The period change of the Cepheid Polaris suggests enhanced mass loss

0.74 MB·English

by  Hilding R. Neilson

Draftversion January6,2012
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
THE PERIOD CHANGE OF THE CEPHEID POLARIS SUGGESTS ENHANCED MASS LOSS
Hilding R. Neilson1, Scott G. Engle2, Ed Guinan2, Norbert Langer1, Richard P. Wasatonic2, and David B.
Williams3
Draft version January 6, 2012
ABSTRACT
Polaris is one of the most observed stars in the night sky, with recorded observations spanning
more than 200 years. From these observations, one can study the real-time evolution of Polaris via
2
the secular rate of change of the pulsation period. However, the measurements of the rate of period
1
changedonotagreewithpredictionsfromstate-of-the-artstellarevolutionmodels. Weshowthatthis
0
2 mayimplythatPolarisiscurrentlylosingmassatarateofM˙ ≈10−6M⊙ yr−1basedonthedifference
between modeled and observed rates of period change, consistent with pulsation-enhanced Cepheid
n
mass loss. A relation between the rate of period change and mass loss has important implications
a
for understanding stellar evolutionand pulsation, andprovidesinsight into the currentCepheid mass
J
discrepancy.
5
Subject headings: stars: individual(Polaris)—stars: evolution—stars: variables: Cepheids—stars:
] mass-loss
R
S
1. INTRODUCTION change for comparison. From this comparison, we con-
.
h strain the physics of stellar evolution models and other
ClassicalCepheidsareradiallypulsatingvariablestars
p fundamental properties of Polaris.
and are ideal laboratories for understanding stellar as-
- Polaris is an ideal candidate for this analysis. It is an
o trophysics and evolution. Radial pulsation constrains
astrometric binary (as part of a multiple star system)
r stellar structure along with Cepheid masses and lumi-
st nosities via the Period-MeanDensity relation. However, with a dynamically measured mass of M = 4.5+−21..24 M⊙
a observations of the rate of pulsation period change di- (Kamper 1996; Evans et al. 2008), has been observed
[ rectly constrain stellar evolution because this measures using K-band interferometry yielding a measurement

the change of the stellar mean density as a function of of the its mean angular diameter (M´erand et al. 2006),
2
time. and has a precise, revised Hipparcos parallax measure-
v
Turner et al. (2006) compiled measurements of rates ment (van Leeuwen et al. 2007). The effective temper-
1
of period change for a sample of Galactic Cepheids and ature of Polaris has also been measured spectroscopi-
6
showed that they broadly agree with rates of period cally (Usenko et al. 2005). The combination of these
7
0 change as a function of pulsation period computed from observations provide strong constraints for stellar evo-
. stellar evolution models. The authors also found that lution models. There have also been a number of mea-
1 observedratesofperiodchangeforPolarisandDX Gem surements of the rate of period change for Polaris based
0
arelargerthanthoseofmostCepheidsandareconsistent on the combination of recent and archival observations.
2
with being a Cepheid onits first crossingofthe instabil- Spreckley & Stevens (2008) measured a rate of period
1
itystrip. Thefirstcrossingoccursasastarevolvesacross change P˙ = 4.90 ± 0.26 s yr−1 based on 50 years of
:
v the Hertzsprung gap after main sequence evolution on a observations, while Turner et al. (2005) found a rate of
Xi Kelvin-Helmholtz timescale. ≈ 4.4 s yr−1 based on 160 years of observations. In
That work illustrated the power of measured rates of this work, we present a rate of period change based on
ar periodchangetoconstrainstellarevolutionmodels,how- datafromTurner et al.(2005)withnewdataaddedfrom
ever, one can go a step further. By combining observa- measurements over the past decade.
tions of the rate of period change with measurements In the next section, we describe the measurements of
of mean stellar radius, mean luminosity and/or effective the rate of period change in greater detail. In Section 3,
temperature, we candirectly test the input physics used wedescribethestellarevolutioncodeandmodelsusedin
in stellar evolution models. In this work, we produce a this study, while in Section 4, we compare the predicted
gridofstate-of-the-artstellarevolutionmodelsandcom- rates of period change with the observed rate where we
pare stellar evolution tracks with the measured radius find disagreement. In Section 5, we discuss the impli-
and effective temperature of the first-overtone Cepheid cations of our study towardunderstanding the structure
Polaris. For evolutionary tracks that cross the Cepheid and evolution of Cepheids as well as the problem of the
instability strip, we compute theoretical rates of period Cepheid mass discrepancy.
