Systematic Differences in Spectral Classifications of G2V (Sun-like) Stars Between the Michigan Spectral Survey and Modern Surveys Relying on Keenan's Revised MK Standard Star Sequence

Or "When is a G2 Dwarf not a G2 Dwarf?"

Eric Mamajek (U. Rochester)

Last updated: 24 April 2016

Synopsis

Given that stars spectrally classified as "G2V" typically have astrophysical stellar properties very similar to that of the Sun, it is worth investigating whether there are systematic differences in classification between investigators. Here I demonstrate that there are systematic differences between the spectral classifications of two major spectral surveys that have been conducted over the past few decades: the Michigan Spectral Survey (e.g. Houk & Cowley 1975) and the recent NStars classifications by Gray, Corbally, and collaborators (e.g. Gray et al. 2001, 2003, 2006). The Michigan survey by Houk relied more closely on the spectral standard grid of Johnson & Morgan (1953) and Morgan & Keenan (1973), whereas the Nstars survey of Gray and collaborators relies more closely on the revised MK standard grid defined by Keenan later in his career (e.g. mainly Keenan & McNeil 1989). To wit: a G2V in one survey is not necessarily a G2V in another survey, and when we say a star has been classified "on the MK system", one needs to be clear about which standards one has used.

I show that stars classifed as "G2V" on the Keenan system of G-dwarf spectral standard stars (using classifications by Gray and collaborators) would actually appear to be near G4V (on average) by Houk in the Michigan Spectral Survey (although the G4 subtype was explicitly not used in the survey, so they would probably appear as a "G3/5V" "slash" type; e.g. Houk & Cowley 1975). In turn, stars classified as "G2V" by Houk in the Michigan Spectral Survey are actually "G0.5V" - on average - on the Keenan system (as classified by Gray and collaborators; e.g. Gray et al. 2001, 2003, 2006). As Houk discussed in a 1994 conference proceedings (Houk 1994), the Michigan classifications are "pretty close" to the MK system (all the more remarkable as >10^5 classifications were completed by one expert classifier!). As we show below, selecting G2V stars from the Michigan Spectral Survey catalogs is unlikely to identify many stars with properties cluster around those of the Sun (i.e. "solar twins"), but will in fact select stars that are 2.5 subtypes hotter (~200K hotter!). These systematic shifts at the >=2 subtype level are significant, and can not be simply attributed to observational and astrophysical scatter in the classifications by different authors.

While the Michigan Spectral Survey is immensely valuable as an enormous catalog of spectral classifications estimated by a single expert classifier, the spectral types among early G-type stars in the Michigan catalog will differ from those on the Keenan system (which is what the majority of astronomers now use; e.g. those recommended by Gray and collaborators; Gray & Corbally 2009).

As the Sun basically defines the G2V spectral type, and if one wants to study solar twins by studying other G2V stars, one should pay attention to these differences in "MK" classifications. As Garrison (1994) has noted, aside from a select minority of stable "anchor point" standards that have remained unchanged since Morgan, Keenan & Kellman (1943; "MK43"), there have been subtle shifts to the "MK" standard stars in the literature over the years - especially at the subtypes between where the anchor standards are well-established. Among the F/G/K dwarfs, there are only stable "anchor" standard stars at F2V, F6V, G0V, G2V, G5V, G8V, K0V, K2V, and K5V. For better or worse, between the 1940s and 1990s there were subtle shifts in the compilations of standard stars by Keenan (but also Morgan) at the intermediate subtypes. There were also numerous instances of old standard stars being introduced in the 1950s, and then later ignored/omitted in later compilations - and of course new standard stars being introduced in the 1970s-1980s that had not appeared in previous compilations.

