# B-V to U-B colour index

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Is there a formula to convert the B-V index to U-B index or are they totally different and separate observations and can't be convert like you can with Fahrenheit->Celsius? (Updated)

I know F->C is not astronomy related directly but there is a formula to convert between the two measurements.

In photometry, we determine the color index (or colour index if you're from my part of the world) as the difference in magnitudes between two wavelength filters. The reason that we use the difference, is because the magnitude system is logarithmic, so using the difference tells us the ratio of the intensities of the two wavelength bands.

To determine the B-V index, you'd need the magnitudes in the B band (which is centered on $lambda = 445$nm) and in the V band, centered on $lambda = 551$nm.

To find the U-B index, you'd also need the U-magnitude, at $lambda = 365$nm.

So, as @zephyr said, there's no way to convert between the two color indices.

Both $B-V$ and $U-B$ are a reflection of how hot the surface of a star is. To first order (inhomogeneous surface temperatures do exist) this has a single value for a given stellar photosphere and so there ought to be a direct relationship between $B-V$ and $U-B$. Here it is, shown below as a graph appropriate for main sequence stars with a composition similar to the Sun. You can reproduce this yourself using data found (for example) in the Handbook of space Astronomy and Astrophysics (pp68-69) compiled by M.V. Zombeck.

You can see that the relationship is complicated; this is because stellar surfaces are not blackbodies and the absorption by various chemical species cuts out chunks of the spectrum, particularly in the blue and ultraviolet. However, given a $B-V$ one could look up the appropriate $U-B$. Note that this is not straightforward the other way around, where there may be two values of $B-V$ possible for a given $U-B$.

In practice things are much more complicated. The plot above assumes the stars are on the main sequence. Stellar atmospheres change a bit as stars evolve and get bigger, with lower surface gravity. Thus changes the relationship a little. The relationship also changes if the composition is not similar to the Sun, especially around the bump at $B-V simeq 0.4$. Finally, this relationship is intrinsic, it assumes you are not viewing the star through extinction caused by dust. If that is not the case then the whole relationship slides redward in both colours (the vector direction of which is shown in the plot above for about 2 magnitudes of visible extinction) but also changes shape slightly, depending on how much extinction there is.

You can convert from B-V to U-B by assuming spectral energy distribution (SED).

For example, if you assume blackbody SED (BBSED). The BBSED is determined by only the temperature (+ scaling constant which is irrelevant here). Therefore, there is a mapping from B-V to the certain temperature. Once you get the temperature, you can find U-B by applying the temperature to the BBSED (again, there is a mapping).

Becareful in the situation where the object's SED is not BB (e.g., galaxy). Or, the object's SED in the range from U to V has issues such as strong line emission or absorption (especially 4000-A break). In these cases, you cannot assume BBSED.

People might provide you more informative idea how to deal with the problem if you specify what kind of object you are dealing with.

## Color index

Stars are classified into spectral types, which are further subdivided into luminosity classes each has a characteristic intrinsic color index, given as (BV )0 and (UB )0. These two indices are defined as zero for unreddened A0 main-sequence stars, such as Vega, and are therefore negative for hotter stars, i.e. those emitting more ultraviolet (O and B stars), and positive for cooler ones (A1 to M stars). Since color index is easily measured, it is usually used on graphs in preference to spectral type or temperature. Any excess of the measured value of color index of a star over the expected intrinsic value indicates that the starlight has become reddened by passage through interstellar dust (see extinction). The difference between the values is the color excess, E , of the star:

The value of E gives the amount of reddening.

There are also color indices relating to magnitudes measured at red and infrared wavelengths. For example, in the indices VR and VI , I and R are the magnitudes measured at 0.7 μm and 0.9 μm.

## Found a chart of RGB values for star colours

I was fooling with my Paint program and got a good RGB equivalent for G2V at 250 255 250.

The chart shows G-types as sort of washed-out orange, though.

Star colours are fascinating!

### #2 GlennLeDrew

Star color is rather more closely tied to surface temperature than it is to spectral type/class. This is because metallicity has an impact. At given spectral type/class, lower metallicity results in a hotter surface and hence bluer color.

