$\pm$0.020 | TTau
2M05285461$+$0305035 |  SDSSd | 14.681 |  11.141$\pm$0.026 |  0.960$\pm$0.038 |  3630$\pm$62 |  4.288$\pm$0.109 |  0.123$\pm$0.012 | RSCVn
2M05303840$-$0525436 |  SDSSd | 14.818 |  11.398$\pm$0.024 |  0.991$\pm$0.031 |  3706$\pm$84 |  3.130$\pm$0.057 |  -0.813$\pm$0.030 | Orion V
2M05321483$-$0620547 |  SDSSd | 15.038 |  11.778$\pm$0.026 |  0.923$\pm$0.033 |  3503$\pm$76 |  3.785$\pm$0.044 |  -0.230$\pm$0.023 | Orion V
2M05325045$-$0035422 |  SDSSd | 15.736 |  12.057$\pm$0.022 |  0.975$\pm$0.036 |  3383$\pm$66 |  4.456$\pm$0.124 |  -0.211$\pm$0.021 | YSO
2M05343005$-$0449506 |  SDSSd | 14.427 |  11.265$\pm$0.032 |  1.042$\pm$0.031 |  |  |  | Orion V
2M05355349$-$0123044 |  SDSSd | 16.066 |  11.894$\pm$0.031 |  1.217$\pm$0.034 |  3313$\pm$63 |  3.986$\pm$0.044 |  -0.261$\pm$0.022 | YSO
2M05361475$-$0613169 |  SDSSd | 15.106 |  11.737$\pm$0.032 |  0.973$\pm$0.028 |  3689$\pm$73 |  4.130$\pm$0.118 |  -0.185$\pm$0.017 | Orion V
2M05393524$-$0436145 |  SDSSd | 15.867 |  12.148$\pm$0.024 |  1.244$\pm$0.033 |  3437$\pm$70 |  3.350$\pm$0.047 |  -0.476$\pm$0.024 | YSO
2M06393441$+$0954512 |  SDSSd | 15.585 |  12.215$\pm$0.023 |  1.059$\pm$0.033 |  3715$\pm$78 |  3.910$\pm$0.047 |  -0.214$\pm$0.018 | Orion V
2M06402564$+$0959597 |  SDSSd | 17.083 |  13.130$\pm$0.026 |  1.275$\pm$0.042 |  |  |  | TTau
2M06404600$+$0917582 |  SDSSd | 15.999 |  12.701$\pm$0.026 |  0.881$\pm$0.042 |  3714$\pm$77 |  4.267$\pm$0.112 |  -0.017$\pm$0.017 | TTau
2M06411837$+$0939411 |  SDSSd | 16.031 |  12.649$\pm$0.025 |  0.947$\pm$0.040 |  3716$\pm$88 |  3.669$\pm$0.045 |  -0.204$\pm$0.023 | Orion V
2M06412562$+$0934429 |  SDSSd | 15.521 |  12.391$\pm$0.022 |  0.960$\pm$0.036 |  3866$\pm$84 |  4.048$\pm$0.116 |  -0.204$\pm$0.018 | TTau
2M08094855$+$3221223 |  SDSSd | 16.604 |  13.085$\pm$0.020 |  0.922$\pm$0.035 |  3529$\pm$68 |  4.946$\pm$0.113 |  -0.016$\pm$0.017 |
2M08424235$+$5128575 |  SDSSd | 13.937 |  10.399$\pm$0.027 |  0.885$\pm$0.030 |  |  |  |
2M08531787$+$1147595 | SDSS/LAMOST | 14.454 |  11.544$\pm$0.028 |  0.743$\pm$0.029 |  |  |  |
2M09463250$+$3903015 |  SDSSd | 15.155 |  11.948$\pm$0.022 |  0.859$\pm$0.030 |  3696$\pm$73 |  4.825$\pm$0.107 |  0.091$\pm$0.015 |
2M10243847$+$1624582 | SDSS | 17.822 |  14.454$\pm$0.054 |  0.771$\pm$0.068 |  3400$\pm$78 |  5.119$\pm$0.113 |  0.063$\pm$0.024 |
2M10552625$+$4729228 | SDSS | 16.664 |  13.227$\pm$0.027 |  0.881$\pm$0.042 |  3500$\pm$74 |  4.868$\pm$0.107 |  0.169$\pm$0.018 |
2M11241545$+$4558412 |  SDSSd | 14.603 |  11.396$\pm$0.032 |  0.863$\pm$0.030 |  3691$\pm$71 |  4.849$\pm$0.110 |  0.025$\pm$0.014 |
2M11463394$+$0055104 |  SDSSd/LAMOSTd | 16.741 |  13.397$\pm$0.023 |  0.924$\pm$0.042 |  3476$\pm$76 |  5.204$\pm$0.116 |  -0.045$\pm$0.022 |
2M12154411$+$5231013 | LAMOST | 12.581 |  9.340$\pm$0.027 |  0.946$\pm$0.030 |  3487$\pm$56 |  5.414$\pm$0.114 |  0.028$\pm$0.012 |
2M12333939$+$1359439 |  SDSSd/LAMOSTd | 16.679 |  13.486$\pm$0.030 |  0.922$\pm$0.036 |  |  |  |
2M12423245$-$0646077 | SDSS | 16.065 |  12.968$\pm$0.027 |  0.915$\pm$0.037 |  3728$\pm$78 |  4.842$\pm$0.112 |  -0.059$\pm$0.017 |
2M13054173$+$3037005 |  SDSSd | 16.237 |  12.761$\pm$0.022 |  0.803$\pm$0.033 |  3424$\pm$72 |  5.420$\pm$0.119 |  -0.113$\pm$0.022 |
2M13090450$+$1411351 |  SDSSd/LAMOSTd | 15.308 |  12.229$\pm$0.023 |  0.845$\pm$0.033 |  |  |  |
2M13115337$+$1549147 |  SDSSd | 16.825 |  13.353$\pm$0.031 |  0.927$\pm$0.048 |  3570$\pm$73 |  5.003$\pm$0.117 |  -0.142$\pm$0.019 |
2M13463968$-$0031549 |  SDSSd | 16.427 |  13.382$\pm$0.035 |  0.823$\pm$0.046 |  |  |  |
2M14244053$+$4929580 | SDSS | 15.694 |  13.542$\pm$0.031 |  0.631$\pm$0.052 |  4111$\pm$111 |  5.208$\pm$0.160 |  -1.415$\pm$0.038 |
2M14544500$+$4626456 |  LAMOSTd | 14.531 |  11.278$\pm$0.032 |  0.925$\pm$0.035 |  3673$\pm$71 |  4.898$\pm$0.106 |  0.148$\pm$0.014 |
2M14551261$+$3810342 | LAMOST | 14.400 |  11.279$\pm$0.022 |  0.802$\pm$0.029 |  3641$\pm$84 |  4.829$\pm$0.122 |  -0.308$\pm$0.024 |
2M15041191$+$3658150 | LAMOST | 17.034 |  13.722$\pm$0.036 |  0.873$\pm$0.043 |  3592$\pm$71 |  4.962$\pm$0.117 |  -0.130$\pm$0.017 |
2M15104562$+$4048271 | SDSS/LAMOST | 14.671 |  11.374$\pm$0.019 |  0.796$\pm$0.028 |  3577$\pm$78 |  4.954$\pm$0.127 |  -0.372$\pm$0.023 |
2M15150334$+$3628203 |  SDSSd | 14.941 |  11.652$\pm$0.022 |  0.906$\pm$0.029 |  3634$\pm$65 |  4.744$\pm$0.104 |  0.240$\pm$0.012 |
2M18454771$+$4431148 | LAMOST | 13.742 |  12.075$\pm$0.020 |  0.445$\pm$0.025 |  5243$\pm$131 |  4.509$\pm$0.085 |  0.093$\pm$0.012 |
2M19202987$+$4000013 |  LAMOSTd | 12.856 |  9.345$\pm$0.021 |  1.084$\pm$0.025 |  3789$\pm$61 |  1.071$\pm$0.046 |  0.135$\pm$0.009 | RG
2M19274650$+$3841111 | LAMOST | 12.006 |  7.951$\pm$0.016 |  1.208$\pm$0.038 |  3586$\pm$60 |  0.497$\pm$0.050 |  -0.326$\pm$0.013 | RG
2M22145972$-$0820200 | SDSS | 17.427 |  14.189$\pm$0.043 |  0.894$\pm$0.069 |  |  |  |
2M22200576$-$0418445 | LAMOST | 15.387 |  12.405$\pm$0.023 |  0.792$\pm$0.035 |  3613$\pm$86 |  5.161$\pm$0.122 |  -0.306$\pm$0.026 |
Notes |  |
a From Gaia Collaboration et al. (2018) |  |
b From APOGEE |  |
c Descriptions follow the condensed object descriptions from SIMBAD |  |
d SDSS photometric candidate or LAMOST spectroscopic candidate |  |

