# How can I convert a GAIA-magnitude "G" to Johnson "V"?

Question: How can I convert the Gaia-magnitude G (and G_ESTIMATE) into a V-magnitude? The solution probably can be found in the Gaia Data Release Documentation for Gaia's EDR3 ("Early Data Release 3"), specifically section 5.5.1, Relationships with other photometric systems, but I have to admit, that I can't make heads or tails of it.

Related Question: The question Relationships between G magnitude, Johnson V magnitude, and spectral type of stars? is related in that it wants to explore the relationship between G and Johnson-V. However, my separate question is not a "duplicate", because the other question has the relation between the magnitudes and spectral type as its focus (perhaps erroneously, shouldn't the relation be between a colour index and spectral type?).

Background: I am exploring the solar neighbourhood based on the paper The 10 parsec sample in the Gaia era (see the CDS-entry). Among other things I want to know the objects' respective brightnesses and what is visible to the naked eye (or a specific instrument). For this I want to use the "V"-filter (column "V" in the catalogue to the paper). A bit more than 50% of the non-planetary objects in the catalogue have a V-mag listed. Most of the remaining non-planetary objects (stars, low-mass stars, white dwarfs, brown dwarfs) have either a Gaia-magnitude G or an estimated Gaia-magnitude G_ESTIMATE. Therefore I need a way to convert G to V. The conversion probably not straight-forward since $$G$$ is a band covering wavelengths 330–1050 nm, and $$V$$ seems to cover only 470-700 nm.

Looking for: I need an equation I can use in a spreadsheet program to convert G/G_ESTIMATE to V. Is there one, or does conversion require more information than is given in the 10 parsec-catalog? Thank you for your help!

There is no function that converts $$G$$ to $$V$$ because the conversion depends on stellar temperature/colour.

For Gaia EDR3 data the most useful transform for you is $$G-V=-0.02704 +0.01424(G_{bp}-G_{rp})-0.2156(G_{bp}-G_{rp})^2 + 0.01426(G_{bp}-G_{rp})^3$$ from Table 5.7 of the EDR3 data guide.

Most sources with $$G$$ data will also have a $$G_{bp}-G_{rp}$$ colour.

Note that the DR2 and EDR3 photometric systems are slightly different.

For Gaia DR3 the transform is the same as for EDR3, from Table 5.9 of the DR3 documentation.

• Thank you, that's it! I tested the equation on the entries having $G$, $V$, $G_{BP}$, and $G_{RP}$. I got 164 entries with a deviation < 0.1m; 60 entries <0.5m; 15 entries <1m; 9 entries > 1m deviation. Feb 18, 2022 at 19:05

To convert from G to V magnitude, use the following formula: $$G-V=-0.0176 -0.00686(G_{bp}-G_{rp})-0.1732(G_{bp}-G_{rp})^2$$

From Table 5.8 of the Gaia DR2 data release documentation.

• Please add some context to your answer including defining the variables used and if possible a reference for the source of this expression. Please also consider formatting you equation with MathJax. Feb 17, 2022 at 11:42
• I'm Guessing $Gbp$ and $Grp$ should really be $G_{bp}$ and $G_{rp}$ ? Feb 17, 2022 at 14:55