2. OBSERVEDRATEOFPERIODCHANGE
[email protected]
1ArgelanderInstituteforAstronomy,UniversityofBonn,Auf The recent comprehensive study by Turner et al.
demHu¨gel71,53121Bonn,Germany (2005) of photometric and radial velocity measurements
2Department of Astronomy & Astrophysics, Villanova Uni- (up to 2004) of Polaris yielded rates of increase in the
versity,800Lancaster Ave. Villanova,PA19085USA
3American Association of Variable Star Observers, 49 Bay pulsation period of Polaris of P˙ = 4.45 ± 0.03 and
State Road,Cambridge,MA02138USA 4.28±0.73syr−1. Thisresultisingoodaccordwithpre-
2 Neilson et al.
shooting. There is no enhanced Cepheid mass loss as-
sumed like that explored by Neilson et al. (2011) and
the models are assumed to have the Grevesse & Sauval
(1998) solar composition. Mass loss is treated using
the de Jager et al. (1988) recipe for cool stars and the
Kudritzki et al. (1989) prescription for hot stars.
Evolutionarytracksformodelswithoutconvectivecore
overshoot are shown in Fig. 2 for a sample of stel-
lar masses along with the measured effective tempera-
ture and luminosity of Polaris. The effective tempera-
ture was spectroscopically determined by Usenko et al.
(2005) to be T = 6015±170 K, while the radius is
eff
R = 43.5±0.8 R⊙ based on angular diameter measure-
ments (M´erand et al. 2006) and the revised Hipparcos
parallax (van Leeuwen et al. 2007), hence logL/L⊙ =
3.347±0.061. InFig.2,notallmodelsareconsistentwith
Figure 1. O-Cdatafrom1844/5-2011, frombothradialvelocity the observed properties, suggesting the observations are
andphotometrymeasures,areshownfortheCepheidPolaris. For
precise enough to constrain models. In the next section,
the purposes of fitting, the data were divided into two sets (pre-
1963 and post-1965) because of the apparent discontinuity in the we compute the rates of period change from the stellar
O-Ccurvearound1963-66(Epoch2400-2600). Theweighted,least evolution models.
squares quadratic fits to the data sets are also shown, where the
bluesolidlineisthefittotheearlierdatasetandthereddashedline 4. RATESOFPERIODCHANGE
isthefittothelater. ThecrossesrepresentdatafromTurneretal.
(2005) and circles our new timing data. The early data show a Turner et al. (2006) derived a relation for computing
period increase of 4.44±0.19 s yr−1 and the later data show a therateofperiodchangefromthepredictedstellarprop-
periodincreaseof4.50±1.45syr−1. ertiesofevolutionmodelsfromthePeriod-MeanDensity
relationandnotingthatthepulsationconstantQ∝P1/8
viousperiodstudiesofPolaris. Weaddedfivephotomet-
(Fernie 1967),
ricallydetermined timings (covering2002-2011)to those
given in Table 1 of Turner et al. (2005). The resulting P˙ 6L˙ 24T˙
O-C analysis plot is given in Figure 1. As noted previ- = − eff. (1)
ously, there is an apparentdiscontinuity in the O-C plot P 7L 7 Teff
occurring near epoch 2400-2600. Analyses of the tim- This relationassumes that mass lossis insignificant. We
ings prior to (1844/5- November, 1962) and after (July, compute rates of period change P˙ using this relation
1965-2011)thissmallanomalyyieldedcommonvaluesof
wherethevaluesofLandT alongwiththetimederiva-
period increase P˙ =4.44±0.19 and 4.50±1.45 s yr−1, tives are given by the stellaerffevolution models.
respectively (the larger uncertainty for the later period When the stellar evolution models predict radii and
change is due to the more limited time span covered). effective temperatures that fall within the boundaries of
When all data are taken as one set, the calculated pe- the Cepheid instability strip, we compute the model rel-
riod increase is 3.93±0.08 s yr−1. For the purpose of ative rate of period change, P˙/P using Eq. 1. This is
this study, we adoptthe value of P˙ =4.47±1.46s yr−1, done to avoid making any assumptions of the pulsation
astheaverageofthetwofitsonthetwoseparatesetsde- period from the theoretical stellar models. We show the
scribed above. In fact, as noted by Turner et al. (2005), predicted rates of period change as a function of stellar
the discontinuity in the O-C curve coincides with the luminosityinFig.3. Theobservedrelativerateofperiod
possiblebeginningofanaccelerateddecreaseinthelight changeisscaledbythecalculatedfundamentalperiodfor
amplitudeofPolaris,howeverthisrequiresfurtherstudy. Polaris,P =5.61days. The calculatedfundamentalpe-
0
riod is the overtone period plus 0.15 dex (Turner et al.