##  4 Analysis of System Architectures

After removing the YSO and red giant systems from the initial set of 45
previously identified WDMS systems, we are left with 28 remaining as candidate
WDMS systems. Of these, 21 have two or more epochs of RV data, which allow
either limits on or solutions to the system orbital parameters.

###  4.1 The Joker Orbital Analysis of the Radial Velocities

Analysis of the multi-epoch RVs was performed using The Joker (Price-Whelan et
al., 2017, 2020), a custom Monte Carlo sampler that uses a given set of input
RV measurements to produce independent posterior samples in Keplerian orbital
parameters. In particular, the code was designed to excel at fitting orbits
for targets with sparse RV data and/or low S/N RV measurements. Here we
provide a brief description of the fitting procedure for clarity, but a more
thorough and technical prescription can be found in Price-Whelan et al. (2017,
2020). First, $2^{24}$ samples are drawn from a prior probability density
function covering the full Keplerian orbit parameter space, allowing rejection
sampling over a dense set of potential solutions. For systems that have a
large number of surviving samples (in this work, 256 samples) that are not
unimodal, we recompute the rejection sampling with 512 requested samples in an
attempt to discover groupings of possible solutions in the period distribution
and period versus eccentricity diagram that can place limits on the orbital
parameters (see Sec. 5.6 and 5.7 for further details). If the number of
surviving samples is fewer than 256 samples, however, these surviving samples
are used to initialize a Markov chain Monte Carlo (MCMC) run. This procedure
typically returns a unimodal set of samples that represent the best fitting
solution for a system.

To limit our analysis to only RVs derived from high-quality spectra, we remove
any visit-level APOGEE data that have the following
STARFLAGs222https://www.sdss.org/dr16/algorithms/bitmasks/#APOGEE_STARFLAG
set: LOW_SNR (visit-$\mathrm{S/N}<5$), VERY_BRIGHT_NEIGHBOR (indicates that a
star with a spectrum adjacent to that of the target star on the spectrograph
detector is more than 100 times brighter and therefore a source of potential
contaminating flux), PERSIST_HIGH (evidence that the spectrum crosses detector
pixels that show super-persistence), PERSIST_JUMP_POS, or PERSIST_JUMP_NEG
(indicating an obvious and artificial positive or negative decrease, or
“jump”, in spectral continuum between two spectrograph detectors — the one
sampling from the 1.585 to 1.644 $\mu$m and the other from 1.514 to 1.581
$\mu$m). These flags correspond to bitmask values: 3, 4, 9, 12, 13.

Because the APOGEE visit-level RV uncertainties (VRELERR in the allVisit file)
are known to be underestimated (e.g., Badenes et al., 2018), for the systems
surviving the above target flag pruning we apply the expression presented in
Brown et al. (in prep.)

$\small{\sigma_{\mathrm{RV}}^{2}=(3.5(\texttt{VRELERR})^{1.2})^{2}+(0.072\,\mathrm{km\,s}^{-1})^{2},}$
(1)

where $\sigma_{\mathrm{RV}}$ is the total, inflated visit velocity error for a
given visit. This asymptotes to a $0.072$ km s-1 minimum for the visit-level
RV uncertainties.

