193 9Ap J. CT) o CT) 1 mwas d o o D1 THE ASTROPHYSICALJOURNAL culis, andthereforei?^toobrightforitsmass,Aistwice asmassiveCand3.3 the photometricdata.IfBisassumedtobesimilar bright componentof£Her- minimum massofCwasfoundtobecomparablewiththat ofA.ThisimpliesthatA A/ determined.Thismassratiowasthencombined withthemassfunctions coefficients foundintheinfraredandblueregionsgivessome indicationthattheequator indicates thatthiscoefficientincreaseswithwavelength.A comparison oftheellipticity volume 90NOVEMBER1939number4 times asmassiveB,andthe bolometricdifferenceinmagnitude(—A)isincreased and Carecomparableinbolometricmagnitude.Suchasolution isdefinitelydeniedby First, themass-luminosityrelationshipwasappliedtothese data,andthemassratio comparison ofthereflectioncoefficientsfoundforAlgolin differentspectralregions, infrared light-curveare0^761ando}i2q,respectively.Thecorrespondingvaluesfound ly attheAmherstCollegeObservatory. determined fromspectroscopicstudiesoftheshort-and long-period ,andthe be completelydark,suchasolutionisstronglycontradicted byconsiderationsofmass. of theeclipsingcompanionismoreeccentricthanthat primary. is near5800.Itsdarksideabout200cooler. is estimatedtobethreeminutes. identical withthatfoundfromthoseat8660A,withintheerrorofmeasurement.This as wellthosefoundbyothersinthevisualandphotographic regionsforotherstars, that theresultsmaybecomparedonasimilarbasis. other spectralregionshasbeenmadeinthesamemannerasinfrareddata,order a B8star,isassumedtobe15,000,thatofthebrightsideeclipsingcompanion by Stebbinsat4500Aarei“i34ando!o42.Ifthecolortemperatureofprimary, different spectralregionsatAmherstwhenAlgolwasnearquarter-phase. The infraredobservationshavebeencontinuedatotherphases,firstSproulandfinal- and intheinfraredregion(8660A)nearprimaryminimumatSproulObservatory. red light-curve,arefoundtobe+0.034±.003and+0.007-oo6,respectively.A © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The valuesofthereflectionandellipticitycoefficients,determinedfrominfra- Although thephotometricdatacanbesatisfiedifthird body,C,isassumedto The discussionofdatafromseveralaccuratephotometricinvestigationsAlgolin The timeofprimaryminimumdeterminedfromtheobservationsat5500Ais The differenceinmagnitude(AlgolminusßTauri)hasbeenobservedthirteen The rectifieddepthsoftheprimaryandsecondaryminimadeterminedfrom Photoelectric observationsofAlgolhavebeenmadeinthevisualregion(5500A) A SPECTROPHOTOMETRICSTUDYOFALGOL AN INTERNATIONALREVIEWOFSPECTROSCOPYAND ASTRONOMICAL PHYSICS JOHN S.HALL ABSTRACT 449 193 9Ap J. CT) o CT) d1 An especiallyconstructedspectrometer,located inthefocalplane pare Algolwithanotherbrightstarinboththevisualandinfrared of eachtelescope,enabledmetolimitand,atthe sametime,tomeas- of lightexperiencedinchangingfroma24-inch toan18-inchtele- persion onlyslightlylessthanthatofthewiregratingsusedat mm infrontofthefocus18-inchrefractor,givesadis- observe thefirst-orderinfraredenergywithoutinterferencefrom panions toAlgolhavethereforebeenidentified. is probablyanearlyG-typestar,this“A-companion”mustbeathirdbody.Twocom- of twostarsequalluminosityandcolor.Thecomponentswouldstillhavetobe confused withthefirst-orderinfrared,aSchott glassfilter,OG5,was grating, constructedbyProfessorR.W.Wood,havingunusualeffi- regions bymerelychangingthequalityoflightadmittedtoits ones willbementioned,astheopportunitiesarise. bibliography issorepletewithreferencesthatonlythemorerecent early spectraltypeinordertosatisfyallcriteria. it isassumedthatA5,therelativeluminositiesshowninTable12result. it isimprobablethatCearlierthantheprimary,orB8;andifparallax always usedinadditiontothereplicagratingfor theseobservations. . Inordertobesurethatnosecond-order visualenergywas second-order visual.AttheAmherstCollegeObservatoryareplica so constructedthatevenorderspectraaremissing,itispossibleto spectra bymeansoffine-wireobjectivegratings.Sincethesewere this cellissensitiveoveranextensivespectralregion,onemaycom- electric photometercontainingaCs-O-Agphotoelectriccell.Since issowellknown,nohistoricalbackgroundnecessary.Its sively studiedbyastronomersasthe“demon”star,Algol.Sincethis class Acompanionhasbeenrepeatedlyphotographed.”Sincetheeclipsing of Algoliscorrect,itwouldbeanA-typestarinordertoonthemainsequence.When is ofearlierspectraltypethanG.Fromwhatweknowtheluminositiesstars from zerotoi!94.Thissolutioniscompatiblewiththephotometricdata,providedC Pearce’s spectroscopicobservationsofAlgol,that“duringeclipsethespectrum Sproul. Itsremarkableefficiencyhasmorethan madeupfortheloss ciency inthefirst-orderred,wasused.Thisgrating,mounted351 cathode. AttheSproulObservatorystarlightwasbrokenupinto 45O © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The assumptionregardingBmaybelargelyavoidedifCisassumedtomadeup A veryrecentreportoftheDominionObservatorystates,withreferencetoDr. All observationsrecordedinthispaperweremadewithaphoto- With theexceptionofsun,probablynostarhasbeensointen- OBSERVATIONAL PROCEDURE JOHN S.HALL 193 9Ap J. CT) 1 unused portionofeachgratingwasalwaysshielded, inordertocut parisons withaPerseiintwodifferentwave-lengthbands;andspec- Amherst rangement andthemethodofcalibrationhasalreadybeenpub- urements intheinfrared,focuswasalwayschangedordertobe vice alsomakesitpossibletoutilizetheenergyofbothfirst-ordersat ure thewavelengthofstellarenergystrikingcell.Thisde- focus, andhasbeendeterminedwithsufficient accuracytopredict vational materialaregiveninTable1.Thesmall wiregratingmen- We shallnowdiscussthefirstgroup. lished. trometer wassharplydefined.Amoredetaileddescriptionofthear- sure thattheenergyfallingoneithersideoftwoslitsspec- the sametime.Inpassingfrommeasurementsinvisualtomeas- tioned inthesecondcolumnoftablecovered only40percentof different spectralregions,madewhenAlgolwasnearquarter-phase. trophotometric comparisonswithßTaurioraPerseiinatleastten Sproul Observatory down backgroundeffects.Thedispersionisthat presentatthevisual the 24-inchobjective,whilelargeonecovered 90percent.The 1 College © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Ap./.,84,372,1936;85,146,1937. The observationsofAlgolmaybedividedintotwogroups:com- Visual andinfraredobservations.—Detailsconcerningthisobser- Large (wire) Large (wire) A SPECTROPHOTOMETRICSTUDYOFALGOL451 Small (wire) . W.Wood (replica) Grating Description oftheObservations Fall-win ter, Fall-winter, Nov. 30,1936- Nov., 1935— (also Oct.14, Mar. 22,1937 (also Dec.14, Nov. 27,1936 1938-39 1937-38 IQS?) 1936) Period TABLE 1 (483•5 A) (483.5 A) (967 A) (500 A) 2 mm i mm i mm i mm Width Slit 8660 8660 8660 8660 5500 A 5500 Eff. X Near primary All phases All phases Near primary minimum minimum Observed Phase 193 9Ap J. CT) m m period irregularitiesintheatmospherethanthoseinfraredre- gratings ineachwave-lengthregionactuallyreachedthephotocell. These averaged0^22+0^04inthevisualand oi2 +o“o4inthein- observed atlargehouranglesorwhenrepeated comparisonsofthe tinction wasunusual,theobservedextinctioncoefficients wereused. In general,anextinctioncoefficientof0^25for thevisualando^io gion, wheretheextinctioncoefficientisabouthalfaslarge. visual regionundoubtedlysufferedmoreinthisprocedurefromshort served asanintermediatecomparisonstar.Theobservationsinthe sponse fromastandardlamp,measuredatfifteen-minuteintervals, served onanaverageofthreetimeseachthesenights.There- nineteen differentnightsatSproul.Thecomparisonstarwasob- observations ofvariablestarsbyotherobservers.Boththeinfrared wasdamagedandreplacedbyanothersimilarone.No primary minimum.Thespectralregionsadmittedtothecellatany energy fromaPerseiandthestandardlampindicated thattheex- for theinfraredregion,wasused.Onafewnights whenAlgolwas minute nearprimaryminimum,andthebackgroundcurrentwas to Amherst. perature near8000AismorenearlyA2atmaximumandFo and visualenergyofAlgolwascomparedwiththataPerseion star wasobservedratherinfrequently,comparedwithphotoelectric uring thesesmallphotocurrentswassogreatthatthecomparison In thecaseofsmallergrating,eachreadingrequiredabouta similar advantageofthemethodwasevidentinmovingfromSproul systematic differenceswerenotedorexpectedfromthisfact.A could produceachangeofeffectivewavelengthnomorethan one timeweresosharplydefinedthatthischangeincolorwithphase F5 