Table Of ContentAstronomy&Astrophysicsmanuscriptno. AAPolaris (cid:13)cESO2013
December11,2013
The Hipparcos parallax for Polaris
FloorvanLeeuwen
InstituteofAstronomy,Cambridge
Received<date>/Accepted<date>
ABSTRACT
ThisletterfollowsarecentclaimthattheHipparcosparallaxforPolariscouldbetoosmallby2.5mas. Itexaminesindetailthe
HipparcosepochastrometricdataforPolaris,aswellastheviabilityofotherobservationsthatwereputforwardtosupportalarger
parallax. TheHipparcosdeterminationofthePolarisparallaxisshowntobesufficientlyrobusttofullyexcludeasignificantlylarger
3 parallax,andthereisnoobservationalsupportfromotherobservations,suchasasupposedpresenceofacluster,either.
1
0 Keywords. Astrometry-Parallaxes-Polaris
2
n
1. Introduction
a
J Epoch
In a recent letter to the Astrophysical Journal, Turner et al.
5 3
(2013) (TKUG from here on) suggested that the parallax as
2
measured by Hipparcos (van Leeuwen 2007a,b) for Polaris
] 1
R(HIP 11767, HD 8890) is significantly lower than it should be. mas) 0
.STthheeadssisutmanecdepoufls9a9tio±n2mpocdesuogfgPeosltaerdisbiyseTqKuUivGaleonntttoheapbaarsaisllaoxf Resid.(--21
hof10.1±0.2mas,verydifferentfromtheparallaxasmeasured -3
p -4
by Hipparcos, 7.54±0.11 mas. Consequently, I have recently
- -5
ofrequently been asked if it is at all possible for the Hipparcos -1.25 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
rparallaxmeasurementtobesofaroff. ThislettershowstheHip- Epoch (yr - 1991.25)
stparcosastrometricsolutionforPolarisinalldetailasameansto Epoch EpochE
aassesstherobustnessofthatsolution,toassesswhetheritsmea-
[surementoftheparallaxcouldbeoffsetby23timesitsstandard
1error. It also briefly discusses other arguments that have been Fig.1. Distributionoverepochoftheastrometricsolutionresidualsof
vused to suggest a significantly shorter distance for Polaris than theHipparcosmeasurementsforPolaris. Bluedotsrepresentrejected
0whathasbeenmeasuredbyHipparcos. measurements.
9
8
0
.2. HipparcosepochastrometryforPolaris The correction to the parallax is determined by the correla-
1
tionbetweentheweightedresidualsandtheparallaxfactors.For
0
The Hipparcos astrometric data at epoch resolution consists Polaristhespreadinstandarderrorsonthemeasurementsisrel-
3
of one-dimensional measurements of transit times, which, atively small, ranging from 0.61 to 0.81 mas. The main reason
1
by means of the reconstruction of the satellite attitude (van for this is that the errors are dominated by a calibration-noise
:
vLeeuwen&Fantino2005),aretransformedtoscanphases. Any contribution from the along-scan attitude reconstruction, with
Xiobject in the Hipparcos catalogue has been scanned multiple a relatively small contribution from the photon-noise statistics.
timesindifferentdirectionsoverthe3.3yearperiodofthemis- There are therefore no individual measurements with relatively
r
asion. For Polaris there are 127 such measurements, of which highweightthatcoulddominateordistorttheastrometricsolu-
three were rejected in the iteration for the astrometric solu- tion.Thedistributionofresidualsasafunctionofparallaxfactor
tion. Twoofthesemeasurementswereobtainedduringthefinal is shown in Fig. 3. To reconcile the Hipparcos data for Polaris
monthsofthemission,whentheconditionofthesatellitehadal- withaparallaxof10.1masitwouldtakesystematicerrorsinthe
readysignificantlydeteriorated. Thethirdrejectedmeasurement epoch astrometric data that are only depending on the parallax
wasonlymarginallylargerthanexpected. Thedistributionover factor,asthedistributionsoverscandirectionandepocharenot
epochofthosemeasurementisshowninFig.1. Thedistribution correlatedwiththeparallaxfactor. Theerrorswouldneedtobe
of measurements over epoch for Polaris is quite homogeneous, atalevelofabout1.5mas,whichismorethantwicethestandard
whichisduetoitspositionbeingrelativelyclosetotheecliptic errorsonthemeasurements. Consideringthatthegoodness-of-
pole. The distribution of the scan directions is also homoge- fitofthecurrentastrometricsolutionisverygood,anysuchsys-
neous, and there is no significant correlation between the scan tematicerrorswouldneedtobeverystronglycorrelatedwiththe
directionsandtheparallaxfactor(Fig.2). Thelatterrepresents parallaxfactorsoftheindividualmeasurements.Thisanomalous
theeffectachangeintheparallaxvaluehasonameasurement. behaviouroftheresidualsthenneedstoberestrictedtoPolaris,
Articlenumber,page1of3
Fig.2. Distributionofparallaxfactorsasafunctionofscandirection.
