CWISE J075853.12$-$232645.8 | New discovery | This paper (Table 2) | 1209$\pm$79
L186-67 Ab (0822$-$5726) | Overlooked companion | Bergfors et al. (2010) | 2091$\pm$88llWe use the $\Delta{i^{\prime}}$ magnitude listed in Bergfors et al. (2010) to estimate a type of L1, which we use for the temperature estimation.
CWISE J083130.98+154018.4 | New discovery | This paper (Table 2) | 566$\pm$79
CWISE J092710.37$-$474155.5 | New discovery | This paper (Table 2) | 624$\pm$79
LP 788-1 B (0931$-$1717) | Overlooked companion |  Winters et al. (2017), Vrijmoet et al. (2020) | 1200$\pm$333mmWe assume a huge temperature range to encompass the full substellar regime, as this object is only known as a likely brown dwarf (Vrijmoet et al. 2022).
WISEU J100241.49+145914.9 | New companion to G 43-23 | This paper (Table 2 and Section 2.2) | 624$\pm$79
CWISE J100521.10$-$691226.8 | New discovery | This paper (Table 2) | 1190$\pm$79
CWISE J100628.98+105408.5 | New discovery | This paper (Table 2) | 566$\pm$79
CWISE J105349.12$-$460239.1 | New discovery | This paper (Table 2) | 686$\pm$79
1RXS J121408.0-234516 B | New companion | Gaia + this paper (Table 3.1) | 1250$\pm$150nnThe $M_{G}$ value derived from Gaia DR3 data suggests an early-T dwarf, and we assign a temperature appropriate for late-L through mid-T given that no spectrum yet exists.
e Vir Ab (1316+0925) | Overlooked companion | Kuzuhara et al. (2013); Bonnefoy et al. (2018) | 624$\pm$79
2MASSW J1326201$-$272937 B | New companion | Best et al. (2021) | 1400$\pm$200eeNo information is yet available on this companion, so the temperature estimate is set to cover the spectral type range from mid-L to early-T.
WT 460 B (1411$-$4132) | Overlooked companion | Montagnier et al. (2006) | 2096$\pm$134
SSSPM J1444$-$2019 | Revised spectral type | Kirkpatrick et al. (2016) | 2207$\pm$88
DENIS-P J1454078$-$660447 B | Overlooked companion | Vrijmoet et al. (2020) | 1100$\pm$250ffLittle information is available on this companion, so the temperature estimate is set to cover the spectral type range from mid-L to mid-T.
WISEA J153429.75$-$104303.3 | New parallax | Kirkpatrick et al. (2021b) | 686$\pm$79
2MASS J15345325+1219495 | New parallax | Gaia DR3 | 1532$\pm$88
SCR J1546$-$5534 B | New companion | Vrijmoet et al. (2022) | 2085$\pm$88ppWe base our temperature estimate on the estimated L1 type we derive in Table 3.1.
CWISE J161546.07+671227.4 | New discovery | This paper (Table 2) | 1254$\pm$79
CWISE J163336.14$-$325305.3 | New discovery | This paper (Table 2) | 819$\pm$79
VVV J165507.19$-$421755.5 | New discovery |  Schapera et al. (2022) and this paper (Table 2) | 1125$\pm$79
DENIS-P J170548.38$-$051645.7 B | Overlooked companion | Dieterich et al. (2014) | 1838$\pm$134
CWISE J171221.50+495318.2 | New discovery | This paper (Table 2) | 624$\pm$79
CWISE J171338.81$-$183322.7 | New discovery | This paper (Table 2) | 1227$\pm$79
CWISE J173830.94$-$773024.3 | New discovery | This paper (Table 2) | 624$\pm$79
2MASS J17502484$-$0016151 B | Overlooked companion | Henry et al. (2018) | 1100$\pm$250ffLittle information is available on this companion, so the temperature estimate is set to cover the spectral type range from mid-L to mid-T.
CWISE J180308.71$-$361332.1 | New discovery | This paper (Table 2) | 686$\pm$79
CWISE J181005.77$-$101001.2 | New parallax | Lodieu et al. (2022) | 800$\pm$100ggTemperature estimate is taken from Lodieu et al. (2022).
CWISE J181125.34+665806.4 | New discovery + parallax | This paper (Table 2 and Section A.3.2) | 412$\pm$79
CWISE J184803.45$-$143232.3 | New companion to G 155-42 | This paper (Table 2 and Section 2.2) | 686$\pm$79
CWISE J203438.09$-$462543.1 | New discovery | This paper (Table 2) | 624$\pm$79
CWISE J210057.80$-$624555.4 | New discovery | This paper (Table 2) | 1296$\pm$134
CWISE J215841.48+732842.8 | New discovery | This paper (Table 2) | 624$\pm$79
2MASSW J2224438$-$015852 B | New companion | Best et al. (2021) | 1400$\pm$200eeNo information is yet available on this companion, so the temperature estimate is set to cover the spectral type range from mid-L to early-T.
CWISE J222701.50+260450.0 | New discovery | This paper (Table 2) | 460$\pm$79
CWISE J223002.32+424655.3 | New discovery | This paper (Table 2) | 751$\pm$79
CWISE J224547.21$-$433341.5 | New discovery | This paper (Table 2) | 686$\pm$79
CWISE J230930.81+145630.6 | New discovery | This paper (Table 2) | 686$\pm$79
CWISE J233817.04$-$732930.3 | New discovery | This paper (Table 2) | 624$\pm$79
CWISE J233819.49$-$385421.2 | New discovery | This paper (Table 2) | 1254$\pm$79
CWISE J235120.60$-$700026.2 | New discovery | This paper (Table 2) | 460$\pm$79
Subtractions
CWISE J061741.79+194512.8 A | Revised distance estimate | Humphreys et al. (2023) | 1465$\pm$134
CWISE J061741.79+194512.8 B | Revised distance estimate | Humphreys et al. (2023) | 686$\pm$79
Kelu-1 A (1305$-$2541) | New parallax | Gaia DR3 | 1931$\pm$134
Kelu-1 B (1305$-$2541) | New parallax | Gaia DR3 | 1750$\pm$134
2MASSI J1526140+204341 | New parallax | Gaia DR3 | 1518$\pm$157
SDSS J163022.92+081822.0 | New parallax | This paper (Section A.3.1) | 970$\pm$88
2MASS J23174712$-$4838501 | New parallax | Gaia DR3 | 1537$\pm$197
2MASS J23312378$-$4718274 | New parallax | This paper (Section A.3.1) | 1125$\pm$79

###  6.2 Other complications

####  6.2.1 Youth

Will the estimation of masses for young objects be biased if those estimates
use a relation based on much older stars? Evolutionary models suggest that
below a mass of $\sim 0.4M_{\odot}$, the contraction of a star down to the
main sequence follows a Hayashi track along which the star’s effective
temperature remains approximately fixed (section 16.2.5 of Stahler & Palla
2004). If a temperature-based metric is used for estimating the masses of such
stars, then such estimates will be accurate. At higher masses, however, the
descent along the Hayashi track will be interrupted when a radiative zone
develops. The star then moves via a Henyey track along which the temperature
slowly increases until the star reaches the main sequence. For stars with
masses above $\sim 0.4M_{\odot}$, this evolution to the main sequence occurs
within the first 100 Myr.

Table 17: 20-pc Members of Young Associations and Moving Groups with Ages $<$ 100 Myr Objects in System | Coords. | Spectral TypeaaReferences for spectral type are listed in Table 3.1 along with information on whether the types are based on optical or near-infrared data. Spectral types in brackets are estimates based on the absolute $G$-band magnitude. | Membership | LikelihoodbbOur notes translate to the following codes in the moca_mtid column in table moca_membership_types of the MOCA database: confirmed = BF (bona fide member), high = HM (high-likelihood candidate member), and possible = CM (candidate member). Objects with MOCA codes of LM (low-likelihood candidate member), AM (ambiguous candidate member), and R (rejected candidate member) were ignored.
---|---|---|---|---
| J2000 |  |  |
(1) | (2) | (3) | (4) | (5)
2MASSW J0045214+163445 | 0045+1634 | L2 $\beta$ | Argus | high
Ross 15 | 0159+5831 | M4 | Carina | possible
$[$BHR2005$]$ 832-2 | 0311+0106 | M5.5 |  $\beta$ Pic | possible
LP 944-20 | 0339$-$3525 | M9 | Argus | possible
BD$-$21 1074 ABC | 0506$-$2135 | M1.5 V e, $[$M1$]$, $[$M2.5$]$ |  $\beta$ Pic | confirmed
PSO J076.7092+52.6087 | 0506+5236 | T4.5 | Argus | possible
V2689 Ori, PM J05366+1117 | 0536+1119 | M0.5 V ek, M4 |  $\beta$ Pic | possible
$\beta$ Pic | 0547$-$5103 | A6 V |  $\beta$ Pic | confirmed
AP Col | 0604$-$3433 | M4.5 V e | Argus | confirmed
2MASS J06244595$-$4521548 | 0624$-$4521 | L5 | Argus | high
LSPM J0714+3702 | 0714+3702 | M8 | Argus | possible
WISEPA J081958.05$-$033529.0 | 0819$-$0335 | T4 |  $\beta$ Pic | high
G 161-71ccOn the $G_{BP}-G_{RP}$ vs. $M_{G}$ and $G-J$ vs. $M_{G}$ diagrams of Figure 5, this M4.5 dwarf appears to be $\sim$1.5 mag above the locus of other objects of the same color despite having a Gaia DR3 RUWE value of 1.114. This could alternatively be interpreted as this object’s being $\sim$0.5 mag redder than the bulk of objects of similar absolute magnitude. In colors not involving Gaia magnitudes, no discrepancy is seen; this object falls at an M dwarf spectral type where many of these other colors ($J-K_{s}$, $J-$W2, W1$-$W2) are degenerate with spectral type over a large range, so such a discrepancy may not be noticeable. Malo et al. (2014b) and Ujjwal et al. (2020) identify this as a possible member of the Argus Association, so these discrepancies may be related to a young, active chromosphere. | 0944$-$1220 | M4.5 V | Argus | high
TWA 22 AB | 1017$-$5354 | M5:, M5.5: |  $\beta$ Pic | confirmed
WISE J104915.57$-$531906.1 AB | 1049$-$5319 | L7.5, T0.5: | ArgusddAlso identified as a member of the 500-Myr old Oceanus Group (Gagné et al. 2023). | high
SDSS J121951.45+312849.4 | 1219+3128 | L9.5 | Argus | confirmed
G 164-47 | 1309+2859 | M4 V | Carina | possible
$\alpha$ Cir AB | 1442$-$6458 | A7 Vp SrCrEu, K5 V |  $\beta$ Pic | possibleeeThe possible $\beta$ Pic Moving Group association for $\alpha$ Cir A is listed for both components, as the "high" likelihood Greater Scorpius-Centaurus association for $\alpha$ Cir B is highly suspect.
2MASS J17534518$-$6559559 | 1753$-$6559 | L4 | Argus | possible
WISE J180001.15$-$155927.2 | 1800$-$1559 | L4.5 |  $\beta$ Pic | possible
UCAC3 152-281185, UCAC3 152-281176 | 1845$-$1409 | M5 V e, M5 V e | Argus | possible
HD 182488 AB | 1923+3313 | G9+ V, T7: | Argus | confirmed
LEHPM 2-1265 AB | 2033$-$4903 |  $[$M5 composite$]$ |  $\beta$ Pic | possible
AU Mic, AT Mic AB | 2041$-$3226 | M1, M4.5 V, M4 V |  $\beta$ Pic | confirmed
PSO J319.3102$-$29.6682 | 2117$-$2940 | T0: |  $\beta$ Pic | high
WISEPC J225540.74$-$311841.8 | 2255$-$3118 | T8 |  $\beta$ Pic | high
HD 220140 AB, LP 12-90 | 2319+7900 | K2 V k, M4, M5: V | Columba | possible
G 190-28, G 190-27 | 2329+4128 | M3.5, M4.5 | Columba | possible
LP 704-15, LP 704-14 | 2357$-$1258 | M3 V, M4 V | Argus | possible

This means that objects in the 20-pc census that have masses above $\sim
0.4M_{\odot}$ and ages less than 100 Myr should have their mass estimates more
carefully considered. The Montreal Open Clusters and Associations database
(https://mocadb.ca/, Gagné et al., in prep., Gagné et al. 2018) is a
compilation of known stellar associations, stellar streams, moving groups, and
open clusters within 500 pc of the Sun. A search of this database on 2023 May
18 for objects within 20 pc of the Sun and likely belonging to one of these
young groups yielded 217 systems. The only objects in this list with ages
below 100 Myr are those believed to be members373737Several 20-pc objects are
tentatively associated with Greater Scorpius-Centaurus (age $\approx$ 15 Myr)
according to Kerr et al. (2021), but closer investigation of kinematics,
color-magnitude diagrams, lithium abundances, rotation periods, and non-
detections at X-ray wavelengths suggests that these are much older objects. of
the $\beta$ Pic Moving Group ($\sim$26 Myr), the Columba Association ($\sim$42
Myr), the Argus Association ($\sim$45 Myr), the Carina Assocation ($\sim$45
Myr), and the Octans-Near Association ($\sim$55 Myr)383838These age estimates
are taken directly from the table calc_association_properties in the Montreal
Open Clusters and Associations database.. These are listed in Table 17.

Because a mass of $0.4M_{\odot}$ corresponds to a spectral type of M2.5-M3
(table 7 of Mann et al. 2019), we can use spectral type to identify which of
the young 20-pc objects are the ones whose mass estimations may need special
handling. The only objects in Table 17 with spectral types earlier than this
are BD$-$21 1074 ABC, V2689 Ori, $\beta$ Pic, $\alpha$ Cir AB, HD 182488 A, AU
Mic, and HD 220140 A. Three of these are early M dwarfs for which the brief
jog along the Henyey track before reaching the main sequence covers such a
small range in temperature that their mass estimates should not be unduly
affected.

This leaves only four individual objects to consider, and two of these have
dynamical mass measurements already. For $\beta$ Pic, Lacour et al. (2021)
used astrometry of the exoplanet system to derive the mass of the host star
(1.75$\pm$0.03 $M_{\odot}$) using only a uniform mass prior between 1.4 and
2.0 $M_{\odot}$ on $\beta$ Pic itself. HD 182488 A has a loosely constrained
dynamical mass measurement from Brandt et al. (2019) of
$0.94^{+0.17}_{-0.27}M_{\odot}$. This leaves only two young systems with
possibly skewed mass estimates, and this represents such a small percentage of
20-pc stars with types earlier than M0 ($<1\%$) that no bias will be imparted
on the overall derived mass distribution.

We acknowledge that our understanding of young moving groups near the Sun is
still evolving. Our Sun is currently moving through three groups – the $\beta$
Pic Moving Group, the AB Dor Moving Group, and the recently identified (but
older) Oceanus Group (Gagné et al. 2023) – but it remains unlikely that many
new early-M and hotter dwarfs within 20 pc will be associated with any newly
recognized groups. Such young objects would have already revealed themselves
through, for example, high chromospheric activity.

Young brown dwarfs, on the other hand, require their own special handling. For
brown dwarfs, we deduce the form of the mass function via the empirical
temperature distribution. It has been well established, however, that young
brown dwarfs follow a different spectral type (or color) to $T_{\rm eff}$
relation than their older counterparts (Faherty et al. 2016). Corrections to
the temperature estimates for these objects were already established for the
brown dwarf portion of the 20-pc census in Kirkpatrick et al. (2021a), and
none of the new brown dwarfs discussed in Table 16 are known to be youthful
themselves. Therefore, no additional work is required here.

####  6.2.2 Non-solar metallicity

Objects with non-solar metallicity raise two concerns. The first is that
metal-poor objects may belong to the Galactic halo population and could skew
our calculation of the nearby mass function, which concentrates on the
Galactic disk. The second is that these objects, even if true disk members,
may be sufficiently metal poor that standard solar-metallicity relations will
not adequately predict their masses. Are either of these concerns justified?