star.AlthoughAlgolisclassifiedasB8,itscompositecolortem- duce amagnitudeerrorofooiinthecomparisonswithPersei,an In thecaseofinfraredobservations,anerror100Awouldpro- the effectivewavelengthat8660A,withaprobableerrorof20A. 452 JOHNS.HALL about 25percentofthephotocurrent.Thetimeconsumedinmeas- 10 A.InMay,1936,thephotocellwhichhadbeeninuseforthree © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem All observationshavebeencorrectedfordifferentialextinction. Approximately 16percentoftheenergyincidentonwire 193 9Ap J. CT) mary minimumthemagnitudeofstandard lampwasdetermined lows: Theywerefirstcorrectedforbackground effects.Thediffer- correction wasapplied.FortheearlySproulobservations nearpri- constitutes anobservation—wasthendetermined, andtheextinction method firstused,despiteitsobviousinefficiency. ence inmagnitudebetweeneachstarandthe standardlamp—this night. However,itseemedbesttofinishtheobservationsby increasingly evident,astheobservationsprogressed,thatatable with thepositionoftelescope.Allobservationswere,therefore, because theLindemannelectrometerwasusedatsuchahighsensi- lamp, fiveonAlgol,andthestandardlamp.Suchaseries function ofthehourangleforeachstar,whichwouldbevalidany could beconstructedgivingtherelativeelectrometerresponseasa corrected fordifferentialsensitivityofthephotometer.Itbecame tivity thatitsresponsetothesamephotocurrentvariesnoticeably served sofrequentlythroughoutthecourseoftheseobservationsis standard lamp.Thereasonthatthelamphasbeenob- represents twoobservations.Thissequencewasalternatedwith servatory theseobservationswereusuallymadeinthefollowingor- were continued,andadifferentprocedurewasused.Ateachob- eight ortenreadingsonaPersei,flankedbyfivethe der: fiveonthestandardlamp,Algol, the lightfromAlgolvariesbutslowly,onlyinfraredobservations visual, threeinfrared,andtwovisual.Sincethecomparisonstar length fortheearlySproulobservations.Adefiniteeffortwasmade secured wheneverthetelescopewaspointedinitsdirection. was muchbrighterthanAlgol,morenumerousreadingswerealways nearly equalaspossible.AfewofthemostrecentSprouLobserva- Amherst morethanfive,hoursoffthemeridian. stituted oneobservationofthevariableforeacheffectivewave to keepthenumberofobservationsintwospectralregionsas frared. AtSproul,Algolwasneverobservedmorethansix,orat tions nearprimaryminimumweremadeinthefollowingorder:two © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The generalprocedureinreducingtheobservations wasasfol- In thecaseofobservationsbetweenprimaryminima,when Two readingsinthevisual,followedbytwoinfrared,con- A SPECTROPHOTOMETRICSTUDYOFALGOL453 193 9Ap J. CT) 2 reasonably well.ThemeanperiodfoundbyHellerich,2.86731077 weight oftheothersindiscussion. been corrected,ofcourse,forbackgroundandextinction.Forthe differences observedpriortoSeptember,1937,aregivenhalfthe nitude ofthestandardlamp.Partlyforthisreasonandpartlybe- Persei flankingtheAlgolobservationsservedtodeterminemag- from themeanofallobservationsaPerseiafterlatterhad 454 JOHNS.HALL in Table2havenotbeensocorrected.Nocorrections 0.0012 tothecomputedphasesfordiscussion.Thedatagiven December 1,1938.TheseminimaoccurredatheliocentricJD all SproulobservationsbetweenNovember,1935,andMarch,1937, nineteen nightsatSproulandfourAmherst,leastaportionof made forthelight-timeinthird-bodyorbit. have beenaccuratelyobservedontwonights—October14,1937,and sense: AlgolminusaPersei.SinceMarch,1937,primaryminima days, hasbeenused.Theobserveddifferenceinmagnitudeisthe centric phasecorrespondstoheliocentricJD2428113.5689andsuits corresponds totheheliocentricphasedirectlybelowit.Zerohelio- with thefirstthreefiguresomitted(giveninparenthesesTable2), the principaleclipsewasobserved.TheheliocentricJulianday, cause fewerreadingsareincludedineachobservation,themagnitude remaining observationsthemeanoftwocomparisonswitha from thepreviousdata,formerisfiveminutesearly.Although seems tohaveoccurredtwominutesaheadoftheminimumpredicted ent nights(thirty-nineatSproulandtwenty-twoAmherst).On They weremadewhenthestarsatverynearly thesamezenith regions, each500Ainlengthandextendingfrom 4250Ato8790A. These comparisonsweremadeinatleastten different wave-length four occasionsandindirectlyonthreewith ß TauriatAmherst. servations ofOctober14havebeencorrectedbytheaddition there issomedoubtoftherealitythisshift,phasesallob- setting foreachstar.Differentialextinctioncorrections werealways distance, andtheyincludefourormorereadings ateachwave-length 2428821.7917 andatJD2429234.6859.Whilethelatterofthese 2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A.N.,209,231,1919. Spectrophotometric observations.—Algolwascompareddirectlyon Infrared observationsofAlgolhavebeenmadeonsixty-onediffer- 193 9Ap J. ^ ASPECTROPHOTOMETRICSTUDYOFALGOL455 CT) (8113 (8127 (8116 (8136 (8173 Nov. 1935 Helioc. Phase d e c b a 6, (Helioc. JD) © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Hazybutuniform.Magnitudesinterpolatedwithtime. Observedextinctioncoefficientsused. * Themeaningofthesymbolsusedinthistableare: Observationsstoppedbymoonlightongrating. Observationsstoppedbyclouds. Observationsinterruptedbyclouds. Uniformly hazy.sTroublecheckingstandardlamp,owingtouncertainty ingalvanometer. 2b b b 020Ó 495) 0001. 0351 O286 9415 9364 9189 0069. 0040. 9805. 451S) 9384- 9319- O465 O429 O36I O264 9787.. 5078)* OSSI•• 9884.. 9386 9352 9262 9233 0171. 0151. 9907. 9832. 9522. 9288. 9313 9284 9982. 7°i3) 5499) 1 0.42 0-37 0.63 0.67 0.81 0.79 0.92 0.81 0.43 0-37 0.35 0.43 0-93 5500 A 0-37 0.38 0.36 iro4 i-45 i .09 i .12 -35 i .42 1-45 I-3I 115 i .06 1-33 1.18 Am Visual andInfraredObservations O.9794 Helioc. Phase .0346 .9871 0050 0009 9350 0458 0434 0354 0201 9375 9339 9320 9308 9257 9179 0166 0074 0023 9900 9825 9536 9307 O29I 0200 9291 9235 9106 9807 9619 9474 9391 9274 996s 0. 9 8 0.98 8660 A 0.95 0.90 0.91 0.89 0.92 0.93 0.95 0.97 0.93 1-34 i“5° 1. 16 1.02 1.23 1-39 1.44 1-57 1.63 i. 84 1-59 1-34 1.19 i .02 i-25 1-47 1.63 i .80 i .84 1.87 1-85 1-75 1.63 Am TABLE 2* (8193 (8182 (8196 (8173.5499)- Helioc. Phase Cont. (Helioc. JD) 0397- 0320. 0303 • 4713) 9526. 9463. 9287 9226 9432. OO43 OOI9 OOO7 9430 9394 9323 8850 9567. OO3I 99SS 9936 9885 9875 9800 9783 9740 9505 9483 9452 9360 9338 9301 5239) 9408 9993 9981 9969 6463) 0^49 0.76 O.77 0.77 0.65 0.38 0.40 0-37 0.66 0.61 0.56 0.57 0.48 0.48 0.42 0-39 5500 A 0.48 0-45 0-39 1.42 1.44 1.33 1.07 1-33 1-39 1.42 1.47 1.42 1-45 1-38 i. 29 1.14 i 13 Am 48 O.9397 Helioc. Phase 0397 0320 9520 9455 9407 9331 9295 0303 9554 9436 0036 0000 9962 9948 9913 9864 9806 9744 9469 9459 9418 9379 9218 0012 9988 9976 9775 9508 9348 0^99 O.99 0-95 8660 A O.9I O.93 O.96 0-95 I .02 I .21 I-3I I.32 I .21 I .l6 I.04 I .62 I .62 I OS I.05 I .64 I .IO I 05 i. 69 1.79 1.78 Am 80 72 77 74 77 79 193 9Ap J. ^ TABLE2—Continued CT) their meanphasesarethesame. (8497 (8615 (8199 (8612 Helioc. Phase (Helioc. JD) © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem t Thevisualandinfraredobservationsofthefollowingninenightswere madeinsuchawaythat b 9674.. . 9609.. . 9553- 6603) | 0696 0676 0652 0666 0638 0597 0584 0581 0560 0555 0542 5037) 0385 0368 0358 0340 0279 0257 0243 0204 0067 0234 0188.. 0176 0144 0091 0079 0057 0045 0033 0019 0007 9789 9770 0161 9997 9963 9871 9849 9837 5222) 9985 9973 9932 9888 5314) 1 0.80 0.54 0.56 0.30 0.34 0.38 0.38 0.36 0.41 0.45 0-45 0.46 0.49 0.58 0.63 0.69 0.67 0.71 0.91 0.94 0.97 5500 A i .01 i. 10 i. 10 r^ii i. 12 1.30 1-39 1-35 1-43 1-43 1.42 1.41 -4 1.37 1-25 i. 20 i. 29 i. 16 1.23 i .42 1.41 1.41 i .40 1.38 i. 29 Am o.0698 0.9782 Helioc. Phase .0674 .0672 .0650 .0640 •O595 .0588 •0578 •OSS© .0564 •O543 .0378 .O37I .0360 .0346 .0280 •O253 .0248 .0212 .O23I .OI9O .0183 OO73 OO5I OO27 0002 GISS OO97 OO39 OOI4 9990 9956 9937 9879 9845 9980 9968 0.97 0.98 0.99 0.97 8660 A i. 28 i .08 i .02 i .01 i .01 1.03 i .04 i .08 i .04 i. 12 i. 26 i. 28 i. 27 1-33 i.41 1-47 i-50 1-57 1.56 i .61 1.78 1-75 1.80 1.65 1^57 i .60 1.63 1-73 1-73 1.78 1.77 1.77 1-75 1-75 1.61 1.78 1.77 Am 456 d gb (8589.5416) (8566.5472)8 (8529.5070) (8517.6682) (8503.5602)° (85°°-5535) (8497.6603) Helioc. Phase Cont. (Helioc. JD) .0036.. .0058.. .9997.. .0200.. .0125.. .9980.. •9953-• .0123.. .9826.. .9802.. .0621.. .9686 •9501 .9606 •9552 .9388 •9332 •0556. .0259. .O223. .OI58. .97O9 .9867 •984s .9766 .0578. .0498. •O425. .O29O. .O187. .OI29. .9682 .9906 •9797 •0459- .O360. ■9845 •9765 ■9643 0.46 0.94 0.79 0.57 0.52 0.49 0.81 0.84 0.96 0.81 0.75 5500 A 0.57 0.37 0.44 0-59 0.68 0.64 0.99 0.75 1-34 1-37 1-37 i .40 1.32 1-45 1.32 I^OÓ i. 22 i .08 i .07 i .06 I .27 1.23 i. 21 i. 27 1-33 I .27 1.17 1-34 Am Helioc. Phase 0.98 8660 A 0.98 0- 9 5 1.74 i. 64 1.86 1- 5 2 1.47 1-73 1^50 i .80 1.79 1.83 1-73 1.78 1-57 1-55 1.36 115 i. 16 i 15 1.04 i. 21 1.36 1-55 1.64 1-59 1.60 1.77 1.50 1-39 1-34 i .69 1.67 1.52 1.14 1.19 1.38 1-34 Am 193 9Ap J. CT) (8871.6532) (8807.7724) (8860.5157) (8847.8250) (8837.7682) (8796.8536) (8795.8426) (8821 (8592 1937 Oct. 14, Helioc. Phase Helioc. Phase (Helioc. JD) (Helioc. JD) © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem •3970. .3886. •5322 •5135 •5043 •5395 •5215 .0916. .0783. •5709- .3016. .1096. .9490. 