Basic Astronomical Data for the Sun (BADS?)

Eric Mamajek 
University of Rochester
Department of Physics & Astronomy

last updated 4 September 2009

list of updates at bottom
________________________________________ 

This is a list of fundamental values adopted for the Sun. I am not a
solar astronomer, but I occasionally need a solar value time and again
for my calculations. If you do not like the values that I have
adopted, feel free to email me and justify why I should adopt a
different value. 

I have not had time to properly include complete bibliographic
information -- usually I list just the author and a year. The correct
references can be easily retrieved using the author name and year from
the Smithsonian/NASA ADS server at:
http://adsabs.harvard.edu/abstract_service.html

In addition to the data, I've included a discussion on a
parameterization of the luminosity evolution of the Sun
from the ZAMS through the end of its Main Sequence stage.

Here is an overview of the constants that I adopt, followed by
a brief discussion of each. - EEM 

####################################################################
# Apparent V Magnitude:               V = -26.75 mag
# Absolute V Magnitude:             M_V =  4.82 mag
# Solar Color:                    (B-V) =  0.65 mag
# Absolute B Magnitude:             M_B =  5.47 mag
# Bolometric Correction:            BCv = -0.07 mag
# Absolute Bolometric Magnitude:   Mbol =  4.75 mag
# Angular Photospheric Radius:       Ro =  959".680 +- 0".018 
# Photospheric Radius:                R =  695508 +- 26 km
# Spectral Type:                    SpT =  G2V
# Effective Temperature:           Teff =  5778 K = 10^3.7618 K 
# Heliocentric Grav. Constant        GM =  1.32712440018e20 m^3 s^-2
# Solar Mass:                         M =  1.98842e30 kg = 10^33.29851 g
# Moment of Inertia:                  I =  5.96e47 kg m^2 = 5.96e53 g cm^2
# Inertia Constant:                   k =  0.062 = I/MR^2
# Astronomical Unit:                 AU =  149597870700 +- 3 m
# Mean Earth-Sun Distance:          <r> =  149618753000 m 
# Solar Flux Constant:          S(@1AU) =  1366 W/m^2 
# Luminosity:                     L_bol =  3.842e33 erg/s = 10^33.585 erg/s
# Mt. Wilson S-value:              S_MW =  0.176
# Chromospheric Activity        logR'HK = -4.905 dex
# X-ray Luminosity (0.1-2.4 keV)    L_X =  2.24e27 erg/s = 10^27.35 erg/s
# X-ray Surface Flux (0.1-2.4 keV)  f_X =  36800 erg/s/cm^2 = 10^4.566 erg/s/cm^2
# X-ray/Bol. Ratio       log(L_X/L_bol) =  -6.24
# Age(Solar System)                   t =  4572 +- 5 Myr = 10^(9.6601+-0.0005) yr
# Surface Metal Fraction:             Z ~  0.013-0.018?
# Equatorial Rotation Period:         P =  25.38 days
# Mean Rotation Period:             <P> =  26.09 days
# Mean Solar Wind Mass Loss:    <dM/dt> =  2e-14 Msun/yr
# Median Daily Int'l Sunspot #:   <ISN> =  40        (years 1818-2008)
####################################################################

#############################################
# Apparent V Magnitude: V(Sun) = -26.75 mag  
#############################################

This value varies slightly in the literature. Here are various quoted
values summarized in Bessell, Castelli, & Plez (1998, A&A 333, 231;
Table A4), plus Cox 2000. These are mostly from review articles, and
so not primary references:

Vmag
-26.70  Durrant81 (Landolt Bornstein vol VI/2A, p.82)
-26.74  Allen76 (Astrophysical Quantities)
-26.74  Schmidt-Kaler82 (Landolt Bornstein, Num. Data..., Vol 2, p.451)
-26.75  Cox00 (Allen's Astrophysical Quantities, 4th Ed., p.341)
-26.76  Bessell+98 (A&A 333, 231)
-26.78  Lang91 (Astrophysical Data: Planets and Stars, p.103)

Bessell has found that some quotes combinations of V, Mv, Mbol, and BC
from some authors are not mutually consistent. 

Two important papers from the mid-1980s on the subject appear to given
consistent values. 

-26.75 +- 0.025 mag ; Neckel (1986; A&A 159, 175; synthetic photometry)
-26.75          mag ; Hayes (1985; IAU Symp. 111, 225; synthetic photometry)
-26.75 +- 0.06  mag ; Hayes (1985; IAU Symp. 111, 225; direct estimate)

The Hayes (1985) mean of published "direct" Vmag estimates comes from
Nikonova (1949), Stebbins & Kron (1957), and Gallouert (1964).  Both
the Hayes (1985) and Neckel (1986) "synthetic" estimates assume that
V=0.03 mag for Vega. 

As V(Sun) = -26.75 mag is favored by Hayes85, Neckel86, and adopted in Cox00
in the modern edition of Allen's Astrophysical Quantities, I'm inclined to 
adopt this value. 

############################################
# Absolute V Magnitude: Mv(Sun) = 4.82 mag 
############################################

This value varies slightly in the literature. Here are various quoted
values summarized in Bessell, Castelli, & Plez (1998, A&A 333, 231;
Table A4).

Mv 
4.81  Bessell+98 (A&A 333, 231)
4.82  Lang91 (Astrophysical Data: Planets and Stars, p.103)
4.82  Cox00 (Allen's Astrophysical Quantities, 4th Ed., p.341)
4.83  Allen76 (Astrophysical Quantities)
4.83  Schmidt-Kaler82 (Landolt Bornstein, Num. Data..., Vol 2, p.451)
4.87  Durrant81 (Landolt Bornstein vol VI/2A, p.82)

Bessell has found that some quotes combinations of V, Mv, Mbol, and BC
from some authors are not mutually consistent.

Note that the distance modulus for the Sun is constant, independent
of what particular value you adopt for the AU in physical units.
The distance modulus for 1 AU will always be (m-M) = -31.5721. 

So the absolute magnitude of the Sun is set by the adopted Vmag for the
Sun. I have adopted Vmag(Sun) = -26.75 based on the values from Hayes85,
Neckel86, and the value adopted by Cox00 (Allen's Astrophysical Quantities).

Hence, I adopt Mv = -26.75 - (-31.5721) 
               Mv =  4.8221  
               Mv =  4.82 (correct sig. figures)

######################################
# Solar Color (B-V)o(Sun) = 0.65 mag  
######################################

Here is sorted list of recently published solar B-V values. It is
probably not exhaustive, but it should be fairly representative of the
quoted values. As you can see, even if you don't like a few of the
published values, it will have a negligible effect on the median
value.

