122.166.16.186 at 03:08, 6 July 2009

2009-07-06T03:08:13Z

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In [[astronomy]], '''color–color diagrams''' are a means of comparing the [[apparent magnitude]]s of [[star]]s at different [[wavelength]]s. [[Astronomer]]s typically observe at narrow bands around certain wavelengths, and objects observed will have different [[luminosity|brightnesses]] in each band. The difference in brightness between two bands is referred to as [[color index|color]]. On color–color diagrams, the color defined by two wavelength bands is plotted on the horizontal [[coordinate axis|axis]], and then the color defined by another brightness difference (though usually there is one band involved in determining both colors) will be plotted on the vertical axis.

==Background==
{{See also|Black body|Black-body radiation}}
[[File:Effective temperature and color index.png|thumb|Effective temperature of a black body compared with the ''B-V'' and ''U-B'' [[Photometric system|color index]] of main sequence and super giant stars in what is called a ''color-color diagram''.<ref name=UBV>
Figure modeled after {{cite book |title=Introduction to Stellar Astrophysics: Basic stellar observations and data |author=E. Böhm-Vitense |url=http://books.google.com/books?id=JWrtilsCycQC&pg=PA26 |page=26 |chapter=Figure 4.9 |publisher=Cambridge University Press |isbn=0-521-34869-2 |year=1989}}
</ref> Stars emit less [[ultraviolet radiation]] than a black body with the same ''B-V'' index.]]
While stars are not perfect [[black body|blackbodies]], to first order the [[spectrum|spectra]] of light emitted by stars conforms closely to a [[black-body radiation]] curve, also referred to sometimes as a [[thermal radiation]] curve. The overall shape of a black-body curve is uniquely determined by its [[temperature]], and the wavelength of peak intensity is inversely proportional to temperature, a relation known as [[Wien's Displacement Law]]. Thus, observation of a stellar spectrum allows determination of its [[effective temperature]]. Obtaining complete spectra for stars through [[astronomical spectroscopy|spectrometry]] is much more involved than simple [[photometry (astronomy)|photometry]] in a few bands. Thus by comparing the magnitude of the star in multiple different [[color index|color indices]], the [[effective 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 a [[Hertzsprung–Russell diagram]], and stars of different [[stellar classification|spectral 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 absortions 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 <ref name=Ballesteros>Ballesteros, F.J. (2012). "New insights into black bodies ". EPL (Europhysics Letters) 97 (2012) 34008. http://arxiv.org/pdf/1201.1809.pdf.</ref> deduced for pure blackbodies:

:<math>C - D = \frac{\nu_c - \nu_d}{\nu_a - \nu_b} (A - B) + k, </math>

where A, B, C and D are the magnitudes of the stars measured through filters with central frecuencies <math>\nu_a</math>, <math>\nu_b</math>, <math>

\nu_c</math> and <math>\nu_d</math> respectively, and k is a constant depending on the central wavelength and width of the filters, given by:

:<math> k = -2.5 \log_{10} \left[ {\left( {\frac{{\nu_c }}{{\nu_d }}} \right)^2
\left( {\frac{{\Delta_c }}{{\Delta_d }}} \right) \left( {\frac{{\nu_b }}{{\nu_a }}} \right)^{2\frac{{\nu_c - \nu_d }}{{\nu_a - \nu_b }}} \left( {\frac{{\Delta_b }}{{\Delta_a }}} \right)^{\frac{{\nu_c - \nu_d }}{{\nu_a - \nu_b }}} } \right] </math>

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 a 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.