0435 O396 O27O O23I 6590) O34I O3O4 9828 9795 976s 9698 9659 9628 0537 0479 0419 0397 0375 0351 9996 9731 9598 9527 0593 5104) m i1 0.906 0.900 0.933 O8 0-945 0.919 0.900 0.949 0.912 8660 A 0.670 0.806 0.602 0.809 o. 889 0.998 0. 963 0.886 0.638 0.45 0.51 0.57 o. 71 O.77 O.79 5500 A 0.762 I 034 1.056 1.014 1.078 i. 102 i1I4 1-430 1. 108 i .064 i .001 1-253 3 Am Am 0.4082 O.5914 Helioc. Helioc. Phase Phase .1052 5576 5491 5781 5641 TABLE 2—Continued 0.930 8660 A 8660 A O.99 i .486 1-564 1.392 1-357 I .189 1.18 1-25 I .29 l^ó i. 172 1.238 1.390 1592 i. 662 1-597 1-529 1.440 1.290 1.09 1.30 i .312 i .800 •974 Am Am 922 929 881 952 457 f a f (9189.6637) (8946.5066) (8934- 5°58) (8877.4844) (8875.5519) (8926.4787) (8917.5364) (8908.4884) (8879.5724) (8904.4681) (8903.4714) (8889.5346) (888o.48o5) Helioc. Phase (Helioc. JD) I I0 1 .2976.. • 4944-• .5017.. -35-• .3090.. •3963-• .2456.. .4672.. •55- •4583 •4490 .4420 .4328 .4223 .7561. • 7483• •5095-• •2352.. .8399.. • 833 .5002.. -4855-• .5210.. .5118.. .5042.. ■4975-• •4723 .3908.. •4930.. .6249.. na o934 o. 882 0.900 0.972 0- 975 0-935 0.995 0-955 0.927 0.947 o. 896 0.853 0-953 8660 A 0.992 0.881 0.851 0.941 0.991 0.968 0.869 0.917 0.962 0.940 0.980 0-957 0.931 i .017 1- 0 5 i .022 i .026 Am 0.5181 0.7634 io Helioc. Phase • 54 .3211 •2539 •8472 4921 4827 4080 4036 5572 5367 5283 5263 5156 5066 5490 1636 5147 5075 0^910 O.982 O.954 O.959 O.95I O.981 O.972 8660 A O.99I O.9OO O.919 O.89O O.893 O.972 O.887 0.937 I .002 1.008 I .OO9 I.O32 I .OI3 Am 193 9Ap J. ^ TABLE2—Continued CT) 2f a b f (9244- 5oo) (9234.5327) (9228.6o73) (9224.5i79) (9223.5462) (9204.5795) (9203.6330) (9202.5884) (9193-5986) (9198.6o52) Helioc. Phase (Helioc. JD) © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 10 .4292.. .0387 .0072 .9601 • 9544 .0414 •9585 .9532 •9507 .9520 •9479 .9460 .8872.. .8841.. .4634.. .4562.. •4533-• .8795-• .1236.. .1200.. .5166 .5142 • 5 .5037 .1144.. .4996 .1768.. .1695.. .4300.. .4160.. .6699.. .8151.. .8052.. .6876.. .6779.. 0.915 O.934 O.94O O.970 0.987 O.913 O.93O O.92O O.971 O.917 O.942 i. 221 i .178 i. 161 0.989 O.949 0.975 0^963 i .828 i. 162 0.907 O.922 Ó.934 0.948 8660 A i. 229 1-305 1.230 1.125 i .071 1-053 I.OO3 1.020 1.022 I .021 1.017 Am o.0464 Helioc. Phase >.6960 .9980 .9748 •9732 .9712 •0445 •0433 .0021 •9673 .9661 .9609 -9333 •9259 .9211 . 7069 4780 4740 4661 4387 5771 5730 8224 5331 5302 5246 1357 1277 1840 1 O.943 O.971 0.968 0.987 0.989 0.989 0.961 0.915 0-937 0^942 0.994 0.948 0.960 0.906 8660 A I-159 i. 180 1.231 1-833 1.807 1-556 1.483 -4 O.922 1.449 1.361 I.251 I.005 1.023 1.026 Am 458 2b b (9318.5009) (9311.5577) (9306•579) (9308.4852)6 (9279.5884) (9299•5345) (9284.5233) (9278.6355) (9276.4613)* (9249.4859) (9248.4944) 1939 .2409. Feb. .2307. 23, .2380.. Helioc. Phase (Helioc. JD) •7534-- • 7493-• .7406.. •7377.. .8092.. .0656.. .0584.. .0550.. .6160.. .4098 •4054 .3989 •3953 .3880 .3807 •3341.- .6079. .6026. .6739.. .6684.. .6657.. .6596.. -3437-• .3372.. .6009. .5818. .5782. •5721. .5690. .1611. •3273-. •8153- O.921 0-935 0.936 O.927 0.921 0^929 0.892 O.914 0.906 0.883 0.892 0.862 0.889 0.938 0.903 0.902 0.871 0.890 0.895 0.890 0.876 0.930 O.912 O.927 O.906 8660 A 0-853 0.901 0.892 0.916 0.927 0.926 0.908 1.003 1.070 1.084 Am 0.2541 0.8189 Helioc. Phase •2493 4390 4309 4268 4195 0731 0700 4159 8354 3553 7772 6867 3524 3464 6499 7655 7619 6819 6766 6426 6390 6308 6192 6123 1642 I 0.900 o?940 8660 A •907 .962 .914 .892 .891 .971 •955 .867 •859 .878 •913 .911 •930 .881 Am 898 861 888 889 883 899 879 864 894 855 894 193 9Ap J. CT) 1 intermediate starfortheseobservationswasalwaysaPersei.The of Table3.TheobservationsDecember13areincompletebecause , whichIhavebeenmakingduringthelastthreeyears.The of clouds.Weightsarerecordedaftereachmagnitudedifference,and mean ofthethreeindirectcomparisonsisgivenintenthcolumn general spectrophotoelectricintercomparisonofaboutsixtybright applied. Theindirectcomparisonsweremadeinconnectionwitha Phase ofAlgol 0.425. Night lieve thattheobservedresponseislinearwith light intensitytobet- mean differenceinmagnitudeforeacheffectivewavelengthisgiven values andaregivenatthebottomofeachcolumn.Theweighted night corrections(theamountbywhichthedifferencesofeach very nearzerophase.Thesearenotsufficiently accuratetojustify made inamanneralreadydescribed.There is everyreasontobe- publication atthistime. in thelastcolumnofthistable. differ systematicallyfromthemean)areincludedintabulated ter than0^02permagnitudefortherangesinvolved intheobserva- tions giveninthispaper. 475- 450- 600. tion 650. 849- 525- 500. 879. 550- 799- 749- 700. Effective X © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Three indirectcomparisonshavealsobeenmade whenAlgolwas Several investigationsofthescalephotometer havebeen GO correc- A SPECTROPHOTOMETRICSTUDYOFALGOL459 ni +0^528 +ooi4 +0 Dec. 193S 0.13 13 Magnitude Differences(Algol—/?Tauri) 498 407 444 30S 321 301 368 504 260 233 +0^553 +0 I Dec. 1938 0?02I O.82 iS 485 404 427 454 488 379 498 347 328 359 250 250 TABLE 3 +0^513 +0 - 0^025 Dec. 1938 O.82 iS 462 464 425 459 485 354 392 320 350 309 290 292 +o“55 +0 Feb. 1939 O^OOO O.82 16 479 421 448 479 412 337 533 309 374 312 253 262 2 +0^52 +0^033 +0 direct 1938 o. 18 In- 44 42 39 30 31 39 30 25 27 1-5 i i i i i i i +o'?537 +0.268 Weight- Mean o. 17 ed 453 476 4SI 409 418 499 356 303 302 340 291 193 9Ap J. CT) 567 8 Iwere nal oftheFranklinInstitute,228,411,1939. containing twosuccessiveobservations.TheobservationsofOctober 460 JOHNS.HALL nights, itshouldbementionedthathewasthefirstofthisgroupto verse tobetrue.AlthoughheobservedAlgolvisuallyononlytwo on fivevisualestimates.Itisevident,therefore,thathehasbeen by thirteenminutes.Heestimatestheaccuracyofthisintervalas central linethroughzerophase. and areplottedtogetherwiththesenormalsinFigure1.Thetwo regions wereunderobservation(withtheexceptionofOctober14, curves drawnthroughthedataaresymmetrical withrespecttoa stars ofsimilarmagnitude. desirable inthecaseofAlgol,sincetherearenoclosecomparison apply correctionsfordifferentialextinction.Thisisparticularly Maggini, Hnatek,andMustelhaveallfoundthattheminimaob- somewhat optimisticconcerningtheaccuracyoftheseobservations. whereby thetimeofminimumlightisafunctionwavelength. observations weremadeinsuchamannerthatthedifference tions ofAlgol.Themostrecentobserver,Skoberla,foundthere- served intheredprecedethoseobservedblue,fromobserva- gol, usingblueandredliquidfilters.Onthebasisofhisdatahecon- sidereal time)ismade,itappearsthatthisdiscoveryrestsheavily three minutes.Whenaplotofhisdata(publishedinstepsand the so-called“Nordmann-Tikhoffeffect,”orallegedphenomenon curately determined.Theeffectivewavelengthsweresowidelysep- time ofminimumlightinthetwowave-lengthregionscouldbeac- cludes thattheredminimum(6800A)precedesblue(4500 arated thatitseemedthiswasagoodopportunitytoinvestigate 14 weregiventhephasecorrectionmentionedinprevioussection 937) arrangedaccordingtophase,andnormalswereformed 4 2, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem M.A., 184,305,1910.*Zs.f.Ap.,ii,i,1935. 3 Amoredetaileddescriptionofthispartthediscussion is publishedintheJour- 4 B.A.,26,22,1909. My ownobservationsofprimaryminimumwhenbothspectral Nordmann discoveredtheeffectfromvisualobservationsofAl- Visual andinfraredobservationsofprimaryminimum.—These 35, 131,1918.1A.J.SovietUnion,11,514,1934. DISCUSSION CT)