For systems with $\gtrsim$8 visits that are well distributed in orbital phase,
The Joker generally converges to a single, unimodal period solution. This is
because The Joker fits six orbital elements, i.e., has 6 degrees of freedom.
Of the 21 WDMS binary candidates having at least two APOGEE RV visits, eight
have at least eight visits, and thus are good candidates for full Keplerian
orbit fitting with The Joker, although not all will return satisfactory
solutions because of undetectable orbital amplitudes in the cases of wide
binaries. The four systems with six or seven RV visits often converge to a
single solution, but not universally. In cases where no single solution is
reached (i.e., those with multimodal period solutions), only limits can be
placed on the period of the system. This is typical for the nine systems with
two to five visits.

In the end, we report full orbital solutions for five short period (relative
to the APOGEE temporal baseline) systems. In all five cases, these are the
first solutions ever presented for these systems, including RV variations that
warrant a PCE classification. We discuss these five systems in more detail in
Sections 5.1-5.5. For another seven systems that are sampled reasonably to
very well by APOGEE (i.e., $\geq 6$ RV epochs) no good solution converges
because the period of the WDMS binary may be longer than their APOGEE time
series data; therefore we report them as “wide binary” systems and provide
lower limits on the orbital period and the main sequence star velocity
amplitude. These systems are discussed in Section 5.6. For an additional nine
systems having 2-5 visits, we also provide upper and lower limits to the
orbital period (Sec. 5.7), and among these are two well known PCE systems and
two newly discovered systems that have RV variations warranting a PCE
classification. A few of the WDMS systems observed by APOGEE are left with 1
or 0 useful visits after imposition of the quality cuts described in Section
4.1, and we briefly mention these in Section 5.8.

###  4.2 Estimating the Stellar Masses

Along with the orbital parameters provided by The Joker, we can estimate the
primary star masses via the empirically-derived Torres et al. (2010) relation
for main sequence stars:

$\displaystyle\log{M_{\star}}$
$\displaystyle=a_{1}+a_{2}X+a_{3}X^{2}+a_{4}X^{3}+a_{5}(\log{g})^{2}$ (2)
$\displaystyle+a_{6}(\log{g})^{3}+a_{7}[\mathrm{Fe/H}],$

which has a relatively small scatter ($\sigma_{M_{\star}}=0.064M_{\star}$) for
stars down to $\sim$0.5 $M_{\odot}$. Here, $X=\log{T_{\mathrm{eff}}}-4.1$ and
the coefficients, $a_{i}$, are given in Torres et al. (2010). For the systems
with unimodal samples returned by The Joker, we additionally calculate the
minimum masses of the secondary (i.e., the WD companions), $m\sin{i}$ using
the calculated primary masses. In Table 2, we report the masses for all the MS
stars in our clean sample that have ASPCAP parameters, and we report the
minimum masses of the WD stars and derived orbital parameters in systems with
well-constrained orbital periods.

##  5 Descriptions of Individual Systems

###  5.1 2M10243847+1624582

High-quality APOGEE observations of the spectroscopically-confirmed WDMS
system 2M10243847+1624582 exist for 28 epochs spanning just over a year, from
2015 February to 2016 February. APOGEE spectroscopic analysis reveals the cool
($T_{\rm eff}$ = 3400 K) M dwarf primary to be approximately solar metallicity
([Fe/H]=$+0.06$). The combined The Joker plus MCMC run returned a unimodal
solution, and this best-fit solution is presented in Figure 2. With an RV
semi-amplitude of 146 km s-1 and an orbital period of just over 12 hours, this
system is fairly typical for a PCE WDMS system. Schreiber et al. (2010)
identified this system as a PCE candidate, and our solution confirms this
classification. The lower limit on the WD mass of $m\sin{i}$ = 0.537
$\pm$0.013 M⊙ is consistent with typical masses reported by both Rebassa-
Mansergas et al. (2016a) for all SDSS systems and Ren et al. (2018) for all
LAMOST systems. In this case, however, the mass derived from SDSS with a
combined atmospheric parameters and cooling track fitting is $M_{WD}=0.830\pm
0.063$ $M_{\odot}$, which is well above our derived mass limit, possibly
indicating a slightly inclined orbit.

Figure 2: Upper panel: The best fitting RV curve derived from the orbital
solution to the 28 phase-folded APOGEE RVs for the WDMS system
2M10243847+1624582. Two periods are shown for clarity. Lower panel: The
residuals to the fit shown in the upper panel.

###  5.2 2M10552625+4729228

The WDMS system 2M10552625+4729228 was observed with high S/N eleven times
over 277 days from 2017 May to 2018 February. APOGEE spectroscopic analysis
again reveals a cool ($T_{\rm eff}$ = 3500 K) M dwarf primary, this one with a
super-solar metallicity ([Fe/H]=+0.17) Our analysis with The Joker yields a
unimodal solution to the RV variations of the M dwarf primary, shown in Figure
3. The solution reveals this binary to be another PCE system; with a derived
period of a little more than 2 days, though slightly longer than the 8 hour
average for PCE WDMS systems, the system is still in a much shorter period
orbit than the longest known for PCE binaries. Schreiber et al. (2010) also
identified this system as a PCE candidate, and our solution confirms this
classification. The lower limit on the WD mass of $m\sin{i}$ = 0.476
$\pm$0.009 M⊙ is similar to that of 2M10243847+1624582, which again could
indicate a slightly inclined orbit since it is well below the SDSS mass of
$M_{WD}=0.790\pm 0.081\,M_{\odot}$. This value is, however, consistent with
typical SDSS and LAMOST WD masses.

Figure 3: The same as Figure 2 but for the eleven APOGEE RV epochs for
2M10552625+4729228. The error bars are smaller than the plotted points in the
upper panel.

###  5.3 2M11463394+0055104

The target 2M11463394+0055104, determined by APOGEE spectroscopic analysis to
be another approximately solar metallicity M dwarf ([Fe/H]=$-0.05$), received
33 high-quality visits spanning just over 4 years from 2012 February to 2016
March. With such extensive coverage, it is not surprising that a unimodal
solution was achieved for this system; the best-fit solution is shown in
Figure 4. A roughly 9 hour orbital period places this system just above the
typical 8 hour period for PCE WDMS systems. LAMOST flagged this system as a
candidate WDMS binary based on their spectra, and, combined with our derived
orbital solution, we confirm this system to be another PCE WDMS binary. The
derived lower limit to the WD mass of $0.717\pm 0.014$ $M_{\odot}$ places this
companion near the upper end of the mass distributions reported by both SDSS
and LAMOST. While this is not atypical nor the most massive WD by far, this
larger mass is worth pointing out, since it is in contrast to the mass limits
of the other systems with unimodal solutions.

