# Magnitude System and Color Conversion Formulas # Conversion Formulas

## General

R = V - 0.508 * (B - V) - 0.040   (0.3 < B - V < 0.9)

Johnson-Cousins BVRI photometry for faint field stars
ftp://ftp.lowell.edu/pub/bas/starcats/loneos.phot

(B - I) = 2.36 * (B - V)

The use of the (B-I) color index and applications of the (B-I) versus (B-V) relationship
Natali F., Natali G., Pompei E., Pedichini F., 1994, A&A 289, 756

## Tycho-2 Catalogue

V = VT - 0.090 * (BT - VT)
B - V = 0.850 * (BT - VT)

The Tycho-2 Catalogue

V = VT + 0.00097 - 0.1334 * (BT - VT) + 0.05486 * (BT - VT)^2 - 0.01998 * (BT - VT)^3   (-0.25 < BT - VT < 2.0)
B - V = (BT - VT) - 0.007813 * (BT - VT) - 0.1489 * (BT - VT)^2 + 0.03384 * (BT - VT)^3   (0.5 < BT - VT < 2.0)
B - V = (BT - VT) - 0.006 - 0.1069 * (BT - VT) + 0.1459 * (BT - VT)^2   (-0.25 < BT - VT < 0.5)

Post-T Tauri Stars in the Nearest OB Association
Mamajek, Eric E.; Meyer, Michael R.; Liebert, James
Astronomical Journal, Volume 124, Issue 3, pp. 1670-1694
2002AJ....124.1670M
* Note that +0.007813 in this paper is typo, -0.007813 is correct.

Erratum:
Mamajek, Meyer, Liebert, 2006, AJ, 131, 2360

## USNO-A1.0

V = r + 0.375 * (b - r)
B - V = 0.625 * (b - r)

[vsnet-chat 700] Re: Comparison sequences
Taichi Kato
http://vsnet.kusastro.kyoto-u.ac.jp/vsnet/Mail/vsnet-chat/msg00700.html

## USNO-A2.0

B = 1.097 * USNO(B) - 1.216   (12 < USNO(B) < 19)
V = 1.064 * USNO(V) - 0.822   (12 < USNO(V) < 19)
R = 1.031 * USNO(R) - 0.417   (12 < USNO(R) < 19)

The USNO A2.0 photometric scale compared to the standard Landolt BVR magnitudes
http://www.iac.es/galeria/mrk/comets/USNO_Landolt.htm

## USNO-B1.0

B - V = 0.556 * (B1 - R1)

Crude USNO B1.0 B1-R1 to B-V transformation
John Greaves
http://www.aerith.net/astro/color_conversion/JG/USNO-B1.0.html

## 2MASS

V - Rc = 0.8625 * (J - Ks) + 0.0202   (0.1 < J - Ks < 0.8)
V - Ic = 1.6069 * (J - Ks) + 0.0503   (0.1 < J - Ks < 0.8)

2MASS J and K Photometry Conversion to V-Rc and V-Ic
Doug West
http://members.aol.com/dwest61506/page72.html

## Sloan Digital Sky Survey

V = r + 0.44 * (g - r) - 0.02
B = V + 1.04 * (g - r) + 0.19

The Sloan Digital Sky Survey Moving Object Catalog
http://www.astro.princeton.edu/~ivezic/sdssmoc/sdssmoc.html
The Sloan Digital Sky Survey Photometric System
Fukugita, M.; Ichikawa, T.; Gunn, J. E.; Doi, M.; Shimasaku, K.; Schneider, D. P.
Astronomical Journal v.111, p.1748
1996AJ....111.1748F

## Carlsberg Meridian Catalogue, Vol. 13 (CMC13)

V = 0.6 * (J - Ks) + r'_CMT - 0.03   (-0.2 < J - Ks < 1.2, 9 < r'_CMT < 14)
Rc = r'_CMT - 0.2   (9 < r'_CMT < 14)

[vsnet-chat 6758] (fwd) Johnson V estimation from r'_CMT and 2MASS J-Ks
John Greaves
http://vsnet.kusastro.kyoto-u.ac.jp/vsnet/Mail/vsnet-chat/msg06758.html
[vsnet-chat 6762] (fwd) Re: Johnson V estimation from r'_CMT and 2MASS J-Ks
John Greaves
http://vsnet.kusastro.kyoto-u.ac.jp/vsnet/Mail/vsnet-chat/msg06762.html