==Applications==

===Photometric calibration===

[[File:Stellar-locus-regression.png|thumb|right|A schematic illustration of the stellar locus regression method of photometric calibration in astronomy.]]
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 (unlike [[apparent magnitude]]s) are independent of the distance to the stars. Stellar locus regression (SLR)<ref name=slr>
{{Cite journal
|author=F. W. High et al.
|title= Stellar Locus Regression: Accurate Color Calibration and the Real-Time Determination of Galaxy Cluster Photometric Redshifts
|journal= The Astronomical Journal
|year=2009
|doi=10.1088/0004-6256/138/1/110
|volume= 138
|issue=1
|pages= 110–129
|bibcode=2009AJ....138..110H
|arxiv = 0903.5302 }}
</ref> 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 the [http://www.noao.edu/noao/noaodeep/ NOAO Deep Wide-Field Survey] region used it to arrive at more accurate colors than would have otherwise been attainable by traditional calibration methods, and [[South Pole Telescope]] used SLR in the measurement of redshifts of [[galaxy clusters]].<ref name = high10>
{{Cite journal
|title = Optical Redshift and Richness Estimates for Galaxy Clusters Selected with the Sunyaev-Zel'dovich Effect from 2008 South Pole Telescope Observations
|author = F. W. High et al.
|bibcode = 2010ApJ...723.1736H
|journal = The Astrophysical Journal
|year=2010
|doi=10.1088/0004-637X/723/2/1736
|volume= 723
|issue=2
|pages= 1736–1747
|arxiv = 1003.0005 }}
</ref> The blue-tip method<ref>
{{Cite journal
|title = The Blue Tip of the Stellar Locus: Measuring Reddening with the SDSS
|author = E. Schlafly et al.
|arxiv = 1009.4933
|bibcode = 2010ApJ...725.1175S |doi = 10.1088/0004-637X/725/1/1175 }}
</ref> is closely related to SLR, but was used mainly to correct [[Extinction (astronomy)|Galactic extinction]] predictions from [[IRAS]] data. Other surveys have used the stellar color-color diagram primarily as a calibration diagnostic tool, including The Oxford-Dartmouth Thirty Degree Survey<ref>
{{Cite journal
|title = The Oxford-Dartmouth Thirty Degree Survey – I. Observations and calibration of a wide-field multiband survey
|author = E. MacDonald et al.
|bibcode = 2004MNRAS.352.1255M
|journal = Monthly Notices of the Royal Astronomical Society
|year=2004
|doi=10.1111/j.1365-2966.2004.08014.x
|volume= 352
|issue=4
|pages= 1255–1272
|arxiv = astro-ph/0405208 }}
</ref> and [[Sloan Digital Sky Survey]] (SDSS).<ref>
{{Cite journal
|title = Sloan Digital Sky Survey Standard Star Catalog for Stripe 82: The Dawn of Industrial 1% Optical Photometry
|author = Z. Ivezic et al.
|bibcode = 2007AJ....134..973I
|journal = The Astronomical Journal
|year=2007
|doi=10.1086/519976
|volume= 134
|issue=3
|pages= 973–998
|arxiv = astro-ph/0703157 }}
</ref>

===Color outliers===
Analyzing data from large observational surveys, such as the [[Sloan Digital Sky Survey|SDSS]] or [[2 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 the [[main sequence]] stellar population. Once these outliers are identified, they can then be studied in more detail. This method has been used to identify ultracool [[subdwarf]]s.<ref name="subdwarf1">{{cite journal | author = Burgasser, A. J., Cruz, K.L., Kirkpatrick, J.D. | title = Optical Spectroscopy of 2MASS Color-selected Ultracool Subdwarfs | journal = Astrophysical Journal | volume = 657 | issue = 1 | pages = 494–510 | year = 2007 | bibcode = 2006astro.ph.10096B | doi = 10.1086/510148|arxiv = astro-ph/0610096 }}</ref><ref name="subdwarf2">{{cite journal | author = Gizis, J.E. et al. | title = New Neighbors from 2MASS: Activity and Kinematics at the Bottom of the Main Sequence | journal = Astronomical Journal | volume = 120 | issue = 2 | pages = 1085–1099 | url = http://www.iop.org/EJ/abstract/-link=9084013/1538-3881/120/2/1085 | doi = 10.1086/301456 | year = 2000 | bibcode=2000AJ....120.1085G|arxiv = astro-ph/0004361 }}</ref> Unresolved [[binary star]]s, which appear [[photometry (astronomy)|photometrically]] to be points, have been identified by studying color-color outliers in cases where one member is off the main sequence.<ref name="binary">{{cite journal | author = Covey, K.R. et al. | title = Stellar SEDs from 0.3 to 2.5 micron: Tracing the Stellar Locus and Searching for Color Outliers in the SDSS and 2MASS | journal = Astronomical Journal | volume = 134 | issue = 6 | pages = 2398–2417 | year = 2007 | url = http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0707.4473 | doi = 10.1086/522052 | bibcode=2007AJ....134.2398C|arxiv = 0707.4473 }}</ref> The stages of the evolution of stars along the [[asymptotic giant branch]] from [[carbon star]] to [[planetary nebula]] appear on distinct regions of color–color diagrams.<ref name="agb_evolution">{{cite journal | author = Ortiz, R. et al. | title = Evolution from AGB to planetary nebula in the MSX survey | journal = Astronomy and Astrophysics | volume = 431 | issue = 2 | pages = 565–574 | year = 2005 | bibcode = 2004astro.ph.11769O | doi = 10.1051/0004-6361:20040401|arxiv = astro-ph/0411769 }}</ref> [[Quasar]]s also appear as color-color outliers.<ref name="binary"/>