Comments on the Sun as the G2V standard star

The Sun is the G2V "anchor" standard according Garrison (1994), i.e. its disk-averaged spectrum provides one of the immovable spectral types that provides the backbone of the MK spectral classification system going back to the 1950s. Unfortunately the MKK 1943 atlas did not explicitly list a G2V standard. The Sun was listed as one of three G2V standards by Johnson & Morgan (1953), however it is the only standard to survive to the modern day through Keenan's revisions (both HR 483 and 16 Cyg A were reclassified by Keenan to G1V and G1.5Vb)! See notes on G2V "standards" at http://www.pas.rochester.edu/~emamajek/spt/G2V.txt. The Sun was listed as the only G2V standard in Morgan's 1965 and 1971 papers, and is listed as a "dagger" standard in the Morgan & Keenan (1973) review. Keenan & McNeil (1976) list "Sun (moon)" as their G2V standard, and Keenan (1980) calls the Sun the "defining zero point" for G2V. Keenan later repeated listed the Sun as a G2V standard star in his 1983, 1985, and 1988 standard star compilations. Keenan (1991) observationally looked for variations in the Sun's spectral type, but was (unsurprisingly) unable to detect any variations - and concluded that aside from rare white-light flares, the Sun is essentially solid as a G2V standard star. Gray et al.'s NStars survey program adopts spectra of the Sun (via Jupiter IV & Moon) as a G2V standard.

Note that some confusion regarding classification of G dwarfs may stem from the fact that Houk adopted Beta Com as a G2V standard in the Michigan spectral survey. Unfortunately, Beta Com was considered a G0V "dagger" standard in Morgan & Keenan (1973), but has only been used sparingly as a G0V standard by Keenan (only in 1976 atlas) and Gray (digital atlas and Nstars standard). Unfortunately, Gray (1989) later adopted Beta Com as a primary F9.5V standard star! Given its inglorious history, it may be better if Beta Com is never used as a spectral standard star again (indeed, if a G0V standard is needed - Beta CVn is the undisputed anchor; Garrison 1994). From this disagreement alone, we should not be surprised to see systematic differences in the classifications of early G-type stars at the 2-subtype level between Houk's Michigan classifications and those relying on Keenan's standards (e.g. Gray and collaborators).

Comparison of Gray+ and Houk Classifications of "G2V" stars

As an example, here I compare the classifications of Gray et al. (2001, 2003, 2006) vs. those of Houk (Michigan Spectral Survey, as compiled in the Hipparcos catalog). Gray et al. (2001, 2003, 2006) report spectral classifications for 372, 664, and 1676 stars, respectively. Of those, 53 are classified as "G2V" or a minor variant (e.g. "G2V+", "G2V Fe-1.0"). Of these 53, some 36 are "pure" G2V stars, whereas 16 are variants. I queried all of these stars through the Michigan Catalogue of HD stars Volumes 1-5 (Houk and collaborators 1975, 1978, 1982, 1988, 1999). Of the 53 stars classified as G2V or variant by Gray and collaborators, 35 of these had Houk classifications. A comparison of the types is shown in Table 1.

NameSpT(Gray)Ref.Spt(Houk)numeric typeQual.Flag.Notes
HD 1320G2VGray06G5V51
HD 2071G2VGray06G8IV+(F)81R
HD 20619G2VGray03G5V51
HD 25874G2VGray06G2V21
HD 35041G2V_Fe-0.4_CH-0.5Gray06G6V61
HD 37962G2VGray06G5V52
HD 38858G2VGray03G3V31B
HD 45289G2VGray06G5V51L
HD 51929G2V_Fe-1.4_CH-0.7Gray06F8/G0V-12
HD 59711G2VGray06G5V51
HD 59967G2VGray06G3V31B
HD 66653G2VGray06G5V52
HD 75519G2VGray06G5V53
HD 76151G2VGray01G3/5V42BL
HD 76932G2V_Fe-1.8_CH-1Gray06F7/8IV/V-2.52B
HD 78429G2VGray06G5V52
HD 88084G2VGray06G5V52
HD 89707G2V_Fe-1.5_CH-0.8Gray06G1V11
HD 95521G2VGray06G5V51
HD 98553G2V_Fe-0.7Gray06G2/3V2.52
HD 102365G2VGray06G3/5V3.51B
HD 103743G2VGray06G3V33R
HD 104982G2VGray06G5V53
HD 106489G2VGray06G5V52
HD 108309G2VGray06G3/5V41LB
HD 145809G2V_Fe-0.7Gray06G3V31
HD 145825G2VGray06G1V11
HD 146233G2VGray03G5V51BL
HD 153075G2V_Fe-0.8_CH-0.5Gray06G0/2V11
HD 177758G2V_Fe-1.0_CH-0.6Gray06G1V11
HD 195564G2VGray03G6V61B
HD 196141G2VGray06G3V31
HD 199288G2V_Fe-1.0Gray06G0V01L
HD 202457G2VGray06G5V51
HD 210918G2VGray06G5V51LB