Figure 4: The same as Figure 3 but for the 33 APOGEE RV epochs for
2M11463394+0055104.

###  5.4 2M13054173+3037005

This target received only six high-quality visits spanning just over a month
from 2018 April 24 to 2018 May 31. To compensate for the smaller number of RV
epochs, we decrease the number of degrees of freedom in the solution by
setting the eccentricity of all attempted fits to $e=0$ (as we do not have
sufficient data to prefer an eccentric orbit over a circular one at this
time). We then performed runs with The Joker using a succession of minimum
periods starting with 0.055, 0.1, 0.23, 0.3, 0.64, 0.73, and 1.1 days and a
maximum period of 7.0 days; that maximum period was selected because the first
four RVs collected looked like they formed a possible full orbital period of
that length. After running The Joker on this system multiple times, it was
evident that there were multiple solutions that fit the data even though any
individual run could return a single solution depending on the specified
minimum orbital periods. With only six data points, the phase coverage and RV
spread (${\rm RV_{\rm max}-RV_{\rm min}}=\Delta\rm RV_{max}$, as in Table 2)
for all solutions in one The Joker run of a given set lower period limit were
inconsistent with one another, and not all of the runs returned realistic
solutions. The solution we report was selected because it contains the most-
well-sampled phase coverage over one proposed orbital period while also
aligning well with the current RV spread; however, it is important to stress
that is only one of many potential solutions to the data. This solution shows
an orbital period of $P=0.22$ days with the eccentricity fixed to $e=0$, which
is a reasonable assumption for such a short orbital period, given that we do
not have any reason to believe that such a small orbit would not be
circularized. There were shorter period solutions when The Joker was given a
shorter minimum period parameter, but the current RV spread appeared far too
small to warrant these solutions as they require the $\Delta\rm RV_{max}$ to
be $\sim$30–40 $\rm\>km\,s^{-1}$ larger than observed. There are also longer
period solutions that one can achieve by imposing a larger minimum orbital
period; however, these solutions generally depended on the observations being
poorly distributed in orbital phase, and, in some case, bunch the observations
in such a way as to also, ironically, result in $\Delta\rm RV_{max}$ that are
$\sim$30–40 $\rm\>km\,s^{-1}$ larger than observed. The period and $m\sin{i}$
from our adopted solution are likely lower limits, and clearly additional data
are required to fully constrain the orbital parameters for this system. This
system comes from the Rebassa-Mansergas et al. (2013) catalog of
photometrically selected WDMS candidates, and we keep this classification and
update it to be a PCE candidate given our updated contributions to the RV
variation.

Figure 5: The same as Figure 3 but for the six APOGEE RV epochs for
2M13054173+3037005 and assuming a circular orbit. While the number of epochs
is small, their phase coverage is very good for this adopted solution, while
the RV amplitude is very large, which results in a solution that converges to
a tight match with the data.

###  5.5 2M14544500+4626456

APOGEE observed this target with seven high-quality APOGEE visits spanning
almost four years from 2013 March to 2017 March. APOGEE spectroscopic analysis
again reveals an M dwarf primary with super-solar metallicity ([Fe/H]=+0.15).
The Joker returned a unimodal solution for this system, and an MCMC run
confirmed that result shown in Figure 6. Similarly to the situation with
2M13054173+3037005, we fix the eccentricity to be $e=0$ to limit the degrees
of freedom as we do not currently have sufficient data to prefer an eccentric
orbit at this time. As with 2M11463394+0055104, our solution yields a minimum
WD mass of $m\sin i=0.693\pm 0.001$ $M_{\odot}$, which places the mass near
the upper end of the SDSS and LAMOST distributions. The orbital period
corresponding to this solution is $P=15.10$ days, which would make this system
second longest known orbital periods for the typical, compact PCE WDMS
systems, behind the five self-lensing systems ($P\sim 88-683\;$days; Kruse &
Agol, 2014; Kawahara et al., 2018; Masuda et al., 2019) as well as IK Peg
($P=21.72\;$days; Vennes et al., 1998) and just above SDSS J222108.45+002927.7
and SDSS J121130.94$-$024954.4 ($P=9.59\;$days and $P=7.82\;$days,
respectively; Rebassa-Mansergas et al., 2012). With the given number of
visits, the phase sampling could be such that this solution is not an accurate
model for the system. Additional RV data will be necessary to adjust or
falsify this model in the future; however, we report the best-fit solution we
derived as the most likely estimate for the period given the APOGEE data. As
this system was flagged as a candidate WDMS system by LAMOST, this
classification will need to be confirmed. If the WDMS classification and our
orbital solution is confirmed, 2M14544500+4626456 will be a useful PCE system
for applying the methods in Rebassa-Mansergas et al. (2012) to explore the
earlier phases of such systems and the energy budget of CE evolution.

Figure 6: The same as Figure 3 but for the seven APOGEE RV epochs for
2M14544500+4626456. While the number of epochs is relatively small, the
combination of very good phase coverage and a large RV amplitude means that a
very good solution is possible, under the assumption of a circular orbit.

###  5.6 Wide Binaries

There are seven systems with 6+ high quality epochs that have a small
($\Delta{\rm RV_{\rm max}}<10-20\,{\rm km\,s}^{-1}$) RV spread that may
correspond to $K_{\rm MS}<5-10\,{\rm km\,s}^{-1}$. This low RV spread could be
due to a lower inclination angle, which would make detecting shifts in the
radial velocity more difficult. As we cannot place limits on this inclination
given the present data, we proceed under the assumption that these relatively
small shifts are a by-product of a system with a large orbital separation and
long orbital period. Indeed, Willems & Kolb (2004) showed that wide-WDMS
binaries should typically have small RV shifts $\left(K_{\rm MS}\sim 1-5\ {\rm
km\,s}^{-1}\;{\rm at}\;i=60^{\circ}\right)$ at longer orbital periods
$\left(P>100\;{\rm days}\right)$. For this reason, we classify these seven
systems as wide binaries, with the understanding that lower inclination angles
could mean that we simply cannot detect more massive, unresolved systems.