3. STELLAREVOLUTIONMODELS 2005).
We compute state-of-the-art stellar evolution models We find that evolutionary models with masses 5.4 -
using the Yoon & Langer (2005) version of the code de- 6.4 M⊙ and convective core overshooting αc ≤ 0.4 pre-
velopedbyHeger et al.(2000). Modelsarecomputedfor dict effective temperatures and radii consistent with ob-
the mass range of 3 - 6.8 M⊙ in steps of 0.1 M⊙, con- servations,butthepredictedmassisdegeneratewiththe
sistentwith the measuredmassofPolarisdeterminedby assumed amount of overshooting. This can be seen in
Evans et al. (2008). We also vary the amount of con- Fig. 2 for models with α = 0, and masses, M = 5.9 -
c
vective core overshooting. Convective core overshooting 6.4 M⊙; smaller masses are measured for αc > 0. The
is parameterized as the distance that convective eddies degeneracy between mass and α is discussed in detail
c
penetrate above the core boundary in a star over its by Keller(2008). Increasingα instellar evolutionmod-
c
evolutionary timescale. The distance is defined, in the els decreasesthe blue loopwidth, however,this does not
Yoon & Langer (2005) code, to be α H , where H is change the rate of period change for a given stellar lu-
c P P
the pressure scale height and α is a free parameter. In minosity during blue loop evolution. The rate of period
c
this work, we compute models for α =0-0.4 in steps of change is dominated by the most important timescale
c
0.1. We vary the amount of overshooting because over- at each stage of stellar evolution. On the Hertzsprung
shooting during main sequence stellar evolution acts to gap, a star undergoes thermal relaxation, meaning the
produce a more massive helium core and hence a more timescaleandthe rateofperiodchangeis definedby the
luminousCepheidforthesamestellarmasswithnoover- Kelvin timescale τ , which is ∝ M2. The evolutionary
K
Mass Loss and Evolution of Polaris. 3
3.5
4
3.4
3.5
6
⊙ ⊙ 3.3
L/L 3 6 L/L 5.8
Log 2.5 5 Log 3.2 5.6
4
5.4
2 3.1
3 5.2
1.5 3
4.4 4.2 4 3.8 3.6 3.4 3.9 3.85 3.8 3.75 3.7
Log T Log T
eff eff
Figure 2. Stellar evolution tracks computed using the Yoon&Langer (2005) code for initial masses ranging from 3 M⊙ to 6.8 M⊙,
assuming no convective core overshooting, αc = 0 (left) and the region of the HR diagram containing the effective temperature and
luminosityofPolaris(right). Theblackdashed linesrepresentthe boundaries oftheCepheid instabilitystrip(Bonoetal.2000)whilethe
boxesdenote theeffective temperatureandluminosityofPolaris.
175 timescale of a star on the blue loop is defined by the
12 helium nuclear burning timescale, τ , which itself de-
150 He
pends on the helium core mass M , i.e. the luminosity.
125 8 The helium core mass is determineHde by the combination
-1Myr) 1 7050 4 ocofrseteolvlaerrsmhoaosts. aTnhdutsh,ethaemroautentofofpearsisoudmcehdancognevfeocrtiavne
.P/P ( 50 0 3.2 3.3 3.4 3.5 eovvoerlushtiooontimngodiselawppitrhoxaimgaivteenlyltuhmeinsaomsitey,asmfaosrs,aamndodneol
25 withthesameluminosity,butadifferentamountofover-
0 shooting and corresponding mass.