Thescandirectioncanbeseenastheconnectionfromthepoint(0,0)to
adatapoint. Theparallaxfactor(adimensionlessratio)isindicatedby
thedistanceofthedatapointfromthereferencepoint(0,0).Theredand
bluedotsrefertopositiveandnegativeparallaxfactors,respectively. Fig.4. Colour-magnitudediagramforstarswithina3degreesradius
fromPolaris,andwithrelativeparallaxerrorsbelow15percent. This
diagramshouldbecomparedwithFig.4inTurner(2009).Thecolours
ofthedotsreflectthespectraltypesofthestars, fromblue(B)tored
(M).
observed from the HR diagram of stars within 3 degrees from
PolarisbasedonapparentmagnitudesasfoundintheHipparcos
catalogue. Twoobservationsareinplacehere:
1. ThediagramaspresentedinFig.4ofTurner(2009)as"Po-
laris neighbours" cannot be reproduced; in fact, the actual
HR diagram for stars within 3 degrees from Polaris looks
verydifferentindeed(seeFig.4),andshowsnosignofclus-
tering;
2. Thereisnosignatureofaclusterineitherthedistributionof
proper motions (see Fig. 5) or the distribution of parallaxes
inthedirectionofPolaris.
Fig. 3. Distribution of measurement residuals as a function of the
parallaxfactorfortheHipparcosparallaxsolutionof7.54±0.11mas. There simply is no cluster at the supposed distance of 100 pc
Also shown, by means of the diagonal line, is the expected relation
inthedirectionofPolaris, andtheHRdiagramasproducedby
betweenparallaxfactorsandresidualsfortheparallaxof10.1masthat
Turner in his 2009 paper does not appear to have any relation
hasbeensuggestedbyTKUG.
withrealityforthatfield.
The argument on the cluster was replaced by TKUG with
or at most to a very small number of stars in the catalogue. If the suggestion that the distance of Polaris could be determined
it were more general, errors at this level would show up in the throughmain-sequencefittingoftheF3VcompanionofPolaris,
distributionofnegativeparallaxes,whichiscontrarytowhathas PolarisB,ofmagnitudeV=8.60,andB−V=0.39(Turner1977).