B-V(Sun) reference
0.626  Sekiguchi00
 0.628  Taylor98
  0.63   Tayler94 
   0.63   Colina96
    0.642  Cayrel96
     0.642  Holmberg+05 (+-0.016)
      0.648  Gray95  (+-0.006)
       0.649  Colina96 (as cited by Bessell98)
        0.649  Pasquini08 (+- 0.016)
         0.650   Neckel86 (+-0.005)
          0.650  Cox+2000  <= MEDIAN
         0.651  Freil93 (+-0.008)
        0.652  Cayrel96 (as cited by Bessell98, Table 6 analog)
       0.656  Gray92 (+-0.005)
      0.66   Wamsteker81
     0.661  Valenti05(relation,used Teff=5778K)
    0.665  Hardorp80
   0.667  Bessell98 ("Sun-Nover")
  0.679  Bessell98 ("Sun-over")
 0.68   Lang+92
0.686  Tug & Schmidt-Kaler 1982

* B-V colors of Gray et al. G2V stars: 
The nearby star survey of Gray et al. (2003,2006) lists a total of 44
G2V stars. Using Hipparcos B-V colors, I find a median B-V
0.648+-0.001 mag, and Chauvenet-clipped mean B-V = 0.641+-0.006 mag
(N=42, 2 clipped).  The sample has Chauvenet mean Teff = 5766+-11 K,
so close to the solar value, and median [M/H] = -0.09.

* B-V colors of G2V stars from Houk and listed in Hipparcos: Most of
the stars classified as "G2V" in the Hipparcos catalog are taken from
the Michigan Spectral Survey catalogs published by N. Houk and
colleagues.  For the 265 stars classified as "G2V" in the Hipparcos
catalog with parallaxes of >13.33 mas (distance < 75 pc; i.e.
probably within the Local Bubble with negligible reddening) and
parallax errors of <12.5%, the median and mean (regular, probit, and
Chauvenet-clipped) values of B-V *all* converge towards 0.620+-0.003
mag, with a standard deviation of ~0.03 mag. Hence, among the
Houk/Hipparcos G2Vs, the Sun appears to be ~1 sigma redder than the
typical G2V in the field (for (B-V)sun = 0.65, 83% of G2Vs are bluer,
17% are redder). 

Hence, there appear to be subtle differences between what stars are
classified as G2V by Gray vs. those of Houk. This may be due to MK
"standards" which appeared to have changed by 1-2 subtypes over the
years as the MK system aged (notably eta Cas [G0V ~> F9V] and beta Com
[Morgan, Keenan, and Gray call G0V, but Houk calls G2V]. These subtle
changes among the standards may be responsible for the color offset
between the Houk/Hipparcos <B-V> for G2V stars, and that measured for
the Gray et al. G2V stars.

* Brian Skiff has written a memo with useful data
tables and references on "Near-Solar MK Standards and Photometric Standards of
Similar Color" at: ftp://ftp.lowell.edu/pub/bas/starcats/solar.list

############################################
# Absolute B Magnitude: Mv(Sun) = 5.47 mag  
############################################
I simply calculate this from the adopted values for Mv and B-V:
M_B = M_V + (B-V) = 4.82 + 0.65 = 5.47 mag

########################################################
# Bolometric Correction:         BCv(Sun)  = -0.07 mag  
# Absolute Bolometric Magnitude: Mbol(Sun) =  4.75 mag  
########################################################

WARNING! Different authors have different ways of setting the
zero-point for their bolometric correction and bolometric magnitude
scales.  I recommend reading Appendix D of Bessell, Castelli, & Plez
(1998; A&A 333, 231) for a more detailed discussion. If you mix and
match systems, you can systematically affect the stellar luminosities
that you calculate (which can affect the ages and masses you infer
from putting stars on theoretical isochrones; and possibly deny you
tenure!). Since the Bessell et al. 1998 paper was published, however,
two IAU commissions have agreed upon a zero point flux for the
bolometric magnitude scale (see below).

Kurucz (1979; ApJS, 40, 1) set the zero-point of his bolometric
correction scale for the object which had the minimum bolometric
correction in his suite of stellar models: a Teff=7000, log(g) = 1.0
model. On this system, the bolometric correction for the Sun (Teff ~
5780K) is BCv = -0.194. One sometimes sees authors use this scale. 

Bessell, Castelli, & Plez (1998) adopt a consistent system where
V(Sun) = -26.76, and the solar bolometric magnitude is *defined* as
Mbol = 4.74. This gives a bolometric correction of BCv(Sun) = -0.07.

IAU Commissions 25 (Stellar Photometry and Polarimetry) and 36 (Theory
of Stellar Atmospheres) adopted a zero point in 1999 for the
bolometric luminosity scale, where M_bol = 0 corresponds to a absolute
bolometric luminosity of L = 3.055e28 W. From the text from IAU
Commission 36 attributed to Cram & Pallavicini, "This choice is
intended to be close to the most current practice, and its equivalent
to taking the value M_bol = 4.75 (C. Allen, "Astrophysical
Quantities") for the nomical bolometric luminosity adopted for the Sun
by international GONG project (L_Sun = 3.846e26 W)." The choice of
constant also dethrones the Sun (a variable, evolving, and
surprisingly poorly calibrated source of luminosity!) as the defining
body for the bolometric magnitude and luminosity scale. 

Using the IAU zero point for the bolometric luminosity scale, and
the solar luminosity that I calculated (adopting solar constant of 
1366 W/m^2 and AU = 149597870700 m => L_Sun = 3.842e33 erg/s), then
the bolometric magnitude of the Sun becomes:

M_bol(Sun) = 4.751 mag
           = 4.75 mag (correct sig. figures)

As I have adopted V = -26.75 and Mv = 4.82, then the bolometric
correction of the Sun will be defined as:

BC_V(Sun) = -0.071 mag
          = -0.07 mag (correct sig. figures)

Hence, if one adopts the IAU bolometric flux zero point constant, and
M_bol(Sun) = 4.75, then one should make sure that one's choice of
bolometric correction relations as a function of stellar Teff (and/or
other variables) is calibrated to BC_V(Sun) for the solar Teff and/or
color.

#######################################
# Radius: R(Sun) = 959".680 +- 0".018  
# Radius: R(Sun) = 695508 +- 26 km     
#######################################

Here is a non-exhaustive list of quoted angular radii for the Sun:

959".63   +- 0".10  ; Auwers 1891 AN 128, 361 (diam = 1919".26 +- 0".10)
959".63   +-        ; Allen 1963 (Astrophys. Quan. 2nd Ed.)
959".53   +- 0".06  ; Sofia+ 1994
959".62   +- 0".03  ; Neckel+ 1995
959".58   +- 0".05  ; Laclare+ 1996
959".73   +- 0".05  ; Wittmann 1997
959".6795 +- 0".018 ; Brown & Christensen-Dalsgaard 1998 ApJ 500, L195 (D=1919".359)
959".64   +- 0".02  ; Chollet & Sinceac 1999 A&AS 139, 219
959".63   +-        ; Cox 2000 (Allen's Astrophys. Quan. 4th Ed; rad = 959".63)
959".03   +- 0".07  ; Golbasi+ 2000 (A&A 368, 1077)
959".52   +- 0".03  ; Emilio & Leister 2005 MNRAS 361, 1005 (visual data)
959".61   +- 0".05  ; Emilio & Leister 2005 MNRAS 361, 1005 (CCD data)

Surprisingly, Cox 2000 quotes the physical radius from Brown &
Christensen-Dalsgaard 1998, but not their angular radius. Cox 2000
quotes an oblateness as the semidiameter equator-pole difference as
0".0086. Golbasi+ 2000 contains a table of many previously published
angular solar radius measurements.