The better indicator of color (for visual purposes) is the B-V color index.

### #3 Rich (RLTYS)

Hi,

Found this: http://www.isthe.com. -byhrclass.html

I was fooling with my Paint program and got a good RGB equivalent for G2V at 250 255 250.

The chart shows G-types as sort of washed-out orange, though.

Star colours are fascinating!

Interesting chart, thanks for the info.

### #4 68Kustom

Star color is rather more closely tied to surface temperature than it is to spectral type/class. This is because metallicity has an impact. At given spectral type/class, lower metallicity results in a hotter surface and hence bluer color.

The better indicator of color (for visual purposes) is the B-V color index.

But what did you think of the colours in the chart?

Mitchell N. Charity has an interesting site as well: http://www.vendian.o. dir3/starcolor/

### #5 GlennLeDrew

I haven't entered Landon's (?) RGB values into a paint program to see what I get. Charity's colors as shown on his page are rather exaggerated at the blue end, I think. The color shown for A stars might even be a bit strong for O stars.

Our eye's spectral response, which notably attenuates toward the red and blue, effectively filters star colors into a pretty subtle 'mostly white.' The cool stars can exhibit rather strong reddish hues mostly because of the significant attenuation by molecular absorption bands which are more prominent on the bluer side of the visual spectrum.

### #6 68Kustom

Our eye's spectral response, which notably attenuates toward the red and blue, effectively filters star colors into a pretty subtle 'mostly white.' The cool stars can exhibit rather strong reddish hues mostly because of the significant attenuation by molecular absorption bands which are more prominent on the bluer side of the visual spectrum.

Naked eye, I see Vega and Sirius as distinctly blue-white. Regulus is very blue.

At the eyepiece, Mizar, Castor, and Cor Caroli I see distinctly blue-white as well Alkaid is even more blue.

It's the F and G stars that I find tricky. F0 Polaris seems to have almost a gold tint, but A7 Altair is white with a faint blue hint. Next clear, dry night I'm going to compare various F-types: Polaris, Procyon, Pi 3 Orionis. Eta Cas I've seen labeled as G0 and F9.

Bob Berman wrote that the sun radiates an essentially perfect white not yellow!

### #7 68Kustom

I haven't entered Landon's (?) RGB values into a paint program to see what I get. Charity's colors as shown on his page are rather exaggerated at the blue end, I think. The color shown for A stars might even be a bit strong for O stars.

Here's a photo of Crux with Alpha and Beta Cen to left. These defocused star trails show colours well. Note G2V Alpha Cen:

Edited by 68Kustom, 11 February 2015 - 02:58 PM.

### #8 GlennLeDrew

2900K color temperature is rather like that of an M5 dwarf.

If you could be transported to a series of planets orbiting a variety of stars, you might be surprised at the not so pronounced differences in lighting.

A solar metallicity A0 main-sequence star (Vega being almost the archetype) is a fiducial in that it's assigned a B-V index of 0. This is why our G2 Sun is described as yellow-ish. But Berman is correct in one sense we've evolved under Sol's light, and so from a biological standpoint this light could be called 'white.' But we still perceive sunlight as yellowish when compared to a truly balanced, neutral tint.

### #9 68Kustom

If you could be transported to a series of planets orbiting a variety of stars, you might be surprised at the not so pronounced differences in lighting.

Yes! Barnard's Star in place of our sun would be so bright at mag -18.2 we'd see it as white (as we do our low-albedo, charcoal-coloured Moon). Artists always depict red giants and dwarfs as tomato-soup colour as envisioned from a nearby planet.

One time I tried an experiment with sunlight when the early-afternoon sun was casting white disc images through a fully-closed Venetian blind onto a white-painted wall.

I turned on all lamps with incandescent bulbs which flooded the room with the

2900 K light you describe. The solar-disc images on the white wall turned a distinct blue in the wash of 'yellow' light from incandescent bulbs. Lights off and the images became white again.

I'm trying to convert a star's B-V color index to an apparent RGB color. Besides look up tables and color ramps, it seems like there's no well known algorithm for doing this.