A number of objects in Table 3.1 have spectroscopic classifications indicating
subsolar metallicity. For objects earlier than early-M, these classifications
can generally be identified via the iron index, "Fe#", which attempts to
encode the abundance of metals relative to hydrogen in the spectrum if the
spectrum does not match the standards of solar-metallicity (Gray & Corbally
2009). Underabundances are encoded as negative numbers. For objects of
spectral type late-K and later, metal poor spectral types (Gizis 1997; Lépine
et al. 2003; Kirkpatrick 2005; Lépine et al. 2007; Burgasser et al. 2007c;
Zhang et al. 2017) are usually denoted with prefixes of sd (subdwarf), esd
(extreme subdwarf), or usd (ultra subdwarf). Table 6.2.2 lists all objects in
the 20-pc census that have one of these low-metallicity classifications.

Table 18: 20-pc Objects with Low-metallicity and/or Halo Kinematics

Name | Coords | SpTypeaaReferences for spectral type are listed in Table 3.1 along with information on whether the types are based on optical or near-infrared data. Spectral types sometimes encode information about metallicity. For the coldest objects, this is generally done via a prefix such as sd (subdwarf), esd (extreme subdwarf), or usd (ultra subdwarf), with variations such as d/sd (indicating a spectral morphology intermediate between a normal, solar metallicity dwarf and a subdwarf) also possible (figure 11 of Kirkpatrick 2005). For hotter stars, the metallicity is included in one of two ways. A suffix type such as "mF1" for an F4 V star would indicate that the metal lines better match that of an F1 standard, despite the fact that the hydrogen line morphology matches the F4 standard. An alternative way of expressing this is to subtract the metal-line best-match subtype from the H-line best-match subtype and to convert that to a metal index; for example, if the iron lines best matched an F1 dwarf although the hydrogen lines best matched a F9 dwarf ($\Delta=+8$ subtypes), the metallicity index for iron would be expressed as Fe $=-0.13{\Delta}-0.26$, or more compactly as Fe$-$1.3. See chapter 6 of Gray & Corbally (2009) for more details. | Radial Vel. | RV Ref. | Kinem.
---|---|---|---|---|---
| J2000 |  | (km s-1) |  | Group
(1) | (2) | (3) | (4) | (5) | (6)
85 Peg | 0002+2704 | G5 V Fe-1 |  $-$35.57$\pm$0.35 | 1 | thin disk
6 Cet | 0011$-$1528 | F8 V Fe-0.8 CH-0.5 | 14.95$\pm$0.13 | 3 | thin disk
HD 4391 | 0045$-$4733 | G5 V Fe-0.8 |  $-$10.92$\pm$0.12 | 3 | thin disk
$\mu$ Cas | 0108+5455 | K1 V Fe-2 |  $-$97.09$\pm$0.25 | 3 | thick disk
LP 410-38 | 0230+1648 | sdM6e | 49.56$\pm$6.65 | 3 | thin disk
LP 651-7 | 0246$-$0459 | M6 V | 33.28$\pm$2.32 | 3 | halo
BD+33 529 | 0252+3423 | (sd)K5 V ([Fe/H]=$-$0.63) |  $-$49.89$\pm$0.15 | 3 | thick disk
G 174-25 | 0258+5014 | sdM3 |  $-$30.24$\pm$0.45 | 3 | thin disk
LP 994-33 | 0302$-$3950 | sdM5 |  $\cdots$ | - | thick disk?
Ross 578 | 0338$-$1129 | d/sdM2 |  $-$84.88$\pm$0.56 | 3 | halo
HD 25329 | 0403+3516 | K3 Vp Fe-1.7 |  $-$25.57$\pm$0.13 | 3 | halo
$\zeta$ Dor | 0505$-$5728 | F9 V Fe-0.5 |  $-$1.45$\pm$0.12 | 3 | thin disk
Kapteyn’s Star | 0511$-$4501 | sdM1p | 245.05$\pm$0.13 | 3 | halo
EGGR 290 | 0556+0521 | DAP8.7 |  $-$414.02$\pm$10.41 | 3 | (RV in error)hhThese objects are flagged by our analysis as belonging to the halo population, but their Gaia DR3 radial velocities are believed to be erroneous. For EGGR 290, the radial velocity measurement is likely incorrect due to the fact that this is a magnetic white dwarf and the fact that the Gaia DR3 radial velocity pipeline lacks white dwarf templates (Bailer-Jones 2022). For UPM J0812$-$3529, its status as a DC white dwarf (O’Brien et al. 2023) means that there should not be any lines in the optical spectrum with which Gaia could measure a radial velocity, but this suspicious radial velocity measurement has nonetheless created much discussion regarding the object’s possible close (future) fly-by of the Sun (Bobylev & Bajkova 2022; de la Fuente Marcos & de la Fuente Marcos 2022; Bailer-Jones 2022). For G 188-48 B, the Gaia DR3 radial velocity is assumed to be spurious because the A component has a much more reasonable – and better measured – value of 20.06$\pm$0.14 km s-1.
2MASS J06453153$-$6646120 | 0645$-$6646 | sdL8 |  $\cdots$ | - | thick disk?
YY Gem | 0734+3152 | M0.5 Ve Fe-2 | 32.66 | 2 | thin disk
212 Pup | 0752$-$3442 | F5 V Fe-0.5 | 28.03$\pm$0.16 | 3 | thin disk
HD 65583 | 0800+2912 | K0 V Fe-1.3 | 14.79$\pm$0.12 | 3 | thick disk
UPM J0812$-$3529 | 0812$-$3529 | DC |  $-$373.74$\pm$8.18 | 3 | (RV in error)hhThese objects are flagged by our analysis as belonging to the halo population, but their Gaia DR3 radial velocities are believed to be erroneous. For EGGR 290, the radial velocity measurement is likely incorrect due to the fact that this is a magnetic white dwarf and the fact that the Gaia DR3 radial velocity pipeline lacks white dwarf templates (Bailer-Jones 2022). For UPM J0812$-$3529, its status as a DC white dwarf (O’Brien et al. 2023) means that there should not be any lines in the optical spectrum with which Gaia could measure a radial velocity, but this suspicious radial velocity measurement has nonetheless created much discussion regarding the object’s possible close (future) fly-by of the Sun (Bobylev & Bajkova 2022; de la Fuente Marcos & de la Fuente Marcos 2022; Bailer-Jones 2022). For G 188-48 B, the Gaia DR3 radial velocity is assumed to be spurious because the A component has a much more reasonable – and better measured – value of 20.06$\pm$0.14 km s-1.
$\alpha$ Cha | 0818$-$7655 | F5 V Fe-0.8 |  $-$12.60$\pm$0.12 | 3 | thin disk
WISE J083337.83+005214.2 | 0833+0052 | (sd)T9 |  $\cdots$ | - | thick disk?
$\psi$ Vel | 0930$-$4028 | F3 V Fe-0.7 | 8.80$\pm$1.80 | 4 | thin disk
L 750-42 | 0943$-$1747 | sdM3 | 97.36$\pm$0.58 | 3 | thick disk
HD 88230 | 1011+4927 | K6e V Fe-1 |  $-$26.48$\pm$0.12 | 3 | thin disk
CWISE J105512.11+544328.3ccThis object does not yet have spectroscopic observations, so its status as a subdwarf is assumed based on its location on color-magnitude diagrams. | 1055+5443 | [sdT8] |  $\cdots$ | - | thick disk?
HD 103095 | 1152+3743 | K1 V Fe-1.5 |  $-$98.05$\pm$0.12 | 3 | halo
10 CVn | 1244+3916 | F9 V Fe-0.3 | 80.49$\pm$0.12 | 3 | thick disk
HD 114837 | 1314$-$5906 | F6 V Fe-0.4 |  $-$63.57$\pm$0.12 | 3 | thin disk
SDSS J141624.08+134826.7bbThese two objects form a common-proper-motion pair. | 1416+1348 | sdL7 |  $-$87$\pm$33 | 7 | thin disk
ULAS J141623.94+134836.3bbThese two objects form a common-proper-motion pair. | 1416+1348 | (sd)T7.5 |  $-$87$\pm$33ggThe space motion of the primary in this system is used in lieu of an independent measurement for this object. | 7 | thin disk
HD 125276 | 1419$-$2548 | F9 V Fe-1.5 CH-0.7 |  $-$22.28$\pm$0.13 | 3 | thin disk
WISE J142320.84+011638.0ddThis is the companion to HD 126053, which is typed as a G1.5 V. | 1423+0116 | sdT8 |  $-$19.21$\pm$0.14ggThe space motion of the primary in this system is used in lieu of an independent measurement for this object. | 3 | thin disk
$\sigma$ Boo | 1434+2944 | F4 V kF2 mF1 (metal weak) | 0.75$\pm$0.12 | 3 | thin disk
SSSPM J1444$-$2019 | 1444$-$2019 | sdL0 |  $\cdots$ | - | halo
WISEA J153429.75$-$104303.3ffAlso known as The Accident, this object does not yet have spectroscopic observations because it is too faint for ground-based spectroscopy. Its status as a subdwarf is assumed based on its highly unusual location on color-magnitude and color-color diagrams. See Kirkpatrick et al. (2021b) for details. | 1534$-$1043 | [esdT/Y?] |  $\cdots$ | - | halo
$\chi$ Her | 1552+4227 | G0 V Fe-0.8… |  $-$55.99$\pm$0.12 | 3 | thin disk
HD 144579 | 1604+3909 | K0 V Fe-1.2 |  $-$59.44$\pm$0.12 | 3 | thin disk
HD 145417 | 1613$-$5734 | K3 V Fe-1.7 | 8.68$\pm$0.13 | 3 | thick disk
b Her | 1807+3033 | F9 V metal-weak |  $-$0.38$\pm$0.13 | 3 | thin disk
CWISE J181005.77$-$101001.2 | 1810$-$1010 | esdT0: |  $\cdots$ | - | thick disk?
$\chi$ Dra | 1821+7243 | F7 V (metal-weak) | 31.90$\pm$0.14 | 5 | thin disk
HD 190067 | 2002+1535 | K0 V Fe-0.9 | 20.37$\pm$0.12 | 3 | thin disk
WISE J200520.38+542433.9eeThis is the wide companion in the $\xi$ Ursae Majoris quintuple system, the primary of which is generally typed as M1 V. | 2005+5424 | sdT8 |  $-$107.6ggThe space motion of the primary in this system is used in lieu of an independent measurement for this object. | 8 | thick disk
Ross 769 | 2104$-$1657 | M1 V |  $-$10.89$\pm$0.27 | 3 | halo
$\gamma$ Pav | 2126$-$6521 | F9 V Fe-1.4 CH-0.7 |  $-$29.78$\pm$0.12 | 3 | thin disk
G 188-49 B | 2214+2751 |  $\cdots$ |  $-$351.15$\pm$8.18 | 3 | (RV in error)hhThese objects are flagged by our analysis as belonging to the halo population, but their Gaia DR3 radial velocities are believed to be erroneous. For EGGR 290, the radial velocity measurement is likely incorrect due to the fact that this is a magnetic white dwarf and the fact that the Gaia DR3 radial velocity pipeline lacks white dwarf templates (Bailer-Jones 2022). For UPM J0812$-$3529, its status as a DC white dwarf (O’Brien et al. 2023) means that there should not be any lines in the optical spectrum with which Gaia could measure a radial velocity, but this suspicious radial velocity measurement has nonetheless created much discussion regarding the object’s possible close (future) fly-by of the Sun (Bobylev & Bajkova 2022; de la Fuente Marcos & de la Fuente Marcos 2022; Bailer-Jones 2022). For G 188-48 B, the Gaia DR3 radial velocity is assumed to be spurious because the A component has a much more reasonable – and better measured – value of 20.06$\pm$0.14 km s-1.
53 Aqr | 2226$-$1644 | G1 V + G5 V Fe-0.8 CH-1 | 2.28$\pm$0.15 | 6 | thin disk

References. — The references for radial velocity are – (1) Gaia Collaboration
et al. 2018, (2) Fouqué et al. 2018, (3) Gaia Collaboration et al. 2022, (4)
Holmberg et al. 2007, (5) Pourbaix et al. 2004, (6) Maldonado et al. 2010, (7)
Abazajian et al. 2009, (8) Gizis 1997.

To answer the first concern, we use the sky positions, parallaxes, and proper
motions in Table 3.1 along with published radial velocities in Table 6.2.2 to
calculate the $U,V,W$ space velocities with respect to the Local Standard of
Rest (LSR). We also calculate the $U,V,W$ values for all objects in Table 3.1
with Gaia-based radial velocity measurements to see if any objects lacking
low-metallicity spectral classifications are found to be halo members merely
from their kinematics393939Two such objects were found – LP 651-7 and Ross 769
– and for ease of reference, these have also been added to Table 6.2.2..
Figure 10 shows the Toomre diagram for both sets of objects. Also shown for
comparison are stars having radial velocity measurements in Gaia DR2 and lying
within 100 pc of the Sun, color coded as thin disk ($V_{\rm tot}\leq 85$ km
s-1), thick disk ($85<V_{\rm tot}\leq 180$ km s-1), or halo ($V_{\rm tot}>180$
km s-1) in accordance with the kinematic criteria of Nissen (2004). This
comparison demonstrates that only six objects – LP 651-7, Ross 578, HD 25329,
Kapteyn’s Star, HD 103095, and Ross 769 – appear to belong to the kinematic
halo population. All others most likely belong to the thin or thick disk
populations.

Figure 10: Toomre diagram of $UVW$ space motions corrected to the Local
Standard of Rest (LSR) for 74,066 Gaia DR2 stars within 100 pc of the Sun and
having parallax errors $<10\%$ (Kirkpatrick et al. 2021b). Thin disk (light
grey dots), thick disk (medium grey crosses), and halo (dark grey pluses)
objects are marked, with halo stars falling outside the outer dashed circle
(red) and thin disk objects falling inside the inner dashed circle (navy).
Objects with measured radial velocities in Table 3.1 or Table 6.2.2 are shown
in navy if lying in the thin disk velocity zone, yellow for the thick disk
zone, and red for the halo zone. The six halo members are highlighted with
black labels.

As stated in Section 3.5, Gaia contains radial velocities only for those
objects having $G_{RVS}\lesssim 14$ mag, which omits many of the M dwarfs and
all of the L, T, and Y dwarfs within 20 pc. For these objects, we leverage
spectroscopic indications of low metallicity to build a list of potential halo
members, then we scour the literature for other published radial velocities.
These objects are also listed in Table 6.2.2. Many of these lack any radial
velocity measurements, so assumed values from $-$200 to +200 km s-1, in
increments of 50 km s-1, were used to calculate a range of possible $U,V,W$
velocities. These results, shown in Figure 11, suggest that only two of these
colder objects – SSSPM J1444$-$2019 and WISEA J153429.75$-$104303.3 (aka "The
Accident") – are likely to be true halo members.

Figures 10 and 11 taken together suggest that only eight objects (all of them
believed to be single) out of 3,589 total in the 20-pc census, or $0.22\%$,
are halo interlopers. Although this is slightly higher than the percentage of
$0.15\%$ used in Table A of Bensby et al. (2014) based on F and G stars alone,
it nevertheless confirms that contamination by halo objects in the 20-pc
census is extremely small. Although these objects will still be included in
our mass function, any systematic offset imprinted upon their mass estimates
can be ignored in subsequent analyses.

Figure 11: Toomre diagram of the 100-pc sample from Figure 10, now overplotted
with the seven objects (various colors and symbols) from Table 6.2.2 that lack
radial velocity measurements. For these, results are shown for nine assumed
radial velocities ranging from $-200$ to +200 km s-1, in steps of 50 km s-1.
As in Figure 10, the demarcation of the thin disk, thick disk, and halo
populations are shown by the dashed circles in red and navy.