A SPECTROPHOTOMETRIC STUDY OF ALGOL 461

The method of computing the times of primary minimum and its probable error for each of these wave-length regions was kindly sug- gested to me by Dr. Schilt and is as follows:

It was first assumed that the minimum of one curve is at phase P0. Magnitude residuals, observed minus curve, were recorded and weighted according to the numerical slope of the curve. Let the sum

0. 9 i .0 1. i i. 2 1 -3 g 1.4 §

1.6 £ ï.7 I 18 'Í <1

Fig. i .—This graph includes observations obtained on those nights when both spec- tral regions were utilized. Consequently, only observations made at the Sproul Observa- tory are included. The infrared curve is above the visual curve.

of their squares (pvv) be denoted by S2- A similar summation was

then computed after the same curve had been shifted to P0 + 0.002,

and S3 was found. The curve was next shifted to P0 — 0.002, and Yi was determined. If we assume that the sum of the squares of the residuals is a quadratic function of the phase, the true minimum is at Sx - S3 P0 + 0.002 2(Sl + S3 - 2S2) ’

© American Astronomical Society • Provided by the NASA Astrophysics Data System 193 9Ap J. CT) o CT) the observations.Sinceitisevidentlypresent intheobservations other branchisadeterminationofthephase of primaryminimum and isgivenforeachwave-lengthregioninTable 4. The mid-pointbetweeneachphaseonthedescending branchsode- termined andthecorrespondingphaseof observationonthe of thesixobservedmagnitudedifferences ascendingbranch. of eachmeancurveonitsdescendingbranchcorrespondingto on thisnight,theirphasesarethesame.Letusnowreadphase nine observationswelldistributedonthedescendingbranchofeach Since theinfraredreadingsweresandwichedbetweenvisualones ter primaryminimumcrossthemeancurvesonascendingbranch. curve followthemeancurvesverynicely,andsixobservationsaf- of October14,1937.After0.0012hasbeenaddedtoallphases,the independent ofthoseintheother.Theerrordifference was suchthattheerrorsoccurringinonewave-lengthbandarenot times ofminimumisthereforelessthaneightminutes. were madeentirelyindependentofoneanother—forexample,ifthe visual andinfraredobservationsweremadeatdifferentobserva- latter figureshouldbetheprobabledifferenceifobservations probable differenceinthetimesofminimaiseightminutes.This tories. However,themannerinwhichtheseobservationsweremade for eachwave-lengthregionisaboutsixminutes,andthereforethe of thecurvesdrawnthroughdata,sizeandevensign this differencecouldbechangedinarbitrarymanner. infrared minimumprecededthevisualbyabouttwentyseconds. in thismannerforeachcurve.Thesecomputationsshowedthatthe Since thecomputedtimesofminimadependsomewhatonshapes minimum value,thenthemeanerrorisgivenby and ifthemeanerrorisphaseshiftforwhichSdoubleits 462 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem It isevidentfromthesedatathatasystematic error hascreptinto A goodexampleofthisreasoningistobefoundintheobservations The probableerrorofthedeterminationtimeminimum The phaseofprimaryminimumanditsmeanerrorwerecomputed JOHN S.HALL 193 9Ap J. CT) o CT) 91011 by Skoberla,withthepossibleexceptionofRZ Cass,indicatethat paper, allgivestrongindicationthatforthese starsthiseffect,ifit wave-length regions.Subsequentpapersbysuchexperiencedob- mann-Tikhoff phenomenon.Hehascollectedtheresultsofstudies when attackingthisparticularproblem. liance ontheerrorsasgiven,neverthelesstheydoillustratead- primary minimumissmall—0.00025,orverynearlyaminute.The the redminimumforeachofforegoingstars precedestheblueby servers asBuffer,Hellerich,andWalterrelatingtoWUMa, of thetimesminimumthirty-fiveeclipsingstarsindifferent ously, withanuncertaintyofnotmorethanthreeminutes. Although thesedataarenotsufficientlynumeroustoplacemuchre- probable errorofthisdifferencepredictedfromtheerrorsatbot- both spectralregions,thesystematicdifferenceintwophasesof vantage ofmakingtheobservationspracticallyatsametime 0.00018 derivedfromtheobserveddifferencesinthirdcolumn. RZ Cass,UCep,andSag,aswellthedata presentedinthis exists, ismaskedbytheerrorsofobservation. The resultstabulated tom ofthefirsttwocolumnsis0.00044,ascomparedwithvalue (5500 A)andinfrared(8660timesofminimumoccursimultane- 1011 8 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A.N.,256,405,1935,and261,120,1937.Zs.f. Ap., 16,167,1938. 9Ap. J.,79,370,1934- I believethatmyobservationsofAlgolshowthevisual Skoberla hasrecentlydiscusseddatapertainingtotheNord- A SPECTROPHOTOMETRICSTUDYOFALGOL463 P.E Mean. . (Observations ofOctober14,1937) Phase ofPrimaryMinimum +0.00010 + .0002 + -0003 + .0011 +0.0015 — O.OOI5 — .OOIO ±0.00032 5SOO A TABLE 4 + .0006 +0.0017 —0.00015 —0.0012 — .0007 — .0008 — .0005 ± o.00030 8660 A +0.0003 + .0003 +0.0002 — .0008 — .0005 —0.00025 — .0010 ±0.00018 Difference 193 9Ap J. CT) 12 ber, 1936,observedbySmart.TheheliocentricJuliandayhefound pare theresultsoftheseobservationswithminimumNovem- with aprobableerroroffourminutes.Itmaybeinteresttocom- problem relatingtothechangeinperiodofAlgol.Aninteresting of sixminutesineachspectralregion,andsincetheyseemtooccur observational accuracyincreases,theeffectseemstodecreasein never beprovednottoexist.Butitisinterestingnotethat,as phase, andeighteennormalswereformed,having sixobservations have notbeenincludedinthiscomparison. sensitive photoelectriccell,whilethatpredictedbymyownobserva- for thisminimumis2428483.4560,fromobservationswithablue- mum fortheintervalbetweenNovember,1935,andMarch,1937, from theSproulobservations. spectral regionatAmherst,inordertoincreasetheweightofin- in thispaperarenotsufficientlynumeroustocontributemuchthe correction fordifferencesinthelight-timeoflong-periodorbit agree, withinerrorofobservation.Thisisparticularlysosincethe tions is0.0041day,orsixminutesearlier.Theseresultsseemto simultaneously, thecombineddatagiveustimeofprimarymini- about thesameproportion. servations. several timestheerrorsofthesemorerecentandaccurateob- each. Thesenormals,togetherwiththosepertaining toobservations frared dataandtocheckanypossiblechangesinperiodsincethe the primaryminimumwasobservedonfourdifferentnightsinthis the light-curvewascompletelycovered.Also,atleastaportionof the infraredobservationswerecontinuedafterOctober,1937,until ten. discussion ofthispuzzlingproblemhasrecentlybeenmadebyLuy- 464 JOHNS.HALL tween minimashowanydefinitesystematicdifferences inmagnitude Sproul observations.Neithertheseobservations northosemadebe- 128 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Zs.f.Ap.,15,97,IQ3- Infrared light-curveofAlgol.—Ashasbeenpreviouslymentioned, The Nordmann-Tikhoffphenomenon,byitsverynature,can The observationsbetweenminimaweregrouped accordingto The resultsofobservationsthetimesprimaryminimagiven Since theactualtimesofminimaareknownwithaprobableerror 193 9Ap J. CT) m 0 14 15 0 o 13 lowed theminimum.Therectifiednormalsresulting fromthisproc- minimum, withoutregardtowhetherornot they precededorfol- The observationswerearrangedaccordingto phasefromprimary means oftheformula shape ofprimaryminimum,normalswereformedandrectifiedby able errorofasinglenormalisooo8.Inthedetermination The differenceinmagnitudewhen6=gowas0^918,andtheprob- intensity outsideeclipse. symmetrical. mary-minima-curves, formyowndataaswellthoseofStebbins bital eccentricity.Severalspectroscopicdeterminationsindicate and Smart,indicatedthatthisportionofthelight-curveishighly curately. Furthermore,acarefuldiscussionoftheshapepri- differ by127,itisprobablethatetoosmalltobemeasuredac- between thesideoffainterstarwhichistowardbrighterand that theorbitaleccentricityinshort-periodorbitisverysmall. where aisthebrightnessat0=90,2bdifferenceinintensity Since McLaughlin’stwodeterminationsofcoseparatedbyayear term hasbeenincludedtoallowforpossibleasymmetrydueor- the otherside,c=^2isellipticityconstantthatdetermines five observationseach.Conditionalequationswereformedgiving of secondaryminimum,areshowninFigure2.Thelattercontain equatorial eccentricityofthestars,anddisphaseangle.No the light-intensitybetweeneclipse ^ Ap.J.,53,105,1921.«M.N.,97,396,1937. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem ^ Bull.U.ofMichiganOhs.,6,3,1937. The least-squaressolutiongavethefollowingvaluesforlight- A SPECTROPHOTOMETRICSTUDYOFALGOL465 2 l=i.000 —o.0344cos60.0074. ± 0.00280.0029+0.0065 lr cos2 ~ 7Tb* _/o+¿>(10)^0cos6 7 2 l =a—bcosdc6, 193 9Ap J. CT) o CT) 2 m 17 u m umn givesi—l.Thelastcolumnshowsthenumberofobserva- tions includedineachnormal. column givestheargument/=sin6/(1—zcos6).Thefourthcol- ess aregiveninTable5.Thefirstcolumngivesthemeanphase,and 466 large asthismightchangethecomputedvalue ofkbyasmuch is onlyo7Óat8660A,itdifficulttodeterminekaccuratelyfrom the secondmeanobserveddifferenceinmagnitude.Thethird from limbdarkening.AccordingtoPannekoek, for B-typestars these observations.Althoughthetheoreticalcurvecorrespondingto and ais0.683.Sincethecorrecteddepthofprimaryminimum a probableerrorofooo8forsinglenormal, a systematicerroras the foregoingvaluesofkandarepresents datainTable5with 20 percent.Iestimatetheprobableerrorofk tobe10percent. r 0 0 16 16 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Ap.36,404,I9I2-vM.N.,95,733? I findbyRussell’smethodthatthesedataaresatisfiedifkis0.79 Observations intheinfrared,however,should berelativelyfree o.0698. o.0009 .0576. .0617. .0661. .0091, .0204. .0237. .0290. .0346. •0375. • 0396. .0420. .0450. .0466. .0502. •°544' .0026 .0048, ■0143 .0179, .0260. .0324, Phase Normals, PrimaryMinimum JOHN S.HALL Da 12 o944 0. 968 1.004 i. 298 1-254 1.230 1. 162 1.176 1.132 1.068 1-034 1.772 i. 680 i .624 1-574 1.562 1.494 -45 1.370 1-346 i .800 i .806 1-744 Am TABLE 5 o.1824 o.0000 . 