## Number Densities of Stars of Different Types in the Solar Vicinity

### Eric Mamajek

What fraction of the stars in the solar neighborhood of are of given spectral class?

A good starting point is Chapter 19 of Cox's (2000) "Allen's Astrophysical Quantities" (AIP Press: Springer, New York). However I wanted to be able to answer this question by stellar type. I decided to check the latest census of nearby stars from Todd Henry's RECONS survey, and I'd like to acknowledge the hard work of his team which has been helping fill in the census of nearby objects from all angles (fast-moving stars, slow-moving stars, "blue" stars, "red" stars, etc.). T. Henry has made several plots describing the nearby 10 pc sample here. I also refer back to calculations done by Kroupa et al. (1993).

The overall number density of stars in the solar neighborhood is approximately 0.0984±0.0068 star/pc^3 (i.e. ~0.10 stars per cubic parsec), including white dwarfs, but not including brown dwarfs, neutron stars, or black holes. Approximately ~0.092 star/pc^3 of this number density is just M dwarfs, with the remaining ~0.026 due to all other types of stars. Hence, M dwarfs represent approximately ~78% of all stars (depending on how it is calculated, this number seems to consistently come up in the 70-80% range).

 Star Type # Density (pc^-3) Fraction of stars Reference Comments O stars 4.4e-8(±2.0e-8)[#1] ~5e-7(1 in ~2,000,000) EEM #1: cross-referenced GOSS (Sota+2014) catalog w/van Leeuwen(2007) & Gaia DR1 TGAS. N=5 O-type stars w/ plx > 3.33 mas (d<300pc): zeta Oph, delta Ori, zeta Ori, 15 Mon, HD 37737. Parallaxes very poor beyond that for most stars. B stars 3.2e-5(±4.7e-6) [#1] 3.9e-4(1 in 2600) EEM #1: calc from HIP2 (B-type, Mv < 2, plx/e(plx)>8, d<70pc, N=46) A stars 4.9e-4(±6.6e-5) [#1] 6.0e-3(1 in 170) EEM #1: calc from HIP2 (A-type, Mv<4, plx/e(plx)>8, d<30pc, N=55) F stars(all lum classes) 0.0025(±0.0003)[#1] 0.031(1 in 33) EEM #1: see http://www.pas.rochester.edu/~emamajek/Fstars_dens.txt F dwarfs 0.0024(±0.0003)[#1] 0.029(1 in 34) EEM #1: see http://www.pas.rochester.edu/~emamajek/Fstars_dens.txt G stars(all lum class) 0.0048(±0.0011) [#1] 0.00332(±0.00044)[#2] 0.059(1 in 17) #1: calc from RECONS (10pc, N=20, likely complete) #2: EEM SIMBAD plx>62.5 (d<16pc) (N=57), vetted for binarity, best SpTs, junk parallaxes. G dwarfs 0.0033(±0.0004) [#1] 0.0038(±0.0010) [#2] 0.0037(±0.0013) [#3] 0.041(1 in 25) EEM #1: calc from Mamajek+08 (16pc, N=57, likely complete) #2: calc from Mamajek+08 (10pc, N=16, likely complete) #3: calc from Kirkpatrick+12 (8pc, N=8, complete) Note: del Pav (6.1pc) classified G8IV, but within 0.8 mag of MS (so "dwarf") K dwarfs 0.0105(±0.0016) [#1] 0.0135(±0.0025) [#2] 0.0153(±0.0054) [#3] 0.0083(±0.0007) [#4] 0.129(1 in 7.8) EEM #1: calc from RECONS (10pc, N=44, likely complete) #2: calc from Kirkpatrick+12 (8pc, N=29, likely complete) #3: calc from Kirkpatrick+12 (5pc, N=8, likely complete) #4: all K stars: calc from SIMBAD (16pc, N=143, 7 are evolved; looks incomplete for dwarfs) M dwarfs 0.0676(±0.0040) [#1] 0.0859(±0.0086) [#2] 0.0917(±0.0132) [#3] 0.0917(±0.0132) [#4] 0.725(1 in 1.38) EEM #1: calc from RECONS (10pc, N=283, 2018.3) #2: calc from Kirkpatrick+12 (6.527pc, N=100) #3: calc from Kirkpatrick+12 (5pc, N=48, likely complete) #4: calc from Winters+19 (5pc, N=48, likely complete) white dwarfs (e.g. DA, DB, DC, DQ, DZ, etc.) 0.0048(±0.0011)[#1] 0.0051(±0.0015)[#2] 0.0048(±0.0005)[#3] 0.0055(±0.0001)[#4] 0.00449(±0.00038)[#5] 0.059(1 in 17) EEM #1: calc from RECONS 10 pc sample (N=20 as of 2012.0) #2: calc from Kirkpatrick+2012 8 pc sample (N=11) #3: Holberg+ 2016 #4: Munn+ 2017 #5: Hollands+ 2018 "Evolved stars" 8.8e-4 0.011(1 in 93) EEM includes stars just leaving main sequence, subgiants, giants, calc using HIP2 for Mv > 1 mag away from Wright 2004 main sequence, Mv < 4.5(d < 35 pc; N=158) "Red Giants" 2.7e-4(±4.9e-5)[#1] 3.3e-3(1 in 300) EEM #1: G/K/M giants only, N=31 w/i d<30pc (using van Leeuwen 2007 HIP parallaxes) all starsOBAFGKM *s + WDsignoring NSs & BHs 0.0902(±0.0046)[#1] 0.0936(±0.0134)[#2] 0.0984(±0.0068)[#3] 1 EEM #1: calc from RECONS 10 pc sample (N=378; 2018.3) #2: calc from Kirkpatrick+2012 5 pc sample (N=49) #3: calc from Kirkpatrick+2012 8 pc sample (N=211) Star Type # Density (pc^-3) Fraction of stars Reference Comments

All of the densities should be interpreted as lower limits. HIP2 = revised HIPPARCOS catalog (van Leeuwen 2007). Volume limits were selected to ensure reasonable completeness in Hipparcos catalog, taking into account the observed HR diagram for nearby stars constructed here. The giants and evolved stars are assumed to be single (i.e. each HIP entry is a single giant), so the number is a lower limit.