ar
X
iv
:1
00
8.
39
13
v1
[
as
tro
-p
h.S
R]
2
3 A
ug
20
10
Draft version August 25, 2010
Preprint typeset using LATEX style emulateapj v. 11/10/09
ON THE USE OF EMPIRICAL BOLOMETRIC CORRECTIONS FOR STARS
Guillermo Torres
Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA; e-mail: gtorres@cfa.harvard.edu
Draft version August 25, 2010
ABSTRACT
When making use of tabulations of empirical bolometric corrections for stars (BCV ), a commonly
overlooked fact is that while the zero point is arbitrary, the bolometric magnitude of the Sun (Mbol,⊙)
that is used in combination with such tables cannot be chosen arbitrarily. It must be consistent with
the zero point of BCV so that the apparent brightness of the Sun is reproduced. The latter is a
measured quantity, for which we adopt the value V⊙ = −26.76± 0.03. Inconsistent values of Mbol,⊙
are listed in many of the most popular sources of BCV . We quantify errors that are introduced by
not paying attention to this detail. We also take the opportunity to reprint the BCV coefficients of
the often used polynomial fits by Flower (1996), which were misprinted in the original publication.
Subject headings: stars: fundamental parameters — stars: general — Sun: fundamental parameters
— Sun: general
1. INTRODUCTION
Bolometric corrections are widely used in Astronomy
to infer either luminosities or absolute magnitudes of
stars. Empirical corrections in the visual band, BCV ,
are perhaps the most frequently needed, and numerous
tabulations exist in the literature that differ sometimes
significantly. This has been a persistent source of confu-
sion among users. The most common way in which these
tables are employed is in combination with the bolomet-
ric magnitude of the Sun, Mbol,⊙, which is not a directly
measured quantity. Many different values of Mbol,⊙ can
be found in the literature as well, adding to the con-
fusion. For a given table of bolometric corrections the
choice of Mbol,⊙ is not arbitrary, however, since there is
an observational constraint that must be satisfied, given
by the measurement of the visual brightness of the Sun.
This fact is often ignored, and as a result it is common
to see inconsistent uses of BCV that can lead to errors
in the luminosity of 10% or larger, or errors in MV of
0.1 mag or more. The primary motivation for this pa-
per is to call attention to this fact, to illustrate common
misuses of some of the most popular BCV tables, and to
offer some perspective on the problem.
One frequently used source of bolometric corrections
is the tabulation by Flower (1996), which is an update
on his earlier work (Flower 1977) based on a compila-
tion of effective temperatures (Teff) and BCV determi-
nations for a large number of stars. Many authors find
this source convenient because, in addition to the table,
it presents simple polynomial fits for BCV valid over a
wide range of temperatures. Unfortunately the original
publication had misprints in the coefficients of those for-
mulae that have prevented their use, and an erratum was
never published. The present author has received numer-
ous inquiries about this problem over the years. Thus,
a second motivation for this paper is to make the cor-
rect coefficients available to the community, as well as
to amend the form of the equation and one of the coef-
ficients for a color/temperature calibration in the same
paper that were also misprinted. We begin by present-
ing these corrections, and follow with a discussion of the
practical use of BCV tables.
2. COEFFICIENTS FOR THE FLOWER (1996) BCV AND
log TEFF FORMULAE
Flower (1996) expressed the bolometric corrections as
a function of the effective temperature of the star, and
presented polynomial fits for BCV of the form
BCV = a + b (logTeff) + c (log Teff)2 + · · · , (1)
for three different temperature ranges. The coefficients
a, b, c, · · · were given in his Table 6 for each interval, but
are missing powers of ten. We rectify this situation here
and present them with a larger number of significant dig-
its (see Table 1). While this formulation is certainly
very handy for many applications, it must be kept in
mind that bolometric corrections become less reliable for
cooler stars due to the limited number of observational
constraints, and they break down completely for the M
dwarfs. Two of the very few such constraints available
are for the low-mass eclipsing binaries CU Cnc (compo-
nents with M ≈ 0.42 M⊙) and CM Dra (M ≈ 0.24 M⊙),
which have known parallaxes. For these stars one may
compute the BCV values for the components directly
from the estimated MV values and the bolometric mag-
nitudes based on the absolute radius and temperature de-
terminations (Ribas 2003; Morales et al. 2009). Compar-
ing the measured values with the predicted ones shows
that the Flower relations give a BCV that is too negative
by ∼1.2 mag for CU Cnc, and ∼1.7 mag for CM Dra.
