Effective temperatures and bolometric corrections from 2MASS IR photometry
E. Masana1, C. Jordi1 and I. Ribas2
1Departament
d’Astronomia i Meteorologia, Universitat de Barcelona, Av. Diagonal 647, Barcelona, E-08028, SPAIN
2Institut d’Estudis Espacials de Catalunya/CSIC, Campus UAB, Facultat de Ciències, Torre C-5 – parell – 2ª planta, E-08193 Bellaterra, SPAIN
THE 2 MICRON ALL SKY SURVEY
(2MASS) CATALOGUE
ABSTRACT
We present new determinations of effective temperature for a wide sample of FGK stars. The method we have devised is based on the fit
of the spectral energy distribution from the optical (V) to IR (JHK) bands with synthetic photometry computed from atmosphere models.
Since the flux in the IR bands is mostly insensitive to log g and [Fe/H], no accurate values of these parameters are needed to obtain
precise (about 1%) temperature determinations. The 2MASS All Sky Catalogue was used as source of the IR photometry. The fit also
yields the semi-angular diameter of the star, that can eventually be translated into radius when the parallax is available. From both the
temperature and semi-diameter, bolometric corrections can also be inferred. The application of the method to a wide sample of stars
permits the establishment of both temperature and bolometric correction calibrations as functions of the metallicity [Fe/H] and (V-K)0
colour of the star. Comparisons with spectroscopic temperature determinations were carried out and resulted in a good agreement.
• Over 491 million stars
• Sky coverage: 99.998 %
• Three near-infrared bands:
• J (1.25 µm)
• H (1.65 µm)
STELLAR SPECTRAL ENERGY DISTRIBUTION FIT
Effective temperature
⎛1
Teff = ⎜
⎝σ
∞
0
2MASS photometric accuracy
1
1
∫
• K (2.17 µm)
⎛ F ⎞4
Teff = ⎜ 2Bol ⎟
⎝θ σ ⎠
⎞4
⎠
φ (λ )dλ ⎟
φ(λ): Flux density at the star’s surface
Infrared image of the Milky Way
FBol: Total flux at the Earth’s surface
σ: Stefan-Boltzmann constant
θ: Semi-angular diameter
Observed VJHK photometry
The method
The determination of the effective temperature though the stellar spectral energy distribution fit is based
on finding the best possible agreement between the observed and synthetic photometry. The algorithm
itself minimises the χ2 function of the difference between the observed and synthetic VJHK magnitudes:
2
2
2
V: The V magnitude was taken from several catalogues B Hipparcos (ESA, 1997), Hauck & Mermilliod
(1998), …
JHK from 2MASS catalogue
The magnitudes were dereddened when possible using Strömgren photometry or a model of the galactic
interstellar extinction
2
⎛ V −Vsyn ⎞ ⎛ J − Jsyn ⎞ ⎛ H − Hsyn ⎞ ⎛ K − Ksyn ⎞
⎟⎟
⎟⎟ + ⎜⎜
⎟⎟ + ⎜⎜
⎟⎟ + ⎜⎜
⎝ σV ⎠ ⎝ σ J ⎠ ⎝ σ H ⎠ ⎝ σ K ⎠
χ 2 = ⎜⎜
Synthetic VJHK photometry
The two adjustable parameters are the effective temperature Teff and the magnitude zero point A, which is the
difference between the synthetic (star’s surface) and the observed (Earth surface) magnitude. A is directly
related to the semi-angular diameter and, if the distance to the star (r) is known, it allows for the determination
of the star radius (R):
θ = 10
0 .2 A
θ =
R
r
⇒
R = r 10
To compute the synthetic magnitudes misin we employ the Kurucz (1993) atmosphere models
(ATLAS9) and the absolute flux calibration by Cohen et al. (2003a,b):
Absolute flux calibration
0 .2 A
Bolometric correction
⎛
⎞
Fcalib
i
⎟
msyn
(Teff , g , [ Fe / H ]) = 2.5 log⎜
⎜ F (T , g , [ Fe / H ]) ⎟
⎝ i eff
⎠
The bolometric correction in any band can be inferred from the effective temperature (Teff), the semi-angular
diameter (θ) and the observed magnitude (m):
Fi (Teff , g , [ Fe / H ]) = ∫ φ (Teff , g , [ Fe / H ]) τ i (λ ) dλ
BC
X
= M
Bol
− M
X
T eff
⎛
θ ⎞
⎟ − 10 log
= − 5 log ⎜⎜ Κ
− 0 . 26 − m X
R SUN ⎟⎠
T SUN
⎝
Accuracy of the method
To determine the uncertainty of the derived effective temperature we have considered different error sources:
• Observed magnitude errors
• Zero point uncertainties in the flux calibration: 0.016 - 0.019 mag, according to Cohen et al. (2003)
∞
0
V
J
H
K
Transmission: Earth atmosphere
+ instrument + filter
Atmosphere models
A value of the surface gravity (log g) and metallicity
( [Fe/H] ) are needed
• Metallicity error: 0.10 dex (spectroscopic determinations) or 0.15 dex (photometric determinations)
• Surface gravity error: 0.18 dex (photometric determinations) or 0.5 dex (for main sequence stars with
unknown log g)
From these values, the relative accuracy is:
Resulting relative accuracy (%)
of the effective temperature: for
[Fe/H] = 0 (left panel) and for
log g = 4.5 (right panel)
σTeff ≈ 1.5%
σ θ ≈ 2.0% ⇒ σ R ≤ 5.0% (for stars with σπ≤ 5.0%)
CALIBRATIONS AS FUNCTION OF (V-K)0 AND [Fe/H]
Using a sample of more than 11000 FGK main sequence stars we obtained calibrations as function of
(V-K)0 and metallicity for both effective temperature and bolometric correction. The stars of the sample
belong to the Hipparcos and 2MASS catalogues and have spectroscopic or photometric
determination of their metallicities. The surfaces gravities were obtained using photometric
calibrations based on Strömgren photometry.