The rates of period change are plotted in Fig. 4 as a
-25
2 2.5 3 3.5 4 function of luminosity for the models that have a pre-
Log L/L⊙ dicted radius and effective temperature consistent with
the observedvaluesduring the blue loopevolution. This
plot differs from the results in Fig. 3 such that the the-
Figure 3. Predicted rates of period change scaled by pulsation oretical value of the pulsation period is assumed to be
periodas afunction ofstellar luminositycomputed fromthe stel- that of Polaris. Any uncertainty introduced by this as-
lar evolution models when the evolution tracks intersect assumed
sumption will not affect the results. The stellar evolu-
boundaries of the Cepheid instability strip (see Bonoetal. 2000,
for details). The different colors represent differingamount of as- tion models predict rates of period change that occur in
sumedconvectivecoreovershooting,αc=0(green),0.1(blue),0.2 three regions for the plot in Fig. 3. The first region in-
(light blue), 0.3 (yellow), and 0.4 (magenta). The box represents cludes rates of period change where P˙ > 15 s yr−1 in
the observed luminosity and the rate of period change range for
Polaris. The inset zooms in on the luminosity range for Polaris Fig4, whichcorrespondsto stellarmodels rapidlyevolv-
and shows a distinct difference between theoretical and observed ing across the Hertzsprung gap. The second region is
ratesofperiodchange. for P˙ < 0 s yr−1, that corresponds to blueward evolu-
tionduringtheblueloopphaseofstellarevolution,while
25 the third region is 0 < P˙ ≤ 1 s yr−1 corresponding to
redward evolution during the blue loop phase.
20
Theobservedrateofperiodchangeisinconsistentwith
15 any of the three phases of stellar evolution, and con-
-1s yr) 10 tCreapryhetiodp(rTeuvrionuesrceltaiaml.s2P0o0l5a,ri2s0c0a6n).noTthbiesadififfresrte-cnrcoesswinags
.P ( also found by Spreckley & Stevens (2008). The question
5 iswhatphysicsismissingthatcanresolvethisdifference.
We rewrite the rate of period change from Eq. 1 to be
0
-5 3.25 3.3 3.35 3.4 3.45 P˙ =−4M˙ + 6L˙ − 24T˙eff, (2)
P 7M 7L 7 T
Log L/L⊙ eff
where we assume that the change of mass provides a
non-negligible contribution to the rate of period change
Figure 4. Predictedrates ofperiodchange asafunctionofstel-
lar luminosity computed from stellar evolution models when the (Turner et al. 2006; Neilson & Lester 2008). Since Po-
models have effective temperature and radius consistent with ob- laris has not been observed accreting material then the
servations. ThecolorshavethesamemeaningasinFig.3. rate of change of stellar mass is due to mass loss only
and is always < 0. This means that mass loss only acts
4 Neilson et al.
to increase the rate of period change. observedrate;hencePolarisismostlikelyevolvingalong
If we consider the largest value for the rate of pe- the blue loop. The observed rate of period change for
riod change during the blue loop evolution in Fig. 4, Polarisis similar to that of BY Cas and DX Gem, while
P˙ ≈1 s yr−1, then to resolve the difference between the forHDE344787,P˙ =12.96±2.41syr−1,suggestingthat
theoretical and observed rates of period change the rate the rates for BY Cas and DX Gem may also be consis-
ofchangeofstellarmassmustbe≤−7×10−6 M⊙ yr−1. tent with extreme mass loss for evolution along the blue
We note this result ignores the possibility for feedback loop. Observationsconstrainingtheradius,temperature,
on the stellar radius due to mass loss, but the feedback and/orluminosity along withrates ofperiodchange will
isexpectedtodecreasethemass-lossratebylessthanan testifallfirstovertoneCepheidshaveextrememassloss.
order of magnitude. Theresultsalsosuggestthatmoretime-seriesobserva-
5. DISCUSSION tions of Polaris in multiple wavelength regimes will help
constrainthemass-losshistoryandmass-lossmechanism
We find that the observedrate of period change, from
for this star and unravel a mystery of the North Star.
all sources, is inconsistent with predictions from stel-
larevolutionmodels unless one includes significantmass
loss. PreviousevidenceforCepheidmasslossisbasedon HRN is grateful for funding from the Alexander von
observationsofinfraredexcess(Neilson et al.2009,2010; Humboldt Foundation, and to Dr. Matteo Cantiello for
Marengo et al. 2010; Barmby et al. 2011), as well as 21- helpful conversations regarding stellar evolution calcu-
cm radio observations of a nebula surrounding δ Cephei lations. EG and SE are grateful for the support from
(Matthews et al.2011). These previousobservationsdid NASA Grants HST-GO-11726.01, HST-GO-12302.01,
not confirm mass loss because any circumstellar mate- NNX08AX37G and NASA/JPL Grant No. 40968.
rial could be relics from earlier stages of stellar evolu-
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