##### What's a B-V color index?

It's a number astronomers assign to a star to indicate its apparent color. Hot stars (low B-V) are blue/purple and cool stars (high B-V) are red with those white/orange stars in between.

##### Kelvin to xyY

If you model a star as a blackbody, then you can use a numerical approximation of the Planckian locus to compute the xy coordinates (CIE chromaticity)

##### Question

I ran this algorithm with the B-V color indexes: 1.2, 1.0, 0.59, 0.0, -0.29. This is what I got as output.

Why did I get this strange output? Hot stars are bluish but cold stars are brownish and there doesn't seem to be white/orange intermediate stars.

##### Update

Following on a comment by Ozan, it seemed like I was using a wrong matrix to convert XYZ to RGB. Since sRGB is the default color space on the web (or is it?), I'm now using the correct matrix followed by a gamma correction function ( a = 0.055 ).

I now get this nice color ramp,

but there's still no red/violet at the extremities.

There's also a fiddle now that you can play with.

##### Update 2

If use a gamma of 0.5 and extend the range of B-V color indexes to be from 4.7 to -0.5, I get red at one extreme but still no violet. Here's the updated fiddle.

Color index, In astronomy, the color index is a simple numerical expression that determines the color of an object, which in the case of a star sensitive to ultraviolet rays, B is sensitive to blue light, and V is sensitive to visible (green-yellow) light (see also​: UBV system). "A STUDY OF THE B-V COLOR-TEMPERATURE RELATION". a star with (B-V) 0 is bluer than Vega a star with (B-V) > 0 is redder than Vega By this criterion, the constellation Crux is unusual in its wealth of very blue stars. Most stars you can see with your naked eye are considerably redder than Vega, and thus have positive (B-V) values. Another way to look at the color index is to go back to the convolution of spectrum with passband.

Star color - details, Color indices: The relative brightness of this star between certain frequency filters​, or "colors", of light. it can also be measured in the blue-centered end of the visible spectrum, or in the red-centered For example, our sun has a B-V index of +0.65, while the much hotter star Sirius has a Add (sp xy rgb src alldata) table. So the colors of stars are described by quantities such as U-V and B-V. But in another fairly arbitrary choice of astronomers, each color magnitude is normalized differently (that is, they each have a different F 0). A common choice is normalizing so that the star Vega (which is about 10,000 K) has color indices U-V = B-V = 0.

Just in case anybody else needs to convert the handy C++ of @Spektre to python. I have taken some of the duplication out (that the compiler would no doubt have fixed) and the discontinuities for g when bv>=2.0 and b when 1.94<bv<1.9509

Astronomical "color", Most stars you can see with your naked eye are considerably redder than Vega, and thus have positive (B-V) values. Another way to look at the color index is to go The B–V color indexes of stars range from −0.4 for the bluest stars, with temperatures of about 40,000 K, to +2.0 for the reddest stars, with temperatures of about 2000 K. The B–V index for the Sun is about +0.65. Note that, by convention, the B–V index is always the “bluer” minus the “redder” color.

As a correction to the code of @paddyg, which did not work for me (especially for color with bv < 0.4) : here is the exact same version of the C++ code of @Spektre, in Python :

Colour of Stars, Colour of Stars and colour index page for astrophysics option for NSW HSC Physics. The colours of stars, however, are not obvious in most stars for several (The colours shown in the above table are the correct hexadecimal codes for rgb The B-V color index'' is a way of quantifying this using two different filters one a blue (B) filter that only lets a narrow range of colors or wavelengths through centered on the blue colors, and a visual'' (V) filter that only lets the wavelengths close to the green-yellow band through.

Why no violet or deep blue? Infinite color temperature, before being made less bluish by our atmosphere, has 1931 CIE coordinates of X=.240, y=.234.

The spectrum of a blackbody at infinite color temperature has spectral power distribution, in power per unit wavelength of bandwidth, being inversely proportional to wavelength to the 4th power. At 700nm, this is 10.7% as great as at 400nm.