1269 .0615 .0689 .0788 .0845 .0974 .1137 .1446 .1647 .0470 •0551 .0008 .0081 .0128 .0165 .0224 .0268 .0331 • 0413 .0002 .0034 1 + .062 + -038 + .008 + .221 + .205 + .158 + .169 + -137 + -089 + .362 + -339 + .292 + .279 4- •249 + -480 + .4SI + .426 + -403 + .396 +0.502 + -505 + -491 — 0.0I2 -h 193 9Ap J. CT) 18 2 14 blue, stronglydecreasinginthelongerwavelengths.”Theobserva- blue. when comparedwiththeobservationsofothersinvisualand concerning theselight-curvesaregiveninthefollowingparagraphs. photographic regionsofthespectrum.Inmakingacomparativedis- the limbincaseofsunismuchlessinfraredthan the limbdarkeningissmall,forA-typestarsitverylargein between minimaandatsecondaryminimumareofparticularinter- observer byexactlythesamemethod.Fourotherlight-curveshave, tions oftheSmithsonianobservershaveshownthatdarkeningat this valuewouldobtainatabout5200A.Consequently,ifweassume nection withtheinfraredobservations.Severalpointsofinterest accordingly, beendiscussedinthemanneralreadyexplainedcon- cussion ofthissort,itseemsimportanttodiscussthedataeach His reductionsweremadeinpracticallythesame wayasthereduc- order toderivetheellipticitycoefficientanditsprobableerror. not beusedinthesubsequentdiscussion.Inaccordancewith precision ofabout0^01forthesevisualobservations, acomparison servations betweenminima,containingatermincos0,wasmade general policyofthisdiscussion,aleast-squaressolutionfortheob- pared withthesubsequentmoreaccurateseriesmadebyStebbins very littleweight.Consequently,theseparticularobservationswill thirty years,thiswastheeffectivewavelengthofhisseries.Com- that therelativebrightnesshasremainedunchangedduringlast est. StebbinsfoundthedifferenceinmagnitudebetweenAlgoland and ofnegligiblesignificance. tions ofmyowndata;suchdifferencesaswere foundareverysmall a KHphotoelectriccellwithaneffectivewavelengthnear4500A. ten yearslater,theearlyobservationsofprimaryminimumhave comparisons ofthesetwostars,whichIhavemade,indicatethat a Perseitobe0^15atquarter-phase.Recentspectrophotometric 1920 18 20 19 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Ap.J.,32,185,1910.Ann.defobs,Strassbourg, fase.2,p.1,1933. The discussionoftheinfraredlight-curveisparticularinterest Handb.d.Ap.,3,PartI,149,1930. 3. Danjoriscat’s-eyephotometer.—^Although Danjonclaimsa 2. Stebbins’photoelectricphotometer?*—Thisphotometercontained 1. Stebbinsseleniumphotometer?—Theobservationsofthisseries A SPECTROPHOTOMETRICSTUDYOFALGOL467 193 9Ap J. CT) m with theeffectivewavelength.Thisconclusion isconfirmedbythe parable discussionofhisdatacouldbemade.Ilookforwardwith comparison oftheresultsaccurateobservations ofsimilarstars for thefivedifferentspectralregions,aregiven inTable6. ticity andreflectioncoefficients,togetherwith theirprobableerrors interest toreadinghiscompletepaper,whichhestatedwasinpress means ofaphotometer,usingtwophotocellsdifferentspectralre- which hehasmadeintwospectralregions(4080Aand5800A)by lished arésuméoftheresultshehasobtainedfromobservations at thetimeofpublicationrésumé. servations, itappearsthatthiscomparisonstarisattimesvariable, of Smart’sobservations.Inviewtheaccuracybothseriesob- sponse. Sincehehasnotpublishedtheobservationaldetails,nocom- although itsradialvelocityisnotknowntovary. had foundthisstaronseveraloccasionstobe“unmistakablyfaint the extentofoo4or0^05”aboutfifteenyearsprevioustotime to notethatSmartusedôPerseiasthecomparisonstar.Stebbins four normalswereformedfromhisobservationsbetweenminima, is thusmadethateachobservationhasthesameweight.Twenty- vation, Ihavederivednewonesinanefforttoequalizetheirweights. and alsotwenty-fourduringtheprincipalminimum.Itisinteresting In viewofthelackanyevidencetocontrary,assumption patible withthephotometricresultsofothers.Ihaveusedhisdata and spectraldomain.Smarthasgroupedhisobservationsintoso- called “normals.”Sincesomeofthesenormalscontainbutoneobser- cussed hisdata,theyarecomparablewithStebbins’inbothaccuracy for thedeterminationofvisualdepthsminima. makes theinterestingsuggestionthatprimaryeclipseofAlgolis annular andthatthesecondaryistotal.Thissolutionnotcom- curacy isnotashightobeexpectedfromsuchprecision.He of hisresultswiththoseothersgivestheimpressionthattheirac- 468 JOHNS.HALL 21 21 15 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Soc.astron.Italiana(3dser.),p.10,1937. Ellipticity andreflection.—ThevaluesIhavefoundfortheellip- There issomeevidencethatthereflectioncoefficient bincreases In additiontothesefourseriesofobservations,Magginihaspub- 4. Smart’sphotoelectricphotometer.—^AlthoughSmarthasnotdis- 193 9Ap J. CT) 22 given byWalterfortheupperandlowervalues ofbareat6160A and 4300A,respectively.Krat’sspectrophotometric observations servatory. Inthecaseoflaststar,effective wavelengths was foundfromphotographicobservationsmade attheLawsOb- U Sag... RS Vulp. TV Cass. RZ Cass. U Ceph. Hall Danjon.. Smart. . Stebbins. Stebbins. visual observations,mostlybyDugan.Thevaluedirectlybeneath Table 7. made inthevisualandphotographicregions.Thesearegiven 22 Zs.f.Ap.,ii,71,1935. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The topvalueofbforeachthefirstfourstarsisthatfoundfrom Observer Star +0 +0.0285 A SPECTROPHOTOMETRICSTUDYOF.ALGOL469 Reflection 0130 0215 039 033 016 020 037 0215 005 +0.0344 +0.0150 .0192 .0247 .0149 0.0038 P.E. Reflection 0048 0039 0047 0037 004 012 0047 0069 B G2 B8 B? B (F5) Ao G8 A2 (G) 9 9 9 3 Spectra O.OO29 O.OOIO P.E. .OO16 .OO28 .0012 TABLE 7 TABLE 6 Ibid. Walter, Zs.f.Ap.,16,167,1938 Baker, Pub.LawsObs.,32,1921 Dugan, Contr.PrincetonObs.,No.6,1924 McDiarmid, Contr.PrincetonObs.,No.7, Baker, Pub.LawsObs.,30,1921 Hodgen, Pub.LawsObs.34 Cummings, Pub.LawsObs.,27,1917 Dugan, Contr.PrincetonObs.,No.5,1920 Dugan, Contr.PrincetonObs.No.4,1916 } } 1924 +0.0074 +0.0132 .0306 .0011 .0027 Observer andReference Elltpticity 0.0024 0.0065 P.E. .0036 .0065 .0023 Effective \ 4500 4500 8660 5200 5500 (A) 193 9Ap J. CT) o or f o can beshownbysimilarreasoning,usingthedata inTable9forthe rections tobeappliedbecauseoftheinfluence ofthethirdbody. we haveneglectedtheenergyreflectedfrom primaryandthecor- of 2bat8660Awouldbeonly0.024.Ineach ofthesecomparisons and thatofthefaintersideitseclipsingcompanion is5600,it 0.129. Thisismuchlargerthantheobservedvalue0.069±0.006. of thelightsystem,andvalue2bwouldbef(0.193), secondary. Ifourassumptionwerecorrect,thisresultshouldbein- reflection atfullphase,2b,is0.030thatofthesystem.Themaximum as thatoftheexcitingstar,andfollowthissame procedure,thevalue dependent ofthewavelengthusedindeterminationlight- reflected lightisthereforetwo-thirdstheoffaintside side ofthisbodyconstitutes0.045thatthesystem,and length maybeillustratedbyacomparisonofthevaluesbfound found fromobservationsat4500Athatthelightfainter brightness, 2bwouldequal2&",andnoreflectionbeobserved. curve. At8660Athefaintersideofsecondarycontributes0.193 reflected bythesecondaryhasitscolortemperature.Stebbins unit involvingonlytheeclipsingpair. at 4500Aand8660forAlgol.Letusfirstassumethattheenergy secondary. Theobservedreflectionfromahemisphere,2b,isthen efficient shouldbedividedby1—Lc,inordertoreduceitthe If athirdbodyispresentinthesystem,observedreflectionco- system when6=90.Ifthetwostarswereofequalsizeandsurface ponent atfullphaseduetothepresenceofprimary,and2&'be the correspondingradiationfromprimaryatfullphasedueto which termwasusedinhisderivationofthereflectioncoefficient, I prefernottostresshisresultswithoutfirstseeingfinalpaper. Maggini inhisrésumé.Sincethereissomedoubtthiscaseasto evidence whichIhaveseentendstodenythetentativecon- of uHeralsoshowthatbincreaseswithwavelength.Theonly 2b' —2b"andisexpressedasthefractionoftotalenergy clusion thatbincreaseswitheffectivewavelengthisgivenby 470 JOHNS.HALL o © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem If weassumethattheB8starhasacolortemperature of15,000 If wenowassumethatthere-emittedenergyhassamequality A crudeexplanationofthechangethesecoefficientswithwave Let betheadditionalenergyradiatedbysecondarycom- 193 9Ap J. CT) o CT) 1 o 13 23 his discussionofUSag. Algol, IhavefollowedthemethoddevelopedbyWalterandusedin be predictedfromthatfoundat4500Aiftheenergystrikingsec- ondary isre-emittedatablack-bodytemperatureofabout6500. more distortedthantheB8star.Thisresultagreesinaqualitative fined asthesquareofitsequatorialeccentricity,or ratio L/L,thattheobservedreflectioncoefficientat8660Awould while thecorrespondingvaluesgivenbyMcLaughlin forAlgolare way withthatofWalterinhisdiscussion U Sag.Hegivesthe by substitutingthe3’sandFsfoundfromobservationsat4500A where lreferstotheluminosityofdarksidesecondary. disks isthen the reflectionconstant.Thecorrectedmeanellipticityforuniform 0.15 and0.02.Walterfindsthevalue0.40for zandzerofor, rately withmyown,andtheresultsaregiveninTable8. the individualstars.Stebbins’andSmart’svalueswereusedsepa- Walter hasfoundthattoasufficientapproximation tially maskedbyreflectionandshouldbeincreased0.36times Eddington hasshownthattheobservedellipticityconstantispar- density ofthebrighterandfaintercomponents as0.17and0.011, and 8660A,thetwoequationsmaybesolvedforellipticitiesof and hedescribestheshapeofhisredlight-curve betweenminimaas Since the2’sareindependentofwavelengthand/’snot, ba w B BA © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem If aiandbjarethesemimajoraxes,ellipticityofastarisde- In determiningtheellipticityoftwoprincipalcomponents There isindication,therefore,thatthemoretenuousGstar M.N., 86,320,1926. A SPECTROPHOTOMETRICSTUDYOFALGOL471 Zu/2 ~ (1-zy(1-'*’ BA _ Ib%b,Ia%a 2 = (2c+o.72Ô)coseci. CT)