Djafer, Thuillier, & Sofia (2008; ApJ 676, 651) cross-analyze a few
solar diameter datasets and confirm that there are (unsurprisingly)
systematic differences between measurements from different
instruments. They conclude that once systematic effects are taken
account of (plausibly modeled by the authors), the Calern, SDS, and
MDI angular radii for the Sun are consistent within their quoted
errors. Their re-analysis of the three datasets give corrected
estimates of: 

959".705 +- 0".150 (MDI data; Djafer+ 2008) 
959".811 +- 0".075 (Calern data; Djafer+ 2008) 
959".898 +- 0".091 (SDS data; Djafer+ 2008)

Djafer et al. do not estimate a mean value.  Calculating an unweighted
mean of these three estimates gives: 
959".805 +- 0".056 (mean)

Here are some recently quoted values for the apparent photospheric
solar radius (by no means exhaustive).

Rsun  
695508 +-  26 km  Brown & Christensen-Dalsgaard 1998 (adopted by Cox 2000) 
695680 +- 300 km  Schou et al. 1997 (helioseismic)
695740 +- 110 km  Kuhn et al. 2002 (SOHO MDI experiment)
695990            Allen 1973 (Astrophysical Quantities, 3rd Ed.)

I follow Cox 2000 (Allen's Astrophysical Quantities, 4th Ed.), and
adopt the value from the Solar Diameter Monitor from Brown &
Christensen-Dalsgaard (1998).

######################
# Spectral Type: G2V  
######################

G2V   ubiquitous

The integrated solar spectrum (as inferred from reflection spectra of
bodies like the moon, Uranus, Callisto, etc.) is *the* G2V standard or
"dagger type" of the MK system (Morgan & Keenan 1973; Houk 1988;
Garrison 1994).

The Sun's spectral type varies as a function of angle from the
limb, from roughly ~G0 near the center to ~K0 near the limb. 
Morgan & Keenan (1939) listed the following spectral types
as a function of distance from center of the Sun. The spectral
types are on the "MW" system, which, given the authorship of the
paper, can be construed as "Morgan-Keenan" system. 

Distance  Spectral
from      Type
Center    (MW system)   Teff
_____________________________
Center    G1            5990K
0.750R    G4            5720K
0.945R    G9p^1         5070K
0.985R    K0p^2         ..... 

(1) Spectral type determined from ratio Fe4045/Hdelta; the strong
metallic arc lines are weaker than in a G9 dwarf.

(2) Metallic arc lines and Ca+ are much weaker than in a K0 dwarf.
Spectral type determined from ratio Fe4045/Hdelta. The H-lines are
very weak.

I have been unable to find out why the Sun was called "G2" instead of
"G0" or "A1" or "obviously the best spectral type in the universe",
but rumor has it that God mentioned it to Aaron somewhere deep in the
passages of Leviticus.

########################################
# Effective Temperature: Teff = 5778 K  
########################################

5777 K  Cox 2000 (Allen's Astrophysical Quantities, 4th Ed.)
5781 K  Bessell et al. 1998 A&A 333, 231

If one takes the luminosity calculated from the median solar
irradiance from Frohlich & Jean (see below), the JPL DE405 ephemeris
astronomical unit (which lead to Lsun = 3.8416e33 erg/s), the Brown &
Christensen-Dalsgaard solar radius, and use the CODATA 2006 value for
the Stefan-Boltzmann constant sigma (sigma_SB = 5.670400e-8
W/m^2/K^4), I derive

Teff = ((S*4*pi*AU^2)/(4*pi*Rsun^2)/sigma_SB)^(1/4) 
     = ((Lsun/(4*pi*Rsun^2))/sigma_SB)^(1/4)
     = 5777.91 K 
     ~ 5778 K

This is only a degree cooler than the Cox (2000) value. 

#############################################################
# Solar Mass: M(Sun) = 1.98842e30 kg                          
# Solar Gravitational Constant = 1.32712440018e20 m^3 s^-2   
#############################################################
Cox 2000 (Allen's Astrophysical Quantities, 4th Ed.) lists
Msun = 1.989e30 kg 

Historical values: 

Heliocentric Gravitational Constant (GMsun) values:
1.32712438   e20 m^3 s^-2 (IAU 1976 constant)
1.32712440   e20 m^3 s^-2 (Cox 2000)
1.32712440018e20 m^3 s^-2 (DE405 ephemeris; Klioner 2005 astro-ph/0508292)

In "SI" units, the same constant varies a bit:
1.32712442076e20 m^3 s^-2 (Kovalenvsky & Seidelmann 2004,SI)
1.3271244208 e20 m^3 s^-2 (DE405 ephemeris; Klioner 2005 astro-ph/0508292, SI)

The CODATA 2006 value for Newtonian constant G 
(also adopted by 2009 IAU resolution) is:
6.67428e-11 m^3 kg^-1 s^-2 (1e-4 uncertainty)
http://physics.nist.gov/cgi-bin/cuu/Value?bg

Adopting the CODATA 2006 value for G, and the standard solar GM from DE405,
we calculate: M(Sun) = GMsun/G = 1.98842e30 kg,
where the uncertainty is completely dominated by the uncertainty in G (~1e-4).

Amusingly, the minor change in the CODATA recommended value of the
Newtonian Gravitational Constant "G" between 2002 and 2006 effectively
resulted in the Sun "losing" 2e25 kg of mass, or roughly 4 Earth
masses!

##################################################################
# Moment of Inertia          I = 5.96e53 g cm^2 = 5.96e47 kg m^2  
# Inertia Constant           k = 0.062                            
##################################################################

The moment of inertia is calculated by integrating int(r^2 dm) from
the core to the surface. Moment of inertia is usually parameterized
by the form I = k M R^2.

Given our adopted solar mass (1.98842e30 kg) and radius (695508 km),
the product of (M R^2) = 9.61861e54 g cm^2 = 9.61861e47 kg m^2

Allen's Astrophysical Quantities quotes I = 5.7e53 g cm^2 (implying k = 0.059)

The value estimated for a 1 Msun solar metallicity star 
from the Lyon models (assuming mixing length = pressure scale height) 
is k = 0.062 (implying I = 5.96e53 g cm^2 = 5.96e46 kg m^2). 

Here is a list of quoted k-values:
0.059         Allen's Astrophysical Quantities (Cox 2000)
0.06          Moons & Planets, 5th Edition, W.K. Hartmann (2005, p. 198)
0.062         Lyon models

I've adopted the k-value and MOI inferred from the Lyon models. 

###########################################################
# Distance = Astronomical Unit (AU) = 149597870700 +- 3 m  
# Mean Earth-Sun Distance       <r> = 149618753000 m       
###########################################################

The astronomical unit is that length for which the heliocentric
gravitational constant (GM_Sun) is equal to (0.01720209895)^2
AU^3/d^2, where the mean sidereal motion of the Earth's orbit is
0.01720209895 radians per day. This Gaussian gravitational constant
(0.0172...) was originally defined by Simon Newcomb (1895) in "Tables
of the Motion of the Earth on its Axis and Around the Sun". This
constant has remained so now for over a century.