Similar discrepancies are found in other tabulations of
empirical bolometric corrections.
A useful color/temperature calibration was also pre-
sented by Flower (1996) in his Table 5, separately for
supergiants and for main-sequence, subgiant, and giant
stars, but unfortunately the formula given there was
printed incorrectly, and should have expressed the tem-
perature (log Teff) as a function of the B−V color index,
rather than the reverse. The polynomial fits are similar
to those used for BCV :
logTeff = a+ b (B−V ) + c (B−V )2 + · · · . (2)
One of original coefficients was also misprinted, and a

2 Torres
TABLE 1
Bolometric corrections by Flower (1996) as a function of temperature:
BCV = a+ b(log Teff ) + c(log Teff )2 + · · ·
Coefficient log Teff < 3.70 3.70 < log Teff < 3.90 log Teff > 3.90
a −0.190537291496456E+05 −0.370510203809015E+05 −0.118115450538963E+06
b 0.155144866764412E+05 0.385672629965804E+05 0.137145973583929E+06
c −0.421278819301717E+04 −0.150651486316025E+05 −0.636233812100225E+05
d 0.381476328422343E+03 0.261724637119416E+04 0.147412923562646E+05
e · · · −0.170623810323864E+03 −0.170587278406872E+04
f · · · · · · 0.788731721804990E+02
TABLE 2
Effective temperature as a function of color
(Flower 1996): log Teff = a+ b(B−V ) + c(B−V )2 + · · ·
Main-Sequence Stars,
Coefficient Supergiants Subgiants, Giants
a 4.012559732366214 3.979145106714099
b −1.055043117465989 −0.654992268598245
c 2.133394538571825 1.740690042385095
d −2.459769794654992 −4.608815154057166
e 1.349423943497744 6.792599779944473
f −0.283942579112032 −5.396909891322525
g · · · 2.192970376522490
h · · · −0.359495739295671
correction was issued by Prsˇa & Zwitter (2005). We
present all coefficients again in Table 2 to higher pre-
cision.
3. THE USE OF EMPIRICAL BOLOMETRIC
CORRECTIONS
As is well known, the apparent bolometric magnitude
of a star is defined as
mbol = −2.5 log
(
∫ ∞
0
fλdλ
)
+ C1 , (3)
where fλ is the monochromatic flux from the object per
unit wavelength interval received outside the Earth’s at-
mosphere, and C1 is a constant. The bolometric correc-
tion is usually defined as the quantity to be added to
the apparent magnitude in a specific passband (in the
absence of interstellar extinction) in order to account for
the flux outside that band:
BCV = mbol − V = Mbol −MV . (4)
We focus here on the visual band because that is the
context in which bolometric corrections were historically
defined, although of course the definition can be general-
ized to any passband. Note that this definition is usually
interpreted to imply that the bolometric corrections must
always be negative, although many of the currently used
tables of empirical BCV values violate this condition. We
return to this below. Eq.(4) may also be written as
BCV = 2.5 log
(∫∞
0 Sλ(V )fλdλ /
∫∞
0 fλdλ
)
+ C2 , (5)
where Sλ(V ) is the sensitivity function of the V magni-
tude system. The constant C2 contains an arbitrary zero
point that has been a common source of confusion. This
zero point has traditionally been set using the Sun as the
reference. By noting that
BCV,⊙ = mbol,⊙ − V⊙ = Mbol,⊙ −MV,⊙ , (6)
it is immediately clear that setting a value for the bolo-
metric correction of the Sun is equivalent to specifying
the zero point of the bolometric magnitude scale, since
V⊙ is a known quantity. A common practice when using
one of the many available tables of empirical bolometric
corrections is to adopt a value for Mbol,⊙, but all too
often this is done without regard for whether the cho-
sen value is consistent with BCV,⊙ from the same table.
