Acolor–color diagram is a means of comparing the colors of an astronomical object at differentwavelengths.Astronomers typically observe at narrow bands around certain wavelengths, and objects observed will have differentbrightnesses in each band. The difference in brightness between two bands is referred to as an object'scolor index, or simplycolor. On color–color diagrams, the color defined by two wavelength bands is plotted on the horizontalaxis, and the color defined by another brightness difference will be plotted on the vertical axis.

Although stars are not perfectblackbodies, to first order thespectra of light emitted by stars conforms closely to ablack-body radiation curve, also referred to sometimes as athermal radiation curve. The overall shape of a black-body curve is uniquely determined by itstemperature, and the wavelength of peak intensity is inversely proportional to temperature, a relation known asWien's Displacement Law. Thus, observation of astellar spectrum allows determination of itseffective temperature. Obtaining complete spectra for stars throughspectrometry is much more involved than simplephotometry in a few bands. Thus by comparing the magnitude of the star in multiple differentcolor indices, theeffective temperature of the star can still be determined, as magnitude differences between each color will be unique for that temperature. As such, color-color diagrams can be used as a means of representing the stellar population, much like aHertzsprung–Russell diagram, and stars of differentspectral classes will inhabit different parts of the diagram. This feature leads to applications within various wavelength bands.

In the stellar locus, stars tend to align in a more or less straight feature. If stars were perfect black bodies, the stellar locus would be a pure straight line indeed. The divergences with the straight line are due to the absorptions and emission lines in the stellar spectra. These divergences can be more or less evident depending on the filters used: narrow filters with central wavelength located in regions without lines, will produce a response close to the black body one, and even filters centered at lines if they are broad enough, can give a reasonable blackbody-like behavior.

Therefore, in most cases the straight feature of the stellar locus can be described by Ballesteros' formula^[2] deduced for pure blackbodies:$${\displaystyle C-D=\frac{{\nu }_{\text{c}}-{\nu }_{\text{d}}}{{\nu }_{\text{a}}-{\nu }_{\text{b}}}(A-B)+k,}$$whereA,B,C andD are the magnitudes of the stars measured through filters with central frequenciesν_a,ν_b,ν_c andν_d respectively, andk is a constant depending on the central wavelength and width of the filters, given by:$${\displaystyle k=-2.5{\log }_{10}\left[{\left(\frac{{\nu }_{\text{c}}}{{\nu }_{\text{d}}}\right)}^2\left(\frac{{\mathrm{\Delta }}_{\text{c}}}{{\mathrm{\Delta }}_{\text{d}}}\right){\left(\frac{{\nu }_{\text{b}}}{{\nu }_{\text{a}}}\right)}^{2\frac{{\nu }_{\text{c}}-{\nu }_{\text{d}}}{{\nu }_{\text{a}}-{\nu }_{\text{b}}}}{\left(\frac{{\mathrm{\Delta }}_{\text{b}}}{{\mathrm{\Delta }}_{\text{a}}}\right)}^{\frac{{\nu }_{\text{c}}-{\nu }_{\text{d}}}{{\nu }_{\text{a}}-{\nu }_{\text{b}}}}\right]}$$

Note that the slope of the straight line depends only on the effective wavelength, not in the filter width.

Although this formula cannot be directly used to calibrate data, if one has data well calibrated for two given filters, it can be used to calibrate data in other filters. It can be used to measure the effective wavelength midpoint of an unknown filter too, by using two well known filters. This can be useful to recover information on the filters used for the case of old data, when logs are not conserved and filter information has been lost.

The color-color diagram of stars can be used to directly calibrate or to test colors and magnitudes in optical and infrared imaging data. Such methods take advantage of the fundamental distribution of stellar colors in our galaxy across the vast majority of the sky, and the fact that observed stellar colors (unlikeapparent magnitudes) are independent of the distance to the stars. Stellar locus regression (SLR)^[3] was a method developed to eliminate the need for standard star observations in photometric calibrations, except highly infrequently (once a year or less) to measure color terms. SLR has been used in a number of research initiatives. The NEWFIRM survey of theNOAO Deep Wide-Field Survey region used it to arrive at more accurate colors than would have otherwise been attainable by traditional calibration methods, andSouth Pole Telescope used SLR in the measurement of redshifts ofgalaxy clusters.^[4] The blue-tip method^[5] is closely related to SLR, but was used mainly to correctGalactic extinction predictions fromIRAS data. Other surveys have used the stellar color-color diagram primarily as a calibration diagnostic tool, including The Oxford-Dartmouth Thirty Degree Survey^[6] andSloan Digital Sky Survey (SDSS).^[7]

Analyzing data from large observational surveys, such as theSDSS or2 Micron All Sky Survey (2MASS), can be challenging due to the huge number of data produced. For surveys such as these, color-color diagrams have been used to find outliers from themain sequence stellar population. Once these outliers are identified, they can then be studied in more detail. This method has been used to identify ultracoolsubdwarfs.^[8][9] Unresolvedbinary stars, which appearphotometrically to be points, have been identified by studying color-color outliers in cases where one member is off the main sequence.^[10] The stages of the evolution of stars along theasymptotic giant branch fromcarbon star toplanetary nebula appear on distinct regions of color–color diagrams (carbon stars tend to be redder than expected from their temperature due to the formation of carbon compounds in their atmospheres which absorb blue light).^[11]Quasars also appear as color-color outliers.^[10]

Color–color diagrams are often used ininfrared astronomy to studystar forming regions. Stars form inclouds ofdust. As the star continues to contract, a circumstellar disk of dust is formed, and this dust is heated by the star inside. The dust itself then begins to radiate as a blackbody, though one much cooler than the star. As a result, anexcess of infrared radiation is observed for the star. Even without circumstellar dust, regions undergoing star formation exhibit high infraredluminosities compared to stars on the main sequence.^[12] Each of these effects is distinct from the reddening of starlight which occurs as a result ofscattering off of dust in theinterstellar medium.

Color–color diagrams allow for these effects to be isolated. As the color–color relationships ofmain sequence stars are well known, a theoretical main sequence can be plotted for reference, as is done with the solid black line in the example to the right.Interstellar dust scattering is also well understood, allowing bands to be drawn on a color–color diagram defining the region in which starsreddened by interstellar dust are expected to be observed, indicated on the color–color diagram by dashed lines. The typical axes for infrared color–color diagrams have (H–K) on the horizontal axis and (J–H) on the vertical axis (seeinfrared astronomy for information on band color designations). On a diagram with these axes, stars which fall to the right of the main sequence and the reddening bands drawn are significantly brighter in the K band than main sequence stars, including main sequence stars which have experienced reddening due to interstellar dust. Of the J, H, and K bands, K is the longest wavelength, so objects which are anomalously bright in the K band are said to exhibitinfrared excess. These objects are likelyprotostellar in nature, with the excess radiation at long wavelengths caused by suppression by thereflection nebula in which the protostars are embedded.^[13] Color–color diagrams can be used then as a means of studying stellar formation, as the state of a star in its formation can be roughly determined by looking at its position on the diagram.^[14]

• Hertzsprung–Russell diagram
• Stellar evolution
• Nebula
• Color index
• Infrared astronomy

• Stellar Locus Regression
• Color-Color and Color-Magnitude Diagrams (examples of color-color diagrams)
• Near-Infrared Photometric Variability of Stars Toward the Chamaeleon I Molecular Cloud

• Stellar evolution
• Star formation

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• Short description is different from Wikidata