Editing Light curve

{{Short description|Graph of light intensity of a celestial object or region, as a function of time}}
{{about|astronomical graphs of brightness variations|photosynthetic response graphs|Light curve (botany)}}
[[File:201 Penelope light curve.png|thumb|upright=1.4|Light curve of the asteroid [[201 Penelope]] based on images taken on 6 October 2006 at [[Mount John University Observatory]]. Shows just over one full [[rotation period|rotation]], which lasts 3.7474 hours.]]

In [[astronomy]], a '''light curve''' is a [[graph (discrete mathematics)|graph]] of the [[Radiance|light intensity]] of a [[celestial object]] or region as a function of time, typically with the [[magnitude (astronomy)|magnitude]] of [[light]] received on the ''y''-axis and with time on the ''x''-axis. The light is usually in a particular frequency interval or [[frequency band|band]].

Light curves can be periodic, as in the case of [[eclipsing binary|eclipsing binaries]], [[Cepheid variable]]s, other periodic variables, and [[Methods of detecting extrasolar planets#Transit photometry|transiting]] [[extrasolar planets]]; or [[aperiodic]], like the light curve of a [[nova]], [[cataclysmic variable star]], [[supernova]], [[gravitational microlensing|microlensing event]], or binary as observed during [[occultation]] events. The study of a light curve and other observations can yield considerable information about the physical process that produces such a light curve, or constrain the physical theories about it.

== Variable stars ==
{{main|Variable star}}
[[File:Delta Cephei lightcurve.jpg|thumb|Light curve of [[δ Cephei]] showing [[apparent magnitude|magnitude]] versus pulsation [[phase (waves)|phase]]]]

Graphs of the [[apparent magnitude]] of a variable star over time are commonly used to visualise and analyse their behaviour. Although the categorisation of variable star types is increasingly done from their spectral properties, the amplitudes, periods, and regularity of their brightness changes are still important factors. Some types such as [[Cepheid variable|Cepheids]] have extremely regular light curves with exactly the same period, amplitude, and shape in each cycle. Others such as [[Mira variable]]s have somewhat less regular light curves with large amplitudes of several magnitudes, while the [[semiregular variable]]s are less regular still and have smaller amplitudes.<ref name=gcvs/>

The shapes of variable star light curves give valuable information about the underlying physical processes producing the brightness changes. For eclipsing variables, the shape of the light curve indicates the degree of totality, the relative sizes of the stars, and their relative surface brightnesses.<ref name=russell/> It may also show the [[Eccentricity (astronomy)|eccentricity]] of the orbit and [[Ellipsoidal variable|distortions in the shape]] of the two stars.<ref name=kron/>  For pulsating stars, the amplitude or period of the pulsations can be related to the luminosity of the star, and the light curve shape can be an indicator of the pulsation mode.<ref name=wood/>

=== Supernovae ===
{{main|Supernova}}
[[File:Comparative supernova type light curves.png|thumb|Comparative [[supernova]] type light curves]]

Light curves from [[supernova]]e can be indicative of the type of supernova. Although supernova types are defined on the basis of their spectra, each has typical light curve shapes. [[Type I supernova]]e have light curves with a sharp [[Maxima and minima|maximum]] and gradually decline, while [[Type II supernova]]e have less sharp maxima. Light curves are helpful for classification of faint supernovae and for the determination of sub-types. For example, the type II-P (for plateau) have similar spectra to the type II-L (linear) but are distinguished by a light curve where the decline flattens out for several weeks or months before resuming its fade.<ref name=hyperphysics/>

== {{anchor|Planetology}} Planetary astronomy ==
{{main|Planetary science}}

In [[planetary science]], a light curve can be used to derive the [[rotation period]] of a [[minor planet]], [[natural satellite|moon]], or [[comet]] nucleus. From the [[Earth]] there is often no way to resolve a small object in the [[Solar System]], even in the most powerful of [[telescope]]s, since the apparent angular size of the object is smaller than one pixel in the detector. Thus, astronomers measure the amount of light produced by an object as a function of time (the light curve). The time separation of peaks in the light curve gives an estimate of the rotational period of the object. The difference between the maximum and minimum brightnesses (the [[amplitude]] of the light curve) can be due to the shape of the object, or to bright and dark areas on its surface. For example, an asymmetrical asteroid's light curve generally has more pronounced peaks, while a more spherical object's light curve will be flatter.<ref name="lc"/> This allows astronomers to infer information about the shape and spin (but not size) of asteroids.