CT)O 47 2 JOHN S. HALL

the ß Lyra type and that of the blue light-curve as the Algol type. CT) CT)00 No such obvious difference exists in the light-curves of Algol plotted in Figure 2. Further evidence that the secondary in Algol stars suf-

TABLE 8 Ellipticity of the Eclipsing Components of Algol

Observer X (A) Ib U P.E. ZB ZA Stebbins 4500 0.045 0.925 0.0380 0.0048 0.06 0.04 Smart. . 4500 .022 .948 .0165 .0046 o. 16 0.01 Hall. . . . 866o 0.193 0.738 o.0404 0.0132 Mean. o. II 0.025 b/a. 0.94 0.99

‘tí cäbß

Fig. 2.—The lower curve is that found by Stebbins with his photoelectric photom- eter, in blue light (4500 A). The infrared (8660 A) light-curve shown directly above it includes both Sproul and Amherst observations. Four observations are included in each normal of the primary minimum for the infrared curve. The curves are theoretical curves derived from elements obtained from data they represent. Although the readings made for Algol by Stebbins in the blue are about 1J times as numerous as those made in the infrared, the infrared data are distributed over nearly twice as many nights.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 193 9Ap J. CT) m m 4 0^325 +ooo6at5500A.Whenthisvalue is comparedwiththe minimum isogJS.Ihavefoundthedifference inmagnitudebe- greater confidence. been suspectedofvariability,IbelieveStebbins’elementsdeserve tween AlgolandaPersei,whentheformerisat quarter-phase,tobe Danjon’s visualobservations.rectified depthofprimary is themeanofthatfoundfromStebbins’selenium observationsand gleaned fromvarioussources.Thedepthofthesecondaryminimum brightnesses foundfromthesetwoseriesofobservations.Since mum, thereisconsiderabledifferenceintheratioofsurface ference ineffectivewavelength,sincehissecondaryminimumis between thevioletandinfraredvaluesoik.Inviewofwhatisknown shape ofhisprimaryminimum,andsincecomparisonstarhas o^oiq shallower.Asaresultofthisdifferenceinthesecondarymini- found byStebbins.Itisdifficulttoattributethisapossibledif- uniform solutionintheviolet.ThethreesolutionsgivenTable9 not seemreasonabletocompareadarkenedinfraredsolutionwith Smart’s secondaryminimumisflatterthantobeexpectedfromthe are thereforeuniformsolutions. the valueofkanddecreasea.Inotherwords,ifdarkeningwerein- good. Itcanbeshownthatthedarkeningatlimbwouldincrease used inmydiscussionhasnotbeencorrectedforthethirdbody.If about darkeningatthelimbasafunctionofwavelength,itdoes troduced intoStebbins’solution,greaterdiscordancewouldresult them inthecaseofAlgol,agreementkandaisreasonably tations, whichIhavemade,aregiveninTable9forStebbins’, that thethirdbodyiscompletelydark.Theresultsofthesecompu- the resultsaresimilartoforegoinginbothcases. this bodyissimilartothatsuggestedinthesubsequentdiscussion, on Krat’sobservationsofuHer.HereagainthevalueL/ fers moretidaldistortionthantheprimaryisgiveninKopalVnote Smart’s, andmyowndata.Inviewofthedifficultydetermining 0 0 AB 2 m © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem *Zs.f. Ap.,16,304,1938. The datapertainingtothevisualregion,giveninTable9,were Elements.—The elementswerefirstderivedontheassumption Smart’s depthofprimaryminimumisoo3ishallowerthanthat A SPECTROPHOTOMETRICSTUDYOFALGOL473 193 9Ap J. CT) Light offaintbody(brightside) Light ofbrightbody Light offaintbody(faintside) by Stebbins’valuesofbandc(seleniumphotometer),thevisual visual dataofTable2pertainingtoprimaryminimumandrectified Area ofbrightbodyobscuredatmini- Depth ofprimaryminimum(rectified) 474 JOHNS.HALL Depth ofsecondaryminimum(recti- Effective wavelength depth iso^ggo.Themeanofthesetwodeterminationsgivenin minimum, usingStebbins’valueofa.Thedifference betweenL value ofLwascomputedfromtherectifiedloss oflightatprimary more accuratelydeterminedthanthatofthe secondary, thevisual Table 9.Sincethedepthofprimaryminimum ispresumably and unityisgivenfortheluminosityofbright sideoftheeclips- Range ofprimaryminimum(rectified) Range ofsecondaryminimum(recti- Semiduration ofeclipse Radius ofbrightbody(=1).. Cosine oftheinclination Ratio ofsurfacebrightness(faint Radius offaintbody(orbit=1) Ratio oftheradii 0 A a fied) fied) side Lb) mum © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Observer o.OOOO o.1000 0.2500 O.0719 Phase . 2019 •0534 .0423 .0319 .0210 Elements andInfraredLight-Curve Infrared Light-Curve OS —a)Per 0.953 0.918 0.958 1^805 i .084 i. 226 1-575 1.386 •930 TABLE 9 Lb—2b Jl/J I —X2 I—Xi 2 cos i d/2 Lb La a r Tl 0 k 2 o.5000 0.4017 o. 3000 0.4281 hm Phase 0^042 Stebbins O.O38 O.648 449 0.144 0.035 0.244 o. 207 4500 A 0.045 0.075 0.925 0.700 0.85 I”I34 .4681 •4578 .4467 .4790 hm 1 0“028 447 0.152 0.017 O.O25 O.638 0.242 0.022 4500 A 0.206 0.052 0.948 0.673 0.85 I?! 03 Smart (0-a) Per na o9o6 0.894 0.892 1.018 .940 -915 .992 .966 ni hm OI29 0^761 0.169 o. 189 O. 112 0.504 45 0.258 o. 204 0.193 o. 262 0.738 0.683 0.79 8660 A Hall D1 0^056 o982 0.050 0-595 5500 A Mise. 193 9Ap J. CT) o CT) o o o 2 2 Although thechanceofaccuratelydeterminingphasesecond- in thefollowingcolumn.Agreementhasbeen forced at8660A.For length regionsinthethirdcolumnofTable10. The computedvalue, prevented fromdoingthisbyunfavorableweatherconditions. was usedtofindtheluminosityofdarksidethisstar. ing companion.Stebbins’visualvalueforthereflectioncoefficient Hall find thecolortemperatureoflatter.WeassumethatB8star we assumethatLciszero,findtheratioof surfacebrightness the sakeofcomparison,asimilarcomputation isgivenfor6000.If light atthetwominima,whilethatinvolvingfaintersideof bodies. Theratioofthesurfacebrightnesseswhenbrighterside has acolortemperatureof15,000andthatbothstarsradiateasgray Mise, (vis.) ary minimumisobviouslygreaterinthelongerwavelengths,Iwas amined inordertoseewhethertherewasanydefinitephotometric the companiontothatofprimaryisgiven fordifferentwave- of thesecondaryisusedmerelyratiorectifiedlosses assuming thecompanionhasacolortemperature of5800,isgiven third body. k cancelsout.Inthefirstcasecomputationisindependentof evidence ofaneccentricorbitfortheeclipsingpair.Nonewasfound. Since weuse(J/(/i//)xyinfindingthecolortemperature, companion foragivenwavelengthis/i/J=k(L—2b)/L. Stebbins... companion inthethreedifferentspectralregionsmaybeusedto x2 2x © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The ratioofthesurfacebrightnessAlgoltothatitseclipsing The observedphasesofsecondaryminimumhaveallbeenex- The observedratioofthesurfacebrightness thebrightsideof Observer A SPECTROPHOTOMETRICSTUDYOFALGOL475 Color TemperatureoftheSecondaryComponent 4500 A 8660 5500 Eff. X 0.059 o. 222 Obs. .084 Bright Side O. 222 0.056 Comp. 5800° TABLE 10 ■095 +0 .OO3 — .Oil o O-C 5800 0.000 — .018 — 0.001 o O-C 6000 0.000 o. 262 0.049 Obs. .119 Faint Side 0.060 o. 262 Comp. . 109 + .010 —O.OII o O-C 5600 0.000 193 9Ap J. CT) 26 25 o21 constant, anditspositionmagnitudearefavorable. Perhapsthe nearly thatofanA2thanaB8star. cal ofB8starsoveranextensivespectralregion, itsradialvelocityis system, andconsequentlythecompositecolor atmaximumismore indicate alargepositivecolorexcess.Inthisspectralregionthecool- made atYalein1932effectivewavelengths7000Aand8200 er secondarycontributesamuchlargerpercentageofthelight such isthecase.TheseweremadeontwonightswhenAlgolwasat would besimilartothatofaB8star.Thephotoelectricobserva- quarter-phase. Ontheotherhand,colorimetricobservationswhichI tions at4250Aand4750giveninBecker’scataloguesuggestthat find thatthecompositecolorofsysteminthisspectralregion tle lightattheshorterwavelengths,wewouldnaturallyexpectto dispersion. Sincetheeclipsingcompanioncontributesrelativelylit- plained. ornegligibleobscurationthecolorsofB8starsshowverylittle be possibletocorrectthedatafromlight-curvesandrepeat third orremainingbodies.Whensuchdeviationsarefound,itshould this processuntilallobservedphenomenaaresatisfactorilyex- predicted differencesmaybeattributedtoadditionallightfromthe perature andmagnitudeofthesecondarycomponentAlgolcanbe change withwavelengthoutsideeclipse.Anydeviationsfromthese in magnitudebetweenAlgolandaB8starofaveragecolorshould spectral regions,itshouldbepossibletopredicthowthedifference Algol nearquarter-phasewithanormalB8star.Sincethecolortem- found toafirstapproximationfromthelight-curvesindifferent ence ofthethirdbodyhasbeenmadebycomparingenergyfrom near 5600.Magginifindsacolorindexforthebrighterandfainter of thefaintersidecompaniontothatprimaryshownin side ofthiscompanionequivalenttoanF6andG5star,respectively. column 7.Thecolortemperatureofthesecondaryappearstobe 476 JOHNS.HALL 26 2 Ap.J.,79,145,I934- s Veröf.SternwarteBerlinBabelsberg,10,No.3,1933. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem ß Tauriwaschosen,forthecomparisonstar,since itscoloristypi- We areassistedinthisprocedurebythefactthatregionsof Spectrophotometric observations.—Anattempttodetectthepres- CT)