From eq.(6) we have
Mbol,⊙ = MV,⊙ +BCV,⊙ = V⊙ + 31.572+BCV,⊙ , (7)
where the numerical constant (with the opposite sign)
corresponds to the distance modulus of the Sun at 1 AU.
This formulation shows that once a particular tabula-
tion of BCV values is adopted, the absolute bolometric
magnitude of the Sun is no longer arbitrary. This fact
has been emphasized by Bessell et al. (1998), and other
authors, but is still largely overlooked.
Direct measurements of V⊙ are difficult to make be-
cause of the extreme difference in brightness between the
Sun and the stars that are used as the reference in the V
system, and also because the Sun is spatially resolved.
Nevertheless, many careful determinations have been
carried out over the years (although not very recently,
as far as we are aware), and the most reliable of the pho-
toelectric measurements have been reviewed by Hayes
(1985).1 Among them, one that carries particularly high
weight is that of Stebbins & Kron (1957), which was ad-
justed slightly (by −0.02 mag) by Hayes (1985) for an
error in the treatment of horizontal extinction, and fur-
ther updated by Bessell et al. (1998) using modern V
magnitudes for the reference stars. The result is V⊙ =
−26.76±0.03.2 Two additional determinations discussed
by Hayes (1985) are those of Nikonova (1949), trans-
formed to the standard Johnson system by Martynov
(1960), and Galloue¨t (1964): V⊙ = −26.81 ± 0.05 and
V⊙ = −26.70 ± 0.01, respectively. Because systematic
1 A useful compilation and discussion of solar data may
be found in “Basic Astronomical Data for the Sun (BADS?)”,
maintained by Eric Mamajek, Univ. of Rochester (NY), at
http://www.pas.rochester.edu/∼emamajek/sun.txt.
2 The uncertainty we assign is slightly larger than the ±0.02 mag
given by Bessell et al. (1998) because it includes contributions from
systematic effects described by Stebbins & Kron (1957). We also
re-examined the corrections made in the later work to reduce
the measurements to the distance of 1 AU, since variations in
the Earth-Sun distance throughout the year lead to non-negligible
brightness changes of ±0.036 mag. This leads to only a very mi-
nor difference in the third decimal place compared to the value
reported by Bessell et al. (1998), which we have ignored here.

Bolometric corrections 3
effects likely dominate the differences, we follow Hayes
(1985) and adopt as a consensus value a simple average
of the three estimates, giving V⊙ = −26.76± 0.03, with
an error that is probably realistic. The absolute visual
magnitude of the Sun then becomes MV,⊙ = 4.81± 0.03.
Measurements of V⊙ based on absolute flux-calibrated
spectra of the Sun (Colina et al. 1996; Thuillier et al.
2004, and others) or synthetic spectra based on model
atmospheres such as ATLAS9 and MARCS have also
been made by many authors, and generally range from
−26.74 to −26.77, with minor differences depending on
the author even when using the same spectrum (see, e.g.,
Bessell et al. 1998; Casagrande et al. 2006). These esti-
mates agree well with the direct measurements.
While the zero point of BCV is completely arbitrary,
and no particular scale has been officially endorsed by
the International Astronomical Union (IAU) (but see
Sect. 5), it is common for some authors of these tabu-
lations to define the scale by adopting a certain value for
BCV,⊙, sometimes for historical reasons. For example,
the widely used reference by Cox (2000), the successor
to Allen’s Astrophysical Quantities (Allen 1976, and ear-
lier editions) indicates that it adopts BCV,⊙ = −0.08 (p.
341, but see also the next section), a value inherited from
earlier compilations. Similar scales have been chosen in
many other empirical tables. On the other hand, the the-
oretical BCV values that are incorporated in the stellar
evolution models of Pietrinferni et al. (2004) are based
onBCV,⊙ = −0.203, while the Yi et al. (2001) isochrones
use either BCV,⊙ = −0.109 or BCV,⊙ = −0.08, for
the two different color transformation tables offered with
their models (Lejeune et al. 1998; Green et al. 1987).