Additionally, we perform a separate rejection sampling with The Joker with a
higher than normal number (512 as opposed to 256) requested samples for these
systems. By analyzing the period distribution and a period versus eccentricity
diagram for the potential solutions for these systems (examples shown in
Figure 7), we attempted to find groupings of possible solutions that are
indicative of limits to the orbital period of the system. In the case of WBs,
this would be a lower limit based on the smaller RV spread. This exercise
sometimes does not yield conclusive results; therefore, we present lower
limits on the orbital period for these WB systems in Column 3 of Table 2, but
we advise caution in interpreting these results as they may not be indicative
of the true solution. The $\Delta{\rm RV}_{\rm max}$ value presented in Column
2 similarly act as a rough limit of twice the potential velocity semi-
amplitude for each system based on the current data.

(a)

(b)

Figure 7: Plots used to place limits on the orbital periods of WBs and two PCE
systems. In this example for 2M12423245$-$0646077, two predominant groupings
are found in the period versus eccentricity diagram (right) for the 512
possible solutions. We then place the cautious lower limit of $P=150$ d as the
period distribution (left) clearly shows that a majority of the solutions fall
at longer orbital periods. For some systems, there is more random solutions
amongst the groupings. The limits on the two PCE systems were evaluated with
the eccentricity fixed to $e=0$ and with upper rather than lower limits.

###  5.7 Targets with 2-5 RV Visits

There are ten systems that have from two to five high-quality visits in
APOGEE. Two of these systems (2M01575656$-$0244460 and 2M15150334+3628203)
have an RV spread of $\Delta{\rm RV_{\rm max}}>60\,{\rm km\,s}^{-1}$, which is
sufficiently large to classify them safely as PCE systems, despite the fact
that there is insufficient data to derive a full orbital solution. These two
systems were identified as candidate WDMS systems from the SDSS photometric
catalog, and we again update the classification to a PCE WDMS candidate;
however, 2M01575656$-$0244460 shows a significantly blue GALEX (Bianchi et
al., 2017) FUV-NUV color (-0.26 mag) which is likely indicative of a WD
companion. Additionally, there are two other systems that are well known PCE
WDMS systems (2M04322373+1745026 and 2M12154411+5231013; HZ 9 and EG UMa; see
Rios-Venegas et al. 2020 and Bleach et al. 2000 and references therein,
respectively) that were observed. We do not attempt to add to the previous
orbital studies of EG UMa and HZ 9 as we have only have two and three data
points, respectively, that are temporally close to one other; however, we do
still report the MS star mass derived from our ASPCAP parameters for each. The
mass we derive for EG UMa’s MS component is consistent with previous studies,
and the mass for HZ 9 is only slightly higher than those shown in Rios-Venegas
et al. (2020) and references therein. Using similar reasoning to that in
Section 5.6, we provisionally classify the remaining six systems as candidate
wide-WDMS binaries.

Additional RV epochs will be necessary for the candidates to confirm these
classifications because, for a variety of reasons, the current data are not
sufficient to reveal their true nature. Similar to what was done in Section
5.6, though, we view period distributions and period eccentricity diagrams in
an attempt to place limits on the periods of these systems. For the WB
candidates, we again set cautious lower limits on the period. For the two PCE
candidates, we first fix the eccentricity to $e=0$ (under the same reasoning
employed in Sec. 5.4 and 5.5) and then place a cautious upper limit to the
current data. As the RV spread on these systems is significantly larger than
the WB candidates, this limit is more robust than the lower limits on the WBs;
however, the number of data points is still small and, therefore, abundant
caution should still be exercised in adopting these values until additional
data can test the significance of each limit.