I've split discussion on the AU into three sections: 

I: Pre-2009 values for the astronomical constant
II: The 2009 IAU value for the astronomical constant
III: Notes on the astronomical constant

The astronomical unit is perhaps best thought of a convenient
"yardstick" rather than a true "constant" as the sun is losing mass
via nuclear reactions (via photons and neutrinos) and the solar wind
(via hot coronal plasma escaping the solar system). The predicted
change in the AU due to these known mechanisms results in +0.3
meter/century (Krasinsky & Brumberg 2004, Celestial Mechanics and
Dynamical Astronomy, 90, No. 3-4, p. 267). The semi-major axis of the
Earth's orbit may also vary due to subtle interactions between the
planets, asteroids, comets, etc. Indeed, there is some evidence for a
(at least recent) trend where the AU is increasing at the ~7-15
meters/century level (Krasinsky & Brumberg 2004; Standich 2004).  If
this trend is significant, a perusal of the literature suggests that
the bulk of the motion is not as yet satisfactorily explained.


___

I: Pre-2009 values for the astronomical constant

Here is a list of some pre-2009 published values for the AU:

149597870000            m  IAU 1976 constant (standard value)
149597870660            m  IAU 1976 value used in preparing ephemerides (not clear why different)
149597870660    +- 2    m  JPL DE118/LE118 (DE200/LE200), Seidelmann 1992
149597870691            m  JPL DE403 (1995), 
                           IAA's EPM2000, 
                           IERS2003 values 
149597870691    +- 3    m  DE405 (1997)
149597870698    +- 2:   m  Standich (2004; IAU 196, p. 163; see below)
149597870696.0  +- 0.1  m  EPM2004 (Pitjeva 2005)
149597870697    +- 1    m  DE410 
149597870700.8  +- 0.15 m  DE414 (Standich 2006)
149597870699.6  +- 0.15 m  DE421
149597870695.4  +- 0.1  m  EPM2008 (Pitjeva 2008)
149597870699.22 +- 0.11 m  INPOP2008 (Fienga et al. 2009)
149597870700    +- 3    m  Pitjeva & Standich (2009; proposal to IAU
                           Working Group on Numerical Standards for  
                           Fundamental Astronomy)

Table 2 of Fienga et al. 2009 summarizes recent results regarding
estimation of the astronomical unit and some other physical parameters
for planetary ephemerides. The Fienga et al. 2009 value is fitted by
adopting the GM_sun value from DE405. The paper can be found at:
http://www.imcce.fr/fr/presentation/equipes/ASD/inpop/
Pitjeva (2005) tabulates the recent ephemeris updates and what new data
was included in the new analyses. 

Standish (2004, "Transits of Venus: New Views of the Solar System and
Galaxy, IAU 196, p. 163) reports that "The recent addition of the MGS
and Odyssey ranges tend to indicate a value for the au which is a
couple of meters shy of 149,597,870,700 m", and lists 149,597,870,698
with a ~2 meter uncertainty (in Q&A discussion after paper).

II: The 2009 IAU value for the astronomical unit

Pitjeva & Standich (2009; Celestial Mechanics and Dynamical Astronomy,
103, 365) "proposed the... astronomical unit in meters obtained from
the ephemeris improvement processes at JPL in Pasadena and at IAA RAS
in St. Petersburg... AU = 149597870700(3) m." 

On 13 Aug 2009, the XXVIIth General Assembly of the IAU at the meeting
in Rio de Janeiro, passed resolution B2, which adopted a set of
current best estimates for astronomical constants proposed by the IAU
Working Group on Numerical Standards for Fundamental Astronomy (NSFA
WG).  The table of adopted constants is at:

http://maia.usno.navy.mil/NSFA/CBE.html

The 2009 IAU value for the astronomical constant was adopted directly
from Pitjeva & Standich (2009): a = 149597870700+-3 m.

III: Notes on the astronomical unit

Note that one finds the AU quoted in two conventions: based on
barycentric dynamical time (TDB) and "SI" (calculated for a
hypothetical observer measuring proper length and proper time at the
solar system barycenter). To my knowledge, all values listed are TDB
values.

Note that the AU is *not* the mean distance between the Earth and Sun!

One must take into account the fact that a planet will spend a longer
portion of its orbit near aphelion and shorter time near perihelion.
The *mean distance* is then (Standish 2004, D. Williams 2003):

<r> = a(1+e^2/2)

Where a is the semi-major axis, and e is the mean eccentricity.
(e_Earth = 0.016708617; IAU 1976 value). From the adopted 
value for AU and e_Earth, I estimate

<r> = 149618753000 m (with uncertainty in the last four digits)

##############################################
# Solar Flux Constant: S(1AU) = 1366 W/m^2  
##############################################

1365.5    W/m^2  Brusa 1983 (Publ. Phys.-Meteorol. Obs. Davos, No. 598)
1367      W/m^2  Frohlich 1983 (Publ. Phys.-Meteorol. Obs. Davos, No. 599)
1367.2976 W/m^2  Tobiska 2002 (Adv. Space Res. 29, 1969)
1368.2    W/m^2  Willson 1982 (The Symp. on the Solar Constant..., p.3)
1372.7    W/m^2  Hickey et al. 1982 (The Symp. on the Solar Constant..., p.10)

1365-1369 W/m^2  Cox 2000 (error in units)

I found several of the published values in Neckel (1986; A&A 159, 175). 

There is a table of total solar irradiance data that is regularly
updated by Frohlich and Jean which can be downloaded from the NGDC at:
http://www.ngdc.noaa.gov/stp/SOLAR/ftpsolarirradiance.html#composite

From their dataset for the Sun from Nov. 1978-Oct. 2003, 
I find that the total solar irradiance (TSI) has the
following statistics, based on 8405 measurements
(all in W/m^2):

median = 1365.922 
mean   = 1366.001 (unweighted)
mean   = 1366.003 (Chauvenet clipped; N=8 data points clipped)

and "dispersion statistics": 
       68%CL  = +0.705 -0.444 (+-0.574) 
probit st.dev =  +-0.552 (from probability plots)

I do not list the standard error or error in the true median, as the
uncertainties are no doubt dominated by the absolute calibration. Note
that they already normalize the data to 1AU, and the flux is
calibrated to the SARR: Space Absolute Radiometer Reference.

Frohlich et al. (2006, Nature 443, 161) lists an average solar 
irradiance at solar minimum of 1365+-0.009 W/m^2, with the irradiances
from one solar minimum to another during 1978-2005 only varying in
their average minima by +-<0.09 W/m^2. 

The unweighted mean, clipped mean, and median are all very close,
so I would adopt 1366 W/m^2

######################################
# Luminosity: Lsun = 3.842e33 erg/s  
######################################

3.845e33 erg/s  Cox 2000
3.846e33 erg/s  GONG project value (IAU Commission 36; Andersen, Trans. IAU, 1999)

Using the mean total solar irradiance from the 1978-2003 dataset from
Frohlich & Jean (1366 W/m^2), and the 2009 IAU value for the astronomical
unit (149597870700 m), I estimate:

L(Sun) = S*4*pi*AU^2 = 3.842e33 erg/s = 3.842e26 W

This is only 0.09% lower than that from Cox (2000), and 0.10% lower
than that from value adopted by the GONG project.  I do not quote an
uncertainty here. The uncertainty in the 2009 IAU definition of the AU
is +-3 meters, however it is not clear to me of what order the errors
are in the solar flux constant (likely dominated by instrumental
calibration errors).