=== Asteroid lightcurve database ===

==== {{anchor|LCDB quality code}} Light curve quality code ====

The ''Asteroid Lightcurve Database'' (LCDB) of the Collaborative Asteroid Lightcurve Link (CALL) uses a numeric code to assess the quality of a period solution for minor planet light curves (it does not necessarily assess the actual underlying data). Its quality code parameter ''U'' ranges from 0 (incorrect) to 3 (well-defined):<ref name="LCDB"/>
* ''U'' = 0 → Result later proven incorrect
* ''U'' = 1 → Result based on fragmentary light curve(s), may be completely wrong.
* ''U'' = 2 → Result based on less than full coverage. Period may be wrong by 30 percent or ambiguous. 
* ''U'' = 3 → Secure result within the precision given. No ambiguity.
* ''U'' = n.a. → Not available. Incomplete or inconclusive result.

A trailing plus sign (+) or minus sign (−) is also used to indicate a slightly better or worse quality than the unsigned value.<ref name="LCDB" />

=== Occultation light curves ===
{{Further|Occultation#Occultations by minor planets}}
[[File:LightCurve AsteroidOccultation.png|thumb|Light curve of the asteroid [[1241 Dysona]] occulting 4UCAC 174-171272, showing instantaneous disappearance and reappearance. Duration is 6.48 seconds.]]

The [[Asteroid occultation|occultation]] light curve is often characterised as binary, where the light from the star is terminated instantaneously, remains constant for the duration, and is reinstated instantaneously. The duration is equivalent to the length of a [[Chord (astronomy)|chord]] across the occulting body.

Circumstances where the transitions are not instantaneous are;
* when either the occulting or occulted body are double, e.g. a [[double star]] or [[Binary asteroid|double asteroid]], then a step light curve is observed.
* when the occulted body is large, e.g. a star like Antares, then the transitions are gradual.
* when the occulting body has an atmosphere, e.g. the moon [[Titan (moon)|Titan]]<ref name=sicardy1990/>

The observations are typically recorded using [[video]] equipment and the disappearance and reappearance timed using a [[Global Positioning System|GPS]] disciplined Video Time Inserter (VTI).

Occultation light curves are archived at the [[VizieR]] service.<ref name=dave2016/>

==Exoplanet discovery==
[[File:TOI-5293b Transit - Copy.jpg|thumb|Light curve of exoplanet TOI-5293Ab taken through a red filter and an amateur telescope. Credit: Jeff Lesperance]]
Periodic dips in a star's light curve graph could be due to an [[exoplanet]] passing in front of the star that it is orbiting. When an exoplanet passes in front of its star, light from that star is temporarily blocked, resulting in a dip in the star's light curve. These dips are periodic, as planets periodically orbit a star.  Many exoplanets have been discovered via this method, which is known as the [[astronomical transit]] method. 

== Light curve inversion ==
Light curve inversion is a mathematical technique used to model the surfaces of rotating objects from their brightness variations. This can be used to effectively image [[starspot]]s or asteroid surface [[albedo]]s.<ref name=harmon/><ref name=roettenbacher/>

== Microlensing ==
{{main|Gravitational microlensing}}

Microlensing is a process where relatively small and low-mass astronomical objects cause a brief small increase in the brightness of a more distant object. This is caused by the small [[general relativity|relativistic effect]] as larger [[gravitational lens]]es, but allows the detection and analysis of otherwise-invisible stellar and planetary mass objects. The properties of these objects can be inferred from the shape of the lensing light curve. For example, [[PA-99-N2]] is a microlensing event that may have been due to a star in the [[Andromeda Galaxy]] that has an [[exoplanet]].<ref name=haugan/>

== References ==
{{reflist|refs=

<ref name=dave2016>{{Cite journal|last1=Dave|first1=Herald|last2=Derek|first2=Breit|last3=David|first3=Dunham|last4=Eric|first4=Frappa|last5=Dave|first5=Gault|last6=Tony|first6=George|last7=Tsutomu|first7=Hayamizu|last8=Brian|first8=Loader|last9=Jan|first9=Manek|date=2016|title=VizieR Online Data Catalog: Occultation lights curves (Herald+ 2016)|bibcode=2016yCat....102033H|journal=VizieR On-line Data Catalog|language=en|volume=1}}</ref>

<ref name=sicardy1990>{{Cite journal|last1=Sicardy|first1=B.|last2=Brahic|first2=A.|last3=Ferrari|first3=C.|last4=Gautiert|first4=D.|last5=Lecacheux|first5=J.|last6=Lellouch|first6=E.|last7=Reques|first7=F.|last8=Arlot|first8=J. E.|last9=Colas|first9=F.|date=1990-01-25|title=Probing Titan's atmosphere by stellar occultation|journal=Nature|language=En|volume=343|issue=6256|pages=350–353|doi=10.1038/343350a0|issn=0028-0836|bibcode=1990Natur.343..350S|s2cid=4330667}}</ref>

<ref name=russell>{{cite journal|bibcode=1912ApJ....35..315R|title=On the Determination of the Orbital Elements of Eclipsing Variable Stars. I|journal=Astrophysical Journal|volume=35|pages=315|last1=Russell|first1=Henry Norris|year=1912|doi=10.1086/141942|doi-access=free}}</ref>