Star B-V color index to apparent RGB color, I'm trying to convert a star's B-V color index to an apparent RGB color. Besides look up tables and color ramps, it seems like there's no well known algorithm for star: Stellar colours. The conventional colour index is defined as the blue magnitude, B, minus the visual magnitude, V the colour index, B − V, of the Sun is thus +5.47 − 4.82 = 0.65.…. parallax: Indirect measurement. …its light and called its colour index.

Magnitudes and Colors, After calibrating the detector using standard stars, and correcting for the The faintest stars visible with the naked eye from a dark site are about sixth a star with the temperature of the Sun (5,770 K) has a B-V color of 0.65. The Color Index The Color index is deﬁned as the difference between the magnitude of an object measured in two different colors: U - B is the color index between ultraviolet and blue light. B - V is the color index between blue and visual light. Note that U - B = M U - M B and B - V = M B - M V Because magnitudes decrease with increasing ﬂux, an object

Cluster Distances From Color-Magnitude Diagrams, The brightness (magnitude) of a star depends only on its distance, radius, A cluster color/magnitude plots a "one-dimensional color" against apparent Color is independent of distance, so the measured B-V magnitudes are intrinsic to the stars. of color index 0.5 and 1.0 to get Mv for main sequence stars of these colors. can tell you about the temperature, or color, of the star. This diﬀerence is referred to as the color index. 6 Color Index (B −V) One way to classify stars or galaxies is by the ratio of the ﬂux at one wavelength to the ﬂux at anotherwavelength. Thinking back tothe Planckcurvefora black

Properties of Stars, Here are the steps to determine the B-V color index: Measure the apparent brightness (flux) with two different filters (B, V). The flux of energy Even though you were forced to pick an arbitrary white-point, you can still represent every possible color. RGB is not like that. With RGB: not only is the color relative to some white-point but is is also relative to three primary colors: red, green, blue If you specify an RGB color of (255, 0, 0), you are saying you want "just red".

## B-V to U-B colour index - Astronomy

An analysis of the new U,B,V,R C ,I C -photometry of the cataclysmic variable RZ LMi obtained in 2016-17 showed the largest (U-B) colour excess in quiescence as well as during the decline of brightness, associated with the outbursts activity. The smallest (U-B) colour excess was found during the brightness increase from the quiescence. In contrast to the (U-B) colour index, the (B-V),(V-R C ),(R C -I C ) colour indices exhibits the largest colour excesses near the maximum of the outburst and the smallest during the quiescence. The (B-V) colour index showed also a large excess 1-2 days before a minimum. The detailed study of superhumps during the maximum of activity reveals the largest (U-B) colour excess at the time of the minimum brightness of superhumps. The (B-R C ) colour index exhibits a similar behaviour, but with a phase shift of +0.1-<+>0.2 period of superhumps. The tracks in two-colour and colour-magnitude diagrams during superoutbursts are compared with the data for other cataclysmic variables during their outbursts as well as with published theoretical calculations.

## B-V to U-B colour index - Astronomy

We present stellar photometry in the UBV passbands for the globular cluster M5≡NGC 5904. The observations, taken from short-exposure photographic plates and CCD frames, were obtained in the Ritchey-Cretien (RC) focus of the 2-m telescope of the National Astronomy Observatory Rozhen'. All stars in an annulus with radius 1<=r<=5.5arcmin were measured. We show that the ultraviolet (UV) colour-magnitude diagrams (CMDs) describe different evolutionary stages in a better manner than the classical' V, B-V diagram. We use HB stars, with known spectroscopic T eff to check the validity of the colour zero-point. A review of all known UV-bright star candidates in M5 is made and some of their parameters are catalogued. Six new stars of this kind are suspected on the basis of their position on the CMD. New assessment of the cluster reddening and metallicity is done using the U-B, B-V diagram. We find that [Fe/H]=-1.38, which confirms the Zinn & West value, contrasting with recent spectroscopic estimates. In an effort to clarify the question of the gap in the blue horizontal branch (BHB) stellar distribution and to investigate some other peculiarities, we use the relatively long-base colour index U-V. A comparison of the observed V, (U-V) 0 distribution of horizontal branch (HB) stars with a canonical zero-age horizontal branch (ZAHB) model reveals that the hottest stars rise above the model line. This is similar to the `u-jump' found in the Strömgren photometry. 18 BHB stars with (B-V) 0 ∈[-0.02/0.18] are used to estimate their ultraviolet deficiency. It is shown that low-gravity (logg<=2) Kurucz's atmospheric models fit the observed distribution of these stars along the two-colour diagram well.