The luminosity in log10 cgs units is then: 
log(L_(Sun,bol)) = 33.585 (in erg/s) 

#################################################
# Main Sequence Luminosity Evolution of the Sun  
#################################################

I have not seen a useful formula for the luminosity evolution
of the Sun during its main sequence phase. So I estimate one here.

The estimate of the luminosity vs. time comes from a 1 solar mass
model from the Yale-Yonsei evolutionary tracks, where I adopted
Z=0.0181 (their recommended solar value) and [alpha/Fe]=0.0. 

Between an age of 45 Myr (when the Sun reached the Zero-age main
sequence, a luminosity minimum) and 11.1 Gyr (the end of the main
sequence stage), one can approximate the luminosity of the Sun as:

log10(L/Lsun,now) = a0 + a1*(t/Gyr) + a2*(t/Gyr)^2 + a3*(t/Gyr)^3

where the coefficients are:
 a0 = -0.152212064  
 a1 =  0.0400317 
 a2 = -0.002721567   
 a3 =  2.745474E-4

Note that I rescaled the actual Y^2 track by ~0.01 dex so as to force 1
solar luminosity at age 4.567 Gyr.

Here are the inferred normalized solar luminosities at
some interesting points in the Sun's life:

             L/Lsun(now)  Time         Notes
Runaway GH   1.410     3730 Myr future "Runaway Greenhouse limit" (Kasting+1993)
10% brighter 1.100     1210 Myr future "Water loss limit" (Kasting+1993)
Now          1.000        0 Myr ago    This is now, now 
K/T boundary 0.995       65 Myr ago    Asteroid 1, Dinosaurs 0
P/T boundary 0.982      251 Myr ago    The Great Dying
Cryogenian   0.947     ~750 Myr ago    Snowball Earth epoch ~850-630 Myr ago?
First life   0.750     3850 Myr ago    Evidence of life in Greenland rocks?

#####################################################
# Mt. Wilson S-value:                S = 0.1762      
# Chromospheric Activity Index logR'HK = -4.905 dex  
#####################################################

S_MW 
0.179  Baliunas+1995 (~1966-1993; cycle 20,21,22)
0.170  Hall+2007 (~1994-2006; cycle 23)
0.1762 Baliunas+95 & Hall+07 year-weighted mean (1996-2006)***

Using equations from Noyes et al. 1984
for B-V=0.650, S=0.1762 => logR'HK = -4.905 (1966-2006)

Donahue (1998; Cool Stars, Stellar Systems, and the Sun, ASPC
Vol. 154) provides the following table of representative activity
levels (Mt. Wilson S-values; Ca H&K emission lines) for the Sun:

Epoch                       Smean  Est.     log
                                  Age(Gyr)  R'HK
Activity Maximum (Cycle 22) 0.205  2.5     -4.780
Mean Activity (Cycle 20-22) 0.182  3.5     -4.877
Mean Activity (Cycle 20)    0.171  4.5     -4.932
Activity Cycle Minimum      0.165  5       -4.966
Maunder Minimum             0.145  8       -5.102  

The "estimated age" would be the age inferred from the Sun's Ca HK
activity index via the R'HK-to-age calibration in Donahue's thesis
(1993; NMSU; also listed in the 1998 Cool Stars conference
proceedings).  I calculated the last column from Donahue's Mt.  Wilson
S-values following Noyes et al. 1984 and assuming B-V(Sun)=0.65 (Cox
2000; median of 19 published values).

The estimated activity during the Maunder minimum (~1645-1715)
(logR'HK = -5.10) was estimated by Baliunas & Jastrow (1990; Nature
348, 520), which they quote as Mt. Wilson S-value ~ 0.145.

Radick et al. (1998; ApJS 118, 239; Sec. 3.2.2) combined data from the
Mt. Wilson survey and the NSO/Kitt Peak K-index data, and found that
the typical mean activity level for the Sun near solar minimum is S =
0.169.  For adopted solar color (B-V=0.65 mag), this converts to
<logR'HK(solar minimum)> = -4.943.

Keil, Henry, & Fleck (1998; ASPC 140, 301) present NSO/Kitt Peak
K-index data on Solar cycles 21 and 22. I convert their K-index data
to logR'HK following the K-index-to-Mt. Wilson S-index conversion of
Radick et al. (1998), and the Mt. Wilson S-index to logR'HK conversion
of Noyes et al. (1984). The extrema measured during these two cycles
correlated with logR'HK = -4.804 (Cycle 22 peak) and -4.958 (Cycle 22
minimum).

Baliunas & Jastrow (1990; Nature 348, 520) says that the Mt Wilson
S-value for the Sun "ranges between 0.164 and 0.178 during the 11-year
sunspot cycle (cycle 20) and averages ~0.171 (Wilson 1978)." Using the
Noyes et al. 1984 conversion, and adopting B-V(Sun)=0.65, I estimate
these three S-values to correspond to logR'HK=-4.972, -4.896, -4.932.
They define a "Maunder minimum" star as a star "exhibiting prolonged
low levels of magnetic activity." That is, it is not defined by a
given activity level, but by the very flat evolution of the activity
seen over time.

Livingston, Wallace, White, & Giampapa (2007; ApJ 657, 1137) present
~33 years of Ca II K 3933A K-index data integrated over the solar
disk. They present 1302 measurements of the K-index between 1974.82
and 2008.07. Based on their full disk measurements described in the
Appendix to their paper, and converting the K-indices to logR'HK
following Radick et al. (1998) and Noyes et al.  (1984), and assuming
(B-V)Sun = 0.65, I find the following moments:

Measurements for 1A K-index [logR'HK in brackets]

Minimum: 0.082747 ; [-4.978]
Maximum: 0.107183 ; [-4.803]
Mean:    0.091993 ; [ -4.903]
St.Dev.: 0.004818 ; [+-0.036]
skew   : 0.5229 (platykurtic)

 +95%CL: 0.102362 [-4.832 ; median + 0.076]
 +68%CL: 0.097365 [-4.865 ; median + 0.043]
Median : 0.091358 [-4.908                 ]
 -68%CL: 0.086900 [-4.942 ; median - 0.034]
 -95%CL: 0.085389 [-4.955 ; median - 0.047]

If you force symmetric confidence intervals,
then the Sun's activity can be approximately
stated as:
logR'HK = -4.908 (+-0.039; 68%CL) (+-0.063; 95%CL)

######################################################################
# Solar X-ray Luminosity (0.1-2.4 keV):   L_X = 10^27.35 (+-50%) erg/s
# Solar X-ray/Bolometric 
#    Luminosity Ratio:         log(L_X/L_bol) = -6.24 +- 0.24 dex
# Solar X-ray Surface Flux (0.1-2.4 keV): f_X =  36800 erg/s/cm^2 
#                                             = 10^4.566 erg/s/cm^2
######################################################################

When comparing X-ray luminosity and X-ray/bolometric flux ratios, the
largest uniform database of X-ray data for nearby stars and members of
clusters and associations is the ROSAT All Sky Survey (Voges et
al. 1999) which covers the 0.1-2.4 keV bandpass. For this reason, here
I only discuss the Sun's X-ray luminosity in this bandpass.