<ref name=kron>{{cite journal|bibcode=1952ApJ...115..301K|title=A Photoelectric Study of the Dwarf M Eclipsing Variable YY Geminorum|journal=Astrophysical Journal|volume=115|pages=301|last1=Kron|first1=Gerald E.|year=1952|doi=10.1086/145541}}</ref>

<ref name=roettenbacher>{{cite journal|bibcode=2013ApJ...767...60R|arxiv=1302.6268|title=Imaging Starspot Evolution on Kepler Target KIC 5110407 Using Light-Curve Inversion|journal=The Astrophysical Journal|volume=767|issue=1|pages=60|last1=Roettenbacher|first1=Rachael M.|last2=Monnier|first2=John D.|last3=Harmon|first3=Robert O.|last4=Barclay|first4=Thomas|last5=Still|first5=Martin|year=2013|doi=10.1088/0004-637X/767/1/60|s2cid=119221231}}</ref>

<ref name=harmon>{{cite journal|bibcode=2000AJ....120.3274H|title=Imaging Stellar Surfaces via Matrix Light-Curve Inversion|journal=The Astronomical Journal|volume=120|issue=6|pages=3274|last1=Harmon|first1=Robert O.|last2=Crews|first2=Lionel J.|year=2000|doi=10.1086/316882|doi-access=free}}</ref>

<ref name=hyperphysics>{{cite web |url=http://hyperphysics.phy-astr.gsu.edu/hbase/astro/snovcn.html |work=Georgia State University – Hyperphysics – Carl Rod Nave |title=Supernova |date=1998}}</ref>

<ref name="LCDB">{{cite web |title=Asteroid Lightcurve Data Base (LCDB) – 4.1.2 U (QUALITY) CODE |publisher=Collaborative Asteroid Lightcurve Link |url=http://www.minorplanet.info/datazips/LCDB_readme.txt |date=30 October 2011 |access-date=16 March 2016 |archive-date=16 November 2015 |archive-url=https://web.archive.org/web/20151116190637/http://www.minorplanet.info/datazips/LCDB_readme.txt |url-status=dead }}</ref>

<ref name="lc">{{cite journal|bibcode=2016PDSS..246.....H|title=Asteroid Lightcurve Derived Data V16.0|journal=NASA Planetary Data System|volume=246|pages=EAR-A-5-DDR-DERIVED-LIGHTCURVE-V16.0|last1=Harris|first1=A. W.|last2=Warner|first2=B. D.|last3=Pravec|first3=P.|year=2016}}</ref>

<ref name=haugan>{{cite conference|bibcode=1996IAUS..173..277H|arxiv=astro-ph/9508112|title=Separating Intrinsic and Microlensing Variability Using Parallax Measurements|conference=Symposium of the International Astronomical Union|book-title=Astrophysical Applications of Gravitational Lensing|location=Melbourne; Australia|editor1-last=Kochanek|editor1-first=C.S.|editor2-last=Hewitt|editor2-first=Jacqueline|publisher=Kluwer Academic Publishers|volume=173|pages=277|last1=Haugan|first1=S. V. H.|year=1996}}</ref>

<ref name=gcvs>{{cite journal|bibcode=2009yCat....102025S|title=VizieR Online Data Catalog: General Catalogue of Variable Stars (Samus+ 2007–2013)|journal=VizieR On-line Data Catalog: B/GCVS. Originally Published in: 2009yCat....102025S|volume=1|display-authors=etal|last1=Samus|first1=N. N.|last2=Durlevich|first2=O. V.|year=2009}}</ref>

<ref name=wood>{{cite journal|bibcode=1996MNRAS.282..958W|title=On the pulsation mode of Mira variables: Evidence from the Large Magellanic Cloud|journal=Monthly Notices of the Royal Astronomical Society|volume=282|issue=3|pages=958|last1=Wood|first1=P. R.|last2=Sebo|first2=K. M.|year=1996|doi=10.1093/mnras/282.3.958|doi-access=free }}</ref>

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== External links ==
* [https://www.aavso.org/lcg The AAVSO online light curve generator] {{Webarchive|url=https://web.archive.org/web/20201221041542/http://www.aavso.org/lcg |date=2020-12-21 }} can plot light curves for thousands of variable stars
* [https://web.archive.org/web/20171202102819/https://astrocats.space/ The Open Astronomy Catalogs] have light curves for several transient types, including supernovae
* [https://imagine.gsfc.nasa.gov/science/toolbox/timing1.html Lightcurves: An Introduction] by NASA's Imagine the Universe
* [http://astro.troja.mff.cuni.cz/projects/asteroids3D/web.php DAMIT] Database of Asteroid Models from Inversion Techniques

[[Category:Variable stars]]
[[Category:Concepts in stellar astronomy]]
[[Category:Planetary science]]