A SPECTROPHOTOMETRIC STUDY OF ALGOL 477

best reason for believing that ß Tauri and the primary in Algol are similar in color is to be found in the spectroscopic determinations of their absolute magnitudes. Dr. Schlesinger’s General Catalogue of Stellar Parallaxes gives the mean of four determinations of the spec- troscopic parallax (made at the same observatories) of each of these stars as o''03 5. This indicates that their absolute magnitudes differ by 0^5 and that the two spectra, and hence their colors, are similar.

Fig. 3.—Spectrophotometric comparison with ß Tauri. The heavy curve which passes just above the data represents the predicted departure from the horizontal line shown at the top of the figure, when C is assumed to be an A5 star of the proper bolo- metric magnitude. When this line is tilted by the amount indicated by the broken line, which implies that the primary in Algol is slightly redder than ß Tauri, the predicted curve fits the data very well. The corresponding curves predicted when C is assumed to be completely dark are very similar to those just mentioned. The curve at the bot- tom of the figure would result if C were of the same magnitude and color as the eclipsing companion. It is therefore highly probable that the third body is not cooler than the eclipsing companion.

The mean observed difference in magnitude (Algol minus ß Tauri) for thirteen different spectral regions, given in Table 3, is plotted against the reciprocal of the wave length, expressed in microns, in Figure 3. If the influence of the light from other bodies in the system is disregarded, one would expect these data to be satisfied by a straight line which differs but little from the horizontal. The mean phase of these observations is 0.17 of the period from primary mini- mum. It has already been shown that, if the primary has a color temper-