The more negative values above tend to come from
the practice by many stellar modelers (starting with
Buser & Kurucz 1978, if not earlier) of computing theo-
retical bolometric corrections from a grid of model atmo-
spheres for a large range of metallicities, temperatures,
and surface gravities, and then shifting all values by ar-
bitrarily setting the smallest BCV to zero. This usually
corresponds to late A-type stars of low surface gravity.3
The scale adopted by Flower (1996) is such that
BCV,⊙ = −0.080. As a result, his bolometric corrections
for stars between Teff ≈ 6400 K and Teff ≈ 8500 K (spec-
tral type approximately F5 to A5) are positive, seem-
ingly conflicting with the idea that bolometric magni-
tudes ought to be brighter than V magnitudes, accord-
ing to eq.(4). Other tables with a similar zero point as
Flower’s share the same problem. In reality, however,
the contradiction is of no consequence because of the ar-
bitrary nature of the zero point. Luminosities inferred
for stars are never affected if a consistent value of Mbol,⊙
is used, because the bolometric magnitudes are always
compared to the Sun. To see this more clearly one may
make use of
Mbol −Mbol,⊙ = −2.5 log(L/L⊙) (8)
along with eq.(4) and eq.(7) to express the luminosity
of a star in terms of its absolute visual magnitude and
3 An example of a table of theoretical bolometric corrections of-
ten used is that of Lejeune et al. (1998), mentioned above. These
authors initially followed the procedure just described, leading to
BCV,⊙ = −0.190, but then chose to adjust the zero point to pro-
vide the best fit to the BCV table of Flower (1996).
bolometric correction as
log(L/L⊙) = −0.4 [MV − V⊙ − 31.572 + (BCV −BCV,⊙)] .
(9)
Alternately, if seeking to determine the absolute magni-
tude from knowledge of the luminosity (e.g., in eclips-
ing binaries if the temperature and absolute radius are
known), one has
MV = −2.5 log(L/L⊙)+V⊙+31.572− (BCV −BCV,⊙) .
(10)
The last two equations involve only the difference be-
tween two bolometric corrections, so that the zero point
cancels out. The apparent contradiction is thus irrele-
vant since any table of BCV may be shifted arbitrarily
with no impact on the results from these expressions.
4. INCONSISTENCIES IN PUBLISHED TABLES OF
EMPIRICAL BCV
As an illustration of the confusing state of affairs
brought about by the proliferation of zero points, and
to make readers aware of the sometimes serious inconsis-
tencies lurking in these BCV sources, we examine here
several of the widely used tables of empirical bolometric
corrections and spell out their assumptions. It is not un-
common for tabular information of this kind to be copied
over from earlier sources, but assumptions are sometimes
changed along the way, so that each table has its own
problems:
• In the chapter on the Sun, the latest edition of the
popular Allen’s Astrophysical Quantities (Cox 2000, p.
341) adopts an internally consistent set of solar pa-
rameters given by BCV,⊙ = −0.08, Mbol,⊙ = 4.74,
MV,⊙ = 4.82, and V⊙ = −26.75. However, inspection
of the table of bolometric corrections for dwarfs in the
chapter on normal stars (p. 388), which is the one em-
ployed in practice, reveals that the BCV,⊙ there is −0.20
rather than the value advocated earlier. This implies
V⊙ = −26.63. Therefore, the use of this table together
with Mbol,⊙ = 4.74 will introduce a systematic error of
0.13 mag, which is the same as produced by a differ-
ence of 500 K in the input temperature. In order to
be consistent with the measured value of V⊙ = −26.76
discussed in the previous section, the bolometric magni-
tude that should be used for the Sun is Mbol,⊙ = 4.61.
An earlier edition of Allen’s Astrophysical Quantities has
inconsistencies of its own and adopts a rather different
BCV scale which, interestingly, does not have as seri-
ous a problem. For example, the solar parameters in the
3rd edition by Allen (1976) are also internally consistent,
and again use BCV,⊙ = −0.08, but with Mbol,⊙ = 4.75
(p. 162 of that work). The BCV table on p. 206, how-
ever, lists a bolometric correction for a normal star with
the solar temperature as BCV,⊙ = −0.05. Nevertheless,
if used in conjunction with the solar bolometric magni-
tude advocated, this table implies V⊙ = −26.77, which
is much more accurate than in the later edition.