Effective temperature
0.40 < (V-K)0 < 1.35 (4207 stars):
θ ef = 0.556 + 0.170(V − K ) 0 + 0.019(V − K ) 02 + 0.015 [ Fe / H ] + 0.004[ Fe / H ]2 − 0.004(V − K ) 0 [ Fe / H ]
1.35 ≤ (V-K)0 < 3.4 (6455 stars):
θ ef = 0.496 + 0.262(V − K )0 −
Send requests to: E. Masana (emasana@am.ub.es)
− 0.015(V − K )02 + 0.028[ Fe / H ]2 −
− 0.017(V − K )0 [ Fe / H ]
σTeff = 20 K
where
θ eff
5040
=
Teff
Bolometric correction
DISCUSSION
• Our method can be applied to stars between 4000 and 8000 K. The upper limit is defined by the increasing
dependence of the results on log g and the lower limit is set by the decreasing performance of the models
because of molecular band opacity.
• As it is based mainly in the infrared photometry, the method is mostly insensitive to the (often not well known)
input values of log g and [Fe/H].
We carried out comparisons of the our temperatures (MDEE method) with other determinations, both photometric
and spectroscopic:
• In general the temperatures are in good agreement. Except for the sample from Alonso et al., the differences
are within 1σ.
• The differences are independent of log g or [Fe/H]
• On average, our temperatures are 0.5 – 2.0% greater the other determinations, probably because of the use of
different models and absolute flux calibrations.
Furhmann 1998:
• FG type stars
• Spectroscopic temperatures
(from Balmer line wings)
Santos et al. 2004:
• Planet host stars
• Spectroscopic temperatures
• 28 stars in common
• 106 stars in common
• ∆T(FURH-MDEE) = –63 ± 62 K
• ∆T(SANTOS-MDEE) = –31 ± 67 K
Edvardsson et al. 1993:
Alonso et al. 1996:
• Nearby FG type stars
• FGK type stars
0.40 < (V-K)0 < 1.15 (4232 stars):
• Photometric (uvby-β)
determinations
• Infrared Flux Method (IRFM)
BCK = 0.004 + 1.055(V − K )0 − 0.084(V − K )02 + 0.094[ Fe / H ] + 0.016[ Fe / H ]2 − 0.014(V − K )0 [ Fe / H ]
• 122 stars in common
σBC = 0.007 mag
• ∆T(EDVARD-MDEE) = –62 ± 62 K
1.15 ≤ (V-K)0 < 3.4 (6485 stars):
BCV = −0.135 + 1.252(V − K )0 −
− 0.151(V − K )02 + 0.126[ Fe / H ] +
− 0.001[ Fe / H ]2 −
− 0.049(V − K )0 [ Fe / H ]
σBC = 0.005 mag
REFERENCES
• 335 stars in common
• ∆T(IRFM-MDEE) = –146 ± 79 K
•Alonso, A., Arribas, S. and Martínez-Roger, C. 1996, A&A, 117, 227
•Cohen, M., Megeath, S.T., Hammersley, P.L., Martín-Luis, F. and Stauffer J. 2003a, AJ, 80, 955
•Cohen, M., Wheaton, W.A. and Megeath, S.T. 2003b, AJ, 126, 1090
•Cutri, R.M., Skrutskie, M.F., van Dyk. S., et al. 2003, VizieR On-line Data Catalog: II/246
•Edvardsson, B., Andersen, J., Gustafsson, B., et al. 1993, A&A, 275, 101
•ESA. 1997, The Hipparcos and Tycho Catalogues (ESA SP-1200)
•Fuhrmann, K. 1998, A&A,338, 161
•Hauck, B. and Mermilliod, M. 1998, A&AS, 129, 431
•Kurucz, R.L. 1993 http://kurucz.harvard.edu/grids.html
•Ribas, I., Solano, E., Masana. E. and Giménez, A. 2003, A&A, 411, L501
•Santos, N.C., Israelian, G. and Mayor, M. 2004, A&A, 415, 1153