Here is a statistical comparison of the Gray et al. "G2V" stars with Houk's types:

Sample # SpT(Houk,median)SpT(Houk,mean)s.e.m.rms
Gray: "G2V" only, no variants26G5.0G4.40.31.4
Gray: all G2Vs & variants 35G5.0G3.60.42.2
Gray: all G2Vs. Houk: qual=1 23G4.0G3.70.42.0

So the Gray et al. G2V stars classified using Keenan's standards are basically G4Vs on Houk's system. Remarkably, only 1 of Gray's G2V stars was similarly classified G2V by Houk (HD 25874). The lack of agreement is stunning given that both Houk and Gray et al. explicitly use the Sun as a spectral standard (Houk lists Uranus, Gray NStar's WWW page lists spectra of the Moon and Jupiter IV).

This begs the question: What are the G2V stars in Houk's catalog on the Keenan/Gray system?

To answer this, I cross-compared Houk's G2V stars with classifications by Gray et al. The 5 Michigan volumes contain a total of 1106 stars classified as " G2V ", where I have chosen to ignore variants and "slash" types. I found 44 stars classified by Gray and collaborators (which rely on the Keenan & McNeil 1989 grid and the MK "anchor" standards compiled by Garrison 1994).

NameSpT(Houk)SpT(Gray)numeric type
HD 105328G2VG0V0
HD 114853G2VG1.5V1.5
HD 117618G2VG0V0
HD 119638G2VF8.5V-1.5
HD 125881G2VG0-V-0.25
HD 1273G2VG5V_Fe-1.2_CH-0.95
HD 128620G2VG2V2
HD 134060G2VG0V_Fe+0.40
HD 134331G2VG0+V0.25
HD 134664G2VG1.5V1.5
HD 1388G2VG0V0
HD 143846G2VG0V0
HD 14802G2VG0V0
HD 15064G2VG1V1
HD 153631G2VG0V0
HD 155918G2VG2V_Fe-1.0_CH-0.62
HD 158630G2VG0V0
HD 165401G2VG0V0
HD 177409G2VG1V_CH-0.41
HD 180409G2VF9V-1
HD 183216G2VF8.5V_Fe+0.4-1.5
HD 189340G2VF9V-1
HD 202628G2VG1.5V1.5
HD 205905G2VG1V1
HD 206301G2VG1_IV1
HD 20807G2VG0V0
HD 209779G2VG1V1
HD 217877G2VG0-V-0.25
HD 221420G2VG2_IV-V2
HD 222669G2VG1V1
HD 25874G2VG2V2
HD 31527G2VG0V0
HD 33093G2VG0_IV0
HD 33095G2VG1V1
HD 38973G2VG0V0
HD 4307G2VG0V0
HD 45184G2VG1.5V1.5
HD 56662G2VG0V0
HD 64096G2VG0V0
HD 67458G2VG0V0
HD 68978G2VG0.5V0.5
HD 73744G2VG5V_Fe-1.3_CH-0.95
HD 8076G2VG1V1
HD 84991G2VG0-V-0.25

There is excellent agreement among the luminosity types, with only 3 of 44 (7%) of the Houk luminosity class V G2 stars being considered either luminosity class "IV" or "IV-V" by Gray and collaborators. Unfortunately the agreement in the subtypes is not as good. Only 3 of the 44 stars agree in temperature subtype (HD 128620, 155918, 25874).

Sample # SpT(Gray,median)SpT(Gray,mean)s.e.m.rms
Houk: "G2V" only, no variants44G0.0G0.60.21.3

After clipping two significant outliers (HD 1273, HD 73744; both of which were classified as very metal poor F5V stars by Gray), the mean Gray type for the "Houk G2V" stars is G0.4, with s.e.m. +-0.14 and rms scatter 0.9 subtype.

Hence, a star classified as "G2V" by Houk in the Michigan survey would be classified as approximately "G0.5V" by Gray and collaborators using the Keenan & McNeil (1989) standard star grid. Hence, the "G2V" stars in the Michigan survey will probably be systematically hotter than the Sun and solar twins by ~200K (on average; see e.g. SpT vs. Teff scale of Pecaut & Mamajek 2013).