## Carlsberg Meridian Catalogue, Vol. 14 (CMC14)

V = 0.6278 * (J - K) + 0.9947 * r'   (9 < r' < 16)

A method for determining the V magnitude of asteroids from CCD images
Roger Dymock & Richard Miles
J.Br.Astron.Assoc. 119,3,2009 149-156
http://www.britastro.org/asteroids/JBAA%20119%20149-156%20Dymock1.pdf

V = 0.6 * (J - Ks) + r'_CMT - 0.03 +/- 0.06   (0 < J - Ks < 1, 9 < r'_CMT < 15)

[vsnet-alert 9907] re DA55 aka QSO B0133 +47
John Greaves
* Note that the formula is corrected in [vsnet-alert 9908].

Rc = r' - 0.21 +/- 0.13   (9 < r' < 15.5, 0 < V - Rc < +0.6)
Rc = 0.984 r' +/- 0.13 (9 < r' < 15.5, 0 < V - Rc < +0.6)

Red Magnitudes
John Greaves
http://www.aerith.net/astro/color_conversion/JG/redmags.pdf

## Northern Sky Variability Survey (NSVS) = ROTSE-1

mag = Vt - (Bt - Vt) / 1.875

ROTSE All-Sky Surveys for Variable Stars. I. Test Fields
Akerlof, C. et al.
The Astronomical Journal, Volume 119, Issue 4, pp. 1901-1913.

V = 0.9425 * ROTSE1 + 0.6914   (+/- 0.2)
V - ROTSE1 = 0.8360 * (J - Ks) - 0.4576   (0.0 < J - Ks < 1.2, +/- 0.07)

* Note that ROTSE-1 magnitudes may have a systematic offset of up to +/- 0.1 depending on what part of the sky.

John Greaves
personnal communication

## Unfiltered CCD Instrumental Mag.

(V - inst) = 0.2600 * (B - V)   (SITe back-illuminated)
(V - inst) = 0.3602 * (B - V)   (KAF-E)
(V - inst) = 0.5174 * (B - V)   (KAF)
(V - inst) = -0.0606 * (B - V)   (Sony)
(V - inst) = 0.4292 * (B - V)   (TI TC245)
(V - inst) = 0.2905 * (B - V)   (TI TC241 (VP))

(R - inst) = -0.2716 * (V - I)   (SITe back-illuminated)
(R - inst) = -0.1541 * (V - I)   (KAF-E)
(R - inst) = 0.0005 * (V - I)   (KAF)
(R - inst) = -0.6256 * (V - I)   (Sony)
(R - inst) = -0.1021 * (V - I)   (TI TC245)
(R - inst) = -0.2510 * (V - I)   (TI TC241 (VP))

The M67 Unfiltered Photometry Experiment
2000, Journal AAVSO vol. 29, page 35.
Arne A. Henden
ftp://ftp.nofs.navy.mil/pub/outgoing/aah/m67/paper/

# Links

## Conversion between color indices

Statistical Relations between the Photometric Colours of Common Types of Stars in the UBV(RI)c, JHK and uvby Systems
Caldwell J.A.R., Cousins A.W.J., Ahlers C.C., van Wamelen P., Maritz E.J., South African Astron. Obs. Circ., 15, 1-29 (1993)

## Conversion between color index and spectral type.

Intrinsic b-y, H-beta (for B stars), and V-I colors, and absolute magnitudes
ftp://ftp.lowell.edu/pub/bas/starcats/uvby.calib
Intrinsic colours as a function of spectral type
http://www-int.stsci.edu/~inr/intrins.html
A Stellar Spectral Flux Library, 1150-25000 A
Pickles A.J., PASP, 110, 863 (1998)
http://webast.ast.obs-mip.fr/stelib/literature/Pickles_tbl2.txt
http://webast.ast.obs-mip.fr/stelib/literature/Pickles_1998.ps

## Conversion between color index and absolute magnitude.

Photometric properties of low-mass stars and brown dwarfs
http://www-int.stsci.edu/~inr/cmd.html

## Conversion between 2MASS magnitude system and other infrared systems.

2MASS Color Transformations
http://www.astro.caltech.edu/~jmc/2mass/v3/transformations/ 