The second concern is difficult to address, as very few low-metallicity
objects have had their masses measured via direct methods. The coldest
subdwarfs, for instance, have a multiplicity fraction of only ${\sim}1\%$
(González-Payo et al. 2021); therefore, few such objects exist for dynamical
analyses (e.g., Rebassa-Mansergas et al. 2019). Single subdwarfs are obvious
targets for lensing-based mass measurements, as their high velocities increase
the likelihood of "encounters" with background objects, but accurate whole-sky
astrometry is just now advancing to the stage at which such measurements can
be predicted and planned for (e.g. Sahu et al. 2020). So, to address this
concern, we instead note that only forty-two low-metallicity systems are known
within the 20-pc census404040It is worth noting that other low-luminosity,
low-metallicity objects are likely to be found within this volume given the
fact that parallaxes for both WISEA J153429.75$-$104303.3
($d_{true}=16.3^{+1.4}_{-1.2}$ pc vs. $d_{est}=38.0^{+5.6}_{-4.9}$ pc;
Kirkpatrick et al. 2021b; Meisner et al. 2020a) and CWISE
J181005.77$-$101001.2 ($d_{true}=8.9^{+0.7}_{-0.6}$ pc vs. $d_{est}=$ 14 - 64
pc; Lodieu et al. 2022; Schneider et al. 2020) placed them far closer to the
Sun than original estimates predicted. (Table 6.2.2), which represents only
$1.5\%$ of the total. Thus, if small biases are present in converting a
subdwarf’s spectral type, colors, or absolute magnitudes to masses, the bias
in the overall 20-pc mass distribution will be negligible.

The above logic on the scarcity of objects also holds for systems with higher
metallicity than the Sun. This set of objects has a much smaller range in
metallicity than the metal-poor objects above, and there are just a handful of
examples. Only the higher-mass stars $\iota$ Hor AB (Fe+0.3), $\nu$ Phe
(Fe+0.4), HD 176051 AB (slightly metal strong), and HD 207129 (Fe+0.4) have
spectroscopic classifications that fall into this class. Another object, 14
Her, has a supersolar metallicity ([Fe/H] $\approx 0.4$; Rosenthal et al.
2021) although its listed spectral type in Table 3.1 gives no indication of
this. Curiously, even though members of the Hyades Cluster have metallicities
that are slightly supersolar ([Fe/H] $=0.14{\pm}0.05$; Perryman et al. 1998)
and lie, on average, only 47.0$\pm$0.2 pc from the Sun (Lodieu et al. 2019),
there are no confirmed Hyads within the 20-pc volume (Gaia Collaboration et
al. 2020; Schneider et al. 2022).

####  6.2.3 Formation process

Because we are interested in objects formed via the star formation process, we
need a criterion to distinguish objects that may have formed via alternative
formation mechanisms at the lowest masses. When brown dwarfs were first
theorized (Kumar 1963; Hayashi & Nakano 1963), they were regarded as direct
products of the star formation process – ones that had insufficient mass to
sustain prolonged thermonuclear fusion in their cores – and as such
represented the lower-mass extension of hydrogen-burning stars themselves.
These could be contrasted with another low-mass formation product, planets,
that were believed to be formed via a secondary process – from a
protoplanetary disk created around a newly formed protostar or brown dwarf. In
the early 1960s, there were no known examples of brown dwarfs, and our own
Solar System provided the only known examples of planets.

As brown dwarf and exoplanet discoveries began in earnest (see reviews by
Kirkpatrick 2005; Winn & Fabrycky 2015), it became clear that nature produces
some low-mass products that are difficult to classify as either brown dwarf or
exoplanet (e.g., 2MASSWJ 1207334$-$393254b, Chauvin et al. 2004). The earlier
definition based on formation was cumbersome to use in practice; unless an
object was still in its infancy, its exact formation process would be
difficult, if not impossible, to ascertain from observations. As an
alternative, Burrows et al. (1997) proposed another theoretically based
definition. This alternative uses mass to distinguish between a brown dwarf
and an (exo)planet, the dividing line being the somewhat arbitrarily chosen
deuterium burning limit, which is $\sim 13M_{Jup}$ for solar metallicity.
Somewhat surprisingly, this definition was thereafter widely (though not
universally) adopted, in no small part because lower-mass discoveries that
earlier would have been called "brown dwarfs" could now be referred to by a
more attention-grabbing label of "exoplanet."

This alternative definition, however, came three and a half decades after the
original brown dwarf definition, and the concept of planets having being born
from a protoplanetary disk (the "nebular hypothesis") had been in the
astronomical lexicon for over two centuries (Kant 1755; Laplace 1796). Thus,
labeling an object below 13 $M_{Jup}$ as a planet often leads to confusion, as
some readers – and even researchers – unwittingly apply both definitions in
tandem. That is, they assume that a so-named "planet" (by the new, mass-based
definition) must have formed via a protoplanetary disk (by the former,
formation-based definition). It is difficult to divorce the term "planet" from
its formation scenario.

In this paper, one of our goals is to define, or place limits on, the low-mass
terminus of star formation. If we were to use the newer definition to
include/exclude objects for the mass function analysis, our results would
return a terminus of 13$M_{Jup}$, which merely reflects the dividing line
chosen by the arbitrary definition. We must, therefore, more carefully
consider whether the lowest mass objects in the 20-pc census should be counted
as star-formation products or planetary-formation products.

As stated earlier, this definition also lacks easy observational verification.
Nonetheless, some methods have been proposed to distinguish formation
mechanisms. Öberg et al. (2011) postulated that the carbon to oxygen ratio
could be used as one tracer. Planets that formed close to a star would have a
solar-like $C/O$ value, like brown dwarfs formed via gravitational collapse,
whereas planets formed via accretion of ices beyond the water snowline would
have a supersolar $C/O$ value. Those authors acknowledged, however, that
measuring an accurate value of $C/O$ is fraught with difficulties (even within
our own Solar System), and Calamari et al. (2022) made a similar conclusion
based on their analysis of the spectrum of the brown dwarf Gliese 229B.
Mollière et al. (2022) show that this simplified picture of the $C/O$ ratio is
somewhat more complicated when disk chemical evolution and pebble accretion
are taken into account, as well.

Similarly, Morley et al. (2019) showed that the deuterium to hydrogen ratio
could be used to distinguish between planets with solar $D/H$ values like
Jupiter and Saturn, that formed directly from accretion of gas in the
protostellar nebula, and planets with enhanced $D/H$ values like Neptune and
Uranus, that presumably formed from accretion of ices. Both $C/O$ and $D/H$
thus have limitations: some objects formed via a protoplanetary disk have
values indistinguishable from those of objects born via star formation.

Another promising avenue is the overall metallicity. The giant planets of our
Solar System have metal enhancements well above solar values (Wong et al.
2004, Fletcher et al. 2009), and exoplanets are preferentially found around
metal-rich host stars (Fischer & Valenti 2005, Wang & Fischer 2015). These
facts led Fortney et al. (2008) to propose metallicity-based diagnostics that
could distinguish between formation scenarios. Specifically for objects with
$T_{\rm eff}<1400K$, a strong 4.5 $\mu$m CO absorption band along with
enhanced $H$\- and $K$-band fluxes (from a relative lack of collision-induced
absorption by $H_{2}$) are proposed as fingerprints of planet-like formation.
However, these diagnostics are likely only useful when comparing populations
of objects and not when establishing the formation pathway of individual
objects. Metal enrichment is not unique to planet formation, as a collapsing
metal-rich cloud can also produce low-mass objects.

Bowler et al. (2023) note that the orientation between the spin axis of the
star and the orbital plane of the companion shows promise as another marker of
formation, as star-like formation shows a wide range of orientations, whereas
planet-like formation prefers values near $90^{\circ}$. This is, however,
another marker that can distinguish between populations but cannot be used on
an individual object basis.

Schlaufman (2018) demonstrates that companions above $\sim 10M_{Jup}$ lack the
tendency to fall primarily around metal-rich hosts that companions below $\sim
4M_{Jup}$ exhibit, which is taken as evidence of core accretion in the lower-
mass set. Hoch et al. (2023) likewise find a tentative difference in the trend
of $C/O$ values at $\sim 4M_{Jup}$, which is taken as further evidence that
those objects are primarily formed via core accretion, although, as stated
above, $C/O$ ratios can be difficult to interpret. Similarly, Ribas & Miralda-
Escudé (2007) find differing radial velocity distributions above and below
$M\sin(i)$ values of $\sim 4M_{Jup}$. Schlaufman (2018) states that planet-
like formation appears to cease above $\sim 4M_{Jup}$, but not necessarily
that star-like formation ceases below $\sim 10M_{Jup}$. There might still be a
range in mass, below $\sim 4M_{Jup}$, where both processes contribute.

The methods addressed above require data that are so far lacking for most
exoplanets or can be used only in comparing populations. Instead, for this
paper, we propose a simple scheme whose purpose is merely to exclude objects
with a high likelihood of having been formed via a protoplanetary disk while
including all others as possible products of star formation. For our scheme,
we require at least three bodies in a system because the only parameters
available for two-body systems – mass ratio, separation, etc. – can lead to
ambiguities when trying to distinguish between formation scenarios.

As an example, Bowler et al. (2020) have used twenty-seven long-period
companions labeled as giant planets and brown dwarfs to search for differences
in parameters. They find that the population of brown dwarfs has an
eccentricity distribution peaking in the range $0.6<e<0.9$, whereas binaries
with mass ratios significantly different from one have an eccentricity
distribution peaking closer to $e\approx 0$. These results indicate that the
star formation process tends to create binaries with large eccentricity, and
the protoplanetary process tends to form binaries with near-zero eccentricity.
To reiterate a point from above, while such trends may be indicative of a
population of objects, eccentricity alone cannot be used on an object-by-
object basis to distinguish between formation scenarios. The same is true for
mass ratio, as doing so can bias our list of potential companions to only the
higher mass ones, which could impact our ability to determine star formation’s
low-mass cutoff. (Similarly, not selecting on mass ratio can bias our results
in the opposite direction, a point we address further in the next section.)

In triple (and higher-order) systems, however, we have other parameters
available. Specifically, we note that the hierarchy of empirically observed
triple star systems is such that the period of the outer component must be at
least five times that of the inner pair (Tokovinin 2004). This is in good
agreement with dynamical stability expectations for objects in circular
orbits, and the period of the outer component must be even larger than five
times the inner one when elliptical orbits are considered (Mardling & Aarseth
2001). Planets that have formed from a protoplanetary disk, on the other hand,
can often arrange themselves in stable orbital configurations (e.g., in
resonances with one another) that violate the above law. A multi-star system
that formed via a collapsing cloud could, presumably, arrange itself in a
similar manner if conditions were ideal, but such examples must be exceedingly
rare. Therefore, we will use the ratios of orbital periods to identify
"exoplanet" systems in the 20-pc census that most likely formed via a
protoplanetary disk, and we retain all others for consideration as possible
products of star formation.

To this end, Table 6.2.3 lists all of the host objects from Table 3.1 that
were labeled as having one or more confirmed exoplanets in the NASA Exoplanet
Archive as of 2022 Sep 01414141One additional complication, as stated in
Section 3.6.4, is that the NASA Exoplanet Archive uses a $30M_{Jup}$ dividing
line, not $13M_{Jup}$, to distinguish between brown dwarfs and exoplanets.
Hence, some of the brown dwarfs already listed in Table 3.1 will be double
counted; that is, they will have their own separate row in the table while
also being listed under the ”#Planets” column. Such objects are flagged in
Table 6.2.3.. For systems in which any pair of "exoplanets" violate the
$P_{outer}<5P_{inner}$, we indicate the innermost pair that violates the rule
and exclude all of the planets, thus including only the host star in later
analysis. For all others, we have used the NASA Exoplanet Archive to compile
their mass measurements. For objects identified only through radial velocity
monitoring, we list the $M\sin(i)$ values, since the inclination of the system
is not known. For other objects – transiting systems, radial velocity systems
with astrometric imaging, etc. – we list the actual measured masses.
Incorporating these objects in to the stellar mass function analysis will be
discussed further in Section 7.

Table 19: 20-pc Objects Hosting "Planets"