beenobserved(vanLeeuwen2007a). Itseemsthereforethatthe Throughmain-sequencefitting,TKUGderivedadistancemod-
Hipparcos data cannot in any way support the shorter distance ulusof5.0,whichthereforemustbebasedonanabsolutemag-
andlargerparallaxforPolarissuggestedbyTKUG. nitude of V=3.6. The Hipparcos catalogue contains 390 stars
for which the spectral type is given as F3 V, and for which the
relativeerrorontheparallaxislowerthan10percent. Figure6
3. Otherargumentsusedtosuggestalarger showsthedistributioninabsolutemagnitudeandcolourforthese
stars. Themeanabsolutemagnitudeforthisselectionofstarsis
parallaxforPolaris
Hp=3.17, with a standard deviation of 0.48. The equivalent in
One other main argument has been used in the past to suggest V is3.08±0.48(ESA1997). Themeancolouris0.434witha
J
that the Hipparcos parallax for Polaris could be too small. Al- standard deviation of 0.029. There is a significant correlation
though no longer directly referred to in the paper by TKUG, coefficient of 0.237 between the magnitude and colour distri-
it is indirectly used by referring to earlier publications on the butions, which simply reflects the spread over the B−V colour
same subject (Turner et al. 2005; Turner 2009) as part of the index among the F3 V stars. The Hipparcos measurement of
"evidence" presented. It concerns the suggestion that there is a the parallax implies an absolute V magnitude for Polaris B of
cluster, at a distance of 100 pc, with which Polaris is supposed V=2.99. This value, as well as the value given by TKUG for
tobelinked. InTurner(2009)thisclusterispresentedasbeing Polaris B, falls within the observed distribution of F3 V stars,
Articlenumber,page2of3
FloorvanLeeuwen:TheHipparcosparallaxforPolaris
lax has been derived that could possibly justify a correction by
nearly2.5mas.Thereisnootherdirectobservationalsupportfor
suchanadjustmenteither. Theexplanationforadiscrepancyas
presentedbyTKUGmustthereforebefoundelsewhere,andthe
most obvious place to look for it is the pulsation mode for Po-
larisasassumedbyTKUG.Inparticularastheredoesnotappear
tobeanydiscrepancyontheluminosityifPolarisisnotassumed
tobepulsatinginfundamentalmode(vanLeeuwenetal.2007).
Theobservedchangesinperiodmaythen,ontheotherhand,also
becomemoreinterestingbybeinganunexpectedbehaviour.
References
ESA(ed.)1997,TheHipparcosandTychoCatalogues,no.1200inSP,ESA
TurnerD.G.,Aug.1977,PASP,89,550
TurnerD.G.,Sep.2009,In:GuzikJ.A.,BradleyP.A.(eds.)AmericanInstituteof
PhysicsConferenceSeries,vol.1170ofAmericanInstituteofPhysicsCon-
ferenceSeries,59–68
TurnerD.G.,SavoyJ.,DerrahJ.,Abdel-SabourAbdel-LatifM.,BerdnikovL.N.,
Fig.5. Propermotionsfor124starswithinaradiusof3degreesfrom Feb.2005,PASP,117,207
Polarisandwithrelativeerrorsontheparallaxeslowerthan15percent. TurnerD.G.,KovtyukhV.V.,UsenkoI.A.,GorlovaN.I.,Jan.2013,ApJ,762,L8
Thereare18additionalstarsforwhichthepropermotionsfalloutside vanLeeuwenF.,Nov.2007a,A&A,474,653
thediagramboundaries. ThepropermotionofPolarisisindicatedby vanLeeuwenF.(ed.),2007b,Hipparcos,theNewReductionoftheRawData,
vol.350ofAstrophysicsandSpaceScienceLibrary
the cross-bars. Errors on the proper motions are in all cases smaller
vanLeeuwenF.,FantinoE.,Aug.2005,A&A,439,791
than the dot size. No clustering in proper motions is being observed.
vanLeeuwenF.,FeastM.W.,WhitelockP.A.,LaneyC.D.,Aug.2007,MNRAS,
Thecoloursofthedotsreflectthespectraltypesofthestars,fromblue 379,723
(B)tored(M).
Fig. 6. Distribution in colours and absolute magnitudes for 389 of
the390F3VstarscontainedintheHipparcoscatalogue,andwithrel-
ative errors on the parallaxes below 10 per cent. One data point (for
HIP 84034) falls outside the diagram boundaries. The error bar at
eachdatapointillustratestheuncertaintyinthedistancemodulus. The
coloursofthedotsreflecttheparallaxes,rangingfromblue(small,large
distance)tored(large,shortdistance).
withasomewhathigherprobabilityfortheHipparcosestimate.
ItisclearthatPolarisBcannotprovideconclusiveevidencefor
eitherclaim.
4. Conclusions
There may be a discrepancy in the luminosity predictions or
measurements as obtained with different methods, but the un-
certainty is not in the determination of the Hipparcos parallax
for Polaris. There is nothing in the data from which the paral-
Articlenumber,page3of3
