A color–color diagram is a means of comparing the colors of an astronomical object at different wavelengths. Astronomers typically observe at narrow bands around certain wavelengths, and objects observed will have different brightnesses in each band. The difference in brightness between two bands is referred to as color. On color–color diagrams, the color defined by two wavelength bands is plotted on the horizontal axis, and the color defined by another brightness difference will be plotted on the vertical axis.
Effective temperature of a black body compared with the B−V and U−Bcolor index of main sequence and supergiant stars in what is called a color-color diagram.[1] Stars emit less ultraviolet radiation than a black body with the same B−V index.
Although stars are not perfect blackbodies, to first order the 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 spectrometry is much more involved than simple photometry in a few bands. Thus by comparing the magnitude of the star in multiple different 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 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 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:
where A, B, C and D are the magnitudes of the stars measured through filters with central frequencies νa, νb, νc and νd respectively, and k is a constant depending on the central wavelength and width of the filters, given by:
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 usedfor the case of old data, when logs are not conserved and filter information has been lost.
Applications
Photometric calibration
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 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 the 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.[4] The blue-tip method[5] is closely related to SLR, but was used mainly to correct 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[6] and Sloan Digital Sky Survey (SDSS).[7]
Color outliers
Analyzing data from large observational surveys, such as the 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 subdwarfs.[8][9] Unresolved binary stars, which appear photometrically 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 the asymptotic giant branch from carbon star to planetary nebula appear on distinct regions of color–color diagrams.[11]Quasars also appear as color-color outliers.[10]
Star formation
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 forming regions. Stars form in clouds of 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 excess of infrared radiation is observed for the star. Even without circumstellar dust, regions undergoing star formation exhibit high infrared luminosities compared to stars on the main sequence.[12] 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.
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 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.[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]
^Figure modeled after Böhm-Vitense, Erika (1989). "Figure 4.9". Introduction to Stellar Astrophysics: Basic stellar observations and data. Cambridge University Press. p. 26. ISBN0-521-34869-2.
^Ballesteros, Fernando J. (2012). "New insights into black bodies". Europhysics Letters. 97 (3): 34008. arXiv:1201.1809. Bibcode:2012EL.....9734008B. doi:10.1209/0295-5075/97/34008. S2CID 119191691.
^High, F. William; et al. (2009). "Stellar Locus Regression: Accurate Color Calibration and the Real-Time Determination of Galaxy Cluster Photometric Redshifts". The Astronomical Journal. 138 (1): 110–129. arXiv:0903.5302. Bibcode:2009AJ....138..110H. doi:10.1088/0004-6256/138/1/110. S2CID 16468717.
^High, F. William; et al. (2010). "Optical Redshift and Richness Estimates for Galaxy Clusters Selected with the Sunyaev-Zel'dovich Effect from 2008 South Pole Telescope Observations". The Astrophysical Journal. 723 (2): 1736–1747. arXiv:1003.0005. Bibcode:2010ApJ...723.1736H. doi:10.1088/0004-637X/723/2/1736. S2CID 119189086.
^Schlafly, Edawrd F.; et al. (2010). "The Blue Tip of the Stellar Locus: Measuring Reddening with the SDSS". The Astrophysical Journal. 725 (1): 1175. arXiv:1009.4933. Bibcode:2010ApJ...725.1175S. doi:10.1088/0004-637X/725/1/1175. S2CID 29269150.
^MacDonald, Emily C.; et al. (2004). "The Oxford-Dartmouth Thirty Degree Survey – I. Observations and calibration of a wide-field multiband survey". Monthly Notices of the Royal Astronomical Society. 352 (4): 1255–1272. arXiv:astro-ph/0405208. Bibcode:2004MNRAS.352.1255M. doi:10.1111/j.1365-2966.2004.08014.x. S2CID 16095072.
^Ivezić, Željko; et al. (2007). "Sloan Digital Sky Survey Standard Star Catalog for Stripe 82: The Dawn of Industrial 1% Optical Photometry". The Astronomical Journal. 134 (3): 973–998. arXiv:astro-ph/0703157. Bibcode:2007AJ....134..973I. doi:10.1086/519976. S2CID 26430584.
^Burgasser, Adam J.; Cruz, Kelle L.; Kirkpatrick, J. Davy (2007). "Optical Spectroscopy of 2MASS Color-selected Ultracool Subdwarfs". Astrophysical Journal. 657 (1): 494–510. arXiv:astro-ph/0610096. Bibcode:2007ApJ...657..494B. doi:10.1086/510148. S2CID 17307898.