Name | Coords | # of | NoteaaIndicates whether the "exoplanets" in this system should be considered in our stellar mass function analysis. Notes regarding period violations indicate objects that are excluded, as these are likely objects formed via a protoplanetary disk. In these cases, we list at least one example of component pairs ("b" vs. "c", "c" vs. "d", etc.) that violate the rule. | $M\sin(i)$ | $M$ | Mass
---|---|---|---|---|---|---
| J2000 | Planets |  | ($M_{Jup}$) | ($M_{Jup}$) | Ref.
(1) | (2) | (3) | (4) | (5) | (6) | (7)
Sun | $\cdots$ | 8 | $P_{\rm Venus}<5P_{\rm Mercury}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 1237 A | 0016$-$7951 | 1 | consider | 3.37$\pm$0.09 | $\cdots$ | 1
GX And | 0018+4401 | 2bbThe "b" planet is currently considered controversial by the NASA Exoplanet Archive, so only the "c" planet is considered for inclusion in our mass function analysis. | consider | $0.11^{+0.08}_{-0.06}$ | $\cdots$ | 2
54 Psc AB | 0039+2115 | 1 | consider | 0.228$\pm$0.011 | $\cdots$ | 3
HD 3765 | 0040+4011 | 1 | consider | $0.173^{+0.014}_{-0.013}$ | $\cdots$ | 4
G 268-38 | 0044$-$1516 | 2 | consider | $\cdots$ | 0.0201$\pm$0.0014 | 5
$\cdots$ | $\cdots$ | - | consider | $\cdots$ | $0.00554^{+0.00053}_{-0.00050}$ | 5
BD+61 195 | 0102+6220 | 1 | consider | 0.0177$\pm$0.0021 | $\cdots$ | 6
YZ Cet | 0112$-$1659 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
CD$-$54 269 | 0114$-$5356 | 1 | consider | 0.026$\pm$0.005 | $\cdots$ | 7
HD 7924 | 0121+7642 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\upsilon$ And A | 0136+4124 | 3 | consider | 0.6876$\pm$0.0044 | $\cdots$ | 8
$\cdots$ | $\cdots$ | - | consider | 1.981$\pm$0.019 | $\cdots$ | 8
$\cdots$ | $\cdots$ | - | consider | 4.132$\pm$0.029 | $\cdots$ | 8
q01 Eri | 0142$-$5344 | 1 | consider | 0.94$\pm$0.08 | $\cdots$ | 9
$\tau$ Cet | 0144$-$1556 | 4 | $P_{h}<5P_{g}$ | $\cdots$ | $\cdots$ |  $\cdots$
TZ Ari | 0200+1303 | 2ccThis object was reported to have two exoplanets at the time of our original query to the NASA Exoplanet Archive, but it is now believed that the "b" component was a false positive. | consider | 0.21$\pm$0.02 | $\cdots$ | 10
HD 13445 A | 0210$-$5049 | 1 | consider | 4.42$\pm$0.20 | $\cdots$ | 11
BD+47 612 | 0222+4752 | 1 | consider | $0.0619^{+0.0076}_{-0.0072}$ | $\cdots$ | 12
$\iota$ Hor AB | 0242$-$5048 | 1ddThis exoplanet, aka HR 810b, has a period from radial velocity variations of 302.8$\pm$2.3d (Stassun et al. 2017) and is presumably the same object listed in Tabe 3.1 as $\iota$ Hor B, the companion giving rise to the 331.7d orbital period in the Gaia DR3 non-single star table. | already included | 2.27±0.25 | $\cdots$ | 11
Teegarden’s Star | 0253+1652 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
G 245-61 | 0257+7633 | 1 | consider | $\cdots$ | 0.00733$\pm$0.00063 | 13
BD$-$17 588 A | 0301$-$1635 | 2 | $P_{b}<5P_{c}$ | $\cdots$ | $\cdots$ |  $\cdots$
CD Cet | 0313+0446 | 1 | consider | $0.0124^{+0.0013}_{-0.0014}$ | $\cdots$ | 14
e Eri | 0319$-$4304 | 4 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 21749 | 0326$-$6329 | 2 | $P_{b}<5P_{c}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\epsilon$ Eri | 0332$-$0927 | 1 | consider | $\cdots$ | $0.66^{+0.12}_{-0.09}$ | 15
HD 22496 | 0335$-$4825 | 1 | consider | $0.0175^{+0.0023}_{-0.0021}$ | $\cdots$ | 16
L 372-58 | 0335$-$4430 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
L 229-91 | 0409$-$5322 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\omicron^{2}$ Eri A | 0415$-$0739 | 1 | consider | 0.0266$\pm$0.0015 | $\cdots$ | 17
$\epsilon$ Ret A | 0416$-$5918 | 1 | consider | 1.56$\pm$0.14 | $\cdots$ | 18
L 375-2 AB | 0432$-$3947 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 285968 | 0442+1857 | 1 | consider | 0.0285$\pm$0.0043 | $\cdots$ | 4
Wolf 1539 | 0452+0628 | 1 | consider | 0.82$\pm$0.07 | $\cdots$ | 19
L 736-30 | 0453$-$1746 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
LP 656-38 | 0501$-$0656 | 2 | consider | $0.00636^{+0.00082}_{-0.00079}$ | $\cdots$ | 20
$\cdots$ | $\cdots$ | - | consider | $0.0073^{+0.0016}_{-0.0015}$ | $\cdots$ | 20
UCAC4 211-005570 | 0505$-$4756 | 1eeThis transiting exoplanet, aka TOI-540 b, has no mass measurement. | consider | $\cdots$ | $\cdots$ |  $\cdots$
Kapteyn’s Star | 0511$-$4501 | 1 | consider | $0.022^{+0.004}_{-0.003}$ | $\cdots$ | 21
$\pi$ Men | 0537$-$8028 | 3 | consider | $0.0113^{+0.0015}_{-0.0014}$ | $\cdots$ | 22
$\cdots$ | $\cdots$ | - | consider | 0.0421$\pm$0.0043 | $\cdots$ | 23
$\cdots$ | $\cdots$ | - | consider | $\cdots$ | 12.2$\pm$1.3 | 22
$\beta$ Pic | 0547$-$5103 | 2 | excludeffThe inner and outer planets do not violate the $P_{outer}<5P_{inner}$ rule, but the imaging of this youthful system nonetheless shows the debris disk remaining from protoplanetary formation. | $\cdots$ | $\cdots$ |  $\cdots$
HD 40307 | 0554$-$6001 | 5 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
Gl 229 A | 0610$-$2151 | 2 | $P_{b}<5P_{c}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 260655 | 0637+1733 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 265866 | 0654+3316 | 1 | consider | 0.0126$\pm$0.0013 | $\cdots$ | 24
BD+05 1668 | 0727+0513 | 2 | $P_{b}<5P_{c}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\beta$ Gem | 0745+2801 | 1 | consider | 2.30$\pm$0.45 | $\cdots$ | 25
L 34-26 | 0749$-$7642 | 1ggThis "exoplanet" is the T dwarf WISEPA J075108.79$-$763449.6, already included as its own row in Table 3.1. | already included | $\cdots$ | $\cdots$ |  $\cdots$
CD$-$24 6144 | 0754$-$2518 | 2 | consider | 0.025$\pm$0.005 | $\cdots$ | 26
$\cdots$ | $\cdots$ | - | consider | 0.152$\pm$0.023 | $\cdots$ | 26
L 97-3 A | 0806$-$6618 | 1hhThis "exoplanet" is the Y dwarf L 97-3 B (sometimes referred to as WD 0806$-$661 B), already included as its own row in Table 3.1. | already included | $\cdots$ | $\cdots$ |  $\cdots$
L 98-59 | 0818$-$6818 | 4 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 69830 | 0818$-$1237 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
L 675-81 | 0840$-$2327 | 2 | consider | 1.753$\pm$0.058 | $\cdots$ | 26
$\cdots$ | $\cdots$ | - | consider | 1.644$\pm$0.060 | $\cdots$ | 26
G 234-45 | 0841+5929 | 2 | consider | $0.46^{+0.02}_{-0.01}$ | $\cdots$ | 27
$\cdots$ | $\cdots$ | - | consider | 0.20$\pm$0.01 | $\cdots$ | 27
$\rho^{1}$ Cnc A | 0852+2819 | 5 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 79211 | 0914+5241 | 1 | consider | 0.0334$\pm$0.0038 | $\cdots$ | 28
L 678-39 | 0936$-$2139 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
CD$-$45 5378 | 0944$-$4546 | 1 | consider | $\cdots$ | 0.00172$\pm$0.00025 | 29
HD 85512 | 0951$-$4330 | 1 | consider | 0.011$\pm$0.002 | $\cdots$ | 30
BD+63 869 | 0956+6247 | 1 | consider | 0.0721$\pm$0.0088 | $\cdots$ | 26
BD+48 1829 | 1002+4805 | 1 | consider | $0.0410^{+0.0064}_{-0.0063}$ | $\cdots$ | 31
HD 87883 | 1008+3414 | 1 | consider | $\cdots$ | $5.37^{+0.51}_{-0.59}$ | 22
L 320-124 | 1014$-$4709 | 2 | consider | $\cdots$ | 0.00522$\pm$0.00072 | 32
$\cdots$ | $\cdots$ | - | consider | 0.0083$\pm$0.0014 | $\cdots$ | 32
BD+01 2447 | 1028+0050 | 1 | consider | 0.00538$\pm$0.00076 | $\cdots$ | 33
47 UMa | 1059+4025 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
Lalande 21185 | 1103+3558 | 2 | consider | $0.00846^{+0.00060}_{-0.00057}$ | $\cdots$ | 34
$\cdots$ | $\cdots$ | - | consider | $0.0428^{+0.0076}_{-0.0072}$ | $\cdots$ | 34
BD$-$18 3106 | 1107$-$1917 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 97101 A | 1111+3026 | 2 | consider | $0.0239^{+0.0077}_{-0.0069}$ | $\cdots$ | 35
$\cdots$ | $\cdots$ | - | consider | $0.169^{+0.029}_{-0.027}$ | $\cdots$ | 35
HD 304043 | 1116$-$5732 | 1 | consider | 0.0348$\pm$0.0035 | $\cdots$ | 7
83 Leo B | 1126+0300 | 1 | consider | 0.070$\pm$0.050 | $\cdots$ | 11
CD$-$31 9113 | 1135$-$3232 | 3 | $P_{d}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
Ross 1003 | 1141+4245 | 2 | consider | $0.3043^{+0.0044}_{-0.0032}$ | $\cdots$ | 36
$\cdots$ | $\cdots$ | - | consider | $0.214^{+0.015}_{-0.007}$ | $\cdots$ | 36
Ross 905 | 1142+2642 | 1 | consider | $\cdots$ | 0.070$\pm$0.007 | 37
HD 102365 A | 1146$-$4030 | 1 | consider | 0.050$\pm$0.008 | $\cdots$ | 38
Ross 128 | 1147+0048 | 1 | consider | 0.00440$\pm$0.00066 | $\cdots$ | 39
HD 238090 | 1212+5429 | 1 | consider | $0.0217^{+0.0029}_{-0.0030}$ | $\cdots$ | 24
Wolf 433 | 1238+1141 | 1 | consider | 0.0415$\pm$0.0053 | $\cdots$ | 26
Wolf 437 | 1247+0945 | 1 | consider | $\cdots$ | $0.00887^{+0.00035}_{-0.00038}$ | 40
BD+13 2618 AB | 1300+1222 | 1iiThis "exoplanet" is the T dwarf ULAS J130041.74+122114.7, already included as its own row in Table 3.1. | already included | $\cdots$ | $\cdots$ |  $\cdots$
HD 113538 | 1304$-$5226 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
e Vir | 1316+0925 | 1jjThis "exoplanet" is the late-T/early-Y dwarf e Vir Ab, already included as its own row in Table 3.1. | already included | $\cdots$ | $\cdots$ |  $\cdots$
61 Vir | 1318$-$1818 | 3 | $P_{d}<5P_{c}$ | $\cdots$ | $\cdots$ |  $\cdots$
Ross 1020 | 1322+2428 | 1 | consider | 0.025$\pm$0.002 | $\cdots$ | 41
70 Vir | 1328+1346 | 1 | consider | 7.416$\pm$0.057 | $\cdots$ | 42
BD+11 2576 | 1329+1022 | 1 | consider | 0.016$\pm$0.003 | $\cdots$ | 43
$\tau$ Boo A | 1347+1727 | 1 | consider | 4.32$\pm$0.04 | $\cdots$ | 44
HD 122303 | 1401$-$0239 | 1 | consider | $0.0169^{+0.0022}_{-0.0020}$ | $\cdots$ | 45
Proxima Centauri | 1429$-$6240 | 1 | consider | 0.00337$\pm$0.00019 | $\cdots$ | 46
HD 128311 | 1436+0944 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
BD$-$07 4003 | 1519$-$0743 | 3 | $P_{b}<5P_{e}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\nu^{2}$ Lup | 1521$-$4819 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
Ross 508 | 1523+1727 | 1 | consider | 0.0126$\pm$0.0017 | $\cdots$ | 47
$\lambda$ Ser | 1546+0721 | 1 | consider | 0.0429$\pm$0.0046 | $\cdots$ | 4
G 180-18 | 1558+3524 | 2 | consider | $\cdots$ | 0.0055$\pm$0.0014 | 48
$\cdots$ | $\cdots$ | - | consider | 0.0180$\pm$0.0030 | $\cdots$ | 48
$\rho$ CrB | 1601+3318 | 2kkThis assumes that the exoplanet candidate $\rho$ CrB b is real. | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
GJ 3942 | 1609+5256 | 1 | consider | 0.0225$\pm$0.0019 | $\cdots$ | 49
14 Her | 1610+4349 | 2 | consider | $\cdots$ | $8.1^{+1.6}_{-1.0}$ | 22
$\cdots$ | $\cdots$ | - | consider | $\cdots$ | $5.0^{+0.9}_{-1.0}$ | 22
LP 804-27 | 1612$-$1852 | 1 | consider | 2.1 | $\cdots$ | 50
HD 147379 | 1616+6714 | 1 | consider | $0.0898^{+0.0047}_{-0.0046}$ | $\cdots$ | 12
HD 147513 | 1624$-$3911 | 1 | consider | 1.21 | $\cdots$ | 51
G 202-48 | 1625+5418 | 1 | consider | 0.0089$\pm$0.0016 | $\cdots$ | 52
BD$-$12 4523 | 1630$-$1239 | 3 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
BD+25 3173 | 1658+2544 | 1 | consider | 0.328$\pm$0.032 | $\cdots$ | 53
HD 154345 | 1702+4704 | 1 | consider | 0.82$\pm$0.07 | $\cdots$ | 11
HD 154088 | 1704$-$2834 | 1 | consider | 0.021$\pm$0.003 | $\cdots$ | 54
G 139-21 | 1715+0457 | 1 | consider | $\cdots$ | 0.0257$\pm$0.0014 | 55
BD+11 3149 | 1716+1103 | 2 | consider | 0.00777$\pm$0.00085 | $\cdots$ | 56
$\cdots$ | $\cdots$ | - | consider | $0.0197^{+0.0025}_{-0.0024}$ | $\cdots$ | 56
HD 156384 C | 1718$-$3459 | 5 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
CD$-$46 11540 | 1728$-$4653 | 1 | consider | 0.035 | $\cdots$ | 57
CD$-$51 10924 | 1730$-$5138 | 4 | consider | 0.0120$\pm$0.0010 | $\cdots$ | 22
$\cdots$ | $\cdots$ | - | consider | $0.0211^{+0.0022}_{-0.0020}$ | $\cdots$ | 22
$\cdots$ | $\cdots$ | - | consider | $\cdots$ | $5.78^{+0.48}_{-0.46}$ | 22
$\cdots$ | $\cdots$ | - | already includedllIn Table 3.1, we label the object causing the Gaia DR3 acceleration (from the non-single star list) as CD$-$51 10924 B. For the purposes of accounting, we will equate that object with this one, GJ 676 A c. | $\cdots$ | 13.43$\pm$1.1 | 22
G 226-66 | 1735+6140 | 1 | consider | $0.0283^{+0.0053}_{-0.0057}$ | $\cdots$ | 58
BD+68 946 | 1736+6820 | 2 | consider | 0.0541$\pm$0.0031 | $\cdots$ | 26
$\cdots$ | $\cdots$ | - | consider | 0.050$\pm$0.013 | $\cdots$ | 26
CD$-$44 11909 | 1737$-$4419 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
BD+18 3421 | 1737+1835 | 1 | consider | 0.0208$\pm$0.0014 | $\cdots$ | 59
$\mu$ Ara | 1744$-$5150 | 4 | $P_{b}<5P_{e}$ | $\cdots$ | $\cdots$ |  $\cdots$
BD+45 2743 A | 1835+4544 | 1 | consider | 0.0429$\pm$0.0025 | $\cdots$ | 60
HD 176029 | 1858+0554 | 1 | consider | $0.0093^{+0.0016}_{-0.0015}$ | $\cdots$ | 61
HD 177565 | 1906$-$3748 | 1 | consider | $0.048^{+0.020}_{-0.019}$ | $\cdots$ | 62
HD 180617 | 1916+0510 | 1 | consider | 0.0384$\pm$0.0033 | $\cdots$ | 59
HD 189733 | 2000+2242 | 1 | consider | $\cdots$ | 1.13$\pm$0.08 | 11
HD 190007 | 2002+0319 | 1 | consider | 0.0518$\pm$0.0052 | $\cdots$ | 59
HD 190360 | 2003+2953 | 2 | consider | 0.0600$\pm$0.0076 | $\cdots$ | 63
$\cdots$ | $\cdots$ | - | consider | $\cdots$ | 1.8$\pm$0.2 | 64
HD 189567 | 2005$-$6719 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 192263 | 2013$-$0052 | 1 | consider | 0.56$\pm$0.05 | $\cdots$ | 11
HD 192310 | 2015$-$2701 | 2 | consider | 0.0532$\pm$0.0028 | $\cdots$ | 30
$\cdots$ | $\cdots$ | - | consider | 0.076$\pm$0.016 | $\cdots$ | 30
AU Mic | 2045$-$3120 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
LSPM J2116+0234 | 2116+0234 | 1 | consider | $0.0418^{+0.0031}_{-0.0035}$ | $\cdots$ | 65
LSPM J2122+2255 | 2122+2255 | 1 | consider | 0.33$\pm$0.02 | $\cdots$ | 10
HD 204961 | 2133$-$4900 | 2mmThe "c" planet is currently considered controversial by the NASA Exoplanet Archive, so only the "b" planet is considered for inclusion in our mass function analysis. | consider | 0.68$\pm$0.09 | $\cdots$ | 66
HN Peg AB | 2144+1446 | 1nnThis "exoplanet" is the T dwarf HN Peg B, already included as its own row in Table 3.1. | already included | $\cdots$ | $\cdots$ |  $\cdots$
G 264-12 | 2146+6648 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\epsilon$ Ind A | 2203$-$5647 | 1 | consider | $\cdots$ | $3.25^{+0.39}_{-0.65}$ | 67
BD$-$05 5715 | 2209$-$0438 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
L 788-37 | 2213$-$1741 | 1 | consider | 0.023$\pm$0.002 | $\cdots$ | 41
HD 211970 | 2222$-$5433 | 1 | consider | 0.0409$\pm$0.0079 | $\cdots$ | 68
L 119-213 | 2241$-$6910 | 1 | considerooThis object has no mass determination. | $\cdots$ | $\cdots$ |  $\cdots$
HD 216520 | 2247+8341 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
BD$-$15 6290 AB | 2253$-$1415 | 4 | $P_{b}<5P_{c}$ | $\cdots$ | $\cdots$ |  $\cdots$
51 Peg | 2257+2046 | 1 | consider | 0.472$\pm$0.039 | $\cdots$ | 18
HD 217987 | 2305$-$3551 | 2 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
TRAPPIST-1 | 2306$-$0502 | 7 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
HD 219134 | 2313+5710 | 6 | $P_{c}<5P_{b}$ | $\cdots$ | $\cdots$ |  $\cdots$
$\gamma$ Cep AB | 2339+7737 | 1 | consider | 1.85$\pm$0.16 | $\cdots$ | 69