Orlando, Peres, & Reale (2001; ApJ 560, 499) convert flux measurements
taken with the Yohkoh X-ray satellite between 1992-1996 to ROSAT X-ray
luminosity, and claim that the whole solar corona was consistent with
having an X-ray luminosity (0.1-2.4 keV) of 1e26-5e27 erg/s during the
four years of observations. This suggests log(L_X) = 26.0-27.7 erg/s,
or a mean log(L_X) = 26.85 erg/s. Note that Orlando et al. 2001 did
not attempt to estimate a mean X-ray luminosity averaged out over a
full solar activity cycle. From a look at the smoothed sunspot number
data: ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/SMOOTHED
it appears that most of the Orlando et al. data covered the bottom
half of the solar cycle (1993-1996). The midway between solar maximum
(~1989.6) and solar minimum (~1996.4) was roughly 1993.0. At this
point in the Orlando et al. data, the X-ray luminosity of the "whole
solar corona" was ~1e27 erg/s (their Figure 6). This is probably a
fair assessment of the "mean" solar X-ray luminosity from the Orlando
et al. data averaged out over a full activity cycle.

Judge, Solomon, & Ayres (2003; ApJ 593, 534) made an extensive study
of the solar X-ray emission with the SXP instrument on the SNOE
satellite. After accounting for the differences in sensitivities
between SNOE-SXP and ROSAT, and correcting for the fact that SNOE only
observed the Sun for a partial solar cycle (~1998-2000), Judge et
al. conclude "We find that the Sun's 0.1-2.4 keV luminosity lies
between 10^27.1 and 10^27.75 [erg/s] (measured over the time space of
the SNOE-SXP data) and between 10^26.8 and 10^27.9 [erg/s]
(extrapolated over a full activity cycle)." They claim an accuracy of
50% in their calibration between the SNOE-SSXP and ROSAT bandpasses.

From the discussion of Judge et al., I adopt a mean solar X-ray
luminosity (0.1-2.4 keV) of:
     L_X  = 2.24e27 erg/s (+-1.12e27 erg/s = 50% unc.)
 log(L_X) = 27.35 (+0.18,-0.30; +-0.24; 1sigma) erg/s

Adopting a solar luminosity of 3.8416e33 erg/s (see above), and
assuming negligible error in the solar luminosity (correct to first
order given the huge error in the X-ray luminosity), I derive:

     L_X/L_bol =  5.82e-7 (+-2.91e-7; 50%; 1sigma) 
log(L_X/L_bol) = -6.24 (+0.18,-0.30; +-0.24; 1sigma)
           f_X =  36800 erg/s/cm^2 = 10^4.566 erg/s/cm^2

Check: I used 157 stars with chromospheric activity log(R'HK) > -4.3
and X-ray luminosity data to measure the correlation between log(R'HK)
and log(L_X/L_bol), first demonstrated by Sterzik et al. 2007. I find:
log(L_X/L_bol) = 7.081 + 2.63075*log(R'HK), with rms scatter in
log(L_X/L_bol) of 0.24 dex. For the mean log(R'HK) estimated
previously (-4.905), I estimate log(L_X/L_bol) = -5.82 +- 0.24 dex.
This would translate into a solar X-ray luminosity of log(L_X) =
27.76+-0.24 erg/s.  This is only 1.2 sigma off of the value derived
from Judge et al., given the 0.24 dex rms in the chromospheric-X-ray
fit, and the quoted error in Judge et al.'s X-ray luminosity. So we
have an independent check that the solar log(L_X/L_bol) value is
probably ~ -6, and log(L_X) ~ 27 erg/s.


#####################################
# Age(Solar System) = 4572 +- 5 Myr  
#####################################

In nature, there appears to be a continuum of objects ranging
from cold molecular clouds to protostars to optically visible,
accreting T Tauri stars. Where to define t=0 for the "birth" of
a star or planetary system is a matter of taste or definition.
The radioactive isotopes in meteorites give us samples of the
first "rocks" to have accreted from the protosolar nebula,
orbiting the still accreting proto-Sun, and hence are our
best "clocks" for dating the age of the solar system and Sun.

In a well-cited paper, G.J. Wasserburg wrote an appendix on the age of
the Sun in the paper by Bahcall, Pinsonneault, & Wasserburg (1995,
Rev. Mod. Phys. 67, 781). He concludes that the meteoritic evidence is
consistent with an age of the sun between 4563 and 4576 Myr. The upper
bound comes from consideration of the decay of 26Al between the source
(supernova?) and injection into CAIs. The lower bound of this age
(4563 Myr) should be revised upward given the ages of the oldest CAIs
(4567-4568 Myr).

Here are two recent, relevant ages from isotopic studies of meteorites:
>4569.5  +- 0.2  Myr ; Baker+(2005; Nature, 436, 1127)
 4567.2  +- 0.6  Myr ; Amelin+(2002; Science 297, 1678)
 4567.11 +- 0.16 Myr ; Amelin+(2006; update to 2002; Lun.Pl.Sci.Conf. 37, 1970)
 4568    +0.91-1.17 Myr Moynier+ (2007; ApJ 671, L181)

The Baker et al. study claims "the accretion of differentiated
planetesimals pre-dated that of undifferentiated planetesimals, and
reveals the minimum Solar System age to be 4.5695+-0.0002 billion
years." They find the basaltic angrite (read: igneous rock from a
large asteroid or planet!) is 4566.2 +- 0.1 Gyr old, suggesting that
there were large, differentiated planetary bodies with volcanism by
this time. From dating of a carbonaceous chrondrite, Moynier+2007 says
"therefore the formation of the first solid igneous objects as well as
the accretion of the undifferentiated kilometer-sized carbonaceous
chondrite parent bodies must have been complete within +0.91 to -1.17
Myr at 4568 Myr ago."

The age from Amelin et al. is from isotopic studies of Ca-Al-rich
inclusions (CAIs) in the chondrite Efremovka. CAIs are the oldest
known parts of meteorites, and are thought to be the most primitive
solids to have survived the protosolar nebula (the Sun likely accreted
>99% of the material that ever passed through the protosolar nebula
disk). Connelly et al. (2008; ApJ 675, L121) says "the currently most
precise and accurate estimate of the timing of primary CAI formation -
and consequently the age of the solar system - is that defined by the
E60 Efremovka CAI at 4567.11 +- 0.16 Myr (Amelin et al. 2002, 2006)."

Combining Wasserburg's upper limit (4576 Gyr) and the ages of the oldest
CAI (4567 Gyr; Amelin+ 2006, Connelly+ 2008), it would appear that a 
consensus age for the Sun with conservative uncertainty bars would be:

4572 +- 5 Myr

Note that the accretion ("protoplanetary") disk lifetime for
solar-type stars is typically ~2-3 Myr on average, and ~1-9 Myr (95%
CL), as constrained from Spitzer Space Telescope observations of
nearby stellar nursuries (Mamajek, unpublished). Assuming that the
ages of the oldest CAIs corresponds either with the age of the Sun as
a protostar or the age of the Sun when it lost its accretion disk
(almost certainly within <10 Myr of the protostellar phase; based on
observations of other young ~1 Msun stars). The +-5 Myr uncertainty
bar should encapsulate both extremes. At +1 sigma it is consistent
with upper limit given by Wasserburg (in Bahcall+ 1995) and at -1
sigma it is consistent with the ages of the oldest CAIs (Amelin+
2006).