^Gizis, John E.; et al. (2000). "New Neighbors from 2MASS: Activity and Kinematics at the Bottom of the Main Sequence". Astronomical Journal. 120 (2): 1085–1099. arXiv:astro-ph/0004361. Bibcode:2000AJ....120.1085G. doi:10.1086/301456. S2CID 18819321.
^ abCovey, Kevin R.; et al. (2007). "Stellar SEDs from 0.3 to 2.5 micron: Tracing the Stellar Locus and Searching for Color Outliers in the SDSS and 2MASS". Astronomical Journal. 134 (6): 2398–2417. arXiv:0707.4473. Bibcode:2007AJ....134.2398C. doi:10.1086/522052. S2CID 17297521.
^Ortiz, Roberto; et al. (2005). "Evolution from AGB to planetary nebula in the MSX survey". Astronomy and Astrophysics. 431 (2): 565–574. arXiv:astro-ph/0411769. Bibcode:2005A&A...431..565O. doi:10.1051/0004-6361:20040401. S2CID 15147139.
^Struck-Marcell, Curtis; Tinsley, Beatrice M. (1978). "Star formation rates and infrared radiation". Astrophysical Journal. 221: 562–566. Bibcode:1978ApJ...221..562S. doi:10.1086/156057.
^Lada, Charles J.; et al. (2000). "Infrared L-Band Observations of the Trapezium Cluster: A Census of Circumstellar Disks and Candidate Protostars". The Astronomical Journal. 120 (6): 3162–3176. arXiv:astro-ph/0008280. Bibcode:2000AJ....120.3162L. doi:10.1086/316848. S2CID 16456003.
^Lada, Charles J.; Adams, Fred C. (1992). "Interpreting infrared color-color diagrams – Circumstellar disks around low- and intermediate-mass young stellar objects". Astrophysical Journal. 393: 278–288. Bibcode:1992ApJ...393..278L. doi:10.1086/171505.
External links
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
color, color, diagram, color, color, diagram, means, comparing, colors, astronomical, object, different, wavelengths, astronomers, typically, observe, narrow, bands, around, certain, wavelengths, objects, observed, will, have, different, brightnesses, each, ba. A color color diagram is a means of comparing the colors of an astronomical object at different wavelengths Astronomers typically observe at narrow bands around certain wavelengths and objects observed will have different brightnesses in each band The difference in brightness between two bands is referred to as color On color color diagrams the color defined by two wavelength bands is plotted on the horizontal axis and the color defined by another brightness difference will be plotted on the vertical axis Contents 1 Background 2 Applications 2 1 Photometric calibration 2 2 Color outliers 2 3 Star formation 3 See also 4 References 5 External linksBackground EditSee also Black body and Black body radiation Effective temperature of a black body compared with the B V and U B color index of main sequence and supergiant stars in what is called a color color diagram 1 Stars emit less ultraviolet radiation than a black body with the same B V index Although stars are not perfect blackbodies to first order the 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 spectrometry is much more involved than simple photometry in a few bands Thus by comparing the magnitude of the star in multiple different 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 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 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 C D n c n d n a n b A B k displaystyle C D frac nu text c nu text d nu text a nu text b A B k where A B C and D are the magnitudes of the stars measured through filters with central frequencies na nb nc and nd respectively and k is a constant depending on the central wavelength and width of the filters given by k 2 5 log 10 n c n d 2 D c D d n b n a 2 n c n d n a n b D b D a n c n d n a n b displaystyle k 2 5 log 10 left left frac nu text c nu text d right 2 left frac Delta text c 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 Delta text b 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 usedfor the case of old data when logs are not conserved and filter information has been lost Applications EditPhotometric calibration Edit 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 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 the 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 4 The blue tip method 5 is closely related to SLR but was used mainly to correct 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 6 and Sloan Digital Sky Survey SDSS 7 Color outliers Edit Analyzing data from large observational surveys such as the 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 subdwarfs 8 9 Unresolved binary stars which appear photometrically 