References. — References for the mass measurements: 1 = Naef et al. (2001), 2
= Pinamonti et al. (2018), 3 = Wittenmyer et al. (2019), 4 = Rosenthal et al.
(2021), 5 = Lillo-Box et al. (2020), 6 = Perger et al. (2019), 7 = Feng et al.
(2020), 8 = Curiel et al. (2011), 9 = Marmier et al. (2013), 10 = Quirrenbach
et al. (2022), 11 = Stassun et al. (2017), 12 = Hobson et al. (2018), 13 =
Soto et al. (2021), 14 = Bauer et al. (2020), 15 = Llop-Sayson et al. (2021),
16 = Lillo-Box et al. (2021), 17 = Ma et al. (2018), 18 = Butler et al.
(2006), 19 = Howard et al. (2010), 20 = Astudillo-Defru et al. (2017), 21 =
Anglada-Escude et al. (2014), 22 = Feng et al. (2022), 23 = Hatzes et al.
(2022), 24 = Stock et al. (2020), 25 = Hatzes et al. (2006), 26 = Feng et al.
(2020b), 27 = Lopez-Santiago et al. (2020), 28 = DiTomasso et al. (2023), 29 =
Lam et al. (2021), 30 = Pepe et al. (2011), 31 = Hobson et al. (2019), 32 =
Bonfils et al. (2018), 33 = Amado et al. (2021), 34 = Hurt et al. (2022), 35 =
Dedrick et al. (2021), 36 = Trifonov et al. (2018), 37 = Maciejewski et al.
(2014), 38 = Tinney et al. (2011), 39 = Bonfils et al. (2018b), 40 = Trifonov
et al. (2021), 41 = Luque et al. (2018), 42 = Luhn et al. (2019), 43 = Damasso
et al. (2022), 44 = Borsa et al. (2015), 45 = Suárez Mascareño et al. (2017),
46 = Faria et al. (2022), 47 = Harakawa et al. (2022), 48 = Beard et al.
(2022), 49 = Perger et al. (2017), 50 = Apps et al. (2010), 51 = Mayor et al.
(2004), 52 = Suárez Mascareño et al. (2017b), 53 = Johnson et al. (2010), 54 =
Unger et al. (2021), 55 = Cloutier et al. (2021), 56 = Affer et al. (2016), 57
= Bonfils et al. (2007), 58 = Pinamonti et al. (2019), 59 = Burt et al.
(2021), 60 = González-Álvarez et al. (2021), 61 = Toledo-Padrón et al. (2021),
62 = Feng et al. (2017), 63 = Wright et al. (2009), 64 = Feng et al. (2021),
65 = Lalitha et al. (2019), 66 = Wittenmyer et al. (2014), 67 = Feng et al.
(2019), 68 = Feng et al. (2019b), 69 = Endl et al. (2011).

###  6.3 Objects on the main sequence

Main sequence objects with directly measured masses can be used to calibrate
relations of mass vs. absolute magnitude or mass vs. spectral type. Studies
have shown that the relation with the smallest intrinsic scatter for K and M
dwarfs is the one using absolute $K$-band magnitude (Delfosse et al. 2000).
The fact that the $K$-band relation shows the least scatter across the optical
to near-infrared range is also predicted by model atmospheres, as this is the
wavelength regime where competing physical effects modulated by metallicity
variations largely cancel one another (Delfosse et al. 2000; Mann et al.
2019). More (and improved) dynamical mass measurements of binary stars424242In
reality, the total mass of the binary system was used, rather than the masses
of the individual components, the latter of which are not generally known. The
resulting relation is nonetheless applicable to individual objects, as
sections 7.3 and 7.4 of Mann et al. (2019) discuss in detail. See in
particular their figure 15, which shows a direct comparison between directly
measured individual masses and the resulting mass-$M_{Ks}$ relation. along
with improved Gaia parallaxes have enabled Mann et al. (2019) to construct a
mass vs. $M_{Ks}$ relation that results in estimated masses with only 2-3%
uncertainty. Specifically, $K_{s}$ is used because 2MASS provides all-sky
coverage at this band. We use the Mann et al. (2019) mass-$M_{Ks}$ relation
(their equation 2) over the range $5.0\leq M_{Ks}\leq 11.0$, roughly
corresponding to spectral types from early-M to late-M434343Their relation
covers the range from $M_{Ks}\approx 4.0$ mag down to a spectral type of
$\sim$L1. However, the bright end of the relation is poorly constrained, so
for these objects we defer to the TIC mass estimates (see the next paragraph).
At the faint end, we use the effective temperature analysis for objects cooler
than M9.5, as further described in Section 7.1.. These estimates and their
propagated uncertainties are listed in columns "EstMassMKs" and
"EstMassMKsErr" of Table 3.1.

For other main sequence stars, we can use the methodology employed by Stassun
et al. (2019). Using $\sim$20,000 (non-reddened) stars within 100 pc of the
Sun with spectroscopically determined effective temperatures, they established
a relation between $T_{\rm eff}$ and $G_{BP}-G_{RP}$ color. This is then mated
with the results of Torres et al. (2010) that relate $T_{\rm eff}$ to mass for
stars with dynamically measured masses (Stassun et al. 2018b). This gives mass
estimates with uncertainties of ${\sim}6.4\%$ (Stassun et al. 2019). We take
mass estimates and their uncertainties directly from the revised TESS Input
Catalog (TIC; Stassun et al. 2019) for stars in our Table 3.1. These values
are listed in columns "EstMassTIC" and "EstMassTICErr". We note, however, that
the Stassun et al. (2019) prescription for stars with $T_{\rm eff}\lesssim
4000$K (see their appendix A.1 along with Muirhead et al. 2018) followed a
different methodology. For these objects, masses were estimated using $K_{s}$
magnitudes, Gaia DR2 parallaxes, and the Mann et al. (2019) mass-vs.-$M_{Ks}$
relation.

Some main sequence stars lack both $K_{s}$ magnitudes and an entry in the TESS
Input Catalog. For these, we resort to two other estimation methods. The first
is the mass vs. $M_{G}$ relation. Chontos et al. (2021) took a list of well-
studied late-K and M dwarfs (tables 5-7 from Mann et al. 2015) and refined
their mass estimates using more precise Gaia DR3 parallaxes and the Mann et
al. (2019) mass-vs.-$M_{Ks}$ relation from above. They derived a relation
between this estimated mass and the absolute G-band magnitude. However, the
coefficients in Chontos et al. (2021) are published with insufficient accuracy
to re-create the relation show in their figure 7, so we have re-derived them
here. Our methodology is identical to theirs except that we exclude the sdM3
object L 750-42 (Gizis 1997) and do not incorporate a dependence on
metallicity because the metallicity has not been measured for most of the M
dwarfs within 20 pc. Using a functional form of

${\rm Mass}=\sum_{i=0}^{4}c_{i}(M_{G}-10.5)^{i},$ (18)

where $M_{G}$ is the G-band absolute magnitude in magnitudes and Mass is in
units of $M_{\odot}$, we find best-fit coefficients of $c_{0}=0.30548$,
$c_{1}=-0.10588$, $c_{2}=0.011471$, $c_{3}=0.0021352$, and
$c_{4}=-0.00041023$. Our fit is illustrated in Figure 12. The relation is
valid from $7.5\leq M_{G}\leq 15.0$ (spectral types from $\sim$K7 to
$\sim$M8). For uncertainty propagation, we adopt the Chontos et al. (2021)
practice of a 2.2% uncertainty added in quadrature to the $\sim$3% uncertainty
inherent to the Mann et al. (2019) relation. This mass-$M_{G}$ relation is
particularly useful for estimating masses of individual components of close
double systems that are currently resolved only by Gaia. In Table 3.1 we
provide columns labeled "EstMassMG" and "EstMassMGErr" listing mass estimates
for all objects for which these $M_{G}$-based estimates can be computed.

Figure 12: Absolute G-band magnitude plotted against estimated mass for 180
well studied late-K and M dwarfs from Mann et al. (2015). The solid blue line
shows our fitted relation from Equation 18. See text for details.

The second alternative estimation method is StarHorse (Anders et al. 2022),
which uses Gaia EDR3 data cross-matched to photometry from Pan-STARRS1,
SkyMapper, 2MASS, and AllWISE to estimate stellar parameters from stellar
isochrones (from PARSEC 1.2S; Marigo et al. 2017) providing the closest match.
When Anders et al. (2022) mass estimates are available, these are listed in
columns "EstMassSH" and "EstMassSHErr" of Table 3.1. These published mass
uncertainties can be anomalously low compared to the other estimates discussed
in this section because they pertain only to the internal model errors and do
not include the systematic component coming from a model-to-truth comparison.

Figure 13 shows the four estimation techniques compared to each other. The top
three panels show the intercomparisons between the TESS Input Catalog
estimates, the $M_{Ks}$ estimates, and the $M_{G}$ estimates. As these are all
based on the same underlying mass vs. $M_{Ks}$ relation of Mann et al. (2019),
the correspondence is generally excellent. (In fact, the correspondence
between the TESS Input Catalog estimates and estimates from our $M_{Ks}$
technique are nearly perfect, differing only in the Gaia data release from
which the parallax values were obtained.) The only deviation is for masses
greater than $\sim 0.65M_{\odot}$ in the comparison between the TESS Input
Catalog values and those derived from $M_{Ks}$, where the difference can be as
large as 13%.

The bottom three panels of Figure 13 show small systematics between the three
estimation techniques above and StarHorse. As stated above, masses from
StarHorse are based on theoretical models, so such systematics might be
expected between theory and observation. At masses of $\sim 0.3M_{\odot}$,
StarHorse tends to overpredict (by $\sim$10%) the mass relative to the other
techniques, and at smaller masses may significantly underpredict (by
$\sim$35%). At masses near $0.8M_{\odot}$, a small underprediction (by $<$5%)
relative to the TESS Input Catalog becomes an overprediction (by $\sim$5%)
relative to masses from the $M_{Ks}$ relation. At masses closer to
$1.0M_{\odot}$, StarHorse leads to underpredictions (by $\sim$10%) relative to
estimates from the TESS Input Catalog.

Given that systematic offsets of up to 15% are seen even between the sets with
empirical underpinnings, we are reluctant to apply corrections to offsets
smaller than this value. The only exception to this is the $\sim$35% offset
seen for StarHorse estimates below StarHorse values of $\sim 0.275M_{\odot}$.
In this case, rather than applying an offset, we will simply not use any
StarHorse estimates below $0.275M_{\odot}$.

Figure 13: Intercomparisons of results from our four mass estimation
techniques. The line of one-to-one correspondence is shown by the blue dashes.
See text for details.

##  7 Further Analysis

For each individual object ("#CompsOnThisRow" = 1) in Table 3.1, we have
adopted a mass and its uncertainty. These are listed in columns
"AdoptedInitialMass" and "AdoptedInitialMassErr" along with an additional
column, "AdoptedInitialMassNote", indicating the origin of the data from
elsewhere in the table. These are labeled with the term "Initial" as a
reminder that for white dwarfs, we need their initial masses on the main
sequence; for all other objects, their current masses are assumed identical to
their initial masses. The codes for "AdoptedInitialMassNote" are as follows,
listed in their order of selection:

  * •

wd IFMR, wd low, wd ultra-low, or wd conjecture: The initial mass and its
uncertainty have been computed via the initial-to-final mass relation or other
means (see Table 6.1.1), if this object is a white dwarf.

  * •

measured: Directly measured mass values from "Mass" and "MassErr" are used.
The methodology used and its reference are listed in columns "MassMethod" and
"MassRef". (For L, T, and Y dwarfs, directly measured masses are not retained
because these are estimated in bulk through statistical means; see the Teff
bullet, below.)

  * •

M_Ks: The mass and its uncertainty from the Mann et al. (2019) $M_{Ks}$
relation ("EstMassMKs" and "EstMassMKsErr") are used.

  * •

TIC: The mass and its uncertainty from the TESS Input Catalog (Stassun et al.
2019; "EstMassTIC" and "EstMassTICErr") are used.

  * •

M_G: The mass and its uncertainty from the $M_{G}$ relation of Equation 18
("EstMassMG" and "EstMassMGErr") are used.

  * •

SH: The mass and its uncertainty from StarHorse (Anders et al. 2022;
"EstMassSH" and "EstMassSHErr") are used, unless that estimate falls below
$0.275M_{\odot}$ (see section 6.3).

  * •

literature: The mass and its uncertainty are taken from columns "EstMassLit"
and "EstMassLitErr", the mass estimation method and reference for which are
listed in "EstMassLitMethod" and "EstMassLitRef". (Literature values can
supersede other values above if the object is listed as a giant or subgiant in
Table 6.1.2.)

  * •

see GeneralNotes: For objects with this code, the mass and its uncertainty
were computed by us, as detailed in the "GeneralNotes" column of the table.

  * •

Teff: For objects of type L, T, or Y, individual masses are not computed.
These are handled statistically via the distribution of $T_{\rm eff}$ values
and their uncertainties ("Teff" and "Teff_unc"), as described in detail below.

For cases in which literature values did not list a mass uncertainty, a value
of 10% is arbitrarily assumed. The quoted StarHorse uncertainty is also
replaced with a 10% uncertainty, based on the under- and over-predictions
noted when comparing StarHorse values to other estimates (see discussion at
end of Section 6.3), unless the quoted StarHorse internal uncertainty is
already larger, in which case we retain the published value.

For cases where only a miscellaneous magnitude or delta magnitude of a
companion were available, it is instructive to estimate a spectral type for
the object in order to estimate its mass. Figure 14 shows a comparison between
masses and measured spectral types for those Table 3.1 objects having mass
estimates (or direct measures) from one of the other methods. The piecewise
fit shown in the figure is the one we use to translate a dwarf spectral type
estimate into a mass estimate. Other per-object details can be found in the
General Notes column of Table 3.1.

Figure 14: Mass as a function of spectral type for 20-pc objects with measured
(black points) or estimated (grey points) masses and optical spectral types in
Table 3.1. The adopted initial mass (see text) is used for each object. For
objects with estimated (not measured) masses, a random value between $-$0.25
and +0.25 has been added to the spectral type to better visualize otherwise
overlapping data points. Our piecewise fit to the relation for dwarf stars is
shown by the solid red line and is quantified in Table 20. For comparison, we
show the average mass per spectral type as tabulated in the 2022.04.16 version
of https://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt
(Pecaut & Mamajek 2013; magenta dashed line). Table 20: Piecewise Fit to Mass
vs. Dwarf Spectral Type Relation

Spectral Type | Spectral Index | Mass ($M_{\odot}$)
---|---|---
(1) | (2) | (3)
A6 | 6.0 | 1.75
G0 | 20.0 | 1.06
K0 | 30.0 | 0.86
K3 | 33.0 | 0.71
M0 | 40.0 | 0.59
M3 | 43.0 | 0.39
M4 | 44.0 | 0.20
M5.5 | 45.5 | 0.11
L0 | 50.0 | 0.075

Note. — Each row in this table represents an inflection point in the red,
piecewise fit of Figure 14.

###  7.1 Analysis of brown dwarfs

We use the methodology adopted by Kirkpatrick et al. (2019, 2021a) and Raghu
et al. (submitted) to determine the mass function for L, T, and Y dwarfs, most
of which are brown dwarfs lacking any color (or spectral type or absolute
magnitude) to mass correlation. Specifically, the mass function for these
objects is determined by comparing the distribution of present-day
temperatures to predicted temperature distributions. Predictions are drawn
from a grid of models with varying mass functions, birthrates, and low-mass
cutoffs. For each point in the grid, we build a predicted mass/age
distribution that is then passed through a set of evolutionary models to
predict the current-day $T_{\rm eff}$ distribution. Using this grid of
predictions allows us to find the combination of mass function, birthrate, and
cutoff mass that best fits the observed temperature distribution.