Houk's G Dwarf Standard Stars

Here is a comparison between the F7-K0-type dwarf spectral standards adopted by Houk in the "University of Michigan Catalogue of Two-Dimensional Spectral Types for the HD Stars: Volume 1" (Houk & Cowley 1975) and those from Keenan, and other recent classifications by Gray and collaborators (using the MK standard grid largely finalized by Keenan in the 1980s).

Name SpT(Houk) ref Spt(Keenan) SpT(Gray)
iot Psc (HR 8969)F7V JM53 ... F7V [G89,G01]
bet Vir (HR 4540)F9V [F8V] MK73 [JM53]F9V [MK73] F8.5IV-V [G01]
HD 27836 G1V MK73 G1V [MK73] G1V [G89], G0V(e) [G01]
bet Com (HR 4983)*G2V ... G0V [MK73,K76], F9.5V [K89]G0V [G01]
Sun (Uranus) G2V MK73 G2V [MK73,K76,K80,K83,K85] G2V [G09]
85 Peg (HR 9088)*G3/5V ... G5Vb Fe-2 [K88,K89]G5Vb Fe-2 [G01], G5V Fe-1 [G03]
kap Cet (HR 996) G5V JM53 G5V [K83,K89]G5V [G01]
xi Boo (HR 5544) G8V JM53 ... G7V [G03]
54 Psc (HR 166) K0V JM53 K0V [K80,K83], K0.5V [K89]K0V [G03]
* = Houk's "revised standards" - she states in notes "We do not suggest that other classifiers use the types we have assigned as these are only based one plate. Others may well come to other conclusions." References: JM53 = Johnson & Morgan (1953), MK73 = Morgan & Keenan (1973), K76 = Keenan & McNeil (1976), K80 = Keenan & Pitts (1980), K83 = Keenan (1983), K85 = Keenan (1985), K89 = Keenan & McNeil (1989), K88 = Keenan & Yorka (1988), G89 = Gray (1989), G01 = Gray et al. (2001), G09 = Gray (2009; "A Digital Spectral Classifciation Atlas"). A few notes are in order. Bet Vir: Houk adopted this as the F8V standard following Johnson & Morgan (1953), but halfway through classifying Volume 1, Morgan & Keenan (1973) published their revised MK73 standard list, and made beta Vir a F9V instead (which Houk then adopted). Bet Com: Obviously the biggest difference, which Houk adopting G2V (same as the Sun), while Keenan first considered it G0V, then F9.5V (1989)! Xi Boo: despite being listed as a G8V standard in the 1943 MKK atlas and again in Johnson & Morgan (1953) - was inexplicably never listed later by Keenan in any of his 1970s-1990s compilations. Gray et al. (2003) list Xi Boo as one subtype earlier (G7V) than the G8V "anchor" standard 61 UMa (Garrison 1994; i.e. its type has been consistently G8V since the 1943 MKK atlas).

So there are some subtle differences between the classifications of the G-type dwarf standards adopted by Houk and those used by Gray and collaborators (mostly relying on Keenan & McNeil 1989).

A Comparison of B-V Colors of "G2V" Stars

A star classified as "G2V" by Gray and collaborators (using Keenan's standards) would normally be classified near "G4V" (or typically within +-2 subtypes rms) in Houk's Michigan Spectral catalog. This likely explains why the mean B-V color of G2V stars in the Hipparcos catalog (w/i 75 pc, with S/N(parallax) > 8) which are mostly classified by Houk are so blue ( = 0.617; sem=0.003, rms=0.032; N=223) compared to the color of the Sun (B-V=0.653; Ramirez et al. 2012) and the mean color of Gray-classified G2V stars (=0.647; sem=0.003, rms=0.035), and why the mean color of Hipparcos G4V stars (mostly classified by Houk) is so similar to that of the Sun and Gray G2V stars: ((G4V) = 0.663 ; sem=0.013, rms=0.034; N=13).

What are the Best Standards for AFGK Dwarfs that Represent the Modern MK System?