© American Astronomical Society • Provided by the NASA Astrophysics Data System 193 9Ap J. CT) m interval i/A=2.22to1.11,thebrokencurve would result. in magnitudechangedby0^03alinearfashion withi/Ainthe the primarywasslightlyredderthanßTauriand thatthedifference drawn throughthenormalsshowninFigure3. Had weassumedthat mately forotherwavelengthsaswell.Ifwe nowsubtractm— very similarspectra,wewouldexpectthisdifference toholdapproxi- would beincreasedto0^579.SincetheprimaryandßTaurihave the secondaryweremadecompletelydark,thismagnitudedifference represented inFigure3passesthrougho^oóatthiswavelength.If {m +in)fromo57g,wefindacurvesimilar totheheavyone amounts to0^073.Asmoothcurvedrawnthroughtheobservations tude ofAlgolcausedbytheadditioncompanionB.At4500Athis lengths notgiveninthetable,andmagnitudedifferencesm— A This samefactorwasthenusedtocomputesimilarratiosforwave multiplying byafactorinordertorepresenttheobservedratios. , usingStebbins’valueofa.Thecomputedratioswere derived fromPlanck’slaw,usingtheforegoingtemperaturesand (wib +W4)wereformed.Theserepresentthechangeinmagni- while thesecondvalueisthatfoundinsamemannerasvisual BA A 0 L/ aregiveninTable11. use ofthereflectioncoefficientsTable6.Theresultingvalues values ofLTable9mustfirstbecorrectedtophase0.17bythe ratio ofLb/Lasafunctionthewavelength.Indoingthis, caused bythepresenceofeclipsingcompanion,wemustfind near 5600°.Inordertopredictthedeparturefromahorizontalline ba ature of15,000°,thatthedarksideeclipsingcompanionis 478 JOHNS.HALL B a © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The firstinfraredvalueisthatfoundentirelyfromthelight-curve, Hall Hall Vis. (mise.) Stebbins.. . Observer Ratio ofLuminosities 4500 A 8660 8660 5500 Eff. X TABLE 11 L/{Obs.) BA 0.286 0.057 •318 ■134 (Comp.) Lb/La 0.304 0.069 • 304 .124 + .014 + .010 —0.018 —0.012 O-C 193 9Ap J. CT) is then1.9,andA/Cisonly1.1.Inotherwords, thebolometricmag- by meansofthereflectioncoefflcientstophase 0.00insteadof0.17, in Table12.InthiscasetheobservedvaluesofLwerecorrected visual region.Thisratiowasfoundfromtheobservationsinaman- The ratiooftheluminosities,usingdarkside5,is9.9in taken intoaccount. ner similartothatexplainedinthederivationofcomputedratios quently, althoughtheobserveddifferencein visualmagnitudeis and theinfluenceofathirdbody(tobediscussed presently)hasbeen stars isgivenby equation canbeusedtogiveusthatofAC. Obviously, wemustknowthemassratioof^4to5beforelast then the massfunctionofsmaller,andcthatlargerorbit, solution isnotcompatiblewithmassconsiderations. 2?5, thebolometricdifferenceisi^S.Thecomputed massratioA/B curves ifweassumethatthethirdbodyiscompletelydark.This tions canbesatisfactorilypredictedfromdataderivedthelight- B 2 I/3 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The twocomponentsAandBareofdifferenttemperature; conse- A goodapproximationtothemass-luminositylawforbright The value(c/cj),derivedfromMcLaughlin’selements,is1.31. Assuming that=i,wehave Relative massesofthecomponentsAlgol.—Ifwelet^represent It thereforeseemsevidentthatthespectrophotometricobserva- 2 2 C22 _0S c026 A SPECTROPHOTOMETRICSTUDYOFALGOL479 ~T*Wa+1ÍÜMe)'° '~— ■ 3 _ (asin¿)i 20 3 (&! sin¿0i x /3 1+ M Ic.V'ilV Mb W/\M+Mb)‘ c = a 2/5 Mb \L)‘ Ma [La\ b = 193 9Ap J. CT) 13 2728 o versity ofChicagoPress,1939. panion, B. value isarbitrary,thediscussionofmassratios stillgivestrong of therotationeffect.Hestates,however,thathebelieveshisearlier is i“5toobrightforitsmass,wefindthatthemassratioH/Bin- parallaxes, is3.1,avaluewhichseemstobewelldetermined. indication thatCisbolometricallybrighterthan theeclipsingcom- bolometric differenceinmagnitude(C—^4)is 1^94.Althoughthis value of5.0,determinedin1923,meritsgreaterconfidence.Amass lin’s 1924determinationof3.65forthismassratiofromhisstudy onometric parallaxiscorrect.Whenweadopttheratio3.3, ratio of4.5wouldplaceAonthemass-luminositycurveiftrig- The value3.3(M=1.60O)agreesreasonablywellwithMcLaugh- creased from1.9to3.3andthatof4/Cisincreased1.12.0. mass ofthebrightGocomponent0.86sun’smass;butits brighter componentoffHerculis.ThedeparturetheGocompo- curve.Hedrawsananalogybetweenthisstarandthe plies thatitshouldbeevenbrighterthanA.Inviewofboththe ,determinedfromseveralseriesoftrigonometric sekhar. VandeKamphasveryrecentlypublishedavalueforthe nent ofthisstarfromthemass-luminositycurveisevidentlywell yet wehavenoapriorireasontosuspectthattheB8componenthas probable. the mainsequenceandisoflowdensity,maybeoffmass- suggests (byletter)thattheeclipsingcompanion,whichiswellabove unusual luminosityormassforitsspectraltype.ProfessorRussell nitude of—0.4fortheprimary.Thespectroscopicvalueispracti- spectroscopic andthephotometricevidence,thisseemshighlyim- C’s orbitdiffersmuchfrom90,themass-luminosityrelationshipim- nitude ofCiscomparablewiththatA;andiftheinclination 480 JOHNS.HALL established. IthasbeendiscussedbyStrömgrenandChandra- of StellarParallaxesiso''031±o''004,suggestinganabsolutemag- cally thesame.Althoughthisevidenceisbynomeansconclusive, A 2 38 7 Chandrasekhar,IntroductiontotheStudyofStellarStructure, p.279,Chicago:Uni- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A/.,47,168,1938. When wefollowProfessorRussell’ssuggestionandassumethatB The parallaxofAlgolgiveninDr.Schlesinger’sGeneralCatalogue 193 9ApJ. . . .90. .449H part tothethirdbody. primary andthesecondaryarevisiblewhenlightfrom primary isreinforcedbythatofitseclipsingcompanion.Shefound conceivable thattheextralinesfoundbyMiss Barney maybelongin the velocity-curvesofshort-andlong-period orbitsis4.5,it stars. MissBarneyconcludedthattheselinesbelongtoboththe nitude. FouroftheextralinesareusuallypresentinB8spectrum ion isanearlyG-typestar,andsincetheratio oftheamplitudes that manyoftheseextralineswereironlines. radial velocitiesofthesamesignasprimarybutsmallermag- numerous nearprimaryandsecondaryminimum,indicated velocity-curve oftheprimary.Shefoundthattheselinesweremost been previouslyusedbyDr.Schlesingerinthedeterminationof primary minimum,itsspectrumwouldbepresumablymoreinevi- and oneinA2;fiveareusuallypresentA5prominentF5 that CisbolometricallybrighterthanBbutfainterphotographically tion ofnumerousextralinesordoubtfuloriginwhichhadnot than ^(A+B)atprimaryminimum. ones refuteit. observations supportthehypothesismorestronglythanlater with thoseofthethirdbody.Hefindsthathis1924observations spectroscopic observations.IfCwerehalfasbrightA+J3a.t minima (correctedforreflection)representabout0.62thelightof cured byDr.SchlesingerandothersattheAlleghenyObservatory. distribution oftheobservationsshowninhisdiagramsthat1923 some ofthelinesprimarynearminimumareblended dence. McLaughlinfoundthathis1923observationsindicated the system,andthereforeCcannotpossiblycontributemorethan0.38 tend tocontradictthishypothesis.Itappearsfromthenumberand the visuallightofsystem.Amorecriticaltestistobefoundin She measuredtheradialvelocitiesandrecordedphasedistribu- the photometricdata.Thesumofvisualdepthstwo 29 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem ^ AJ.,35,95,1923- Since recentphotometricdataindicatethatthe eclipsingcompan- Miss Barneyhasmadeastudyof250spectrogramsAlgolse- Consideration ofthemassratiosandspectroscopicdataindicates An upperlimittothevisualluminosityofCisgivenatoncefrom A SPECTROPHOTOMETRICSTUDYOFALGOL481 193 9Ap J. CT) m D1 o an 482 JOHNS.HALL such apossibilityisnotcontradictedbythespectrophotometricob- an early-typemain-sequencestar.Itwillpresentlybeshownthat star ascoolas,orcoolerthan,theeclipsingcompanionhavingre- servations. However,theseobservationswoulddefinitelyruleouta parallax iscorrect,Cwouldthenbeanormalmain-sequencestarand peratures ofAandCenableustocomputethelight-ratiosL/Lfor would beabouto9fainterthanH+J3atprimaryminimum. quired bolometricmagnitude.ThisisillustratedbyFigure3. difference inmagnitude(C—A)isthatgivenabove,ori94.Ifthe bolometric differenceinmagnitudeof1.94for(C—^4)andthetem- the light-curves.Thiswasdoneinfollowingmanner: different wavelengths.TheratioL/Lmustbedeterminedfrom Lc =o.i22Z,¿,wehave and inRussell’snotation 10,000, and5600forA,C,B,respectively,areadopted.The of theprimaryminimumlight-curveat4500 A. After substitutingStebbins’data,wefindfromthese: 0.78 and0.79,respectively,insteadof0.85 0.700foundforthe the pointofintersectionthiscurveandthat foundbysetting CA two-body case.Cosiis0.133dandrare 0.252and0.197,re- x(£, i)=1.870.Thislastvaluewasdetermined fromtheshape BA 2 o © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem If thediscussioninpreviousparagraphsiscorrect,Cmustbe Let uspostulateanA5starforCandassumethatthebolometric Let L+LbLç=1;and,sincebyourhypotheses,at4500A In thefollowingcomputations,colortemperaturesof15,000, We findinthiswaythatStebbins’datagivevalues ofkanda a 0 The bestvaluesofkandacannowbereadily determinedfrom 0 do =O.727 I .122L+Lb=, A 2 1z(IoLb —iA2. ^oL —iAi, a + 0-038 2 k ' (1) (3) (2) 193 9Ap J. ^ ASPECTROPHOTOMETRICSTUDYOFALGOL483 CT) mine, IhaveadoptedhisvaluesofkandacomputedL infrared, andsinceStebbins’observationsaremorenumerousthan ma forthevisualandinfraredregionsshowninTable9.Lcisthen mean phaseofthespectrophotometricobservations. were thencorrectedforreflectionfromphase0.50to0.17,orthe the differencebetweenL+andunity.Thethreevaluesof and Lbymeansofequations(2)(3),usingthedepthsmini- 4000 4500 Since theprimaryminimumismuchdeeperinbluethan light-curves reasonablywell.TheratiosL/(+Lc)arede- 6000 spectively. Theinfrareddataindicatethatkis0.69anda0.831. 8000 body considerationswhichseemtofitthevaluescomputedfrom 9000 8660 5000 12 forthethreedifferenteffectivewavelengthsinsecondand SSO© predicted differenceinmagnitudebetweenastar thecolorofA(in rived fromthesecomputedratios.ThecontributionofLand fourth columns.Thecomputedratiosarethosederivedfromblack- 0A to themagnitudeofAwasthenfound.Whenweforceagreementby 7000 an additiveconstantat4500A,asinthetwo-bodycase,wefind AB we assume,asbefore,thatstarAandßTauri have slightlydifferent the wavelength.Thesedifferencesaregiven in thefinalcolumnof this caseßTauri)andthemagnitudeofsystem asafunctionof b spectrophotometric datatendtofallslightly below thiscurve.If the tableandarerepresentedbycurveinFigure 3.Theobserved colors andthattheirdifferenceinmagnitude changeswithwave AB 0 Bc © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The ratiosL/LandLc/LfoundinthiswayaregivenTable BA length Wave (A) Prediction oftheSpectrophotometricOps.0=0.17 l/ ba O.071 0.287 Obs. Comp. .090 0.042 O.29O .086 .062 .244 . I92 •ISS .112 . 270 TABLE 12 lí ca O. 122 0.202 Obs. . I90 Lc/l l+ Comp. L abc A O. IIO o. 186 .122 •ISS .I?? •ISI .144 . 166 . 182 0.868 0.678 .820 .844 .776 .796 .684 .704 ■736 Comp. o“53Ó Am 442 475 415 309 357 506 268 278 193 9Ap J. CT) 30 13 length inthemannerindicatedbybrokenlineattopof very satisfactory. methods ofprocedureindeterminingtheluminosityeclipsing figure, wefindthattheagreementbetweentheseindependentdatais luminosity forCsmallenoughtosatisfyallothercriteria.Onecould hold; inthiscaseLcwouldrefertothetotallightofsecondsys- would besatisfied,providedthethirdandfourthbodiesareearly- of twostarsequalbrightness.Inthiscasethebolometricdiffer- B isnotonthemass-luminositycurve;yettheresomeoutsidejus- istics ofthethirdbody. unimportant whencomparedwiththeuncertaintyincharacter- 484 JOHNS.HALL type stars.ResultssomewhatsimilartothoseinTable12wouldstill also avoidthisdifficultytosomeextentbyassumingthatCconsists slight differencesaswouldappeartheresultofthisarbitrationare companion fromthevisualandinfrareddata.However,such of Algol.Itisgratifyingtolearnthatastrometric platesarebeing has examinedtherichphotometricmaterialaccumulatedduring orbit shouldbeaboutfiveminutes.Smarthasfound,fromhisphoto- metric observationsnearprimaryminimum,achangeinperiod tem. ence inmagnitude(C—Ä)wouldbei^óó,andthephotometricdata tification forthisprocedure.Itisotherwisedifficulttopredicta value ofthemassratioCj{A+5),willaddgreatly toourknowledge second halfofthenineteenthcenturyandhas found thatthislight- ing, despitethehighaccuracyofhisobservations.Dr.Schlesinger data wouldbecorrespondinglyincreased.Thevalueofasiniis the massofCwouldbestilllargeranddifficultyinreconcilingall amounting to2§timestheexpectedvalue.Sincetheseactuallyin- 88,000,000 km;and,consequently,thelight-timeoflong-period equation wasactuallypresent. clude thisminimumononlyfournights,hisresultsarenotconvinc- o © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem It is,ofcourse,unfortunatethatIhavebeenforcedtoassume In thisdiscussionIhavehadtochoosebetweenslightlydifferent If theinclinationoflong-periodorbitdiffersgreatlyfrom90, The determinationofthisorbitalinclination, togetherwiththe Science, 41,115,1915. 193 9Ap J. CT) 31 pose. accumulated attheSproulandAlleghenyobservatoriesforthispur- mostly onconsiderationsofmass,photometricdata,andtheRussell graphed.” MyassumptionthatthethirdbodyisanA5starrests cal Observatoryhasappearedinwhichitisstated,referenceto observed byPearcemustbeathirdbody.Hisstatementstrengthens Dr. Pearce’sspectroscopicobservationsofAlgol,that“duringeclipse diagram. Ihavealsobeenguidedsomewhatbythenatureof the spectrumofclassAcompanionhasbeenrepeatedlyphoto- ponents; andProfessorDuganverykindlyreadcriticizedthe me valuableassistanceinthediscussionofmassescom- Dr. JohnMerrillkindlysentmeanadvancecopyofhisextensive serve Algol.IamalsogratefultoMr.R.W.Delaplaine,whovolun- cate thattheeclipsingcompanionisanearlyG-typestar,Astar extra linesfoundbyMissBarney.Sincethephotometricdataindi- manuscript. tarily recordedobservationsandcheckedmanyofthereductions. tion. Ilookforwardwithmuchinteresttoreadingthefinaldiscus- tity oftwocompanionsAlgolisnowknowntoafirstapproxima- the validityofmydiscussionandleadsmetobelievethatiden- and veryconvenienttableofxfunctions;ProfessorRussellhasgiven Observatory, fortheopportunityofusing24-inchtelescopetoob- sion ofhisspectroscopicobservations. © American Astronomical Society Since thispaperwaswritten,areportoftheDominionAstrophysi- I wishtothankDr.JohnA.Miller,formerdirectoroftheSproul t'M.N., 99,354,1939. Amherst CollegeObservatory A SPECTROPHOTOMETRICSTUDYOFALGOL485 June 1939 Provided bytheNASA Astrophysics DataSystem