For the empirical distribution, we estimate the $T_{\rm eff}$ value for each
L, T, or Y dwarf (see Table 16 in this paper and table 11 of Kirkpatrick et
al. 2021a) and then calculate space densities as a function of $T_{\rm eff}$.
To compute space densities, we need to determine the distances at which our
brown dwarf subsamples are truly complete, as the coldest Y dwarfs are so
intrinsically dim that we are unable to push their completeness to the 20-pc
limit targeted in this paper. As described in Kirkpatrick et al. (2021a), we
determine completeness via the $V/V_{max}$ test (Schmidt 1968) using 150K bins
and computing $\langle{V}/{V_{max}}\rangle$ at half-parsec steps within each
bin. The computation starts with the first half-parsec step falling just
larger than the distance of the bin’s nearest object and advances in distance
out to $d=20$ pc. These results are shown in Figure 15.

A comparison of this figure to figure 23 of Kirkpatrick et al. (2021a) shows
that, despite the many new discoveries (and many fewer retractions) noted in
Table 16, each 150K bin has the same completeness limit as before. As one
example, consider the bin with the largest change, 600-750K. In both
Kirkpatrick et al. (2021a) and here, this bin is complete out to 20 pc, but
the number of objects has nonetheless increased from eighty-three in
Kirkpatrick et al. (2021a) to ninety-eight in this paper; see also Table 21.
(The $V/V_{max}$ test is only as robust as the Poisson statistics allow, which
is why both sets of numbers were deemed to be complete.) As another example,
the number of objects interior to the completeness limit of 15.0 pc in the
450-600K bin has increased from fifty-three to fifty-six.

Figure 15: The average $V/V_{\rm max}$ value in 0.5-pc intervals across
fourteen 150-K bins encompassing L, T, and Y dwarfs. Blue dots show the
empirical sample, and red labels denote the number of objects at each 0.5-pc
computation. The black dashed line shows the $\langle{V}/{V_{max}}\rangle=0.5$
level indicative of a complete sample. The grey error bars show the
approximate 1$\sigma$ range that a sample of the size shown in red would
exhibit, given random statistics. The brown error bars, offset by +0.05 pc
from the grey error bars for clarity, show the 1$\sigma$ variation obtained by
simulations using 10,000 Monte Carlo realizations having the number of objects
and completeness limit listed in Table 21. See section 8.2 of Kirkpatrick et
al. (2021a) for more details.

As noted in Kirkpatrick et al. (2021a), the $V/V_{max}$ test does not check
for inhomogeneities in surface area, the most likely cause of which would be
confusion along the Galactic plane that hinders our ability to find nearby
brown dwarfs. Do the increased densities now reported in this paper indicate
that these corrections can be reduced or dropped altogether?

Figure 16 shows the positions in Galactic coordinates of all 583 L, T and Y
dwarfs in the 20-pc census. As was done in Kirkpatrick et al. (2021a), we
divide the sky into two zones: a zone along the Galactic plane
($|glat|<14{\fdg}48$) and another ($|glat|\geq 14{\fdg}48$) well outside of
the plane. This value of $|glat|$ was chosen so that the non-plane zone
contains exactly three times the area of the plane zone. If there is no
incompleteness along the Galactic plane, then the ratio of non-plane to plane
objects should be three. For the volume-complete portions of our 20-pc census,
we find that this ratio is $138/44=3.1$ for L dwarfs, $257/65=4.0$ for T
dwarfs, and $31/4=7.8$ for Y dwarfs, suggesting that the Galactic plane does
not introduce any significant incompleteness ($<1$%) for L dwarfs but does
still impede the discovery of fainter T and Y dwarfs. In contrast, Kirkpatrick
et al. (2021a) derived ratios of $137/34=4.0$, $234/34=6.9$, and $24/4=6.0$
for the L, T and Y dwarf samples, respectively.

Incompleteness along the Galactic plane has improved in the current 20-pc
census for the L and T dwarfs. For the Y dwarfs, the view is complicated by
smaller number statistics. Taking the non-plane numbers of Y dwarfs as truth,
then the number of plane Y dwarfs in the current sample should be
$31/3\pm(\sqrt{31})/3=10.3\pm 1.9$, which is $3.3\sigma$ different from the
value of 4 actually found. The same computation for the Kirkpatrick et al.
(2021a) numbers gives a number of plane Y dwarfs that was only $2.5\sigma$
different. Hence, the under-density of Y dwarfs in the plane is now
significantly worse, due to the fact that all new discoveries of Y dwarfs
within the volume have been found outside of the plane zone.

Figure 16: Plots of the 20-pc L, T, and Y dwarf census in Galactic coordinates. The four panels display (a) the sample in its entirety (black), (b) only the L dwarfs (blue), (c) only the T dwarfs (green), and (d) only the Y dwarfs (red). New additions to the sample since Kirkpatrick et al. (2021a) are plotted with grey haloes in panels (b) through (d).  Table 21: Space Densities for Early-L through Early-Y Dwarfs Teff | Complete- | Raw | Corr. | Adjusted | Adopted
---|---|---|---|---|---
Bin | ness Limit | No. of | FactoraaAs the $T_{\rm eff}$ bins from 1050 to 1350K encompass both L and T dwarfs (see figure 22b of Kirkpatrick et al. 2021a), we average the correction factor for L dwarfs (1.00) and T dwarfs (1.06). | No. of | Space DensitybbThis value is computed via the equations  $dens=\Bigl{(}raw\Bigr{)}\Bigl{(}corr\Bigr{)}\bigg{/}\Bigl{(}\frac{4}{3}{\pi}{d_{max}}^{3}\Bigr{)}$ and  $\sigma_{dens}=\sqrt{\bigl{(}{\sigma_{raw}}^{2}+{\sigma_{adj}}^{2}\bigr{)}}\Bigl{(}corr\Bigr{)}\bigg{/}\Bigl{(}\frac{4}{3}{\pi}{d_{max}}^{3}\Bigr{)}$ where $\sigma_{raw}=\sqrt{raw}$.
(K) | (pc) | Objects |  | Objects | ($\times$10-3 pc-3)
| $d_{max}$ | $raw$ | $corr$ | $adj$ | $dens$
(1) | (2) | (3) | (4) | (5) | (6)
2100-2250 | 20.0ccThis bin is complete only for its L dwarf complement. Since late-M dwarfs are also expected to populate this bin, the derived space density is considered to be a lower limit. | 12 | 1.00 | 13.3$\pm$2.8 |  $>$0.36
1950-2100 | 20.0 | 27 | 1.00 | 21.2$\pm$3.4 | 0.81$\pm$0.19
1800-1950 | 20.0 | 16 | 1.00 | 21.1$\pm$3.6 | 0.48$\pm$0.16
1650-1800 | 20.0 | 24 | 1.00 | 23.0$\pm$3.8 | 0.72$\pm$0.19
1500-1650 | 20.0 | 26 | 1.00 | 25.1$\pm$3.9 | 0.78$\pm$0.19
1350-1500 | 20.0 | 35 | 1.00 | 34.2$\pm$4.7 | 1.04$\pm$0.23
1200-1350 | 20.0 | 69 | 1.03 | 54.6$\pm$5.4 | 2.12$\pm$0.30
1050-1200 | 20.0 | 45 | 1.03 | 44.3$\pm$5.3 | 1.38$\pm$0.26
900-1050 | 20.0 | 50 | 1.06 | 43.5$\pm$5.0 | 1.58$\pm$0.27
750-900 | 20.0 | 63 | 1.06 | 54.9$\pm$5.6 | 1.99$\pm$0.31
600-750 | 20.0 | 98 | 1.06 | 77.6$\pm$6.3 | 3.10$\pm$0.37
450-600 | 15.0 | 56 | 1.06 | 44.8$\pm$4.9 | 4.20$\pm$0.67
300-450 | 11.0 | 15 | 1.15 | 17.2$\pm$3.0 |  $>$3.09ddThis temperature bin is not fully populated, as WISE sensitivity limits cannot probe to the quoted completeness distance for Y dwarfs below $T_{\rm eff}\approx 400$K.
150-300 |  $\cdots$ | 1 |  $\cdots$ |  $\cdots$ |  $\cdots$

L dwarfs no longer show an underdensity in the plane, so no correction is
needed for our derived L dwarf space densities. T dwarf space densities
should, however, be multiplied by 1.06 to account for the observed
incompleteness. The Y dwarf incompleteness is harder to assess given the small
number of Y dwarfs in the plane, but the raw numbers suggest a conservative
correction factor of 1.15, slightly larger than the 1.13 factor adopted by
Kirkpatrick et al. (2021a). These factors are listed in Table 21.

The final step in measuring the space densities of L, T, and Y dwarfs is
assessing their measurement uncertainties. For this we adopt the same
methodology used in Kirkpatrick et al. (2021a). To summarize, our confidence
in assigning an object to a $T_{\rm eff}$ bin is directly related to the
measurement uncertainty on $T_{\rm eff}$, which is often comparable to the bin
size itself. To estimate our confidence in the numbers of objects in each bin,
we have run simulations with 10,000 Monte Carlo realizations wherein we take
the uncertainty in $T_{\rm eff}$ and multiply it by a random value generated
from a normal distribution having a mean of 0 and a standard deviation of 1.
For each simulation, this uncertainty is added onto the measured value and the
object (re-)assigned to the appropriate $T_{\rm eff}$ bin. The computed means
and standard deviations across all 10,000 realizations are given in column 5
of Table 21. We use only these computed standard deviations in our adopted
space densities, but not the adjusted means. As further explained in
Kirkpatrick et al. (2021a), the reason for this is that the number of objects
is not preserved across the Monte Carlo simulations because some objects
scatter into the hotter, incomplete bin at 2100-2250K and are lost, while
objects at the other temperature extreme may be lost because they fall outside
the completeness limit of the colder bin. This last loss is one-sided,
however, as any colder objects scattering into the warmer bin would be
necessarily retained. Hence, we compute our adopted space densities using the
raw number counts, but including the uncertainties derived from our
simulations, as shown in the footnote of Table 21. These densities are
graphically illustrated in Figure 17.

Figure 17: Our measured L, T, and Y dwarf space densities from Table 21 (black
dots) as a function of effective temperature overplotted on different
simulations from Raghu et al. (submitted). In all panels, simulations assuming
a constant birthrate are shown, along with the results for three different
low-mass cutoffs: 10 $M_{Jup}$ (light blue), 5 $M_{Jup}$ (green), and 1
$M_{Jup}$ (red). Panels in the left column use the Saumon & Marley (2008)
evolutionary models, and panels in right column use Baraffe et al. (2003). The
top row shows simulations with a power law of $\alpha=0.8$, the middle row
shows $\alpha=0.6$, and the bottom row shows $\alpha=0.4$. The best overall
fits are those shown in the left panel in the middle row, using $\alpha=0.6$
and the Saumon & Marley (2008) models.

The measured space densities can now be compared to the simulated $T_{\rm
eff}$ distributions (Raghu et al., submitted) to infer the form of the mass
function at this low-mass end. Following on the results of Kirkpatrick et al.
(2021a), which showed the best match to be a power law, $dN/dM\propto
M^{-\alpha}$, with $\alpha\approx 0.6$, Raghu et al. (submitted) assume power-
law functional forms with $\alpha$ values between 0.3 and 0.8 and, like
Kirkpatrick et al. (2021a), choose low-mass cutoffs of $\sim$1, 5, and 10
$M_{Jup}$. Unlike Kirkpatrick et al. (2021a), however, they vary the birthrate
to include not only a constant birthrate over the lifetime of the Milky Way,
but also consider two other birthrates – called inside-out and late-burst –
from Johnson et al. (2021) that are constrained by new results from Gaia. The
inside-out birthrate represents a declining birthrate over the 10 Gyr lifetime
of the Galactic disk, and the late-burst birthrate is identical to the inside-
out form, except with an abrupt increase (by a factor of $\sim$3) in star
formation $\sim$3-5 Gyr ago.

Evolutionary models are used to infer the current $T_{\rm eff}$ value of each
simulated object (using its mass and age). Raghu et al. (submitted) expand the
model set used in Kirkpatrick et al. (2021a) by including the newer Marley et
al. (2021) predictions and show (again) that the only evolutionary models able
to fit the bump in the L/T transition in the $T_{\rm eff}$ distribution are
those of Saumon & Marley (2008).

It has been shown in Kirkpatrick et al. (2021a) and Raghu et al. (submitted)
that the low-mass cutoff has little effect on the shape of the mass function
at $T_{\rm eff}$ values above 450K, where our fitting is taking place.
Therefore, we consider each $\alpha$ \+ birthrate pair and compute the median
of the least squared values for the simulations across all three cutoff
masses. The minimum is achieved for $\alpha=0.6$ and a constant birthrate,
identical to the findings in Kirkpatrick et al. (2021a). The second best fit
is achieved for $\alpha=0.5$ and a constant birthrate. The third best fit is a
tie among the $\alpha=0.7$ \+ constant, the $\alpha=0.4$ \+ late-burst, and
$\alpha=0.5$ \+ late-burst models. Use of either the late-burst or inside-out
birthrates results in a slightly reduced $\alpha$ because those birthrates
create a small overabundance, relative to the constant birthrate models, of
older brown dwarfs that have already cooled to cooler temperatures.

In Figure 17, we show the fits for three values of $\alpha$ (0.4, 0.6, and
0.8) all paired with a constant birthrate. The panels in the left column of
the figure show that the $\alpha=0.6$ model with a constant birthrate and
using the Saumon & Marley (2008) evolutionary models is an excellent
representation of the empirical data. Can any new conclusions be gleaned
regarding the low-mass cutoff? As figure 4 of Raghu et al. (submitted)
illustrates, the Saumon & Marley (2008) models are incomplete below masses of
$\sim$0.015$M_{\odot}$ ($\sim$16$M_{Jup}$), so they are a poor choice for
determining what the low-mass cutoff might be. Instead, we revert back to the
Baraffe et al. (2003) models, that are complete down to $\sim$5$M_{Jup}$. As
the rightmost panels in Figure 17 illustrate, our ability to distinguish
between low-mass cutoffs depends on measuring accurate space densities below
450K. Using the 20-pc census to say confidently that star formation’s terminus
is below 10$M_{Jup}$ or even 5$M_{Jup}$ depends on surveying the sky more
deeply at the wavelengths of these objects’ peak emission and obtaining the
necessary astrometry to measure accurate distances. As the simulations using
the Baraffe et al. (2003) models show, measuring an accurate space density for
the 300-450K bin will allow us to distinguish between the cutoff masses, and
even a few more objects discovered in the 150-300K bin, which currently has
only the 250K Y dwarf WISE J085510.83$-$071442.5 in it, will provide even
tighter constraints.

Have some of these ultra-low mass products of star formation already been
identified, and are they masquerading in the literature as exoplanet
discoveries to higher mass objects? We use our analysis in Table 6.2.3 to see
first if the omission of these objects has biased our derivation of the brown
dwarf mass function above. With the exception of the two objects (the
companions to UCAC4 211-005570 and L 119-213) lacking mass estimates, we take
all objects labeled as "consider" in column 4 of Table 6.2.3 and estimated
their contribution to the overall mass function. For objects with $M\sin(i)$
measurements only, we pull a random number from a distribution of values
uniformly distributed between 0 and 1 and multiply that number by 90 degrees
to assign each an inclination, which we then use to assign an actual mass
value. For all masses, whether or not they are true masses or adjusted
$M\sin(i)$ measurements, we then pull a random number from a normal
distribution with a mean of 0 and standard deviation of 1 and multiply that
number by the uncertainty, which we then add back to the mass value. We
perform this methodology over 10,000 Monte Carlo iterations and find the mean
and standard deviation of the resulting space density, binned over
0.001-$M_{\odot}$ mass intervals, as illustrated in Figure 18.

Figure 18: Plots of the implied space densities of brown dwarfs (brown) in
0.001$M_{\odot}$ bins compared to the measured space densities of other
possible low-mass star formation products from Table 6.2.3 (blue). The brown
dwarf space densities are divided into three mass zones – $M>10M_{Jup}$ (solid
brown), $5M_{Jup}<M<10M_{Jup}$ (dashed brown), and $1M_{Jup}<M<5M_{Jup}$
(dotted brown). Note that the densities of the possible pseudo-exoplanets do
not affect our measurement of the brown dwarf space densities, as their
numbers only become appreciable at masses well below $5M_{Jup}$.