• The solar values adopted by Schmidt-Kaler (1982) (p.
451) are BCV,⊙ = −0.19, Mbol,⊙ = 4.64, MV,⊙ = 4.83
and V⊙ = −26.74, which are internally consistent. Their
BCV table for main-sequence stars on p. 453 gives a
slightly different value of BCV,⊙ = −0.21 for a star of so-
lar temperature. This implies V⊙ = −26.72 rather than
their adopted value. To be consistent with V⊙ from the
previous section, the bolometric magnitude to be used

4 Torres
for the Sun is Mbol,⊙ = 4.60.
• The extensive compilation by Lang (1992) adopts the
following values for the Sun (p. 103): V⊙ = −26.78,
MV,⊙ = 4.82, and Mbol,⊙ = 4.75. The first two are
slightly inconsistent with the distance modulus of the
Sun. The last two imply BCV,⊙ = −0.07, yet the listing
of bolometric corrections on p. 138 gives BCV,⊙ = −0.20
for a star of solar temperature. According to eq.(7),
the proper value of Mbol,⊙ to use with this table is
Mbol,⊙ = 4.61. Consequently, the systematic error in-
curred by using the Lang (1992) table in combination
with their Mbol,⊙ is 0.14 mag.
• A BCV table still often used mainly in the binary star
field, is that of Popper (1980). The bolometric correction
and absolute visual magnitude adopted there for the Sun
are BCV,⊙ = −0.14 and MV,⊙ = 4.83, from which V⊙ =
−26.74. These imply Mbol,⊙ = 4.69. To be in exact
agreement with our apparent magnitude for the Sun, the
solar bolometric magnitude should be adjusted slightly
to Mbol,⊙ = 4.67.
• The BCV table in the textbook by Gray (2005) gives
BCV,⊙ = −0.09 for a star of solar temperature, and
adopts V⊙ = −26.75 (and the corresponding value of
MV,⊙ = 4.82). Together these imply Mbol,⊙ = 4.73. For
exact consistency with V⊙ from the previous section, we
recommend using Mbol,⊙ = 4.72.
• The work of Straizˇys & Kuriliene (1980) contains many
useful tables of average stellar properties, and adopts a
zero point for the BCV scale that is adjusted to give
BCV,⊙ = −0.07. These authors also adopt Mbol,⊙ =
4.72, which leads to MV,⊙ = 4.79 and V⊙ = −26.78.
Perfect agreement with our V⊙ requires Mbol,⊙ = 4.74.
• Kenyon & Hartmann (1995) presented a table of bolo-
metric corrections that is often used in the field of pre-
main sequence stars, and has been incorporated into
some model isochrones for young stars such as those
by Siess et al. (2000). It is compiled from a variety of
sources, and the zero point is such that a star of solar
temperature has BCV,⊙ = −0.21. No value of Mbol,⊙ is
specified.
• Finally, as mentioned earlier, the BCV table by Flower
(1996) gives BCV,⊙ = −0.08 for a star of solar temper-
ature, but there is no associated value of Mbol,⊙ given
in the text. For consistency with V⊙ from the previous
section, the number to be used is Mbol,⊙ = 4.73.
Table 3 summarizes the various empirical BCV scales,
along with the Mbol,⊙ values listed by each source, as well
as the Mbol,⊙ recommended here to maintain consistency
with the adopted V⊙. The systematic error introduced
when using the former instead of the latter is presented
in the last column.