Note that the early Sun was powered predominantly by the release of
gravitational energy as it contracted to the main sequence. Based on
contemporary models (which agree well with the back-of-the-envelope
Kelvin-Helmholtz contraction timescale), the Sun likely did not reach
the main sequence for another ~40 Myr after its protostellar
phase. The transition in the Sun's dominant fuel source from
gravitational energy to proton-proton (PP) chain fusion probably had
negligible impact on the evolution of meteorites, so the timescales
from isotopic studies should *not* be confused with the timescale
since the Sun reached the "zero-age main sequence" or "the start of
main sequence behaviour" (e.g. Bahcall et al. 1995). In the author's
opinion, starting t=0 at the zero-age main sequence is a very bad
habit still used by some theorists. As it appears that stars in
clusters form within <few Myr of one another (e.g. Hartmann+2001,
Preibisch+2002), defining t=0 using the ZAMS complicates
cross-comparison of evolutionary tracks of different masses (all of
which have different pre-MS contraction times). A more useful metric
for t=0 might be the "stellar birth-line" which corresponds to the
deteurium-burning sequence for young stars, and corresponds well with
the observed distributions of luminosities for accreting T Tauri stars
(Stahler 1983, 1988).


#####################################
# Surface Metal Fraction: Z ~ 0.017  
#####################################

There is a healthy debate on this right now, and the situation has yet
to be resolved. Solar Z is somewhere between Z(Sun) ~ 0.12-0.19, with
the some atmospheres/abundances experts favoring smaller values, and
the helioseismologists and various stellar interiors theorists
favoring higher values.

"Canonical" (high-Z) values: 

P. Demarque and D. Guenther in Allen's Astrophysical Quantities, 4th
Edition (Cox 2000) cite Z = 0.0188, which could be considered the
current "canonical" value. The well-cited review on the standard solar
composition by Grevesse & Sauval (1998; Space Sci. Rev. 85, 161) lists
Z = 0.0168. An excellent recent review by Basu & Antia (2008, Physics
Reports, 457, 217-283) states that "Seismic determinations of the
solar heavy-element abundances yield results that are consistent with
the older, higher values of the solar abundance, and hence no major
changes o the inputs to solar models are required to make
higher-metallicity models consistent with the helioseismic data."

Grevesse & Sauval (1998; Space Sci. Rev. 85,161) listed "canonical"
abundances of the present Sun as:
  X = 0.7352
  Y = 0.248
  Z = 0.0168  
Z/X = 0.0229 

A recent review by Lodders (2003; ApJ 591, 1220, Table 4) lowered
the solar metal fraction slightly:
      Sun             Sun
      "Protosolar"    Present 
  X = 0.7110+-0.0040  0.7491+-0.0030  Hydrogen mass fraction
  Y = 0.2741+-0.0120  0.2377+-0.0030  Helium mass fraction
  Z = 0.0149+-0.0015  0.0133+-0.0014  Metals mass fraction
Z/X = 0.0177          0.0178

Lodders (2003; Table 5) shows that estimates of Z/X have been declining
from 1984 through 2003, from values of Z/X ~ 0.027 in the mid-1980s to
Z/X ~ 0.018 in 2003. 


"Heretical" (low-Z) values: 

The "heretical" value is approximately Z = 0.012 (Grevesse, Asplund, &
Sauval 2007, Space Science Reviews 130, 105). Asplund, Grevesse, &
Sauval 2006 (Comm. in Asteroseismology 147, 76) report Z=0.0122 and
Z/X=0.0165.  The canonical value can be used to match the
helioseismological sound speed profile of the Sun with ease, however
the lower Z would require that there is some missing opacity source in
the Sun. The groups that first proposed the lower Z have claimed to
have ruled out enhanced Ne as the culprit (see Asplund et al. 2005
astro-ph/0510377 in response to Drake & Testa 2005; Nature 436,
525). Stay tuned.

Asplund, Grevesse & Sauval (2006; Comm. in Asteroseismology 147, 76)
list the following "heretical" solar composition:
X = 0.7393    Hydrogen mass fraction
Y = 0.2485    Helium mass fraction
Z = 0.0122    Metals mass fraction
Z/X = 0.0165
The estimated protosolar abundances are:
   Zo = 0.0132
Zo/Xo = 0.0185

Where the metal fraction is a bit larger due to the effects of
diffusion. They conclude that "[t]he widely used metallicity Z=0.02
should be definitely forgotten and replaced by the new value,
Z=0.0122."

Conclusions on Solar Z: 

Antia & Basu (2006) estimate Z = 0.0172+-0.002 from modeling of
helioseismological sound speed profiles for the solar interior.  In
their review (Basu & Antia, 2008, Physics Reports, 457, 217-283), they
provide a comprehensive review of helioseismic constraints on the
solar abundances, and conclude that "if the GS98 [Grevesse & Sauval
1998, Space Sci. Rev. 85, 161] abundances are correct then the
currently known input physics is consistent with seismic data."  While
the low solar metal fraction corroborates studies of CNO abundances in
nearby B-stars and ISM, it cannot account for the shape of the main
sequence turn-off for the ~4 Gyr-old cluster M67 as well as the high Z
models (Vandenberg et al. 2007, ApJ, 666, L105; and references
therein).

Based on the Antia & Basu (2006, 2008) study and review, I would adopt
a canonical solar Z = 0.017, and adopt the Grevesse and Sauval 1998
abundances.

################################################
# Equatorial Rotation Speed: P_eq = 25.38 days  
################################################

R. Howard states in "Allen's Astrophysical Quantities" (2000,
Sec. 14.9, P. 363) that "The period of sidereal rotation adopted for
heliographic longitudes is 25.38 days".

##########################################
# Mean Rotation Period: <P> = 26.09 days  
##########################################

This refers to the mean rotation period as inferred from searching for
periodicities in chromospheric activity measurements or due to
starspots (a rotation that can be more directly compared to periods
measured for other stars).

Donahue, Saar, & Baliunas (1996; ApJ 466, 384) studied 19 seasons of
solar chromospheric activity (as measured with the Mt. Wilson S-index;
>= 30 days of observations each) over a 8-year period, and was able to
detect periodicity due to solar rotation in 8 seasons. The detected
periods range from 24.5 to 28.5 days, with a mean detected period of
26.09 days. Although individual periods within a given season can be
measured to tenths or hundreds of a day accuracy, from season to
season as the active regions vary by longitude, the measured period
can vary by rms ~ 10% for the Sun (+- ~2 days).

##########################################################
# Mean Solar Wind Mass Loss Rate <dM/dt> = 2e-14 Msun/yr  
##########################################################

The flow of charged particles escaping the Sun (the solar wind) has
been measured by many spacecraft. Here is a very brief summary.