After the author has 1) been "burned" by taking spectra of spectral "standards" that have apparently shifted in the literature (e.g. Beta Com), and 2) mistakenly assuming that spectral types listed in one survey are on the same system as those in other surveys, I decided several years ago to compile some notes on the MK standard stars, and come to some conclusions on which standard stars had the best "pedigree", and make those notes public. This was also done in parallel with a taking spectra of many standard stars using the CTIO 1.5-m telescope (some results reported in Pecaut, Mamajek, Bubar 2012 and Pecaut & Mamajek 2013). After conducting this literature exercise over the years, I can highly recommend to the reader that they do not adopt spectral standards blindly from compendia like e.g. Garcia (1989). My notes are compiled, rather unceremoniously, in ASCII text format at: http://www.pas.rochester.edu/~emamajek/spt/. Eventually I hope to make a more respectable website for them, but for now they are probably sufficient as is for anyone really interested in the subject. In the same files I've also compiled my estimates of the best stellar parameters (e.g. Teff, colors, etc.) for the various spectral types.

Here I list what I believe are the "best" dwarf standards for the AFGK-type stars - i.e. those that have the best pedigrees and appear to represent the long-term structure of the MK classification system. This table includes the "anchor" standards listed by Garrison (1994), but includes additional stars in the intermediate subtypes. The stars in italics may be somewhat controversial as standards, or have limited pedigrees, but appear to be the best available (however their status as "best" may change).

Spec. Type Standard StarReferences Notes
A0 Valf LyrMK43,JM53,MK78,K85,G87,G94,96G87 & G96 assign "Va" lum class
A0 Vgam UMaMK43,JM53,MK73,G87,G94,G96G87 & G96 assign "Van" lum class, "n"=high vsini
A0 VHD 71155MK43,JM53,GG87,G03GG87 & G03 assign "Va" lum class
A1 VHD 10939 G87G87 assigns "Va" lum class
A1 V48 Cet G87G87 assigns "Va" lum class
A2 VnHD 56405 GG87GG87 assigns "Va" lum class, "n"=high vsini
A2 VHD 88955 G87,G06G06 assigns "Va" lum class
A3 Valf PsA MK43,JM53,MK73,GG89,G94,G96GG89 & G96 assign "Va" lum class
A3 Vbet Leo MK43,JM53,GG89,G96GG89 & G96 assign "Va" lum class
A4 Vdel LeoJM53But GG89 calls "A4IV", G03 calls "A5IV(n)"
A5 VHD 23194 GG89,G01
A5 VnHD 23886 MK78,K85,GG89,G01"n" = high vsini
A6 Vbet PicGG89(non-standard)
A7 Vn21 LMi JM53,GG89,G03Praesepe
A7 Vnalf Aql MK43,GG89,G96,G03
A8 VHD 158352PM13
A9 VHD 73450 PM13Praesepe
A9 Vn44 Cet GG89"n" = high vsini
F0 VHD 23585 MK73,MK78,K85,G89,GG89,G01Pleiad
F1 V37 UMa M53,C69,C74,GG89But G03 says "F2V"
F2 V78 UMa MK43,JM53,MK73,MK78,K85,G89,G94UMa cluster
F3 VHD 26015 M65,MK73,MK78,K85,G89,G01Hyad
F4 VHD 27561M65,PMB12Hyad
F5 VHD 27524 M65,MK73,MK78,K85,G89,G01Hyad
F6 Vpi03 Ori MK43,JM53,M65,M71,MK73,G89,G94G01 calls "F6V-IV"
F7 Vtet PerJM53,G01none of the F7V "standards" have great pedigrees
F8 VHD 27808 MK73,MK78,K85,G89,G01Hyad
F9 VHD 10647 K88,K99,G03
G0 Vbet CVn MK43,JM53,M65,MK73,K76,K85,K85,G94,G01,G03
G2 VSun JM53,M65,M71,MK73,K76,K80,K85,K91,G94
G2 V18 Sco K88,G03"solar twin"
G3 V16 Cyg B K85,K88,K89,G03,G06
G5 Vkap01 Cet MK43,JM53,M65,K76,K85,K88,
K89,G94,K99
G7 VHD 111395 M53,G03not a Keenan standard
G8 V61 UMa MK43,JM53,M65,K76,K85,K88,
K89,G94,G03
K0 Vsig Dra MK43,JM53,MK73,KM76,K85,K88,
K89,G94
K1 V107 Psc MK43,JM53,M53,K88,K89,K99,G06
K2 Veps Eri MK43,JM53,M65,KM76,K85,G94,
K99,G03
K3 VHD 219134 MK43,JM53,K83,K85,K88,K89,G03
K3 VHD 16160 KM76,K89,K99,G03
K4 VHD 216803 K85,K89Fomalhaut B. G06 calls "K4+Vk"
K5 V61 Cyg A MK43,JM53,M65,MK73,KM76,K80,
K85,K88,K89,G94,KHM91,H94,H02
K5 VHD 36003 K89,K99,G03,PM13G06 calls "K5-V"
K6 VHD 120467 K88,K89G06 calls "K5.5V(k)"
K7 V61 Cyg B JM53,MK73,KM76,K80,K88,K89,KHM91,H02
K7 VHD 157881 JM53,H94,H02,G03,PM13
K8 VHIP 111288G06,PM13G06 appends "k" (Ca K emission)
K9 VHIP 3261G06,PM13
References: MK43 = Morgan, Keenan, & Kellman (1943), JM53 = Johnson & Morgan (1953), M65 = Morgan & Hiltner (1965), C69 = Cowley et al. (1969), M71 = Morgan, Hiltner, Garrison (1971), MK73 = Morgan & Keenan (1973), C74 = Cowley & Fraquelli (1974), K76 = Keenan & McNeil (1976), MK78 = Morgan, Abt, Tapscott (1978), K80 = Keenan & Pitts (1980), K83 = Keenan (1983), K85 = Keenan (1985), K88 = Keenan & Yorka (1988), K89 = Keenan & McNeil (1989), K99 = Keenan & Newsom (1999, The Revised Catalog of MK Spectra Types for the Cooler Stars; Keenan's final list), G89 = Gray (1989), GG89 = Gray & Garrison (1989), K91 = Keenan (1991), KHM91 = Kirkpatrick, Henry, & McCarthy (1991), G94 = Garrison (1994; "Anchor standards" ;1994ASPC...60....3G), H94 = Henry et al. (1994), G96 = Garrison & Beattie (1996; "The Brightest Stars"; Observer's Handbook), G01 = Gray et al. (2001), H02 = Henry et al. (2002), G03 = Gray et al. (2003), PMB12 = Pecaut, Mamajek, Bubar (2012), PM13 = Pecaut & Mamajek (2013). Note that not all of the references specifically mention the star as a standard star.