5. DISCUSSION
From a practical point of view one may approach the
use of published tables of empirical BCV values in several
ways, but it is essential to always maintain consistency
with the measured brightness of the sun, V⊙. Errors
introduced when overlooking this requirement are seen
rather often in the literature, and are quantified in Ta-
ble 3. Bessell et al. (1998) chose to define Mbol,⊙ = 4.74,
from which one derives BCV,⊙ = −0.07. If one follows
this path then it is necessary to adjust the BCV table
one is using, in order to match this zero point. In general
each table will require a different offset. However, most
users find it more convenient to adopt a particular BCV
table ‘as is’, in which case care must be taken to use the
proper Mbol,⊙ as listed in Table 3, and not an arbitrary
value from another source (or even from the same source
if it is inconsistent). Yet another approach is to use eq.(9)
or eq.(10) directly, as advocated by Gray (2005), which
dispenses with having to find a formal Mbol,⊙ value, and
requires only to read off BCV for the Sun from the same
table used for the star of interest. These three approaches
are of course completely equivalent.
Somewhat surprisingly the IAU has not issued a for-
mal resolution on the matter of BCV zero points, al-
though two of its Commissions did agree at the Kyoto
meeting of 1997 (Andersen 1999, pp. 141 and 181) on
a preferred scale that is equivalent to adopting a value
for Mbol,⊙. The scale was set by defining a star with
Mbol = 0.00 to have an absolute radiative luminosity of
L = 3.055×1028 W (see also Cayrel 2002). The rationale
was that this value together with the nominal bolomet-
ric luminosity of the Sun adopted by the international
GONG project (L⊙ = 3.846× 1026 W, according to the
IAU Commission reports cited above) leads exactly to
Mbol,⊙ = 4.75, which is the bolometric magnitude for the
Sun listed in the 1976 edition of Astrophysical Quantities
(Allen 1976). This was a widely used source at the time
(and still is, by some), so it was thought to be a logical
choice. Effectively, therefore, the scale is set by this value
of Mbol,⊙. Combined with our adopted solar brightness
of V⊙ = −26.76, it implies BCV,⊙ = −0.06. As it turns
out, however, the most recent edition of Astrophysical
Quantities (Cox 2000) did not follow that recommenda-
tion, and adopted a slightly different zero point. So have
some other recent BCV compilations (see Table 3).
In practice the adoption of a value of BCV,⊙ or a value
of Mbol,⊙ may not be the most convenient way to solve
the immediate problem faced by users. The first alterna-
tive would not be of much help to those wishing to make
use of an existing BCV table, and the second would force
them to adjust the table to match V⊙. To conclude, one
may argue that it would perhaps be more useful instead
to agree on the best value for the apparent visual mag-
nitude of the Sun, which is directly measured.
I am indebted to Phillip Flower for providing
me with the correct coefficients for his BCV and
color/temperature relations, which were misprinted in
his original work (Flower 1996). They are presented here
with his permission. I also thank Gene Milone for stim-
ulating discussions and motivation for this paper, Todd
Henry for alerting me to the significant errors in BCV for
cool stars, and the anonymous referee for helpful com-
ments. Correspondence with Martin Asplund, Dainis
Dravins, Arlo Landolt, Pedro Mart´ınez, Gene Milone,
and Chris Sterken regarding IAU deliberations on the
matter of BCV is also acknowledged. This work was
partially supported by NSF grant AST-0708229. The re-
search has made use of NASA’s Astrophysics Data Sys-
tem Abstract Service.
REFERENCES
Allen, C. W. 1976, Astrophysical Quantities, 3rd Ed. (London:
The Athlone Press)
Andersen, J. 1999, Proceedings of the Twenty-Third General
Assembly, Transactions of the IAU, Vol. XXIIIB (Dordrecht:
Kluwer)

Bolometric corrections 5
TABLE 3
Empirical BCV scales and Mbol,⊙ values from the literature
Advocated Actual Adopted Recommended
BCV,⊙ BCV,⊙ Mbol,⊙ Mbol,⊙ Error
Source (mag) a (mag) b (mag) c (mag) d (mag) e
Cox (2000) −0.08 −0.20 4.74 4.61 +0.13
Allen (1976) −0.08 −0.05 4.75 4.76 −0.01
Schmidt-Kaler (1982) −0.19 −0.21 4.64 4.60 +0.04
Lang (1992) −0.07 −0.20 4.75 4.61 +0.14
Popper (1980) −0.14 −0.14 4.69 4.67 +0.02
Gray (2005) · · · −0.09 4.73 4.72 +0.01
Straizˇys & Kuriliene (1980) · · · −0.07 4.72 4.74 −0.02
Kenyon & Hartmann (1995) · · · −0.21 · · · 4.60 · · ·
Flower (1996) · · · −0.08 · · · 4.73 · · ·
a Value that each source states to have adopted as the zero point of their BCV scale.