Table 2: Orbital parameters derived using The Joker for systems with more than one RV visit. For WB systems, the period reported is a cautious lower limit on the period. For two of the marked PCE systems, the period reported corresponds to a cautious upper limit based on the small number of data point; the other marked PCE system has entries that represent one of many possible solutions. Here $m\sin i$ refers to the WD as the MS star $\left(M_{*}\right)$ is the star being fit by the RV template. Here $\Delta{\rm RV}_{\rm max}$ serves as a rough limit of twice the velocity semi-amplitude ($K$). 2M22145972$-$0820200 does not have ASPCAP parameters and, therefore, no mass can be derived. APOGEE ID | $\rm\Delta RV_{max}$ | $P$ | $e$ | $K$ | $\gamma$ | $M_{\star}$ | $m\sin i$ | $T_{\rm eff,WD}\\!^{\dagger}$
---|---|---|---|---|---|---|---|---
| $\left[\rm km\,s^{-1}\right]$ | $\rm\left[days\right]$ |  | $\left[\rm km\,s^{-1}\right]$ | $\left[\rm km\,s^{-1}\right]$ | $\left[M_{\odot}\right]$ | $\left[M_{\odot}\right]$ | [K]
PCE Systems
2M01575656$-$0244460a,e | $75.13\pm 0.07$ | 3.5 | 0 | - | - | $0.534\pm 0.034$ | - | -
2M04322373$+$1745026 | - | - | - | - | - | $0.440\pm 0.028$ | - |  29727$\pm$691
2M10243847$+$1624582 | $293.19\pm 11.63$ | $0.5258733\pm 0.0000056$ | $0.0295660\pm 0.0143324$ | $145.6\pm 2.3$ | $-8.5\pm 1.7$ | $0.423\pm 0.027$ | $0.537\pm 0.013$ |  15246$\pm$482
2M10552625$+$4729228 | $148.07\pm 0.08$ | $2.1866303\pm 0.0023683$ | $0.0033047\pm 0.0157235$ | $82.4\pm 1.0$ | $8.2\pm 0.9$ | $0.446\pm 0.029$ | $0.476\pm 0.009$ |  26801$\pm$113
2M11463394$+$0055104 | $373.00\pm 2.07$ | $0.4087104\pm 0.0000114$ | $0.0272674\pm 0.0135032$ | $186.8\pm 2.1$ | $-12.5\pm 2.8$ | $0.440\pm 0.028$ | $0.717\pm 0.014$ | -
2M12154411$+$5231013 | - | - | - | - | - | $0.485\pm 0.031$ | - |  15601$\pm$586
2M13054173$+$3037005b,e | $68.26\pm 0.15$ | $0.2165179\pm 0.0000015$ | 0 | $48.2\pm 0.4$ | $92.0\pm 0.2$ | $0.453\pm 0.029$ | $0.091\pm 0.001$ | -
2M14544500$+$4626456e | $99.53\pm 0.04$ | $15.0957084\pm 0.0000698$ | 0 | $53.41\pm 0.06$ | $-22.20\pm 0.05$ | $0.488\pm 0.031$ | $0.693\pm 0.001$ | -
2M15150334$+$3628203a,e | $228.08\pm 0.11$ | 13.5 | 0 | - | - | $0.489\pm 0.031$ | - | -
WB Systems
2M03160020+0009462c,e | $0.87\pm 0.02$ | - | - | - | - | $0.483\pm 0.031$ | - |  19416$\pm$1144
2M03452349$+$2451029 | $1.08\pm 0.01$ | 20.0 | - | - | - | $0.502\pm 0.032$ | - | -
2M08094855$+$3221223 | $0.91\pm 0.05$ | 200.0 | - | - | - | $0.436\pm 0.028$ | - | -
2M09463250$+$3903015c | $0.37\pm 0.08$ | - | - | - | - | $0.486\pm 0.031$ | - | -
2M12423245$-$0646077e | $2.58\pm 0.07$ | 150.0 | - | - | - | $0.478\pm 0.031$ | - | -
2M13115337$+$1549147 | $1.01\pm 0.12$ | 100.0 | - | - | - | $0.436\pm 0.028$ | - | -
2M14244053$+$4929580 | $3.52\pm 0.59$ | 100.0 | - | - | - | $0.438\pm 0.028$ | - |  36572$\pm$475
2M14551261$+$3810342d,e | $0.43\pm 0.01$ | - | - | - | - | $0.431\pm 0.028$ | - |  14728$\pm$2041
2M15041191$+$3658150 | $1.03\pm 0.06$ | 100.0 | - | - | - | $0.440\pm 0.028$ | - | -
2M18454771$+$4431148e | $0.43\pm 0.00$ | 400.0 | - | - | - | $0.913\pm 0.058$ | - |  33740$\pm$3576
2M22145972$-$0820200c,e | $0.04\pm 0.01$ | - | - | - | - | - | - | -
2M22200576$-$0418445c,e | $0.11\pm 0.00$ | - | - | - | - | $0.442\pm 0.028$ | - | -
Notes |
† Estimate from the system’s respective catalog |
a Here $P$ refers to a cautious upper limit with an eccentricity fixed to $e=0$ |
b Here the entries are for one of many possible solutions |
c Here there are only two RVs that are too close temporally to place accurate limits |
d Here the data produced incommensurate potential solutions such that no limit can be placed on the period |
e Candidate system |

###  5.8 Targets with a Single Visit

There are seven of the remaining 28 systems that only received one high-
quality visit throughout the course of the APOGEE survey and two that were
targeted by APOGEE, but for which the data were insufficient for either the
derivation of a radial velocity and/or ASPCAP parameters. No RV variations for
these systems can be determined in this work, and it is unlikely that these
systems will receive additional APOGEE visits in the future; however, the RV
measurement (when present) for each system is included in Appendix A for
completeness. In the future, these measurements can be combined with those
from dedicated follow-up studies or other spectroscopic sky surveys. Available
APOGEE measurements for these systems are listed in Table 3 in Appendix A.

##  6 Metallicity Distribution of WDMS Systems

The APOGEE database, featuring chemical abundances derived from high
resolution spectroscopy and multi-epoch radial velocities, provides a unique
opportunity to explore correlations between stellar chemistry and binary star
architectures (e.g., Mazzola et al., 2020). The metallicities of M dwarfs,
which constitute most of the MS companions in the present sample, are
notoriously difficult to measure (e.g., Newton et al., 2014), however Souto et
al. (2020) show that ASPCAP is sufficient to measure metallicities for these
low-mass stars within about 0.1 – 0.2 dex. The ASPCAP fits do not take into
account irradiation effects from the WD or tidal distortion effects in
determining stellar parameters, but, based on available temperature estimates
for the WDs in our sample, we do not expect these to significantly affect the
metallicities of the M dwarfs in our sample. We therefore exploit these ASPCAP
parameters here to explore the metallicity distribution of our vetted and
cleaned WDMS sample, which is a parameter space not often explored for these
systems, but one that has been questioned as potentially correlated to other
system characteristics. For example, among the few studies looking at WDMS
metallicities, Rebassa-Mansergas et al. (2016b) explored the age-metallicity
relation for a dataset of 23 WDMS systems and found no significant correlation
between the MS star’s [Fe/H] value and the WD’s age. Meanwhile, Parsons et al.
(2018) measured metallicities for thirteen eclipsing, PCE WDMS systems and did
not find clear evidence for the metallicity to be the cause of over-inflation
in the radii of their M dwarf sample.

Figure 9 shows the metallicity distribution of our 21 systems, separated into
their respective classifications of WB or PCE systems. As discussed in Section
3, there is one system (2M14244053+4929580), found here to be a WB, that is
extremely metal-poor ([Fe/H] $=-1.4$) compared to all other systems in this
paper. In fact, this [Fe/H] is $\sim$0.6 dex more metal poor than that for the
most metal-poor system from Rebassa-Mansergas et al. (2016b). Recently,
however, Rebassa-Mansergas et al. (2019) studied another eclipsing, PCE WDMS
system, SDSS J235524.29+044855.7, a short period binary containing a halo
subdwarf with [Fe/H] = $-1.55\pm 0.25$, which then relegates
2M14244053+4929580 to the second most metal-poor WDMS system reported to date.
As in the case of the former system, a metallicity this low is typically
indicative of a star system that belongs to the Milky Way halo population;
however, a kinematical analysis does not support that assumption. We used the
astro-gala (Price-Whelan, 2017) Python package along with the combined APOGEE
RV and Gaia parallax and proper motion to calculate the system’s orbit. The
result, shown in Figure 8, reveals the system to have a rather prototypical
(old) disk star orbit, with a maximum excursion from the disk of only 0.48 kpc
over a radial variation ranging from 3 to 10 kpc. The juxtaposition of this
rather planar orbit with such a low metallicity makes 2M14244053+4929580 a
somewhat unusual system (even ignoring that it is also a WDMS binary). Because
it seems an outlier, in the following analyses we consider statistics that
both include and exclude this unusual system.