This figure shows that our derived space density of brown dwarfs, (which we
find to be $\xi(M)=dN/dM=0.0469\times M^{-0.6}$ in units of #
$pc^{-3}[1M_{\odot}]^{-1}$, with $M$ in units of $M_{\odot}$; see Section 8),
overwhelms the space density above $5M_{Jup}$ where our fitting took place.
So, the omission of these objects has no impact on our derivation. However,
the second question is whether any of these objects could be products of star
formation itself rather than the secondary by-products of a proto-planetary
disk. That question cannot be answered from this diagram, but it is a
statistical certainty that at least a few of the objects on the high-mass tail
of this distribution are star formation products. One striking result from
Figure 18, however, is the high space density of objects in the lowest mass
bin, given that the census of such low-mass objects, whether resulting from
star formation or proto-planetary disks, is still woefully incomplete. There
is clearly no shortage of ultra-low mass objects in the Milky Way.

###  7.2 Combined stellar and brown dwarf space densities

With the brown dwarf portion of the mass function now fitted, we can combine
the stellar and brown dwarf portions to determine the shape of the overall
mass function.

First we take the number counts across the stellar regime and perform a
similar Monte Carlo analysis as was done on the brown dwarfs. Specifically,
for each object we pull a random number from a normal distribution with a mean
of 0 and a standard deviation of 1. We then multiply the mass measurement
uncertainty by the random number and add that back to the mass value to get a
true mass. We do this for each of the stars in our sample, and repeat the
process 10,000 times to simulate 10,000 possible histograms. We then compute
the mean value in each histogram bin along with its standard deviation.
Because the 20-pc volume around the Sun is just one of many such volumes that
can be taken as a sample of the Milky Way, we add the Poisson uncertainty and
the standard deviation from above in quadrature to provide the final
uncertainty per bin. (This parallels the brown dwarf space density analysis of
Table 21.)

We can now append the substellar contribution onto this stellar distribution.
To do this, we look at the predictions from the best fit Raghu et al.
(submitted) model to the brown dwarf $T_{\rm eff}$ distribution from above,
which is the $\alpha=0.6$ power law with a constant birthrate function and
passed through the Saumon & Marley (2008) evolutionary models. We also choose
a 0.005$M_{\odot}$ ($\sim 5M_{Jup}$) cutoff to parallel the more detailed
cutoff analysis from Kirkpatrick et al. (2021a). This simulation gives the
predicted mass distributions shown in Figure 19. Each histogram is scaled so
that the total number of objects in each histogram matches the raw numbers of
objects per bin listed in Table 21. As one example, the 27 objects in the
1950-2100K bin are predicted to fall almost exclusively in the 0.075-0.080
$M_{\odot}$ bin, and these predictions suggest that our 27 objects be
apportioned as 20.5 objects in the 0.075-0.080 $M_{\odot}$ bin, 2.0 objects in
the 0.070-0.075 $M_{\odot}$ bin, 1.0 object in the 0.065-0.070 $M_{\odot}$
bin, and fractional numbers of objects in bins of lower mass. As another
example, the 63 objects in the 750-900K bin are spread over a wide range of
masses from 0.005-0.060$M_{\odot}$ and are apportioned as 2.6 objects in the
0.055-0.060$M_{\odot}$ bin, 10.8 objects in the 0.050-0.055$M_{\odot}$ bin,
12.3 objects in the 0.045-0.050$M_{\odot}$ bin, 10.7 objects in the
0.040-0.045$M_{\odot}$ bin, 8.3 objects in the 0.035-0.040$M_{\odot}$ bin,
etc.

Figure 19: The predicted distributions of brown dwarf masses in each of our
150K effective temperature bins based on the best-fit Raghu et al. (submitted)
simulation to our measured L, T, and Y dwarf space densities (see text for
details). Each histogram is scaled to match the total number of objects listed
for that $T_{\rm eff}$ bin in Table 21.

We take the apportionment across all thirteen temperature bins and tally the
results in each of the 0.005$M_{\odot}$-wide mass bins, after also applying
the factor (corr in Table 21) to correct for losses of objects along the
Galactic plane and extrapolating the numbers to the full 20-pc volume if that
temperature bin was not complete to 20 pc. For example, the raw number counts
in the 450-600K bin shown in both Table 21 and Figure 19 were multiplied by
the 1.06 correction factor then multiplied by $(20/15)^{3}$ to extrapolate to
the full volume. In Table 21, we find that our lowest temperature bin with a
space density measurement, 300-450K, is considered to be incomplete, and the
mass distribution for that bin in Figure 19 suggests that that bin’s objects
fall exclusively below 0.025$M_{\odot}$. Therefore we consider any space
density measurements below this mass value to be lower limits only.

Figure 20: The 20-pc initial mass function across all stellar and substellar
masses. Our measured values and their uncertainties are shown in black. The
raw number counts for stars of type M9.5 and earlier are shown by the blue
histogram. (a) The full mass range, 0.0-8.0$M_{\odot}$, with 0.1$M_{\odot}$
binning; (b) A zoom-in of the high-mass end, from 1.5 to 8.0 $M_{\odot}$, with
the same binning; (c) A zoom-in of the mid-range, from 0.4 to 1.5 $M_{\odot}$,
with 0.02$M_{\odot}$ binning. (d) A zoom-in of the low-mass portion,
0.0-0.4$M_{\odot}$, with 0.005$M_{\odot}$ binning. Our fit to the mass
function is shown by the orange line.

We now add these brown dwarf masses to the results of our Monte Carlo analysis
of stellar masses above to produce a mass function across the entire mass
range. This initial mass function is illustrated in Figure 20. Panel (a) shows
the mass function across the full mass range from 0 to 8 $M_{\odot}$, binned
in 0.1$M_{\odot}$ increments. The mass function rises with decreasing mass,
and it continues to rise beyond our 0.025$M_{\odot}$ ($\sim 26M_{Jup}$)
completeness limit. Subsequent panels show details. Panel (b) shows the high-
mass end of the initial mass function from 1.5 to 8.0 $M_{\odot}$, again with
0.1$M_{\odot}$ binning. The statistics above 3$M_{\odot}$ are poor but
nonetheless show a steady increase from there down to 1.5$M_{\odot}$. Panel
(c) shows the mid-mass range ($0.4<M<1.5M_{\odot}$), now binned into smaller
0.02$M_{\odot}$ increments because the statistics here are richer. Panel (d)
zooms in on the smallest mass portion, below 0.4$M_{\odot}$, and chooses yet a
smaller mass binning of 0.005$M_{\odot}$. With the exception of a few small
features (discussed below), the mass function is seen to rise monotonically
from 1.5 to 0.025$M_{\odot}$. Mostly within the measurement errors (see more
discussion below), the initial mass function is seen to continue rising well
below our 0.025$M_{\odot}$ completeness limit and at least down to
0.015$M_{\odot}$.

The numbers on which Figure 20 is based are given in Table 22. For ease of
reference, both the number of stars and the space density is given for each
mass bin. Three mass binnings are tabulated, roughly paralleling what is shown
in Figure 20: 0.1$M_{\odot}$ binning across the entire 0.0-8.0$M_{\odot}$
range (80 bins), 0.02$M_{\odot}$ binning across the range 0.0-1.6$M_{\odot}$
(80 bins), and 0.005$M_{\odot}$ binning across the range 0.0-0.4$M_{\odot}$
(80 bins). Mass bins with incomplete statistics are labeled as lower limits in
the final column of the table.

Table 22: Number of Objects and Space Densities per Mass Bin for the 20-pc
Census

Mass Bin | Total # | Space DensityaaThe [$M$ bin]-1 portion of the units should be replaced with the bin size for that row. For example, for the first row of the table, the units will be pc-3 [$0.10M_{\odot}$]-1 because that bin is $0.10M_{\odot}$ wide. | Lower Limit?
---|---|---|---
($M_{\odot}$) |  | (pc-3 [$M$ bin]-1) |
(1) | (2) | (3) | (4)
0.00-0.10 | 924.9$\pm$30.4 | 0.0276005$\pm$0.0009072 | yes
0.10-0.20 | 761.0$\pm$28.9 | 0.0227094$\pm$0.0008624 |
0.20-0.30 | 511.6$\pm$24.2 | 0.0152669$\pm$0.0007222 |
0.30-0.40 | 351.7$\pm$20.5 | 0.0104953$\pm$0.0006118 |
0.40-0.50 | 265.6$\pm$18.2 | 0.0079259$\pm$0.0005431 |
0.50-0.60 | 214.3$\pm$16.8 | 0.0063950$\pm$0.0005013 |
0.60-0.70 | 127.0$\pm$14.1 | 0.0037899$\pm$0.0004208 |
0.70-0.80 | 94.5$\pm$12.6 | 0.0028200$\pm$0.0003760 |

Note. — (This table is available in its entirety in machine-readable form.)

There are a few features in Figure 20(c) and (d) that warrant special
attention. The first is the bump in the object counts near 0.55$M_{\odot}$ in
panel (c). This falls near the point at which our mass estimation switches
from that of the TIC relations of Stassun et al. (2019) at higher masses to
that of the $M_{Ks}$ relation of Mann et al. (2019) at lower masses.
Currently, we switch between these two relations at $M_{Ks}=5.0$ mag,
corresponding to a mass of $\sim 0.6M_{\odot}$. As a test, if we change the
switchover point to be at $M_{Ks}=4.0$ mag ($M\approx 0.7M_{\odot}$) instead,
we find that this bump in the space densities moves to higher masses, with a
deficit around $0.8M_{\odot}$, as shown in Figure 21. We also note that the
uncertainties in the masses resulting from the Mann et al. (2019) relation are
three to four times smaller than those derived from the Stassun et al. (2019)
relation. As another test, we can artificially inflate the mass uncertainties
on the Mann et al. (2019)-derived masses while keeping the current switchover
point at $M_{Ks}=5.0$ mag. That result is also shown in Figure 21. In this
case, the bump is greatly diminished in the number counts, but an inflection
point is still seen near 0.6$M_{\odot}$. Given that this feature in the number
counts moves in response to the mass estimation used, we believe it is an
artificial effect. Furthermore, given that the Stassun et al. (2019) mass
estimation relies on dynamically measured individual masses whereas the Mann
et al. (2019) relation uses Bayesian statistics to ferret out individual
masses from binaries in which only the total system mass is measured, this
likely indicates a small systematic offset that slightly deflates the Mann et
al. (2019)-derived masses relative to truth. In fact, an effect in this
direction and representing a systematic offset of $\sim 2\%$ is seen when
comparing results of the $M_{Ks}$ relation to individually derived masses
(figure 15 of Mann et al. 2019). Obtaining more directly measured individual
masses in this regime, corresponding to late-K and early-M dwarfs, would help
to put this issue to rest.

Figure 21: Tests of the bump in the initial mass function seen near
0.55$M_{\odot}$ in Figure 20. (a) A zoom-in showing the bump in Figure 20(c).
(b) The number counts over the same mass range but where we have moved the
switchover in the mass estimate from $M_{Ks}=5.0$ mag to $M_{Ks}=4.0$ mag. (c)
The number counts over the same mass range but where we have kept the
$M_{Ks}=5.0$ mag switchover point and inflated the uncertainties on the
$M_{Ks}$-derived masses by a factor of four. For other details, see the
caption to Figure 20.

Other features are seen in Figure 20(d). There is a small drop in the number
counts near 0.13$M_{\odot}$ followed by a sudden rise near 0.11$M_{\odot}$.
This feature is likely artificial, as the bump at 0.11$M_{\odot}$ is due
primarily to components in multiple systems about which little information is
known, and these were arbitrarily assigned masses of 0.11$M_{\odot}$ based on
an anticipated spectral type of M5.5. This type lies at a very sharp
inflection point (see Table 20) in our mass vs. spectral type relation (Figure
14).

The other feature is the rapidly changing number count between masses of 0.06
and 0.08 $M_{\odot}$, a mass range that straddles the stellar/substellar
break. Some of the early- to mid-L dwarfs that we have included in our brown
dwarf mass function analysis are likely very low-mass stars and not brown
dwarfs themselves. As a consequence, these are assigned masses that are a bit
too high (the extraneous high point in the 0.075-0.080$M_{\odot}$ bin), which
likely leads to concomitant deficits in the next higher mass bins. In fact,
Table 3.1 lists three early-L dwarfs in the 20-pc census that have dynamical
mass measurements, and one of these (LP 388-55 B; Dupuy & Liu 2017) has a mass
just above the 0.075-0.080$M_{\odot}$ mass bin (0.083$\pm$0.03 $M_{\odot}$).

##  8 Discussion

How do our 20-pc results compare to other attempts in the literature to
measure the initial mass function? Pioneering work by Salpeter (1955) found
that a power law form $\xi(M)=dN/dM\propto M^{-\alpha}$ with $\alpha=2.35$
best fit the initial mass function over the range $0.3\leq M\leq 10M\odot$.
Subsequent work by Miller & Scalo (1979) found $\alpha=1.4$ for $0.1\leq M\leq
1M_{\odot}$ and $\alpha=2.5$ for $1\leq M\leq 10M_{\odot}$. Scalo (1986)
determined $\alpha=2.7$ for $2\leq M\leq 10M_{\odot}$, and Reid et al. (2002)
found $\alpha=1.3$ for $0.1\leq M\leq 0.7M_{\odot}$.

As more accurate measurements of the initial mass function became possible,
researchers realized the importance of distinguishing whether the masses used
for the computation were that of the stellar system or of its individual
components. For example, in an analysis of data from the Sloan Digital Sky
Survey, Bochanski et al. (2010) found $\alpha=2.38$ for $0.32<M<0.80M_{\odot}$
and $\alpha=0.35$ for $0.10<M<0.32M_{\odot}$ for the mass function of systems
but $\alpha=2.66$ and $\alpha=0.98$ for the mass function of single stars over
the same two mass regimes, respectively. Earlier, Kroupa (2001) had found that
single-star initial mass functions resulting from the analysis of young star
clusters generally gave values of $\alpha$ that were higher by $\sim$0.5 (for
$0.1<M<1.0M_{\odot}$) than the field initial mass function, for which systems
were not resolved. Reid (2005) cautions that unresolved multiplicity
complicates interpretation of the initial mass function; the initial mass
function of systems is more directly tied to the fragmentation of the original
molecular cloud, but the initial mass function of individual objects give the
mass distribution of the (sub)stellar bodies formed.

Our work on the 20-pc census has concentrated on analysis of the individual
products of star formation, as we are curious to know how frequently this
process produces, for example, very low-mass brown dwarfs compared to higher-
mass objects. We will therefore restrict subsequent analysis here to the
single-object initial mass function and leave analysis of the 20-pc census
regarding multiplicity and the system mass function to those investigating how
the formation of systems relates back to cloud fragmentation.

###  8.1 Comparison of Initial Mass Functions

Here we compare two very well established forms of the initial mass function
and compare their predictions to our results based on the 20-pc census.

Chabrier (2001, 2003a, 2003b) developed several functional forms for the
initial mass function. The latest one relating to single objects is given by
Chabrier (2003b) and is comprised of a power law at high masses and a log-
normal form at lower masses:

$\begin{split}\xi(M)&=\frac{C_{1}}{\ln{10}}M^{-\alpha},\>\textrm{for}\;M>1.0M_{\odot}\\\
&=\frac{C_{2}}{M\ln{10}}e^{\frac{-(\log{M}-\log{M_{c}})^{2}}{2\sigma^{2}}},\>\textrm{for}\;M\leq
1.0M_{\odot}\end{split}$ (19)

where $C_{1}=0.0443$, $\alpha=2.3$, $C_{2}=0.158$, $M_{c}=0.079M_{\odot}$, and
$\sigma=0.69M_{\odot}$. The value of $\xi(M)$ is in units of # of objects per
pc3 per $M_{\odot}$. See equation 2 and table 1 of Chabrier (2003b) for the
derivation shown above. We note that the values of $C_{1}$ and $C_{2}$ are set
by Chabrier (2003b) to match an empirical space density measurement (at
1$M_{\odot}$ from Scalo 1986) of the initial mass function in the Milky Way’s
disk population.