b Value read off from the relevant BCV table for each source.
c Bolometric correction for the Sun adopted by each source.
d Mbol,⊙ value required for consistency with V⊙ = −26.76 (Sect. 3), when using the BCV table as
published.
e Error incurred when using the published BCV table combined with Mbol,⊙ from the source,
instead of the recommended Mbol,⊙ value in the previous column.
Bessell, M. S., Castelli, F., & Plez, B. 1998, A&A, 333, 231
Buser, R., & Kurucz, R. L. 1978, A&A, 70,555
Casagrande, L., Portinari, L., & Flynn, C. 2006, MNRAS, 373, 13
Cayrel, R. 2002, in Observed HR diagrams and stellar evolution,
ASP Conf. Ser. 274, eds. T. Lejeune & J. Fernandes (San
Francisco: ASP), p. 133
Colina, L., Bohlin, R. C., & Castelli, F. 1996, AJ, 112, 307
Cox, A. N. 2000, Allen’s Astrophysical Quantities, 4th Ed.
(Berlin: Springer)
Flower, P. J. 1977, A&A, 54, 31
Flower, P. J. 1996, ApJ, 469, 355
Galloue¨t, L. 1964, An. Ap., 27, 423
Gray, D. F. 2005, The Observation and Analysis of Stellar
Photospheres (Cambridge: CUP), p. 506
Green, E. M., Demarque, P., & King, C. R. 1987, The Revised
Yale Isochrones and luminosity Functions (New Haven: Yale
Univ. Obs.)
Hayes, D. S. 1985, in IAU Symp. 111, Calibration of Fundamental
Stellar Quantities, eds. D. S. Hayes et al. (Reidel: Dordrecht),
p. 225
Kenyon, S. J., & Hartmann, L. 1995, ApJS, 101, 117
Lang, K. R. 1992, Astrophysical Data: Planets and Stars (New
York: Springer-Verlag)
Lejeune, Th., Cuisinier, F., & Buser, R. 1998, A&A, 130, 65
Martynov, D. Ya. 1960, Soviet Ast., 3, 633
Morales, J. C., Ribas, I., Jordi, C., Torres, G., Gallardo, J.,
Guinan, E. F., Charbonneau, D., Wolf, M., Latham, D. W.,
Anglada-Escude´, G., Bradstreet, D. H., Everett, M. E.,
O’Donovan, F. T., Mandushev, G., & Mathieu, R. D. 2009,
ApJ, 691, 1400
Nikonova, E. K. 1949, Izv. Krymsk. Astrofiz. Observ., 4, 114
Pietrinferni, A., Cassisi, S., Salaris, M., & Castelli, F. 2004, ApJ,
642, 797
Popper, D. M. 1980, ARA&A, 18, 115
Prsˇa, A., & Zwitter, T. 2005, ApJ, 628, 426
Ribas, I. 2003, A&A, 398, 239
Schmidt-Kaler, Th. 1982, in Landolt-Bo¨rnstein, Numerical Data
and Functional Relationships in Science and Technology, Vol. 2,
eds. K. Schaifers & H. H. Voigt (Berlin: Springer)
Siess, L., Dufour, E., & Forestini, M. 2000, A&A, 358, 593
Stebbins, J., & Kron, G. E. 1957, ApJ, 126, 266
Straizˇys, V., & Kuriliene, G. 1980, Ap&SS, 80, 353
Thuillier, G., Floyd, L., Woods, T. N., Cebula, R., Hilsenrath, E.,
Herse´, M., & Labs, D. 2004, Adv. Space Res., 34, 256
Yi, S. K., Demarque, P., Kim, Y.-C., Lee, Y.-W., Ree, C. H.,
Lejeune, T., & Barnes, S. 2001, ApJS, 136, 417