Solar Wind Velocity:

Using data from the Ulysses spacecraft, which sampled the solar wind
at a wide range of heliographic latitudes (-80deg to +80 deg) in
1994-1995, Goldstein et al. (1996 A&A 316, 296; Figure 1) show that
the solar wind velocity varies as a function of heliographic latitude.
For heliographic latitudes of +-20-80 degrees, the solar wind velocity
was in the range of ~600-830 km/s (mean ~750 km/s; values are inferred
by-eye and ruler from their Fig. 1). There appears to be a sharp
discontinuity in solar wind velocities at plus and minus 20
deg. heliographic latitude. At latitudes below +-20 deg latitude
(i.e. where the ecliptic plane is), the solar wind velocity ranged
from ~320-700 km/s, with an approximate mean of ~460 km/s (again, by
eye from their Fig. 1). 

Gosling et al. 1976 (Jrnl. Geophys. Res. 81, 5061) reports solar
wind velocity statistics for the period 1962-1974, presumably sampled
near the Earth, and hence at low heliographic latitudes. The median
solar wind velocity over this period was 408 km/s. 

Data from the Voyager 2 probe sampled the solar wind between 1977 and
2008, between radii of 1 and 87.07 AU (as of 10/31/2008). The probe
reached the termination shock and entered the heliosheath at a
distance of 83.6 AU.  During the period 1977.64-2007.64, the median
solar wind velocity was 432 km/s, and the mean was 439 km/s. Since its
pass of Neptune in 1989, Voyager 2 is heading towards a point in the
sky 47 degrees below the ecliptic plane. It appears to have been
sampling the denser, slower moving solar wind (that Ulysses detected
within 20 deg of the heliographic equator) throughout.

Solar Wind Density: 

The proton densities measured by Ulysses as a function of heliographic
latitude show a discontinuity similar to that seen for velocities. The
mean proton densities at high heliographic latitude (>+-20 deg) were
typically 2-3 cm^-3 (range: ~1.5-4 cm^-3), while at low latitudes
(<+-20 deg) the densities were typically ~8 cm^-3 (approximate range:
~2-20 cm^-3).

Taking the Voyager 2 data and correcting for distance
(i.e. normalizing the densities to what one would find at 1 AU), it
detected a median proton density of 5.63 cm^-3 and a mean of 6.68
cm^-3 between 1977.64-2007.64. This agrees well with the Ulysses data
at low heliographic latitudes.

Calculation:

A nice derivation for estimating the solar mass loss from the
parameters for the solar wind is Example 11.2.1 (p. 374) of Carroll &
Ostlie's "An Introduction to Modern Astrophysics (Second Edition)"
(2007).

In the special case of the solar wind velocity and density being
independent of heliographic latitude (not true), and assuming that the
detected particles are all protons (not true), one can estimate the
mass loss due to solar wind as measured at some radial distance R (in
AU) from the Sun using the following derived formula:

dM/dt [Msun/yr] = 7.41e-18 Msun/yr * n[cm^-3] * V[km/s] * (R[AU]^2)

Where n is the proton density in cm^-3, and V is plasma velocity in
km/s.

Using the Voyager 2 mean solar wind parameters (<n>=6.68 cm^-3,
<V>=439 km/s, assume all protons) and this formula, I estimate:

dM/dt = ~2.2e-14 Msun/yr

From Goldstein et al.'s Ulysses data it appears that the product
density X velocity for the solar wind is approximately double at lower
latitudes (<20 deg) than at higher latitudes. Hence approximately
1/3rd of the heliographic latitudes and longitudes are emitting
protons at the rate we measured, while ~2/3rds has a product of n X V
that is roughly half. This suggests that a more realistic ~2nd-order
estimate might be:

dM/dt = ~1.5e-14 Msun/yr

Given the uncertainties, I would just adopt 2e-14 Msun/yr.

#############################################
# Median International Sunspot Number (ISN)  
#############################################

The Solar Influences Data Analysis Center (SIDC) has a nice database
of historical sunspot number measurements:
http://sidc.oma.be/sunspot-data/

The SIDC lists a daily estimate of the International Sunspot Number
(ISN) going back to January 1818 (although not every day had a
measurement in the early data), with 66515 daily measurements between
8 Jan 1818 and 31 Dec 2008.

The moments of the ISN can be summarized as such:

      median = 40
      mean   = 54
68% interval = 4 to 105  
95% interval = 0 to 187
      max    = 355 (measured at year = 24 & 25 Dec 1957)
      min    = 0   (measured 10243 times, or 15.4% of daily observations)

#########################
# UPDATES & CORRECTIONS  
#########################

29 May 2007: Fixed solar mass units correctly to kg & g, where appropriate
 2 Jun 2007: Added comments on solar spectral type from Morgan & Keenan (1939)
13 Jun 2007: Added Sun's B magnitude
28 Aug 2007: Added brief discussion on B-V of G2Vs in the field
28 Aug 2007: Added Solar GM value discussion and value
28 Aug 2007: Updated AU value and discussion
12 Sep 2007: Added logR'HK discussion on Maunder minimum
23 Oct 2007: Added solar X-ray luminosity (Judge et al. 2003, Orlando et al. 2001)
12 Nov 2007: Added log of bolometric luminosity and age/yr
29 Nov 2007: Added X-ray surface flux and defined ROSAT X-ray energy ranges (0.1-2.4 keV)
29 Nov 2007: Edited comments on age of solar system 
 7 Dec 2007: Added discussion of solar B-V using Gray et al. 2003,2006 samples. 
 2 Feb 2008: Added equatorial rotation period and mean rotation period 
26 Mar 2008: Added discussion on solar abundances
 1 Apr 2008: Added calculations for statistics regarding logR'HK
 2 Apr 2008: Added discussion on temporal evolution of luminosity
24 Apr 2008: Added discussion on Maunder minimum to chromospheric activity section
 1 Sep 2008: Changed author's affiliation to U. Rochester
31 Oct 2008: Added discussion and estimate regarding the solar wind/mass loss
 1 Dec 2008: Added B. Skiff reference to solar-type MK stars & colors
 2 Dec 2008: Edited solar wind/mass loss discussion, Added reference
 2 Jan 2009: Added daily International Sunspot Number observations
 7 Jan 2009: Updated and reorganized discussion on solar Z value
30 Mar 2009: Updated solar radius and age discussion (new age listed)
21 Apr 2009: Added discussion on moment of inertia
15 Jun 2009: Updated astronomical unit to Pitjeva & Standich (2009) value
23 Jun 2009: Corrected year in Bessell+ reference (thanks to M. Cushing)
 1 Jul 2009: Added B-V estimate using relation from Valenti & Fischer (2005)
25 Aug 2009: Revised AU following 2009 IAU resolution
 4 Sep 2009: Revised solar bolometric magnitude to reflect 2009 IAU definition of AU
 4 Sep 2009: Thanks to Erik Bergren for pointing out the IAU Mbol zero point.
 4 Sep 2009: Adopted Vmag(Sun) from Hayes85, Neckel86, Cox00
 4 Sep 2009: Revised bolometric correction (negligibly) due to revised Mv and Mbol