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 the asymptotic giant branch from carbon star to planetary nebula appear on distinct regions of color color diagrams 11 Quasars also appear as color color outliers 10 Star formation Edit 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 forming regions Stars form in clouds of 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 excess of infrared radiation is observed for the star Even without circumstellar dust regions undergoing star formation exhibit high infrared luminosities compared to stars on the main sequence 12 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 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 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 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 See also EditHertzsprung Russell diagram Stellar evolution Nebula Color index Infrared astronomyReferences Edit Figure modeled after Bohm Vitense Erika 1989 Figure 4 9 Introduction to Stellar Astrophysics Basic stellar observations and data Cambridge University Press p 26 ISBN 0 521 34869 2 Ballesteros Fernando J 2012 New insights into black bodies Europhysics Letters 97 3 34008 arXiv 1201 1809 Bibcode 2012EL 9734008B doi 10 1209 0295 5075 97 34008 S2CID 119191691 High F William et al 2009 Stellar Locus Regression Accurate Color Calibration and the Real Time Determination of Galaxy Cluster Photometric Redshifts The Astronomical Journal 138 1 110 129 arXiv 0903 5302 Bibcode 2009AJ 138 110H doi 10 1088 0004 6256 138 1 110 S2CID 16468717 High F William et al 2010 Optical Redshift and Richness Estimates for Galaxy Clusters Selected with the Sunyaev Zel dovich Effect from 2008 South Pole Telescope Observations The Astrophysical Journal 723 2 1736 1747 arXiv 1003 0005 Bibcode 2010ApJ 723 1736H doi 10 1088 0004 637X 723 2 1736 S2CID 119189086 Schlafly Edawrd F et al 2010 The Blue Tip of the Stellar Locus Measuring Reddening with the SDSS The Astrophysical Journal 725 1 1175 arXiv 1009 4933 Bibcode 2010ApJ 725 1175S doi 10 1088 0004 637X 725 1 1175 S2CID 29269150 MacDonald Emily C et al 2004 The Oxford Dartmouth Thirty Degree Survey I Observations and calibration of a wide field multiband survey Monthly Notices of the Royal Astronomical Society 352 4 1255 1272 arXiv astro ph 0405208 Bibcode 2004MNRAS 352 1255M doi 10 1111 j 1365 2966 2004 08014 x S2CID 16095072 Ivezic Zeljko et al 2007 Sloan Digital Sky Survey Standard Star Catalog for Stripe 82 The Dawn of Industrial 1 Optical Photometry The Astronomical Journal 134 3 973 998 arXiv astro ph 0703157 Bibcode 2007AJ 134 973I doi 10 1086 519976 S2CID 26430584 Burgasser Adam J Cruz Kelle L Kirkpatrick J Davy 2007 Optical Spectroscopy of 2MASS Color selected Ultracool Subdwarfs Astrophysical Journal 657 1 494 510 arXiv astro ph 0610096 Bibcode 2007ApJ 657 494B doi 10 1086 510148 S2CID 17307898 Gizis John E et al 2000 New Neighbors from 2MASS Activity and Kinematics at the Bottom of the Main Sequence Astronomical Journal 120 2 1085 1099 arXiv astro ph 0004361 Bibcode 2000AJ 120 1085G doi 10 1086 301456 S2CID 18819321 a b Covey Kevin R et al 2007 Stellar SEDs from 0 3 to 2 5 micron Tracing the Stellar Locus and Searching for Color Outliers in the SDSS and 2MASS Astronomical Journal 134 6 2398 2417 arXiv 0707 4473 Bibcode 2007AJ 134 2398C doi 10 1086 522052 S2CID 17297521 Ortiz Roberto et al 2005 Evolution from AGB to planetary nebula in the MSX survey Astronomy and Astrophysics 431 2 565 574 arXiv astro ph 0411769 Bibcode 2005A amp A 431 565O doi 10 1051 0004 6361 20040401 S2CID 15147139 Struck Marcell Curtis Tinsley Beatrice M 1978 Star formation rates and infrared radiation Astrophysical Journal 221 562 566 Bibcode 1978ApJ 221 562S doi 10 1086 156057 Lada Charles J et al 2000 Infrared L Band Observations of the Trapezium Cluster A Census of Circumstellar Disks and Candidate Protostars The Astronomical Journal 120 6 3162 3176 arXiv astro ph 0008280 Bibcode 2000AJ 120 3162L doi 10 1086 316848 S2CID 16456003 Lada Charles J Adams Fred C 1992 Interpreting infrared color color diagrams Circumstellar disks around low and intermediate mass young stellar objects Astrophysical Journal 393 278 288 Bibcode 1992ApJ 393 278L doi 10 1086 171505 External links EditStellar 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 Portals Astronomy Spaceflight Outer space Solar System Retrieved from https en wikipedia org w index php title Color color diagram amp oldid 1118352966, wikipedia, wiki, book, books, library,