I am still undecided on which G1V, G4V, G6V, and G9V standards are best (or if any of them are adequate), as their use has been somewhat inconsistent in the literature.

Recommendation and Future Work


Given:
1) the shear number of Houk classifications, and their obvious utility for various purposes (e.g. characterizing new debris disk and exoplanet host stars, reddening studies, etc.), but also
2) the modern day acceptance of Keenan's 1980s-era standard star grid defining the F9V-K5V spectral sequence (e.g. Keenan & McNeil 1989; see Gray & Corbally 2009),
then
it may be worth constructing a look-up table between the Houk and Keenan systems so that samples of classified stars may be more meaningfully intercompared (and differences not simply attributed to error or astrophysical scatter).

In closing, the early-G stars in the Houk Michigan Spectral Survey volumes are not technically on the MK system as realized by Keenan's later compilations of G-dwarf standards which are now in common use (e.g. Keenan & McNeil 1989), but they appear to be systematically different at the ~+-2 subtype level in some places! G2V stars classified using Keenan spectral standard stars are not comparable to the stars classified as "G2V" by Houk. This obviously needs to be taken into account when investigators use spectral types for inferring effective temperatures, intrinsic colors, estimating reddenings and extinctions, etc.

If there are questions about which of the standard stars are probably the best modern-day representation of the MK system, I suggest that you consult my notes on the MK standard stars: http://www.pas.rochester.edu/~emamajek/spt/. I have attempted to assess which standards are best (i.e. have been repeatably used by expert classifiers and listed in compilations), and those which are worst (i.e. those whose types which have changed - sometimes repeatably - over the decades according to expert classifiers). Gray & Corbally (2009; "Stellar Spectral Classification") have reproduced tables of MK standards in Appendix A of their book, however the compilation is not complete (missing especially many Keenan standards), some of the choices of standards are not necessarily the best available (after a thorough literature review), and the compilation is missing many M standards adopted by Kirkpatrick & Henry. That said, Gray & Corbally (2009) is a great resource for understanding spectral classification and a great distillation of the past several decades of literature on the subject.

Acknowledgements: I thank Omar Lopez-Cruz, Giannina Dalle Mese, Miguel Chavez, Richard Gray, Chris Corbally, and Mark Pecaut for discussions over the past several years on spectral classification.