===Star formation===

[[File:Trapezium cluster optical and infrared comparison.jpg|thumb|left|The optical image (left) shows clouds of dust, while the infrared image (right) displays a number of young stars. ''Credit: C. R. O'Dell-Vanderbilt University, NASA, and ESA''.]]

Color–color diagrams are often used in [[infrared]] astronomy to study [[star formation|star forming]] regions. Stars form in [[interstellar cloud|clouds]] of [[cosmic dust|dust]]. 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, an [[infrared excess|excess of infrared radiation]] is observed for the star. Even without circumstellar dust, regions undergoing star formation exhibit high infrared [[luminosity|luminosities]] compared to stars on the main sequence.<ref>{{cite journal | author=C. Struck-Marcell and B.M. Tinsley | year = 1978 | title = Star formation rates and infrared radiation | journal=Astrophysical Journal | volume=221 | pages=562–566 | bibcode=1978ApJ...221..562S | doi=10.1086/156057}}</ref> Each of these effects is distinct from the reddening of starlight which occurs as a result of [[scattering]] off of dust in the [[interstellar medium]].

[[File:Trapez ccdiag.jpg|thumb|right|Color–color diagram of the Trapezium cluster shows that many cluster members exhibit infrared excess, which is characteristic of stars with circumstellar disks.]]

Color–color diagrams allow for these effects to be isolated. As the color–color relationships of [[main 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 stars [[interstellar reddening|reddened]] 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 (see [[infrared 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 exhibit [[infrared excess]]. These objects are likely [[protostellar]] in nature, with the excess radiation at long wavelengths caused by suppression by the [[reflection nebula]] in which the protostars are embedded.<ref>{{cite journal | author = Lada, C.J. et al. | title = Infrared L-Band Observations of the Trapezium Cluster: A Census of Circumstellar Disks and Candidate Protostars | journal = The Astronomical Journal | volume = 120 | issue = 6 | pages = 3162–3176 | year = 2000 | bibcode = 2000AJ....120.3162L | doi = 10.1086/316848|arxiv = astro-ph/0008280 }}</ref> 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.<ref>{{cite journal | author=Charles Lada and Fred Adams | year=1992 | title=Interpreting infrared color-color diagrams – Circumstellar disks around low- and intermediate-mass young stellar objects | journal=Astrophysical Journal | volume=393 | pages=278–288 | bibcode=1992ApJ...393..278L | doi=10.1086/171505}}</ref>

==See also==

* [[Hertzsprung–Russell diagram]]
* [[Stellar evolution]]
* [[Nebula]]
* [[Color index]]

==References==
{{reflist|2}}

==External links==
* [http://stellar-locus-regression.googlecode.com/ Stellar Locus Regression]
* [http://www.astro.umass.edu/theses/meyer/ngc2024/node4.html Color-Color and Color-Magnitude Diagrams] (examples of color-color diagrams)
* [http://www.astro.caltech.edu/~jmc/variables/cham1/ Near-Infrared Photometric Variability of Stars Toward the Chamaeleon I Molecular Cloud]

{{Star}}

{{DEFAULTSORT:Color-Color Diagram}}
[[Category:Stellar evolution]]
[[Category:Star formation]]

Boolean conjunctive query - Revision history

122.166.16.186 at 03:08, 6 July 2009