Figure 8: The calculated orbit for 2M14244053+4929580 aged 5 Gyr backwards
from the present day, shown in the Galactic Cartesian coordinate system with a
1:1 aspect ratio in both projections to emphasize the planar nature of the
orbit. The red dot marks the system’s current location. It is clear that this
system has a very disk-like orbit despite being having a metallicity ([Fe/H]
$\sim$ -1.4) rather typical of the Galactic halo.

At the other end of the MDF, four of the PCE systems, and many WBs, appear to
have super-solar [Fe/H] values. However, the overall metallicity distribution
of PCE systems seems to be significantly higher than that for WB systems. This
is born out by the medians and dispersions of the two groups, which are
$0.114$ dex with $\sigma=0.109$ dex for the PCE, but $-0.059$ dex with
$\sigma=0.409$ dex (-0.037 dex and $\sigma=0.141$ dex excluding the subdwarf)
for the WBs. The latter group have a metallicity distribution function similar
to that for the full APOGEE sample of MS stars with similar effective
temperatures and surface gravities to those of the WDMS sample (shown for
comparison in Figure 9). These values demonstrate that the median
metallicities of the two systems are separated by $\sim 1\sigma$.

Figure 9: Top: The metallicity distribution of the WB and PCE systems listed
in Table 2 shown in blue and orange, respectively. For comparison we also show
in black the distribution of APOGEE MS stars sharing similar effective
temperatures and surface gravities as the MS primaries in the WB and PCE
samples. Bottom: Cumulative distribution for the WB and PCE in blue and
orange, respectively. The thick, black, vertical line shows the KS
$D$-statistic, the maximum distance between the two distributions.

A Kolomogorov-Smirnov (KS) test333All statistical tests here make use of the
scipy.stats (Virtanen et al., 2020) Python module. of the two distributions
with the hypothesis that the WB and PCE systems derive from the same parent
distribution yields a KS statistic of $D=0.556$ (see Fig. 9, bottom panel) and
a $p$-value of $p=0.058$, meaning the hypothesis can be rejected at the 90%
confidence level. Because KS tests are not always sensitive enough to
determine whether two distributions are independent, we also perform an
Anderson-Darling (AD) test, which is more sensitive to a distribution’s wings
and yields a standardized test statistic of $T=3.598$. This value allows us to
firmly reject our hypothesis at the 97.5% confidence level. Repeating these
tests with the metal-poor WB removed does not change the KS $D$ statistic,
and, with only a slight change in sample size, yields similar results: a KS
$p$-value of $0.084$, implying a rejection of the null hypothesis at the 90%
confidence level, and an AD test with $T=2.988$, rejecting the null hypothesis
firmly at the 97.5% confidence level . Meanwhile, in contrast, a KS test
comparing the WBs and the APOGEE MS star sample show them to be essentially
indistinguishable.

Figure 10:  Mass ratio, $q$, versus period for PCE systems with previously
derived orbital parameters and component masses (orange). The five systems
with orbital parameters derived in this work are also shown (blue). The mass
ratios for the latter represent lower limits on $q$ because we derive the
minimum WD mass from the Keplerian orbital parameters.

The difference in the [Fe/H] distribution of WB and PCE systems could
speculatively point to some sort of alteration of a system’s surface chemistry
during the CE phase. However, Hjellming & Taam (1991) showed that CEs have
much higher specific entropies than the surface of the secondary star, meaning
the companion should be thermally isolated from the CE and, as a result,
almost no accretion takes place. Thus, it would seem that the M dwarfs would
not be polluted by metals during the CE phase. The previously discussed
results of Parsons et al. (2018) that M dwarf radii in PCE systems were
indistinguishable from the radii of field M dwarfs would also support this
hypothesis; however, it is worth noting that some M dwarfs in PCE systems in
the center of planetary nebulas are substantially inflated (e.g., Jones et
al., 2015). This may be evidence that the companions are actually slightly
altered by the CE phase, but only affected for a short while. Could a possible
explanation for the obvserved metallicity difference be that the effects of
close binarity alter the metallicities? Could rapid rotation in close systems
affect the metallicities? Of course, the results here must be considered
tentative given the overall small WDMS sample, especially given selection
biases in the parent samples (see Section 3). Nevertheless, the metallicity
differences seen here between the PCE and WB groups offer a tantalizing
incentive for further studies of the chemistry of WDMS systems. A significant
contribution in this direction can be expected from the APOGEE survey itself,
where a large number of newly discovered WDMS candidates have been found
(Anguiano et al., 2020, Anguiano et al., in prep). Moreover, not only do the
majority of these systems have well characterized metallicities by APOGEE, but
more detailed chemical abundance patterns as well, a unique opportunity for
WDMS surveys to gain key insights into the role of chemical composition in the
evolution of WDMS systems.

##  7 Summary

We have presented an analysis of the 45 candidate or confirmed WDMS systems
identified by SDSS and LAMOST that also lie in the APOGEE survey. The results
of our investigation of these systems are as follows:

  * •

By examining the APOGEE-derived stellar parameters for the putative MS star in
each system (Fig. 1a), APOGEE identifies three to be RG contaminants and 14 to
be YSO contaminants of the 45 stars in the parent sample (Sec. 3). We propose
various reasons why YSOs may have a high contamination rate within
photometrically-selected WDMS catalogs and have thereby come to constitute
almost a third of our starting sample.

  * •

After imposing quality cuts on acceptable APOGEE RV measurements, we used The
Joker to derive or place limits on the orbital parameters for 14 of the WDMS
systems having more than two visits (Sec. 4.1). In addition, using the Torres
et al. (2010) relations and the APOGEE stellar parameters, we derive the MS
star mass for each system, when that is possible (Sec. 4.2).