Likewise, Kroupa et al. (2013) found that a tripartite power-law form best
describes the single-object initial mass function:

$\begin{split}\xi(M)&=C\left({\frac{0.5}{0.07}}\right)^{-\alpha_{2}}\left({\frac{M}{0.5}}\right)^{-\alpha_{1}},\>\textrm{for}\;0.5<M<150M_{\odot}\\\
&=C\left(\frac{M}{0.07}\right)^{-\alpha_{2}},\>\textrm{for}\;0.07<M<0.5M_{\odot}\\\
&=\frac{C}{3}\left(\frac{M}{0.07}\right)^{-\alpha_{3}},\>\textrm{for}\;0.01<M<0.15M_{\odot}\\\
\end{split}$ (20)

where $\alpha_{1}=2.3$, $\alpha_{2}=1.3$, and $\alpha_{3}=0.3$. As above, the
value of $\xi(M)$ is in units of # of objects per pc3 per $M_{\odot}$. Note
that there are two components of this mass function that contribute to the
mass range $0.15<M<0.07M_{\odot}$. The value of $C$ is not specified by Kroupa
et al. (2013). However, figure 4-24 of Kroupa et al. (2013) provides a
comparison of this initial mass function with the Chabrier (2003b) version in
Equation 19, showing that they are identical at $\sim$0.85$M_{\odot}$,
resulting in a value of $C\approx 1.15$.

As shown in Figure 22, neither of these parameterizations adequately describes
the 20-pc initial mass function derived here. The main reason for this is that
prior determinations were done pre-WISE, pre-Spitzer, and pre-Gaia before the
L, T, and Y dwarf complement of the mass function was fully characterized and
before exquisite parallax determinations became available for almost all
objects in the 20-pc volume. As such, these prior works relied on poorer
statistics with fits done in logarithmic scaling on both the $dN$ and $dM$
axes. Our careful accounting of objects within the 20-pc volume now allows for
a more precise determination of the single-object initial mass function.

We thus provide a new multi-part power law parameterization that is bounded by
the following caveats: (1) We assume $\alpha=2.3$ at the high mass end, as has
been determined from earlier studies, and we do this because our 20-pc census
has few stars with $M>2M\odot$ to better constrain this. (2) We assume
$\alpha=1.3$ at intermediate masses, as this has also been established by
earlier studies. (3) We take $\alpha=0.6$ in the brown dwarf regime, as was
determined in Section 7.1. We do not constrain the stitch points in mass
between the power law pieces nor do we limit the number of power law pieces to
only three. We perform these fits by eye, keeping in mind the caveats from
Section 7.2 concerning the non-physical bumps and troughs in the number counts
as a function of mass. Given the constraints above, we find that a three-piece
power law does not adequately describe the number counts in the mid- to late-M
dwarf regime ($0.08\lesssim M\lesssim 0.20M_{\odot}$), but that a four-piece
power law can. This best fit is given below and illustrated by the orange line
in Figure 20:

$\begin{split}\xi(M)&=C_{1}(M)^{-\alpha_{1}},\>\textrm{for}\;0.55<M<8.0M_{\odot}\\\
&=C_{2}(M)^{-\alpha_{2}},\>\textrm{for}\;0.22<M<0.55M_{\odot}\\\
&=C_{3}(M)^{-\alpha_{3}},\>\textrm{for}\;0.05<M<0.22M_{\odot}\\\
&=C_{4}(M)^{-\alpha_{4}},\>\textrm{for}\;0.01<M<0.05M_{\odot}\\\ \end{split}$
(21)

where $C_{1}=0.0150$, $\alpha_{1}=2.3$, $C_{2}=0.0273$, $\alpha_{2}=1.3$,
$C_{3}=0.134$, $\alpha_{3}=0.25$, $C_{4}=0.0469$, $\alpha_{4}=0.6$, As above,
the value of $\xi(M)$ is in units of # of objects per pc3 per $M_{\odot}$.

If we integrate under our best fit from 0.075 to 8.0 $M_{\odot}$, we find 3002
stars, which can be compared to the 3000 individual objects in the 20-pc
census that have (measured or implied) types of M9.5 or earlier. The
integration under our fit for 0.020 to 0.075 $M_{\odot}$ gives 789 brown
dwarfs, compared to the 582 individual L, T, and Y dwarfs in Table 3.1. Most
of the missing $\sim 200$ brown dwarfs are ones with $T_{\rm eff}$ values
450-600K and distances of 15-20 pc or ones with 300-450K temperatures and
11-20 pc distances, where our current accounting is known to be incomplete
(see Table 21). These results show that the number of stars relative to brown
dwarfs is 3002/789, or $\sim$4\. However, we believe that the brown dwarf mass
function extends to at least 0.010 $M_{\odot}$, which would give a ratio of
3002/986 ($\sim$3) if the $\alpha=0.6$ functional form continues to that mass.
In the limiting case in which it continues to zero mass, we find a star-to-
brown-dwarf ratio of 3002/1602, or $\sim 2$. We note that as recently as a
decade ago, this ratio in the Solar neighborhood was believed to be as high as
6:1 (Kirkpatrick et al. 2012).

This decrease in the ratio of stars to brown dwarfs is not in tension with
microlensing results, as analysis of OGLE data found that an even steeper
power law in the brown dwarf regime ($\alpha=0.8$ for $0.01<M<0.08M_{\odot}$;
Mróz et al. 2017) best fits the observed distribution of short-timescale (low-
mass) events. Furthermore, the possibility that the mass function extends into
a regime significantly below 0.010 $M_{\odot}$ is bolstered by recent JWST
observations of the Orion Nebula Complex that show a significant population of
objects, down to at least 0.001$M_{\odot}$, that are apparently direct
products of star formation (McCaughrean & Pearson 2023; Pearson & McCaughrean
2023).

Figure 22: A comparison of our 20-pc number counts (black points with error
bars) and our fit of the initial mass function (solid orange line) to the
functional forms of Kroupa et al. (2013) (dotted blue line) and Chabrier
(2003b) (dashed green line). Each panel shows a zoom-in of a different mass
segment: (a) $1.5<M<8.0M_{\odot}$, (b) $0.4<M<1.5M_{\odot}$, (c)
$0.0<M<0.4M_{\odot}$.

Finally, we note that our accounting of the mass of hydrogen-burning stars in
the 20-pc census along with our best fit to the mass function of brown dwarfs
allows us to calculate the average mass of an object in this sample.
Integrating our mass function down to a mass of 0.020 $M_{\odot}$, we find
that value to be 0.41 $M_{\odot}$. There are likely many undiscovered brown
dwarfs in the solar neighborhood too faint to be currently detected, so this
average value could be pushed lower. Assuming there is no low-mass cutoff of
star formation and the brown dwarf mass function continues to zero mass with a
power law slope of $\alpha=0.6$, we find that the average mass of objects in
the 20-pc census would drop to 0.34 $M_{\odot}$. This can be considered as the
limiting case unless the functional form at the lowest masses has an $\alpha$
value considerably greater than 0.6.

##  9 Conclusions

In this paper our aim was to study the initial mass distribution of star
formation’s by-products, from the highest-mass progenitors of present-day
white dwarfs to the lowest-mass brown dwarfs. For this, we have produced a
volume-complete sample of stellar and substellar objects within 20 pc of the
Sun. We have split multiple systems into their separate components and
characterized each individual object to provide an accurate mass assignment.

Our main conclusions can be summarized as follows:

1) The initial mass function steadily increases as a function of descending
mass. Its peak in (linear) mass space is not yet defined but is located below
0.020$M_{\odot}$ ($\sim 20M_{Jup}$; Figure 20). We find that a quadripartite
power-law ($\xi(M)=dN/dM\propto M^{-\alpha}$) fits the observed space
densities well (Equation 21). Going from high mass to low mass, we find
exponents of $\alpha=$ 2.3, 1.3, 0.25, and 0.6, with stitch points between
segments of 0.55, 0.22, and 0.05 $M_{\odot}$, respectively. Although the rate
of ascent of the mass function is slowly retarded as a function of descending
mass through the stellar and high-mass brown dwarf regimes, its ascent
increases again for the lower-mass brown dwarfs.

2) This initial mass function agrees well with previous determinations in the
high-mass regime (by design) but differs markedly from other established
formalisms in the M, L, T, and Y dwarf regimes (Section 8). Functional forms
proposed by Chabrier (2003b) and Kroupa et al. (2013) overpredict the number
of these lower-mass dwarfs relative to their more massive counterparts.

3) The 20-pc census currently consists of $\sim$3000 stars and $\sim$600 brown
dwarfs (Table 3.1). At face value, this implies a stellar-to-substellar ratio
of $\sim$5, but corrections for incompleteness for brown dwarfs with
temperatures from 300-600K shows that the ratio is currently measured at
$\sim$4\. Incompletenesses at lower temperatures may yet bring this ratio as
low as $\sim$3 (Section 8). The average mass of objects in the 20-pc census is
currently measured as 0.41 $M_{\odot}$ but could drop as low as 0.34
$M_{\odot}$ if many colder brown dwarfs, yet to be discovered, actually exist
(Section 8).

4) The 20-pc census of objects colder than 600K, corresponding to spectral
type $\sim$T8.5, is still incomplete beyond 15 pc, and the completeness volume
shrinks to 11 pc at 450K, corresponding to spectral type $\sim$Y0 (Table 21).
Moreover, an additional source of incompleteness for objects as warm as 1350K
is high backgrounds and confusion along the Galactic plane (Section 7.1).

5) There are direct indications that many unrecognized companions still exist
to already identified members of the 20-pc census. Acceleration (aka proper
motion anomaly) has been used to flag many such systems (Section 5.1.1), and
large Gaia RUWE/LUWE values significantly higher than 1.0 flag many others
(Section 5.2). Additional follow-up of these systems would help to better
flesh out the 20-pc census itself while also providing much firmer statistics
on multiplicity and the prevalence of hierarchical systems.

6) Our "complete" (see caveats #4 and #5, above) 20-pc census produced for
this paper is available for additional uses (Table 3.1). As one example, this
nearby sample is particularly useful as the hunting grounds for the closest
habitable worlds to our own Solar System and is thus also available via the
NASA Exoplanet
Archive444444https://exoplanetarchive.ipac.caltech.edu/docs/20pcCensus.html.

7) Except for white dwarfs (Section 6.1.1) and brown dwarfs (Section 6.1.3),
masses are used directly when they have been measured (Section 4). Most
objects, though, lack actual mass determinations. For these we use a variety
of mass estimation methods and select the ones that provide the most reliable
results, when comparison to truth is available (Section 6.3). Nonetheless, our
resulting space density computations binned by mass show some spurious
features that appear to be caused by shortcomings in the estimation method.
These are most obvious in the early-M dwarf region and in the regime from
late-M to early-L dwarfs (Section 7.2). Dedicated programs, such as those by
Vrijmoet et al. (2022) and Dupuy et al. (2022) directly determining masses of
objects in these zones are clearly needed.

8) Dueling definitions in the literature of "brown dwarf" and "exoplanet"
could bias our results if objects tagged as exoplanets are omitted from the
initial mass function. We account for this and find that most of the objects
labeled exoplanets (via the 13$M_{Jup}$-based definition) fall in a small-mass
regime separate from the objects that have been more traditionally labelled as
brown dwarfs (via the formation-based definition) and do not affect our
conclusions regarding the mass function (Section 6.2.3). This having been
stated, future studies of the initial mass function might wisely consider no
such division, as planet formation can be thought of merely as a (delayed)
secondary process resulting from star formation itself. Including planetary
formation products as another branch of the initial mass function will,
however, not be feasible until a statistically robust, volume-complete set of
exoplanets can be reliably measured.

9) Gaia DR3 detections comprise only $\sim 75\%$ of the volume-complete 20-pc
census. Objects within 20 pc of the Sun can be missed by Gaia because they are
too bright for Gaia observations, too faint for Gaia to detect, or are
companions to Gaia-detected host stars that are (presently) inadequately
characterized astrometrically (Section 2.1).

10) Citizen science continues to produce new discoveries within 20 pc (Section
2.1.2), even including a possible new Y dwarf with a "bonus" Spitzer parallax
(Section A.3). Such discoveries are coming largely from WISE data sets, but
these sets are being pushed to their sensitivity limits. Completing the 20-pc
census in the 300-600K temperature range will require a deeper survey at
$\sim$5 um, the best prospect for which is the NASA mission NEO Surveyor
(Kirkpatrick et al. 2019b; Mainzer et al. 2023). Results from that mission,
along with searches for cooler companions to known 20-pc hosts with JWST,
represent our best short-term prospects for determining the occurrence rate of
objects such as WISE J085510.83$-$071442.5 that reside below 300K.

11) The 20-pc census enables us to identify the nearest star or brown dwarf in
each constellation (Table 28). Interestingly, six of the eighty-eight
constellations have a Y dwarf as their nearest member despite the fact that Y
dwarfs have not yet been fully mapped within this 20-pc volume.

NOTE ADDED IN PROOF: The nearby brown dwarf candidate CWISE
J165909.91$-$351108.5 from Table 2 has been confirmed as a late-L dwarf by
Robbins et al. (2023a), but it likely falls outside the 20-pc census.
Additionally, Robbins et al. (2023b) find that CWISE J105512.11+544328.3, from
Table 6.2.2, is not a T subdwarf but rather an anomalously blue Y dwarf.

ACKNOWLEDGMENTS: Davy Kirkpatrick, Federico Marocco, and Chris Gelino
acknowledge support from grant #80NSSC20K0452 awarded for proposal
18-2ADAP18-0175 under the NASA Astrophysics Data Analysis Program. Data
presented here are based on observations obtained at the Hale Telescope,
Palomar Observatory as part of a continuing collaboration between the
California Institute of Technology, NASA/JPL, Yale University, and the
National Astronomical Observatories of China. Some of the data presented
herein were obtained at the W. M. Keck Observatory, which is operated as a
scientific partnership among the California Institute of Technology, the
University of California and the National Aeronautics and Space
Administration. The Observatory was made possible by the generous financial
support of the W. M. Keck Foundation. The authors wish to recognize and
acknowledge the very significant cultural role and reverence that the summit
of Maunakea has always had within the indigenous Hawaiian community. We are
most fortunate to have the opportunity to conduct observations from this
mountain. This research has made use of the Keck Observatory Archive (KOA),
which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science
Institute (NExScI), under contract with the National Aeronautics and Space
Administration. The first author would like to thank Patrick Shopbell at
Caltech for resurrecting an Exabyte drive that successfully read raw CTIO data
from 1997. 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). He would also
like to thank Mike Cushing for discussion of evolved star loci in the 20-pc
color-magnitude diagrams.

One observation reported in this paper was obtained with the Southern African
Large Telescope (SALT) under program 2021-2-SCI-027 (PI: Faherty). Roberto
Raddi acknowledges support from Grant RYC2021-030837-I funded by MCIN/AEI/
10.13039/501100011033 and by “European Union NextGenerationEU/PRTR”, and
partial support by the AGAUR/Generalitat de Catalunya grant SGR-386/2021 and
by the Spanish MINECO grant PID2020-117252GB-I00. Eileen Gonzales acknowledges
support from the Heising-Simons Foundation through a 51 Pegasi b Fellowship.
This publication makes use of VOSA, developed under the Spanish Virtual
Observatory (https://svo.cab.inta-csic.es) project funded by
MCIN/AEI/10.13039/501100011033/ through grant PID2020-112949GB-I00. This
research made use of the Montreal Open Clusters and Associations (MOCA)
database, operated at the Montréal Planétarium (J. Gagné et al., in
preparation). Backyard Worlds research was supported by NASA grant
2017-ADAP17-0067 and by the NSF under grants AST- 2007068, AST-2009177, and
AST-2009136. Johanna Vos acknowledges support from a Royal Society - Science
Foundation Ireland University Research Fellowship
(URF$\backslash$1$\backslash$221932).

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