## Color index for stars

For stars, it can be assumed to a good approximation that their spectrum follows the spectrum of a black body . The color index is therefore dependent on the temperature of the star: hot stars appear bluish and therefore have lower color indices than cool stars that appear reddish. Similarly, the color indices in earlier spectral classes are lower than in later types. For this reason, the same structures are shown in the Hertzsprung-Russell diagram as in the color-brightness diagram .

Some photometric systems have been specially designed to be able to determine certain star properties more precisely using color indices. The Strömgren-Crawford system, for example, offers the possibility of measuring certain spectral characteristics such as the Balmer crack , the metallicity or the strength of the H-beta line . With the help of the color indices, the surface gravity can be determined in addition to the temperature for B, A and F stars .

The UBV system is defined so that the colors of stars of the type A0V (eg. Vega ) form the zero-point: . Accordingly, the color indices of O and B stars in this system are always negative, all other types are always positive. U - B. = B. - V = 0

It should be noted that the color measured on earth generally does not correspond to the star's own color. Blue light is more strongly absorbed by extinction , reddening of the starlight occurs. This effect is also called interstellar discoloration and is described by the excess of color .

## Filters

Although we might sometimes want to know the total amount of light that a star emits (called the bolometric magnitude), this is very difficult to calculate, partly because of absorption in the Earth's atmosphere, but also because telescopes and detectors are not equally sensitive across all wavelengths - a telescope designed to look at infra-red radiation would be useless for studying X-rays and vice versa!

Any observation that we make therefore only detects a fraction of the total flux. T he most common technique at optical wavelengths involves the use of pieces of coloured glass, known as filters, which are designed to isolate light in particular colours. These filters come in two types:

• broad-band filters allow light through of wavelengths which are about 100 nanometres (nm) wide. The commonest system of broad-band filters, devised by Johnson and Morgan, is the system of UBV filters (see Figure 1). Typically, there are 5 filters which cover the whole range of optical light from U (near the boundary between violet and ultraviolet) to I (near the boundary between r ed and infrared). In this activity, we will only use data taken with B and V filters.
• narrow-band filters have typical wavelength ranges of about 5 nm usually centred around the wavelengths of specific electronic transitions such as hydrogen alpha and hydrogen beta.

A V-band magnitude is then referred to as mV or just V, for an apparent magnitude, and M V for an absolute magnitude. V stands for visual, B for blue and U for ultraviolet. Central wavelengths are:

• U 360 nm (or 3600 Angstroms)
• B 440 nm
• V 550 nm
• R 700 nm
• I 900 nm

As examples, the bright star Vega (in the constellation of Lyra) is defined as having m B = m V = 0. Our Sun has M B = 5.48 and M V = 4.83. So in fact, our Sun is not a particularly bright star it's just that it appears very bright to us since it is so near.

The colour of a star can be given a number by taking the ratio of brightnesses at two different wavelengths. Because the magnitude scale is logarithmic this is equivalent to taking the difference of two magnitudes. Astronomers refer to this difference as the colour index defined by, for example,

Note that cooler (and therefore redder) stars emit more light at longer wavelengths and will therefore have larger values of B-V (see Figure 2). From Figure 2, we can see that the B-V colour index is related to the star's temperature as calculated using Wien's Law.

Figure 2: Blackbody curves for stars of different temperatures.

What do broad-band filters allow us to do?

Take a measurement of a star's colour Yes, but they allow us to do more than this Take a measurement of a star's brightness Yes, but they allow us to do more than this Take a measurement of a star's temperature Yes, but they allow us to do more than this All of the above Yes, filters allow us to understand the brightness, colour and temperature of a star