  * •

A key result of our orbital analysis is the confirmation of nine previously
confirmed or candidate PCE systems: two that are well known (Sec. 5.7), three
that are newly confirmed (Sec. 5.1-5.3), and four that are newly discovered
(Sec. 5.4-5.5, 5.7). For three of these systems we present robust orbital
solutions (Sec. 5.1-5.3), while a reasonable solution is given for another
(Sec. 5.5) and a lower-limit solution for the remaining one (Sec. 5.4),
thereby adding to the relatively small ($\sim$90; e.g., Nebot Gómez-Morán et
al., 2011; Rebassa-Mansergas et al., 2016a; Parsons et al., 2015) number of
PCE systems having derived orbital parameters444Orbital parameters and
component masses for 90 PCE systems are available at https://www.sdss-
wdms.org/. and the $\sim$120 having at least spectroscopically or
photometrically defined orbital periods (e.g., Ren et al., 2018).

  * •

Though the mass ratios derived in this work represent lower-limits for $q$,
they tend to imply low mass ratios (with $1\lesssim q\lesssim 2$), which is
similar to what has been found for a majority of previous solutions for other
systems.

  * •

While the three systems for which we derive robust solutions have orbital
periods typical of most PCE systems, our solution for 2M14544500+4626456, if
confirmed to be a WDMS, would make it a PCE WDMS binary with the second
longest period known for typical, compact systems (Sec. 5.5). We also have
contributed 12 tentative WB classifications (Sec. 5.6), however, these may, of
course, change with additional RV data in the future.

  * •

We report 2M14244053+4929580 to be, by far, the most metal-poor WDMS system
known to date, with an [Fe/H] near the mean for the Galactic halo, of which we
initially suspected it to be a member (Sec. 3, 6). However, an analysis of the
orbit of this binary (Fig. 8) shows it to have an orbit more characteristic of
a Galactic disk star (Sec. 6).

  * •

The WB stars in our sample have an MDF that is significantly skewed to lower
metallicities than the PCE stars (Fig. 9). We speculate on reasons for this
MDF difference, but also caution that the analysis is based on a relatively
small sample (Sec. 6).

The results of the present exploration of previously known WDMS systems
demonstrate the efficacy of APOGEE data for not only characterizing the
orbital properties of such systems, but also for identifying new WDMS
candidates by their RV variability, in particular, those sources with short
period solutions that can add to the known number of PCE WDMS binaries having
derived orbital parameters. In a future paper (Anguiano et al., in prep.) we
will not only demonstrate this by further exploiting the APOGEE catalog, but,
in so doing, substantially increase the number of known and characterized WDMS
systems.

We thank the anonymous referee for insightful comments that significantly
improved the content of the manuscript. KAC, HML, BA, SRM, and DJM acknowledge
support from National Science Foundation grant AST-1616636. BA also
acknowledges the AAS Chrétien International Research Grant. ND would like to
acknowledge that this material is based upon work supported by the National
Science Foundation under Grant No. 1616684. ARL acknowledges partial financial
support for APOGEE2 provided in Chile by Comisión Nacional de Investigación
Científica y Tecnológica (CONICYT) through the FONDECYT project 1170476 and
QUIMAL Project 130001. Funding for the Sloan Digital Sky Survey IV has been
provided by the Alfred P. Sloan Foundation, the U.S.Department of Energy
Office of Science, and the Participating Institutions. SDSS acknowledges
support and resources from the Center for High-Performance Computing at the
University of Utah. The SDSS web site is www.sdss.org. SDSS is managed by the
Astrophysical Research Consortium for the Participating Institutions of the
SDSS Collaboration including the Brazilian Participation Group, the Carnegie
Institution for Science, Carnegie Mellon University, the Chilean Participation
Group, the French Participation Group, Harvard-Smithsonian Center for
Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins
University, Kavli Institute for the Physics and Mathematics of the Universe
(IPMU) / University of Tokyo, the Korean Participation Group, Lawrence
Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP),
Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für
Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik
(MPE), National Astronomical Observatories of China, New Mexico State
University, New York University, University of Notre Dame, Observatório
Nacional / MCTI, The Ohio State University, Pennsylvania State University,
Shanghai Astronomical Observatory, United Kingdom Participation Group,
Universidad Nacional Autónoma de México, University of Arizona, University of
Colorado Boulder, University of Oxford, University of Portsmouth, University
of Utah, University of Virginia, University of Washington, University of
Wisconsin, Vanderbilt University, and Yale University. This work presents
results from the European Space Agency (ESA) space mission Gaia. Gaia data are
being processed by the Gaia Data Processing and Analysis Consortium (DPAC).
Funding for the DPAC is provided by national institutions, in particular the
institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia
mission website is https://www.cosmos.esa.int/gaia. The Gaia archive website
is https://archives.esac.esa.int/gaia. This work made use of the SIMBAD
database, operated at CDS, Strasbourg, France; the VizieR catalog access tool,
CDS, Strasbourg, France. This work made use of TOPCAT, an interactive
graphical viewer and editor for tabular data (Taylor, 2005).

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##  Appendix A Systems with One or less High–Quality Visits

The seven systems shown in Table 3 were targeted by APOGEE, but, in the end,
received zero or one quality visit over the duration of the survey. These
systems are not likely to receive additional visits in the APOGEE-2 survey,
but obviously would benefit from additional data. The table summarizes what is
known about these systems from the current APOGEE data in hand.

Table 3: Data for APOGEE systems in the cleaned sample with zero or one quality visit.  Ref. ID | JD | RV | $M_{*}\\!^{a}$ |
---|---|---|---|---
|  | [$\rm km\,s^{-1}$] | [$M_{\odot}$] |
2M08424235$+$5128575 | 2457046.86882 |  38.93282 $\pm$ 18.471933 |  |
2M08531787$+$1147595 | 2458183.56201 |  80.99747 $\pm$ 0.09029441 | $0.463\pm 0.030$ |
2M11241545$+$4558412 | 2457151.67308 |  8.04085 $\pm$ 0.0831778 | $0.478\pm 0.031$ |
2M12333939$+$1359439 | 2458617.65376 |  85.52377 $\pm$ 1.351955 |  |
2M13090450$+$1411351b |  |  |  |
2M13463968$-$0031549b |  |  |  |
2M15104562$+$4048271 | 2457898.68379 |  -22.661102 $\pm$ 0.1061763 | $0.413\pm 0.026$ |
Notes
a If MS star with ASPCAP parameters available
b Received no high-quality visits